PRESSURE AND TEMPERATURE SENSITIVE PAINTS [2 ed.] 9783030680565, 3030680568

Table of contents :
Preface
Contents
Chapter 1: Introduction
1.1 Pressure-Sensitive Paint
1.2 Temperature-Sensitive Paint
1.3 Historical Remarks
Chapter 2: Basic Photophysics
2.1 Kinetics of Luminescence
2.2 Models for Conventional PSP
2.3 Models for Porous PSP
2.3.1 Collision-Controlled Model
2.3.2 Adsorption-Controlled Model
2.4 Thermal Quenching
Chapter 3: Physical Properties of Paints
3.1 Typical PSPs
3.1.1 Platinum Porphyrins
3.1.2 Ruthenium Polypyridyls
3.1.3 Pyrene Derivatives
3.2 Fast PSPs
3.2.1 AA-PSP
3.2.2 PC-PSP
3.2.3 Poly(TMSP)-PSP
3.3 Cryogenic PSPs
3.4 Multiple-Luminophore PSPs
3.5 Ideal PSP
3.6 Typical TSPs
3.6.1 Ruthenium Complexes
3.6.2 Europium Complexes
3.6.3 Cryogenic TSPs
3.6.4 Other Coatings
3.7 Desirable Properties of Paints
3.7.1 Pressure Response
3.7.2 Luminescent Output
3.7.3 Paint Stability
3.7.4 Response Time
3.7.5 Temperature Sensitivity
3.7.6 Physical Characteristics
3.7.7 Chemical Characteristics
Chapter 4: Radiative Energy Transport
4.1 Radiometric Notation
4.2 Excitation Light
4.3 Luminescent Emission
4.4 Photodetector Response
Chapter 5: Intensity-Based Methods
5.1 Measurement Systems
5.1.1 Camera-Based Systems
Cameras
5.1.2 Laser-Scanning System
5.2 Basic Data Processing
5.3 Pressure Uncertainty
5.3.1 System Modeling
5.3.2 Error Propagation, Sensitivity, and Total Uncertainty
5.3.3 Photodetector Noise and Limiting Pressure Resolution
5.3.4 Errors Induced by Model Deformation
5.3.5 Temperature Effect
5.3.6 Calibration Errors
5.3.7 Temporal Variations
5.3.8 Spectral Variability and Filter Leakage
5.3.9 Pressure Mapping Errors
5.3.10 Paint Intrusiveness
5.3.11 Other Error Sources and Limitations
5.3.12 Allowable Upper Bounds of Elemental Errors
5.3.13 Uncertainties of Integrated Forces and Moments
5.3.14 In Situ Calibration Uncertainty
Experiments
Simulation
5.3.15 Example: Subsonic Airfoil Flows
5.4 Temperature Uncertainty
5.4.1 Error Propagation and Limiting Temperature Resolution
5.4.2 Elemental Error Sources of TSP
Chapter 6: Lifetime-Based Methods
6.1 Response of Luminescence to Time-Varying Excitation Light
6.1.1 First-Order Model
6.1.2 Higher-Order Model
6.2 Lifetime Techniques
6.2.1 Pulse Method
6.2.2 Phase Method
6.2.3 Amplitude Demodulation Method
6.2.4 Gated Intensity Ratio Method
6.3 Fluorescence Lifetime Imaging
6.3.1 Intensified CCD Camera
6.3.2 Internally Gated CCD Camera
6.4 Pressure Uncertainty
6.4.1 Phase Method
6.4.2 Amplitude Demodulation Method
6.4.3 Gated Intensity Ratio Method
6.5 Lifetime Measurements
Chapter 7: Time Response
7.1 Time Response of Conventional PSP
7.1.1 Oxygen Diffusion
7.1.2 Pressure Response and Optimum Thickness
7.2 Time Response of Porous PSP
7.2.1 Deviation from the Square-Law
7.2.2 Effective Diffusivity: Geometrical Perspective
7.2.3 Diffusion Timescale
7.2.4 Knudsen Diffusion: Statistical Perspective
7.2.5 Nonlinear Quenching Kinetics
7.2.6 Effect of Lifetime on Time Response
7.3 Measurements of Pressure Time Response
7.3.1 Solenoid Valve
7.3.2 Shock Tube
7.3.3 Acoustic Resonance Tube
7.3.4 Fluidic Oscillator
7.4 Time Response of TSP
7.4.1 Pulsed Laser Heating on Thin Metal Film
7.4.2 Step-Like Jet Impingement Cooling
7.4.3 Shock Tube
Chapter 8: Image and Data Analysis Techniques
8.1 Geometric Calibration of Camera
8.1.1 Collinearity Equations
8.1.2 Direct Linear Transformation
8.1.3 Optimization Method
8.2 Radiometric Calibration of Camera
8.3 Correction for Self-Illumination
8.3.1 View Factor
8.3.2 Correction Scheme
8.3.3 Error Estimate
8.3.4 Bidirectional Reflectance Distribution Function
8.4 Image Registration
8.5 Conversion to Pressure
8.6 Pressure Correction for Extrapolation to Low-Speed Data
8.7 Generation of Deformed Surface Grid
8.8 Noise Reduction Methods
8.8.1 Phase Averaging
8.8.2 FFT-Based Analysis
8.8.3 Mode Decomposition Analysis
8.8.4 Heterodyne Method
8.9 Image Deblurring
8.10 Inverse Heat Transfer Methods
Chapter 9: Applications of PSP
9.1 Subsonic, Transonic, and Supersonic Wind Tunnels
9.1.1 Intensity-Based Measurements
9.1.2 Lifetime-Based Measurements
9.2 Unsteady Measurements
9.2.1 Transonic Wing Buffeting
9.2.2 Unsteady Pressure on Rocket Fairing Model
9.2.3 Oscillating Shock Wave in Transonic Flow
9.2.4 Impinging Jet Resonant Modes
9.3 Hypersonic and Shock Wind Tunnels
9.3.1 Blunt Bodies
9.3.2 Shock/Body Interaction
9.3.3 Moving-Shock-Wave Interaction with Circular Cylinder
9.3.4 Scramjet Nozzle
9.3.5 Hypersonic Boundary-Layer Separation
9.4 Low-Speed Flows
9.4.1 Ground Vehicle Models
9.4.2 Rugby Ball
9.4.3 Unsteady Pressure Fluctuation on Slat as Noise Source
9.5 Rotating Machinery
9.5.1 Rotating Compressor Blades
9.5.2 Helicopter Blades
9.6 Low-Pressure Flows
9.6.1 PSP Properties at Low Pressure
9.6.2 Measurements in the Mars Wind Tunnel
9.7 Other Topics
9.7.1 Cryogenic Wind Tunnels
9.7.2 Subsonic and Sonic Impinging Jets
9.7.3 Flight Tests
9.7.4 Micro Fluidics
9.7.5 Acoustic Resonance Modes
Chapter 10: Applications of TSP
10.1 Small Shock Tube
10.2 Hypersonic Wind Tunnels
10.2.1 Circular Cone
10.2.2 Inlet Ramp
10.2.3 AGARD HB-2 Standard Model
10.2.4 Single and Double Fins
10.3 Quiet Mach-6 Ludwieg Tube
10.3.1 Experimental Setup
10.3.2 Circular Cone
10.3.3 Lateral Heat Conduction Effect
10.4 Boundary-Layer Transition Detection
10.4.1 Heating and Cooling Methods
External and Internal Heating
Freestream Temperature Step
Surface Heating Layer
10.4.2 Swept Wings
10.4.3 Wind Turbine Profile Model and Nacelle
10.4.4 Laminar-Type Airfoil
10.4.5 Flat Plate
10.4.6 Rotating Blades
10.4.7 Hypersonic Boundary-Layer Transition
10.5 Impinging Jet Heat Transfer
Chapter 11: Extended Applications of PSP and TSP
11.1 Film Cooling Measurement Using PSP
11.1.1 Mass Transfer Analogy
11.1.2 Determining Film Cooling Effectiveness
11.1.3 Circular, Shaped, and Sand-Dune-Inspired Holes
11.2 Skin Friction Diagnostics Using PSP and TSP
11.2.1 Basic Relations
Heat Transfer Visualization with TSP
Mass Transfer Visualization with PSP
Pressure Visualization with PSP
11.2.2 Variational Method
11.2.3 TSP-Derived Skin Friction Fields in Water Flow
11.2.4 PSP-Derived Skin Friction Fields in Dual Colliding Impinging Nitrogen Jets
11.2.5 PSP-Derived Skin Friction Field in Junction Flow
11.3 Planar Oxygen Optode
11.4 Other Topics
11.4.1 Pressure-Sensitive Particles
11.4.2 Fuel Cells
11.4.3 Phosphor Thermometry
Appendix A: Chemistry
Luminophores
PSPs
Porphyrin Derivatives
Metalloporphyrins
Free-Base Porphyrins
Transition Metal Polypyridyl Complexes
Cyclometalated Iridium and Complexes
Polycyclic Aromatic Compounds
TSPs
Lanthanide Complexes
Ruthenium Derivatives
Polycyclic Aromatic Hydrocarbons
Rhodamines and Coumarins
Quantum Dots
Thermographic Phosphors
Reference Dyes
Binder Materials
Polymers
Siloxanes
Acetylene Polymers
Fluoropolymers
Other Polymers
Polyurethane Polymers
Porous Binder Materials
Anodized Aluminum
Polymer/Ceramic
Silica Sol-Gel Systems
Solvents
Halogenated Solvents
Nonhalogenated Solvents
Nonpolar Solvents
Polar Solvents
Additives
Particles
Dispersants
Screen Layer
Advanced Concepts
Dye-Pendant Polymers
Bichromophic Molecule (Ru-Pyrene)
Chameleon Luminophore
Light-Emitting Polymer
Monolayers
Langmuir-Blodgett (LB) Film
Self-Assembled Monolayers (SAMs)
Electrically Excited PSP
Appendix B: Paint Calibration and Formulations
Calibration
PSP and TSP Formulations
Appendix C: Recipes
Appendix C: Recipes
Steady PSP
Fast PSP (AA-PSP)
Fast PSP (PC-PSP)
TSP
Spraying Procedure
Pretreatment
Spraying
Safety
Luminophores
Polymers
Particles
Solvents
Appendix D: Vendors
Chemicals
Cameras
Light Sources
Optical Filters
Color Plates
References
Index

Citation preview

Experimental Fluid Mechanics

Tianshu Liu · John P. Sullivan Keisuke Asai · Christian Klein Yasuhiro Egami

Pressure and Temperature Sensitive Paints Second Edition

Experimental Fluid Mechanics Series Editors Wolfgang Merzkirch, Bochum, Germany Donald Rockwell, Bethlehem, USA Cameron Tropea, Darmstadt, Germany

Presenting unified treatments of current aspects of experimental fluid mechanics at a level useful to graduate students, researchers, and practicing engineers, this series serves the research community by consolidating widespread and often scattered knowledge. The books and monographs are equally suitable for learning and reference, and relevant topics are experimental techniques whose mastery requires a knowledge that can conveniently be contained in a book, as well as topics in fluid dynamics where understanding is based largely, though not necessarily exclusively, upon experiments. Thus, the books may contain up to one-third theory, and each one is a complete, integrated discourse, as opposed to a group of essays on selected sub-topics, with an editor or principal author responsible for unifying the conceptual content.

More information about this series at http://www.springer.com/series/3837

Tianshu Liu • John P. Sullivan • Keisuke Asai • Christian Klein • Yasuhiro Egami

Pressure and Temperature Sensitive Paints Second Edition

Tianshu Liu Department of Mechanical and Aerospace Engineering Western Michigan University Kalamazoo, MI, USA Keisuke Asai Department of Aerospace Engineering Tohoku University Sendai, Japan

John P. Sullivan School of Aeronautics and Astronautics Purdue University West Lafayette, IN, USA Christian Klein German Aerospace Center DLR Institute of Aerodynamics and Flow Technology Göttingen, Germany

Yasuhiro Egami Department of Mechanical Engineering Aichi Institute of Technology Toyota, Aichi, Japan

ISSN 1613-222X ISSN 2197-9510 (electronic) Experimental Fluid Mechanics ISBN 978-3-030-68055-8 ISBN 978-3-030-68056-5 (eBook) https://doi.org/10.1007/978-3-030-68056-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Ruomei and Ranya—T. L. Jean, Linda, Keith and Kevin—J. S. Satoko and Chiaki—K. A. Svenja and Charlotte—C. K. Yuriko and Masafumi—Y. E.

Preface

The first edition of the book “Pressure and Temperature Sensitive Paints” published by Springer in 2005 summarizes the early development of pressure- and temperature-sensitive paints (PSP and TSP) for aerodynamics, fluid mechanics, and heat transfer measurements. PSP and TSP as global optical techniques are able to provide quantitative high-resolution surface pressure, temperature, and heattransfer data for complex aerodynamic flows. Since 2005, there has been significant progress with the PSP and TSP techniques, especially with techniques such as timerevolved PSP and TSP measurements in unsteady flows, lifetime-based PSP and TSP measurements on rotating and moving objects, aeroacoustic measurements, and PSP measurements in low-speed, low-pressure, and hypersonic flows. PSP and TSP measurements are now commonly being carried out in various facilities in major aerospace institutions, including subsonic, transonic, supersonic, and hypersonic facilities, in cryogenic wind tunnels and with rotating machinery. The goal of this second edition is to give an updated, systematic description of PSP and TSP with presentation of new results obtained after 2005. This second edition has 11 chapters and four appendices whose content is summarized in brief below. Chapter 1: a concise introduction to PSP and TSP, in which the basic working principles are explained briefly and a historical note is also given. Chapter 2: the basic photophysics of luminescence and quenching mechanisms of luminescence. In particular, the models for the oxygen quenching of luminescence in a homogeneous polymer and a porous medium are discussed in detail, providing a physical foundation for PSP. Furthermore, the thermal quenching of luminescence is described as a physical basis for TSP. Chapter 3: the relevant physical properties of typical PSPs such as platinum porphyrins, ruthenium polypyridyls, and pyrene derivatives as probe luminophores, including their absorption and emission spectra and dependencies of luminescence on air pressure and temperature. Relatively new topics are fast PSPs, cryogenic PSPs, and multi-luminophore PSPs for some specialized applications. The concept of an ideal PSP is introduced. In addition, typical TSPs, cryogenic TSPs, and hightemperature TSPs are discussed. vii

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Chapter 4: the radiative energy transport processes in a luminescent layer, including excitation, luminescent emission, and photodetector response. The derived result is useful for a systematic uncertainty analysis of a PSP (or TSP) measurement system. Chapter 5: the intensity-based methods that are commonly used for PSP and TSP measurements with digital cameras and laser-scanning system. The basic data processing for the intensity-based methods is briefly described. An uncertainty analysis for PSP measurement is given, in which the error propagation equation and various elemental error sources are discussed in detail. An estimate for the limiting pressure resolution is given. Similarly, an uncertainty analysis for TSP measurements is also presented. Chapter 6: the lifetime-based methods for PSP and TSP using the first-order model for the response of luminescence to time-varying excitation light. In particular, the gated intensity ratio method, which is suitable for fluorescent lifetime imaging with digital cameras, is also presented. Uncertainties in lifetime measurements are discussed. Examples of lifetime calibrations and measurements for PSP and TSP are given. Chapter 7: the time response of PSP based on an analysis of oxygen diffusion through a PSP layer. The timescales for a conventional homogeneous PSP and a porous PSP are estimated. It is shown that porous PSP can achieve high time response which depends on the geometry of the pores. Measurement setups for determining time response of PSP are described. Similarly, the time response of TSP is discussed; this depends largely on the rate of thermal diffusion through a TSP layer. Chapter 8: the image and data analysis techniques for PSP and TSP, which include geometric and radiometric calibration of a camera, correction for selfillumination, image registration, intensity-to-pressure conversion, pressure correction, and generation of a deformed surface grid. New topics are noise-reduction methods, image deblurring, and the inverse heat transfer method. Chapter 9: applications of PSP to various facilities. Intensity- and lifetime-based PSP measurements in subsonic, transonic, and supersonic wind tunnels are discussed. New topics are PSP measurements in unsteady flows, hypersonic flows, low-speed flows, low-density flows, and with rotating machinery. Other topics include measurements in cryogenic wind tunnels, flight testing, supersonic and sonic impinging jets, micro fluidics, and the acoustic resonance box. Chapter 10: applications of TSP to various facilities particularly to hypersonic wind tunnels. TSP measurements in a small shock tube are described, revealing complex flow structures in shock/cylinder interactions. TSP results on different models in hypersonic wind tunnels are discussed. To demonstrate the use of quantitative heat flux measurements with TSP, experiments on a circular cone model in a quiet hypersonic wind tunnel are described. Examples in boundary-layer transition detection using TSP on various models are also given. Heat flux measurements in impinging jets are discussed as an example of the application of TSP in general heat transfer problems.

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Chapter 11: extended and special applications of PSP and TSP. PSP as an oxygen sensor is used for global measurements of film cooling effectiveness in turbine machinery. Global skin friction diagnostics with PSP and TSP are explored based on the relations between skin friction and surface pressure, temperature and scalar concentration. Using a solution of the inverse problem, skin friction fields can be reconstructed from surface pressure, temperature, and scalar concentration maps; these are demonstrated with the help of several examples. PSP has also been used as a planar oxygen optode for measurements of oxygen distributions in sand sediments in water beds. Other topics are: particles coated with PSP for simultaneous measurements of velocity and pressure, measurements of oxygen distributions in fuel cells, and phosphor thermometry for surface temperature measurements in an engine cylinder. Appendix A: the chemical synthesis of PSP and TSP. Appendix B: PSP and TSP calibration and formulations. Appendix C: some PSP and TSP recipes. Appendix D: a list of vendors providing chemicals, cameras, lights, and other accessories for PSP and TSP measurements. This second edition includes the published results obtained in several aerospace institutions and universities. These aerospace institutions include NASA Research Centers (Langley, Ames and Glenn), Arnold Engineering Development Center (AEDC), US Air Force Research Laboratory (AFRL), Naval Surface Warfare Center, Boeing Company, Japan Aerospace Exploration Agency (JAXA), German Aerospace Center (DLR), French Aerospace Laboratory (ONERA), Central Aerohydrodynamic Institute (TsAGI) in Russia, National Research Council (NRC) in Canada, and China Aerodynamics Research and Development Center (CARDC). The universities that contribute the materials used in this second edition include Purdue University, University of Washington, Ohio State University, University of Florida, Florida State University, University of Notre Dame, University of Maryland, Tohoku University, Nagoya University, Tokyo University of Agriculture and Technology, Aichi Institute of Technology, Waseda University, Tokyo Metropolitan University, Toyama Prefectural University, Kyushu University, Osaka City University, Tokyo Institute of Technology, Nara Women’s University, Hokkaido University, University of Yamanashi, University of Hohenheim, University of Stuttgart, Bundeswehr University Munich, Technische Universität Darmstadt, University of Applied Sciences Münster, University of Glasgow, Shanghai Jiao Tong University, Peking University, and National Tsing Hua University. We are indebted to our colleagues for providing their publications, offering comments, and giving their permission for us to use their published results in this second edition. Without their helps, this edition could not have been completed. Specifically, we would like to acknowledge the following researchers whose work has formed the basis for this edition: M. Y. Ali, Y. Amao, M. Anyoji, W. Beck, U. Beifuss, M. Bitter, V. Borovoy, A. Bykov, Z. Cai, M. Costantini, J. Crafton, T. Davis, B. Dimond, K. J. Disotell, J. Gößling, K. Goodman, J. W. Gregory, Y. Hasegawa, U. Henne, M. Hilfer, C. Y. Huang, T. J. Juliano, M. Kameda, M. Kammeyer, K. Kontis, M. Kuzmin, W. Lang, S. J. Laurence, Y. Le Sant, C. B. Lee, J. Lemarechal, Y. Liu, Y. Matsuda, Y. Mebarki, M.-C. Merienne, M. Miozzi, K. Mitsuo, H. Mori, V. Mosharov,

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H. Nagai, K. Nakakita, T. Nonomura, D. Numata, M. Obata, K. Oguri, V. Ondrus, H. Ozawa, A. Pandey, M. Pastuhoff, D. Peng, S. Risius, C. L. Running, W. M. Ruyten, H. Sakaue, Y. Sakamura, E. T. Schairer, M. Schäferling, J. Martinez Schramm, M. E. Sellers, K. Seo, S. Someya, T. Streit, Y. Sugioka, A. N. Watkins, A. Weiss, L. Yang, D. Yorita, W. Zhou, and Y. Zhu. In addition, we would like to thank the following colleagues who have over the years worked and collaborated with us: T. Amer, J. H. Bell, T. J. Bencic, M. Benne, O. C. Brown, G. Buck, A. W. Burner, S. Burns, B. Campbell, B. F. Carroll, L. N. Cattafesta, R. C. Crites, G. Dale, R. H. Engler, R. G. Erausquin, U. Fey, W. Goad, L. G. Goss, M. Guille, M. Hamner, J. M. Holmes, J. P. Hubner, J. Ingram, H. Ji, R. Johnston, J. D. Jordan, J. T. Kegelman, N. Lachendro, J. Lepicovsky, X. Lu, R. D. Mehta, C. Obara, D. M. Oglesby, T. G. Popernack, W. K. S. Schanze, A. M. Scroggin, Y. Shimbo, K. Teduka, S. D. Torgerson, and B. T. Upchurch. We would like to dedicate this book to the following three pioneers who have substantially contributed to the evolution of PSP and TSP technology, but had sadly passed away after the first version of this book had been published: Prof. Martin P. Gouterman (1931–2020), Professor of Chemistry at the University of Washington, Seattle, the USA, was a recognized pioneer in the development of PSP. Along with his brilliant scientific accomplishments in basic research with porphyrin molecules, Prof. Gouterman was instrumental in the development of the first PSP that had been used by Boeing and NASA in wind tunnel testing of aircraft wings. His technique has since been adopted by the firm Innovative Scientific Solutions Incorporated (ISSI), Dayton, Ohio, thereby laying the foundation for PSP activities around the world. As an excellent educator with scientific creativity and personal warmth, Prof. Gouterman encouraged young researchers involved in interdisciplinary collaborations between chemistry and engineering. Dr. Sergey Fonov (1952–2010) started his career as a scientist in TsAGI (The Central Aerohydrodynamic Institute), Zhukovsky in Russia. He was an integral part of the TsAGI team that first developed and demonstrated PSP for wind tunnel measurements. After leaving TsAGI in 1998, he worked at DLR in Göttingen, Germany, where he collaborated with the DLR team for the further development of PSP. In 2000, Dr. Fonov moved to the United States and led the ISSI team to develop a variety of PSP systems and measurement techniques for applications in fluid mechanics. Dr. Fonov was truly an international pioneer who helped the spread of PSP technology across national borders. His efforts have furthermore enabled the deployment of PSP into industries worldwide. Prof. Tomohide Niimi (1954–2018) was a Professor in Mechanical Engineering at Nagoya University in Japan. His main area of research was rarefied gas dynamics. In 1999, he joined an interdisciplinary research project called “MOSAIC” (Molecular Sensors for Aero-thermodynamic Research). In this project, he pioneered the development of PSP technology for low-pressure and microfluidic flows. His final goal was to establish molecular sensor technology for high-Knudsen-number (free molecular)

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flows. This goal has since been passed on to the younger generation of researchers who profited from his supervision. Prof. Niimi was well liked for his personal and amiable character, and he played an active role in cementing the relationships between the PSP communities all over the world. Their presence will be sorely missed. We would like to thank Springer/Nature, AIAA, Elsevier, Wiley, AIP, SAGE, MDPI, ARC and Cambridge University Press for permitting the reuse of figures. Kalamazoo, MI, USA West Lafayette, IN, USA Sendai, Japan Göttingen, Germany Toyota, Aichi, Japan

Tianshu Liu John P. Sullivan Keisuke Asai Christian Klein Yasuhiro Egami

Contents

1

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Pressure-Sensitive Paint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Temperature-Sensitive Paint . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . .

1 3 7 9

2

Basic Photophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Kinetics of Luminescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Models for Conventional PSP . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Models for Porous PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Collision-Controlled Model . . . . . . . . . . . . . . . . . . . . . 2.3.2 Adsorption-Controlled Model . . . . . . . . . . . . . . . . . . . 2.4 Thermal Quenching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13 13 16 21 23 25 29

3

Physical Properties of Paints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Typical PSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Platinum Porphyrins . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Ruthenium Polypyridyls . . . . . . . . . . . . . . . . . . . . . . 3.1.3 Pyrene Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Fast PSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 AA-PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 PC-PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Poly(TMSP)-PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Cryogenic PSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Multiple-Luminophore PSPs . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Ideal PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Typical TSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.1 Ruthenium Complexes . . . . . . . . . . . . . . . . . . . . . . . 3.6.2 Europium Complexes . . . . . . . . . . . . . . . . . . . . . . . . 3.6.3 Cryogenic TSPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6.4 Other Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 31 32 36 36 40 40 43 51 52 53 56 58 59 62 65 68

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Contents

3.7

Desirable Properties of Paints . . . . . . . . . . . . . . . . . . . . . . . . 3.7.1 Pressure Response . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.2 Luminescent Output . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.3 Paint Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.4 Response Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7.5 Temperature Sensitivity . . . . . . . . . . . . . . . . . . . . . . 3.7.6 Physical Characteristics . . . . . . . . . . . . . . . . . . . . . . 3.7.7 Chemical Characteristics . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . .

69 70 70 70 70 71 71 71

4

Radiative Energy Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Radiometric Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Excitation Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Luminescent Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Photodetector Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 73 74 77 80

5

Intensity-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Measurement Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1.1 Camera-Based Systems . . . . . . . . . . . . . . . . . . . . . . . 5.1.2 Laser-Scanning System . . . . . . . . . . . . . . . . . . . . . . . 5.2 Basic Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Pressure Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Error Propagation, Sensitivity, and Total Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Photodetector Noise and Limiting Pressure Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Errors Induced by Model Deformation . . . . . . . . . . . . 5.3.5 Temperature Effect . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Calibration Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.7 Temporal Variations . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.8 Spectral Variability and Filter Leakage . . . . . . . . . . . 5.3.9 Pressure Mapping Errors . . . . . . . . . . . . . . . . . . . . . . 5.3.10 Paint Intrusiveness . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.11 Other Error Sources and Limitations . . . . . . . . . . . . . 5.3.12 Allowable Upper Bounds of Elemental Errors . . . . . . 5.3.13 Uncertainties of Integrated Forces and Moments . . . . . 5.3.14 In Situ Calibration Uncertainty . . . . . . . . . . . . . . . . . 5.3.15 Example: Subsonic Airfoil Flows . . . . . . . . . . . . . . . 5.4 Temperature Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Error Propagation and Limiting Temperature Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Elemental Error Sources of TSP . . . . . . . . . . . . . . . .

. . . . . . .

85 85 85 91 92 97 97

.

98

. . . . . . . . . . . . . .

99 102 104 106 106 106 107 107 109 109 111 112 118 124

. 124 . 125

Contents

6

Lifetime-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Response of Luminescence to Time-Varying Excitation Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 First-Order Model . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Higher-Order Model . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Lifetime Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Pulse Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Phase Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.3 Amplitude Demodulation Method . . . . . . . . . . . . . . . 6.2.4 Gated Intensity Ratio Method . . . . . . . . . . . . . . . . . . 6.3 Fluorescence Lifetime Imaging . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Intensified CCD Camera . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Internally Gated CCD Camera . . . . . . . . . . . . . . . . . . 6.4 Pressure Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Phase Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Amplitude Demodulation Method . . . . . . . . . . . . . . . 6.4.3 Gated Intensity Ratio Method . . . . . . . . . . . . . . . . . . 6.5 Lifetime Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xv

. 129 . . . . . . . . . . . . . . . .

129 129 131 132 132 133 135 138 143 143 145 147 147 148 150 153

7

Time Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Time Response of Conventional PSP . . . . . . . . . . . . . . . . . . . . 7.1.1 Oxygen Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Pressure Response and Optimum Thickness . . . . . . . . . 7.2 Time Response of Porous PSP . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Deviation from the Square-Law . . . . . . . . . . . . . . . . . . 7.2.2 Effective Diffusivity: Geometrical Perspective . . . . . . . 7.2.3 Diffusion Timescale . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4 Knudsen Diffusion: Statistical Perspective . . . . . . . . . . 7.2.5 Nonlinear Quenching Kinetics . . . . . . . . . . . . . . . . . . . 7.2.6 Effect of Lifetime on Time Response . . . . . . . . . . . . . . 7.3 Measurements of Pressure Time Response . . . . . . . . . . . . . . . . 7.3.1 Solenoid Valve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Shock Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Acoustic Resonance Tube . . . . . . . . . . . . . . . . . . . . . . 7.3.4 Fluidic Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Time Response of TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4.1 Pulsed Laser Heating on Thin Metal Film . . . . . . . . . . 7.4.2 Step-Like Jet Impingement Cooling . . . . . . . . . . . . . . . 7.4.3 Shock Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

163 163 163 167 170 170 171 174 175 177 178 180 181 184 186 189 189 190 194 196

8

Image and Data Analysis Techniques . . . . . . . . . . . . . . . . . . . . . . 8.1 Geometric Calibration of Camera . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Collinearity Equations . . . . . . . . . . . . . . . . . . . . . . . 8.1.2 Direct Linear Transformation . . . . . . . . . . . . . . . . . . 8.1.3 Optimization Method . . . . . . . . . . . . . . . . . . . . . . . .

199 200 200 204 205

. . . . .

xvi

Contents

8.2 8.3

. . . . . . . . . . . . . . . . .

210 213 213 215 216 218 222 225 227 231 234 234 235 238 240 241 243

Applications of PSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1 Subsonic, Transonic, and Supersonic Wind Tunnels . . . . . . . . . 9.1.1 Intensity-Based Measurements . . . . . . . . . . . . . . . . . . 9.1.2 Lifetime-Based Measurements . . . . . . . . . . . . . . . . . . 9.2 Unsteady Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Transonic Wing Buffeting . . . . . . . . . . . . . . . . . . . . . . 9.2.2 Unsteady Pressure on Rocket Fairing Model . . . . . . . . 9.2.3 Oscillating Shock Wave in Transonic Flow . . . . . . . . . 9.2.4 Impinging Jet Resonant Modes . . . . . . . . . . . . . . . . . . 9.3 Hypersonic and Shock Wind Tunnels . . . . . . . . . . . . . . . . . . . . 9.3.1 Blunt Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Shock/Body Interaction . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Moving-Shock-Wave Interaction with Circular Cylinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.4 Scramjet Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 Hypersonic Boundary-Layer Separation . . . . . . . . . . . . 9.4 Low-Speed Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Ground Vehicle Models . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Rugby Ball . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.3 Unsteady Pressure Fluctuation on Slat as Noise Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Rotating Machinery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Rotating Compressor Blades . . . . . . . . . . . . . . . . . . . . 9.5.2 Helicopter Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6 Low-Pressure Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.6.1 PSP Properties at Low Pressure . . . . . . . . . . . . . . . . . . 9.6.2 Measurements in the Mars Wind Tunnel . . . . . . . . . . .

247 247 248 254 261 261 265 268 271 277 278 281

8.4 8.5 8.6 8.7 8.8

8.9 8.10 9

Radiometric Calibration of Camera . . . . . . . . . . . . . . . . . . . . Correction for Self-Illumination . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 View Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Correction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.3 Error Estimate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.4 Bidirectional Reflectance Distribution Function . . . . . Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conversion to Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pressure Correction for Extrapolation to Low-Speed Data . . . . Generation of Deformed Surface Grid . . . . . . . . . . . . . . . . . . Noise Reduction Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.1 Phase Averaging . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.2 FFT-Based Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.3 Mode Decomposition Analysis . . . . . . . . . . . . . . . . . 8.8.4 Heterodyne Method . . . . . . . . . . . . . . . . . . . . . . . . . Image Deblurring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inverse Heat Transfer Methods . . . . . . . . . . . . . . . . . . . . . . .

286 288 290 292 294 298 299 303 305 310 313 313 316

Contents

9.7

xvii

Other Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7.1 Cryogenic Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . 9.7.2 Subsonic and Sonic Impinging Jets . . . . . . . . . . . . . . . 9.7.3 Flight Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7.4 Micro Fluidics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.7.5 Acoustic Resonance Modes . . . . . . . . . . . . . . . . . . . .

320 320 325 328 336 339

10

Applications of TSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Small Shock Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Hypersonic Wind Tunnels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.1 Circular Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Inlet Ramp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.3 AGARD HB-2 Standard Model . . . . . . . . . . . . . . . . . . 10.2.4 Single and Double Fins . . . . . . . . . . . . . . . . . . . . . . . 10.3 Quiet Mach-6 Ludwieg Tube . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 Circular Cone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Lateral Heat Conduction Effect . . . . . . . . . . . . . . . . . . 10.4 Boundary-Layer Transition Detection . . . . . . . . . . . . . . . . . . . . 10.4.1 Heating and Cooling Methods . . . . . . . . . . . . . . . . . . . 10.4.2 Swept Wings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.3 Wind Turbine Profile Model and Nacelle . . . . . . . . . . . 10.4.4 Laminar-Type Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.5 Flat Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.6 Rotating Blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.7 Hypersonic Boundary-Layer Transition . . . . . . . . . . . . 10.5 Impinging Jet Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . .

345 345 350 352 354 357 360 364 364 365 368 370 372 374 378 381 384 386 390 393

11

Extended Applications of PSP and TSP . . . . . . . . . . . . . . . . . . . . . . 11.1 Film Cooling Measurement Using PSP . . . . . . . . . . . . . . . . . . . 11.1.1 Mass Transfer Analogy . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Determining Film Cooling Effectiveness . . . . . . . . . . . 11.1.3 Circular, Shaped, and Sand-Dune-Inspired Holes . . . . . 11.2 Skin Friction Diagnostics Using PSP and TSP . . . . . . . . . . . . . 11.2.1 Basic Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Variational Method . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.3 TSP-Derived Skin Friction Fields in Water Flow . . . . . 11.2.4 PSP-Derived Skin Friction Fields in Dual Colliding Impinging Nitrogen Jets . . . . . . . . . . . . . . . . . . . . . . . 11.2.5 PSP-Derived Skin Friction Field in Junction Flow . . . . 11.3 Planar Oxygen Optode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Other Topics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.1 Pressure-Sensitive Particles . . . . . . . . . . . . . . . . . . . . . 11.4.2 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.3 Phosphor Thermometry . . . . . . . . . . . . . . . . . . . . . . .

399 399 399 401 402 406 406 410 411 414 416 419 424 424 427 430

xviii

Contents

Appendix A: Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Appendix B: Paint Calibration and Formulations . . . . . . . . . . . . . . . . . 461 Appendix C: Recipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485 Appendix D: Vendors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Color Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 541

Chapter 1

Introduction

Quantitative measurements of surface pressure and temperature in wind tunnels and flight testing are essential for understanding the aerodynamic performance and heat transfer characteristics of flight vehicles. Surface pressure data are required to determine the distribution of aerodynamic load for the design of a flight vehicle, while surface temperature data are used to estimate heat transfer on the vehicle surface. Surface pressure and temperature measurements provide critical information on important flow phenomena such as shocks, flow separation, boundary-layer transition, and vortices. In addition, experimental pressure and temperature data are necessary for the validation and verification of computational fluid dynamics (CFD) codes. Traditionally, in wind tunnel testing, surface pressure is measured by utilizing a pressure tap (or orifice) at a location of interest connected through a small tube to a pressure transducer (Barlow et al. 1999). Hundreds of pressure taps are needed to obtain a crude pressure field on a complex aircraft model. Manufacturing, tubing, and preparing such a model for wind tunnel testing are very labor-intensive and costly. For thin wings and blades, the installation of pressure taps is difficult. Furthermore, pressure measurements at discrete taps ultimately limit the spatial resolution of data such that some details of a complex flow field cannot be revealed. Similarly, a surface temperature field is traditionally measured using temperature sensors (such as thermocouples and resistance thermometers) distributed at discrete locations (Moffat 1990). Optical sensors for measuring surface pressure and temperature have been developed since the 1980s based on the quenching mechanisms of luminescence. These luminescent molecule sensors are called pressure-sensitive paint (PSP) and temperature-sensitive paint (TSP). Compared to conventional techniques, they offer a unique capability for noncontact full-field measurements of surface pressure and temperature on a complex flight vehicle model with a much higher spatial resolution at a lower cost. Therefore, they provide global diagnostics of rich physical phenomena in complex flows around flight vehicles. In PSP and TSP, luminescent molecules as sensors are incorporated into a suitable polymer coating on a surface. In general, luminophore and polymer binder © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_1

1

2

1 Introduction

Fig. 1.1 Schematic of a luminescent paint (PSP or TSP) on a surface

in PSP and TSP can be dissolved in a solvent; the resulting mixture can be applied to a surface using a sprayer or airbrush. After the solvent evaporates, a solid polymer paint in which luminescent molecules are immobilized remains on the surface. Luminescent molecules could also be directly immobilized in a porous solid surface. When a luminescent paint is illuminated by a light with a proper wavelength, luminescent molecules are excited and then the luminescent light with a longer wavelength emits from the excited molecules. Figure 1.1 shows a schematic of a generic luminescent paint layer emitting radiation under excitation by an incident illumination light. The luminescent emission from a paint can be affected by certain physical processes. The main photophysical process in PSP is the oxygen quenching that causes a decrease of the luminescent intensity as the partial pressure of oxygen or air pressure increases. A polymer binder for PSP is oxygen permeable, which allows oxygen molecules to interact with luminescent molecules in the binder. To make a fast responding PSP (simply fast PSP), a mixture of luminophore and solvent can be directly applied to a porous solid surface. Essentially, PSP is an oxygen sensor adapted for aerodynamic experiments. By contrast, the major mechanism in TSP is the thermal quenching that reduces the luminescent intensity as temperature increases. TSP is not sensitive to air pressure since a polymer binder used for TSP is oxygen impermeable. It is noted that due to the thermal quenching, PSP is intrinsically temperature sensitive. PSP or TSP can be calibrated to determine the relationship between the luminescent intensity and pressure or temperature. Therefore, surface pressure or temperature can be remotely measured by a photodetector

1.1 Pressure-Sensitive Paint

3

(e.g., digital camera) detecting the luminescent emission from PSP or TSP. PSP and TSP are companion techniques, which not only utilize luminescent molecules as probes, but also use similar measurement systems and data processing methods.

1.1

Pressure-Sensitive Paint

The basic principle of PSP is briefly described here. After a photon of light with a certain wavelength is absorbed to excite a luminophore from the ground electronic state to the excited electronic state, the excited electron returns to the unexcited ground state through radiative and radiationless processes. The radiative emission is called luminescence (a general term for fluorescence and phosphorescence). The excited state can be deactivated by the interaction of the excited luminescent molecules with oxygen molecules in a radiationless process; in other words, oxygen molecules quench the luminescent emission. According to Henry’s law, the concentration of oxygen in a PSP layer is proportional to the partial pressure of oxygen in the gas above the PSP. Further, air pressure (simply pressure hereafter) is proportional to the oxygen partial pressure. For higher air pressure, more oxygen molecules exist in the PSP layer and as a result more luminescent molecules are quenched. Hence, the luminescent intensity of PSP is a decreasing function of air pressure. The relationship between the luminescent intensity and oxygen concentration is described by the Stern–Volmer relation. In experimental aerodynamics, a convenient form of the Stern–Volmer relation between the luminescent intensity I and pressure p is given by I ref p , ¼AþB pref I

ð1:1Þ

where Iref and pref are the luminescent intensity and pressure at a reference condition, respectively. In typical tests in a wind tunnel, Iref is taken when the tunnel is turned off, and it is called the wind-off intensity (or image); likewise, I is called the wind-on intensity (or image). The Stern–Volmer coefficients A and B, which are generally temperature dependent due to the thermal quenching, are experimentally determined by calibration. Theoretically, the intensity ratio Iref/I in Eq. (1.1) can eliminate the effects of nonuniform illumination, uneven coating, and nonhomogeneous luminophore concentration in PSP. Figure 1.2a, b shows, respectively, the luminescent intensity as a function of pressure at the ambient temperature and the corresponding Stern–Volmer plots for three PSPs: Ru(ph2-phen) in GE RTV 118, Pyrene in GE RTV 118, and PtOEP in GP 197. A measurement system for PSP (or TSP) is generally composed of paint, illumination light, photodetector, and data acquisition/processing unit. Figure 1.3 shows a generic camera system for PSP and TSP. Illumination sources available for PSP and TSP include lasers, light-emitting-diode (LED) arrays, ultraviolet (UV) lamps, and xenon lamps. Scientific-grade charge-coupled device (CCD) cameras are often used

4

1 Introduction 1.0

7 Ru(ph2-phen) in GE RTV 118

6

0.6

4

Iref/I

I/Iref

0.8

Pyrene in GE RTV 118 PtOEP in GP 197

5

3

0.4

2 Ru(ph2-phen) in GE RTV 118

0.2

1 0 0.0

0.2

0.4

0.6

0.8

1.0

Pyrene in GE RTV 118 PtOEP in GP 197

0.0 0.0

0.2

0.4

p/pref

(a)

0.6

0.8

1.0

p/pref

(b)

Fig. 1.2 (a) The luminescent intensity as a function of pressure, and (b) the Stern–Volmer plots for three PSPs at the ambient temperature, where pref is the ambient pressure and Iref is the luminescence intensity at the ambient conditions

as detectors because of their good linear response, high dynamic range, and low noise. Recently, complementary metal oxide semiconductor (CMOS) cameras are popularly used particularly in time-resolved PSP and TSP measurements. In addition, for some special PSP (or TSP) measurements, a photomultiplier tube (PMT) or a photodiode (PD) is used as a photodetector in a laser-scanning system where a laser with a computer-controlled scanning mirror is used as an illumination source (see Chap. 5). Optical filters are used in both the camera and laser-scanning systems to separate the luminescent emission from the excitation light. In principle, once PSP is calibrated, pressure can be calculated from the luminescent intensity using the Stern–Volmer relation. Nevertheless, practical data processing is more elaborate in order to suppress the error sources and improve the measurement accuracy of PSP. For an intensity-based camera system, a wind-on image often does not align with a wind-off reference image due to aeroelastic deformation of a model in wind tunnel testing. Therefore, image registration based on high-contrast targets (markers) distributed on the model surface must be used to re-align the wind-on image to the wind-off image before taking a ratio between those images. Also, since the Stern–Volmer coefficients A and B are temperature dependent, temperature correction is required since the temperature effect of PSP is the most dominant error source in PSP measurements. In wind tunnel testing, the temperature effect of PSP is to some extent compensated by in situ calibration that directly correlates the luminescent intensity to pressure tap data obtained at welldistributed locations on a model. To further reduce the measurement uncertainty, additional data processing procedures are applied, including image averaging, darkcurrent correction, flat-field correction, illumination compensation, and self-illumination correction. After pressure images are obtained, to make pressure data more

1.1 Pressure-Sensitive Paint

5

Fig. 1.3 A generic camera system for PSP and TSP

useful to aircraft design engineers, data in the image plane should be mapped onto a model surface grid in the three-dimensional (3D) object space. Therefore, geometric camera calibration and image resection are necessary to establish the relationship between the image plane and the 3D object space. Besides the intensity-based method, a lifetime-based method has been developed. Theoretically, the luminescent lifetime is independent of the luminophore concentration, illumination level, and coating thickness. Hence, the lifetime-based method has some advantages particularly for PSP measurements on moving surfaces. Multiple-luminophore PSP with probe and reference luminophores is used to eliminate the need of a wind-off reference image and therefore reduce the error associated with model deformation. Also, multiple-luminophore PSP could compensate for the temperature effect of PSP. PSP measurements have been commonly conducted in high subsonic, transonic, and supersonic flows on various aerodynamic models in both large production wind tunnels and small research wind tunnels. PSP is particularly effective in a range of Mach numbers from 0.3 to 3.0. For PSP measurements in large wind tunnels, the accuracy of PSP is typically 0.02–0.03 in the pressure coefficient, while in well-

6

1 Introduction

Fig. 1.4 PSP image for the F-16C model at Mach 0.9 and the angle-of-attack of 4 . (From Sellers 2000)

controlled experiments the absolute pressure accuracy of 1 mbar (0.0145 psi or 100 Pa) can be achieved. In aeroacoustic applications, a pressure change of 10–100 Pa is resolvable. As an example, Fig. 1.4 shows a typical PSP-derived pressure field on a scaled model of the F-16C at Mach 0.9 and the angle-of-attack (AoA) of 4 , which was obtained at the Arnold Engineering Development Center (AEDC) (Sellers 2000). The surface pressure jump generated by a shock wave on the wing is clearly observed. Recently, the application of PSP has been extended to low-speed flows, hypersonic flows, cryogenic flows, low-density flows, rotating machinery, and microfluidics. PSP measurements in low-speed flows are difficult since a very small change in pressure must be resolved and the major error sources particularly the temperature effect must be minimized to obtain acceptable quantitative pressure data. Noise-reduction methods are often applied to PSP data in this case. Low-speed PSP measurements have been conducted at speeds as low as 20 m/s. In shortduration hypersonic tunnels, measurements require very fast time response of PSP and minimization of the temperature effect of PSP. Several porous PSPs have been

1.2 Temperature-Sensitive Paint

7

used in hypersonic tunnels since they have a very short response time of microseconds. In addition, since a porous PSP usually exhibits a good pressure sensitivity at cryogenic temperatures (as low as 90 K) and low-density conditions near vacuum, it is feasible for pressure measurements in cryogenic and low-density flows. Since PSP is a noncontact technique, it is particularly suitable to pressure measurements on high-speed rotating blades where conventional techniques are difficult to use. Both camera and laser-scanning systems have been used for PSP measurements on rotating blades of turbine engines and helicopters.

1.2

Temperature-Sensitive Paint

Temperature-sensitive paint (TSP) is a polymer-based paint in which temperaturesensitive luminescent molecules are immobilized. The quantum efficiency of luminescence decreases with increasing temperature; this effect is the thermal quenching that serves as the major working mechanism for TSP. Over a certain temperature range, a relation between the luminescent intensity I and absolute temperature T can be written in the Arrhenius form, i.e.,   I ðT Þ Enr 1 1 ln  , ¼ R T T ref I ðT ref Þ

ð1:2Þ

where Enr is the activation energy for the non-radiative process, R is the universal gas constant, and Tref is a reference temperature in Kelvin. Figure 1.5a, b shows, respectively, the temperature dependencies of the luminescent intensity and the

Fig. 1.5 (a) Temperature dependencies of the luminescent intensity, and (b) the Arrhenius plots for three TSPs

8

1 Introduction

Arrhenius plots for three TSPs: Ru(bpy) in Shellac, Rodamine-B in dope, and EuTTA in dope. The slopes of the Arrhenius plots (Enr/R) are 3797 for EuTTAdope TSP and 1070 for Ru(bpy)-Shellac TSP. A family of polymer-based TSPs is developed, and their working temperatures cover approximately a range of 90 to 473 K (183 to 200  C). The accuracy of TSP is about 0.2–0.8 K, depending on the temperature sensitivity of TSP. The procedure for applying TSP to a surface is basically the same as that for PSP. Not only does TSP use the same measurement systems shown in Fig. 1.3, but also most data processing methods for TSP are similar to those for PSP. Ideally, TSP can be used in tandem with PSP to correct the temperature effect of PSP and simultaneously obtain surface temperature and pressure fields. Compared to conventional temperature sensors, TSP is a global measurement technique that is able to obtain surface temperature fields with reasonable accuracy at a much higher spatial resolution. TSP has been used in various aerodynamic experiments to measure surface temperature and heat flux fields. In hypersonic flows where friction heating can produce a sufficient surface temperature increase, TSP can provide quantitative heat flux data calculated using the inverse heat transfer methods on various models such as cones, wedges, fins, and blunt bodies. In low-speed, subsonic and supersonic flows, a model is typically heated or cooled to increase a temperature change in TSP measurements. The mapping capability of TSP allows quantitative visualization of heat transfer features associated with complex flow structures such as shock-wave/ boundary-layer interaction, boundary-layer transition, and vortices. TSP is an effective technique for visualizing the boundary-layer transition from laminar flow to turbulent flow. Due to a significant difference in convection heat transfer between the laminar and turbulent flows, TSP can visualize a surface temperature change across the laminar-turbulent transition. Cryogenic TSPs have been developed to detect the boundary-layer transition on wings in cryogenic wind tunnels over a range of the total temperatures from 90 to 150 K. As a molecule sensor, TSP can be applied to microfluidic devices. An example of TSP application is briefly described here, which reveals rich physical phenomena in hypersonic flows. Using a combination of TSP and PSP, Borovoy et al. (2016) studied the influence of small flat-plate bluntness on flow and heat transfer structures in the single-fin and double-fin/boundary-layer interactions at Mach 5. The experiments were carried out in the TsAGI UT-1 M hypersonic wind tunnel operating as a Ludwieg tube. Figure 1.6a shows the Stanton number fields on the sharp plate (r ¼ 0) and on the slightly blunted plate (r ¼ 0.75 mm) with a single fin of the wedge angle of 15 installed vertically at Mach 5 and Reynolds number based on the plate length Re1L ¼ 27  106, where r is the radius of curvature of the plate leading edge. The heat transfer features associated with boundary-layer transition, shock-wave/boundary-layer interaction, and shock-shock interaction are revealed in Fig. 1.6a. The region where the shock affects the heat transfer is much wider than the region between the fin-generated shock and the fin surface. The maximum value of the Stanton number is reached on the reattachment line R1 located between the shock (indicated by a dashed line) and the fin. A small increase

1.3 Historical Remarks

9

Fig. 1.6 (a) The Stanton number fields, and (b) surface pressure coefficient fields on the flat plates with the single fin of the wedge angle θ ¼ 15 at M ¼ 5 and Re1L ¼ 27  106. Left column: sharp plate (r ¼ 0); and Right column: blunted plate (r ¼ 0.75 mm), where r is the radius of curvature of the plate leading edge. Note: (1) plate leading edge, (2) fin, (3) strips, (4) turbulent wedge, and (5) separation. (From Borovoy et al. 2016)

of heat transfer is also observed on the reattachment line R2 behind the secondary separation of the boundary layer. In Fig. 1.6a, turbulent wedges (denoted by 4) are observed in the boundary layers near the leading edge of both the sharp and blunted plates. Laminar-turbulent transition ends as the turbulent wedges merge at some distance from the plate leading edge. The increase of the leading-edge bluntness radius up to r ¼ 0.75 mm displaces the transition line downstream. On the blunted plate, the transition end is observed downstream of the fin leading edge such that the shock interacts with the transitional boundary layer. The maximum value of the Stanton number on the blunted plate is smaller than that on the sharp plate, and the shock-induced separation on the blunted plate occurs more upstream. As shown in Fig. 1.6b, the features in the heat flux fields are highly correlated with those in the surface pressure coefficient fields obtained by PSP.

1.3

Historical Remarks

The oxygen quenching of luminescence was first discovered by Kautsky and Hirsch (1935). The quenching effect of luminescence by oxygen was used to detect small quantities of oxygen in medical applications (Gewehr and Delpy 1993) and

10

1 Introduction

analytical chemistry (Lakowicz 1991, 1999). Peterson and Fitzgerald (1980) demonstrated a surface flow visualization technique based on the oxygen quenching of dye fluorescence, showing the possibility of using oxygen sensors for surface flow measurements. Studies of applying oxygen sensors to aerodynamic experiments were initiated by scientists at the Central Aero-Hydrodynamic Institute (TsAGI) in Russia. Interestingly, PSP was independently investigated by researchers in the University of Washington in collaboration with the Boeing Company and the NASA Ames Research Center in the United States. The conceptual transformation from oxygen concentration measurement to surface pressure measurement was really a critical step in developing PSP, signifying a paradigm shift from conventional point-based pressure measurement to global pressure diagnostics. Brown (2000) gave a historical review with personal notes and recollections from some pioneers on early PSP development. Pervushin and Nevsky (1981) of TsAGI, inspired by the earlier work of Zakharov and Aleskovsky (1964) and Zakharov et al. (1974) on oxygen measurements, suggested the use of the oxygen quenching phenomenon for pressure measurements in aerodynamic experiments. The first PSP measurement at TsAGI was conducted at Mach 3 on a sphere, a half-cone, and a flat plate with an upright block that were coated with a primitive PSP with a long lifetime excited by a flash lamp (Ardasheva et al. 1982, 1985). A photographic film camera was used for imaging the luminescent intensity field. The results were in reasonable agreement with the known theoretical solution and pressure tap data. Radchenko (1985) used a laser-scanning system with a photomultiplier tube as a detector for lifetime-based PSP measurements on a cone-cylinder model at Mach 2.5 and 3.0. At TsAGI, proprietary PSP and TSP formulations were developed and applied extensively to tests in subsonic, transonic, supersonic, shock and dynamic tunnels and rotating machinery (Bykov et al. 1992, 1993, 1996, 1997; Bykov 1998; Borovoy et al. 1995, 2009, 2013, 2016, 2018; Mosharov et al. 1990, 1992, 1994, 1997, 2003, 2005; Mosharov and Radchenko 2012, 2014, 2015; Fonov et al. 1997, 1998, 1999; Troyanovsky et al. 1992, 1993; Andreev et al. 1994; Kuzmin et al. 1998, 2000; Bosnykov et al. 1997; Kulesh et al. 2006). The imaging devices used early at TsAGI were photographic film cameras, TV cameras, scientific-grade CCD cameras, and photomultiplier tubes with laser-scanning systems. In the later 1980s, TsAGI marketed its PSP technology through the Italian firm INTECO and issued a one-page advertisement in the magazine “Aviation Week & Space Technology” on February 12, 1990. Interestingly, scientists in other countries were not aware of TsAGI’s work on PSP until reading the advertisement. TsAGI’s PSP system was demonstrated in wind tunnel tests at the Boeing Company in 1990 and Deutsche Forschungsanstalt fur Luft- und Raumfahrt (DLR, German Aerospace Center) in Germany in 1991, which attracted considerable attention of researchers in experimental aerodynamics (Volan and Alati 1991). PSP was independently developed by a group of chemists led by Profs. Gouterman and Callis at the University of Washington (UW) in the late 1980s (Gouterman et al. 1990; Kavandi et al. 1990). The chemists at UW were initially interested in the use of porphyrin compounds as an oxygen sensor for biomedical

1.3 Historical Remarks

11

applications. After stimulating discussions with experimental aerodynamicists J. Crowder of the Boeing Company and B. McLachlan of NASA Ames, Gouterman and Callis understood the important implication of oxygen sensors in aerodynamic testing and started to develop a luminescent coating applied to the surface for pressure measurements. A classical UW PSP used platinum-octaethylporphorin (PtOEP) as a luminescent probe molecule in a proprietary commercial polymer mixture called GP-197 made by the Genesee Company. PSP measurements on a NACA0012 airfoil model were conducted using PtOEP in GP-197 in the 25 cm  25 cm subsonic wind tunnel at the NASA Ames Fluid Dynamics Laboratory, where the model was set at the angle-of-attack (AoA) of 5 and the Mach numbers from 0.3 to 0.66. A UV lamp was used for excitation, and an analog camera interfaced to an IBM-AT computer with an 8-bit frame grabber for image acquisition. The PSP data showed very favorable agreement with pressure tap data, clearly indicating the formation of a shock on the upper surface of the model as the Mach number increases (Kavandi et al. 1990; McLachlan et al. 1993a). Following the tests at NASA Ames, Kavandi demonstrated the same PSP system in the Boeing Transonic Wind Tunnel on various commercial airplane models, which was briefly discussed by Crowder (1990). Several proprietary paint formulations have been developed at UW, and successfully applied to wind tunnel testing at the Boeing Company and NASA Ames (McLachlan et al. 1993a, b, 1995; McLachlan and Bell 1995; Bell and McLachlan 1993, 1996; Gouterman 1997). PSP was also developed at the former McDonnell Douglas (MD) (Morris et al. 1993a, b; Morris 1995; Morris and Donovan 1994; Donovan et al. 1993; Dowgwillo et al. 1994, 1996; Crites 1993; Crites and Benne 1995). MD’s PSPs were mainly based on ruthenium compounds that were successfully used in subsonic, transonic, and supersonic flows for a generic wing-body model, a full-span ramp, an F-15 model, and a converging-diverging nozzle. PSP research has been contributed by researchers at NASA Langley and Glenn Research Centers, Arnold Engineering Development Center (AEDC), United States Air Force Research Laboratory, Purdue University, the University of Florida, the Ohio State University, and the University of Notre Dame in the USA. Researchers in DLR (German Aerospace Center), Office National d’Etudes et de Recherches Aerospatiales (ONERA, French Aerospace Laboratory), British Aerospace (BAe, UK), and British Defense Evaluation and Research Agency (DERA, UK) have made significant contributions to the field of PSP (Engler et al. 1991, 1992, 1998, 2000; Engler and Klein 1997a, b; Engler 1995; Le Sant 2001a; Lyonnet et al. 1997; Davies et al. 1995; Holmes 1998). In Japan, systematical studies of PSP have been made by researchers in the Japan Aerospace Exploration Agency (JAXA), Tohoku University and other universities, particularly on new PSP formulations, fast PSPs, lifetime-based systems, and PSP applications in various flows (Asai 1999; Asai et al. 2001, 2003; Nakakita et al. 2006). PSP research becomes active in China, particularly at Shanghai Jiao Tong University, China Aerodynamics Research and Development Center, China Academy of Aerospace Aerodynamics, and China Aeronautical Industry Aerodynamic Research Institute (Peng and Liu 2020; Blue Book on Chinese Aerodynamics Research 2017).

12

1 Introduction

TSP has been developed along with PSP, which is relatively new compared to thermographic phosphors and thermochromic liquid crystals. Kolodner and Tyson (1982, 1983a, b) used a europium-based TSP in a polymer binder to measure a surface temperature distribution of an operating integrated circuit. A family of TSPs was developed at Purdue University and used in low-speed, supersonic and hypersonic flows (Campbell et al. 1992, 1994, 1998; Campbell 1993; Liu et al. 1992, 1997b). Typical TSPs are EuTTA in model airplane dope (20 to 100  C) and Ru (bpy) in Shellac (0–90  C). Several cryogenic TSPs (175 to 0  C) were discovered (Campbell et al. 1994; Erausquin 1998; Erausquin et al. 1998) and used for boundary-layer transition detection in cryogenic flows (Asai et al. 1997c; Popernack et al. 1997; Asai and Sullivan 1998). TSP formulations were also studied at the University of Washington (Gallery 1993; Gallery et al. 1994). PSP and TSP have become a global quantitative flow diagnostic tool widely used in experimental aerodynamics and fluid mechanics. Useful reviews were given by Crites (1993), McLachlan and Bell 1995, Crites and Benne (1995), Liu et al. (1997b), Mosharov et al. (1997), Bell et al. (2001), Sullivan (2001), Gregory et al. (2008, 2014a), and Peng and Liu (2020). This book is the second edition of “Pressure and Temperature Sensitive Paints” originally by Liu and Sullivan (2005). It provides a systematically updated description of all the technical aspects of PSP and TSP, including basic photophysics, paint formulations and their physical properties, radiative energy transport, measurement methods and systems, measurement uncertainty, time response, image and data analysis techniques, and various applications in aerodynamics and fluid mechanics.

Chapter 2

Basic Photophysics

This chapter describes the relevant physical processes of luminescence, including excitation, emission, oxygen quenching, and thermal quenching. The kinetic models for conventional and porous PSPs are discussed, while the model for TSP is considered a reduced case. These models provide the physical foundations for the design and characterization of PSP and TSP, measurement uncertainty analysis, and data processing.

2.1

Kinetics of Luminescence

PSP and TSP are, respectively, based on the oxygen and thermal quenching processes of luminescence, which are reversible processes in molecular photoluminescence. The general principles of luminescence are described in detail by Rabek (1987), Becker (1969), and Parker (1968), which are briefly recapitulated here. The different energy levels and photophysical processes of luminescence for a simple luminophore can be clearly described by the Jablonski energy-level diagram shown in Fig. 2.1. The lowest horizontal line represents the ground-state energy of the molecule, which is normally a singlet state denoted by S0. The upper lines are energy levels for the vibrational states of excited electronic states. The successive excited singlet and triplet states are denoted by S1 and S2, and T1, respectively. As is normally the case, the energy of the first excited triplet state T1 is lower than the energy of the corresponding singlet state S1. A photon of radiation is absorbed to excite the luminophore from the ground electronic state to excited electronic states (S0 ! S1 and S0 ! S2). The excitation process is symbolically expressed as S0 + ħν ! S1, where ħ is the Planck constant and v is the frequency of the excitation light. Each electronic state has different vibrational states, and each vibrational state has different rotational states. The excited electron returns to the unexcited ground state by a combination of radiative and radiationless processes. Emission occurs through the radiative processes called © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_2

13

14

2 Basic Photophysics

Singlet Excited States Internal Conversion

Vibrational Relaxation

Triplet Excited State

S2

Interstystem Crossing S1

En e r g y

T1

Adsorption

Fluorescence

Internal and External Conversion

Phosphorescence

So Ground State Vibrational Relaxation

Fig. 2.1 Jablonsky energy-level diagram

luminescence. The radiation transition from the lowest excited singlet state to the ground state is called fluorescence, which is expressed as S1 ! S0 + ħνf. Fluorescence is a spin-allowed radiative transition between two states of the same multiplicity. The radiative transition from the triplet state to the ground state is called phosphorescence (T1 ! S0 + ħνp), which is a spin-forbidden radiative transition between two states of different multiplicity. The lowest excited triplet state, T1, is formed through a radiationless transition from S1 by intersystem crossing (S1 ! T1). Since phosphorescence is a forbidden transition, the phosphorescent lifetime is typically longer than the fluorescent lifetime. Luminescence is a general term for both fluorescence and phosphorescence. Radiationless deactivation processes mainly include internal conversion (IC), intersystem crossing (ISC), and external conversion (EC). The internal conversion (IC) is a spin-allowed radiationless transition between two states of the same multiplicity (S2 ! S1, S1 ! S0). Typically, this process is expressed as S1 ! S0 + Δ, where Δ denotes heat released. IC appears to be particularly efficient when two electronic energy levels are sufficiently close. The intersystem crossing (ISC) is a spin-forbidden radiationless transition between two states of the different multiplicity, which is expressed as S1 ! T1 + Δ or T1 ! S0 + Δ. Phosphorescence depends to a large extent on the population of the triplet state (T1) from the excited singlet state (S1) by the intersystem crossing. In addition, deactivation of an excited electronic

2.1 Kinetics of Luminescence

15

Table 2.1 Photophysical processes involving electronically excited states Step Excitation Fluorescence (F) Internal conversion (IC) Intersystem crossing (ISC) Phosphorescence (P) Intersystem crossing (ISC)

Process S0 + ħν ! S1 S1 ! S0 + ħνf S1 ! S0 + Δ S1 ! T1 + Δ T1 ! S0 + ħνp T1 ! S0 + Δ

Rate ks1[S0] kf[S1] kic[S1] k iscðs1 t1 Þ ½S1  kp[T1] k iscðt1 s0 Þ ½T 1 

Lifetime (s) 1015 1011  106 1014  1011 1011  108 103  102

state may involve the interaction and energy transfer between the excited molecules and the environment like solutes, which is called external conversion (EC). The excited singlet and triplet states can be deactivated by the interaction of the excited molecules with the components of a system. These bimolecular processes are quenching processes, including collisional quenching (diffusion or non-diffusion controlled), concentration quenching, oxygen quenching, and energy transfer quenching. The oxygen quenching of luminescence is the major photophysical mechanism for PSP. Due to the oxygen quenching, air pressure on a model surface is related to the luminescent intensity by the Stern–Volmer equation that will be further discussed. The quantum efficiency of luminescence in most molecules decreases with increasing temperature because the increased frequency of collisions at elevated temperatures improves the possibility for deactivation by the external conversion. This effect associated with temperature is the thermal quenching, which is the major photophysical mechanism for TSP. The population of the excited singlet states (S1) and triplet states (T1) at any given time depends on the competition among different photophysical processes listed in Table 2.1. The singlet state population [S1] and triplet state population [T1] are described by the following first-order kinetic model
 d ½S1  ¼ I a  kf þ k ic þ kiscðs1 t1 Þ þ kqðsÞ ½Q ½S1 , dt
 d ½T 1  ¼ k iscðs1 t1 Þ ½S1   kp þ k iscðt1 s0 Þ þ k qðtÞ ½Q ½T 1 , dt

ð2:1Þ

where Ia is the light absorption rate of generating the excited singlet states, [Q] is the population of the quencher Q, kf and kp are, respectively, the rate constants for fluorescence and phosphorescence, k iscðs1 t1 Þ and kiscðt1 s0 Þ are, respectively, the rate constants for the intersystem crossings S1 ! T1 and T1 ! S0, kic is the rate constant for the internal conversion, and kq(s) and kq(t) are the rate constants for the quenching in the singlet states and triplet states, respectively. The light absorption rate Ia ¼ ks1[S0] is proportional to the population [S0] in the ground state and the rate constant of excitation ks1. After a pulse excitation, the times required for the populations in the excited singlet state and triplet state to decay to 1/e of the initial value are, respectively,

16

2 Basic Photophysics


 τf ¼ 1= kf þ kic þ k iscðs1 t1 Þ þ k qðsÞ ½Q ,
 τp ¼ 1= kp þ k iscðt1 s0 Þ þ k qðtÞ ½Q :

ð2:2Þ

The time constants τf and τp are defined as the fluorescent and phosphorescent lifetimes, respectively. Usually, the lifetime of a specific photophysical process is defined as the reciprocal of the corresponding rate constant. Typical values of the lifetimes for different photophysical processes are listed in Table 2.1. When the intersystem crossing from T1 back to S1 (T1 ! S1 + Δ) is included in the kinetic model, extra terms kiscðt1 s1 Þ ½T 1  and k iscðt1 s1 Þ ½T 1  should be added, respectively, to the right-hand sides of Eq. (2.1) for [S1] and [T1], where k iscðt1 s1 Þ is the rate constant for the intersystem crossing T1 ! S1. In this case, the kinetic model becomes a coupled system of equations (Mosharov et al. 1997; Bell et al. 2001). Since S1 is a higher energy state than T1, this intersystem crossing is thermally activated and therefore the rate constant for the process T1 ! S1 is temperature dependent.

2.2

Models for Conventional PSP

From a standpoint of engineering application, it is unnecessary to analyze all the intermediate photophysical processes and their interactions. Therefore, a simplified model for luminescence (fluorescence and phosphorescence) is given here by considering the main processes: excitation, luminescent radiation, non-radiative deactivation, and quenching. The luminophore is excited by a photon from a ground state L0 to an excited state L, i.e., L0 + ħν ! L. The excited state L returns to the ground state L0 by either a radiative process (emission) or a radiationless process (deactivation). In the radiative process, the luminescent emission releases the energy of ħνl, kr

i.e., L ! L0 þ ħνl, where kr is the rate constant for the radiation process and νl is the frequency of the luminescent emission. In the deactivation process, L returns to L0 knr

by releasing heat, which is expressed as L ! L0 þ Δ, where knr is the rate constant for the combined effect of all the non-radiative processes. If the temperature around a luminophore molecule increases, the deactivation rate increases, reducing the radiative process from L. Thus, the rate constant knr for the non-radiative processes is temperature dependent. The quenching process by a quencher Q is expressed as kq

L þ Q ! L0 þ Q , where kq is the rate constant of the quenching process and Q denotes the excited quencher. The molecular oxygen O2 in the ground state is an efficient quencher for both the excited singlet and triplet states. The molecular oxygen is excited to O2 once it quenches luminescence, i.e., L þ O2 ! L0 þ O2 . By combining the rates of emission, deactivation, and quenching processes, the rate of change of the population of the excited state [L] is given by the first-order equation, i.e.,

2.2 Models for Conventional PSP

17


 d ½L  ¼ I a  k r þ k nr þ k q ½Q ½L : dt

ð2:3Þ

The rate of excitation is Ia ¼ ks1[L0], where [L0] is the population in the ground state and ks1 is the rate constant for excitation. At a steady state d[L]/dt ¼ 0, without quenching ([Q] ¼ 0), we have I a ¼ ð k r þ knr Þ½L :

ð2:4Þ

The amount of luminophore molecules in a given excited state is described by the quantum yield of luminescence defined by Φ¼

rate of luminescence : rate of excitation

ð2:5Þ

The quantum yield Φ for the luminescent emission from L with the quencher Q is expressed by Φ¼

k r ½L  kr I ¼ ¼ , Ia kr þ k nr þ kq ½Q I a

ð2:6Þ

where I is the luminescent intensity. The quantum yield without quenching is Φ0 ¼

kr ½L  kr I ¼ ¼ 0, Ia kr þ knr I a

ð2:7Þ

where I0 is the luminescent intensity without quenching. Dividing Φ0 by Φ, we obtain the well-known Stern–Volmer relation kq Φ0 I 0 ½Q ¼ 1 þ kq τ0 ½Q, ¼ ¼1þ Φ I k r þ knr

ð2:8Þ

where τ0 ¼ 1/(kr + knr) is the luminescent lifetime without quenching. The luminescent lifetime with the quencher is τ¼

1 : k r þ knr þ k q ½Q

ð2:9Þ

Thus, Eq. (2.8) can be written as Φ0 =Φ ¼ τ0 =τ: When the quencher is oxygen, the Stern–Volmer equation is

ð2:10Þ

18

2 Basic Photophysics

I 0 τ0 ¼ ¼ 1 þ kq τ0 ½O2 : I τ

ð2:11Þ

In general, the rate constants knr and kq for the non-radiative and quenching processes are temperature dependent. The temperature dependency of knr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991), i.e.,   E knr ¼ knr0 þ k nr1 exp  nr , RT

ð2:12Þ

where knr0 ¼ knr(T ¼ 0) and knr1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is temperature in Kelvin. The temperature dependency of the rate constant kq for the quenching process is related to oxygen diffusion in a homogeneous polymer layer used for a conventional PSP. According to the Smoluchowski relation, the rate constant kq for the oxygen quenching can be described by k q ¼ 4π RAB N 0 D,

ð2:13Þ

where RAB is an interaction distance between the luminophore and oxygen molecules, and N0 is Avogadro’s number. The diffusivity D has the temperature dependency modeled by the Arrhenius relation   E D ¼ D0 exp  D , RT

ð2:14Þ

where ED is the activation energy for the oxygen diffusion process. Therefore, from Eq. (2.9), the reciprocal of the luminescent lifetime is     1 E E ¼ k r þ knr0 þ knr1 exp  nr þ 4πRAB N 0 D0 exp  D ½O2 polymer , τ RT RT

ð2:15Þ

According to Henry’s law, the oxygen population [O2]polymer in a polymer binder is proportional to the partial pressure of oxygen pO2 or air pressure p, i.e., ½O2 polymer ¼ SpO2 ¼ SϕO2 p,

ð2:16Þ

where S is the oxygen solubility in a polymer binder layer and ϕO2 is the mole fraction of oxygen in the testing gas. The mole fraction of oxygen ϕO2 is 21% in the atmosphere, but it varies depending on testing facilities. For example, ϕO2 is only a few ppm (1 ppm ¼ 104%) in a cryogenic wind tunnel where the working gas is nitrogen. Defining the permeability P0 ¼ SD0, from Eq. (2.15), we have

2.2 Models for Conventional PSP

19

1 ¼ ka þ Kp, τ

ð2:17Þ

where the coefficients ka and K are defined as   E ka ¼ kr þ k nr0 þ knr1 exp  nr , RT

  E K ¼ 4πRAB N 0 P0 exp  D ϕO2 : RT

ð2:18Þ

In normal wind tunnel testing, it is difficult to obtain the zero-oxygen condition since the working gas in most wind tunnels is air containing 21% oxygen. Thus, instead of using the zero-oxygen condition, we usually utilize the zero-speed (windoff) condition as a reference. Taking a luminescent intensity ratio between the windoff and wind-on conditions, we obtain the Stern–Volmer equation suitable to aerodynamic applications, i.e., I ref τref p ¼ ¼ Apolymer ðT Þ þ Bpolymer ðT Þ : pref I τ

ð2:19Þ

The Stern–Volmer coefficients in Eq. (2.19) are Apolymer ¼ Apolymer,ref

ka , ka ref

Bpolymer ¼ Bpolymer,ref

K , K ref

ð2:20Þ

where the reference coefficients are defined as Apolymer,ref ¼

1 , 1 þ K ref pref =k a ref

Bpolymer,ref ¼

pref : ka ref =K ref þ pref

ð2:21Þ

The subscript “polymer” specifically denotes a conventional polymer-based PSP; it will be seen that porous PSPs have somewhat different forms of the Stern–Volmer coefficients. Equation (2.19) indicates that a ratio between the luminescent intensities in the wind-on and wind-off conditions is required to determine air pressure. This intensity-ratio method is commonly employed in PSP and TSP measurements. Using the expressions for ka and K, we can write Apolymer and Bpolymer as a function of temperature  Apolymer ¼ Apolymer,ref Bpolymer ¼ Bpolymer,ref

 1 þ ξ exp ðE nr =RT Þ , 1 þ ξ exp ðE nr =RT ref Þ    E D T ref exp  1 , RT ref T

ð2:22Þ

where the factor ξ is defined as ξ ¼ knr1/(kr + knr0). For (T  Tref)/Tref  1, the linearized expressions for Apolymer and Bpolymer are

20

2 Basic Photophysics

   Enr T  T ref Apolymer ¼ Apolymer,ref 1 þ η , RT ref T ref    E D T  T ref Bpolymer ¼ Bpolymer,ref 1 þ , RT ref T ref

ð2:23Þ

where the factor η is η¼

ξ exp ðE nr =RT ref Þ : 1 þ ξ exp ðE nr =RT ref Þ

ð2:24Þ

Clearly, the Stern–Volmer coefficients Apolymer and Bpolymer satisfy the following constraint Apolymer ðT ref Þ þ Bpolymer ðT ref Þ ¼ 1:

ð2:25Þ

Equation (2.23) indicates that the Stern–Volmer coefficient Bpolymer depends on the activation energy ED for the oxygen diffusion process; this implies that the temperature sensitivity of PSP is mainly related to the oxygen diffusion. Indeed, experiments conducted by Gewehr and Delpy (1993) and Schanze et al. (1997) for two different oxygen sensors showed that the temperature dependency of the oxygen diffusivity in a polymer dominated the temperature effect of PSP. This finding has an important implication in the design of low-temperature-sensitive PSP formulations; the low-temperature-sensitive PSP should have a polymer binder with the low activation energy for oxygen diffusion. In another special case where ED  Enr and η  1 over a certain range of temperature, the coefficients Apolymer(T ) and Bpolymer(T ) have the same temperature dependency; thus a ratio between Apolymer(T ) and Bpolymer(T ) becomes temperature independent. PSP that satisfies the above conditions is so-called “ideal” PSP. This paint is advantageous for correcting the temperature effect since the Stern–Volmer relation becomes temperature independent when the intensity ratio scaled by a single temperature-dependent factor is used as a similarity variable. In many PSP measurements, the linear Stern–Volmer relation Eq. (2.19) is sufficiently accurate in a certain range of pressure. However, over an extended range of the partial pressure of oxygen or air pressure, the nonlinear Stern–Volmer behavior becomes appreciable for microheterogeneous PSPs (Carraway et al. 1991a; Xu et al. 1994; Hartmann et al. 1995). The main physical mechanisms behind the nonlinear Stern–Volmer characteristics are associated with microheterogeneity of the environment of a probe molecule and deviation from Henry’s law. Solid-state matrices like polymers may provide different kinds of environments for a probe molecule, resulting in the non-exponential decay or multiple-exponential decay of luminescence. In some cases, a double exponential model is sufficient for the luminescent decay; thus the oxygen quenching of luminescence in microheterogeneous systems is described by a two-component model, i.e.,

2.3 Models for Porous PSP

21

 1 f 01 f 02 I0 , ¼ þ I 1 þ K SV1 ½O2  1 þ K SV2 ½O2 

ð2:26Þ

where f01 and f02 are the fractional intensity contributions of the two components in the absence of oxygen ( f01 + f02 ¼ 1), KSV1 and KSV2 are the Stern–Volmer constants of the two components. Furthermore, for the probe molecule incorporated into a polymer, dual sorption mechanisms are considered and thus the oxygen concentration is related to the applied partial pressure of oxygen by adsorption isotherm. These mechanisms are responsible for a slight deviation of the actual concentration from that given by Henry’s law. The analytical form of dual sorption in a polymer is obtained by adding the Langmuir isotherm to Henry’s law, i.e., ½O2 polymer ¼ SpO2 þ C0

bpO2 , 1 þ bpO2

ð2:27Þ

where C0 is the Langmuir gas capacity due to adsorption and b is the Langumir affinity coefficient. Based on the dual sorption model Eq. (2.27), Hubner and Carroll (1997) suggested an extended form of the Stern–Volmer relation Dðp=pref Þ I ref p þC ¼AþB : pref I 1 þ Dðp=pref Þ

ð2:28Þ

Equation (2.28) was able to give a good fit to experimental data for some PSPs. From a standpoint of aerodynamic applications, an empirical form of the nonlinear Stern–Volmer relation is usually given by a polynomial  2 I ref p p þ C ðT Þ þ⋯ ¼ AðT Þ þ BðT Þ pref pref I

2.3

ð2:29Þ

Models for Porous PSP

In the preceding section, the photophysical models for a conventional polymer PSP are discussed. Nevertheless, according to Sakaue (1999), the photophysical models for a porous PSP are different. In general, pores in a porous PSP are macroscopic, which are much larger than the size of an oxygen molecule. Figure 2.2 shows schematically a comparison of a conventional polymer PSP with a porous PSP. In a conventional polymer PSP, as shown in Fig. 2.2a, the oxygen molecules in the working gas permeate into a polymer binder layer and quench the luminescence. In contrast, as illustrated in Fig. 2.2b, a porous PSP has a much larger open surface to which luminophore molecules are directly applied; the oxygen molecules can directly quench the luminescence without having to permeate into a binder layer.

22

2 Basic Photophysics

Oxygen Molecules

Oxygen Permeation Incident Light

Luminescence Polymer Layer

(a)

Luminophore

Model

Incident Light

Luminescence Oxygen Molecules

Porous Material Surface

(b)

Luminophore

Model Surface

Oxygen Quenching

Fig. 2.2 Schematic of (a) conventional polymer PSP and (b) porous PSP. (From Sakaue 1999)

Therefore, the use of a porous material as a binder for PSP offers two advantages. First, a porous PSP can achieve a very fast time response (in the order of microseconds) for time-resolved PSP measurements; secondly, it makes PSP measurements possible at cryogenic temperatures at which oxygen diffusion is prevented through a conventional homogeneous polymer. The oxygen quenching process in a porous PSP is different from that in a conventional polymer PSP. Figure 2.3a, b illustrates two scenarios of the oxygen quenching in a porous PSP; in both cases, a luminophore molecule is adsorbed on a porous surface opened to the working gas. In Fig. 2.3a, a gaseous oxygen molecule collides with a luminophore molecule, resulting in the oxygen quenching; in this case, the oxygen quenching process is controlled by a collision between the gaseous oxygen molecule and luminophore molecule adsorbed on the surface. In other cases, as illustrated in Fig. 2.3b, an adsorbed oxygen molecule can cause quenching by diffusing to a luminophore molecule and hence the oxygen quenching process is related to adsorption and diffusion of the oxygen molecule into the

2.3 Models for Porous PSP

23 (b)

(a)

gaseous oxygen

adsorbed oxygen

collision porous surface oxygen quenching luminophore

quencher: gaseous oxygen process: collision

porous surface

surface diffusion

oxygen quenching

quencher: adsorbed oxygen process: adsorption/surface diffusion

Fig. 2.3 Oxygen quenching mechanisms for porous PSP: (a) collision-controlled model and (b) adsorption-controlled model. (From Sakaue 1999)

luminophore molecule. Wolfgang and Gafney (1983) studied the oxygen quenching of tris(2,20 -bipyridyl)ruthenium (Ru(bpy)) on a porous Vycor glass and reported that Ru(bpy) was quenched by either a gaseous oxygen molecule colliding to the adsorbed Ru(bpy) or an adsorbed oxygen molecule. Two photophysical models were developed by Sakaue (1999) to describe the oxygen quenching on a porous surface by considering the Eley-Rideal (ER) mechanism and Langmuir-Hinshelwood (LH) mechanism. The ER mechanism is a target annihilation reaction between a gaseous oxygen molecule and an adsorbed luminophore molecule; it is a collision-controlled reaction (Samuel et al. 1992). The LH mechanism, which is adsorption/surface-diffusion controlled, is a reaction between an adsorbed oxygen molecule and an adsorbed luminophore molecule (Hinshelwood 1940). Samuel et al. (1992) studied the oxygen quenching of Ru (bpy) on a porous silica surface over a temperature range from 88 to 353 K and reported that at low temperatures the oxygen quenching was diffusion controlled (the LH type). As the temperature increased, the reaction remained the LH type in nature, but it was increasingly influenced by the target annihilation reaction (the ER type). At higher temperatures, the ER-type reaction dominated. In these cases, the rate constant kq for the oxygen quenching and the oxygen concentration [O2] were described in a different manner from that for a conventional polymer binder.

2.3.1

Collision-Controlled Model

When the rate constant kq for the oxygen quenching and the oxygen concentration [O2] are considered in a collision-controlled reaction, the Stern–Volmer relation is called the collision-controlled model to distinguish from the diffusion-controlled

24

2 Basic Photophysics

relation (or adsorption-controlled model). The rate of collision of the oxygen molecules on a porous surface is [O2]c/4, where c is the average speed of the molecules. According to the theory of ideal gas, one knows N 0 pO2 ½O2  ¼ , RT

rffiffiffiffiffiffiffiffiffiffiffiffiffi 8RT , c ¼ πM m 

ð2:30Þ

where pO2 is the partial pressure of oxygen, T is temperature in Kelvin, Mm is the molar mass, R is the universal gas constant, and N0 is Avogadro’s number. The rate of the oxygen quenching is modeled by a product of an effective contact area σ eff and the collision rate, i.e., k q ½O2  ¼

σ eff N 0 pO2 σ eff N 0 φO2 p σ eff ½O2  c ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : 4 2πM m RT 2πM m RT

ð2:31Þ

Hence, the rate of the oxygen quenching is proportional to the partial pressure of oxygen or air pressure, but is inversely proportional to the square root of temperature. The Stern–Volmer relation for the luminescent lifetime then becomes σ eff N 0 ϕO2 1 ¼ ka þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p: τ 2πM m RT

ð2:32Þ

For aerodynamic applications, the Stern–Volmer relation for the collisioncontrolled quenching process can be written as I ref p : ¼ Acollision ðT Þ þ Bcollision ðT Þ pref I

ð2:33Þ

In Eq. (2.33), the Stern–Volmer coefficients are Acollision ¼ Acollision,ref

ka ka ref

,

Bcollision

rffiffiffiffiffiffiffiffi T ref ¼ Bcollision,ref , T

ð2:34Þ

where the coefficients at the reference conditions are defined as Acollision,ref ¼ 1=ð1 þ ζ Þ, ζ¼

Bcollision,ref ¼ ζ=ð1 þ ζ Þ,

σ eff N 0 ϕO2 pref pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : ka ref 2πM m RT ref

ð2:35Þ

Although Eq. (2.33) has the same form as that for a conventional polymer PSP, the Stern–Volmer coefficients Acollision and Bcollision have different physical meanings. The coefficient Bcollision has weaker temperature dependency that is inversely

2.3 Models for Porous PSP

25

proportional to the square root of temperature. In contrast, the temperature dependency of Acollision has the same form as that for a conventional polymer PSP; linearization of Eq. (2.34) at T ¼ Tref leads to    E T  T ref Acollision ¼ Acollision,ref 1 þ nr : RT ref T ref

2.3.2

ð2:36Þ

Adsorption-Controlled Model

Besides the collision-controlled quenching, an adsorbed oxygen molecule on a porous surface can also quench the luminescence; if this is the dominant mechanism, the oxygen quenching is controlled by adsorption and surface diffusion of the adsorbed oxygen on the porous surface. The oxygen concentration on a porous surface, [O2]ads, can be described by the fractional coverage of oxygen on the porous surface, i.e., θ¼

½O2 ads , ½O2 adsM

ð2:37Þ

where [O2]adsM is the maximum oxygen concentration on the porous surface. The Stern–Volmer equation is then written as I0 ¼ 1 þ k q τ0 ½O2 adsM θ, I

ð2:38Þ

and accordingly a convenient form of the Stern–Volmer relation for aerodynamic applications is I ref θ ¼ AðT Þ þ BðT Þ , θref I

ð2:39Þ

where A¼

ka , ka þ k q ref ½O2 adsM θref

B¼

kq ½O2 adsM θref : k a þ k q ref ½O2 adsM θref

ð2:40Þ

The rate constant kq for the oxygen quenching, which is surface-diffusion controlled, can be described by (Freeman and Doll 1983) k q ¼ 2πRAB λB D ¼ k 0q exp ðE sdiff =RT Þ,

ð2:41Þ

26

2 Basic Photophysics

where RAB is the relative distance between an adsorbed oxygen molecule and an adsorbed luminophore molecule, and D is the diffusivity, and the parameter λΒ is a ratio of the modified first-order and second-order Bessel functions of the second kind. Basically, kq is temperature dependent due to the Arrhenius relation D ¼ D0 exp (Esdiff/RT). To describe θ, either the Langmuir isotherm or the Freundlich isotherm can be used (Carraway et al. 1991b). The Langmuir isotherm relates θ to the partial pressure of oxygen pO2 in the working gas by θ¼

bpO2 : 1 þ bpO2

ð2:42Þ

The factor b in Eq. (2.42) is a function of temperature (Butt 1980), i.e., b¼

exp ðE ads =RT Þ σ eff pffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , exp ðEads =RT Þ ¼ b0 kd 2πM m RT T

ð2:43Þ

where kd is the desorption rate constant per unit surface area and Eads is the heat of adsorption. Since the oxygen concentration is ½O2  ¼ bpO2 , Eq. (2.38) becomes bpO2 1 þ bref pO2 ref I ref : ¼ ALangmuir þ BLangmuir I bref pO2 ref 1 þ bpO2

ð2:44Þ

Equation (2.44) is the adsorption-controlled model derived from the Langmuir isotherm. For ½O2  ¼ bpO2  ½O2 adsM , it can be approximated by p I ref ¼ ALangmuir ðT Þ þ BLangmuir ðT Þ O2 , I pO2 ref

ð2:45Þ

where the Stern–Volmer coefficients are ALangmuir ¼

ka , k a þ k qref ½O2 adsM bref pO2 ref

BLangmuir ¼

k q ½O2 adsM bpO2 ref : ka þ kq ref ½O2 adsM bref pO2 ref

ð2:46Þ

The coefficient ALangmuir has the same temperature dependency as that for a conventional polymer PSP and that in the collision-controlled model, i.e., ALangmuir ¼ ALangmuir,ref and the linearized form for ALangmuir is

ka , k a ref

ð2:47Þ

2.3 Models for Porous PSP

ALangmuir

27

   E nr T  T ref ¼ ALangmuir,ref 1 þ : RT ref T ref

ð2:48Þ

Hence, Eq. (2.48) indicates that ALangmuir is related to the temperature dependency of the non-radiative processes of the luminophore. On the other hand, BLangmuir has the following temperature dependency kq b kq ref bref rffiffiffiffiffiffiffiffi    T ref E l T ref ¼BLangmuir,ref exp 1 , T RT ref T

BLangmuir ¼BLangmuir,ref

ð2:49Þ

where El ¼ Esdiff + Eads. Rewriting Eq. (2.49) in an exponential form yields 

BLangmuir

    El T ref 1 T ¼ BLangmuir,ref exp   1 þ ln ref , 2 RT ref T T

ð2:50Þ

and furthermore, linearization of Eq. (2.50) at T ¼ Tref gives    E T  T ref BLangmuir ¼ BLangmuir,ref 1 þ L , RT ref T ref

ð2:51Þ

where EL ¼ El  RTref/2 ¼ Esdiff + Eads  RTref/2. Clearly, the temperature dependency of the coefficient BLangmuir, Eq. (2.51), is associated with both surface diffusion and adsorption; but it has a similar form to Eq. (2.23) for a conventional polymer PSP. The reference Stern–Volmer coefficients ALangmuir, ref and BLangmuir, ref (their lengthy expressions are not given here) satisfy the constraint ALangmuir, ref + BLangmuir, ref ¼ 1. The Freundlich isotherm can serve as another model for surface adsorption
γ θ ¼ bF pO 2 ,

ð2:52Þ

where the coefficient and exponent are b0 bF ¼ pffiffiffiffiffi exp ðEads =RT Þ, Tγ

γ¼

RT : E adsM

ð2:53Þ

The exponent γ is an empirical parameter that is temperature dependent. For a known γ ref at a known reference temperature Tref, EadsM is given by

28

2 Basic Photophysics

EadsM ¼

RT ref : γ ref

ð2:54Þ

Substituting Eqs. (2.52)–(2.54) into Eq. (2.39), we obtain the nonlinear Stern– Volmer equation  pO 2 γ I ref , ¼ AFreundlich ðT Þ þ BFreundlich ðT Þ I pO2 ref

ð2:55Þ

where ka
γ , k a þ k q ref ½O2 absM bF ref pO2 ref ref
γ kq ½O2 absM bF pO2 ref ref
γ : ¼ ka þ kq ref ½O2 absM bF ref pO2 ref ref

AFreundlich ¼ BFreundlich

ð2:56Þ

The coefficient AFreundlich has the same temperature dependency as that in other models AFreundlich ¼ AFreundlich,ref

ka , k a ref

ð2:57Þ

and the linearized form for AFreundlich is    E T  T ref AFreundlich ¼ AFreundlich,ref 1 þ nr : RT ref T ref

ð2:58Þ

The coefficient BFreundlich has the temperature dependency BFreundlich


γ kq bF pO2 ref
γ : ¼ BFreundlich,ref kq ref bF ref pO2 ref ref

ð2:59Þ

Substituting Eqs. (2.41) and (2.53) into (2.59) yields BFreundlich

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
γ    ðT ref Þγref pO2 ref E f T ref
γ exp ¼ BFreundlich,ref 1 , Tγ RT ref T pO ref ref

ð2:60Þ

2

where Ef ¼ Esdiff + Eads. When an approximation γ ref  γ is used for a small temperature change, the expression for BFreundlich becomes

2.4 Thermal Quenching

BFreundlich

29

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   γref   T ref E f T ref exp 1 , ¼ BFreundlich,ref T RT ref T

ð2:61Þ

which is similar to BLangmuir. After rewriting all the terms in Eq. (2.61) in an exponential form, linearization at T ¼ Tref yields  BFreundlich ¼ BFreundlich,ref

  E F T  T ref 1þ , RT ref T ref

ð2:62Þ

where  E F ¼ Esdiff  Eads þ γ ref RT ref

 pO2 ref 1 ln pffiffiffiffiffiffiffiffi  : 2 T ref 

ð2:63Þ

Similar to the Langmuir-type model, the coefficient BFreundlich has the temperature dependency associated with surface diffusion and adsorption. However, the photophysical model, Eq. (2.55), describes the nonlinear behavior of the Stern– Volmer plot for a porous PSP.

2.4

Thermal Quenching

For TSP where the paint layer is not oxygen-permeable such that no oxygen quenching occurs, from Eq. (2.8), the quantum yield of luminescence is simply given by Φ¼

I kr ¼ : I a kr þ knr

ð2:64Þ

The temperature dependency of the non-radiative processes knr can be decomposed into a temperature-independent term and a temperature-dependent term modeled by the Arrhenius relation (Bennett and McCartin 1966; Song and Fayer 1991; Schanze et al. 1997), i.e.,   E knr ¼ knr0 þ k nr1 exp  nr , RT

ð2:65Þ

where knr0 ¼ knr(T ¼ 0) and knr1 are the rate constants for the temperatureindependent and temperature-dependent processes, respectively, Enr is the activation energy for the non-radiative process, R is the universal gas constant, and T is temperature in Kelvin. From Eqs. (2.64) and (2.65), we have

30

2 Basic Photophysics

 I ðT Þ½I ð0Þ  I ðT ref Þ E nr 1 1  ln , ¼ R T T ref I ðT ref Þ½I ð0Þ  I ðT Þ

ð2:66Þ

where I(0) ¼ I(T ¼ 0) is the luminescent intensity at the absolute zero temperature. For jI(T )  I(Tref) j /I(0)  1 and I(T )I(Tref)/[I(0)]2  1 over a certain temperature range, a relation between the luminescent intensity and temperature can be approximately written in the Arrhenius form, i.e., ln

 I ðT Þ E 1 1  : ¼ nr R T T ref I ðT ref Þ

ð2:67Þ

Theoretically, the Arrhenius plot of ln[I(T )/I(Tref)] versus 1/T gives a straight line with the slope Enr/R. Experimental results indeed indicate that the simple Arrhenius relation Eq. (2.67) is able to fit data over a certain temperature range. However, for some TSPs, experimental data may not fully obey the simple Arrhenius relation over a wider range of temperature. Thus, as an alternative, an empirical functional relation between the luminescent intensity and temperature is I ðT Þ ¼ f ðT=T ref Þ, I ðT ref Þ

ð2:68Þ

where f (T/Tref) could be a polynomial, exponential, or other function to fit experimental data over a working temperature range. Either Eq. (2.67) or Eq. (2.68) can serve as an operational form of the calibration relation for TSP in practical applications.

Chapter 3

Physical Properties of Paints

This chapter describes typical PSPs that use platinum porphyrins, ruthenium polypyridyls, and pyrene derivatives as pressure-sensing molecules in different polymer binders. The absorption and emission spectra of these PSPs are described and the Stern–Volmer relations of these PSPs are given. Then, fast PSPs (highly porous PSPs) for time-resolved measurements in unsteady flows are discussed, which are based on anodized aluminum (AA), polymer/ceramic (PC) mixture, and poly(TMSP). Furthermore, AA-PSP and poly(TMSP)-PSP can work at cryogenic temperatures. Multiple-luminophore PSP is used to relax the requirement of a windoff reference image and reduce the temperature effect on PSP measurement. The condition for designing an “ideal PSP” is discussed. Similarly, typical TSPs are described for steady, transient, and time-resolved measurements along with cryogenic TSPs. The desirable properties of PSP (or TSP) for wind tunnel testing are discussed. This chapter is supplemented by Appendix A on chemistry, Appendix B on paint calibration and formulations, and Appendix C on paint recipes.

3.1

Typical PSPs

A typical PSP is an oxygen-permeable polymer coating with luminescent molecules embedded in it. PSP is prepared by dissolving a luminescent dye and a polymer binder in a solvent (such as dichloromethane and toluene). The selection of a polymer binder for PSP is important, which should be based on a balanced consideration of some relevant physical properties, including the oxygen permeability, temperature effect, humidity effect, adhesion, mechanical stability, photodegradation, and glass transition temperature. Silicone rubbers, GP-197, silica gel, and sol-gel-derived coatings were used as binders for PSPs and oxygen sensors (Wan 1993; Gallery 1993; Xu et al. 1994; MacCraith et al. 1995; Jordan et al. 1999a, b). Other polymers and porous materials that are potentially useful for PSP can be found in the literature of polymers (Krevelen 1976; Mulder 1991; Fried 1995; © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_3

31

32

3 Physical Properties of Paints

Robinson and Perlmutter 1994; Amao 2003; Akram et al. 2020). The permeability, solubility, and diffusion coefficient of a polymer binder are related to the pressure sensitivity and time response of PSP. Furthermore, the behavior of PSP depends on the interaction between a probe molecule and its surrounding polymer. The microenvironment of a probe molecule in a polymer binder can significantly affect the luminescence and quenching behavior (Hartmann et al. 1995; Meier et al. 1995; Xu et al. 1994; Lu and Winnik 2001; Lu et al. 2001). Also, it was observed that a basecoat (screen layer) might affect the behavior of PSP (Coyle et al. 1995). A useful review on quenching of luminescence by oxygen in polymer films was given by Lu and Winnik (2000), which stressed on luminescent materials and polymers. Currently, three families of luminophores, platinum porphyrins, ruthenium polypyridyls, and pyrene derivatives, are commonly used for PSPs. Some PSP formulations and their properties are listed in tables in Appendix B and typical PSP recipes are given in Appendix C.

3.1.1

Platinum Porphyrins

Figure 3.1 shows the chemical structure, and absorption and emission spectra for platinum meso-tetra(pentafluorophenyl)porphine (PtTFPP). Figures 3.2 and 3.3 show the Stern–Volmer plots and temperature dependencies for two PtTFPP PSP formulations: PtTFPP in the FIB polymer (poly-heptafluoro-n-butyl methacrylateco-hexafluorisopropyl methacrylate) developed by the University of Washington (Gouterman and Carlson 1999) and PtTFPP in the FEM polymer (poly-trifluoroethylmethacrylate-co-isobutylmethacrylate) developed by NASA Langley (Oglesby and Jordan 2000). In these figures, the lower temperature sensitivity of PSP at vacuum represents the intrinsic temperature dependency of the luminophore, while the higher temperature sensitivity of PSP at the atmospheric pressure is associated with an additional temperature effect on the oxygen diffusion in the polymer. In order to examine the effect of a polymer binder on the properties of PSP, Mébarki and Le Sant (2001) calibrated five PSP formulations that used the same porphyrin molecule, PtTFPP, with different polymer binders. Two formulations are not commercially available, which are the PAR PSP from the Institute for Aerospace Research (IAR) of NRC in Canada (Mébarki 2000) and the FEM PSP from NASA Langley (Oglesby and Upchurch 1999). Other paints, the FIB PSP (Gouterman and Carlson 1999), sol-gel PSP (Jordan et al. 1999a, b), and the Uni-Coat PSP (Mébarki 2000), were commercially produced by Innovative Scientific Solutions Inc. (ISSI) in the US. Except for the Uni-Coat PSP that did not require a primer layer, the commercial FIB and sol-gel PSP formulations were supplied with their respective primers. To simplify the application procedures and solve adhesion problems, the FIB active layer was applied on the top of a Tristar (DHMS C4.01TY3) white epoxy primer that was also used as a screen layer for both the FEM PSP and PAR PSP. It was found that the primer had no effect on the pressure or temperature sensitivity of the active layer. However, the polymer binder in which the porphyrin molecule was

3.1 Typical PSPs

33

F

F

F

F

F

F

F

F N

F N F

Pt

F N F

N

F

F

(a)

F

F F

F F

F

(b) Fig. 3.1 (a) Chemical structure of PtTFPP and (b) absorption and emission spectra of PtTFPP. (From Puklin et al. 2000)

immobilized indeed affected both the pressure and temperature sensitivities of PSP. To evaluate the performance of PSP, the pressure sensitivity is defined as SP ¼ |Δ(I/Iref)/Δp| (in %/bar or %/kPa). Similarly, the temperature sensitivity of PSP (or TSP) is defined as ST ¼ |Δ(I/Iref)/ΔT| (in %/K or %/ C). Note that in some papers, ST ¼ Δ(I/Iref)/ΔT is used, which is typically negative. The pressure sensitivity was calculated in a pressure range of 0.15–2 bars and the temperature sensitivity was determined in a temperature range of 10–35  C. Figure 3.4 shows the pressure sensitivity SP as a function of temperature and the temperature sensitivity ST as a function of pressure. The pressure sensitivity SP varied from 55% to nearly 80%/bar, depending on the polymer binder used and temperature as well. The FIB PSP formulation had nearly constant pressure sensitivity over a temperature range of 10–40  C (283.2–313.2 K). The Uni-Coat and sol-gel PSP formulations had a linear dependency of the pressure sensitivity SP on temperature; the temperature sensitivity ST varied from 0.6% to 1.6%/K. The temperature sensitivity was somewhat affected by pressure for all the PSP formulations except the FIB PSP. The FIB PSP also had the lowest temperature sensitivity

34

3 Physical Properties of Paints

Fig. 3.2 (a) The Stern–Volmer plots and (b) temperature dependency for PtTFPP in the FIB polymer. (From Oglesby and Jordan 2000)

among these PSPs. Obata et al. (2014) polymerized three CF3-substituted methyl methacrylates to give oxygen-permeable polymers for application in PSP. They found that PSP composed of a fluoric polymer called poly (HFIPM) and PtTFPP had similar characteristics to the FIB PSP. Generally, PtTFPP-based PSPs are good for both intensity- and lifetime-based measurements.

3.1 Typical PSPs

35

Fig. 3.3 (a) The Stern–Volmer plots and (b) temperature dependency for PtTFPP in the FEM polymer. (From Oglesby and Jordan 2000)

36

3 Physical Properties of Paints 2.2

85

FIB FEM SOLGEL UNICOAT PAR

2.0

80

1.8 1.6

ST (%/deg)

SP (%/bar)

75 70 65

1.4 1.2 1.0

60

FIB FEM SOLGEL UNICOAT PAR

55

0.8 0.6 0.4

50 10

15

20

25

30

35

T (deg. C)

40

0.0

0.5

1.0

1.5

2.0

2.5

p/pref

Fig. 3.4 Pressure sensitivity (SP) and temperature sensitivity (ST) for PtTFPP in five different polymer binders, where pref ¼ 1 bar and Tref ¼ 10  C. (From Mébarki and Le Sant 2001)

3.1.2

Ruthenium Polypyridyls

Figure 3.5 shows the chemical structure, and absorption and emission spectra of bathophen ruthenium chloride (Ru(ph2-phen) or Ru(dpp)). Ruthenium-based oxygen sensors have been studied extensively by analytical chemists (Bacon and Demas 1987; Carraway et al. 1991a, b; Sacksteder et al. 1993; Xu et al. 1994; Klimant and Wolfbeis 1995). Ruthenium-based PSP formulations were developed and used for wind tunnel testing (Schwab and Levy 1994). Figure 3.6 shows the Stern–Volmer plots for Ru(dpp) in GE RTV 118 added with silica gel particles at different temperatures; Fig. 3.7 shows the luminescent lifetime as a function of pressure for Ru(dpp) in GE RTV 118 at 295 K. Ruthenium-based PSP has a shorter lifetime compared to PtTFPP-based PSP, and both are suitable for intensity- and lifetimebased measurements using digital cameras.

3.1.3

Pyrene Derivatives

Figure 3.8 shows the chemical structure and absorption (or excitation) and emission spectra of pyrene. Pyrene-based PSP formulations were developed at TsAGI in Russia (Fonov et al. 1998). One of them was the binary paint (B1 PSP) in which a pressure-insensitive reference component was added to correct the excitation light variations on a surface in performing a ratio between the wind-on and wind-off images. Figure 3.9 shows the Stern–Volmer plots at different temperatures for pyrene complex in GE RTV 118. Obviously, this pyrene-based PSP exhibits the weak temperature dependency over a temperature range of 17–40  C. Besides

3.1 Typical PSPs

37

Fig. 3.5 (a) Chemical structure and (b) absorption and emission spectra of Ru(ph2-phen) or Ru (dpp)

TsAGI, ONERA in France and DLR in Germany developed pyrene-based PSP formulations as well (Engler et al. 2001a). PyGd PSP formulation developed by ONERA contained pyrene as a pressuresensitive dye and a gadolinium oxysulfide as a reference component. Figure 3.10 shows the emission spectrum of the PyGd PSP excited at 325 nm. The two components in the paint absorbed an ultraviolet excitation light and emitted at sufficiently different wavelengths such that the emissions from the two components can be separated using optical filters. Figure 3.11 shows the Stern–Volmer plots at the ambient temperature for three pyrene-based PSP formulations (PyGd, PdGd, and B1). Because the temperature sensitivity of the reference component was similar to that of the pyrene dye in the PyGd PSP, the temperature effect can be compensated by taking a ratio between the luminescent intensities from the pressure-sensitive component (pyrene) and reference component. As a result, the PyGd PSP displayed a very low temperature sensitivity of 0.05%/K. Göttingen Dyes (GD) were

38

3 Physical Properties of Paints 1.0 243K 253K 258K 263K 268K 273K 283K 293K linear fit

0.9 0.8

Iref/I

0.7 0.6 0.5 0.4 0.3 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

P/Pref

Fig. 3.6 The Stern–Volmer plots for Ru(ph2-phen) or Ru(dpp) in GE RTV 110 added with silica gel particles, where the reference pressure pref is 100 kPa and reference temperature is 293 K. (From Lachendro 2000) Fig. 3.7 Lifetime-pressure relation for Ru(ph2-phen) in GE RTV 118 at 295 K, where τref is the lifetime at the ambient pressure (1 atm). (From Liu et al. 1997b)

developed by DLR and the University of Göttingen, and three pyrene-based PSPs (GD145, GD146, and GD147) were tested in wind tunnels (Engler and Klein 1997b). Figure 3.12 shows the Stern–Volmer plots of the Göttingen PSP formulations.

3.1 Typical PSPs

39

Fig. 3.8 (a) Chemical structure of pyrene and (b) absorption (or excitation) and emission spectra of pyrene. (From Mébarki 2000)

Fig. 3.9 The Stern–Volmer plots for pyrene in GE RTV 118, where the reference conditions are Tref ¼ 17  C and pref ¼ 1 bar. Sublimation of pyrene occurs initially at 40  C, resulting in an intensity decrease and thus a different curve at 50  C. (From Mébarki 2000)

3 Physical Properties of Paints

Fig. 3.10 Emission spectra of a binary pyrene-based PSP (PyGd) at 1 bar and vacuum. (From Engler et al. 2001a)

intensity (A.U)

40

vacuum

Pref=1bar

300

400

500

600 λ (nm)

1.02 1 0.98

Iref/I

0.96 0.94 0.92 0.9 PyGd

0.88

PdGd

0.86 0.84 0.82

B1 0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1.02

P/Pref

Fig. 3.11 The Stern–Volmer plots for three pyrene-based PSPs (PyGd, PdGd, and B1). (From Engler et al. 2001a)

3.2 3.2.1

Fast PSPs AA-PSP

To increase the time response of PSP, it is critical to develop porous binders, while the same luminophores such as ruthenium complexes, porphyrins, and pyrenes for conventional PSPs are used (Gregory et al. 2008, 2014a). Asai et al. (1997a) used anodized aluminum (AA) layer as a binder, which has huge numbers of highly ordered micropores with relatively uniform diameter and spacing. Mosharov et al. (1997) also described the development of AA-PSP at TsAGI, and reported that the

3.2 Fast PSPs

41

Fig. 3.12 The Stern–Volmer plots for the Göttingen pyrene-based PSPs (GD 145, GD 146, and GD 147). (From Engler et al. 2001a)

response time of AA-PSP was in a range of 18 to 90 μs, depending on the luminophore used and on some features of the anodization process. AA-PSP was improved by Sakaue (1999). Sakaue and Sullivan (2001) and Sakaue et al. (2002a, b) reported that AA-PSP with a ruthenium complex could reach a response time of the order of 10 μs, depending on the AA layer thickness. The anodization procedure was described in detail by Sakaue et al. (1999, 2003). An AA layer is formed on an aluminum anode in an electrolytic solution through an electro-chemical process where an aluminum model is connected with a direct current power supply as an anode in an electrolytic solution (such as dilute sulfuric acid). Anodization produces an oxide layer with microscopic hexagonal pores of alumina. The layer thickness ranges from a few μm to 100 μm, which is controlled by changing the anodization time. These micropores can be formed not only on pure aluminum but also on aluminum alloy or duralumin that contains zinc and magnesium. To create uniformly distributed micropores, careful pre- and posttreatments are required. Figure 3.13a, b shows a schematic of an AA surface and a scanning electron microscope (SEM) picture, where microscopic pores of 20–100 nm in diameter are distributed on the anodized surface. The anodized model is then dipped into a luminescent dye solution to apply the probe luminophore. The common luminophores, including ruthenium complexes, porphyrin and pyrene derivatives, can be adsorbed on the porous aluminum by dipping (or spraying). The molecules are adsorbed onto the AA surface by intermolecular (van der Waals) force and weak electrostatic force. This approach is physical adsorption. Sakaue (2005) also investigated the effects of the dipping deposition method on AA-PSP, particularly the solvent dependency of the luminescent signal level, pressure sensitivity, and response time. It was found that the

42

3 Physical Properties of Paints

Fig. 3.13 (a) Schematic structure of anodized aluminum and (b) SEM image of anodic porous alumina surface. (From Sakaue 1999, 2003)

solvent in the dipping deposition greatly influenced the luminophore application onto AA. Therefore, the luminescent signal level and the pressure sensitivity depend on the selected solvent. However, the response time is not significantly affected. Sakaue et al. (2006) and Sakaue and Ishii (2010a, b) developed a novel fabrication procedure to reduce the temperature sensitivity (as well as the humidity sensitivity) of the ruthenium AA-PSP by applying alkanoic acid (e.g., myristic acid) onto the AA surface simultaneously with the dye. Figure 3.14 shows the Stern–Volmer plots for ruthenium AA-PSP and the temperature sensitivities, indicating that the application of myristic acid can dramatically reduce the temperature sensitivity to 0.5%/ C while its high pressure sensitivity is retained (Kameda et al. 2004, 2005). In contrast to the physical adsorption, the chemical adsorption technique was developed by Amao et al. (1999a, b) to form AA-PSP. They showed that the molecules with a carboxyl or sulfonic group such as tetrakis(4-carboxyphenyl) porphyrin, pyrene butyric acid (PBA), and pyrene sulfonic acid (PSA) can be adsorbed onto AA via dehydrate ester reaction. Since the molecules are adsorbed onto AA by chemical bonding, the luminophore cannot be removed with any polar solvents. Figure 3.15 shows the Stern–Volmer plots for AA-PSPs with different luminophores. In contrast to conventional PSPs that have the linear Stern–Volmer relationship over a large range of pressure, some AA-PSPs exhibit the nonlinear behavior and high pressure sensitivity near vacuum, which are suitable for pressure measurement in low-density and rarified gas flows. Further, according to Fujiwara and Amao (2003a, b) and Kameda et al. (2004), PBA was chemically adsorbed onto AA via dehydration process. Ishii et al. (2018) developed a dipping method that applies two luminophores into a binding material to improve sensitivity uniformity over an AA surface. Peng et al. (2018a) developed a PSP by using through-hole anodized aluminum oxide (AAO) membrane as a binder to achieve fast response. Further, Li et al. (2020a) found that the thermal quenching of this fast PSP could be effectively suppressed by restricting the lattice relaxation of luminescent molecules.

3.2 Fast PSPs

43

1.2 T = 293.1 K Iref = I(pref, T) pref:atmospheric pressure

1

ref

I /I

0.8 0.6 0.4 0.2 0

[Ru(dpp) ]

2+

[Ru(dpp) ]

2+

3 3

0

0.2

0.4

0.6

p/p

+ myristic acid

0.8

1

ref

(a) 1.4 p: atmospheric pressure Iref = I(p, Tref) Tref=283.1 K

1.2

I/I

ref

1 0.8 0.6 0.4 0.2 280

[Ru(dpp) ]

2+

3

2+

[Ru(dpp) ] +myristic acid 3

290

300

T [K]

310

320

(b)

Fig. 3.14 (a) The Stern–Volmer plots and (b) temperature sensitivities of ruthenium AA-PSP, indicating that chemisorption of myristic acid is effective to reduce the temperature sensitivity. (From Kameda et al. 2004, 2005)

3.2.2

PC-PSP

Polymer/ceramic (PC) PSP is a mixture of a high concentration of ceramic particles with a small amount of polymer to physically hold the ceramic particles to a surface, where the ceramic particles bind with luminophore molecules. Ponomarev and

44

3 Physical Properties of Paints

Fig. 3.15 The Stern–Volmer plots for AA-PSP doped with various luminophore molecules. (From Sakaue 2003)

Gouterman (1998) observed that the addition of a sufficient amount of ceramic particles in PSP could significantly improve the time response of PSP. Scroggin (1999) and Scroggin et al. (1999) developed PC-PSPs based on either aluminum oxide (Al2O3) or titanium dioxide (TiO2) particles in a small amount of polymer, resulting in the highly porous structures. Both PtOEP and [Ru(dpp)3]2+ were used as luminophores. Luminophore was dissolved in a solvent applied to the polymer/ ceramic binder through a dipping process. PtOEP exhibited greater pressure sensitivity. The time response of this formulation decreased with decreasing fraction of polymer. The response times of the PC-PSP formulations developed by Scroggin were on the order of 60 μs. In addition, Lu et al. (2001) used polymer/silica composite films as luminescent oxygen sensors. Gregory et al. (2002a, b, 2006) further developed a sprayable formulation of PC-PSP by diluting the solution with distilled water and maintaining a low polymer weight fraction. The ceramic slurry solution was prepared from distilled water, dispersant (D-3021, Rohm & Haas), and TiO2 particles (DuPont R-900 TiPure). 1.72 g of TiO2 and 12 mg of dispersant were added for every gram of water, and the solution was ball milled for one hour. A polymer emulsion (B-1000, Rohm & Haas) was then added to the ceramic slurry by a weight fraction of 3.5%. This paint binder formulation was then stirred for several minutes and then airbrushed over a model surface in a relatively thin layer, on the order of 5 μm thickness. A luminophore solution, typically [Ru(dpp)3]2+ dissolved in methanol, was then over-sprayed on the polymer/ceramic binder. This sprayable PC-PSP exhibited a response time as low as 25 μs. Figure 3.16 shows the schematic structures and SEM picture of PC-PSP.

3.2 Fast PSPs

45

Fig. 3.16 (a) Schematic of polymer/ceramic PSP structure, with the luminophore adsorbed to the ceramic particles (Gregory et al. 2006), and (b) SEM image of polymer/ceramic PSP from a tapecasting procedure (Scroggin 1999)

Fig. 3.17 The Stern–Volmer plots for polymer/ceramic PSP. (From Gregory et al. 2002a)

Figure 3.17 shows the Stern–Volmer plots for Gregory’s PC-PSP at different temperatures. In general, there are three deposition methods to apply PC-PSP on a model: (1) dipping the binder into a luminophore solution, (2) over-spraying a luminophore solution on the binder surface, and (3) spraying premixed solution of the

46

3 Physical Properties of Paints

luminophore and the binder. A selected deposition method could affect the dynamic response of PC-PSP since it determines how luminophore molecules are distributed inside the binder. The dipping and over-spraying methods generate a luminophore layer near the binder surface, enabling immediate interaction between oxygen and the luminophore and achieving a response time less than 100 μs (Hayashi and Sakaue 2017; Egami et al. 2019b). Since the polymer in PC-PSP has a relatively low oxygen diffusion coefficient, its concentration should be controlled at a low value for a fast time response (Sakaue et al. 2011). To reduce the delaying effect of polymer, the mixture of dye and particles was adsorbed onto a polymer-coated film (Sugioka et al. 2018b). In contrast, spraying a premixed PC-PSP produces a relatively uniform luminophore distribution throughout a binder. A shortcoming is a slower time response, since a longer time is required for oxygen to penetrate and interact with luminophore through the whole paint layer (Klein et al. 2007b; Li et al. 2018). To achieve a response time of less than 100 μs, a fairly thin layer of 5–10 μm without addition of polymer was used (Kameda et al. 2012). However, the improvement in dynamic response by using such a thin layer is often accompanied by the reduced mechanical strength and durability of PSP (Lo and Kontis 2016; Peng et al. 2016a). Sugioka et al. (2018b) compared two different procedures of embedding particles into a binder layer for making PC-PSP in terms of their effects on the properties of PSP. In the conventional procedure in which dye was adsorbed onto a polymer/ ceramic coating film, the resulting coating was referred to as a dye-adsorbed (D-adsorbed) PSP. In a new procedure, the mixture of a dye and particles in a solvent was adsorbed onto a polymer coating film, and the coating was referred to as the particle/dye-adsorbed (PD-adsorbed) PSP. PtTFPP was used as a sensing dye, TiO2 particles as particles, toluene as the solvent, and a commercially available ester polymer as a binder. The effects of particle mass content and solvent on PSP characteristics were evaluated. Figure 3.18a, b shows the effects of particle mass content on the cutoff frequency of pressure response and surface roughness (Ra) of PSP, respectively. The critical pigment volume concentration (CPVC) is a point at which the cutoff frequency starts to rapidly increases. The CPVC for the PD-adsorbed PSP was 88% in weight (wt%) to achieve a high time response, which was smaller than that of the D-adsorbed PSP (93 wt%). Therefore, the PD-adsorbed PSP had a higher frequency response comparing with the D-adsorbed PSP while maintaining the same surface roughness. For PC-PSPs, the cutoff frequency and the roughness are highly correlated. Figures 3.19 and 3.20 show surfaces and cross sections of PSP coupons imaged using a scanning electron microscope (SEM). For the D-adsorbed PSP, images of coupons with particle mass contents of 80 and 93 wt% are shown in Fig. 3.19. For the PD-adsorbed PSP, coupons with particle mass contents of 80, 90, and 93 wt% are selected for SEM observation in Fig. 3.20. Based on the observation from SEM images, the coating film structure can be roughly classified into two states depending on the particle mass content. In the first state, the coating film consisted of a lower particle-rich layer and an upper polymer-rich layer. This type of structure was observed in the PD-adsorbed PSP (see Fig. 3.20a) and the D-adsorbed PSP (see Fig. 3.19a). In the other state,

3.2 Fast PSPs

47

Fig. 3.18 Effects of the particle mass content on (a) cutoff frequency and (b) surface roughness. (From Sugioka et al. 2018b)

Fig. 3.19 SEM images of the D-adsorbed PSP with the particle mass contents of (a) 80 wt% and (b) 93 wt%. (From Sugioka et al. 2018b)

polymer and particles are homogeneously distributed in the film, and pores are formed (see Fig. 3.19b). This difference in the coating structure results in a change in the time response. The film structure was conceptually modeled in Fig. 3.21. Egami et al. (2021a) developed a sprayable fast-responding PC-PSP where the luminescent dye was Ru(dpp)3, the particles were room-temperature-vulcanizing silicone (silicone) and TiO2 particles, and the binder was RTV silicone. The effects of the particle mass content and size were evaluated on the properties including the time response, pressure sensitivity, and luminescence intensity. The effects of the hydrophilic and hydrophobic surface treatments of TiO2 particles on the structure

48

3 Physical Properties of Paints

Fig. 3.20 SEM images of the PD-adsorbed PSP with the particle mass contents of (a) 80 wt%, (b) 90 wt%, and (c) 93 wt%. (From Sugioka et al. 2018b)

Fig. 3.21 Schematic diagrams of dye-adsorbed (D-absorbed) PSP and particle/dye-absorbed (PD-absorbed) PSP: (a) when the particle content exceeds the CPVC, and (b) when the particle content is less than the CPVC. (From Sugioka et al. 2018b)

3.2 Fast PSPs

49

Fig. 3.22 Pressure and temperature calibration curves for Ru-based PC-PSP with various particle mass contents of hydrophilic TiO2 of the diameter of 15 nm: (a) pressure and (b) temperature. (From Egami et al. 2021a)

Fig. 3.23 Pressure calibration curves for the Ru-based PC-PSP with various particle sizes of hydrophilic TiO2 particles at the particle mass content of 80 wt%. (From Egami et al. 2021a)

and mechanical robustness of the binder layer were also studied. Figure 3.22 shows the pressure and temperature calibration curves of the PC-PSP with different values of the particle mass content. Both the pressure and temperature sensitivity increases with the increase in the particle mass content. Especially, the pressure sensitivity of the PC-PSP is varied with an increase in the particle mass content. Figure 3.23 shows the pressure calibration curve as a function of averaged particle size. The pressure sensitivity increases as the particle size decreases. Figure 3.24 shows particles and polymer in the binder layer observed with a transmission electron microscope (TEM). The combination of binder materials was

50

3 Physical Properties of Paints

Fig. 3.24 TEM images of fast-PSP with silicone/mesoporous silica. Black dots distributed in the thin polymer layer indicate luminophores. (From Egami et al. 2021a)

silicone RTV and mesoporous silica. It is seen that the particles are covered by the silicone RTV polymer with a thickness of 30–40 nm. Luminophore (black dots in the picture) is distributed in the thin polymer layer. The difference in the binder structure and the time response results from the difference in the specific surface area depending on the particle size. The amount of polymer per surface area becomes small with a decrease in the particle diameter at the constant particle mass content, resulting in the thin thickness of the polymer covering particles, as shown in Fig. 3.24. It is related to the time response of fast-PSP. This observation suggests that a large specific surface area of fast-PSPs with small particles provides a fast time response. Mesoporous hollow particles were used as hosts for luminophore by Sakaue et al. (2013c), Peng et al. (2018b), and Egami et al. (2019b). A sprayable mesoporous particle PSP (MP-PSP) was developed by Peng et al. (2018b), where mesoporous hollow silicone dioxide particles were used as hosts for luminophore (PtTFPP). The highly porous mesoporous particles were formed by nanoparticles through the Van der Waals force and chemical bonds, facilitating oxygen diffusion within the PSP binder and thus leading to a response time as low as 50 μs. MP-PSP prepared by a mixing-and-spraying method had highly porous structure and uniform luminophore distribution throughout the binder. Meanwhile, MP-PSP had increased pressure sensitivity and improved photostability. The effects of particle size, paint thickness, and fabrication method on PSP sensing performance were discussed by Peng et al. (2018b).

3.2 Fast PSPs

3.2.3

51

Poly(TMSP)-PSP

Poly[1-(trimethylsilyl)-1-propyne], abbreviated here as poly(TMSP), is a high molecular-weight polymer that was first synthesized by Masuda et al. (1983). The chemical structure of poly(TMSP) is shown in Fig. 3.25. Table 3.1 compares the properties of poly(TMSP) with those for the common PSP binder, poly (dimethylsiloxane) (poly(DMS)). Although the diffusion coefficient of poly (TMSP) is close to that of poly(DMS), the solubility of poly(TMSP) is much higher, resulting in the much higher permeability of poly(TMSP) to oxygen. Therefore, poly (TMSP) is a suitable binder for fast PSP. Asai et al. (2000, 2002) developed poly(TMSP)-PSP, where platinum porphyrin (PtOEP or PtPFPP) was used as a probe luminophore. This paint could be dissolved in a common solvent (toluene or hexane) and applied on a surface using an airbrush. The time response of poly(TMSP)-PSP to a step change of pressure from vacuum to one atmosphere was measured in comparison with AA-PSP and poly(DMS)-PSP. The results are shown in Chap. 7. Compared to poly(DMS)-PSP that has a time constant of the order of several seconds, the response of poly(TMSP)-PSP is much faster, although it is slower than AA-PSP. Teduka et al. (2000) and Teduka (2001) conducted a systematic study on the response characteristics of poly(TMSP)-PSP in different conditions. The response time of poly(TMSP)-PSP is on the order of 10 ms, which is not dependent on temperature. New compounds could be developed to improve the performance of fast PSPs. The stability of the pressure sensitivity of poly(TMSP)-PSP is a concern (Egami and Asai 2002). Nagai et al. (2001) investigated the negative effects of the membrane thickness and the storage environment on

CH3

Fig. 3.25 Chemical structure of poly(TMSP)

n Si(CH3)3 Table 3.1 Comparison of poly(TMSP) and poly(DMS) properties

Polymer Poly (DMS)a Poly (TMSP)b a

O2 permeability (cm3(STP)cm  1010/ cm2 s cmHg) 960 (@ 35  C) 7700 (@ 30  C)

Poly(dimethylsiloxane) Poly[1-(trimethylsilyl)-1-propyne]

b

Diffusivity (cm2/s  106) 40 (@ 35  C)

Solubility coefficient (cm3(STP)  104/cm3 cmHg) 24 (@ 35  C)

Glass transition temperature ( C) 127

47 (@ 30  C)

170 (@ 30  C)

>200

52

3 Physical Properties of Paints

the gas permeability of poly(TMSP). To stabilize the permeability of membrane, a poly(1-trimethylsilyl-1-propyne-co-1-phenyl-1-propyne) [poly(TMSP-co-PP)] membrane was prepared, which had both the high permeability and good stability.

3.3

Cryogenic PSPs

A challenging problem is the application of PSP in cryogenic wind tunnels such as the NASA Langley National Transonic Facility (NTF) and European Transonic Windtunnel (ETW). Interestingly, cryogenic PSPs share the same features with fast PSPs in terms of the use of highly porous binders. Porous material has a large exposure surface area where the luminescence of a probe luminophore can be directly quenched by oxygen at cryogenic temperatures (Asai and Sullivan 1998; Iijima et al. 2003). Therefore, the use of porous materials as binders allows PSP measurements at cryogenic temperatures, achieving fast time response as well. Figure 3.26 shows the Stern–Volmer plot for Ru(dpp) AA-PSP at cryogenic temperatures, compared with a conventional polymer-based PSP (Ru(dpp) in RTV). This AA-PSP exhibits a good sensitivity to oxygen even at 100 K, whereas the conventional PSP loses its sensitivity to oxygen at 150 K. Upchurch et al. (1998) and Asai et al. (2000, 2002) developed a polymer-based cryogenic PSP by using highly porous poly(TMSP) as a binder. To compare the two cryogenic PSP formulations, Figure 3.27 shows the Stern–Volmer plots for poly(TMSP)-based PSP and AA-PSP that use Ru(dpp) as a luminescent dye. Both the PSPs exhibit the nonlinear behavior in the Stern–Volmer plot. Egami et al. (2006) and Watkins et al. (2012) conducted intensity-based PSP measurements at cryogenic conditions in ETW and NTF, respectively. Yorita et al. (2018) used a lifetime-based PSP system in ETW. Details of these measurements are discussed in Sect. 9.7.1.

2.0

AA-PSP (pO ref=14Pa, T=100K) 2

1.5

Iref/I

Fig. 3.26 The Stern– Volmer plots for a porous AA-PSP and a conventional PSP with silicone rubber as a binder at cryogenic temperatures. Both PSPs use Ru(ph2-phen) as a probe luminophore. (From Sakaue 1999)

1.0

0.5

conventional PSP (pO ref=14Pa, T=150K) 0.0

2

0.0

0.5

1.0

1.5

p /p O2

2.0 O2ref

2.5

3.0

3.5

3.4 Multiple-Luminophore PSPs

53

Fig. 3.27 Comparison of poly(TMSP) PSP with AA-PSP at 100 K, where excitation is at 400  50 nm and emission is at 650  50 nm. (From Asai et al. 2000)

3.4

Multiple-Luminophore PSPs

The intensity-based method for PSP and TSP requires a ratio between the wind-on and wind-off images of a painted model. When a model moves in a nonhomogeneous illumination field during a test, a ratio between two misaligned images inevitably causes an error in determining pressure and temperature. A multiple-luminophore paint is designed to eliminate the requirement of a wind-off reference image. Generally, a two-luminophore PSP consists of a pressure-sensitive luminophore and a pressure-insensitive reference luminophore. The probe and reference luminophores can be excited by the same illumination light. Ideally, there is no overlap between the emission spectra of the probe and reference luminophores such that the luminescent emissions from the two components can be cleanly separated using optical filters. Theoretically, a two-color intensity ratio I λ1 =I λ2 between the probe and reference images could be able to eliminate the effects of spatially nonuniform illumination, paint thickness, and luminophore concentration, where I λ1 and I λ2 are the luminescent intensities at the emission wavelengths λ1 and λ2 of the probe and reference components, respectively. However, McLean (1998) pointed out that since two luminophores cannot be perfectly mixed, the simple ratio I λ1 =I λ2 cannot completely compensate for the effect of nonhomogeneous dye concentration. In this case, a ratio of ratios ðI λ1 =I λ2 Þ=ðI λ1 =I λ2 Þ0 should be used to correct the effects of nonhomogeneous dye concentration and paint thickness variation, where the subscript 0 denotes the wind-off condition. Therefore, wind-off images are still needed in practice. Furthermore, when the temperature dependencies of the probe and reference luminophores are close, a two-color intensity ratio between the two luminophores

54

1.5 1.2

Ro / R

Fig. 3.28 Ratio of ratios of a two-luminophore PSP (PtTFPP in FIB with a reference luminophore) as a function of pressure at different temperatures, where R ¼ I λ1 =I λ2 and R0 ¼ ðI λ1 =I λ2 Þ0 are the two-color intensity ratios between the probe and reference luminophores at the run and reference conditions, respectively. (From Crafton et al. 2002)

3 Physical Properties of Paints

0.9

5C 15 C 25 C 35 C 45 C

0.6 0.3 0 0

0.3

0.6

0.9

1.2

1.5

P/Po

exhibits a much weaker temperature dependency (Engler et al. 2001a). To avoid unwanted molecular interaction between the two luminophores, a thermographic phosphor is usually used as a reference luminophore since it is in the form of a crystal. Figure 3.28 shows a ratio of ratios of a two-luminophore PSP (PtTFPP in FIB with a proprietary reference luminophore) as a function of pressure at different temperatures (Crafton et al. 2002, 2013). Clearly, the data at different temperatures overlap, and a ratio of ratios of this PSP is almost temperature insensitive in a range of 5–45  C. Therefore, a multiple-luminophore PSP can be developed to correct the temperature effect as well as the effect of nonuniform illumination simultaneously. Oglesby et al. (1995b) used PtOEP or PtTFPP as a pressure-sensitive luminophore and Fluorol Green Gold 084 (3,9-perylenedicarboxylic acid, bis (2-methylpropyl)ester) as a reference luminophore in the GP-197 polymer. Harris and Gouterman (1995, 1998) used PtTFPP as a pressure-sensitive luminophore and incorporated a solid-state phosphor BaMg2Al16O27:Eu2+ (BaMgAl) as a reference luminophore in an acrylic copolymer. Since BaMgAl is insoluble, the reference luminophore was not uniformly distributed and therefore the paint suffers from the effect of the uneven layer thickness. Proprietary two-luminophore PSP formulations, LPS B1 and LPS B2, were developed at TsAGI (Bykov et al. 1997; Lyonnet et al. 1997). Three PSPs were also tested by Oglesby et al. (1996), where EuTTA, MgOEP, and Ru(bpy) were used as temperature-sensitive reference luminophores. Hradil et al. (2002) used Ru(dpp) as a pressure-sensitive luminophore and manganese-activated magnesium fluorogermanate (MFG) as a thermographic phosphor. Two-luminophore PSPs indeed enabled point-by-point correction for the temperature effect of PSP. Sano et al. (2018) fabricated dual luminescent polymer sensors based on a pressure-sensitive palladium(II) tetraphenylporphyrin, PdTPP, and a temperature-sensitive europium(III) complex, EuDT, by spray-coating or electrospinning of the solutions containing polystyrene as a host matrix for simultaneous detection of both pressure and temperature. The luminescence intensities of

3.4 Multiple-Luminophore PSPs

55

Fig. 3.29 Emission spectra at (a) constant temperature and different pressures and (b) constant pressure and different temperatures. (From Peng et al. 2013)

Fig. 3.30 Calibration curves of the two-color PSP: (a) intensity ratio as a function of temperature and (b) intensity ratio as a function of pressure. (From Peng et al. 2013)

the temperature-sensitive dye were used for the temperature correction of surface pressure measurements. Peng et al. (2013) developed a two-color PSP with PtTFPP as a probe luminophore and perylene as a reference luminophore, where a 0.2% laser dye was added to enhance the reference emission. Figure 3.29 shows the emission spectra of this two-color PSP for different pressures and temperatures. The reference emission was not sensitive to pressure, but it was a function of temperature. Figure 3.30 shows the calibration results of this PSP. The temperature dependencies of the luminescent intensity of the probe and reference luminophores were not the same such that the temperature effect could be partially compensated by taking a ratio of ratios. To correct the temperature effect, a correction factor was introduced, which was determines as a function of pressure and temperature. This two-color PSP was used to measure pressure fields in an impinging sonic jet and on an oscillating

56

3 Physical Properties of Paints

airfoil at Mach 0.59. Peng et al. (2018d) also integrated PSP with a persistent phosphor as a light-charged pressure-sensing system. Kameya et al. (2014), Egami et al. (2015), and Matsuda et al. (2017) fabricated dual luminescent array sensors by inkjet-printing of PSP and TSP. Similarly, Peng and Liu (2016) used a grid-pattern PSP/TSP system for simultaneous pressure and temperature measurements. The PSP/TSP sensor arrays developed by Kameya et al. (2014) were well-ordered by inkjet-printing of a solution of PtTFPP for PSP and a toluene solution of ZnS-AgInS2 (ZAIS) nanoparticles for TSP. The prepared dualarray sensor was illuminated by an LED light with a central wavelength of 395 nm. Figure 3.31 shows close-up luminescence images of the dual-array sensor. The luminescence image of Fig. 3.31a was captured by a color camera with a longpass filter of 480 nm in order to simultaneously observe both the red luminescence of PtTFPP and the green luminescence of ZAIS. As shown in Fig. 3.31a, the PtTFPP and ZAIS arrays were spatially isolated from each other. The luminescence images in Fig. 3.31b, c were captured by a monochrome camera with a band-pass filter of 690  60 nm and that of 530  60 nm, respectively. The image of the PtTFPP luminescence and the image of the ZAIS luminescence are separately detected with the optical filters. Figure 3.32 shows the emission spectra of the sensors. The spectral result confirms that the dual-array sensor is able to combine the pressure- and temperature-sensitive luminophores and minimize the interaction between the luminophores. In this sense, the PSP/TSP sensor arrays are superior to the dualluminophore paint, but it is noted that this advantage is obtained at the cost of reducing the spatial resolution.

3.5

Ideal PSP

A preferred PSP should be temperature independent. However, since the excitedstate decay rates of a luminophore are intrinsically temperature dependent, it is unlikely to develop an absolutely temperature-insensitive PSP with the constant Stern–Volmer coefficients Apolymer and Bpolymer. Instead, researchers seek a so-called “ideal” PSP exhibiting an invariant temperature dependency at different pressures over a certain range of temperatures (Puklin et al. 1998; Coyle et al. 1999; Bencic 1999; Ji et al. 2000). Consider the Stern–Volmer relation in the following form I 0 ðT Þ ¼ 1 þ K SV ðT Þp, I ðp, T Þ

ð3:1Þ

where I0(T ) ¼ I( p ¼ 0, T ) is the luminescent intensity at zero pressure (vacuum) and KSV(T ) is related to the coefficients Apolymer(T ) and Bpolymer(T ) by

3.5 Ideal PSP

57

Fig. 3.31 Luminescence images of the dual-array sensor: (a) color image of PtTFPP (red) and ZAIS (green) dot patterns, (b) PtTFPP dot pattern, and (c) ZAIS dot pattern. (From Kameya et al. 2014)

Fig. 3.32 Emission spectra of the dual-array sensor at atmospheric pressure and room temperature. (From Kameya et al. 2014)

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3 Physical Properties of Paints


 K SV ðT Þ ¼ Bpolymer ðT Þ=Apolymer ðT Þ =pref :

ð3:2Þ

If the coefficients Apolymer(T ) and Bpolymer(T) have the same temperature dependency, the coefficient KSV(T ) becomes temperature independent. According to Eqs. (2.23) and (2.24), this situation may occur under the conditions ED  Enr and η  1 over a certain range of temperatures. Therefore, for an “ideal” PSP, the coefficient KSV(T ) in Eq. (3.1) is temperature independent rather than the Stern– Volmer coefficients Apolymer(T ) and Bpolymer(T). Consequently, the Stern–Volmer relation can be written as gð T Þ

I ref p , ¼ Apolymer,ref þ Bpolymer,ref pref I

ð3:3Þ

where the function g(T ) is defined as   1   1 E T  T ref E T  T ref gð T Þ ¼ 1 þ D ¼ 1 þ nr , RT ref T ref RT ref T ref

ð3:4Þ

and the coefficients Apolymer, ref and Bpolymer, ref at a fixed reference condition are temperature independent. For an “ideal” PSP, the Stern–Volmer relation Eq. (3.3) enjoys such similarity that it is invariant at different temperatures when the variable g(T )(Iref/I) is used. The temperature effect of PSP is represented by a single scaling factor g(T); this similarity simplifies the temperature correction procedure for PSP.

3.6

Typical TSPs

TSP is prepared by dissolving a luminescent dye and a binder in a solvent. Many commercially available resins and epoxies can be used as polymer binders for TSPs if they are not oxygen-permeable and do not degrade the activity of probe luminophores. Figure 3.33 shows typical temperature dependencies of the luminescent intensity for some TSP formulations. Several TSPs have been used to measure the temperature and heat transfer fields in various applications (Kolodner and Tyson 1982, 1983a, b; Romano et al. 1989; Campbell 1993; Campbell et al. 1994; Liu et al. 1992, 1995a, b; Hamner et al. 1994; Asai et al. 1996, 1997c). Two typical TSPs are Ru(bpy) in an automotive clear coat (DuPont ChromaClear) binder and EuTTA in model airplane dope; both TSPs are easy to prepare and use. Several TSPs in Fig. 3.33 are sensitive at cryogenic temperatures. Some TSP formulations and their properties are listed in tables in Appendix B, and several TSP recipes are given in Appendix C.

3.6 Typical TSPs

59

Fig. 3.33 Temperature dependencies of the luminescent intensity for TSPs: (1) Ru(trpy) in ethanol/ methanol, (2) Ru(trpy)(phtrpy) in GP-197, (3) Ru(VH127) in GP-197, (4) Ru(trpy) in DuPont ChromaClear, (5) Ru(trpy)/Zeolite in GP-197, (6) EuTTA in dope, (7) Ru(bpy) in DuPont ChromaClear, (8) Perylenedicarboximide in sucrose octaacetate (Tref ¼ 150  C). (From Liu et al. 1997b)

3.6.1

Ruthenium Complexes

Figure 3.34a shows the chemical structure of tris(2,20 -bipyridyl) ruthenium or Ru (bpy) and Fig. 3.34b shows the absorption and emission spectra of Ru(bpy) that are similar to those of Ru(dpp) for PSP. Ru(bpy) can be excited by a suitable illumination source such as UV lamp, nitrogen laser, argon laser, doubled YAG laser, and blue LED array. Since the Stokes shift is large (the emission peak is at about 620 nm), the excitation light can be easily separated from the luminescent emission using an optical filter. An automobile urethane clear coat, which is usually used as a top coat on most automobiles, is used as a polymer binder for Ru(bpy). Particularly, DuPont ChromaClear 7500S is used, but other brands should work as well. The advantage of this binder is that it is oxygen-impermeable, readily available, and easy to spray. Figure 3.33 shows the temperature dependency of the luminescent intensity for Ru(bpy) in DuPont ChromaClear along with other TSP formulations. Ru(bpy) can also be mixed with a shellac binder; Ru(bpy)-Shellac TSP is similar to Ru(bpy) in DuPont ChromaClear in terms of the temperature sensitivity. It is also easy to apply. Figures 3.35 and 3.36 show, respectively, the Arrhenius plot and lifetime for Ru(bpy)-Shellac TSP compared with EuTTA-dope TSP.

60 Fig. 3.34 (a) Chemical structure of Ru(bpy) and (b) absorption and emission spectra of Ru(bpy)

Fig. 3.35 The Arrhenius plots for two TSPs: EuTTAdope TSP and Ru(bpy)Shellac TSP, where Tref ¼ 293 K. (From Liu et al. 1997b)

3 Physical Properties of Paints

3.6 Typical TSPs

61

Fig. 3.36 Lifetimetemperature relations for two Ru(bpy)-Shellac TSP and EuTTA-dope TSP. (From Liu et al. 1997b)

Fig. 3.37 Temperature calibration curves for various ruthenium dyes with the PU-C polymer for comparison of different luminophores: (a) normalized intensity and (b) temperature sensitivity. (From Klein et al. 2016)

Klein et al. (2016) tested TSPs based on Ru(terpy)2Cl2 as a reference (dye A) and ruthenium complexes (dyes B–F) with different terpyridine ligands in several polymers for measurements in cryogenic temperatures. Figure 3.37a shows the intensities normalized at a reference temperature of 130 K as a function of the temperature of the dyes in the PU-C polymer, indicating that the dyes B, C, D, E, and F are more sensitive to temperature changes than the reference dye-A. The relative temperature sensitivities for all the dyes are plotted in Fig. 3.37b. The temperature sensitivity of the dye A is less than 2%/K at 130 K. The results showed that the temperature sensitivity of the dyes B–F could be increased to 2–4%/K at 130 K, depending on the ligands.

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3 Physical Properties of Paints

Fig. 3.38 Temperature calibration curves for the Ru(phen)-based TSP: (a) normalized emission intensity spectrum at different temperatures and (b) temperature calibration curve. (From Martinez Schramm et al. 2015)

Martinez Schramm et al. (2015) developed a fast TSP based on dichlorotris (1,10phenanthroline) ruthenium(II) hydrate [Ru(phen)] in an oxygen-impermissible binder for time-resolved temperature and heat flux measurements in the High Enthalpy Shock Tunnel Göttingen (HEG) of DLR. This TSP was capable of measuring the temperature change in a run time of a few microseconds. Figure 3.38a shows the normalized emission spectrum for temperatures of 283, 293, 303, 313, and 323 K at 100 kPa, which demonstrates the temperature sensitivity of the Ru(phen)-based TSP. To examine the pressure sensitivity, the data at 20 and 100 kPa at 303 K are also shown in Fig. 3.38a for comparison, indicating that this TSP is not sensitive to pressure. The temperature calibration curve for this TSP is given in Fig. 3.38b, exhibiting the temperature sensitivity of about 2%/K.

3.6.2

Europium Complexes

Another common TSP is based on europium(III) thenoyltrifluoroacetonate or EuTTA whose structure and absorption and emission spectra are shown in Fig. 3.39. A UV lamp or LED array can be used for excitation. EuTTA has a high quantum yield and a large Stokes shift (the emission peak is at about 620 nm). A suitable oxygen-impermeable binder for EuTTA is a clear model airplane dope that is readily available and easy to spray. Figures 3.35 and 3.36 show, respectively, the Arrhenius plot and lifetime for EuTTA-dope TSP along with those for Ru(bpy)Shellac TSP. Ondrus et al. (2015) synthesized novel Eu complexes with 1,3-di(thienyl)propane-1,3-diones as ligands and measured their luminescence properties in different polymers. These new TSPs exhibit exceptional high temperature sensitivity over a wide range of temperatures, low pressure sensitivity, and marked photostability. Figure 3.40a shows the luminescence intensity of TSP based on Eu complex 1 as a

3.6 Typical TSPs

63

Fig. 3.39 (a) Chemical structure of EuTTA and (b) absorption and emission spectra of EuTTA

Fig. 3.40 Calibration results for TSP based on Eu complex 1: (a) luminescent intensity normalized by its value at 350 K as a function of temperature and (b) temperature and pressure sensitivities. (From Ondrus et al. 2015)

function of temperature normalized with respect to its value at 350 K. Figure 3.40b shows the temperature sensitivity and very low pressure sensitivity of TSP based on Eu complex 1. The temperature sensitivity increases continuously with rising

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3 Physical Properties of Paints

Table 3.2 Temperature sensitivity ST (%/K) of Eu complexes 1–3 and EuTTA in the 3C-PU polymer at 30  C

Complex 1 2 3 EuTTA a

ST in 3C-PUa 4.0 3.36 3.07 0.65

ST in 3C-PUb 3.78 3.25 2.89 0.63

With screen layer Without screen layer

b

temperatures from 0.5%/K at 205 K to a value of 7%/K at 375 K. Table 3.2 lists the temperature sensitivity ST (%/K) of Eu complexes 1–3 and EuTTA in the 3C-PU polymer at 30  C. The TSPs based on Eu complexes exhibit very high temperature sensitivity and very low pressure sensitivity over a wide range of temperatures. Katagiri et al. (2008) synthesized a similar TSP containing tetranuclear Eu(III) complex achieving high temperature-sensitivity of 5.6–2.0%/K under visible light (410 nm) excitation without pressure-sensitivity. Carlotto et al. (2020) developed a new model to predict the temperature dependence of the luminescent emission of Eu complexes. The change of the emission intensity with temperature is essentially driven by thermally activated non-radiative decay of the luminophore excited states. For wide temperature ranges (100–200 K or wider), the common temperature dependence of the luminescent intensity is described by the Mott-Seitz model I ðT Þ 1 P ¼ , I0 1 þ i αi exp ðΔEi =kB T Þ where I0 is the intensity at T ¼ 0 K, αi is the ratio between the probabilities of non-radiative and radiative deactivation paths, ΔEi is the activation energy of the ith thermal quenching process, kB is the Boltzmann constant, and T is the absolute temperature. The model of Carlotto et al. (2020) was based on a modified form of the Mott-Seitz model for a class of Eu complexes. The new model was a product of two factors. One had two sigmoid functions describing the primary deactivation channels; another included a multiplicative ligand-related term taking into account non-radiative deactivation of the antenna triplet. All the terms in the model were deduced from experimental data of selected Eu complexes. Once the relevant parameters were determined, the model was successfully applied to a number of examples. Figure 3.41 shows the experimental and simulated temperature dependencies of the normalized luminescent intensity for several Eu compounds. The model provided the correct temperature range for the maximum temperature sensitivity.

3.6 Typical TSPs

65

Fig. 3.41 Comparison between the experimental and simulated temperature dependencies of the normalized luminescent intensity for (a) Eu2E, Eu2E, and EubtaW, and (b) Eu2T, Eu3T, and EubtaT. (From Carlotto et al. 2020)

3.6.3

Cryogenic TSPs

A family of luminescent compounds of Ru(trpy) (see Fig. 3.42 for its chemical structure) has been studied for making cryogenic TSPs since they are temperature sensitive at cryogenic temperatures (Campbell 1993; Erausquin 1998; Iijima et al. 2003). They have very intense emission at low temperatures, but they are nearly fully quenched at room temperature. The absorption and emission spectra of the family of Ru(trpy) are very similar to those of Ru(dpp) and Ru(bpy). The Ru(trpy) compounds, which can be excited by either a UV light or a blue light, emit red luminescence. Ruthenium complexes with different ligands were synthesized (Erausquin 1998). The dynamics of the metal-to-ligand bond, as well as the electron donating/accepting characteristics of the ligand, has a significant effect on the temperature sensitivity of a luminescent molecule. Thus, this would enable synthesis of a molecule specifically designed for a high sensitivity over a certain range of cryogenic temperatures. DuPont ChromaClear (CC) was selected as a binder for cryogenic TSP due to its low oxygen diffusivity and good surface adhesion at cryogenic temperatures (Erausquin 1998). Figure 3.43 shows comparisons of several synthesized ruthenium compounds in the polymers CC and GP-197. In general, interaction between a polymer binder and a luminescent molecule can affect the mobility of the metalto-ligand bonds, changing the temperature dependency of TSP. Figure 3.44 shows the temperature dependencies for [Ru(trpy)(phtrpy)](PF6)2 in two different polymer binders CC and GP-197. Other ruthenium compounds have a good response at cryogenic temperatures as well. Tables in Appendix B summarize the temperature sensitivities and useful temperature ranges for cryogenic TSPs. To extend a measurement range of TSP from cryogenic temperature to room temperature, Egami et al. (2012) developed a two-component cryogenic TSP (2C-cryoTSP) by combining Ru(trpy)2 with one of two europium complexes [Eu

66

3 Physical Properties of Paints

Fig. 3.42 Chemical structure of Ru(trpy) N N

N Ru

N

2+

N N

2Cl1.6

[Ru(trpy)2] in CC [Ru(trpy)(phtrpy)](PF6)2

1.4

[Ru(ppd-trpy)2](TFPB)2 in CC [Ru(trpy)(VH-127)](PF6)2 in GP-197

I(T) / Iref(T)

1.2 1.0 0.8 0.6 0.4 0.2 0.0

-200

-150

-100

-50

0

50

o

Temperature ( C) Fig. 3.43 Comparison of Ru(trpy)-based cryogenic TSPs, where CC denotes DuPont ChromaClear. (From Erausquin 1998)

(hfc)3 and Eu(facam)3]. Polyurethane was employed as the polymer matrix of the cryoTSP. Figure 3.45 shows the excitation and emission spectra of the two 2C cryogenic TSPs. Ru(trpy)2 can be excited by a blue light, while the europium complexes can be excited by a UV light. The emission spectra of these luminophores are overlapped. Figure 3.46 shows the relative intensity of the 2C cryogenic TSP as a function of temperature. Ru(trpy)2 was a luminophore used in cryogenic TSP measurements (100 K < T < 220 K). The second component, either [Eu(hfc)3 or Eu(facam)3], had the high luminescent intensity and temperature sensitivity in a temperature range of 220–320 K. By using different illumination lights, the 2C-cryoTSP was used to detect transition on an airfoil and a wing in a temperature range of 100–320 K. However, the 2C-cryoTSP requires two different illumination

3.6 Typical TSPs

67

1.6 GP-197 Chromaclear

1.4

I(T) / Iref(T)

1.2 1.0 0.8 0.6 0.4 0.2 0.0 -200

-150

-100

-50

0

50

o

Temperature ( C) Fig. 3.44 Temperature calibration for cryogenic TSPs: [Ru(trpy)(phtrpy)](PF6)2 in GP-197 and DuPont ChromaClear. (From Erausquin 1998)

Fig. 3.45 Excitation (Ex) and emission (Em) spectra of the two 2C cryogenic TSPs: (a) Ru (trpy)2 + Eu(hfc)3 and (b) Ru(trpy)2 + Eu(facam)3. (From Egami et al. 2012)

sources, which is difficult to implement in a facility with very limited optical access. An alternative formulation containing two different ruthenium dyes was developed by Watkins et al. (2019). The two dyes chosen were Ru(trpy)) and Ru(bpy). Ru(trpy) shows excellent temperature sensitivity down to 100 K. However, the luminescence of this dye is highly quenched at ambient temperatures. To account for this, Ru(bpy) was selected, which is traditionally used for temperature measurements at ambient conditions. This combination of the dyes in the same polymer has the same excitation and emission wavelengths, working in a temperature range of 173–313 K. Claucherty and Sakaue (2017a) developed a Rhodamine-B-based AA-TSP. By using AA as a host matrix for Rhodamine B, the sensor provided an expanded

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3 Physical Properties of Paints

Fig. 3.46 Relative intensity of the 2C cryogenic TSP as a function of temperature. (From Egami et al. 2012)

temperature-sensitive range from 150 to 500 K. The highest temperature sensitivity of this TSP was about 3%/K at 150 K. Claucherty and Sakaue (2017b) also developed a CdSe/ZnS quantum-dot-based AA-TSP that was sensitive in a range of 100–315 K. Furthermore, Claucherty and Sakaue (2018) investigated a luminescent material phenol-formaldehyde (PF) resin as an optical temperature sensor and found that several PT resins have a temperature-sensitive range of 100–500 K with the temperature sensitivities up to 0.8%/K. Thus, PF resin could be used as a potential temperature sensor in a wider range of temperatures.

3.6.4

Other Coatings

Other temperature-sensitive coatings for measuring surface temperature distributions include thermographic phosphors and thermochromic liquid crystals. Similar to polymer-based TSPs, thermographic phosphors utilize the thermal quenching of the luminescent emission from ceramic materials that are doped or activated with rare-earth elements (Bradley 1953; Czysz and Dixon 1969; Tobin et al. 1990; Alaruri et al. 1995; Allison and Gillies 1997; Noel et al. 1985, 1986, 1987). However, they are usually in the form of insoluble powders or crystals, in contrast to a polymer-based TSP where luminescent molecules are immobilized in a polymer matrix. The luminescent intensity (or lifetime) of thermographic phosphor and polymer-based TSP follows the same functional relation of temperature. A family of thermographic phosphors can cover a temperature range of 273–1600 K, which

3.7 Desirable Properties of Paints

69

overlaps with a temperature range of 90–423 K for a family of polymer-based TSPs. Hence, a combination of thermographic phosphors and polymer-based TSPs can cover a broad range from cryogenic temperatures to high temperatures. The measurement systems (intensity- and lifetime-based systems) for thermographic phosphors are essentially the same as those for polymer-based TSPs. The emission spectrum of certain phosphor has multiple distinct lines that have very different temperature sensitivities. Thus, an intensity ratio between temperature-sensitive and -insensitive lines could eliminate the effect of nonuniform illumination on a surface. Note that certain emission lines of certain phosphor are also temperature sensitive in cryogenic conditions. Buck (1988, 1989, 1991) used a bluegreen Radelin thermographic phosphor for aerothermodynamic testing that intrinsically exhibited two narrow-band emission peaks at 450 and 520 nm. It was found that a ratio between the blue to green emission intensities was a function of temperature, which is independent of the UV illumination intensity. Another two-color phosphor system used a green-red mixture of rare-earth and Radelin phosphors for a broader range of temperatures. Buck (1988, 1989) and Merski (1998, 1999) gave a detailed description of the multiple-color phosphor thermography system developed at NASA Langley. Yang et al. (2018) and Li et al. (2020a, b) investigated the effect of oxygen partial pressure on phosphorescence for different lanthanide ion-doped (Ln ¼ Eu, Dy, Sm, Er) yttria-stabilized zirconia (YSZ). The phosphorescence lifetime of Eu3+-, Dy3+-, and Sm3+-doped YSZ phosphors decreased as oxygen partial pressure increased, and the oxygen sensitivity was enhanced as temperature increased. This finding can serve as a basis for developing optical pressure sensors suitable for high-temperature environments.

3.7

Desirable Properties of Paints

PSP or TSP is prepared by dissolving a luminescent dye and a polymer binder in a solvent solution; the resulting mixture is then applied on a surface of interest by spraying, brushing, or dipping. After the solvent evaporates, a thin coating of the paint remains on the surface, in which luminescent molecules are immobilized in the polymer matrix. The polymer binder is an important ingredient of the paint adhering to the surface. In some cases, a polymer matrix is only a passive anchor; in other cases, the polymer may significantly affect the photophysical behavior of the paint through complicated interaction between the luminescent molecule and the macromolecule of the polymer. Since it is not known a priori how a polymer affects the properties of PSP or TSP, it is basically a trial-and-error process to find an optimal combination of a luminophore and a polymer. A good paint (PSP or TSP) for aerodynamic measurements should have some required physical and chemical properties. The following notes focus on the required properties of PSP, while some requirements are generally applicable to TSP. A general strategy for the development of improved PSP formulations was proposed by Benne et al. (2002).

70

3.7.1

3 Physical Properties of Paints

Pressure Response

The Stern–Volmer coefficients of PSP should be chosen to match a specified pressure range on a tested article and the performance requirements of a photodetector (e.g., digital camera) used in a particular measurement. Generally, a large Stern–Volmer coefficient B(T ) indicates a good pressure response. However, for aerodynamic experiments at high pressures, a large value of B(T ) may cause unwanted severe oxygen quenching in the ambient reference condition, considerably reducing the luminescent emission from the paint and lowing the signal-to-noise ratio (SNR) of measurement.

3.7.2

Luminescent Output

The luminescent emission of luminophore is characterized by the quantum yield (or efficiency); it is generally desirable to have a high luminescent output to maximize the SNR. The luminescent intensity is proportional to the concentration of probe molecules over a linear range. However, it cannot be increased indefinitely by increasing the dye concentration; if the concentration is too high, self-quenching of luminescence occurs. Similarly, the luminescent intensity is no longer linearly proportional to the excitation light intensity at a very high excitation level, and eventually it saturates when the illumination intensity increases further.

3.7.3

Paint Stability

Ideally, the luminescent intensity of PSP should not change with time under excitation. However, the luminescent intensity usually decreases with time due to the photodegradation of a luminophore (Egami and Asai 2002). A decrease in the luminescent intensity could also be due to the presence of certain chemicals (other than oxygen) that can quench the luminescence. A polymer binder undergoes aging, which can change its characteristics with respect to the oxygen solubility and diffusivity and as a result the Stern–Volmer coefficients of PSP may be altered.

3.7.4

Response Time

The response time of PSP is mainly determined by the oxygen diffusion process through a paint layer when the luminescent lifetime is much shorter than the diffusion timescale. The high porosity of paint will improve the time response. The need for fast time response depends on a particular application; a short response

3.7 Desirable Properties of Paints

71

time of PSP is required for time-resolved measurements. For steady-state measurements, however, the use of a fast-responding PSP does not necessarily offer an advantage. For a highly oxygen-permeable PSP with short response time, the Stern– Volmer coefficient B(T ) is usually large, and thus the weak luminescence of PSP in the ambient condition may lead to a low SNR.

3.7.5

Temperature Sensitivity

A good PSP should have a weak temperature effect. The temperature sensitivity arises from two sources: the intrinsic temperature dependency of a luminophore and the temperature dependency of the solubility and diffusivity of oxygen in a polymer matrix. The latter is a major contributor to the temperature sensitivity of PSP.

3.7.6

Physical Characteristics

The physical properties of a polymer binder, such as adhesion, hardness, coating smoothness, and thickness, should be considered prior to a test. Adhesion should be strong enough to sustain skin friction particularly in high-speed flows, which is related to surface tension, solvent softening, and chemical bonding. Hardness primarily depends on the type of polymer, the molecular weight, and the degree of cross-linking. For example, silicone rubbers (or RTVs) are generally soft, whereas acrylates and methacrylates are generally hard, which can be polished with lapping film. Coating smoothness depends primarily on a paint itself and application techniques; for most paints uniform leveling of the paint is essential to a smooth finish. The coating thickness is very dependent on application techniques for both basecoat and PSP topcoat. It is generally desirable to minimize the coating roughness to avoid any effect on the aerodynamic characteristics of a model. Typically, the maximum RMS roughness of a coating should be less than 0.25 μm, and the coating thickness ranges from 20 to 40 μm.

3.7.7

Chemical Characteristics

Paint toxicity is a major concern of safety; toxic solvents should be avoided. A painter must be protected against contact with paint spray through the use of fresh air breathing equipment and adequate ventilation. A good paint must be easily sprayed, leveled, and cured to give the specified physical characteristics of the coating under different environmental conditions in wind tunnels. The solvent evaporation rate must be controlled under different temperature and humidity. Since the wind tunnel time is expensive, the application of paint should be as fast as possible. The curing

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3 Physical Properties of Paints

temperature must be reasonable (less than 100  C); if the curing temperature is too high, it is difficult to achieve uniform curing over different metallic materials. In addition, paint removal and reapplication on a model is a practical issue in wind tunnel testing. Some paints, particularly those designed for good and robust adhesion, are difficult to remove and generally require an aggressive paint stripper like methylene chloride. This introduces issues with toxicity and ensuring adequate ventilation. “Safety” section is discussed in Appendix C.

Chapter 4

Radiative Energy Transport

This chapter describes the transport processes of radiative energy in a thin luminescent paint, including the absorption of excitation light through the paint layer and the luminescent radiation from the paint layer. The response of a photodetector to the luminescent emission is discussed.

4.1

Radiometric Notation

Luminescent radiation from a luminescent paint (PSP or TSP) on a surface has two major related transport processes of radiative energy. The first process is the absorption of excitation light through a paint layer and the second process is luminescent radiation that is an absorbing-emitting process in the paint layer. These processes can be described by the transport equations of radiative energy (Modest 1993; Pomraning 1973). The luminescent intensity emitted from a paint layer can be analytically determined by solving the transport equations. Thus, the corresponding photodetector output can be derived for an analysis of the measurement system performance and uncertainty. Before giving a detailed analysis, it is necessary to discuss the radiometric notation. In the literature of PSP and TSP, the term “luminescent intensity” or “fluorescent intensity,” which is usually denoted by the notation “I,” has been widely used. In a strict radiometric sense, the luminescent intensity I is the luminescent radiance defined as the radiant energy flux (power) per unit solid angle and per unit projected area of a surface element of PSP or TSP (W/m2/sr or J/s/m2/sr). The radiance is a function of both position and direction, which is graphically represented by a cone of a solid angle element in radiometry, as shown in Fig. 4.1. The direction of the radiance (incident or emitting radiance) is given by the polar angle θ (measured from the surface normal) and the azimuthal angle ϕ (measured between an arbitrary axis on a surface and the elemental solid angle on the surface) in a local coordinate system. In radiometry, the radiance is conventionally denoted by © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_4

73

74

4 Radiative Energy Transport

Fig. 4.1 Incident excitation light and luminescent emission from a surface element in a local polar coordinate system

the notation “L.” The term “intensity” has different definitions in different disciplines. In radiometry, the radiant intensity (W/sr), denoted by the notation “I,” is the radiant flux per unit solid angle, which is different from the radiance (McCluney 1994; Wolfe 1998). However, in the literature of radiative heat transfer, the radiative intensity, denoted by “I,” is essentially equivalent to the radiance in radiometry (Modest 1993). In order to avoid confusion in notation, we specifically define the luminescent intensity “I” as the luminescent radiance from PSP or TSP, which is consistent with the notation and terminology commonly used in the literature of PSP and TSP. In a general case, we still use the traditional radiometric notation “L” to denote the radiance in other radiometric measurements and modeling. The spectral radiance such as Iλ and Lλ at a wavelength λ (W/m2/sr/nm) is usually denoted by a subscript λ; the radiance I (or L ) is the integration of the spectral radiance Iλ (or Lλ) over a certain range of the radiation wavelengths. Since the radiation from a luminescent molecule is isotropic, a plausible assumption is that the luminescent radiance from PSP or TSP is independent of the azimuthal angle ϕ. Under this assumption, an analysis of transport of the luminescent radiative energy in PSP or TSP is considerably simplified. The following analysis is given for PSP, but it is also applicable to TSP that is treated as a special case of PSP when the oxygen quenching vanishes.

4.2

Excitation Light

We consider a PSP layer with a thickness h on a solid wall, as shown in Fig. 4.2. It is assumed that PSP is not a scattering medium and scattering exists only at the wall surface. When an incident excitation light beam with a wavelength λ1 enters a PSP layer (simply layer), without scattering and other sources of the excitation energy,

4.2 Excitation Light

75

Fig. 4.2 Radiative energy transports in a luminescent paint layer

the incident light is attenuated due to absorption through the PSP medium. In plane geometry where the luminescent intensity (radiance) is independent of the azimuthal angle, the intensity of the incident excitation light with λ1 can be described by μ

dI
λ1 þ β λ1 I
λ1 ¼ 0, dz

ð4:1Þ

where I
λ1 is the incident excitation light intensity, μ ¼ cos θ is the cosine of the polar angle θ, and βλ1 is the extinction coefficient of the PSP medium for the incident excitation light with λ1. The extinction coefficient βλ1 ¼ ελ1 c is a product of the molar absorptivity ελ1 and the luminescent molecule concentration c. Here, the spectral intensity is defined as radiative energy transferred per unit time, solid angle, spectral variable, and area normal to the ray (W/m2/sr/nm). The superscript “
” in I
λ1 indicates the negative direction in which the light enters the layer. The incident angle θ ranges from π/2 to 3π/2 (
1  μ  0) (see Fig. 4.2). For the collimated excitation light, the boundary value for Eq. (4.1) is the component penetrating into the layer, i.e.,
 ap I
ð z ¼ h Þ ¼ 1
ρ λ1 λ1 q0 E λ1 ðλ1 Þδðμ
μex Þ,

ð4:2Þ

76

4 Radiative Energy Transport

where q0 and E λ1 ðλ1 Þ are the radiative flux and spectrum of the incident excitation light, respectively, ρap λ1 is the reflectivity of the air-PSP interface, μex is the cosine of the incident angle of the excitation light, and δ(μ ) is the Dirac-delta function. The solution of Eq. (4.1) for
1  μ  0 is
    ap ¼ 1
ρ βλ1 =μ ðh
zÞ : I
λ1 λ1 q0 E λ1 ðλ1 Þδðμ
μex Þ exp

ð4:3Þ

This relation describes a decay of the incident excitation light intensity through the layer. The incident excitation light flux at a wall integrated over the range of θ from either π to π/2 or π to 3π/2 is q
λ1 ð z ¼ 0 Þ ¼


Z

0


1


 ap I
ð z ¼ 0 Þμ dμ ffi C 1
ρ d λ1 λ1 q0 E λ1 ðλ1 Þ,

ð4:4Þ

where Cd is the coefficient representing the directional effect of the excitation light, i.e.,   C d ¼
μex exp βλ1 h=μex

ð
1  μex  0Þ,

ð4:5Þ

When the incident excitation light impinges on a wall, the light reflects and re-enters into the layer. Without a scattering source inside the layer, the intensity of the reflected and scattered light from the wall is described by μ

dI þ λ1 þ β λ1 I þ λ1 ¼ 0, dz

ð4:6Þ

where I þ λ1 is the excitation light intensity in the positive direction emanating from the wall. As shown in Fig. 4.2, the range of μ is 0  μ  1 (0  θ  π/2 and
π/2  θ  0) for the outgoing reflected and scattered excitation light. The superscript “+” indicates the outgoing direction from the wall. For the wall that reflects diffusely, the boundary condition for Eq. (4.6) is
 wp
wp 1
ρap Iþ λ1 ðz ¼ 0Þ ¼ ρλ1 qλ1 ðz ¼ 0Þ ¼ C d ρλ1 λ1 q0 E λ1 ðλ1 Þ,

ð4:7Þ

where ρwp λ1 is the reflectivity of the wall-PSP interface for the excitation light. The solution of Eq. (4.6) for 0  μ  1 is
   wp 1
ρap Iþ λ 1 ¼ C d ρ λ1 λ1 q0 E λ1 ðλ1 Þ exp
βλ1 z=μ :

ð4:8Þ

At a point inside the layer, the net excitation light flux is contributed by the incident and scattering light rays from all the possible directions. The net flux is calculated by adding the incident flux (integrated over θ ¼ π to π/2 and θ ¼ π to 3π/2)

4.3 Luminescent Emission

77

and scattering flux (integrated over θ ¼ 0 to π/2 and θ ¼ 0 to
π/2). Hence, the net excitation light flux is 

q λ1

 net

Z

0

I
λ1 μ dμ

Z

0

¼
2
2 Iþ λ1 μ dμ
1 1 h
  i   wp sE ð λ s Þ exp
β z=μ exp
3β z=2 : ffiCd 1
ρap q þ ρ λ 1 λ ex λ 0 1 λ1 λ1 1 1 ð4:9Þ

Note that the derivation of Eq. (4.9) uses an approximation of the exponential integral of the third order, i.e., E3(x) ffi (1/2) exp (
3x/2).

4.3

Luminescent Emission

After luminescent molecules in a PSP layer absorb the energy from the excitation light with a wavelength λ1, they emit luminescence with a longer wavelength λ2 due to the Stokes shift. Luminescent radiative transfer in a PSP layer is an absorbingemitting process; the luminescent light rays from the luminescent molecules radiate in both the inward and outward directions. For the luminescent emission toward the wall, the luminescent intensity I
λ2 can be described by μ

dI
λ2 þ β λ2 I
λ2 ¼ Sλ2 ðzÞ ð
1  μ  0Þ, dz

ð4:10Þ

where Sλ2 ðzÞ is a luminescent source term and the extinction coefficient βλ2 ¼ ελ2 c is a product of the molar absorptivity ελ2 and the luminescent molecule concentration c. The luminescent source term Sλ2 ðzÞ is assumed to be proportional to the extinction coefficient for the excitation light, the quantum yield, and the net excitation light flux filtered over a spectral range of absorption. Therefore, a model for the luminescent source term is expressed as Z Sλ2 ðzÞ ¼ Φ ðp, T ÞEλ2 ðλ2 Þ 0

1

q λ1



β F ðλ Þdλ1 , net λ1 t1 1

ð4:11Þ

where Φ ( p, T ) is the luminescent quantum yield that depends on air pressure ( p) and temperature (T ), Eλ2 ðλ2 Þ is the luminescent emission spectrum, and Ft1(λ1) is a filter function describing the optical filter used to ensure the excitation light within the absorption spectrum of the luminescent molecules. With the boundary condition I
λ2 ðz ¼ hÞ ¼ 0, for
1  μ  0, the solution of Eq. (4.10) is

78

4 Radiative Energy Transport

I
λ2



β λ2 z 1 ¼ exp
μ μ

Z z    Z h β z β λ2 z  Sλ2 ðzÞ exp λ2 Sλ2 ðzÞ exp dz
dz : μ μ 0 0

ð4:12Þ

The incoming luminescent flux toward the wall at the surface (integrated over θ ¼ π to π/2 and θ ¼ π to 3π/2) is q
λ2 ðz ¼ 0Þ ¼
2

Z

0


1

I
λ2 ðz ¼ 0Þμ dμ,

ð4:13Þ

where I
λ2 ð z

1 ¼ 0Þ ¼
μ

Z 0

h

 β λ2 z Sλ2 ðzÞ exp dz: μ

We consider the luminescent emission in the outward direction and assume that scattering occurs only at the wall. The outgoing luminescent intensity I þ λ2 can be described by μ

dI þ λ2 þ β λ2 I þ λ2 ¼ Sλ2 ðzÞ dz

ð0  μ  1Þ:

ð4:14Þ

Similar to the boundary condition for the scattering excitation light, a fraction of the incoming luminescent flux q
λ2 ðz ¼ 0Þ is reflected diffusely from the wall. Thus, the boundary condition for Eq. (4.14) is wp
wp Iþ λ2 ðz ¼ 0Þ ¼ ρλ2 qλ2 ðz ¼ 0Þ ¼
2ρλ2

Z

0


1

I
λ2 ðz ¼ 0Þμ dμ,

ð4:15Þ

where ρwp λ2 is the reflectivity of the wall-PSP interface for the luminescent light. The solution of Eq. (4.14) with the boundary condition Eq. (4.15) for
1  μ  0 is Iþ λ2

  Z  β λ2 z 1 z β λ2 z þ ¼ exp
S ðzÞ exp dz þ I λ2 ðz ¼ 0Þ : μ 0 λ2 μ μ

ð4:16Þ

At this stage, the outgoing luminescent intensity I þ λ2 can be readily calculated by substituting the source term Eq. (4.11) into Eq. (4.16). In general, I þ λ2 has a nonlinear distribution across the layer, which is composed of the exponentials of βλ1 z and βλ2 z. For simplicity of algebra, we consider an optically thin PSP layer that is an asymptotic but important case.

4.3 Luminescent Emission

79

When a PSP layer is optically thin such that βλ1 h, βλ2 h, βλ1 z, and βλ2 z  1, the asymptotic expression for I þ λ2 (
1  μ  0) is simply expressed as   
Iþ z þ 2ρwp λ2 ðzÞ ¼ Φðp, T Þ q0 E λ2 ðλ2 ÞK 1 βλ1 =μ λ2 hμ ,

ð4:17Þ

where K1 ¼

β
1 λ1

Z

1

0



 wp βλ1 Eλ1 ðλ1 ÞC d 1
ρap 1 þ ρ λ1 λ1 F t1 ðλ1 Þ dλ1 :

Equation (4.17) indicates that for an optically thin PSP layer, the outgoing luminescent intensity is proportional to the extinction coefficient (a product of the molar absorptivity and the luminescent molecule concentration), paint layer thickness, the quantum yield of the luminescent molecules, and incident excitation light flux. The term K1 represents the combined effect of the optical filter, excitation light scattering, and direction of the incident excitation light. The outgoing luminescent intensity averaged over the layer is Z h D E
1 Iþ Iþ ¼h λ2 λ2 ðzÞ dz 0





ð4:18Þ

¼hΦ ðp, T Þq0 E λ2 ðλ2 ÞK 1 βλ1 =μ M ðμÞ, þ where M ðμ Þ ¼ 0:5 þ 2ρwp λ2 μ. The outgoing luminescent energy flow rate Qλ2 (radiant flux) on an area element As of the PSP paint surface collected by a detector is

Qþ λ2

Z D E ¼As Iþ λ2 cos θ dΩ Ω

ð4:19Þ

¼βλ1 h Φ ðp, T Þ q0 E λ2 ðλ2 ÞK 1 hM iAs Ω, where Qþ λ2 is equivalent to the spectral radiant flux in radiometry (W/nm), Ω is a collecting solid angle of the detector, and the extinction coefficient βλ1 ¼ ελ1 c is a product of the molar absorptivity ελ1 and luminescent molecule concentration c. The coefficient hMi represents the effect of reflection and scattering of the luminescent light at the wall, which is defined as hM i ¼ Ω
1

Z Ω

M ðμ Þ dΩ ¼ 0:5 þ ρwp λ2 ðμ1 þ μ2 Þ,

where μ1 ¼ cos θ1 and μ2 ¼ cos θ2 are the cosines of two polar angles in the solid angle Ω .

80

4.4

4 Radiative Energy Transport

Photodetector Response

The response of a photodetector to the luminescent emission can be derived based on a mathematical model of an optical system (Holst 1998). Consider an optical system located at a distance R1 from a luminescent source area, as shown in Fig. 4.3. The collecting solid angle with which a lens is seen from the source can be approximated by Ω  A0 =R21, where A0 ¼ πD2/4 is the imaging system entrance aperture area, and D is the effective diameter of the aperture. Using Eq. (4.19) and additional relations As =R21 ¼ AI =R22 and 1/R1 + 1/R2 ¼ 1/fl, we obtain the radiative energy flux onto the detector 

Qλ2

 det

¼

π AI T op T atm β h Φ ðp, T Þ q0 E λ2 ðλ2 ÞK 1 hM i, 4 F 2 1 þ M op 2 λ1

ð4:20Þ

where F ¼ fl/D is the f-number, Mop ¼ R2/R1 is the optical magnification, fl is the effective focal length, AI is the image area, and Top and Tatm are the optical transmittance and atmospheric transmittance of the optical system, respectively. The output of the detector is Z V ¼G 0

1

  Rq ðλ2 Þ Qλ2 det F t2 ðλ2 Þdλ2 ,

ð4:21Þ

where Rq(λ2) is detector’s quantum efficiency, G is system’s gain, and Ft2(λ2) is a filter function describing an optical filter for the luminescent emission. The dimension of V/G is J/s. Substitution of Eq. (4.20) into Eq. (4.21) yields V ¼G

π AI β hΦðp, T Þq0 K 1 K 2 , 4 F 2 1 þ M op 2 λ1

where

Fig. 4.3 Schematic of an imaging system

ð4:22Þ

4.4 Photodetector Response

Z K2 ¼

81 1

T op T atm Eλ2 ðλ2 Þ hM iRq ðλ2 ÞF t2 ðλ2 Þ dλ2 :

0

The factor K2 represents the combined effect of the optical filter, luminescent light scattering, and system response to the luminescent light. The above analysis is made based on an assumption that the radiation source is on the optical axis. In general, the off-axis effect is taken into account by multiplying a factor cos4θp in the right-hand side of Eq. (4.22), where θp is the angle between the optical axis and light ray through the optical center (McCluney 1994). The directional effect of luminescence is considered. Equation (4.19) gives the directional dependency of the luminescent radiant flux, i.e., wp Qþ λ2 / 1 þ 2ρλ2 ½ cos ðθ
Δθ=2Þ þ cos ðθ þ Δθ=2Þ,

ð4:23Þ

where Δθ ¼ θ2
θ1 is the difference between two polar angles in the solid angle Ω . Clearly, the luminescent radiant flux contains a constant irradiance term and a Lambertian term that is proportional to the cosine of the polar angle. Le Sant (2001b) measured the directional dependency of the luminescent emission of the B1 PSP composed of a derived pyrene dye and a reference component. Recently, Lemarechal et al. (2021a) studied the directional dependency of a Eu-based TSP. A LED and a b/w scientific CCD camera were located above a TSP coated aluminum plate. The orientation of the LED and camera are described by the polar angle θ, as shown in Fig. 4.1. In the initial condition the camera is located at θ ¼ 0 and the LED is tilted by a few degrees to avoid reflections of excitation light on the TSP surface reaching the camera. Initially, camera and LED are in the yz-plane. For the acquisition either the camera or the LED are tilted around the y-axis. One TSP image was recorded for every adjusted angle. The evaluation is performed with the angle θxz, which describes the angle between the z-axis and the projection of the respective optical axis onto the xz-plane. In the evaluation every image is divided by the image acquired at θxz ¼ 0 . Afterwards, the intensity ratio was averaged along the axis of rotation. The increasing area on the TSP plate for increasing θxz, which is recorded by a single pixel, was compensated in the evaluation. Thus, only the angular characteristics of the excitation and the emission of the paint were considered. Figure 4.4 shows the angular dependency of the excitation and emission intensity of the Eu-based TSP. The result shows that the emission of the TSP agrees well with Lambert’s cosine law, when tilting the camera or the LED. A significant influence of the surface roughness could not be observed. When transferring the results for setting up an experiment, it is important that the increasing area, which is recorded by a single pixel, compensates the decrease of emitted light. It is more important to consider the angle of the LED, because the rate of emission also declines but this is not compensated. The photodetector output V responding to the luminescent emission, Eq. (4.22), is re-written as V ¼ Πc Πf βλ1 hq0 Φðp, T Þ:

ð4:24Þ

82

4 Radiative Energy Transport

Fig. 4.4 Angular dependency of the excitation and emission of a Eu-based TSP. (From Lemarechal et al. 2021a)

The parameters Πc and Πf are defined as h  2 i
1 , Πc ¼ ðπ=4ÞGAI F 2 1 þ M op

Πf ¼ K 1 K 2 ,

which are related to the imaging system (camera) performance and filtered physical parameters of a paint, respectively. The quantum yield Φ( p, T ) is described by   Φð p, T Þ ¼ k r = kr þ knr þ kq SϕO2 p , where kr is the radiative rate constant, knr is the radiationless deactivation rate constant, kq is the quenching rate constant, p is air pressure, S is the solubility of oxygen, and ϕO2 is the volume fraction of oxygen in air. In PSP applications, the intensity-ratio method is commonly used, and without any model deformation, pressure p is related to a ratio between the wind-off (reference) and wind-on outputs by the Stern-Volmer relation V ref p : ¼ AðT Þ þ BðT Þ pref V

ð4:25Þ

In Eq. (4.25), the factor Πc Πf βλ1 hq0 in Eq. (4.24) is eliminated by the image ratioing procedure. Therefore, various complex physical effects are theoretically eliminated, including nonuniform illumination, nonhomogeneous paint thickness, nonhomogeneous dye concentration, and surface scattering and direction of the incident excitation light and the luminescent light. Equation (4.25) is a basic relation for the intensity-based method for PSP. Similarly, in the multiple-gate lifetime-based method, the factor Πc Πf βλ1 hq0 is eliminated, where the reference image is provided by the first gated image obtained immediately after a pulsed illumination. Particularly, the effect of the viewing angle is largely canceled out when the factor hMi is

4.4 Photodetector Response

83

the same for the wind-on and wind-off (reference) images. Further, to reduce the effect of the viewing angle particularly on a surface with high curvature (fuselage or the leading edge of a wing), multiple cameras viewing at different directions could be used. Such camera systems with the 360 view are developed in DLR (Engler et al. 2001b) and AEDC (Sellers 2009).

Chapter 5

Intensity-Based Methods

This chapter describes the intensity-based methods that are widely used in PSP and TSP measurements. A generic camera-based system is first described, which includes illumination sources, optical filters, digital cameras (CCD and CMOS cameras), and data acquisition and processing units. Then, a generic laser-scanning system is briefly described for PSP and TSP measurements. Furthermore, the basic data processing for the intensity-based methods is described. Uncertainty analysis of the intensity-based methods for PSP and TSP is a major topic of this chapter, including system modeling, error propagation, sensitivity coefficients, total uncertainty, elemental error sources, and measurement limits.

5.1 5.1.1

Measurement Systems Camera-Based Systems

The essential elements of a measurement system for PSP and TSP include illumination sources, optical filters, photodetectors, and data acquisition and processing units. A camera-based system is most commonly used for PSP and TSP measurements in wind tunnel testing. Figure 1.3 shows a schematic of a generic camera system. A luminescent paint (PSP or TSP) on a model surface is excited to luminescence by an illumination source such as UV lamp, LED array, or laser. This illuminating light has to be filtered optically to prevent it from projecting onto a camera sensor. The luminescent emission is further filtered optically to eliminate the illuminating light before projecting onto a camera sensor. Images (wind-on and wind-off images) are acquired and transferred to a computer for data processing. In order to correct the dark current in a camera, a dark current image is acquired when no light is incident on the camera. A ratio between the wind-on and wind-off images is taken after the dark current image is subtracted from both the images, resulting in a luminescent intensity ratio image. Using a calibration relation for the paint, the © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_5

85

86

5 Intensity-Based Methods

distribution of surface pressure or temperature is then computed from the intensity ratio image. The selection of an appropriate illumination source depends on the absorption spectrum of the luminescent paint and optical access of a specific facility. An illumination source must provide a sufficiently large number of photons in a wavelength band of absorption without saturating the luminescence and causing serious photodegradation. It is desirable to generate a reasonably uniform illumination field over a surface such that the measurement uncertainty associated with model deformation can be reduced. A continuous illumination source should be stable and a flash source should be repeatable. A variety of illumination sources are commercially available (Crites 1993). Pulsed and continuous-wave lasers with fiberoptic delivery systems were used in wind tunnel testing (Morris et al. 1993a, b; Crites 1993; Bykov et al. 1992; Volan and Alati 1991; Engler et al. 1991, 1992; Lyonnet et al. 1997). Lasers have advantages in terms of providing narrow band intense illumination. LED arrays were first developed for illuminating paints at the Air Force Research Laboratory (Dale et al. 1999), and now high-power LED illumination sources are widely used in PSP and TSP measurements (Sellers 2000, 2009; Roozeboom et al. 2016; Yorita et al. 2019). LED arrays are attractive as illumination sources since they are light in weight and they produce little heat; they can be suitably distributed to form a fairly uniform illumination field. In addition, they can be easily controlled to generate either continuous, pulsed, or modulated illumination. Other light sources reported in the literature of PSP and TSP include xenon arc lamps with blue filters (McLachlan et al. 1993a), incandescent tungsten/ halogen lamps with blue filters (Morris et al. 1993a; Dowgwillo et al. 1994), and fluorescent UV lamps (Liu et al. 1995a, b). Instead of having the illumination from the top of the paint, Klein and Schulze (2005) used light emitting surfaces of wind tunnel models for excitation of PSP beneath. Similarly, Peng et al. (2018b) used an embedded organic light-emitting diode (OLED) layer as an excitation source for PSP measurement on a moving surface. The spectral characteristics of various illumination sources can be found in The Photonics Design and Applications Handbook (1999). Optical filters are used to separate the luminescent emission from the excitation light or separate the luminescent emissions from different luminophores. There are two kinds of filters: interference filters and color glass filters. An interference filter selects a wavelength band of light through a process of constructive and destructive interference. It consists of a substrate onto which chemical layers are vacuum deposited in such a fashion that the transmission of certain wavelengths is enhanced, while other wavelengths are either reflected or absorbed. Band-pass interference filters only transmit light in a spectral band; the peak wavelength and spectral width can be tightly controlled. An edge interference filter only transmits light above (long pass) or below (short pass) a certain wavelength. Color glass filters are used for applications that do not need precise control over wavelengths and transmission intensities. A ratio of transmission to blocking is a key filter characteristic. One key characteristic of all filters is the sensitivity to the angle of incidence of incoming light. For interference filters, the peak transmission wavelength decreases as the

5.1 Measurement Systems

87

angle of incidence deviates from the normal, while the bandwidth and transmission characteristics generally remain unchanged. For color glass filters, an increase of the incident angle leads to a longer transmission path, reducing the transmission efficiency, while the cutoff wavelengths remain unchanged.

Cameras Often scientific-grade cooled-charge coupled device (CCD) digital cameras are used as imaging sensors for PSP and TSP, which can provide a high intensity resolution (12–16 bits) and high spatial resolution (typically 1024
1024, 2048
2048 up to 4008
2672 pixels). Because a scientific-grade CCD camera exhibits a good linear response and a high SNR, it is suitable to quantitative measurement of the luminescent emission (LaBelle and Garvey 1995). Less expensive consumer-grade CCD video cameras were used in early PSP and TSP measurements (Kavandi et al. 1990; Engler et al. 1991; McLachlan et al. 1992; Erickson and Gonzalez 2006). When there is a large pressure variation over a model surface, a consumer-grade video CCD camera can be used as an alternative to give acceptable quantitative results after the camera is carefully calibrated to correct the nonlinearity of the radiometric response function of the camera. The SNR can be improved by averaging a sequence of images to reduce the random noise. Note that film-based camera systems were occasionally used in special PSP measurements like flight tests (Abbitt et al. 1996). Complementary metal oxide semiconductor (CMOS) cameras are more recently used particularly in unsteady PSP and TSP measurements. CCD and CMOS image sensors are two different technologies for capturing images digitally. Each has unique strengths and weaknesses, giving advantages in different applications. Both CCD and CMOS sensors convert light into electric charge and process it into electronic signals. In a CCD sensor, every pixel’s charge is transferred through a very limited number of output nodes to be converted to voltage, buffered, and sent off-chip as an analog signal. Since all of the pixels can be devoted to light capture, the CCD output’s uniformity is high. In a CMOS sensor, each pixel has its own charge-to-voltage conversion, and the sensor often also includes amplifiers, noisecorrection, and digitization circuits, so that the chip outputs digital bits. Thus, the charge-to-voltage conversation is massively parallelized, providing large data rates for high speed applications. CMOS image sensor can be adapted for gated intensity measurements in fluorescence lifetime imaging (Franke and Holst 2015). However, with each pixel doing its own conversion, uniformity is lower. These functions increase the design complexity of each pixel and reduce the area available for collecting photons. A comparative review of CMOS and CCD was given by Magnan (2003), including discussions on the sensor architecture, quantum efficiency, and noise. CMOS sensors have intrinsic advantages such as low power consumption, readout rate, noise, radiation hardness, and integration capability. In addition, the performance of CMOS sensors for flow measurements was evaluated by Hain et al. (2002) in comparison with CCDs. It is found that CMOS cameras have a good image quality

88

5 Intensity-Based Methods

comparable to that of CCD cameras. For time-resolved data acquisition, a CMOS camera is the best choice as long as the signal strength is acceptable. The performance of a digital camera sensor is characterized by the responsivity, full-well capacity, and noise. From these quantities, the minimum signal, maximum signal, SNR, and dynamic range can be estimated (Holst 1998; Janesick 1995). The full-well capacity specifies the number of photoelectrons that a pixel can hold before charge begins to spill out, thus leading to the nonlinearity of response. Thus, the maximum signal is proportional to the full-well capacity. Normally, the well size is approximately proportional to the pixel size. Therefore, in a fixed sensor area, increasing the effective pixel size to enhance the SNR may reduce the spatial resolution. The dynamic range, defined as the maximum signal (or the full-well capacity) divided by the RMS readout noise (or noise floor), loosely describes the camera’s ability to measure both low and high light levels. These performance parameters are critical for quantitative radiometric measurements of the luminescent emission, which can be estimated based on the camera model and noise models (Holst 1998). The responsivity, i.e., the efficiency of generating electrons by a photon, is determined by the spectral quantum efficiency Rq(λ) of a photo detector (see Chap. 4). Figures 5.1 and 5.2 show the spectral quantum efficiencies for several CCD and CMOS sensors, respectively. The minimum signal is limited by the camera noises, including the photon shot noise, dark current, reset noise, amplifier noise, quantization noise, and fixed pattern noise. The photon shot noise is associated with the discrete nature of photoelectrons obeying the Poisson statistics in which the variance is equal to the mean. The dark current is due to thermally generated electrons, which can be reduced to a very low level by cooling the sensor device. The reset noise is associated with resetting the sense node capacitor that is temperature dependent. The amplifier noise contains two components: 1/f noise and white noise; a manufacturer usually provides this value and calls it the readout noise, noise equivalent electrons, or noise floor. By careful optimization of the camera electronics, the readout noise or noise floor can be reduced to as low as 4–6 electrons. The quantization noise results from the analogto-digital conversion. The fixed pattern noise (pixel-to-pixel variation) is due to differences in pixel responsivity, which is sometimes referred to as the scene noise, pixel noise, or pixel nonuniformity as well. Although various noise sources exist, for many applications, it is sufficient to consider the photon shot noise, noise floor, and fixed pattern noise associated with pixel non-uniformity. Thus, according to the Poisson statistics, the total system noise hnsysi is given by rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E
2 
2  D nshot þ nfloor þ n2pattern qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
  2 ¼ npe þ n2floor þ Unpe ,


 nsys ¼

ð5:1Þ

5.1 Measurement Systems

89

Fig. 5.1 Comparison of the quantum efficiencies for various CCD sensors: Backside illuminated (EEV 30-11 BI) with broadband AR coating and with IR AR coating, traditional poly-gates (Kodak KAF 1400), ITO gates (Kodak KAF 1401E), and ITO gates with micro-lenses (Kodak). (From Magnan 2003)

Fig. 5.2 Comparison of the quantum efficiencies for high-performance CMOS detectors from Rockwell Scientific: monolithic 0.25μ CMOS process (PROCAM product) and hybrid CMOS detectors (HiViSI product) with NIR AR coating and Blue AR coating. (From Magnan 2003)

90

5 Intensity-Based Methods

D E

 where n2shot , n2floor , and n2pattern are the variances of the photon shot noise, noise floor, and pattern noise, respectively, npe is the number of collected photoelectrons, and U is the pixel non-uniformity. Accordingly, the SNR is SNR ¼ npe =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
  2 npe þ n2floor þ Unpe :

ð5:2Þ

Figure 5.3 shows the total noise, photon shot noise, noise floor (readout noise), and fixed pattern noise of a generic sensor as a function of the number of photo
1=2 electrons for n2floor ¼ 50e and U ¼ 0.25%. For a very low photon flux, the noise floor dominates. As the incident light flux increases, the photon shot noise dominates. At a very high level of the incident light flux, the noise may be dominated by the fixed pattern noise. When the photon shot noise dominates, the SNR asymptotpffiffiffiffiffiffi ically approaches to SNR ¼ npe , and the dynamic range is (npe)max/hnfloori, where (npe)max is the full-well capacity. The dark current only affects applications where the SNR is low. In most applications of PSP and TSP, the pressure and temperature resolutions are limited by the photon shot noise.

Noise Electrons (rms)

10000

Total Noise

1000

100 Noise Floor 10

Fixed Pattern Noise Photon Shot Noise

1 10

100

1000

10000

100000

Photoelectrons Fig. 5.3 Noise curves of a generic imaging sensor for the noise floor ¼ 50e and non-uniformity U ¼ 0.25%

5.1 Measurement Systems

5.1.2

91

Laser-Scanning System

A generic laser-scanning system for PSP and TSP is shown in Fig. 5.4. A low-power laser beam focused to a small point scans over a model surface using a computercontrolled mirror to excite the paint on the model. The luminescent emission is detected using a low-noise photodetector (e.g., PMT); the photodetector signal is digitized with a high-resolution A/D converter in a PC and processed to calculate pressure or temperature based on a calibration relation for the paint. The laserscanning system for PSP and TSP measurements was discussed by Hamner et al. (1994), Burns (1995), Davies et al. (1995, 1997a, b), Torgerson et al. (1996),

Fig. 5.4 Generic laser-scanning system for PSP and TSP

92

5 Intensity-Based Methods

Torgerson (1997), Campbell et al. (1998), Lachendro (2000), Liu et al. (2002), and Pastuhoff et al. (2016). Compared to a camera-based system, a laser-scanning system could offer certain advantages in some special experiments, i.e., it is used for PSP and TSP measurements in a turbine engine where optical access is so limited that a camera-based system was difficult to use (Liu et al. 2002; Pastuhoff et al. 2016). A laser-scanning system was used for differential PSP measurement to capture small fluctuating unsteady pressure (Hayashi and Sakaue 2020). Since a low-noise PMT is used to measure the luminescent emission, before an analog output from the PMT is digitized, standard SNR enhancement techniques are available to improve the measurement accuracy. Amplification and band-limited filtering can be used to improve the SNR. The signal is then digitized with a high-resolution A/D converter (12–24 bits). Additional noise reduction can be accomplished using a lock-in amplifier when a laser beam is modulated. A laser-scanning system is able to provide steady, pulsed, or modulated illumination over a surface by scanning a single laser spot. The laser power is easily monitored and correction for a laser power drift can be made for each measurement point.

5.2

Basic Data Processing

In the intensity-based method, a key processing step for PSP and TSP evaluation is taking a ratio between a wind-on image and a wind-off reference image to correct the effects of nonhomogeneous illumination, uneven paint thickness, and nonuniform luminophore concentration. However, this ratioing procedure is complicated by model deformation generated by the aerodynamic load, resulting in misalignment between the wind-on and wind-off images. Therefore, additional correction procedures are required to reduce (or ideally eliminate) the error sources associated with model deformation, temperature effect of PSP, self-illumination, and camera noises (dark current and fixed pattern noise). The following discussions summarize various correction procedures in data reduction. Figure 5.5 shows a generic data processing flowchart for intensity-based measurements of single-luminophore PSP or TSP with a digital camera. A laser-scanning system has similar data processing procedures for intensity-based measurements. The wind-on and wind-off images are acquired using a digital camera (CCD or CMOS camera) as data images. For steady flows, a sequence of acquired images is usually averaged to reduce the random noise like the photon shot noise. The dark current image and ambient lighting image are subtracted from data images. The dark current image is usually acquired when the camera shutter is closed. In a wind tunnel environment, there is always weak ambient light that may cause a bias error in data images. The ambient lighting image is acquired when the shutter is open while all controllable light sources are turned off. The integration time for the dark current

5.2 Basic Data Processing

93

Fig. 5.5 Generic data processing flowchart for intensity-based measurements of a singleluminophore PSP or TSP

image and ambient lighting image should be the same as that for data images. The data images are then divided by a flat-field image to correct the fixed pattern noise. At a very high signal level, this correction is necessary since the fixed pattern noise may surpass the photon shot noise. Ideally, a flat-field image is acquired from a uniformly illuminated scene. An integrating sphere is a tool for the characterization of digital cameras (both CCD and CMOS) because of its ability to render a very uniform field of traceable luminance or radiance (Ducharme et al. 1997). A simple but less accurate approach is the use of several diffuse scattering glasses mounted in the front of a lens of a camera to generate an approximately uniform illumination field. When a uniform illumination field cannot be achieved, a more complex noisemodel-based approach can be used to obtain a fixed pattern noise field for a digital camera (Healey and Kondepudy 1994). In this stage, even though the noise-corrected wind-on and wind-off images are obtained, we cannot yet calculate a ratio between the wind-off image and the windon image, Vref/V, for conversion to a pressure or temperature image. This is because the wind-on image may not align with the wind-off image due to model deformation caused by aerodynamic load. A ratio between the nonaligned images can lead to a

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considerable error in calculating pressure or temperature. Also, some distinct surface pressure or temperature features associated with shock, boundary layer transition, and flow separation could be smeared. In order to solve this nonalignment problem, an image registration technique should be used to match the wind-on image to the wind-off image (Bell and McLachlan 1993, 1996; Donovan et al. 1993; Ruyten 1999). The image registration technique is based on a mathematical transformation (x0, y0) ° (x, y), which maps the deformed wind-on image coordinate (x0, y0) onto the reference wind-off image coordinate (x, y). For a small deformation, an image registration transformation is given by polynomials ðx, yÞ ¼

m X i, j¼0

0i 0 j

aij x y ,

m X

! 0i 0 j

bij x y

:

ð5:3Þ

i, j¼0

Geometrically, the constant, linear and nonlinear terms in Eq. (5.3) represent translation, rotation and stretching, and higher-order deformation of a model in the image plane, respectively. In PSP and TSP measurements, black fiducial targets are placed in locations on a model where deformation is expected. The displacements of these targets in the image plane represent the perspective projection of real model deformation in the 3D object space. From the corresponding centroids of the targets in the wind-on and wind-off images, the polynomial coefficients aij and bij in Eq. (5.3) can be determined using the least-squares method. More targets used in image registration will increase the statistical redundancy and improve the accuracy of least-squares estimation. For most wind tunnel tests, a second-order polynomial transformation (m ¼ 2) is found to be sufficient. As a pure geometric correction method, however, the image registration technique cannot take into account a variation in illumination level on a model due to model movement in a nonhomogeneous illumination field. An estimate of this error requires the knowledge of an illumination field and the movement of a model relative to the light sources. Bell and McLachlan (1993, 1996) gave an analysis of this error in a simplified circumstance and found that this error was small if an illumination light field was nearly homogeneous and model movement was small. Experiments showed that the image registration technique considerably improved the quality of PSP and TSP data (McLachlan and Bell 1995). Weaver et al. (1999) utilized spatial anomalies (dots formed from aerosol mists in spraying) in a basecoat and calculated a pixel shift vector field of a model using a spatial cross-correlation technique similar to that used in particle image velocimetry (PIV). Based on a shift vector field, the wind-on image was registered. Le Sant et al. (1997) described an automatic scheme for target recognition and image alignment. A detailed discussion on the image registration technique is given in Chap. 8. After a ratio between the wind-off image and the registered wind-on image is taken, a pressure or temperature image can be obtained using a calibration relation (the Stern–Volmer relation for PSP or the Arrhenius relation for TSP). Compared to the relatively straightforward conversion of an intensity ratio image to a temperature image from TSP images, conversion to a pressure image is more difficult since the

5.2 Basic Data Processing

95

intensity ratio image of PSP is a function of not only pressure but also temperature. The temperature effect of PSP is often a dominant contribution to the total uncertainty of PSP measurements if it is not corrected. When the Stern–Volmer coefficients A(T) and B(T ) are determined in a priori laboratory PSP calibration and the surface temperature field is known, a pressure field can be, in principle, calculated from a ratio image. The need of temperature correction provoked the development of multiple-luminophore PSP and tandem use of PSP with TSP (Nakakita et al. 2006; Peng et al. 2013). The surface temperature distribution can also be measured using infrared (IR) cameras (Henne 2004; Mitsuo et al. 2005). Furthermore, a temperature field can be given using theoretical and numerical solutions of the motion and energy equations of flows. However, experiments have shown that the use of a priori PSP calibration data for correcting the temperature effect still leads to a systematic error in the derived pressure distribution due to certain uncontrollable factors in the wind tunnel environment. To correct this systematic error, pressure tap data at a number of locations are used to correlate the intensity ratio values to pressure tap data; this procedure is referred to as in situ calibration of PSP. In the worst case where A(T ) and B(T) are not known and/or a surface temperature field is not available, in situ calibration is still able to provide a pressure field. However, the accuracy of interpretation of PSP data between pressure taps is not guaranteed. Especially, when large pressure and/or temperature gradients occur between pressure taps, the accuracy of the derived pressure field is reduced. Obviously, the selection of locations of pressure taps is critical for assure the accuracy of in situ calibration. The pressure tap data at discrete locations for in situ calibration should reasonably cover the pressure distribution on a surface of interest. The in situ calibration uncertainty of PSP will be discussed later (see Sect. 5.3). PSP and TSP data in the images should be mapped onto a surface grid of the model in the 3D object space since pressure and temperature fields on the surface grid are more useful for researchers. Further, this mapping is necessary for the extraction of aerodynamic load and precise comparison with CFD results. In the literature of PSP and TSP, this mapping procedure, including camera orientation/ calibration, is often called image resection. Note that the meaning of resection in the PSP and TSP literature is somewhat broader and looser than its strict definition in photogrammetry. From the standpoint of photogrammetry, a key of this procedure is the geometric camera calibration by solving the perspective collinearity equations to determine the camera interior and exterior orientation parameters, and lens distortion parameters. Once these parameters in the collinearity equations relating the 3D object space to the image plane are known, PSP and TSP data in images can be mapped onto a given surface grid in the 3D object space. A detailed discussion on analytical photogrammetric techniques is given in Chap. 8. In most PSP and TSP measurements, data in images are mapped onto a rigid CFD or CAD surface grid of a model. However, when a model has significant aeroelastic deformation in wind tunnel testing, mapping onto a rigid grid misrepresents true pressure and temperature fields. Therefore, a surface grid representing the deformed model should be generated for PSP and TSP mapping. Liu et al. (1999, 2012) discussed the generation of a deformed surface grid based on videogrammetric model deformation measurements

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5 Intensity-Based Methods

conducted along with PSP and TSP measurements (see Chap. 8). Finally, the integrated aerodynamic forces and moments of a model can be calculated from a surface pressure distribution. For example, the lift is given by FL ¼ ∑ pi(n  lLΔS)i, where n is the unit normal vector of a panel on the surface, ΔS is the area of the panel, and lL is the unit vector of the lift. The self-illumination correction is sometimes required after the luminescent intensity data are mapped on a surface grid in the 3D object space. The selfillumination is a phenomenon that the luminescent emission from one part of a model surface illuminates another part of the surface, thus increasing the observed luminescent intensity of the receiving surface and producing an additional error in calculation of pressure or temperature. This effect often occurs on the surfaces of neighboring components such as wing/body junctures and concave surfaces. The self-illumination depends on the surface geometry, the luminescent field, and the reflecting properties of a paint layer. Assuming that a paint surface is Lambertian, Ruyten (1997a, b, 2001) developed an analytical model and a numerical scheme for correcting the self-illumination effect. The self-illumination correction scheme is discussed in Chap. 8. The original purpose of developing two-luminophore PSPs is to provide simultaneously a non-pressure-sensitive reference image. The dependency of a two-color intensity ratio I λ1 =I λ2 on pressure p and temperature T is generally expressed as I λ1 =I λ2 ¼ f ðp, T Þ , where I λ1 and I λ2 are the luminescent intensities of a probe luminophore and a reference luminophore at the emission wavelengths λ1 and λ2, respectively. Ideally, a two-color intensity ratio can eliminate instantaneously the effect of spatially nonuniform illumination on a surface. However, since two luminophores cannot be perfectly mixed, a simple two-color intensity ratio I λ1 =I λ2 cannot completely compensate the effect of nonhomogeneous dye concentration. In this case, a ratio of ratios R/R0 should be used to correct the effects of nonhomogeneous dye concentration and paint thickness variation, where R ¼ I λ1 =I λ2 , R0 ¼ ðI λ1 =I λ2 Þ0, and the subscript 0 denotes the wind-off reference condition (McLean 1998; Peng et al. 2013). Since the wind-off images are required, the ratioof-ratios method still needs image registration. The ratio-of-ratios approach was applied to a moving model (Subramanian et al. 2002). Further, Sakaue et al. (2013a, 2016) and Hayashi et al. (2019) developed a motion-capturing method for imaging a two-color PSP-coated moving surface with a high-speed color camera that acquires both pressure and temperature images simultaneously. In addition, when the temperature dependencies of the probe and reference luminophores are approximately the same in a certain temperature range, a two-color intensity ratio between these luminophores has a weak temperature dependency such that the temperature effect of PSP could be compensated.

5.3 Pressure Uncertainty

5.3 5.3.1

97

Pressure Uncertainty System Modeling

Uncertainty analysis is needed in order to establish PSP as a quantitative measurement technique. Based on the Stern–Volmer relation, Sajben (1993) investigated error sources contributing to the uncertainty of PSP measurement and found that the uncertainty strongly depended on flow conditions and surface temperature significantly affected the final results. Oglesby et al. (1995a) presented an analysis of an intrinsic limit of the Stern–Volmer relation to the achievable sensitivity and accuracy. Mendoza (1997a, b) studied CCD camera noise and its effect on PSP measurements and suggested the limiting Mach number for quantitative PSP measurements. From a standpoint of system modeling, Liu et al. (2001a) gave a general and comprehensive uncertainty analysis for PSP. The following uncertainty analysis focuses on the intensity-ratio method widely used in PSP measurements. From Eqs. (4.24) and (4.25), air pressure p can be generally expressed in terms of system’s outputs and other variables p ¼ U1

V ref ð t, xÞ pref AðT Þpref  : BðT Þ V ð t 0 , x0 Þ B ð T Þ

ð5:4Þ

The factor U1 in Eq. (5.4) is defined as U1 ¼

Πc

Πf

Πc ref Π

f ref

hðx0 Þ cðx0 Þ q0 ð t 0 , X0 Þ , href ðxÞ cref ðxÞ q0 ref ðt, X Þ

where x ¼ (x, y)T and x0 ¼ (x0, y0)T are the coordinates in the wind-off and wind-on images, respectively, X ¼ (X, Y, Z )T and X0 ¼ (X0, Y0, Z0)T are the object space coordinates in the wind-off and wind-on cases, respectively, and t and t0 are the instants at which the wind-off and wind-on images are taken, respectively. Here, the paint thickness h and dye concentration c are expressed as a function of the image coordinate x rather than the object space coordinate X since the image registration error is more easily treated in the image plane. In fact, x and X are related through the perspective transformation (the collinearity equations). In order to separate complicated coupling between the temporal and spatial variations of these variables, some terms in Eq. (5.4) can be further decomposed when a small model deformation and a short time interval are considered. The windon image coordinates can be expressed as a superposition of the wind-off image coordinates and an image displacement vector Δx, i.e., x0 ¼ x + Δx. Similarly, the temporal decomposition is t0 ¼ t + Δt, where Δt is a time interval between the instants at which the wind-off and wind-on images are taken. If Δx and Δt are small, a ratio between the wind-off and wind-on images can be separated into two factors,

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5 Intensity-Based Methods

V ref ðt, xÞ=V ðt 0 , x0 Þ  Dt ðΔt ÞDx ðΔxÞV ref ðt, xÞ=V ðt, xÞ, where the factors are defined as Dt ð Δt Þ ¼ 1  ð∂V=∂t ÞðΔt Þ=V,

Dx ðΔxÞ ¼ 1  ð∇V Þ  ðΔxÞ=V,

representing the effects of the temporal and spatial changes of the luminescent intensity, respectively. The temporal change of the luminescent intensity is mainly caused by photodegradation and sedimentation of dust and oil droplets on a surface. The spatial intensity change is due to model deformation generated by aerodynamic load. In the same fashion, the excitation light flux can be written as Dq0 ðΔt Þq0 ðt, X0 Þ=q0 ref ðt, X Þ, where Dq0( Δt) ¼ 1 + (∂ q0/∂ t)(Δt)/q0 ref is a factor representing the temporal variation in the excitation light flux. The use of the above estimates yields the generalized Stern–Volmer relation p ¼ U2

V ref ð t, xÞ pref AðT Þpref  , BðT Þ V ðt, xÞ BðT Þ

ð5:5Þ

where the factor U2 is defined as U 2 ¼ Dt ðΔt ÞDx ðΔxÞDq0 ðΔt Þ

Πc

Πf

Πc ref Π

f ref

hðx0 Þ cðx0 Þ q0 ð t, X0 Þ : href ðxÞ cref ðxÞ q0 ref ðt, X Þ

In an ideal case, without any model motion (x0 ¼ x and X0 ¼ X) and temporal illumination fluctuation, the factor U2 is unity and then Eq. (5.5) recovers the generic Stern–Volmer relation. Equation (5.5) is a general relation that includes the effects of model deformation, spectral variability, and temporal variations in both illumination and luminescence, which allows a complete uncertainty analysis and a clear understanding of how these variables contribute to the total uncertainty in PSP measurements.

5.3.2

Error Propagation, Sensitivity, and Total Uncertainty

According to the general uncertainty analysis formalism (Ronen 1988; Bevington and Robinson 1992), the total uncertainty of pressure p is described by the error propagation equation

5.3 Pressure Uncertainty

  1=2 M varðζ i Þ var ζ j var ðpÞ X ¼ Si S j ρij , ζi ζ j p2 i, j¼1

99

ð5:6Þ

where ρij ¼ cov ( ζ iζ j)/[var(ζ i) var (ζ j)]1/2 is the correlation coefficient between the variables ζ i and ζ j, var(ζ i) ¼ hΔζ i2i and cov(ζ iζ j) ¼ hΔζ iΔζ ji are the variance and covariance, respectively, and the notation hi denotes the statistical ensemble average. Here, the variables {ζ i, i ¼ 1, . . ., M} denote a set of the parameters Dt(Δt), Dx(Δx), Dq0(Δt), V, Vref, Πc/Πc ref, Πf/Πf ref, h/href, c/cref, q0/q0 ref, pref, T, A, and B in Eq. (5.5). The sensitivity coefficients Si are defined as Si ¼ (ζ i/p)(∂p/∂ζ i). Equation (5.6) becomes particularly simple when the cross-correlation coefficients between the variables vanish (ρij ¼ 0, i 6¼ j). Table 5.1 lists the sensitivity coefficients, the elemental errors, and their physical origins. Many sensitivity coefficients are proportional to a factor ϕ ¼ 1 + [A(T )/B(T )]/( p/pref). Consider a typical PSP: bathophen ruthenium chloride [Ru(ph2-phen) or Ru(dpp)] in GE RTV 118 mixed with silica-gel particles, which is referred to as Bath Ruth + silica-gel in GE RTV 118. For Bath Ruth + silica-gel in GE RTV 118, Fig. 5.6 shows the factor 1 + [A(T )/B(T )]/( p/pref) as a function of p/pref for different temperatures, which is only slightly changed by temperature. The temperature sensitivity coefficient is defined as ST ¼ ðdp=dT ÞðT=pÞ ¼ T ½B0 ðT Þ þ A0 ðT Þpref =p=BðT Þ, where the prime denotes differentiation with respect to temperature. Figure 5.7 shows the absolute value of ST as a function of p/pref at different temperatures. After the elemental errors in Table 5.1 are evaluated, the total uncertainty in pressure can be readily calculated using Eq. (5.6). The major elemental error sources are discussed below.

5.3.3

Photodetector Noise and Limiting Pressure Resolution

The uncertainties in the outputs V and Vref from a photodetector (e.g., camera) are contributed from a number of noise sources in the detector such as the photon shot noise, dark current shot noise, amplifier noise, quantization noise, and pattern noise. When the dark current and pattern noise are subtracted and the noise floor is negligible, the detector is photon-shot-noise-limited. In this case, the SNR of the detector is SNR ¼ (V/GħνBd)1/2, where ħ is Planck’s constant, ν is the frequency, Bd is the electrical bandwidth of the detection electronics, G is system’s gain, and V is the detector output. The uncertainties in the outputs are expressed by the variances var(V ) ¼ VGħνBd and var(Vref) ¼ VrefGħνBd. In the photon-shot-noise-limited case in which the error propagation equation contains only two terms related to V and Vref, the pressure uncertainty is

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5 Intensity-Based Methods

Table 5.1 Sensitivity coefficients, elemental errors, and total uncertainty of PSP

1

Variable ζi Dt(Δt)

Sensi. coef. Si φ

2

Dx(Δx)

φ

3

Dq0(Δt)

φ

[(∂ q0/∂t)(Δt)/q0 ref]2

4 5 6

Vref V Πc/Πc ref

φ φ φ

VrefGħνBd VGħνBd [R2/(R1 + R2)]2 (ΔR1/R1)2

7

Πf/Πf ref

φ

var(Πf/Πf ref)

8

h/href

φ

9

c/cref

φ

10

q0/q0 ref

φ

(q0 ref)2| (∇q0)  (ΔX) |2

11

pref

1

var( p)

12 13 14 15

T A B Pressure mapping

ST 1φ 1 1

var( T ) var( A) var( B)

Total uncertainty in pressure

Elemental variance var( ζ i) [(∂V/∂ t)(Δt)/V]2 h

i 2 2 ð∂V=∂xÞ σ 2x þ ð∂V=∂ yÞ σ 2y V 2

h

i 2 2 ð∂h=∂xÞ σ 2x þ ð∂ h=∂yÞ σ 2y h2 ref

h

i 2 2 ð∂c=∂xÞ σ 2x þ ð∂c=∂yÞ σ 2y c2 ref

2

2

ð∂p=∂xÞ σ 2x þ ð∂p=∂yÞ σ 2y and |(∇p)surf  (ΔX)surf |2 var ðpÞ=p2 ¼

PM

Physical origin Temporal variation in luminescence due to photodegradation and surface contamination Image registration errors for correcting luminescence variation due to model motion Temporal variation in illumination Photodetector noise Photodetector noise Change in camera performance parameters due to model motion Illumination spectral variability and filter spectral leakage Image registration errors for correcting thickness variation due to model motion Image registration errors for correcting concentration variation due to model motion Illumination variation on model surface due to model motion Error in measurement of reference pressure Temperature effect of PSP Paint calibration error Paint calibration error Errors in camera calibration and pressure mapping on a surface of a presumed rigid body

2 2 i¼1 Si varð ζ i Þ=ζ i

Note: (1) σ x and σ y are the standard deviations of least-squares estimation in the image registration or camera calibration. (2) The factors for the sensitivity coefficient are defined as φ ¼ 1 + [A(T )/B(T )]( pref/p) and ST ¼  [T/B(T )][B0(T ) + A0(T )( pref/p)].

Δp ¼ p



G Bd ħν V ref



1=2  1=2 AðT Þ pref p 1þ , 1 þ AðT Þ þ BðT Þ pref BðT Þ p

ð5:7Þ

which is valid for both digital cameras and non-imaging detectors. For a digital camera, the first factor in the right-hand side of Eq. (5.7) can be simply expressed by the total number of photoelectrons collected over an integration time (/1/Bd), i.e., npe ¼ V/(GħνBd). When the full-well capacity of a camera is

5.3 Pressure Uncertainty

101

3.0 T = 293 K T = 313 K T = 333 K

1 + (A(T)/B(T))(Pref/P)

2.5

2.0

1.5

1.0

0.5 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref Fig. 5.6 The sensitivity factor 1 + [A(T )/B(T )]/( p/pref) as a function of p/pref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. (From Liu et al. 2001a)

achieved, we obtain the minimum pressure difference that PSP can measure from a single frame of image, i.e.,   1=2 ðΔpÞmin AðT Þ pref 1 p , ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ A ð T Þ þ B ð T Þ 1 þ  pref p BðT Þ p npe ref max

ð5:8Þ

where (npe ref)max is the full-well capacity of a camera in a reference condition. When N images are averaged, the limiting pressure difference given by Eq. (5.8) is further reduced by a factor N1/2. Equation (5.8) provides an estimate for the noise-equivalent pressure resolution for a digital camera without the application of any data reduction method such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) (see Sect. 8.8 in Chap. 8). When (npe ref)max is 500,000 electrons for a camera, for Bath Ruth + silica-gel in GE RTV 118, the minimum pressure uncertainty (Δp)min/p is shown in Fig. 5.8 as a function of p/pref at different temperatures, indicating that an temperature qincreased ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   ffi degrades the limiting pressure resolution. Figure 5.9 shows npe ref max ðΔpÞmin =p as a function of p/pref for different values of the Stern–Volmer coefficient B(T). Clearly, a larger B(T) leads toffi a smaller limiting pressure uncertainty (Δp)min/p. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Figure 5.10 shows npe ref max ðΔpÞmin =p as a function of the Stern–Volmer coefficient B(T) for different values of p/pref. There is no optimal value of B in this case.

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5 Intensity-Based Methods

10 9

T = 293 K T = 313 K T = 333 K

|(dP/dT)(T/P)|

8 7 6 5 4 3 2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref Fig. 5.7 The temperature sensitivity coefficient as a function of p/pref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. (From Liu et al. 2001a)

5.3.4

Errors Induced by Model Deformation

Model deformation generated by aerodynamic load causes a displacement Δx ¼ x0  x of a wind-on image relative to a wind-off image. This displacement leads to the deviations of the quantities Dx(Δx), h/href, c/cref, and q0/q0 ref in Eq. (5.4) from unity because the distributions of the luminescent intensity, paint thickness, dye concentration, and illumination level are not spatially homogeneous on a surface. After the image registration technique is applied to re-align the wind-on and wind-off images, the estimated variances of these quantities are var½Dx ðΔxÞ  W ðV Þ=V 2 , varðh=href Þ  W ðhÞ=ðhref Þ2 , varðc=cref Þ  W ðcÞ=ðcref Þ2 : 2

2

The operator W() is defined as W ðÞ ¼ ð∂=∂xÞ σ 2x þ ð∂=∂yÞ σ 2y, where σ x and σ y are the standard deviations of least-squares estimation for image registration.

Minimum pressure uncertainty (%)

5.3 Pressure Uncertainty

103

0.40

0.36

0.32 T = 333 K T = 313 K

0.28

T = 293 K

0.24

0.20 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

P/Pref Fig. 5.8 The minimum pressure uncertainty (Δp)min/p as a function of p/pref at different temperatures for Bath Ruth + silica-gel in GE RTV 118. (From Liu et al. 2001a)

The uncertainty in q0(X)/q0 ref(X0) is caused by a change in the illumination intensity on a model surface after the model moves with respect to the light sources. When a point on the model surface travels along a displacement vector ΔX ¼ X0  X in the object space, the variance of q0/q0 ref is estimated by var½q0 ðX Þ=q0 ref ðX 0 Þ  ðq0 ref Þ2 j ð∇q0 Þ  ðΔXÞ j2 : Consider a point light source with unit strength that has a light flux distribution q0(X  Xs) ¼ |X  Xs|n, where n is an exponent (normally n ¼ 2) and |X  Xs| is the distance between the point X on the model surface and the light source location Xs. Thus, the variance of q0/q0 ref for a single point light source is var½q0 ðX Þ=q0 ref ðX 0 Þ ¼ n2 jX  Xs j4 j ðX  Xs Þ  ðΔXÞ j2 : The variance for multiple point light sources can be obtained using the principle of superposition. In addition, model deformation leads to a small change in the distance between the model surface and the camera lens. The uncertainty in the camera performance parameters due to this change is given by

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5 Intensity-Based Methods

7

(DP)min/P [(npe ref)max]

1/2

6 5 B = 0.5 4 0.6 3

0.7 0.8

2

0.9

1 0.0

0.5

1.0

1.5

2.0

P/Pref Fig. 5.9 The normalized minimum pressure uncertainty

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   npe ref max ðΔpÞmin =p as a function of

p/pref for different values of the Stern–Volmer coefficient B(T ). (From Liu et al. 2001a)

varðΠc =Πc ref Þ  ½R2 =ðR1 þ R2 Þ2 ðΔR1 =R1 Þ2 , where R1 is the distance between the lens and model surface and R2 is the distance between the lens and sensor. For R1  R2, this error is very small.

5.3.5

Temperature Effect

Since the luminescent intensity of PSP is intrinsically temperature dependent, a temperature change on a model surface during a wind tunnel run results in a significant bias error in PSP measurements if the temperature effect is not corrected. In addition, temperature influences the total uncertainty of PSP measurements through the sensitivity coefficients of the relevant variables in the error propagation equation. Hence, the surface temperature on a model surface must be known in order to correct the temperature effect of PSP. In general, a surface temperature

5.3 Pressure Uncertainty

105

20 P/Pref = 0.2

(DP)min/P [(npe ref)max]

1/2

0.5 15

1.0

1.5

10

2.0 5

0.0

0.2

0.4

0.6

0.8

1.0

B Fig. 5.10 The normalized minimum pressure uncertainty

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi   npe ref max ðΔpÞmin =p as a function of

the Stern–Volmer coefficient B for different values of p/pref. From Liu et al. (2001a)

distribution can be measured experimentally using TSP or IR camera and determined numerically by solving the motion and energy equations of flows coupled with the heat conduction equation for a model. For a compressible boundary layer on an adiabatic wall, the adiabatic wall temperature Taw can be estimated using a simple relation   1 T aw =T 0 ¼ 1 þ r ðγ  1ÞM 2 =2 1 þ ðγ  1ÞM 2 =2 , where r is the recovery factor for the boundary layer, T0 is the total temperature, M is the local Mach number, and γ is the specific heat ratio. In real measurements where a model surface is not adiabatic, the temperature of a PSP layer is related to model material due to heat conduction to a model. The effect of temperature on PSP could be reduced by selecting a suitable material of a model and the coating thickness (Egami et al. 2013b).

106

5.3.6

5 Intensity-Based Methods

Calibration Errors

The uncertainties in determining the Stern–Volmer coefficients A(T ) and B(T) are calibration errors. In an a priori PSP calibration in a pressure chamber, the uncertainty is represented by the standard deviation of data collected in replication tests. Because tests in a pressure chamber are well controlled, a priori calibration results usually show a small precision error. However, a significant bias error is found when a priori calibration results are directly used in data reduction for wind tunnel testing due to unknown surface temperature distribution and uncontrollable testing environmental factors. In contrast, in situ calibration utilizes pressure tap data on a model surface to determine the Stern–Volmer coefficients or the coefficients in a polynomial calibration relation. Because in situ calibration correlates the luminescent intensity with pressure tap data, it can reduce the bias errors associated with the temperature effect and other sources, achieving a better agreement with pressure tap data. The in situ calibration uncertainty, which is usually represented as a fitting error, will be discussed later.

5.3.7

Temporal Variations

In PSP measurements in steady flows, a temporal change in the luminescent intensity mainly results from photodegradation and sedimentation of dusts and oil droplets on a model surface. The photodegradation of PSP may occur when there is a considerable exposure of PSP to the strong excitation light between the wind-off and wind-on measurements. Dust and oil droplets in air sediment on a model surface during windtunnel runs; the resulting dust/oil layer absorbs both the excitation light and luminescent emission on a surface and thus causes a decrease of the detected luminescent intensity. The uncertainty in Dt(Δt) due to photodegradation and sedimentation can be collectively characterized by the variance var[Dt( Δt)]  [(∂V/∂t)(Δt)/V]2. Similarly, the uncertainty in Dq0(Δt), which is produced by an unstable excitation light source, is described by var[Dq0( Δt)]  [(∂q0/∂ t)(Δt)/q0 ref]2 (Possolo and Maier 1998).

5.3.8

Spectral Variability and Filter Leakage

The uncertainty in Πf/Πf ref is mainly attributed to the spectral variability of illumination lights and spectral leaking of optical filters. Possolo and Maier (1998) observed the spectral variability between flashes of a xenon lamp; the uncertainties in the absolute pressure and pressure coefficient due to the flash spectral variability were 0.05 psi and 0.01, respectively. If optical filters are not selected appropriately, a small portion of photons from the excitation light and ambient light may reach a

5.3 Pressure Uncertainty

107

detector through the filters, producing an additional output to the luminescent signal. Gongora-Orozco et al. (2009) also studied effects of filters on the performance and characteristics of PSP.

5.3.9

Pressure Mapping Errors

The uncertainty in pressure mapping is related to the data reduction procedure in which PSP data in the image plane are mapped onto a surface grid of a model in the object space. It is contributed from the errors in camera resection/calibration and mapping onto a surface grid of a presumed rigid body. The camera resection/ calibration error is represented by the standard deviations σ x and σ y of calculated target coordinates in the object space from measured target coordinates in the image plane. Typically, a good camera resection/calibration method gives the standard deviation of about 0.04 pixels in the image plane. For a given PSP image, the pressure variance induced by the camera resection/calibration error is given by 2 2 varðpÞ  ð∂p=∂ xÞ σ 2x þ ð∂p=∂ yÞ σ 2y . Ruyten (2008) developed a method to estimate the pixel-based uncertainties contributed by the mapping error and pressure interpolation error on a surface. The pressure mapping onto a presumably non-deformed model surface grid leads to another deformation-related error because a model may have considerable deformation generated by the aerodynamic load in wind tunnel testing. When a point on a model surface moves by ΔX ¼ X0  X in the object space, the pressure variance induced by mapping onto a presumed rigid body grid without correcting the model deformation is given by var( p) ¼ | (∇p)surf  (ΔX)surf |2, where (∇p)surf is the pressure gradient on a surface and (ΔX)surf is the component of the displacement vector ΔX projected on the surface in the object space. To eliminate this error, a deformed surface grid should be generated for PSP mapping based on optical model deformation measurements under the same testing conditions (Liu et al. 1999).

5.3.10 Paint Intrusiveness A PSP coating may slightly modify the overall shape of a model and produces local surface roughness and topological patterns. These unwanted changes in model geometry may alter near-wall flows over a model and affect the integrated aerodynamic force (Engler et al. 1991; Sellers 1998a; Amer et al. 2001, 2003). Hence, this paint intrusiveness to flow should be considered as an error source in PSP measurements. The effects of a paint coating on surface pressure and skin friction are directly associated with locally changed flow structures and propagation of induced perturbations in flow; these local effects may collectively alter the integrated aerodynamic force. When a local paint thickness variation is much smaller than the boundary layer

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5 Intensity-Based Methods

displacement thickness, a thin coating does not alter the inviscid outer flow. Instead of directly altering the outer flow, a rough coating may indirectly result in a local pressure change by thickening the boundary layer; coating roughness may reduce the momentum of the boundary layer to cause early flow separation at certain positions. Therefore, the effective aerodynamic shape of a model is changed and as a result the pressure distribution on a model is modified; this effect is mostly appreciable near the trailing edge due to the substantial development of the boundary layer on a surface. Vanhoutte et al. (2000) observed an increment in the trailing edge pressure coefficient relative to the unpainted model, which was consistent with an increase in the boundary layer thickness at the trailing edge. For certain models such as high-lift models, a coating may change a gap between the main wing and slat or flap; thus, a pressure distribution on a model is locally influenced. In addition, a coating may influence laminar separation bubbles near the leading edge at low Reynolds numbers and high angles-of-attack. The perturbations induced by a rough coating near the leading edge may enhance mixing that entrains high-momentum fluid from the outer flow into the separated flow region. The perturbations could be amplified by several flow instability mechanisms such as the Kelvin-Helmholtz instability in a shear layer between the outer flow and separated region and the cross-flow instability near the attachment line on a swept wing. Consequently, the coating causes the laminar separation bubbles to be suppressed. Vanhoutte et al. (2000) reported this effect that led to a drag reduction. Schairer et al. (1998a, 2002) observed that a rough coating on the slats slightly decreased the stall angle of a high-lift wing. Also, they found that the empirical criteria for “hydraulic smoothness” and “admissible roughness” based on 2D data given by Schlichting (1979) were not sufficient to provide a satisfactory explanation for their observation. Indeed, in 3D complex flows on the high-lift model, the effect of the coating on the cross-flow instability and its interactions with the boundary layer and other shear layers such wakes and jets are not well understood. Schairer et al. (1998a, 2002) and Mébarki et al. (1999) found that a rough coating moved a shock wave upstream and the pressure distribution was shifted near the shock location. This change might be caused by the interaction between the shock and the incoming boundary layer affected by the coating. In an attached flow at high Reynolds numbers, a rough coating increases skin friction by triggering premature laminar-turbulent transition and increasing the turbulent intensity in a turbulent boundary layer (Mébarki et al. 1999; Vanhoutte et al. 2000). An increase in drag due to a rough coating was observed in airfoil tests in high subsonic flows (Vanhoutte et al. 2000). Amer et al. (2001, 2003) reported that a very smooth coating on the upper surface of a delta wing model at Mach 0.2 and a semi-span arrow-wing model at Mach 2.4 did not significantly change the drag coefficients of these models. Uncertainties of surface pressure, skin friction, and aerodynamic force were investigated by Liu et al. (2020) in CFD simulations at Mach 0.75 for an NLF airfoil with small deviations on the upper surface due to the addition of the PSP thickness. It was found that the small geometric shape alteration of the airfoil due to the paint thickness could lead to an increase of flow compressibility, which in turn caused a

5.3 Pressure Uncertainty

109

slight pressure increase ahead of the shock. The geometrical uncertainty could lead to errors of the measured results to some extent. The pressure coefficient had an error of 0.6%, and the lift coefficient had an error of 3.8%.

5.3.11 Other Error Sources and Limitations Other error sources could contribute to the measurement uncertainty of PSP depending on a specific application. The self-illumination is a potential error source, which is a result of changing the observed luminescent intensity at a point by superposing all the rays reflected from other points (Ruyten 1997a, b, 2001; Le Sant 2001b). The self-illumination effect on the calculation of pressure and temperature will be discussed in Chap. 8. Humidity could affect the response of fast PSP. Kameda et al. (2015) investigated the effect of humidity on the emission characteristic of AA-PSP. Although the normalized intensity I/Iref increases as the relative humidity increases, the pressure sensitivity is constant irrespective of temperature and relative humidity within the experimental range measured by Kameda et al. (2015). Also, the temperature sensitivity at constant pressure and relative humidity remains constant irrespective of relative humidity. The spatial resolution of PSP is limited by the oxygen diffusion in the lateral direction along a paint surface. Quinn et al. (2011) noticed an effect of the substrate on PSP. Considering a pressure jump across a point on a surface (a normal shock wave), Mosharov et al. (1997) gave a solution of the diffusion equation describing a distribution of the oxygen concentration in a PSP layer near a pressure jump point. According to this solution, the limiting spatial resolution is about five times of the paint layer thickness.

5.3.12 Allowable Upper Bounds of Elemental Errors In the design of PSP experiments, we need to give the allowable upper bounds of the elemental errors for the required pressure accuracy. This is an optimization problem subject to certain constraints. In matrix notations, Eq. (5.6) is expressed as σ 2P ¼ σ T A σ , where the notations are defined as σ 2P ¼ var ðpÞ=p2 , Aij ¼ Si Sjρi j, and σi ¼ [var( ζi)]1/2/ζi. For the required pressure uncertainty σ P, a vector σ up is sought to maximize an objective function H ¼ WT σ, where W is the weighting vector. The vector σ up gives the upper bounds of the elemental errors for the given pressure uncertainty  2 σ P. ΤThe use of the Lagrange multiplier method requires H ¼ Τ W σ þ λ σ P  σ Aσ to be maximal, where λ is a Lagrange multiplier. The solution to this optimization problem gives the upper bounds

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5 Intensity-Based Methods

σ up ¼ 

A1 W W Τ A1 W

1=2 σ P :

ð5:9Þ

For the uncorrelated variables with ρij ¼ 0 (i 6¼ j), Eq. (5.9) reduces to X

ðσ i Þup ¼ S2 i W i σP

!1=2 2 S2 k Wk

:

ð5:10Þ

k

When the weighting factors Wi equal the absolute values of the sensitivity coefficients |Si|, the upper bounds can be expressed in a very simple form 1=2

ðσ i Þup =σ P ¼ N V

j Si j1

ði ¼ 1, 2, . . . , N V Þ,

ð5:11Þ

where NV is the total number of the variables or the elemental error sources. The relation Eq. (5.11) clearly indicates that the allowable upper bounds of the elemental uncertainties are inversely proportional to the sensitivity coefficients and the square root of the total number of the elemental error sources. Figure 5.11 shows a distribution of the upper bounds of 15 variables for Bath Ruth + silica-gel in GE RTV 118 for p/pref ¼ 0.8 and T ¼ 293 K. Clearly, the allowable upper bound for temperature is much lower than others, and therefore the temperature effect of PSP must be tightly controlled to achieve the required pressure accuracy.

1.8 1.6 1.4 1.2

(σ i )up

1.0

σP

0.8

1

Dt (Δt )

9

c / c ref

2

D x (Δx )

10

q0 /q0 ref

3

Dq0 (Δt )

11

Pref

4

V Vref

12 13

T A

B

5

0.6

6

Π c /Π c ref

14

7

Π f /Π f ref

15 Pressure mapping

8

h / href

0.4 0.2 0.0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Variable Index

Fig. 5.11 Allowable upper bounds of 15 variables for Bath Ruth + silica-gel in GE RTV 118 at p/pref ¼ 0.8 and T ¼ 293 K. (From Liu et al. 2001a)

5.3 Pressure Uncertainty

111

5.3.13 Uncertainties of Integrated Forces and Moments The uncertainties of the integrated aerodynamic forces and moments can be estimated based on their definitions. For example, the uncertainty in the lift is ΔF L =F L ¼F 1 L F 1 L

h

Δ∯pðn  lL ÞdS

i2 1=2 ð5:12Þ

XX
1=2 ðn  lL ΔSÞi ðn  lL ΔSÞ j Δ pi Δ p j ,

where n is the unit normal vector of a surface panel, ΔS is the area of the surface panel, and lL is the unit vector of the lift. The correlation between the pressure differences at the panel “i” and panel “j” is simply modeled by hΔpiΔpji ¼ δijhΔpiihΔpji, where the Kronecker delta is δij ¼ 1 for i ¼ j and δij ¼ 0 for i 6¼ j. Thus, the uncertainty in the lift can be estimated based on the PSP uncertainty at all the surface panels, i.e., ΔF L =F L 

N X

!1=2 ðn 

lL ΔSÞ2i ðpi =F L Þ2 ðΔp=pÞ2PSP i

:

ð5:13Þ

i¼1

Similarly, the uncertainties in the pressure-induced drag and pitching moment are estimated by ΔF D =F D 

N X

!1=2 ðn  lD ΔSÞ2i ðpi =F D Þ2 ðΔp=pÞ2PSP i

ð5:14Þ

,

i¼1

ΔM c =M c 

N X

!1=2 ½n
ðX 

X m c ÞΔS2i ðpi =M c Þ2 ðΔp=pÞ2PSP i

,

ð5:15Þ

i¼1

where lD is the unit vector of the drag and Xmc is the assigned moment center. In general, the errors in the three aerodynamic forces and three moments of a model in a 3D space are contributed by the surface pressure error. Note that the drag error also depends on skin friction significantly. Considering an inverse problem, Ruyten and Bell (2010) assumed that a surface pressure error distribution (the gap distribution) could be expressed as a linear superposition of the aerodynamic force and moment errors with the coefficients called the base functions depending on the surface geometry only. Then, the base functions were determined by an optimization method to minimize a mean square difference of the aerodynamic forces and moments between PSP and force balance data. Thus, the determined gap distribution was used to improve PSP data.

112

5 Intensity-Based Methods

5.3.14 In Situ Calibration Uncertainty Experiments The use of a priori PSP calibration in large wind tunnels often leads to a considerable systematic error since a surface temperature distribution is not known and an illumination change on a surface due to model deformation cannot be completely corrected by the image registration technique. The systematic error is also related to uncontrollable testing environmental factors. Therefore, in actual PSP measurements, experimental aerodynamicists calibrate PSP in situ by fitting (or correlating) the luminescent intensity to pressure tap data at suitably distributed locations. In a certain sense, in situ PSP calibration eliminates a systematic error associated with the temperature effect and the illumination change by absorbing it into an overall fitting error. Kammeyer et al. (2002a, b) assessed the accuracy of a production PSP system by a statistical analysis of the comparison between PSP and pressure tap data over a large number of data points. The PSP system was a typical intensity-based system that uses eight CCD (1024
1024 or 512
512) cameras for imaging, thirty lamps for illumination, and two IR cameras measuring surface temperature for correcting the temperature effect of PSP. The test article was a 1/12th-scale model of the Cessna Citation that was instrumented with a total of 225 pressure taps. The tests were conducted in the DNW/NLR HST wind tunnel, a variable-density closed continuous tunnel with slotted top and bottom test section walls (12% open). The test section was 6.56 ft (2 m) wide, and it was configured to be 5.25 ft (1.6 m) high. The cameras and lamps were mounted on the floor and ceiling. A run consisted of a lift polar at each of several Mach numbers from 0.22 to 0.82. Tests were conducted at two Reynolds numbers, 4.5 and 8.3 million. Fourteen angles of attack were set from 4 to 10 . Over 8300 visual images and over 2000 IR images were obtained for 676 test points. The wind-off reference images were acquired after the run when the fan had stopped in order to reduce the effect of the model temperature distribution. Figure 5.12 shows a typical pressure distribution on the model obtained by PSP. In situ PSP calibrations were performed by utilizing 78 of 225 pressure taps for each of the cameras. Figure 5.13 shows the variation of the in situ calibration slope (i.e., the Stern–Volmer coefficient B) as a function of test point throughout the tests, where no temperature correction was applied. The variation does not show an overall trend; the repeating pattern mirrors the pattern of the test conditions, wherein sequential angles of attack were run for sequentially increasing Mach numbers. The mean value of the slope is close to one, which is approximately consistent with the paint characteristics given by a priori calibration. The scatter is attributed to a number of factors, including nonhomogeneous temperature distributions, temperature differences between the wind-off and wind-on conditions, lamp intensity drift, and image registration error. The accuracy of the PSP system was directly assessed by comparing the pressure values measured by a transducer/tap combination with PSP data at the same tap

5.3 Pressure Uncertainty

113

Fig. 5.12 Typical pressure distribution obtained from PSP on a Cessna Citation model. (From Kammeyer et al. 2002a)

Fig. 5.13 Variation of PSP in situ calibration slope throughout the tests on a Cessna Citation model. (From Kammeyer et al. 2002a)

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5 Intensity-Based Methods

Fig. 5.14 Histogram of a total set of PSP errors compared with a Gaussian distribution of the equivalent mean and standard deviation. (From Kammeyer et al. 2002a)

locations. After some problematic pressure data were excluded, 130,391 comparisons from 221 taps and 676 wind-on test points were used as an overall set of realizations for a statistical analysis. The PSP data processing included in situ calibration, but did not exercise the explicit temperature correction. When examining the comparisons, the 78 taps were used for in situ calibration to provide residual comparisons, while other taps provided truly independent comparisons. Figure 5.14 shows a histogram for the set of comparisons, where a Gaussian distribution with the same mean and standard deviation is superimposed as a reference. Clearly, the distribution of the data is non-Gaussian. A robust estimate of the 68% confidence level gives an estimate of the standard uncertainty of 0.29 psi, which corresponds to 0.0065 in Cp. Figure 5.15 shows the standard uncertainty as a function of the angle of attack (AoA, Alpha) for the right wing. The behavior of the dependency of the uncertainty on the AoA corresponds to wing deformation. This indicates that the error is associated with the movement of the model in a nonhomogeneous illumination field, which cannot be fully corrected by the image registration technique. Kammeyer et al. (2002a, b) also studied temperature correction using IR cameras. Two sets of PSP data obtained before and after temperature correction were used to assess the effectiveness of the temperature correction. Figure 5.15 shows the standard uncertainty after the temperature correction as a function of AoA. The temperature correction was increasingly effective when AoA was larger than 2 ; it removed the spatial biases associated with a temperature distribution on the model. Overall, the uncertainty, prior to the temperature correction, was in the range 0.16–0.45 psi (0.04–0.1Cp); with the temperature correction, it was in the range 0.17–0.35 psi (0.04–0.09Cp). The work of Kammeyer et al. (2002a, b) identifies the functional dependency of in situ PSP calibration uncertainty on the testing parameters such as AoA and Mach number.

5.3 Pressure Uncertainty

115

Fig. 5.15 Standard deviation uncertainty of PSP on the right wing of a Cessna Citation model as a function of the angle of attack (Alpha in degrees). (From Kammeyer et al. 2002a)

Simulation Inspired by the experimental study of Kammeyer et al. (2002a, b), Liu and Sullivan (2003) studied in situ calibration uncertainty of PSP through simulation of PSP measurements in subsonic flows over a Joukowsky airfoil. The main results are summarized below. It is assumed that in situ calibration uncertainty is mainly attributed to the temperature effect of PSP and illumination change on a surface due to model deformation. The Joukowsky airfoil and subsonic flows around it are generated using the Joukowsky transform plus the Karman-Tsien rule. An adiabatic model is considered, which is coated with Bath Ruth + silica-gel in GE RTV 118. Four point light sources for illuminating PSP and two cameras are placed at the same locations as described in Sect. 5.3.15. The twist θtwist and bending Ty of the airfoil are a function of AoA (α). Based on previous wing deformation measurements  (Burner and Liu 2001), the linear relations θtwist ¼  0.113 α ( ) and Ty ¼ 0.022 α (in.) are used over a certain range of AoA at a certain spanwise location of a wing. Thus, a change of the illumination radiance on the airfoil surface is estimated using a transformation of rotation and translation for the airfoil moving in the given illumination field. In the simulation, the measured luminescent intensity distribution of PSP in the wind-on case (deformation case) is generated by I I ref0

¼

I ref I ref0



1

1 p L p ¼ , AðT Þ þ BðT Þ AðT Þ þ BðT Þ pref L0 pref

where Iref0 and Iref are the reference luminescent intensities (without wind) on the non-deformed airfoil and deformed airfoil, respectively. It is assumed that Iref0 and

116

5 Intensity-Based Methods

0.012 Illumination change only with constant temperature Temperature effect only without illumination change Both temperature effect and illumination change

std[(p - pin-situ)/pref]

0.010 0.008 0.006 0.004 0.002 0.000

Mach = 0.4 -5

0

5

10

15

AoA (deg) Fig. 5.16 In situ PSP calibration error as a function of the angle-of-attack (AoA) for Mach 0.4 in Joukowsky airfoil flows. (From Liu and Sullivan 2003)

Iref are proportional to the corresponding illumination radiance levels L0 and L on the non-deformed airfoil and deformed airfoil, respectively. Surface temperature T is substituted by the adiabatic wall temperature distribution Taw, and the pressure distribution is given by the Joukowsky transform plus the Karman-Tsien rule for subsonic flows. Therefore, the resulting luminescent intensity distribution contains the effects of both illumination change and temperature variation on the surface. By assuming that the wind-on image is already re-aligned with the wind-off image Iref0 on the non-deformed airfoil by the image registration technique, in situ PSP calibration is made to correlate Iref0/I to p/pref using the Stern–Volmer relation based on 104 virtual pressure taps on each of the upper and lower surfaces. For a given AoA and a Mach number, a histogram of in situ calibration error Δp/pref ¼ ( p  pin ‐ situ)/pref is found to be a near-Gaussian distribution, where Δp is a difference between the true pressure from the theoretical distribution and the pressure converted from the luminescent intensity using in situ calibration. The standard deviation (std) of the probability density function is dependent on AoA and Mach number. Figures 5.16 and 5.17 show the std of the in situ calibration error as a function of AoA for Mach 0.4 and as a function of the Mach number for AoA ¼ 5 , respectively. Figures 5.16 and 5.17 also show the isolated effects of the temperature and illumination change on the std. The behavior of the calculated std as a function of AoA is very similar to the experimental results shown in Fig. 5.15.

5.3 Pressure Uncertainty

117

0.004 Illumination change only with constant temperature Temperature effect only without illumination change Both temperature effect and illumination change

std[(p - pin-situ)/pref]

0.003

0.002

0.001

0.000 AoA = 5 deg

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

Mach Number Fig. 5.17 In situ PSP calibration error as a function of the Mach number for AoA ¼ 5 in Joukowsky airfoil flows. (From Liu and Sullivan 2003)

The concavity of the std as a function of AoA in Fig. 5.16 is mainly attributed to the movement of the airfoil. Figure 5.18 shows a simulated histogram for an overall sample set of Δp/pref (a total of 10,920 samples) over the whole range of AoAs and Mach numbers, duplicating the experimental non-Gaussian distribution in Fig. 5.14 given by Kammeyer et al. (2002a, b). The Gaussian distribution with the same std is also plotted in Fig. 5.18 as a reference. In fact, for a union of sample sets having nearGaussian distributions with different std values at different AoAs and Mach numbers, the distribution of the collected data becomes non-Gaussian because more and more samples accumulate near zero when forming a union of sample sets. The probability density function of a union of N sample sets should be given by a sum of the Gaussian distributions rather than the Gaussian distribution, i.e., N 1

N X

  pffiffiffiffiffi exp x2 =2σ 2i = 2π σ i :

i¼1

As shown in Fig. 5.18, this distribution correctly describes the simulated histogram. Although the simulation is made for an airfoil section, the in situ calibration error for a wing can be estimated by averaging the local results over the full wingspan; therefore, the behavior of the error for a wing should be similar.

118

5 Intensity-Based Methods 900 800

Sample Number

700 600

Sum of Gaussian Distributions

500 400

Gaussian Distribution

300 200 100 0 -0.01 -0.008 -0.006 -0.004 -0.002

0

'p/p

0.002 0.004 0.006 0.008

0.01

ref

Fig. 5.18 Histogram of a total set of in situ PSP calibration errors in the whole ranges of AoAs and Mach numbers in Joukowsky airfoil flows. (From Liu and Sullivan 2003)

5.3.15 Example: Subsonic Airfoil Flows To illustrate how to estimate the elemental errors and the total uncertainty, PSP measurements on a Joukowsky airfoil in subsonic flows are simulated by Liu et al. (2001a). The airfoil and incompressible potential flows around it are generated using the Joukowsky transform; the pressure coefficients (Cp) on the airfoil in the corresponding subsonic compressible flows are obtained using the Karman-Tsien rule. Figure 5.19 shows typical distributions of the pressure coefficient and adiabatic wall temperature on a Joukowsky airfoil at Mach 0.4 and AoA ¼ 5 . In the simulated PSP measurements, Bath Ruth + silica-gel in GE RTV 118, is used, which has the Stern–Volmer coefficients over a temperature range of 293–333 K, AðT Þ  0:13½1 þ 2:82ðT  T ref Þ=T ref , BðT Þ  0:87 ½1 þ 4:32ðT  T ref Þ=T ref : The uncertainties in a priori PSP calibration are ΔA/A ¼ ΔB/B ¼ 1%. We assume that the spatial changes of the paint thickness and dye concentration in the image

5.3 Pressure Uncertainty

119

-8

-3

Cp Temperature

-2

-6

-4

0

-2

Cp

-1

1

Taw - Tref (deg C)

AoA = 5 deg, Mach = 0.4

0

Joukowski Airfoil

2

2 0.0

0.2

0.4

0.6

0.8

1.0

x/c Fig. 5.19 Typical distributions of the pressure coefficient and adiabatic wall temperature on a Joukowsky airfoil at Mach 0.4, AoA ¼ 5 , and Tref ¼ 293 K

plane are 0.5%/pixel and 0.1%/pixel, respectively. The rate of photodegradation of the paint is 0.5%/h for a given excitation light level and the exposure time of the paint is 60 s between the wind-off and wind-on images. The rate of reduction of the luminescent intensity due to dust/oil sedimentation on the surface is assumed to be 0.5%/h. In an object-space coordinate system whose origin is located at the leading edge of the airfoil, four light sources for illuminating PSP are placed at the locations X s1 ¼ ðc, 3cÞ, Xs2 ¼ ð 2c, 3c Þ, X s3 ¼ ðc, 3c Þ, and Xs4 ¼ ð 2c, 3c Þ, where c is the chord of the airfoil. For the light sources with unit strength, the illumination flux distributions on the upper and lower surfaces are, respectively,  2  2 ðq0 Þup ¼ X up  X s1  þ Xup  X s2  , ðq0 Þlow ¼ jX low  Xs3 j2 þ jXlow  Xs4 j2 , where Xup and Xlow are the coordinates of the upper and lower surfaces of the airfoil, respectively. The temporal variation of irradiance of these lights is assumed to be 1%/h. It is also assumed that the spectral leakage of optical filters for the lights and cameras is 0.3%. Two cameras viewing the upper surface and lower surface are located at ðc=2, 4c Þ and ðc=2, 4c Þ, respectively.

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5 Intensity-Based Methods

The pressure uncertainty associated with the photon shot noise can be estimated by using Eq. (5.8). It is assumed that a CCD camera has the full-well capacity of (npe)max ¼ 350, 000 electrons. The numbers of photoelectrons collected in a CCD camera are mainly proportional to the illumination field on the airfoil surface. Thus, the photoelectrons on the upper and lower surfaces are, respectively, estimated by h i    npe up ¼ npe max ðq0 Þup = max ðq0 Þup ,       npe low ¼ npe max ðq0 Þlow = max ðq0 Þlow : 

Combination of these estimates with Eq. (5.8) gives the shot-noise-generated pressure uncertainty distributions on the upper and lower surfaces. Movement of the airfoil produced by the aerodynamic load is expressed by a superposition of local rotation (twist) and translation. A transformation between the non-moved and moved surface coordinates X ¼ (X, Y )T and X0 ¼ (X0, Y0)T is X0 ¼ R(θtwist)X + T, where R(θtwist) is the rotation matrix, θtwist is the local  wing twist, and T is the translation vector. Here, for θtwist ¼  1 and T T ¼ ð0:001 c, 0:01 cÞ , the uncertainty in q0(X)/q0 ref(X0) is estimated by var½q0 ðX Þ=q0 ref ðX 0 Þ  ðq0 ref Þ2 j ð∇q0 Þ  ðΔXÞ j2 , where a displacement vector is ΔX ¼ X0  X. The pressure variance associated with mapping PSP data onto a rigid body grid without correcting the effect of model deformation is estimated by var ( p) ¼ | (∇p)surf  (ΔX)surf |2, where (∇p)surf is the pressure gradient on the surface and (ΔX)surf ¼ (X0  X)surf is the component of the displacement vector projected on the surface. To estimate the temperature effect of PSP, an adiabatic model is considered at which the wall temperature Taw is given by   1 T aw =T 0 ¼ 1 þ r ðγ  1ÞM 2 =2 1 þ ðγ  1ÞM 2 =2 , where the recovery factor is r ¼ 0.843 for a laminar boundary layer. Assuming that the reference temperature Tref equals to the total temperature T0 ¼ 293 K, we can calculate a temperature difference ΔT ¼ Taw  Tref between the wind-on and windoff cases. The adiabatic wall is the most severe case for PSP measurements since the surface temperature on a metallic model is much lower than the adiabatic wall temperature due to high heat conduction to the model. The total pressure uncertainty is estimated by substituting all the estimated elemental errors into Eq. (5.6). Figure 5.20 shows the pressure uncertainty distributions on the upper and lower surfaces of the airfoil for different freestream Mach numbers. It is indicated that the temperature effect of PSP dominates the uncertainty of PSP measurements on an adiabatic wall. The uncertainty increases with the Mach number as the adiabatic wall temperature increases. The local pressure uncertainty

5.3 Pressure Uncertainty

121

0.6 Upper Surface

0.5

Uncertainty in P

M = 0.7 0.4 0.3 0.2 M = 0.5

0.1

M = 0.3 0.0

M = 0.1 0.0

0.2

0.4

0.6

0.8

1.0

x/c

(a) 0.06

Uncertainty in P

0.05

0.04

M = 0.5

0.03

0.02

M = 0.3

0.01

M = 0.1 0.0

(b)

Lower Surface

M = 0.7

0.2

0.4

0.6

0.8

1.0

x/c

Fig. 5.20 Relative PSP uncertainty distributions for different freestream Mach numbers on (a) the upper surface and (b) lower surface of a Joukowsky airfoil. (From Liu et al. 2001a)

on the upper surface is as high as 50% at one location for Mach 0.7, which is caused by a local surface temperature change of about 6  C. In order to compare the PSP uncertainty with the pressure variation on the airfoil, the maximum relative pressure variation on the airfoil is defined as  max j Δpjsurf =p1 ¼ 0:5 γ M 21 max ΔCp . Figure 5.21 shows the maximum relative

122

5 Intensity-Based Methods 1

Relative Error or Variation

Upper Surface

 ( ΔP/P)PSP ! aw max ΔP 0.1

surf

/ Pf

0.01

 ( ΔP/P)PSP ! ΔT =0  ( ΔP/P)PSP !ShotNoise 0.001 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach number

(a) 1

Relative Error or Variation

Lower Surface

max ΔP

0.1

surf

/ Pf

 ( ΔP/P)PSP ! aw

0.01

 ( ΔP/P)PSP ! ΔT =0  ( ΔP/P)PSP !ShotNoise 0.001 0.0

(b)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach number

Fig. 5.21 The maximum relative pressure change and chord-averaged PSP uncertainties as a function of the freestream Mach number on (a) the upper surface and (b) the lower surface of a Joukowsky airfoil. (From Liu et al. 2001a)

pressure variation max| Δp |surf/p1 along with the chord-averaged PSP uncertainty h(Δp/p)PSPiaw on the adiabatic airfoil at the Mach numbers of 0.05–0.7. The uncertainty h(Δp/p)PSPiΔT ¼ 0 without the temperature effect is also plotted in Fig. 5.21, which is mainly dominated by the a priori PSP calibration error ΔB/B ¼ 1% in this case. The curves of max| Δp |surf/p1, h(Δp/p)PSPiaw and h(Δp/p)PSPiΔT ¼ 0 intersect near Mach 0.1. When the PSP uncertainty exceeds the maximum pressure variation

5.3 Pressure Uncertainty

123

0.7 0.6

Lift Pitching Moment

Uncertainty

0.5 0.4 0.3 0.2 0.1 0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Freestream Mach Number Fig. 5.22 Relative uncertainties in the lift and pitching moment of a Joukowsky airfoil as a function of the freestream Mach number. (From Liu et al. 2001a)

on the airfoil, the pressure distribution on the airfoil cannot be quantitatively measured by PSP. As shown in Fig. 5.11, because a temperature change on a nonadiabatic wall is smaller, the PSP uncertainty for a real wind tunnel model generally falls into the shadowed region confined by the curves of h(Δp/p)PSPiaw and h(Δp/p)PSPiΔT ¼ 0. The PSP uncertainty associated with the photon shot noise h(Δp/p)PSPiShotNoise is also plotted in Fig. 5.21. The intersection between max| Δp |surf/p1 and h(Δp/p)PSPiShotNoise gives the limiting low Mach number (~0.06) for PSP measurements in this case. The uncertainties in the lift (FL) and pitching moment (Mc) are also calculated from the PSP uncertainty distribution on the surface. Figure 5.22 shows the uncertainties in the lift and pitching moment relative to the leading edge for the Joukowsky airfoil over a range of the Mach numbers for AoA ¼ 4 . The uncertainties in the lift and moment decrease monotonously as the Mach number increases.

124

5.4 5.4.1

5 Intensity-Based Methods

Temperature Uncertainty Error Propagation and Limiting Temperature Resolution

The above uncertainty analysis for PSP can be adapted for TSP since many error sources of TSP are the same as those of PSP. For simplicity, instead of the general Arrhenius relation, we use an empirical relation between the luminescent intensity (or the photodetector output) and temperature T for a TSP uncertainty analysis (Cattafesta and Moore 1995; Cattafesta et al. 1998), i.e., T  T ref ¼ K T ln ðI ref =I Þ ¼ K T ln ðU 2 V ref =V Þ,

ð5:16Þ

where KT is a TSP calibration constant with a temperature unit and U2 is the factor defined in Eq. (5.5). Equation (5.16) can be used to fit TSP calibration data over a certain range of temperatures. The error propagation equation for TSP is M X K 2T var ðT Þ varð ζ i Þ varð K T Þ ¼ þ , 2 2 K 2K ζ 2i ðT  T ref Þ ðT  T ref Þ i¼1

ð5:17Þ

where the variables {ζ i, i ¼ 1, . . ., M} denote a set of the parameters Dt(Δt), Dx(Δx), Dq0(Δt), V, Vref, Πc/Πc ref, Πf/Πf ref, h/href, c/cref, and q0/q0 ref as defined in Sect. 5.3.2. The summation term in the right-hand side of Eq. (5.17) includes the errors associated with model deformation, unstable illumination, photodegradation, filter leakage, and luminescent intensity measurements. The last term in Eq. (5.17) is the TSP calibration error. Similar to the uncertainty analysis for PSP, in the photon-shot-noise-limited case without any model deformation, we are able to obtain the minimum temperature difference that TSP can measure from a single frame of image, i.e., 

1=2 KT T  T ref ðΔT Þmin ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi , 1 þ exp   KT npe ref max

ð5:18Þ

where (npe ref)max is the full-well capacity of a CCD camera in the reference condition. The minimum resolvable temperature difference (ΔT )min is inversely proportional to the square-root of the number of collected photoelectrons, and approximately proportional to the calibration constant KT. When (npe ref)max is 500,000 electrons, for a typical ruthenium-based TSP having KT ¼ 37.7  C, the minimum resolvable temperature difference (ΔT)min is shown in Fig. 5.23 as a function of T at a reference temperature Tref ¼ 20  C. When N images are averaged, the limiting temperature resolution given by Eq. (5.18) should be divided by a factor N1/2.

Minimum Temperature Difference (deg. C)

5.4 Temperature Uncertainty

125

0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 -20

0

20

40

60

80

100

Temperature (deg. C) Fig. 5.23 The minimum resolvable temperature difference as a function of temperature for a ruthenium-based TSP for (npe ref)max ¼ 500,000e, KT ¼ 37.7  C, and Tref ¼ 20  C

5.4.2

Elemental Error Sources of TSP

The elemental error sources of TSP have been discussed by Cattafesta et al. (1998), Liu et al. (1995c) and Lemarechal et al. (2021b). Table 5.2 lists the elemental error sources, sensitivity coefficients, and total uncertainty of TSP. The sensitivity coefficients for many variables are related to φ ¼ KT/(T  Tref). The elemental errors in the variables Dt(Δt), Dx(Δx), Dq0(Δt), V, Vref, Πc/Πc ref, Πf/Πf ref, h/href, c/cref, and q0/ q0 ref can be estimated using the same expressions given in the uncertainty analysis for PSP, which represent the error sources associated with model deformation, unstable illumination, photodegradation, filter leakage, and luminescence measurements. The camera calibration error and temperature mapping error can also be estimated using similar expressions to those for PSP, i.e., 2

2

varðT Þ  ð∂ T=∂ xÞ σ 2x þ ð∂T=∂ yÞ σ 2y ,  2 var ðT Þ ¼  ð∇T Þsurf  ðΔX Þsurf  , where σ x and σ y are the standard deviations of least-squares estimation in camera calibration. In order to estimate the TSP calibration error, the temperature dependency of TSP was repeatedly measured using a calibration setup over days for several TSP formulations (Liu et al. 1995c). Temperature measured by TSP was compared to accurate temperature values measured using a standard thermometer.

126

5 Intensity-Based Methods

Table 5.2 Sensitivity coefficients, elemental errors, and total uncertainty of TSP E 1

Variable ζi Dt(Δt)

Sensi. coef.Si φ

2

Dx(Δx)

φ

3

Dq0(Δt)

φ

[(∂ q0/∂t)(Δt)/q0 ref]2

4 5 6

Vref V Πc/Πc ref

φ φ φ

VrefGħνBd VGħνBd [R2/(R1 + R2)]2 (ΔR1/R1)2

7

Πf/Πf ref

φ

var(Πf/Πf ref)

8

h/href

φ

9

c/cref

φ

10

q0/q0 ref

φ

(q0 ref)2|(∇q0)  (ΔX) |2

11 12

KT Temperature mapping

1 1

var(KT)

Total uncertainty in temperature

Elemental variance var(ζ i) [(∂V/∂ t)(Δt)/V]2

h

i 2 2 ð∂ V=∂xÞ σ 2x þ ð∂V=∂ yÞ σ 2y V 2

h

i 2 2 ð∂h=∂xÞ σ 2x þ ð∂h=∂yÞ σ 2y h2 ref

h

i 2 2 ð∂c=∂xÞ σ 2x þ ð∂c=∂yÞ σ 2y c2 ref

2

2

ð∂ T=∂xÞ σ 2x þ ð∂T=∂yÞ σ 2y and | (∇T )surf  (ΔX)surf |2 var ðT Þ=ðT  T ref Þ2 ¼

PM

Physical origin Temporal variation in luminescence due to photodegradation and surface contamination Image registration errors for correcting luminescence variation due to model motion Temporal variation in illumination Photodetector noise Photodetector noise Change in camera performance parameters due to model motion Illumination spectral variability and filter spectral leakage Image registration errors for correcting thickness variation due to model motion Image registration errors for correcting concentration variation due to model motion Illumination variation on model surface due to model motion Paint calibration error Errors in camera calibration and temperature mapping on a surface of a presumed rigid body

2 2 i¼1 Si varðζ i Þ=ζ i

Note: (1) σ x and σ y are the standard deviations of least-squares estimation in the image registration or camera calibration (2) The factor for the sensitivity coefficient is defined as φ ¼ KT/(T  Tref)

Histograms of temperature errors were obtained for EuTTA-dope and Ru(bpy)Shellac TSPs, exhibiting a near-Gaussian distribution. The standard deviation is about 0.8  C for EuTTA-dope TSP over a temperature range of 15–70  C, and about 2  C for Ru(bpy)-Shellac TSP over a temperature range of 20–100  C. The temperature hysteresis introduces an additional error source in TSP measurement, which was reported in calibration experiments for a Rhodamine(B)-based

5.4 Temperature Uncertainty

127

coating (Romano et al. 1989). The temperature hysteresis is related to the polymer structural transformation from a hard and relatively brittle state to a soft and rubbery state when the temperature exceeds the glass temperature of a polymer. Since the thermal quenching of luminescence in a brittle condition is different from that in a rubbery state, the temperature dependency may be changed after it is heated beyond the glass temperature. To reduce the temperature hysteresis, TSP should be preheated to a certain temperature above the glass temperature before it is used as an optical temperature sensor for quantitative measurements. It was found that for both preheated EuTTA-dope and Ru(bpy)-Shellac paints, the temperature hysteresis was minimized such that the temperature dependency remained almost unchanged in repeated tests over several days (Liu et al. 1995c).

Chapter 6

Lifetime-Based Methods

This chapter describes the response of the luminescent emission of PSP (or TSP) to time-varying excitation light and the luminescent lifetime measurement methodologies, including the pulse method, phase method, amplitude demodulation method, and gated intensity ratio method. Uncertainty analysis of the lifetime-based methods for PSP is given, and typical lifetime measurements are described. Compared to the intensity-based method, the intrinsic advantage of the lifetime-based method is that a relation between the luminescent lifetime and pressure is not dependent on the illumination intensity. The lifetime-based methods were applied earlier to a laserscanning system for PSP and TSP. Currently, multi-gated digital cameras with LED lights for illumination (particularly with the single-shot two-gate lifetime method) are popular for PSP and TSP lifetime measurements.

6.1 6.1.1

Response of Luminescence to Time-Varying Excitation Light First-Order Model

The lifetime method for PSP and TSP is based on the response of luminescence to time-varying excitation light. The response of the luminescent emission I of a paint to an excitation light E(t) can be described as a first-order system dI=dt ¼ I=τ þ E ðt Þ,

ð6:1Þ

where τ is the luminescent lifetime. With the initial condition I(0) ¼ 0 , a solution to Eq. (6.1) is

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_6

129

130

6 Lifetime-Based Methods

Z

t

I ðt Þ ¼

exp ½ð t  u Þ=τ E ðuÞdu:

ð6:2Þ

0

For a pulse light E(t) ¼ Amδ(t) , the luminescent response is simply an exponential decay I ðt Þ ¼ Am exp ðt=τÞ:

ð6:3Þ

We consider a general periodic excitation light that is expressed as a Fourier series E ðt Þ ¼ Am

! 1 a0 X ½an cos ðnω t Þ þ bn sin ðnωt Þ , þ 2 n¼1

ð6:4Þ

where ω ¼ 2π f is the circular frequency of the excitation light. Substitution of Eq. (6.4) into Eq. (6.2) yields the luminescent response after a short transient process, i.e., ! 1 a0 X an cos ðnωt  φn Þ þ bn sin ðn ωt  φn Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi þ I ðt Þ ¼ Am τ : 2 1 þ n2 ω 2 τ 2 n¼1

ð6:5Þ

Here, the phase angles φn are related to the luminescent lifetime by tan φn ¼ nωτ:

ð6:6Þ

In the simplest case where a sinusoidally modulated excitation light is E(t) ¼ Am[1 + H sin (ωt)], the luminescent response Eq. (6.5) is reduced to I ðt Þ ¼ Am τ½1 þ HM eff sin ðωt  φÞ,

ð6:7Þ

where Meff ¼ (1 + τ2ω2)1/2 is the effective amplitude modulation index, Am is the amplitude, and H is the modulation depth. The phase angle φ is related to the luminescent lifetime simply by tan φ ¼ ωτ:

ð6:8Þ

Other waveforms of the excitation light include squares and triangles. Figure 6.1 shows the luminescent response to typical periodic excitations with the square, sine, and triangle waveforms for the nondimensional lifetime of ωτ ¼ π/10.

6.1 Response of Luminescence to Time-Varying Excitation Light 2.5 Excitation Light

2.0 Intensity

Fig. 6.1 Responses of luminescence to timevarying excitations of the (a) square, (b) sine, and (c) triangle waveforms for ωτ ¼ π/10

131

Luminescence

1.5 1.0 0.5 0.0

0

2

4

6

wt (radian)

8

10

12

8

10

12

10

12

(a) 4.0 Excitation Light

3.5

Luminescence

Intensity

3.0 2.5 2.0 1.5 1.0 0.5

0

2

4

6

wt (radian)

(b) 5 Excitation Light

Intensity

4

Luminescence

3 2 1 0

0

2

4

6

8

wt (radian)

(c)

6.1.2

Higher-Order Model

In a micro-heterogeneous polymer matrix, the multiple-exponential luminescent emission decay can be observed in contrast to the single-exponential decay in a

132

6 Lifetime-Based Methods

homogeneous medium (Carraway et al. 1991a; Sacksteder et al. 1993; Xu et al. 1994). This is associated with the fact that a host matrix has domains that vary with respect to their interaction with luminescent probe molecules; as a result, the excited molecules decay at different rates, depending on their environments. Consider a paint system consisting of a number of independently emitting species with different single-exponential lifetimes τi (i ¼ 1, 2, 3, . . .) and relative contributions. The multiple-exponential luminescent decay is described as I ðt Þ ¼

X

αi exp ðt=τi Þ,

ð6:9Þ

where αi is the weighting constant for the ith component. The luminescent lifetime of each component obeys the Stern–Volmer relation τ0i =τi ¼ 1 þ K SV i p,

ð6:10Þ

where KSV i is the Stern–Volmer coefficient for the ith component. Hence, a higherorder model is needed to describe the luminescent response of an inhomogeneous PSP to time-varying excitation light. For example, we consider a third-order model a0 d 3 I=dt 3 þ a1 d2 I=dt 2 þ a2 dI=dt þ a3 I ¼ Eðt Þ:

ð6:11Þ

00

With the initial conditions I(0) ¼ I0 (0) ¼ I (0) ¼ 0, a solution for (6.11) is given by Z I ðt Þ ¼

t

E ð uÞ

0

3 X

αi exp ½ðt  uÞ=τi  du:

ð6:12Þ

i¼1

The lifetimes τi are related to the weighting constants αi through the roots of the characteristic equation a0 s3 + a1 s2 + a2 s + a3 ¼ 0. The weighted mean lifetime is usually expressed as hτi ¼ ∑ αiτi/ ∑ αi. The generalized models for the non-exponential decay of luminescence were discussed by Ruyten (2004, 2005) and Ruyten and Sellers (2004) considering the continuous decay rate spectrum and excitation response function.

6.2 6.2.1

Lifetime Techniques Pulse Method

The goal of PSP lifetime measurement is to measure the luminescent lifetime and to determine pressure through the Stern–Volmer relation. A variety of methods can be used to extract the lifetime from the luminescent response to time-varying excitation

6.2 Lifetime Techniques

133

light. The pulse method is the most direct method widely used in photochemistry (Lakowicz 1991, 1999). After PSP is excited by a pulsed illumination light, the luminescent decay is measured using a fast-responding photodetector and acquired using a PC or an oscilloscope. The lifetime is calculated by fitting the time-resolved data with a single exponential function or a multiple-exponential function. This direct time-domain approach was used by Davies et al. (1995, 1997a, b) for PSP lifetime measurements. For certain PSP with multiple distinct lifetimes, the pulse method allows simultaneous determination of pressure and temperature if the lifetimes have sufficiently different Stern–Volmer coefficients as a function of temperature. In this case, given the lifetimes (τi), a system of equations for pressure and temperature is τiref p ¼ A i ðT Þ þ B i ðT Þ pref τi

ði ¼ 1, 2, . . . , N, N  2Þ:

ð6:13Þ

In principle, unknown pressure and temperature can be simultaneously determined by solving Eq. (6.13).

6.2.2

Phase Method

The phase method is a frequency-domain technique that detects a phase shift of the luminescent signal with respect to a modulated excitation light (Torgerson et al. 1996; Torgerson 1997; Lachendro et al. 1998; Lachendro 2000). Figure 6.2 shows the working principle of the phase method with a lock-in amplifier. For a sinusoidal excitation light with E(t) ¼ Am [1 + H sin ( ω t)], the corresponding modulated luminescent signal from a photodetector is mixed with the in-phase and quadrature reference signals, i.e., cos(ωt ) and sin(ωt ). Next, the use of a low-pass filter generates the DC components Vc ¼  AmτHMeff sin (φ) and Vs ¼ AmτHMeff cos (φ), which are related to the phase angle φ between the luminescent emission and excitation light. A ratio between these filtered signals yields a quantity tan φ ¼ ωτ ¼  Vc/Vs that is uniquely related to the lifetime for a fixed modulation frequency. Therefore, the pressure is given by p¼

K 1 SV



 ωτ0 1 : tan φ

ð6:14Þ

The sensitivity of the phase angle φ to pressure is defined as Sp ¼

dφ ω ∂τ ¼ : dp 1 þ ðωτÞ2 ∂p

ð6:15Þ

The optimal modulation frequency to achieve the maximum sensitivity Sp is

134

6 Lifetime-Based Methods

E(t)

Am [ 1

H sin( ω t )]

PSP

I (t)

cos( ωt)

Am τ [ 1

H M ef f sin(ωt

Mixer

sin( ωt)

Mixer

Low-Pass Filter

Vc

φ) ]

Low-Pass Filter

Vs

Am τ H M eff sin(φ )

Am τ H M eff cos(φ )

Divider

tan(φ )

ωτ

Vc / Vs

Fig. 6.2 Block diagram of the phase method

ωτ ¼ 1:

ð6:16Þ

It must be noted that the maximum sensitivity to pressure does not tell the whole story if noise is not taken into account. Besides a good sensitivity to pressure, the SNR should also be considered in order to select the optimal modulation frequency. At a higher frequency, the modulation amplitude and DC components from PSP decrease, resulting in a lower SNR. Figure 6.3 is a Bode plot showing the response of a typical PSP, PtTFPP in polymer/ceramic composite, to the modulation frequency at different pressures; the behavior of this PSP is very close to the first-order system.

6.2 Lifetime Techniques

135

dB(dB) Gain

3 0 -3 -6 -9 -12

0.07psi 2.32psi 5.37psi 8.49psi 11.42psi 14.68psi

-15 -18 -21 -24 -27 -30

3rd Order Fit

-33 102

103

104

105

Freqeuncy(Hz) Fig. 6.3 The Bode plot of the amplitude/gain (dB) of PSP (PtTFPP in polymer/ceramic composite) at 30  C. (From Lachendro 2000)

6.2.3

Amplitude Demodulation Method

The amplitude demodulation method was used for fluorescent lifetime measurements of tagged biological specimens in a flow cytometer (Deka et al. 1994). For a sinusoidally modulated excitation light, the luminescent response is given by Eq. (6.7) and the effective amplitude modulation index is Meff ¼ (1 + τ2ω2)1/2. Clearly, for a fixed modulation frequency, the lifetime can be obtained from measuring the effective modulation index. Combination of the Stern–Volmer relation Eq. (6.10) with Meff ¼ (1 + τ2ω2)1/2 yields an expression for pressure as a function of the effective amplitude modulation index Meff, i.e., 0 p¼

1

1 B ω τ0 M eff C @qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1A: K SV 2 1  M eff

ð6:17Þ

To measure the effective amplitude modulation index Meff, Deka et al. (1994) used the following expression

136

6 Lifetime-Based Methods

E(t)

Am [ 1

H sin( ω t )]

PSP

I (t)

I

Am τ [ 1

H M eff sin(ωt

std ( I )

Am τ

φ) ]

2 Am τ H M eff

Divider

M eff

( 1 τ 2 ω2 )

1/ 2

2H

1

std ( I ) /

I

Fig. 6.4 Block diagram of the amplitude demodulation method

M eff ¼ H 1

I max ðt max Þ  I min ðt min Þ , I max ðt max Þ þ I min ðt min Þ

ð6:18Þ

where tmax and tmin were the times at which the modulated oscillating luminescent signal went through the maximum intensity Imax(tmax) and minimum intensity Imin(tmin), respectively. Here, as illustrated in Fig. 6.4, a simpler scheme is proposed to determine Meff by calculating the time-averaged quantities of the modulated luminescent signal. The time-averaged oscillating luminescent signal is defined as 1 T!1 2T

hI i ¼ Lim

Z

T T

I ðt Þdt:

ð6:19Þ

The mean and standard deviation of the luminescent intensity I(t) are hIi ¼ Amτ D E1=2 pffiffiffi ¼ Am τHM eff = 2 . Therefore, taking a ratio between and stdðI Þ ¼ ðI  hI iÞ2 these quantities, we obtain a simple formula for the effective amplitude modulation index, i.e.,

6.2 Lifetime Techniques

137

M eff ¼

pffiffiffi 1 stdðI Þ hE i stdðI Þ 2H ¼ : stdðEÞ hI i hI i

ð6:20Þ

It is emphasized that Eq. (6.20) is valid only for a sinusoidally modulated excitation light E(t) ¼ Am[1 + H sin (ωt)]. Instrumentation for utilizing this methodology is particularly simple since only the mean and standard deviation of the sinusoidal luminescent intensity and excitation light intensity are required. The optimal modulation frequency can be obtained by maximizing the sensitivity of Meff to pressure defined as Sp ¼

dðM eff Þ 2ω2 τ ∂τ ¼ : 3=2 ∂p dp 2 2 ð1 þ ω τ Þ

ð6:21Þ

The optimal modulation frequency for the maximum sensitivity is  pffiffiffi ðωτÞop ¼ 1 þ 7 =3  1:215:

ð6:22Þ

For a typical PSP, Ru(dpp) in GE RTV 118, having the lifetime τ ¼ 4.7 μs at the ambient condition, the optimal modulation frequency is 41 kHz. Figure 6.5 shows 1.2

Modulation frequency = 5 kHz

1.0

24 kHz

Meff

0.8

0.6

50 kHz

0.4

100 kHz

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref Fig. 6.5 The effective amplitude modulation index Meff as a function of relative pressure at different sinusoidal modulation frequencies for Ru(dpp) in GE RTV 118 at T ¼ 20  C and pref ¼ 1 atm

138

6 Lifetime-Based Methods

the effective amplitude modulation index Meff as a function of the relative pressure p/ pref at different sinusoidal modulation frequencies for this PSP having the lifetime given by τ ¼ τref/(0.17 + 0.84p/pref). Clearly, the selection of the modulation frequency affects the performance of the system. The amplitude demodulation method is suitable for a laser-scanning system for PSP and TSP shown in Fig. 5.4. When a laser beam is modulated, the phase angle between the modulated excitation light and responding luminescence can be obtained using a lock-in amplifier for phase-based lifetime PSP and TSP measurements. The laser can scan continuously or in steps, which is synchronized to data acquisition such that the position of a laser spot on a surface can be known. The laser-scanning system for PSP and TSP lifetime measurements was discussed by Torgerson et al. (1996), Torgerson (1997), and Lachendro (2000). Franke and Holst (2015) introduced a four-gate method to calculate the demodulation index, which is particularly simple for fluorescent lifetime imaging (FLIM).

6.2.4

Gated Intensity Ratio Method

The gated intensity ratio method, as illustrated in Fig. 6.6, gates the modulated luminescent signal by applying two gain functions over two different intervals, i.e.,

Fig. 6.6 Block diagram of the gated intensity method

E(t,r )

PSP

I (t,r )

I2

T2

I ( t , r ) G 2 ( t ) dt

I1 Divider

I 2 /I1

F( τ )

T1

I ( t , r ) G1 ( t ) dt

6.2 Lifetime Techniques

139

Z I1 ¼

Z

ΔT 1

I ðt ÞG1 ðt Þ dt,

I2 ¼

ΔT 2

I ðt ÞG2 ðt Þ dt,

ð6:23Þ

where the gain functions G1(t) and G2(t) are certain time-varying functions. A ratio between the gated intensity integrals, I2/I1, is a function of the luminescent lifetime when the modulation parameters are given. In the simplest case, the gain function is a top-hat function or a square function where G1(t) ¼ G2(t) ¼ 1 in the time intervals ΔT1 and ΔT2 and G1(t) ¼ G2(t) ¼ 0 elsewhere. In this case, the square waveform of G1(t) and G2(t) serves as an “on-off” gating function. The functional form for the excitation light and gain function can be selected to meet the measurement requirements for a specific test. Common combinations are a pulse excitation with a square gain function (pulse-square), a sine-waveform excitation with a square gain function (sine-square), a square-waveform excitation with a square gain function (squaresquare), and a sine-waveform excitation with a sine-waveform gain function (sinesine). Analyses of the gated intensity ratio techniques were given by Goss et al. (2000) and Bell (2001). Also, it was reported by Kuzmin et al. (2000) that the two-gate lifetime method could compensate for the effect of dusts in PSP measurements. The modulated luminescent intensity is integrated over a gate time interval from 0 to 1/2f (0 to π in ωt ) and over a gate time interval from 1/2f to 1/f (π to 2π in ωt ) relative to a modulated excitation light. For a Fourier-series-form of the modulated excitation light Eq. (6.4), a ratio between the two integrals is Z I 2 =I 1 ¼

Z

1=f

1=2f

I d t= 1=2f

I dt ¼

0

π  DðωτÞ , π þ DðωτÞ

ð6:24Þ

where h i nþ1 1 1 þ ð 1 Þ ð an n w τ þ bn Þ X 2 : D ðωτÞ ¼ a0 n¼1 n ð 1 þ n 2 ω2 τ 2 Þ Obviously, the ratio I2/I1 is only a function of the nondimensional lifetime ωτ and therefore it is related to pressure when the modulation frequency is fixed. In particular, the gated intensity ratio for a sinusoidally modulated excitation light with E(t) ¼ Am[1 + H sin (ωt)] has a simple form Z I 2 =I 1 ¼

Z

1=f

1=2f

I d t= 1=2f

0

I dt ¼

π ð1 þ ω2 τ2 Þ  2H : π ð1 þ ω2 τ2 Þ þ 2H

ð6:25Þ

Figure 6.7 shows the gated intensity ratio I2/I1 as a function of the nondimensional lifetime ωτ for the excitation light with the square, triangle, sine, and cosine waveforms. Although the lifetime is always positive, Fig. 6.7 plots the ratio I2/I1 over a range of 6  ωτ  6 to exhibit the global behavior of I2/I1 as a

140

6 Lifetime-Based Methods 2.4

triangle wave

2.0

cosine wave sine wave

I2/I1

1.6 1.2 0.8 0.4

square wave

0.0 -6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

(radian) Fig. 6.7 The gated intensity ratio as a function of the nondimensional luminescent lifetime

function of ωτ. The behavior of I2/I1 depends on the waveform of the modulated excitation light. Figure 6.8 shows the gated intensity ratio I2/I1 as a function of the relative pressure p/pref at different modulation frequencies for a typical PSP, Ru(dpp) in GE RTV 118, when a sinusoidal excitation light has the modulation depth of H ¼ 1. For a sinusoidal excitation light, the nondimensional modulation frequency and modulation depth can be selected to achieve the greatest sensitivity of the gated intensity ratio to pressure defined as Sp ¼

dðI 2 =I 1 Þ 8πω2 τH ∂τ ¼ : dp ½π ð1 þ ω2 τ2 Þ þ 2H 2 ∂p

ð6:26Þ

The optimal modulation frequency for the maximum sensitivity is ðωτÞop ¼

pffiffiffi 3  1:732:

ð6:27Þ

For Ru(dpp) in GE RTV 118 that has a lifetime of 4.7 μs at the ambient conditions, the optimal modulation frequency is 59 kHz. The appropriate modulation depth H can also be selected according to certain criteria for a balance between the pressure sensitivity and SNR. It is noted that the off-phase intensity I2 ¼ (Amτ/2f )[1  (2H/π)(1 + ω2τ2)1] decreases as H increases and the normalized off-phase intensity at the optimal modulation frequency is I2/(I2)H ¼ 0 ¼ 1  H/2π. Since the SNR is proportional to

6.2 Lifetime Techniques

141

1.2 Modulation frequency = 200 kHz

1.0

100 kHz

I2/I1

0.8 0.6

50 kHz

0.4

25 kHz

0.2

5 kHz

0.0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref Fig. 6.8 The gated intensity ratio as a function of pressure at different modulation frequencies for Ru(dpp) in GE RTV 118 (T ¼ 20  C and pref ¼ 1 atm) when the modulated excitation is sinusoidal

[I2/(I2)H ¼ 0]1/2 ¼ (1  H/2π)1/2, the SNR is a decreasing function of H in a range of 0  H  1. On the other hand, the normalized sensitivity Sp at the optimal modulation frequency, which is proportional to H/(2π + H )2, is an increasing function of H in a range of 0  H  1. Therefore, an appropriate modulation depth H of about 0.5 is chosen to achieve both high SNR and good pressure sensitivity. The gated intensity integrals I1 and I2 are taken over the intervals from 0 to 1/2f (0 to π in ωt ) and 1/2f to 1/f (π to 2π in ωt ). The time variable t in these integrals is relative to a modulated excitation light. The integration is carried out immediately after a measurement system receives a trigger signal that is synchronized with a modulated excitation light. The trigger signal can be provided by a photodiode sensing the excitation light or a driver for a modulator. In practice, however, the trigger signal may have a time delay relative to the excitation light. The time delay, although small, may significantly alter the relation between I2/I1 and pressure especially when the modulation frequency is high. For a sinusoidally modulated excitation light E(t) ¼ Am[1 + H sin (ωt )], if the trigger signal has a time delay Δt, the gated intensity ratio is given by

142

6 Lifetime-Based Methods

0.9 t = /2

0.8

I2/I1

0.7 0.6 0.5 /3

0.4

/4

0.3 0.2 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

P/Pref Fig. 6.9 The gated intensity ratio I2/I1 as a function of p/pref at different phase shifts ωΔt for Ru (dpp) in GE RTV 118 (T ¼ 20  C and pref ¼ 1 atm), where the sinusoidal modulation frequency is 25 kHz and the modulation depth H is one

Z I 2 =I 1 ¼

Z

1=f þΔt

1=2f þΔt

I dt=

1=2f þΔt

Δt

I dt ¼

π  2H cos ðφÞ cos ðφ  ωΔt Þ , π þ 2 H cos ðφÞ cos ðφ  ω Δt Þ

ð6:28Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where cos ðφÞ ¼ 1= 1 þ ðωt Þ2 . For a typical PSP, Ru(dpp) in GE RTV 118, Fig. 6.9 shows the relation between I2/I1 and p/pref for different phase shifts ωΔt, where the sinusoidal modulation frequency is 25 kHz and the modulation depth is H ¼ 1. It is clear that the behavior of the relation is significantly affected by the phase shifts ωΔt and the curve is even no longer monotonous when the phase shift is large. A similar change also occurs for the excitation light having other waveforms like the square waveform. This change due to the trigger signal delay was observed in experiments. Furthermore, the gated intensity ratio method can be applied to an ideal pulse excitation light; in this case, the luminescent intensity signal is described as an exponential decay, i.e., I (t) ¼ Am exp (t/τ). For two gating intervals [t0, t1] and [t2, t3] where a sequence t3 > t2 > t1 > t0 is assumed, the gated intensity ratio is Z I 2 =I 1 ¼

Z

t3

I dt= t2

t0

t1

I dt ¼

exp ðt 3 =τÞ  exp ðt 2 =τÞ : exp ðt 1 =τÞ  exp ðt 0 =τÞ

ð6:29Þ

For two given gating intervals, the ratio I2/I1 is only related to the lifetime. This integration approach was used as an alternative to the time-resolved pulse approach,

6.3 Fluorescence Lifetime Imaging

143

which was called the time-resolved multiple-gate method by Goss et al. (2000). Bell (2001) discussed an optimization problem of the gating parameters (t0, t1, t2, t3) to achieve the maximum sensitivity in an ICCD camera system. In a limiting but representative case where the time tg divides the two gating intervals [0, tg] and [tg, 1] (t0 ¼ 0, t3 ! 1, t1 ¼ t2 ¼ tg), we have a simple relation   exp t g =τ  : I 2 =I 1 ¼ 1  exp t g =τ

ð6:30Þ

The two-gate lifetime method is applied with CCD and CMOS cameras in PSP measurements on models in wind tunnels (Sellers 2000, 2009; Mitsuo et al. 2002, 2006a, b; Watkins et al. 2009; Yorita et al. 2017a, b, 2018; Sugioka et al. 2018). In addition, the single-shot two-gate lifetime method was used in PSP measurements on rotating blades and moving surfaces (Juliano et al. 2011; Disotell et al. 2014; Peng et al. 2017; Weiss et al. 2017b). Although the above methods utilize two gating intervals, three gating intervals can be similarly used and therefore two gatedintensity ratios I1/I2 and I1/I3 can be obtained. If the two gated-intensity ratios have sufficiently different dependencies to pressure and temperature for PSP, surface pressure and temperature distributions can be determined simultaneously from the two gated-intensity ratio images (Mitsuo et al. 2006a). As pointed out by Ruyten (2007), a necessary condition for a three-gate measurement to outperform a two-gate measurement is that the relative temperature sensitivities of I1/I2 and I1/I3 in the three-gate method must be substantially different from each other.

6.3 6.3.1

Fluorescence Lifetime Imaging Intensified CCD Camera

The structure of an intensified CCD (ICCD) system is illustrated in Fig. 6.10. After being impacted by a photon, the photocathode creates photoelectrons that are amplified by the micro-channel plate (MCP); the amplified electrons are converted back into photons by a phosphor screen. These photons are relayed to a CCD by either a fiber-optic bundle or a relay lens; the CCD creates the photoelectrons that are

Fig. 6.10 Structure of ICCD and multiple photon-electron conversions in ICCD

144

6 Lifetime-Based Methods

I(t,r)

Image Intensifier

I(t,r) G(t)

1 TINT

TINT 0

I(t,r)G(t)dt

CCD

G(t) Fig. 6.11 Diagram of lifetime imaging with ICCD for modulated illumination

measured. The advantage of ICCD is its ability of gating that allows the luminescent lifetime imaging over a painted area. Electronic shutter action can be produced by pulsing the MCP voltage and the gain can be modulated by simply changing the voltage on the intensifier. Figure 6.11 illustrates the luminescent lifetime imaging method with ICCD. For a pulse excitation light, the gain function is typically a top-hat function or a square function. The luminescent signal is gated in two different intervals during an exponential decay of luminescence and the gated intensity ratio is related to the luminescent lifetime by Eq. (6.29). This approach was employed for PSP measurements (Goss et al. 2000; Bencic 2001; Bell 2001; Baker 2001; Mitsuo et al. 2002). Another approach uses a sinusoidal excitation light combined with either the square gain function (Holmes 1998) or the sinusoidal gain function (Lakowicz and Berndt 1991). A fluorescent lifetime imaging (FLIM) system based on the sinusoidal excitation light was used for PSP measurements (Holmes 1998; Yorita et al. 2019; Sato et al. 2020). Consider a sinusoidally modulated excitation light E (t) ¼ Am[1 + H sin (ωt)] and the corresponding luminescent signal from PSP is I ðt Þ ¼ Am τ½1 þ HM eff sin ðω t  φÞ, where the effective amplitude modulation index is  1=2 M eff ¼ 1 þ τ2 ω2 ¼ cos ðφÞ: When the gain function has a square-waveform, the gated intensity ratio is given by Eq. (6.25). Instead of using the square function, Lakowicz and Berndt (1991) adopted a sinusoidal gain function for modulating the intensifier. When the MCP is sinusoidally modulated, the gain function of the detector is Gðt Þ ¼ G0 ½1 þ mD sin ðωt  θD Þ, where G0 is the intensifier gain without applying a modulating signal, mD is the gain modulation depth, and θD is the detector phase angle relative to the modulated illumination light. The CCD collecting photons over an integration time actually serves as an integrator; thus, the signal output from the CCD is represented by a time-averaged intensity over an integration time TINT, i.e.,

6.3 Fluorescence Lifetime Imaging

hI i ¼

1 T INT

Z

T INT

I ðt, r Þ Gðt Þdt ¼ Am τG0 ½1 þ 0:5M eff mD cos ðφ  θD Þ:

145

ð6:31Þ

0

To extract the phase angle or lifetime from the CCD output hIi, several values of hIi are obtained by changing the detector phase angle θD. Therefore, a system of equations is given for eliminating Am and G0. These equations can be solved using the least-squares method to determine the phase angle φ that is related to the luminescent lifetime τ. In the simplest case where only two different detector phase angles θD1 and θD2 are chosen, a ratio between the two time-averaged intensities at θD1 and θD2 is hI iðθD2 Þ 1 þ 0:5 mD cos ðφÞ cos ðφ  θD2 Þ ¼ : hI iðθD1 Þ 1 þ 0:5 mD cos ðφÞ cos ðφ  θD1 Þ

ð6:32Þ

Once the parameters mD, θD1, and θD2 are given, the intensity ratio in Eq. (6.32) is only related to the phase angle φ. Lakowicz and Berndt (1991) used three different detector phase angles to recover the luminescent lifetime. A FLIM system with an ICCD camera was used by Holmes (1998) for PSP measurements. Mitsuo et al. (2002) used an ICCD camera to obtain three gated intensities of PSP and simultaneously measure surface pressure and temperature fields in a sonic impinging jet. The FLIM was initially implemented in ICCD cameras, and the recent effort is focused on the application of the FLIM to CMOS sensors (Yorita et al. 2019; Sato et al. 2020).

6.3.2

Internally Gated CCD Camera

An internally gated CCD camera is available for luminescent lifetime imaging. Fisher et al. (1999) developed a phase-sensitive CCD camera system for imaging of concentrations of radical species in reacting flows such as turbulent flames. They modified a commercial scientific-grade CCD camera to perform phase-sensitive imaging as well as to reduce the level of integrated background light. In fact, this internally gated CCD camera has the capability to selectively integrate the timevarying luminescent intensity either in-phase or out-of-phase with respect to a modulated excitation light. A ratio between the out-of-phase and in-phase images is related to the luminescent lifetime, and thus a pressure field can be obtained from a luminescent lifetime image. CCD cameras have some features required to construct a phase-sensitive imaging system. Most notably, the feature commonly referred to as “electronic shuttering” can be suitably modified to serve phase-sensitive imaging or lifetime imaging. The CCD array architecture employed by cameras capable of performing electronic shuttering is referred to as an interline transfer array shown in Fig. 6.12. It consists of photodiodes separated by vertical transfer registers that are covered by an opaque

146

6 Lifetime-Based Methods

Fig. 6.12 Interline transfer CCD architecture and charge flow

metal shield that prevents direct entry of photoelectrons. The charge accumulated in the photosensors can be transferred either to the vertical registers or discarded in the substrate by supplying a high voltage to the Read Out Gate (ROG) or the Over Flow Drain (OFD), respectively. In order to perform phase-sensitive imaging, charge shifting and storage in the CCD must be synchronized with a light-source modulation signal. This requires appropriate modification of the camera controller logic, and of the camera head circuitry and logic. Based on the modulation waveform, a suitable control signal will be generated, which raises the ROG voltage and lowers the OFD voltage during the in-phase half of the cycle. The in-phase luminescent signal is thus integrated into the vertical register. In the out-of-phase half of the modulation cycle, the ROG and OFD voltages are reversed, thus dumping the out-of-phase light into the substrate. This process is repeated for a number of cycles until the full-well capacity of the vertical registers is utilized to maximize the SNR. Finally, after the desired integration time (or the number of cycles) the accumulated charge in the vertical registers can be read out through the horizontal register using conventional frame transfer techniques. The out-of-phase image can be similarly obtained, the only difference being the introduction of a 180 phase lag between the modulation signal and the control signal described above. As pointed out before, a ratio between the out-of-phase and in-phase intensity images, I2/I1, is a function of the phase angle or the luminescent lifetime; therefore, a pressure field can be obtained from a luminescent lifetime image. Mitsuo et al. (2006a, b) used a multi-gated CCD camera (Hamamatsu, C4742-9824ER) for lifetime-based PSP measurements. Franke and Holst (2015) introduced a four-gate method for a CMOS FLIM camera (pco.flim) with a sinusoidal modulation

6.4 Pressure Uncertainty

147

to determine the phase angle and the demodulation index. Yorita et al. (2019) and Sato et al. (2020) applied the four-gate method to a PCO FLIM camera in PSP measurements in wind tunnels.

6.4 6.4.1

Pressure Uncertainty Phase Method

The phase method for PSP measurements determines pressure by p¼

K 1 SV



 ωτ0 1 , tan φ

ð6:33Þ

where tan φ ¼ ωτ ¼  Vc/Vs is uniquely related to the lifetime for a fixed modulation frequency, and Vc ¼  AmτHMeff sin (φ) and Vs ¼ AmτHMeff cos (φ) are the DC components from the low-pass filters. The error propagation equation gives the relative variance of pressure, i.e., varðpÞ varðT Þ varðK SV Þ varðτ0 Þ ¼S2T þ S2K SV þ S2τ0 2 2 2 p τ20 T K SV þ S2V s

varðV s Þ varðV c Þ þ S2V c : 2 Vs V 2c

ð6:34Þ

The first term is the uncertainty related to temperature, the second is the uncertainty in PSP calibration, the third is the error in the given reference lifetime, and the last two terms are the uncertainties associated with a measurement system composed of a photodetector and a lock-in amplifier. The sensitivity coefficients in Eq. (6.34) are ST ¼

T ∂p T ∂K SV 1 þ K SV p T ∂τ0 þ , ¼ p ∂T K SV ∂T K SV p τ0 ∂T SK SV ¼

K SV ∂p ¼ 1, p ∂K SV

Sτ 0 ¼

τ0 ∂ p ¼ 1 þ 1=ðK SV pÞ, p ∂ τ0

SV s ¼

V s ∂p ¼ 1 þ 1=ðK SV pÞ, p ∂V s

148

6 Lifetime-Based Methods

SV c ¼

V c ∂p ¼ SV s : p ∂Vc

Compared to the intensity-based method, some error sources associated with model deformation do not exist, indicating the advantage of the lifetime-based method. When the photon shot noise of a detector dominates, the pressure uncertainty is mainly contributed by the last two terms in Eq. (6.34). In the photon-shotnoise-limited case, the uncertainties in the outputs of the detector and lock-in amplifier are var(Vs) ¼ j Vs j GħνBd and var(Vc) ¼ j Vc j GħνBd, where G is the system gain, Bd is the bandwidth of the system, and ħ is Planck’s constant. Therefore, the photon-shot-noise-limited pressure uncertainty is given by Δp ¼ p

  1=2  1=2 GBd ħν 1 1 þ K SV p 1þ : 1þ K SV p ωτ0 j Vs j

ð6:35Þ

Equation (6.35) for the phase method is similar to Eq. (5.7) for an intensity-based camera system. The behaviors of the pressure uncertainty as a function of pressure and the Stern–Volmer coefficient B are similar to those shown in Figs. 5.9 and 5.10.

6.4.2

Amplitude Demodulation Method

When the amplitude demodulation method is used, the pressure is given by 0 p¼

1 B @ K SV h

1 ωτ0 2

H ðV mean =V std Þ =2  1 2

C i1=2  1A,

ð6:36Þ

where Vmean and Vstd are the mean and standard deviation of the photodetector output, respectively. Thus, the error propagation equation gives the relative variance of pressure, i.e., varðpÞ varðT Þ varðK SV Þ varðτ0 Þ ¼S2T þ S2K SV þ S2τ0 2 2 p2 τ20 T K SV þ S2V mean

varðV mean Þ varðV std Þ þ S2V std : 2 V mean V 2std

:

ð6:37Þ

The first term is the uncertainty related to temperature, the second is the uncertainty in PSP calibration, the third is the error in the given reference lifetime, and the last two terms are the uncertainties associated with the photodetector. The sensitivity coefficients in Eq. (6.37) are

6.4 Pressure Uncertainty

149 50

( P/P)(V h )1/2 Normalized Pressure mean/GBdUncertainty

( P/P)(Vmean Normalized PressuredUncertainty

20

15

10

B = 0.5 0.6 0.7 0.8 0.9

5

0 0.0

0.5

1.0

1.5

2.0

45

P/Pref= 0.2

40 35

0.5

30 25 20

1.0

15

1.5

10

2.0

5 0 0.0

0.2

P/Pref

0.4

0.6

0.8

1.0

B

(a)

(b)

Fig. 6.13 The normalized pressure uncertainty (Δp/p)(Vmean/G ħ νBd)1/2 in the amplitude demodulation method with ωτ0 ¼ 10 and H ¼ 1 as (a) a function of p/pref for different values of the Stern– Volmer coefficient B and (b) a function of B for different values of p/pref

ST ¼

T ∂p T ∂K SV 1 þ K SV p T ∂τ0 ¼ þ , p ∂T K SV ∂T K SV p τ0 ∂T SK SV ¼ Sτ 0 ¼

SV mean

K SV ∂p ¼ 1, p ∂K SV

τ0 ∂ p ¼ 1 þ 1=ðK SV pÞ, p ∂ τ0

! 3 V mean ∂p 1 þ K SV p ð1 þ K SV pÞ ¼ ¼ þ , K SV p p ∂ ðV mean Þ K SV pðωτ0 Þ2 SV std ¼

V std ∂ p ¼ SV mean : p ∂ ðV std Þ

In the photon-shot-noise-limited case, the uncertainties in the detector outputs are var(Vmean) ¼ VmeanG ħνBd and var(Vstd) ¼ Vstd G ħνBd. Thus the photon-shot-noiselimited pressure uncertainty is #  1=2 " 3 Δp GBd ħν 1 þ K SV p ð1 þ K SV pÞ ¼ þ p V mean K SV p K SV pðωτ0 Þ2 8 #1=2 91=2 pffiffiffi " < = 2 ð ωτ Þ 2 0  1þ 1þ : H : ; ð1 þ K SV pÞ2

ð6:38Þ

150

6 Lifetime-Based Methods

The normalized pressure uncertainty (Δp/p)(Vmean/G ħ νBd)1/2 is shown in Fig. 6.13a as a function of p/pref at different values of the Stern–Volmer coefficient B for ωτ0 ¼ 10 and H ¼ 1. Here, for a fixed temperature T ¼ Tref, we use the following relations KSVp ¼ KSVpref( p/pref) ¼ (B/A)( p/pref) and A + B ¼ 1. Figure 6.13b shows the normalized pressure uncertainty (Δp/p)(Vmean/G ħ νBd)1/2 as a function of B at different values of p/pref for ωτ0 ¼ 10 and H ¼ 1. Interestingly, in this case, there is an optimal value of the Stern–Volmer coefficient B at which the normalized pressure uncertainty is minimal. The optimal value of the Stern–Volmer coefficient B varies between 0.7 and 0.9, depending on pressure.

6.4.3

Gated Intensity Ratio Method

In the gated intensity ratio method for a sinusoidally modulated excitation light, pressure can be expressed as a function of the gated detector output ratio V2/V1, i.e.,  1=2 ω τ0 2H 1 þ V 2 =V 1 1 p¼ 1  : K SV K SV π 1  V 2 =V 1

ð6:39Þ

Therefore, the error propagation equation is varðpÞ varðT Þ varðK SV Þ varðτ0 Þ ¼S2T þ S2K SV þ S2τ0 p2 τ20 T2 K 2SV þ S2V 1

ð6:40Þ

varðV 1 Þ varðV 2 Þ þ S2V 2 , V 21 V 22

where the sensitivity coefficients are ST ¼

T ∂p T ∂K SV 1 þ K SV p T ∂τ0 þ , ¼ p ∂T K SV ∂T K SV p τ0 ∂T SK SV ¼

K SV ∂p ¼ 1, p ∂K SV

τ0 ∂p ¼ 1 þ 1=ðK SV pÞ, p ∂τ0 n h i o π 1 þ ω2 τ20 ð1 þ K SV pÞ2  2H ð1 þ K SV pÞ3 Sτ 0 ¼

SV 1 ¼

V1 ∂p ¼ p ∂V1

2π ω2 τ20 K SV p SV 2 ¼

V2 ∂p ¼ SV 1 : p ∂V2

,

6.4 Pressure Uncertainty

151 15 1 d Normalized Pressure Uncertainty

3

( P/P)(V /GB h )1/2

1 d Uncertainty Normalized Pressure

4

B = 0.5

2 0.6 0.7 0.8 0.9

10

P/Pref= 0.2

0.5 5 1.0 1.5 2.0 0

1 0.0

0.5

1.0

1.5

2.0

0.0

(a)

0.2

0.4

0.6

0.8

1.0

B

P/Pref

(b)

Fig. 6.14 The normalized pressure uncertainty (Δp/p)(V1/G ħνBd)1/2 for the gated intensity method using a sinusoid modulation with ωτ0 ¼ 10 and H ¼ 1 as (a) a function of p/pref for different values of the Stern–Volmer coefficient B and (b) a function of B for different values of p/pref

In the photon-shot-noise-limited case, the uncertainties in the detector outputs are var(V1) ¼ V1 G ħ νBd and var(V2) ¼ V2 G ħ νBd. Thus, the photon-shot-noise-limited pressure uncertainty for the gated intensity ratio method is n h i o1=2 2 1=2 pffiffiffiffiffi 2 2 2π π 1 þ ω τ ð 1 þ K p Þ  2H SV 0 Δp GBd ħν ¼ p V1 2πω2 τ20 h i1=2 1 þ ω2 τ20 ð1 þ K SV pÞ2 ð1 þ K SV pÞ3 :  K SV p 

ð6:41Þ

Figure 6.14a shows the normalized pressure uncertainty (Δp/p)(V1/G ħνBd)1/2 as a function of p/pref at different values of the Stern–Volmer coefficient B for ωτ0 ¼ 10 and H ¼ 1. Figure 6.14b shows the normalized pressure uncertainty as a function of B at different values of p/pref for ωτ0 ¼ 10 and H ¼ 1. Similar to the amplitude demodulation method, there is an optimal value of B (around 0.8) to achieve the minimal value of (Δp/p)(Vmean/G ħνBd)1/2. In general, to reduce the noise, the gated intensity ratio method has to collect sufficient photons over many cycles. For example, compared to a standard CCD camera system with an integration time of 1 s, a gated CCD camera with a modulation frequency of 50 kHz needs to accumulate photons over 100,000 cycles to achieve the equivalently small uncertainty. The accumulation of photons can be done automatically in a phase-sensitive camera. When the gated intensity ratio method is applied to the pulse excitation light, pressure can be expressed as a function of the gated detector output ratio V2/V1

152

6 Lifetime-Based Methods

p¼

V 2 =V 1 τ0 1 ln  , t g K SV 1 þ V 2 =V 1 K SV

ð6:42Þ

where the time tg divides the two gating intervals [0, tg] and [tg, 1]. Thus, we have the pressure uncertainty varðpÞ varðT Þ varðK SV Þ varðτ0 Þ ¼S2T þ S2K SV þ S2τ0 p2 τ20 T2 K 2SV þ

S2V 1

varðV 1 Þ varðV 2 Þ þ S2V 2 , V 21 V 22

ð6:43Þ

where the sensitivity coefficients are ST ¼

 

T ∂p T 1 þ K SV p ∂τ ∂K SV ∂K SV ¼ 2 K SV 0  τ0 þ , p ∂T K SV p τ0 ∂T ∂T ∂T SK SV ¼ Sτ 0 ¼

SV 1 ¼

K SV ∂p ¼ 1, p ∂K SV

τ0 ∂ p ¼ 1 þ 1=ðK SV pÞ, p ∂ τ0

    V1 ∂p τ0 1  exp ð1 þ K SV pÞ t g =τ0 , ¼ p ∂V1 t g K SV p SV 2 ¼

V2 ∂p ¼ SV 1 : p ∂V2

In the photon-shot-noise-limited case, only the terms associated with V1 and V2 remain in Eq. (6.43) and the uncertainties of the system outputs are var(V1) ¼ V1 G ħνBd and var(V2) ¼ V2 G ħνBd. The photon-shot-noise-limited pressure uncertainty for the time-resolved multiple-gate method is Δp ¼ p

    1=2 1  exp ð1 þ K SV pÞ t g =τ0 GBd ħν 1      : V1 K SV p t g =τ0 exp 0:5ð1 þ K SV pÞ t g =τ0

ð6:44Þ

The factor V1/G ħ νBd equals to the number of photoelectrons collected in the first gating interval [0, tg]. Figure 6.15a shows the normalized pressure uncertainty (Δp/p)(V1/Għ νBd)1/2 as a function of p/pref at different values of the Stern– Volmer coefficient B for a fixed gating time tg/τ0 ¼ 0.2, where the relations KSVp ¼ (B/A)( p/pref) and A + B ¼ 1 are imposed. Figure 6.15b shows the normalized pressure uncertainty (Δp/p)(Vmean/G ħνBd)1/2 as a function of B at different values of p/pref for tg/τ0 ¼ 0.2. The optimal value of the Stern–Volmer coefficient B is in a range of 0.8–0.9. For tg/τ0 < 0.5, the pressure uncertainty Δp/p remains small, but Δp/p rapidly increases as tg/τ0 approaches one.

6.5 Lifetime Measurements

153

4

15

1/2

( P/P)(V1/GBdh ) Normalized Pressure Uncertainty

Normalized Pressure Uncertainty

P/Pref= 0.2

3 B = 0.5

0.6

2

0.7 0.8 0.9

10

0.5

1.0

5

1.5 2.0

0

1 0.0

0.5

1.0

1.5

2.0

0.0

(a)

0.2

0.4

0.6

0.8

1.0

B

P/Pref

(b)

Fig. 6.15 The normalized pressure uncertainty (Δp/p)(V1/Għ νBd)1/2 for the gated intensity method with a pulse excitation and tg/τ0 ¼ 0.2 as (a) a function of p/pref for different values of the Stern– Volmer coefficient B and (b) a function of B for different values of p/pref

6.5

Lifetime Measurements

Yorita et al. (2018) studied the effects of illumination sources (LED and laser) on the lifetime of a typical DLR PSP where PtTFPP was used as a sensor dye and poly (4-tert-butyl styrene) was used in both active layer and basecoat. Figure 6.16a shows normalized excitation and lifetime decay curves of this PtTFPP-based PSP. PSP was excited either by LED (pulse width of 12 μs) or laser (pulse width of 10 ns). Normalized PSP signals for the LED excitation show almost no sensitivity to pressure during excitation, whereas the lifetime decay part shows significant pressure sensitivity for both the excitations. The measured shorter lifetime for the laser excitation was related to the length of the excitation pulse. To examine the effect of excitation wavelength, a green-LED was operated exactly like the UV-LED. As shown in Fig. 6.16b, only a slightly shorter decay time was measured when PSP was excited by the green-LED in comparison to the UV-LED excitation. The decay curves for a pyrene-based PSP used in DLR are given in Fig. 6.17a at three different pressure values in comparison with a ruthenium-based PSP (Engler et al. 2000). Figure 6.17b shows typical luminescence decay curves for a pyrenebased sensor at three different pressure values with the finer time scale. Due to the very short lifetime of pyrene-based PSP (nanoseconds), it is not suitable for lifetimebased measurements using cameras. Lachendro (2000) used an experimental set-up for phase calibration of PSP and TSP formulations at temperatures as low as 30  C, which was capable of holding pressures down to 207 Pa. In order to make phase calibrations, LED arrays were used as a modulated excitation light source; a blue LED array was used for ruthenium-

154

6 Lifetime-Based Methods

Fig. 6.16 Luminescent decay curves of a PtTFPP-based PSP for (a) excitation pulse widths, and (b) different excitation wavelengths. (From Yorita et al. 2018)

based luminophores and a green LED array for porphyrin-based luminophores. The light from the LED array was passed through an appropriate interference filter to eliminate unwanted emission. A function generator was used to directly power and modulate the arrays; the TTL signal from the function generator was used as an external reference signal for a lock-in amplifier. After passing through a focusing lens, the luminescent response of PSP (or TSP) was detected using a PMT fitted with an interference filter centered at 620 nm and then was sampled by the lock-in

6.5 Lifetime Measurements

155

Fig. 6.17 Luminescent decay curves for a pyrene-based PSP: (a) comparison with a rutheniumbased PSP and (b) zoomed-in view. (From Engler et al. 2000)

0 -5

Phase Shift (Degrees)

-10 -15 -20

-30 C -20 C -15 C -10 C -5 C 0C 10 C 20 C 3rd Order

-25 -30 -35 -40 -45 -50 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Pressure (psia)

Fig. 6.18 Phase calibration for PSP, Ru(dpp) in RTV 110 with silica gel. (From Lachendro 2000)

amplifier. A PC was used to acquire calibration data from the lock-in amplifier. Figures 6.18, 6.19, and 6.20 show phase calibration results for three PSP formulations: Ru(dpp) in a silicone polymer with silica gel, PtTFPP in a silicone polymer with silica gel, and PtTFPP in a porous polymer/ceramic(Al2O3) composite tape casting. Figures 6.21, 6.22, and 6.23 show phase calibration results for three TSP formulations: PtTFPP, Ru(trpy)(C6F5-trpy)(NO3)2, and Ru(bipy)2(p-bipy)2 in DuPont ChromaClear. Goss et al. (2000) evaluated the lifetime techniques based on several different modulation/gating combinations, such as the time-resolved multiple-gate method for a pulse excitation, sine-square method, and square-square method. The detectors were ICCD, phase-sensitive interline-transfer CCD, and back-lit CCD with a liquidcrystal shutter. A xenon strobe light and a Nd:YAG laser were used as a pulse light

156

6 Lifetime-Based Methods

0 -2

Phase Shift (Degrees)

-4 -6 -8 -10

-30 C -18 C -3 C 10 C 20 C 5th Order Fit

-12 -14 -16 -18 -20 -22 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Pressure(psia) Fig. 6.19 Phase calibration for PSP, PtTFPP in RTV 110 with silica gel. (From Lachendro 2000)

4 0

-50 C -45 C -40 C -35 C -30 C -25 C -20 C -15 C -10 C -5 C 0C 5C 10 C 15 C 20 C 25 C

Phase Shift (Degrees)

-4 -8 -12 -16 -20 -24 -28 -32 -36 -40 -44 0

1

2

3

4

5

6 7 8 9 10 11 12 13 14 15 Pressure (psia)

Fig. 6.20 Phase calibrations for PSP, PtTFPP in a porous polymer/ceramic(Al2O3) composite tape casting. (From Lachendro 2000)

6.5 Lifetime Measurements

157

0 -1

Phase Shift (degrees)

-2 -3 -4 -5 -6 -7 -8 -9 -10 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 Temperature ( C)

0

5

10 15 20

Fig. 6.21 Phase calibration for TSP, PtTFPP in DuPont ChromaClear. (From Lachendro 2000)

0 -2 Phase Shift (degrees)

-4 -6 -8 -10 -12 -14 -16 -18 -20 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5

0

5

10 15 20

Temperature ( C) Fig. 6.22 Phase calibration for TSP, Ru(trpy)(C6F5-trpy)(NO3)2 in DuPont ChromaClear. (From Lachendro 2000)

source, while an LED array was used for sinusoidal and square-wave excitation. PSP tested was PtTFPP in a sol-gel binder. The gated intensity ratio was measured as a function of pressure using the detectors with different gating strategies. They found that the time-resolved multiple-gate method had a greater sensitivity to pressure than

158

6 Lifetime-Based Methods

2 0 Phase Shift (degrees)

-2 -4 -6 -8 -10 -12 -14 -16 -18 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5

0

5 10 15 20 25

o

Temperature ( C) Fig. 6.23 Phase calibration for TSP, Ru(bipy)2(p-bipy)2 in DuPont ChromaClear. (From Lachendro 2000) 1.8 1.6

Multiple-Gate Method Square-Square Method

Gated Intensity Ratio

1.4

PtTFPP-sol-gel PSP

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0

20

40

60

80

100

Pressure (kPa)

Fig. 6.24 Calibration of the gated intensity ratio for PtTFPP-sol-gel PSP with ICCD using the time-resolved multiple-gate method and square-square method. (From Goss et al. 2000)

other lifetime methods and the intensity-based method. The square-square method had the second best sensitivity to pressure. Figure 6.24 shows calibration results of the gated intensity ratio for that PSP obtained with ICCD employing the time-

6.5 Lifetime Measurements

159

resolved multiple-gate method and square-square method. One of the problems with ICCD was the high noise level of the system; the RMS variation of the gated intensity ratio was as high as 3–5% even after binning. Bell (2001) studied the time-resolved multiple-gate method for a pulse excitation light to optimize the gating parameters. He found that the gated intensity ratio was not constant over a PSP-coated surface even at constant pressure and temperature. The variation was 0.5–3% depending on the homogeneity of the paint. This indicated that the lifetime was different at different locations even when pressure and temperature are uniformly invariant over a surface. In laser-scanning PSP measurements, Torgerson et al. (1996) observed a variation of about 0.5 in the phase angle (related to the lifetime) across a measurement domain in the flow-off case where pressure and temperature were constant. Similar to Bell’s observation on the gated intensity ratio, the spatial phase pattern was repeatable, dependent on the location. Hartmann et al. (1995) also observed similar results and attributed this phenomenon to the microheterogeneity of the polymer environment. The small lifetime or phase variation may not significantly affect PSP measurements at higher Mach numbers, whereas it can introduce a considerable error in low-speed PSP measurements. To correct this intrinsic spatial variation of the lifetime, Torgerson et al. (1996) and Bell (2001) used raw lifetime or phase distributions in the flow-off conditions as a reference and took a ratio between the wind-on and reference lifetime images (signals). Unfortunately, this correction method to a certain degree defeats the original purpose of using the lifetime method to eliminate the wind-off reference. Bencic (2001) compared the lifetime method with the intensity-based method for PSP measurements at high viewing polar angles and in a shadowed region and found that the lifetime-based measurements achieved better results in these cases. Mitsuo et al. (2002) studied the luminescent decay of a PtTFPP-based PSP using a streak camera and found that the multiple-exponential decay of the paint was sensitively dependent on pressure and temperature. This characteristic allowed simultaneous determination of pressure and temperature from three gated intensities obtained by an ICCD camera since two ratios between the three gated intensities had sufficiently different dependencies on pressure and temperature. They selected the first and third gating intervals ΔT1 ¼ 0–0.8 μs and ΔT3 ¼ 30–82.8 μs. The gated intensity I1 in ΔT1 was almost independent of both pressure and temperature, whereas the gated intensity I3 in ΔT3 was very sensitive to pressure and temperature. The second gating interval ΔT2 ¼ 12–19.4 μs was chosen based on the minimization of the pressure error due to a small perturbation of the intensity ratio signal. Their calibration experiments showed that pressure could be well described by polynomials of the gated intensity ratios I1/I2 and I1/I3 with the temperature-dependent coefficients. Using the calibration relations, they were able to obtain surface pressure and temperature fields in a sonic impinging jet simultaneously. Later, Mitsuo et al. (2006a, b) used a multi-gated CCD camera (Hamamatsu, C4742-98-24ER) in threegate lifetime-based PSP measurements. Also, Watkins et al. (2003) used a new internally gated interline transfer CCD camera to alleviate noise sources associated with ICCD.

160

1.6

Gate ratio (Gate1/Gate2)

Fig. 6.25 Pressure sensitivity curves of the two-gate lifetime-based method for the DLR PtTFPP-based PSP. (From Yorita et al. 2017a)

6 Lifetime-Based Methods

1.4 1.2 1 0.8

20 °C

0.6

30 °C

0.4 0.2

40 °C 0

20

40

60 80 Pressure [kPa]

100

120

Fig. 6.26 PSP images obtained by the two-gate lifetime method on a delta wing: (a) before and (b) after image alignment. (From Yorita et al. 2017a)

Yorita et al. (2017a, b) applied the two-gate method to PSP measurements in large wind tunnels with a multi-gated CCD camera (PCO, PCO4000). This camera was operated in on-chip accumulation (modulation) mode in which the camera shutter was opened many times with a constant time delay relative to each LED light pulse. Therefore, PSP luminescence images were accumulated on the CCD chip via multiple exposures. Figure 6.25 shows the sensitivity of the two-gate ratio to pressure for a DLR PSP based on PtTFPP in a polymer [poly(4-tert-butyl styrene)]. Lifetime-based PSP measurements on a delta wing were conducted at Mach numbers of 0.3–0.75 in the Transonic Wind Tunnel in Göttingen (TWG). PSP results before and after image alignment at Mach 0.5 and AoA ¼ 15 are shown in Fig. 6.26. Watkins et al. (2009) also used the two-gate lifetime method in PSP measurements.

6.5 Lifetime Measurements

161

A fluorescent lifetime imaging (FLIM) system, originally proposed by biochemists for oxygen detection in a small area (Szmacinski and Lakowicz 1995; Hartmann and Ziegler 1996), was adapted for PSP and TSP measurements in wind tunnels (Holmes 1998). Franke and Holst (2015) introduced a four-gate method for a CMOS fluorescent lifetime imaging camera (PCO FLIM). Four gated images I1, I2, I3, and I4 are acquired at the phases of 0, π/2, π, and 3π/2 of a modulation signal with an integration width of each image being a half of the sinusoidal modulation period. The tangent of the phase angle and the demodulation index can be evaluated by I4  I2 , I1  I3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðI 1  I 3 Þ2 þ ðI 4  I 2 Þ2 ¼ : I1 þ I2 þ I3 þ I4 tan ϕ ¼

M eff

0

0.5

-1

0.4

-2 -3

-4 -5

(a)

293 K 303 K 313 K 0

20

40 60 Pressure, kPa

80

Demodulation index mem

Phase angle tanΦ

Yorita et al. (2019) evaluated the application of a PCO FLIM camera to PSP measurements in wind tunnels. The DLR PtTFPP-based PSP was used, which has the lifetime of approximately 10 μs at the ambient condition and 50 μs at the vacuum condition. The modulation frequency of a sinusoidal excitation light was set to 20 kHz, and consequently the image gate width was 25 μs. Figure 6.27 shows the pressure and temperature dependency of the tangent of the phase angle and the demodulation index for the DLR PSP. Sato et al. (2020) further investigated the effects of the relevant parameters, such as the modulation frequency on PSP

0.3 0.2

0

100

293 K 303 K 313 K

0.1

0

20

40 60 Pressure, kPa

80

100

(b)

Fig. 6.27 Pressure and temperature dependencies of (a) the phase angle and (b) the demodulation index for the DLR PtTFPP-based PSP when the sinusoidal excitation light is set to 20 kHz. (From Yorita et al. 2019)

162

6 Lifetime-Based Methods

Fig. 6.28 Pressure distributions obtained by the FLIM-PSP technique at Mach 0.85 and a high AoA from (a) phase angle and (b) demodulation index. (From Yorita et al. 2019)

measurements with a PCO FLIM camera. Figure 6.28 shows a surface pressure field measured by the FLIM-PSP technique at Mach 0.85 and a high AoA in TWG. Pressure patterns generated by the leading-edge vortices are visualized by both the phase angle and the demodulation index.

Chapter 7

Time Response

This chapter describes the time responses of PSP and TSP to unsteady flows, which are determined by the oxygen and thermal diffusion processes in thin paint layers, respectively. The solutions of the 1D unsteady oxygen diffusion equation for a PSP layer are given, which describe the pressure response of PSP, diffusion timescale, and effect of the layer thickness. Theoretical analysis and experimental data indicate that a conventional polymer PSP has a slow time response such that it is not suitable for unsteady flow measurements. In contrast, a porous PSP can achieve a short response time of about microseconds. The relevant topics of time responses of porous PSP are discussed, including the pore geometry, effective diffusivity, Knudsen diffusion, nonlinear quenching kinetics, and the effect of the luminescent lifetime on the time response. The time response measurement apparatus for PSP are described, including solenoid valve, shock tube, acoustic resonance tube, and fluidic oscillator. Similarly, the solutions of the 1D unsteady heat conduction equation for a TSP layer are described along with time response measurement setups for TSP.

7.1 7.1.1

Time Response of Conventional PSP Oxygen Diffusion

Fast time response of PSP is required for unsteady flow measurements, which is related to two characteristic timescales of PSP. One is the luminescent lifetime of PSP, representing an intrinsic physical limit for an achievable temporal resolution of PSP. Another is a timescale of oxygen diffusion across a PSP layer. Because a timescale of oxygen diffusion across a conventional polymer layer is usually much larger than the luminescent lifetime, the time response of PSP is mainly determined by oxygen diffusion. In a thin homogeneous polymer layer, when diffusion is © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_7

163

164

7 Time Response

Fickian, the oxygen concentration [O2] can be described by the one-dimension diffusion equation 2

∂½O2  ∂ ½O2  ¼ Dm , ∂t ∂ z2

ð7:1Þ

where Dm is the diffusivity of oxygen mass transfer, t is time, and z is the coordinate directing from a wall to the polymer layer. The boundary conditions at a solid wall and the air-paint interface for Eq. (7.1) are ∂½O2 =∂ z ¼ 0

at z ¼ 0,

ð7:2Þ

½O2  ¼ ½O2 0 f ðt Þ at z ¼ h,

where the nondimensional function f(t) describes a temporal change of the oxygen concentration at the air-paint interface, [O2]0 is a constant concentration of oxygen, and h is the paint layer thickness. The initial condition for Eq. (7.1) is ½O2  ¼ ½O2 0 f ð0Þ at t ¼ 0:

ð7:3Þ

Introducing the nondimensional variables nðt 0 , z0 Þ ¼ ½O2 =½O2 0  f ð0Þ,

z0 ¼ z=h,

t 0 ¼ tDm =h2 ,

ð7:4Þ

we have the nondimensional diffusion equation 2

∂n ∂ n ¼ , ∂ t 0 ∂ z0 2

ð7:5Þ

with the boundary and initial conditions ∂n=∂ z0 ¼ 0

at z ¼ 0,

n ¼ gð t 0 Þ

at z0 ¼ 1,

n¼0

at t ¼ 0,

ð7:6Þ

where the function g(t0) is defined as g(t0) ¼ f(t0)  f(0) that satisfies the initial condition g(0) ¼ 0. Applying the Laplace transform to Eq. (7.5) and the boundary and initial conditions Eq. (7.6), we obtain a general convolution-type solution for the normalized oxygen concentration n(t0, z0) nð t 0 , z 0 Þ ¼

Z

t0

gt ðt 0  uÞW ðu, z0 Þdu:

ð7:7Þ

0

In Eq. (7.7), the function gt(t) ¼ dg(t)/dt ¼ df(t)/dt is the differentiation of g(t) with respect to time and the function W(t, z) is defined as

7.1 Time Response of Conventional PSP

165

  X   1 1 þ 2k  z 1 þ 2k þ z k pffi pffi W ðt, zÞ ¼ ð1Þ erfc ð1Þ erfc þ : 2 t 2 t k¼0 k¼0 1 X

k

ð7:8Þ

The derivation of Eq. (7.7) uses the following expansion in negative exponentials 1    pffiffi1 X pffiffi ¼ ð1Þn exp 2n s , 1 þ exp 2 s n¼0

where s is the complex variable of the Laplace transform. In particular, for a step change of the oxygen concentration at the air-paint interface, after gt(t) ¼ δ(t) is substituted into Eq. (7.7), the oxygen concentration distribution in a paint layer is simply n(t0, z0) ¼ W(t0, z0), which is a classical solution given by Crank (1995) and Carslaw and Jaeger (2000). Winslow et al. (2001) studied a solution of the diffusion equation using an approach of linear system dynamics. The special solutions for a step change and a sinusoidal change of oxygen were used for PSP dynamical analysis by several researchers (Winslow et al. 1996, 2001; Carroll et al. 1995, 1996; Mosharov et al. 1997; Fonov et al. 1998). A trigonometrical-series-type solution for a step change of oxygen given by Carroll et al. (1996) is 1  X   ½O2 ðt, zÞ  ½O2 min ¼1 Ak cos ðλk zÞ exp λ2k Dm t , ½O2 max  ½O2 min k¼1

ð7:9Þ

where Ak ¼  2(1)k/(hλk), λk ¼ (2k  1)π/(2h), [O2]max ¼ [O2](t, h), and [O2]min ¼ [O2](0, z). Similarly, Winslow et al. (1996) used a trigonometrical-seriestype solution for a sinusoidal change of oxygen ½O2 ðt, zÞ  ½O2 0

1 k1 ð2k  1Þπ z 4 X ð1Þ sin ðωt  βk Þ cos ðβk Þ, ¼ ½O2 1 cos 2h π k¼1 ð2k  1Þ

ð7:10Þ

where " βk ¼ tan

1

# 4h2 ω : π 2 ð2k  1Þ2 Dm

The constants [O2]0 and [O2]1 are given in the initial and boundary conditions [O2](0, z) ¼ [O2]0 and [O2](t, h) ¼ [O2]0 + [O2]1 sin (ω t). Mosharov et al. (1997) also presented a trigonometrical-series-type solution of the diffusion equation to Eq. (7.9) for a step change at a surface. Note that they defined a coordinate system in such a way that the air-paint interface was at z ¼ 0 and the wall was at z ¼ h. For a sinusoidal change of oxygen

166

7 Time Response

[O2](t, 0) ¼ [O2]0 + [O2]1 sin (ω t) at the air-paint interface, they gave a solution composed of two harmonic terms, i.e., ½O2 ðt, zÞ ¼ ½O2 0 þ ½O2 1 ½X ðγ, z0 Þ sin ðω t Þ þ Y ðγ, z0 Þ cos ðω t Þ,

ð7:11Þ

where γ ¼ (ω h2/Dm)1/2 is a nondimensional frequency and z0 ¼ z/h is a nondimensional coordinate normal to a wall. The coefficients in Eq. (7.11) are X ðγ, z0 Þ ¼

cosh

pffiffiffi pffiffiffi pffiffiffi   pffiffiffi   2 γ ð1  z0 =2Þ cos γ z0 = 2 þ cos 2 γ ð1  z0 =2Þ cosh γ z0 = 2 pffiffiffi  pffiffiffi  , cosh 2 γ þ cos 2 γ

Y ðγ, z0 Þ ¼

sinh

pffiffiffi pffiffiffi pffiffiffi   pffiffiffi   2 γ ð1  z0 =2Þ sin γ z0 = 2 þ sin 2 γ ð1  z0 =2Þ sinh γ z0 = 2 pffiffiffi  pffiffiffi  : cosh 2 γ þ cos 2 γ ð7:12Þ

These trigonometrical-series-type solutions, which are often obtained using the method of separation of variables, should be equivalent to the general convolutiontype solution Eq. (7.7) in these special cases. The solutions of the diffusion equation give a classical square-law estimate for a diffusion timescale τdiff through a homogeneous PSP layer, i.e., τdiff / h2 =Dm :

ð7:13Þ

The square-law estimate is actually a phenomenological manifestation of the statistical theory of the Brownian motion. Interestingly, this estimate is still valid even when the diffusivity of a homogeneous polymer is concentration dependent. The 1D diffusion equation with the concentration-dependent diffusivity can be reduced to an ordinary differential equation by using Boltzmann’s transformation ξ ¼ z/(2t1/2); hence, the solution for the concentration distribution can be expressed by this similarity variable (Crank 1995). Clearly, Boltzmann’s scaling indicates that a timescale for any point to reach a given concentration is proportional to the square of the distance (or thickness). Using the solution of the diffusion equation for a step change of pressure, Carroll et al. (1997) estimated the mass diffusivity Dm for oxygen in a typical silicon polymer binder and gave Dm ¼ 1.23  1.88  109 m2/s over a temperature range of 9.9 – 40.2  C. The values of Dm ¼ 3.55  109 m2/s for the pure polymer poly(dimethyl siloxane) (PDMS) and Dm ¼ 1.2  109 m2/s for PDMS with 10% fillers were also reported (Cox and Dunn 1986; Pualy 1989). For a 10 μm thick polymer layer having the diffusivity of Dm ¼ 1010  109 m2/s, a diffusion timescale is in the order of 0.1 – 1 s. Therefore, a conventional nonporous polymer

7.1 Time Response of Conventional PSP

167

PSP has a slow time response, and it is not suitable to unsteady pressure measurements.

7.1.2

Pressure Response and Optimum Thickness

Schairer (2002) studied the pressure response of PSP based on the solution Eq. (7.11) of the diffusion equation given by Mosharov et al. (1997). In a simpler notation, the luminescent intensity integrated over a paint layer is expressed as Z

h

I ðt Þ ¼ C 0

exp ðβzÞ dz, a þ k½O2 ðt, zÞ

ð7:14Þ

where β is the extinction coefficient for the excitation light, C is a proportional constant, and a and k are the coefficients. In a quasi-steady case, the indicated pressure by PSP is pPSP ðt Þ ¼ ½I ref =I ðt Þ  A=B,

ð7:15Þ

where the Stern–Volmer coefficients are determined from steady-state calibration of PSP. As shown in Eq. (7.15) coupled with Eqs. (7.11), (7.12), and (7.14), the indicated pressure pPSP(t) is a nonlinear function of the true pressure that sinusoidally varies with time, i.e., p(t) ¼ p0 + p1 sin (ω t), although the diffusion equation is linear. However, if the unsteady pressure amplitude is small compared to the mean pressure ( p1  p0), the PSP response can be linearized and it is given by pPSP ðt Þ ¼p0PSP þ p1PSP sin ðω t þ φÞ ¼p0 þ p1 ½αðγ Þ sin ðω t Þ þ βðγ Þ cos ðω t Þ,

ð7:16Þ

where δ ln ð10Þ αðγ Þ ¼ 1  10δ β ðγ Þ ¼

δ ln ð10Þ 1  10δ

Z

1

10δ η X ðγ, ηÞdη,

0

Z

1

10δ η Y ðγ, ηÞdη:

ð7:17Þ

0

The quantity δ ¼ βh/ ln (10) represents the optical thickness of a paint layer. The unsteady amplitude ratio and phase shift are given by

168

7 Time Response

Fig. 7.1 The unsteady amplitude ratio as a function of the PSP thickness for δ/h ¼ 0.01/μm and Dm ¼ 103 μm2/s. (From Schairer 2002)

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p1PSP =p1 ¼ α2 þ β2 , ϕ ¼ tan 1 ðβ=αÞ:

ð7:18Þ

Figure 7.1 shows the attenuated amplitude ratio p1PSP/p1 at different frequencies for δ/h ¼ 0.01/μm and Dm ¼ 103 μm2/s. The paint thickness affects both the frequency response and the SNR of PSP. As the thickness increases, the luminescent signal from PSP and thus the SNR increase, whereas the frequency response of PSP decreases as a result of the attenuation of the unsteady amplitude ratio. Hence, there exists an optimum thickness that balances the two conflicting requirements to achieve both high frequency response and SNR. Considering the unsteady luminescent signal I(t) ¼pIffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 + I1 sin (ω t), Schairer (2002) 2 þ β 2 and then the unsteady α introduced the unsteady signal amplitude I ¼ I 1 0 pffiffiffiffi pffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 0 SNR, SNR ¼ I 1 = I 0 ¼ I 0 α2 þ β . Figure 7.2 shows the normalized SNR0 as a function of the relative thickness h/h(1.25 dB), where h(1.25 dB) is the thickness that corresponds to 1.25 dB ( p1PSP/p1 ¼ 0.866) attenuation of the unsteady amplitude ratio as illustrated in Fig. 7.1. Thus, an empirical estimate for the optimum thickness is hop/h(1.25 dB)  1 that corresponds to the maximum value of the normalized SNR0. As shown in Fig. 7.3, the optimum thickness hop  h(1.25 dB) decreases with the unsteady pressure frequency for a given diffusivity and a relative optical thickness. Figure 7.3 indicates that the optimum thickness is less than 5 μm for Dm < 16  103 μm2/s when the pffiffiffiffipressure frequency is 100 Hz. For such a thin paint layer, the absolute SNR (/ I 0 ) is so low that accurate measurement of the luminescent emission becomes difficult. This indicates that a conventional polymerbased PSP is not suitable to unsteady measurements. When an unsteady pressure variation is no longer small, the nonlinear effect of PSP response is appreciable, and a waveform of PSP signal is distorted. In this case,

7.1 Time Response of Conventional PSP

169

Fig. 7.2 The normalized SNR’ as a function of the relative PSP thickness for δ/h ¼ 0.01/μm and Dm ¼ 103 μm2/s. (From Schairer 2002)

Fig. 7.3 The optimum thickness of PSP as a function of the unsteady pressure frequency for δ/h ¼ 0.01/μm. (From Schairer 2002)

the recovery of the true unsteady pressure from the distorted signal is nontrivial. Assuming that the oxygen concentration is uniform across a thin paint layer, we substitute pPSP ðt Þ  p ¼ ½O2  S1 ϕ1 into Eq. (7.15) and use the general O2 convolution-type solution Eq. (7.7) for [O2], where S is the oxygen solubility of the binder and ϕO2 is the mole fraction of oxygen in air. Thus, at the air-paint interface (z0 ¼ z/h ¼ 1), we obtain a Volterra-type integral equation for the function gt(t) ¼ dg(t)/dt ¼ df(t)/dt

170

7 Time Response



Z t0 1 I ref gt ðt 0  uÞ W ðu, 1Þ du,  A  f ð 0Þ ¼ B p0 I ð t Þ 0

ð7:19Þ

where p0 ¼ ½O2 0 S1 ϕ1 O2 is the initial pressure amplitude. In principle, after Eq. (7.19) is solved for f(t), the unsteady pressure can be recovered, i.e., p(t) ¼ p0 f(t). However, since the nondimensional time variable t0 ¼ tDm/h2 in Eq. (7.19) contains the diffusion timescale τdiff ¼ h2/Dm, recovery of the true unsteady pressure is affected by the local paint thickness unlike steady-state PSP measurements where the effect of the thickness is eliminated by the intensity ratio procedure.

7.2 7.2.1

Time Response of Porous PSP Deviation from the Square-Law

Compared to a conventional homogeneous PSP, a porous PSP has a much shorter diffusion timescale ranging from 18 to 500 μs due to enlarged air-polymer interface (Sakaue and Sullivan 2001; Sakaue et al. 2002a, 2013b). Interestingly, measurements of response time for three polymers, GP197, GP197/BaSO4 mixture, and poly(TMSP), showed that the classical square-law estimate Eq. (7.13) did not hold for a porous PSP (Teduka et al. 2000; Teduka 2001; Asai et al. 2001). As shown in Fig. 7.4, measurements gave the power-law relations for the diffusion timescale

Time constant, msec

1000

diff

h 1.83

GP197

100

h 1.07

diff

10 diff

1

h 0.29

diff

0.1

GP197/BaSO4

poly(TMSP)

h 0.573

AA-PSP

0.01

1

10

Thickness, micron Fig. 7.4 The power-law relationship between the response time and coating thickness for three polymers GP197, GP197/BaSO4 mixture, and poly(TMSP) at 313.1 K, and AA surface at 300 K. (Experimental data are collected from Teduka 2001, Asai et al. 2001, and Sakaue 1999)

7.2 Time Response of Porous PSP 0.5

0.4

Power-law exponent

Fig. 7.5 The exponent of the power-law relation between timescale and coating thickness for the polymer poly(TMSP) as a function of temperature. (Experimental data are collected from Teduka 2001 and Asai et al. 2001)

171

0.3

0.2

0.1

0.0 290

295

300

305

310

315

320

325

Temperature, K

τdiff / h1.83 for GP197, τdiff / h1.07 for GP197/BaSO4 mixture, and τdiff / h0.29 for poly(TMSP) at 313.1 K. For a porous anodized aluminum (AA) surface, the powerlaw relation is τdiff / h0.573 (Sakaue 1999; Sakaue and Sullivan 2001). For the GP197 silicone polymer, the power-law exponent is close to 2 as predicted by the classical estimate for a homogeneous polymer film. However, the power-law exponent for the porous materials GP197/BaSO4 mixture, poly(TMSP), and AA-PSP is significantly smaller than 2. Figure 7.5 shows that the power-law exponent for the polymer poly(TMSP) linearly increases with temperature over a temperature range from 293.1 to 323.1 K. In addition, Hayashi and Sakaue (2017) found τdiff / h0.208 for another porous PSP (PC-PSP).

7.2.2

Effective Diffusivity: Geometrical Perspective

In order to understand the time response of a porous PSP, from a standpoint of phenomenology, Liu et al. (2001b) derived an expression for the effective diffusivity and diffusion timescale of a porous layer. Diffusion in a porous material can be considered as a diffusion problem in a two-phase system. In PSP, the disperse phase is composed of numerous pores filled with air. Consider an element of a porous polymer layer of the length l, width l, and thickness h, as shown in Fig. 7.6. The coordinate z is directed normally into a polymer layer from the upper surface of the layer. First, we assume that many cylindrical (tube-like) pores are distributed and oriented in the z-direction in the element. The effective radius and depth of a pore are denoted by rpore and hpore, respectively. The radius of a pore is much larger than the size of a molecule of oxygen. In general, the depth of a pore is smaller than or equal to the layer thickness, i.e., hpore h. For simplicity of expression, the normal

172

7 Time Response

Fig. 7.6 Element of a porous binder layer

directional derivative of the oxygen concentration [O2] at the air-polymer interface is denoted by vn ðzÞ ¼

∂½O2  : ∂n

ð7:20Þ

The effective diffusivity Dmeff of a porous polymer layer with many cylindrical pores is given by a balance equation between the mass transfer through the apparent homogeneous upper surface and the total mass transfer across the air-polymer interface, i.e.,    Dmeff l2 vn ð0Þ ¼Dm l2  N pore π r 2pore vn ð0Þ þ Dm N pore π r 2pore vn hpore Z hpore þ Dm N pore 2π r pore vn ðzÞdz,

ð7:21Þ

0

where Npore is the total number of pores in an element and Dm is the diffusivity of a polymer continuum. The integral term in Eq. (7.21) is the total mass transfer across the peripheral surface of the pores in the element. Thus, the effective diffusivity Dmeff is given by     Dmeff =Dm ¼1 þ vn hpore =vn ð0Þ  1 N pore πr 2pore l2 Z hpore þ N pore 2πr pore l2 v1 ð 0 Þ vn ðzÞdz: n

ð7:22Þ

0

In a simplified case where vn(z) ¼ const. across a thin layer, Eq. (7.22) becomes

7.2 Time Response of Porous PSP

173

Dmeff =Dm ¼ 1 þ 2aV r 1 pore h,

ð7:23Þ

where aV ¼ N pore πr 2pore hpore l2 h1 is the volume fraction of cylindrical pores in a polymer layer. Equation (7.23) indicates that an increase of the effective diffusivity is proportional to the volume fraction of pores and a ratio between the polymer layer thickness and the radius of a pore. Eq. (7.23) for Dmeff is valid only for an ideal porous polymer layer with straight cylindrical pores oriented normally. Nevertheless, this model can be generalized for real porous polymers where topology of pores is often highly complicated. For more realistic modeling, the topological structure of a pore is considered as a highly convoluted and folded tube in a polymer layer, while the cross-section of the tube remains unchanged. The integral in Eq. (7.22) should be replaced by an integral along the path of a highly convoluted tube-like pore. In this case, the fractal dimension should be introduced because the length of a highly convoluted tube is no longer proportional to the linear length scale of the tube in the z-direction (e.g., hpore) (Mandelbrot 1982). According to the length-area relation for a fractal path, an dfr =2 fr or hdpore , where dfr (1 dfr < 2) is the integral along the path is proportional to Apore fractal dimension of the path of a pore and Apore / h2pore is a characteristic area covering over the path. Loosely speaking, the fractal dimension represents the degree of complexity of a pore pathway. In order to take the fractal nature of pores into account, Eq. (7.22) is generalized using a Riemann-Liouville fractional integral of the order dfr, i.e., (Nishimoto 1991)     Dmeff =Dm ¼1 þ vn hpore =vn ð0Þ  1 N pore πr 2pore l2 Z hpore þ N pore 2πr pore l2 v1 ð 0 Þ vn ðzÞðdzÞdfr : n

ð7:24Þ

0

  Note that a unitary constant with the dimension m1dfr is implicitly embedded in the third term in the right-hand side of Eq. (7.24) to make Eq. (7.24) dimensionally consistent. This dimensional constant is implicitly contained in all the results derived from Eq. (7.24). In a simplified case where vn(z) ¼ const. across a thin layer, a generalized expression for Dmeff is   2aV r 1 hpore dfr 1 dfr Dmeff pore ¼1þ h , Dm h Γð1 þ dfr Þ

ð7:25Þ

where Γ(1 + dfr) is the gamma function. Here, hpore is interpreted as a linear length scale of a convoluted tube in the z-direction and aV is the volume fraction of apparent cylindrical pores. Equation (7.25) clearly shows that the effective diffusivity Dmeff is not only proportional to hdfr , but also related to the porosity parameters aV r 1 pore and hpore/h. For dfr ¼ 1, Eq. (7.25) is simply reduced to Eq. (7.23) for straight cylindrical pores.

174

7.2.3

7 Time Response

Diffusion Timescale

For a porous polymer layer where diffusion is Fickian under some microscopic assumptions (Cunningham and Williams 1980; Neogi 1996), the diffusion equation Eq. (7.1) is still a valid phenomenological model as long as the diffusivity Dm is replaced by the effective diffusivity Dmeff. Hence, an estimate for a diffusion timescale of a porous PSP layer is τdiff /

2aV r

h2 =Dm  dfr 1 1

1 þ Γð1þdporefr Þ

hpore h

hdfr

:

ð7:26Þ

Equation (7.26) as a generalized form of Eq. (7.13) clearly illustrates how the fractal dimension dfr and the porosity parameters aV r 1 pore and hpore/h affect a response timescale of a porous PSP. For aV r 1  1 or h pore/h  1, Eq. (7.26) naturally pore approaches to the classical square-law estimate Eq. (7.13) for a homogeneous polymer layer. On the other hand, for aV r 1 pore 1 and hpore/h  1, another asymptotic estimate for τdiff is a simple power-law τdiff / 

h2dfr =Dm  : N pore =l2 r pore

ð7:27Þ

Equation (7.27) is asymptotically valid for a very porous polymer layer. The exponent in the power-law relation between the response timescale τdiff and thickness h deviates from 2 by the fractal dimension dfr due to the presence of fractal pores in a polymer layer. Equation (7.27) provides an explanation for the experimental finding that the exponent q in the power-law relation τdiff / hq is less than 2 for a porous PSP. In addition, Eq. (7.27) indicates that the diffusion timescale inversely proportional to the number of pores per area and radius of pores. This relation can serve as a useful tool to extract the fractal dimension of tube-like pores in a very porous polymer layer from measurements of a diffusion response timescale. For example, the fractal dimension dfr of a pore in the polymer poly(TMSP) is dfr ¼ 1.71, while for GP197/BaSO4 mixture the fractal dimension dfr is close to one. In addition, based on the experimental results shown in Fig. 7.5, it is known that the fractal dimension dfr for poly(TMSP) linearly decreases with increasing temperature in a temperature range of 293.1–323.1 K. This implies that the geometric structure of a pore in poly(TMSP) may be altered by a temperature change. Note that the diffusivity Dm of oxygen mass transfer is also temperature dependent, but it is independent of the coating thickness h. Therefore, the experimental results in Fig. 7.5 mainly reflect the temperature effect on the geometric structure of pores in the polymer rather than the diffusivity.

7.2 Time Response of Porous PSP

7.2.4

175

Knudsen Diffusion: Statistical Perspective

Kameda et al. (2004) presented a statistical analysis of the gas molecule transport through a single capillary pore in AA-PSP. A single capillary pore having a straight cylindrical shape is considered. The mechanism of transport depends on the Knudsen number Kn ¼ λ/d, where d is the diameter of micropore, λ is the mean free path of gas molecules (Clifford and Hillel 1986). Except for Kn  1, the gas in a pore is no longer treated as a continuum. When the gas is composed of rigid, non-attracting pffiffiffi spherical molecules of diameter σ, the mean free path is given by λ ¼ 1= 2πσ 2 n, where n denotes the number of the molecules per unit volume (Bird et al. 1960). Since the perfect gas law is applicable, the number of molecules is given by n ¼ p/(κT), κ is the Boltzmann constant. Thus, the mean free path is pffiffiffi where  λ ¼ κ= 2πσ 2 ðT=pÞ . The diameter of molecules σ is 3.617  1010 m for air (Bird et al. 1960). The Boltzmann constant κ is 1.38  1023 J/K. When pressure p is 1 atm (101.3 kPa) and temperature T is 20  C (293.15 K), the mean free path λ is 68.7 nm. On the other hand, the diameter of micropore is within a range of 20–100 nm (Sakaue and Sullivan 2001; Kameda et al. 2004). Therefore, the Knudsen number for this case is Kn  1, indicating that the gas in micropores is no longer treated as a continuum. When the mean free path of gas molecules exceeds the diameter of pores, the gaseous transport is dominated by collisions with the pore walls, which is known as the Knudsen diffusion. The effective diffusion coefficient is given by the Bosanquet formula Deff ¼

Dkg Dgg , Dkg þ Dgg

ð7:28Þ

where Dkg and Dgg denote the Knudsen and bulk diffusion coefficients, respectively. The Knudsen diffusion coefficient Dkg is given by Dkg

d ¼ 3

rffiffiffiffiffiffiffiffiffi 8RT , πM

ð7:29Þ

where R and M are the universal gas constant and the molecular weight of the gas, respectively. Note that the Knudsen diffusion coefficient is linearly proportional to the diameter of micropore. According to the Chapman-Enskog theory, the bulk diffusion coefficient Dgg can be estimated by Dgg ¼ 2:63  107

T 3=2 , pM 1=2 σ 2 Ω

ð7:30Þ

where Dgg is in [m2/s], T is in [K], p is in [bar], M is in [g/mol], and σ is in [1010 m], respectively. In Eq. (7.30), the collision integral Ω for diffusion is a function of temperature, and it is given by

176

7 Time Response

15

(p = 10 kPa)

D

(p = 100 kPa)

eff

D

kg

2

10

5

0 10

Ω¼

D

eff

D [mm /s]

Fig. 7.7 Effective diffusion coefficient for gas permeation in a straight cylindrical pore at T ¼ 293.1 K. (From Kameda et al. 2004)

d [nm]

C1 C3 C5 C7 þ þ þ , ðT Þc2 exp ðC 4 T Þ exp ðC 6 T Þ exp ðC8 T Þ

100

ð7:31Þ

where T* ¼ κT/ε, C1 ¼ 1.06036, C2 ¼ 0.15610, C3 ¼ 0.19300, C4 ¼ 0.47635, C5 ¼ 1.03587, C6 ¼ 1.52996, C7 ¼ 1.76474, C8 ¼ 3.89411, and ε is the characteristic Lennard-Jones energy. Figure 7.7 shows the effective diffusion coefficient as a function of the diameter of micropore, where the parameters for air are R ¼ 8.314 J/(mol K), M ¼ 28.97 g/mol, s ¼ 3.617  1010 m, and ε ¼ 97.0 K (Bird et al. 1960). The two solid lines in Fig. 7.7 represent the effective diffusion coefficients for p ¼ 10 kPa and for p ¼ 100 kPa when temperature is 293.15 K. The bulk diffusion coefficient is estimated as Dgg ¼ 198  106 m2/s for p ¼ 10 kPa and Dgg ¼ 19.8  106 m2/s for p ¼ 100 kPa. The dashed line represents the Knudsen diffusion coefficient. When pore sizes fall in the Knudsen flow regime, Deff approximately equals to Dkg, because Dkg  Dgg. Since the mean free path is inversely proportional to the pressure, the flow in micropore is close to the Knudsen flow in a low-pressure environment. Therefore, the effective diffusion coefficient for p ¼ 10 kPa coincides with the Knudsen diffusion coefficient in a range where d < 100 nm. The effective diffusion coefficient is approximately 3  106 m2/s in the case where d ¼ 20 nm. This value is extremely larger than the diffusion coefficient for a polymer binder, which is typically less than 109 m2/s. The characteristic time for the diffusion phenomena is generally given by τdiff ¼ h2/Deff, where h denotes the thickness of a binder layer. Typically, AA-PSP has h ¼ 10 μm, so that τdiff ¼ 33 μs. Thus, AA-PSP overcomes the diffusion barrier problem in a conventional PSP with a polymer binder.

7.2 Time Response of Porous PSP

7.2.5

177

Nonlinear Quenching Kinetics

A fast porous PSP usually exhibits the nonlinear Stern–Volmer curve particularly at very low pressures (see Chap. 3). The effect of this nonlinear quenching kinetics on the time response of PSP was investigated by Gregory and Sullivan (2006). The nonlinear quenching kinetics of PSP was modeled by the modified Stern–Volmer relation  γ I ref p ¼ AðT Þ þ BðT Þ , pref I

ð7:32Þ

where γ is an exponent for the Freundlich isotherm (see Chap. 2). The time response of PSP could be affected by the nonlinear nature of the Stern–Volmer relation. Figure 7.8 shows the PSP-indicated pressure response to a step change of pressure for γ ¼ 1.0 and 0.1, where A ¼ 0.9 and B ¼ 0.1. It was found that a porous PSP responded quickly to a pressure decrease and relatively slowly to a pressure increase. This observed effect was more pronounced for larger changes in pressure, particularly in the nonlinear portion of the Stern–Volmer curve at low pressures. The effect of the Freundlich isotherm on the Stern–Volmer relation produced an appreciable but minimal variation of the indicated pressure response. They measured the unsteady flowfield of a fluidic oscillator to verify their analysis and evaluate the response characteristics of PC-PSP and FIB-PSP. Results with the FIB paint

Fig. 7.8 PSP-indicated pressure step response for γ ¼ 1.0 and 0.1 when A ¼ 0.9 and B ¼ 0.1. (From Gregory and Sullivan 2006)

178

7 Time Response

formulation demonstrated the nonlinear response characteristics predicted by the diffusion model. It was found that the nonlinear effect was significant only when a characteristic timescale of the flowfield is smaller than the response timescale of the paint.

7.2.6

Effect of Lifetime on Time Response

There are two timescales involved in time-resolved PSP measurements. The first is the luminescent lifetime of PSP that is an intrinsic timescale of the photo-physical process of PSP. Another is a timescale of oxygen diffusion across a PSP layer. The time response of a conventional PSP is dominated by its oxygen diffusion timescale since it is much larger than the luminescent lifetime; thus, the solution of the diffusion equation can provide a reasonable estimate of the time response of PSP. However, when a fast porous PSP reaches a response time of microseconds, the effect of the luminescent lifetime is no longer negligible. In this case, both the kinetics of luminescence and the dynamics of oxygen diffusion should be incorporated into the modeling of PSP time response. The response of the luminescent intensity of PSP to a time-dependent change of oxygen is described by   ∂I ðt, zÞ ½O2 ðt, zÞ 1 þ τref A þ B I ðt, zÞ ¼ EðzÞ, ½O2 ref ∂t

ð7:33Þ

lifetime of PSP at a reference condition, E ðzÞ ¼ where τref is the luminescent  E 0 exp βλ1 ðh  zÞ is the local excitation light intensity inside PSP, E0 is the incident excitation light intensity, z is the vertical coordinate pointing to PSP from a wall, h is the thickness of a PSP layer, and βλ1 is the extinction coefficient of the excitation light. At the air-PSP surface (z ¼ h), the unsteady surface pressure change ps(t) is given, which is proportional to the oxygen concentration described as [O2]0f(t), where the nondimensional function f(t) describes a temporal change, and [O2]0 is a constant concentration of oxygen. As indicated in Sect. 7.1, the distribution of [O2] in PSP can be obtained by solving the diffusion equation using analytical and numerical methods. For a given solution for [O2], the luminescent intensity of PSP, I (t, z), is calculated by solving Eq. (7.33) and thus the averaged luminescent intensity Rh hIih is evaluated, where h • ih ¼ h1 0 • dz is an average operator across a PSP layer. Therefore, the indicated pressure change pPSP(t) by PSP is obtained by using the Stern–Volmer relation hIrefih/hIih ¼ A + B( pPSP/pref). The gain is defined as Gain ¼ 20log10( pPSP/ps) to evaluate the effect of the lifetime on the time response. Kameda (2012) studied the effect of the luminescent lifetime on the time response of a fast PSP to a sinusoidal pressure change based on a Fourier-series solution of the diffusion equation. The effect of the luminescent lifetime and the diffusion timescale was evaluated using the Bode plot. Figure 7.9 shows the Bode plot of PSP-indicated

7.2 Time Response of Porous PSP

179

Fig. 7.9 Bode plots of PSP-indicated pressure response for different values of τL0/τD for A ¼ 0.8 and B ¼ 0.2: (a) gain, and (b) phase delay, where τL0 and τD are the luminescent lifetime and diffusion timescale at a reference condition, respectively. (From Kameda 2012)

pressure response for different values of τL0/τD when A ¼ 0.8 and B ¼ 0.2, where τL0 and τD are the luminescent lifetime and diffusion timescale at a reference condition, respectively. The luminescent lifetime alters the PSP time response in both the gain and phase when the lifetime is close to the diffusion timescale. The gain and phase difference due to each timescale are linearly decomposed in the Bode plot. In

180

7 Time Response

general, the luminescent lifetime alters the response dominated by the diffusion when τL0/τD > 0.1. Pandey and Gregory (2016) developed a model of PC-PSP by considering oxygen diffusion, excited-state-luminophore population dynamics, and attenuation of excitation light. They found that the inclusion of light attenuation in the model improved the accuracy of the model in comparison with experimental data. Jiao et al. (2018) developed a two-layer PSP model by considering both the roughness effect and the thickness effect based on the principles of oxygen diffusion and light transmission. Their model was in good agreement with the step responses of PC-PSP samples obtained experimentally using a shock tube. Nonomura and Asai (2019) gave a simple analytical estimation of the frequency response of a two-layer PSP model.

7.3

Measurements of Pressure Time Response

The fast time response of PSP was achieved by Baron et al. (1993) using a commercial porous silica thin-layer chromatography (TLC) plate as a binder; the observed response time of this PSP was less than 25 μs. Although this fragile PSP cannot be practically used for wind tunnel testing, Baron’s work suggests that a short response time of PSP can be obtained using a porous binder. Mosharov et al. (1997) reported that a response timescale of AA-PSP was in a range of 18–90 μs, depending on a probe luminophore and an anodization process. Asai et al. (2001, 2002) also measured a response timescale of AA-PSP with Ru(dpp) as a probe luminophore using a pressure chamber with a solenoid-type valve. Fujii et al. (2013) and Numata et al. (2017) fabricated ultrafast AA-PSP based on phosphoric acid and PBA. They evaluated the response of the ultrafast AA-PSP using a shock tube and found that the time constant was shorter than one microsecond. According to Jordan et al. (1999b), a sol-gel-based PSP achieved the frequency response of as high as 6 kHz. Ponomarev and Gouterman (1998) and Scroggin et al. (1999) developed binders by mixing hard particles with polymers to increase the degree of porosity. Ponomarev and Gouterman found that increasing the number of hard particles above a critical pigment volume concentration drastically shortened the response time. Along this line, PC-PSPs have been developed (Gregory et al. 2002a, b, 2006, 2007; Sakaue et al. 2011; Hayashi and Sakaue 2017; Sugioka et al. 2018a, b; Peng et al. 2018c; Egami et al. 2019a, b, 2021a, b). To determine a response timescale of PSP, dynamic calibration methods have been developed. A dynamic calibration device should provide a known unsteady pressure field at sufficiently high frequency or in a short transient process, where the detected PSP response can be directly compared to a known standard. A time sequence of PSP signal is determined by dynamic calibration, and the signal amplitude and phase delay are obtained as a function of pressure frequency, thus establishing the limit of PSP response and enabling dynamic compensation of PSP signal. Devices for unsteady PSP calibration will be discussed below, including

7.3 Measurements of Pressure Time Response

181

solenoid valve system, shock tube, acoustic resonance tube, and fluidic oscillator. In Appendix B, Table B2 summarizes the measured response timescales of some PSP formulations along with their luminescent lifetimes.

7.3.1

Solenoid Valve

Solenoid-valve-type switching has been used to generate a step change in pressure for measurements of PSP response by several researchers (Engler 1995; Carroll et al. 1995, 1996; Winslow et al. 1996; Mosharov et al. 1997; Fonov et al. 1998). Figure 7.10 shows a typical pressure jump apparatus used by Asai et al. (2002). This apparatus had a small test chamber connected directly to a fast opening valve having a time constant of a few milliseconds. Sample plates used in this apparatus were typically aluminum coupons coated with PSP. Figure 7.11 shows the time response of the luminescent intensity for several PSP formulations using PtOEP as a probe luminophore in binders GP197, AA, and poly(TMSP) to a step change in pressure from vacuum to the atmospheric pressure. The pressure signal from a kulite pressure transducer was also shown in Fig. 7.11 as a reference. The PSP based on GP197 was very slow and its time constant was in the order of seconds. Figure 7.12 shows the thickness effect on the time response of PtOEP in GP-197 (a conventional PSP) to a step change of pressure (Carroll et al. 1996). In contrast, AA-PSP and poly (TMSP)-PSP had comparable response timescales since poly(TMSP) is very porous due to its large free volume. The time constant of poly(TMSP)-PSP was less than one millisecond. Measurements indicate that high porosity is required to achieve high Light Guide from Xe Lamp Bandpass Filter for Excitation Light Pressure Transducer

PSP Sample

Solenoid Valve

Dichroic Filter Vacuum or Atmosphere

Sharp Cut Filter

Photomultiplier Tube (PMT)

Bandpass Filter for Luminescence Emission

Fig. 7.10 Schematic of a pressure jump apparatus. (From Asai et al. 2002)

182

7 Time Response

voltage, V

1.0 0.0 -1.0 -2.0

Kulite(ref)

-3.0 -4.0

0

50

100

150

200

250

300

350

400

time, msec

(a) voltage, V

1.5 1.4

GP197

1.3 1.2 1.1 1.0

0

50

100

150

200

250

350

400

time, msec

(b)

1.0

voltage, V

0.8

Anodized

0.6 0.4 0.2 0.0

0

50

100

150

200

250

300

350

400

time, msec

(c)

1.0 voltage, V

0.9

poly(TMSP)

0.8 0.7 0.6 0.5 0.4

(d)

300

0

50

100

150

200

250

300

350

400

time, msec

Fig. 7.11 Time responses of several PSPs to a step change in pressure: (a) kulite sensor (reference), (b) GP197-PSP, (c) AA-PSP, and (d) poly(TMSP)-PSP, where PtOEP is used as a probe molecule. (From Asai et al. 2002)

7.3 Measurements of Pressure Time Response

183

Fig. 7.12 Time response of PtOEP in GP197 to a step change of pressure, depending on the paint thickness. (From Carroll et al. 1996)

(P-Pmin)/(Pmax-Pmin)

1.2 1.0 0.8 increasing particle numbers

0.6

BaSO4:GP197=0g:1g

0.4

BaSO4:GP197=0.5g:1g

0.2

BaSO4:GP197=2g:1g

0.0 -0.2

transducer

-1

0

1

2

3 4 time, sec

5

6

7

8

Fig. 7.13 Effect of the BaSO4 particle concentration in the polymer GP-197 on the time response of BaSO4/GP197 PSP at 313.1 K. (From Asai et al. 2001)

time response of PSP. This observation was examined by Asai et al. (2001) for a mixture of GP-197 with hard particles of BaSO4. Figure 7.13 shows the reduced response timescale to a step change of pressure with elevating the concentration of BaSO4 as a result of the increased porosity. Asai et al. (2001) also noticed that a fast porous PSP usually had a lower temperature sensitivity.

184

7.3.2

7 Time Response

Shock Tube

Another apparatus for creating a step pressure change is a shock tube (Sakaue et al. 2001; Teduka et al. 2000; Sakamura et al. 2005; Pandey and Gregory 2015; Fujii et al. 2013; Numata et al. 2017; Egami et al. 2019b). A shock tube can generate a pressure rise in a few microseconds, and therefore it is a good device for testing a porous PSP having a response timescale less than a millisecond. Figure 7.14 shows a schematic of a simple shock tube for testing the time response of PSP (Sakaue and Sullivan 2001). The shock tube had a 55 mm  40 mm cross-section, a 428 mm long driver section, and a 485 mm long driven section. An aluminum foil diaphragm was burst by a pressure difference between the driver and driven sections, where the driver pressure was one atmospheric pressure. A pressure transducer, which was connected to a 2 mm diameter pressure tap on the shock tube wall, was used to measure the unsteady reference pressure. Absolute pressures were measured using an Omega pressure transducer connected to the driven section. PSP was applied to a 25.4 mm square aluminum block flush mounted to the shock tube wall. The reference pressure transducer and PSP sample were mounted 300 mm from the diaphragm. A 532-nm laser was used as an illumination source for PSP and the laser spot size was about 2 mm on the sample surface. The luminescent emission from PSP was collected by a PMT through a long pass filter (>570 nm) and the readout voltage from the PMT was acquired using a LeCroy oscilloscope. The response time

Fig. 7.14 Schematic of a simple shock tube setup for testing PSP time response. (From Sakaue 1999)

7.3 Measurements of Pressure Time Response

AA-PSP pressure tap theoretical calculation

pressure (kPa)

100

80

185

incident normal shock

60

40

reflected normal shock

20 0.0

0.3

0.6

0.9

1.2

1.5

time (ms) Fig. 7.15 Pressure data obtained from AA-PSP with a thickness of 9 μm and pressure transducer compared with theoretical values. (From Sakaue 1999)

of the PMT was about 2 μs. The time resolution of the apparatus was also limited by the laser spot size. The laser spot size dspot and the shock velocity us give the limiting detectable pressure rising time tlimit ¼ dspot/us (about 3–5 μs) for this setup. Figure 7.15 shows typical pressure signals from a Ru(dpp) AA-PSP (9 μm thick) and the pressure transducer along with the theoretical pressure jumps associated with the incident and reflected normal shock waves. This AA-PSP was able to follow the sharp pressure rises after the incident and reflected shock waves passed through the laser-illuminated spot. Figure 7.16 shows the normalized pressure signals from the AA-PSP with different thickness values (4.3, 9.0, 13.2, and 27.2 μm). It was found that the diffusion response timescale of this AA-PSP followed the power-law relation τdiff / h0.573. Figure 7.17 shows comparisons of the time response of four PSP formulations to a step change of pressure. These formulations used the same probe luminophore Ru(dpp) with four different binders: AA, TLC, polymer/ceramic (PC), and conventional polymer RTV. The response timescales of AA-PSP and TLC-PSP were in the order of ten microseconds, whereas the conventional RTV-PSP had a much longer response time (in the order of hundred milliseconds). In addition, it was found that PC-PSP had a longer response timescale (about 1 ms) than the thicker but more porous TLC-PSP. For a very porous PSP, the porosity of a binder had more pronounced influence on the time response of PSP than the binder thickness. This is consistent with the theoretical analysis presented in Sect. 7.2.2.

186

7 Time Response

normalized pressure

1.2 1.0 0.8 0.6

l = 4.3 l = 9.0 l = 13.2 l = 27.2

0.4 0.2

m, m, m, m,

= 34.8 = 70.9 = 80.0 = 102

s s

s s

0.0 0.0

0.1

0.2

0.3

time (ms)

0.4

0.5

0.6

Fig. 7.16 Normalized pressure response of AA-PSP with different values of the paint thickness (l ). (From Sakaue 1999)

7.3.3

Acoustic Resonance Tube

An acoustic resonance tube can generate sinusoidal pressure fluctuations over a large frequency range based on the principle of standing waves, which is suitable for characterizing the frequency response of fast PSP. The use of an acoustic tube for PSP calibration was first proposed by McGraw et al. (2003) and employed by Sugimoto et al. (2012, 2017), Pandey and Gregory (2016), and Gößling et al. (2020). Figure 7.18 shows an acoustic tube designed and used by Pandey and Gregory to determine the frequency response of PC-PSPs. The resonance tube had a total length 1.5 m and a radius of 32 mm. A loudspeaker was used to generate standing waves in the tube as pressure waves reflect between the closed ends, while a PSP sample was placed on an aluminum plug at another end. The loudspeaker was driven by an amplified sinusoidal signal of a fixed frequency generated using a function generator. A piezoresistive transducer was installed on the aluminum plug at the fixed end of the tube to obtain true pressure variation. An LED array provided continuous violet excitation (405 nm) for a PSP sample. The luminescent emission from the PSP sample was captured using a PMT fitted with a 620 nm colored-glass long-pass filter to block the excitation light. The signal was recorded by an oscilloscope. To improve the signal level of the fluctuating part, the signal was passed through an analog filter with a low-pass cutoff frequency of 200 kHz and input gain of 50 dB. Figure 7.19 shows the Bode plot of the frequency response of five typical PtTFPP-based PC-PSP samples that had a similar thickness and roughness properties. The frequency response data of these samples were fairly close over a range of measured frequencies. Figure 7.19 also provides an indication of uncertainty arising

7.3 Measurements of Pressure Time Response

normalized pressure

(a)

187

1.2 1.0 0.8 0.6

AA-PSP TLC-PSP polymer/ceramic PSP

0.4 0.2 0.0 0.0

normalized pressure

(b)

0.2

0.4

time (ms)

0.6

0.8

1.2 1.0 0.8 0.6 0.4

polymer PSP

0.2 0.0 0

50

100

150

200

250

time (ms)

300

350

400

Fig. 7.17 Comparison of the time response between (a) porous Ru(dpp)-based PSPs (AA-PSP, TLC-PSP, and PC-PSP) and (b) conventional polymer PSP Ru(dpp) in RTV. (From Sakaue 1999)

from sample-to-sample variations in the paint thickness and roughness. In addition, Gößling et al. (2020) measured the time response of a similar PtTFPP-based PC-PSP at two different temperatures in a different acoustic resonance box. Their results are shown in Fig. 7.20.

188

7 Time Response

Fig. 7.18 Schematic of an acoustic resonance tube. Note that the pulsed LED light is used only with lifetime measurement, and only one excitation source is used at a time. (From Pandey and Gregory 2016)

Fig. 7.19 The Bode plots of the gain and phase for PC-PSP obtained from measurements in an acoustic resonance tube. (From Pandey and Gregory 2016)

Fig. 7.20 The Bode plots of the gain and phase for PC-PSP obtained from measurements in an acoustic resonance tube at two different temperatures. (From Gößling et al. 2020)

7.4 Time Response of TSP

189

Fig. 7.21 Schlieren images of the fluidic oscillator flow field at two phase positions in an oscillation cycle. (From Gregory et al. 2002a)

7.3.4

Fluidic Oscillator

Gregory et al. (2002a, 2006, 2007) used fluidic oscillators as a dynamic calibration device providing high dynamic pressures at high frequencies. A fluidic oscillator produces an oscillating jet when supplied with a pressurized fluid. The frequency of an oscillating jet increases with the supply pressure; smaller devices produce higherfrequency oscillation. The typical operating range of a fluidic oscillator is 1–10 kHz. Figure 7.21 shows Schlieren images of the flowfield of a typical fluidic oscillator. When an oscillating jet impinges on a PSP sample, the PSP response can be directly compared with a known pressure time history obtained by a reference pressure transducer placed in the flowfield. Figure 7.22 shows typical dynamic PSP calibration data from this setup, where power spectra from a kulite pressure transducer are directly compared with data from TLC-PSP. Sakamura et al. (2002) used periodic pulse-jets generated by chopping an impinging air jet issuing from a converging nozzle onto a flat plate coated with PSP. Pressure fluctuations on the order of kHz with the amplitudes of 70–80 kPa were produced on the flat plate, which were measured using PSP via Cassegrain optics.

7.4

Time Response of TSP

Similar to PSP, TSP has two characteristic timescales: the luminescent lifetime and a thermal diffusion timescale. The luminescent lifetimes of EuTTA-dope and Ru (bpy)-Shellac TSPs at room temperature are about 0.5 ms and 5 μs, respectively. Time response of EuTTA-dope TSP is intrinsically limited by its long luminescent

190

7 Time Response

Fig. 7.22 Power spectra of time response of TLC-PSP calibrated with a fluidic oscillator. (From Gregory et al. 2002a)

lifetime, while Ru(bpy)-Shellac TSP has a much shorter luminescent lifetime. Overall, the time response of TSP is strongly dependent upon heat transfer into a model in a specific application. Based on a transient solution of the heat conduction equation, a thermal diffusion timescale for a thin TSP coating is in the order of h2/αT, where h is the coating thickness and αT is the thermal diffusivity of TSP. In a convection-dominated case, a thermal diffusion timescale can also be expressed as hk/αThc, where k is the thermal conductivity and hc is the convective heat transfer coefficient. In general, the thermal diffusion timescale is much larger than the luminescent lifetime for many TSP formulations, and therefore the time response of TSP is limited by thermal diffusion. In contrast to PSP where oxygen diffusion always obeys the no-flux condition at a solid boundary, heat transfer to a model (or base) through a nonadiabatic wall inevitably affects the thermal time response of TSP in experiments. Hence, a timescale of TSP depends on not only the thermal conductivity of a paint itself, but also a specific heat transfer problem for TSP application. To measure the time response of TSP to a rapid change of temperature, Liu et al. (1995c) conducted experiments of pulse laser heating on a metal film and step-like jet impingement cooling. Martinez Schramm et al. (2015) tested the time response of TSP in a small shock tube.

7.4.1

Pulsed Laser Heating on Thin Metal Film

We consider pulsed laser heating on a thin metal film to determine a thermal diffusion timescale of TSP applied to the film. The heat conduction equation for this problem is

7.4 Time Response of TSP

191

∂θ ¼ αT ∇2 θ, ∂t

ð7:34Þ

where θ ¼ T  Tin is a temperature change of the film from an initial temperature Tin and αT is the thermal diffusivity of the metal film. The Laplace operator in Eq. (7.34) is defined as ∇2 ¼ ∂ =∂r 2 þ r 1 ∂=∂r þ ∂ =∂z2 , 2

2

where r is the radial distance from the center of a hot spot heated by a laser and z is the coordinate normal to the metal film directing from the heated side to other side. The initial temperature Tin is assumed to be the ambient temperature. After heated by a laser pulse, the film is cooled down due to natural convection on both sides of the metal film. When the surface temperature of the metal film decreases fast enough along the radial direction from the center of the hot spot (i.e., rθ ! 0 as r ! 1), we introduce a spatially averaging operator 2π hθ i2 ¼ Aeff

Z

1

rθ dr,

ð7:35Þ

0

where Aeff is the effective area of the hot spot. Hence, applying the spatially averaging operator to Eq. (7.34), we have the unsteady 1D heat conduction equation 2

∂ hθ i2 ∂ hθ i2 ¼ αT : ∂t ∂z2

ð7:36Þ

The initial and boundary conditions for Eq. (7.36) are hθi2 ðz, 0Þ ¼ 0, ∂hθi2 ð0, t Þ ¼ Plaser δðt Þ  hc hθi2 ð0, t Þ, k ∂z ∂hθi2 ðηm , t Þ k ¼ hc hθi2 ðηm , t Þ, ∂z

ð7:37Þ

where hc is the average heat transfer coefficient for natural convection, k is the thermal conductivity, δ(t) is the Dirac-delta function, ηm is the metal film thickness, and Plaser represents the strength of a pulse-laser heating source. There are two physical processes involved: rapid heating of the film by a pulsed laser and relatively slow cooling due to natural convection. At the beginning, since the film is heated in a very short time interval, the natural convection terms in the boundary conditions in Eq. (7.37) can be neglected; thus, the problem is simplified for the rapid heating process. For a thin metal film (ηm  1), the application of the Laplace transform Θ(z, s) ¼ La(hθi2) to Eqs. (7.36) and (7.37) yields

192

7 Time Response

 pffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffi exp  s=αT η m 2Plaser αT  pffiffiffiffiffiffiffiffiffiffi pffiffi Θðηm , sÞ ¼ k s 1  exp 2 s=αT η  pffiffiffiffiffiffiffiffiffiffi P α  laser T exp ηm s=αT , kηm s

m

ð7:38Þ

where s is the complex variable in the Laplace transform. The inverse Laplace transform leads to an asymptotic expression for the pulsed laser heating when t is small, i.e., hθ i2 ¼

pffiffiffiffiffiffiffiffi Plaser αT erfc τ1 =t : kηm

ð7:39Þ

The characteristic timescale for the pulsed laser heating is τ1 ¼ η2m =ð4αT Þ. For the slow cooling process due to natural convection after the pulsed laser heat source ceases, we introduce an additional average operator across the metal film hθi3 ¼

1 ηm

Z

ηm 0

hθi2 dz:

ð7:40Þ

Applying the operator given in Eq. (7.40) to Eq. (7.36) leads to a simple lumped model for the cooling process, i.e., d hθ i3 α P δ ðt Þ 2α h : ¼  T c hθi3 þ T laser kηm dt ηm k

ð7:41Þ

The solution to Eq. (7.41) is hθ i3 ¼

Plaser αT exp ð2t=τ2 Þ: kηm

ð7:42Þ

Equation (7.42) describes an exponential decay of the averaged temperature, which gives the characteristic timescale τ2 ¼ kηm/(2αT hc) for the cooling process due to natural convection. Obviously, for the problem of pulsed laser heating on a thin film, there are a fast timescale τ1 ¼ η2m =ð4αT Þ and a slow timescale τ2 ¼ kηm/(2αT hc). The time response of Ru(bpy)-Shellac TSP to a rapid temperature rise was tested by utilizing pulsed laser heating on a 25-μm thick steel film. Figure 7.23 is a schematic of the experimental setup (Liu et al. 1997b). One side of the steel film was heated by a pulsed laser beam with an 8-ns duration from a Nd:YAG laser (532 nm at an 800-mJ maximum output) through a focusing lens. The opposite side of the steel film was coated with a 10-μm thick Ru(bpy)-Shellac TSP illuminated by a 457-nm blue beam from a 1-mW Argon laser at the hot spot. The response of the luminescent emission from TSP to pulsed laser heating was detected using a PMT, and the signal was

7.4 Time Response of TSP

193

Fig. 7.23 Schematic of a pulsed laser heating setup for testing TSP time response. (From Liu et al. 1997b)

acquired using an oscilloscope. The surface temperature was calculated from the luminescent intensity using a priori calibration relation for this TSP. Figure 7.24 shows a typical transient response of the surface temperature to pulsed laser heating on the steel film. The surface temperature increases rapidly after heating at the film and then decays due to natural convection. To estimate the response times, the asymptotic solutions Eqs. (7.39) and (7.42) were used to fit the experimental data. The response timescale of TSP for the pulsed laser heating process was τ1 ¼ 0.25 ms, while the timescale for the cooling process due to natural convection was τ2 ¼ 12.5 ms. Horagiri and Nagai (2014) evaluated the response of Ru(phen)-TSP mixed with scattering particles with the low thermal conductivity (silica aerogel and calcium silicate). A thin layer of the paint was applied on a ceramic base and heated using a high-power pulse CO2 laser set at 40 W. Two blue LED lights were used to evenly illuminate the samples at 470 nm. A 12-bit high-speed camera (Photron FASTCAM SA-X) was used. The resolution was 512  512 pixels. A high-pass filter (>560 nm) was used on the camera lens to detect the luminescence of the TSP sample. The frame rate of the camera was set at 20,000 fps. The inverse heat transfer method was used to determine a time constant by calculating the heat flux change history from the measured temperature change history. For a pure Ru(phen)-TSP sample with a thickness of 1 μm, the heat flux time constant was 0.9–1.7 ms. In contrast, for a TSP sample with a particle mixing ratio of 50% and a thickness of 1 μm, the time constant was about 0.205 ms, indicating a faster time response.

194

7 Time Response

Fig. 7.24 Temperature response of Ru(bpy)-Shellac TSP to pulsed laser heating on a steel foil. (From Liu et al. 1997b)

7.4.2

Step-Like Jet Impingement Cooling

Sudden fluid jet impingement to TSP coated on a hot body, producing a rapid decrease of surface temperature, can be used for testing the time response of TSP. A lumped heat transfer model gives an approximate solution for a temporal evolution of temperature on a paint layer during step jet impingement cooling, i.e., T  T min ¼ exp ðt=τ3 Þ, T in  T min

ð7:43Þ

where Tin is the initial temperature of the paint and Tmin is the minimum temperature of the paint that is asymptotically reached as t ! 1. The timescale for this cooling process is τ3 ¼ kh/(αT hc), where hc is the average heat transfer coefficient for the impinging jet and h is the paint thickness. Figure 7.25 shows an experimental setup for step jet impingement cooling. A 475-nm blue laser beam was used for illumination at the jet impingement point. The luminescent intensity was measured using a PMT and then was converted into temperature using a priori calibration relation. A sub-zero temperature impinging Freon jet generated by a Freeze-it® sprayer was utilized, where a mechanical camera shutter was used as a valve to control issuing of the jet. After the shutter opened within 1 ms, the Freon jet impinged on the surface of a hot soldering iron (about

7.4 Time Response of TSP

195

Fig. 7.25 Schematic of a step-like jet impingement cooling setup for testing TSP time response

Fig. 7.26 Temperature response of Ru(bpy)-Shellac TSP to step-like Freon jet impingement cooling

100  C), which was coated with a 19-μm thick Ru(bpy)-Shellac TSP. Figure 7.26 shows a rapid decrease in the surface temperature on the thin paint coating to the minimum temperature of about 44  C. The measured timescale τ3 of TSP for this cooling process was 1.4 ms. Cool air impingement jet was also tested; the measured timescales were 16 and 25 ms for 19 and 38 μm thick Ru(bpy)-Shellac TSP coatings, respectively.

196

7.4.3

7 Time Response

Shock Tube

Martinez Schramm et al. (2015) tested the time response of a Ru(phen)-based TSP in a shock tube of a length of 4.5 m. The shock tube was equipped with thermocouples and thin film gauges, providing reference dataset for comparison with time-resolved TSP data. The TSP wall insert was manufactured from polyurethane/polyol, and flush mounted on a sidewall near the end of the driven section of the shock tube. The TSP thickness was 0.2 μm. At the opposite side a window insert was installed which allowed observation of the TSP wall insert. The test time for the experiment was of the order of 250 μs, starting prior to the arrival of the shock at the TSP wall insert and ending when the reflected shock passes the wall insert again. High-power commercial LEDs, operating in continuous mode with a wavelength of 461 nm, were employed to excite the TSP. TSP images were acquired at 250 kfps using a Phantom v1210 with an exposure time of 3.5 μs. To give representative data of the shock tube flow, 100 runs with the shock tube were performed with thermocouple and thin film gauge sampled at 1 MHz. The timeresolved TSP results were compared to the averaged data of thermocouple and thin films measurements in 100 runs. Figure 7.27 shows a comparison between the timeresolved TSP signal and the time signals from the thermocouple and thin film gauge measurements at the same location. The TSP was able to capture the same temporal history of surface temperature as the thermocouple and thin film gauges. Figure 7.28 shows a wave diagram of heat flux in the (x, t) plane extracted from the TSP images along the symmetry line, where x is the streamwise coordinate and t is time. Heat flux

Fig. 7.27 Time-resolved temperature traces measured by thermocouples, thin film gauges, and TSP in a shock tube. (From Martinez Schramm et al. 2015)

7.4 Time Response of TSP

197

Fig. 7.28 Wave diagram in the (x, t) plane extracted from the time-resolved TSP data in the symmetry line. (From Martinez Schramm et al. 2015)

data were extracted from the TSP-derived temperature data using the CookFelderman method, where the thermal penetration parameter was determined by fitting the thermocouple and thin film data in the x–t region (0 mm < x < 50 mm; 150 μs < t < 250 μs) marked in Fig. 7.28 in in situ calibration. The incident and reflected shocks can be clearly identified as discontinuous interfaces. Their slopes determine the incident shock speed of 1250 m/s, and the reflected shock speed of 477 m/s.

Chapter 8

Image and Data Analysis Techniques

This chapter describes image and data analysis techniques for PSP and TSP. For quantitative measurements, cameras should be calibrated to establish the accurate relationship between the image plane and the 3D object space (Euclidean space) and then map data in images onto a surface grid in the object space. Analytical camera calibration techniques, especially the Direct Linear Transformation (DLT) and an optimization calibration method, are discussed. For PSP and TSP measurements, an ideal camera should have a linear response to the luminescent radiance. A simple effective technique is described to determine the radiometric response function of a camera. The self-illumination of PSP and TSP may cause a significant error near a conjuncture of surfaces when a strong exchange of the radiative energy occurs between neighboring surfaces. The numerical methods for correcting the selfillumination are described and the errors associated with the self-illumination are estimated. A standard procedure in the intensity-based method for PSP and TSP is to take a ratio between the wind-on and wind-off images to eliminate the effects of nonhomogeneous illumination intensity, dye concentration, and paint thickness. An image registration technique is described to re-align the wind-on and wind-off images based on a mathematical transformation between them. A crucial step for PSP is to accurately convert the luminescent intensity to pressure; cautious use of the calibration relations with a correction of the temperature effect of PSP is discussed. Since PSP measurements in low-speed flows are particularly difficult, a pressurecorrection method is described as an alternative to extrapolate the incompressible pressure coefficient from PSP measurements at suitably higher Mach numbers. A method for generating a deformed wing grid is described based on videogrammetric aeroelastic deformation measurements conducted simultaneously with PSP and TSP measurements to map PSP and TSP data in images onto a model surface deformed by aerodynamic load. For unsteady PSP measurements at low-speed flows, the noise-reduction methods are described to increase the SNR and extract surface pressure structures, including the phase-averaging, FFT-based methods, and mode decomposition methods. Image deblurring is discussed, which is required to improve © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_8

199

200

8 Image and Data Analysis Techniques

the quality of PSP and TSP images of fast moving objects. Finally, inverse heat transfer methods are discussed for calculating heat flux from TSP images.

8.1 8.1.1

Geometric Calibration of Camera Collinearity Equations

After pressure and temperature data are extracted from images of PSP and TSP, it is necessary to map the data onto a surface grid in the 3D object space (Euclidean space or physical space) to make the data more useful for design engineers and researchers. The collinearity equations in photogrammetry provide the perspective relationship between the 3D coordinates in the object space and corresponding 2D coordinates in the image plane (Wong 1980; McGlone 1989; Mikhail et al. 2001; Cooper and Robson 2001; Liu 2004). For quantitative image-based measurements in wind tunnels, simple and accurate camera calibration is a key to determine the camera interior and exterior orientation parameters, and lens distortion parameters in the collinearity equations (Liu et al. 2012). Image resection methods were used in PSP and TSP systems to determine the camera exterior orientation parameters under the assumption that the interior orientation and lens distortion parameters are known (Donovan et al. 1993; Le Sant and Merienne 1995). The Direct Linear Transformation (DLT) was also used to obtain the interior orientation parameters in addition to the exterior orientation parameters (Bell and McLachlan 1993, 1996). An optimization method for comprehensive camera calibration was developed by Liu et al. (2000), which can determine the exterior orientation, interior orientation, and lens distortion parameters (as well as the pixel aspect ratio of a sensor array) from a single image of a known 3D target field. The optimization method, combined with the DLT, allows automatic camera calibration without an initial guess of these orientation parameters; it particularly facilitates PSP and TSP measurements in wind tunnels. Besides the DLT, a closed-form resection solution given by Zeng and Wang (1992) is also useful for initial estimation of the exterior orientation parameters of a camera based on three known targets. On the other hand, researchers in computer vision adopt different formulations and more versatile mathematical methods in perspective geometry, differential geometry, and image algebra (Mundy and Zisserman 1992; Faugeras 1993; Cipolla and Giblin 2000). The discussions in this section are based on the formulation in photogrammetry. The pinhole camera model describes the mathematical relationship between the coordinates of a point in the 3D object space and its projection onto the image plane of an ideal pinhole camera, where the camera aperture is described as a point known as the perspective center. Figure 8.1 illustrates the perspective relationship between the 3D coordinates (X, Y, Z ) in the object space and the corresponding 2D coordinates (x, y) in the image plane. The perspective center is at the location (Xc, Yc, Zc) in the object space. The orientation of a camera is characterized by three Euler orientation angles. The orientation angles and location of the perspective center

8.1 Geometric Calibration of Camera

201

Fig. 8.1 Camera imaging process and the interior orientation parameters

together are referred to as the exterior orientation parameters in photogrammetry. In addition, the relationship between the perspective center and the image coordinate system is defined by the camera interior orientation parameters, namely, the camera principal distance c and the photogrammetric principal-point location (xp, yp). The principal distance, which equals the camera focal length for a camera focused at infinity, is a perpendicular distance from the perspective center to the image plane, whereas the photogrammetric principal point is where a perpendicular line from the perspective center intersects the image plane. Due to lens distortion, however, perturbation to an imaging process leads to departure from collinearity that can be represented by the shifts dx and dy of the image point from its “ideal” position on the image plane. The shifts dx and dy are modeled and characterized by the lens distortion parameters.

202

8 Image and Data Analysis Techniques

The perspective relationship is described by the collinearity equations m11 ðX
X c Þ þ m12 ðY m31 ðX
X c Þ þ m32 ðY m21 ðX
X c Þ þ m22 ðY y
yp þ dy ¼
c m31 ðX
X c Þ þ m32 ðY

x
xp þ dx ¼
c


Y c Þ þ m13 ðZ
Z c Þ U ¼
c , W
Y c Þ þ m33 ðZ
Z c Þ
Y c Þ þ m23 ðZ
Z c Þ V ¼
c , W
Y c Þ þ m33 ðZ
Z c Þ

ð8:1Þ

where mij (i, j ¼ 1, 2, 3) are the elements of the rotation matrix that are functions of the Euler orientation angles (ω, ϕ, κ), m11 ¼ cos ϕ cos κ m12 ¼ sin ω sin ϕ cos κ þ cos ω sin κ m13 ¼
cos ω sin ϕ cos κ þ sin ω sin κ m21 ¼
cos ϕ sin κ m22 ¼
sin ω sin ϕ sin κ þ cos ω cos κ

ð8:2Þ

m23 ¼ cos ω sin ϕ sin κ þ sin ω cos κ m31 ¼ sin ϕ m32 ¼
sin ω cos ϕ m33 ¼ cos ω cos ϕ: The orientation angles (ω, φ, κ) are essentially the pitch, yaw, and roll angles of a camera in an established coordinate system. The terms dx and dy are the image coordinate shifts induced by lens distortion, which can be modeled by a sum of the radial distortion and decentering distortion (Fraser 1992; Fryer 1989), i.e., dx ¼ dxr þ dxd

and

dy ¼ dyr þ dyd ,

ð8:3Þ

where

 dxr ¼ K 1 x0
xp r 2 þ K 2 x0
xp r 4 ,

 dyr ¼ K 1 y0
yp r 2 þ K 2 y0
yp r 4 , h
2 i

 dxd ¼ P1 r 2 þ 2 x0
xp þ 2P2 x0
xp y0
yp , h
2 i

 þ 2P1 x0
xp y0
yp , dyd ¼ P2 r 2 þ 2 y0
yp
2
2 r 2 ¼ x0
xp þ y0
yp :

ð8:4Þ

Here, K1 and K2 are the radial distortion parameters, P1 and P2 are the decentering distortion parameters, and x0 and y0 are undistorted coordinates in the image plane. When lens distortion is small, unknown undistorted coordinates can be approximated by measured distorted coordinates, i.e., x0  x and y0  y. For large lens distortion, an iterative procedure can be employed to determine undistorted

8.1 Geometric Calibration of Camera

203

coordinates to improve the accuracy of estimation. The initial approximations are (x0)0 ¼ x and (y0)0 ¼ y, and the iterative relations are ð x0 Þ

kþ1

ð y0 Þ

kþ1

h i k k ¼ x þ dx ðx0 Þ , ðy0 Þ , h i k k ¼ y þ dy ðx0 Þ , ðy0 Þ ,

where the superscripted iteration index is k ¼ 0, 1, 2, . . . The collinearity equations, Eq. (8.1), contain a set of the camera parameters to be determined by camera calibration; the sets (ω, φ, κ, Xc, Yc, Zc), (c, xp, yp), and (K1, K2, P1, P2) in Eq. (8.1) are the exterior orientation, interior orientation, and lens distortion parameters of a camera, respectively. Analytical camera calibration techniques have been used to solve the collinearity equations with a lens distortion model for the camera exterior and interior parameters (Rüther 1989; Tsai 1987). Since Eq. (8.1) is nonlinear, iterative methods of least-squares estimation have been used as a standard technique for the solution of the collinearity equations in photogrammetry (Wong 1980; McGlone 1989). However, direct recovery of the interior orientation parameters is often impeded by inversion of a nearly singular normal equation matrix in least-squares estimation. The singularity of the normal-equation-matrix mainly results from strong correlation between the exterior and interior orientation parameters. In order to reduce the correlation between these parameters and enhance the determinability of (c, xp, yp), Fraser (1992) suggested the use of multiple camera stations, varying image scales, different camera roll angles, and a well-distributed target field in three dimensions. These schemes for selecting suitable calibration geometry improve the properties of the normal equation matrix. In general, iterative least-squares methods require a good initial guess to obtain a convergent solution. Mathematically, the singularity problem can be treated using the singular value decomposition that produces the best solution in a least-squares sense. Also, the Levenberg-Marquardt method can stay away to some extent from zero pivots (Marquardt 1963). Nevertheless, multiple-station and multiple-image methods for camera calibration are not easy to use in a wind tunnel environment where only a limited number of windows are available for cameras and the positions of cameras are fixed. Thus, it is highly desirable for PSP and TSP measurements to have a single-image, easy-to-use calibration method devoid of the singularity problem and an initial guess. In computer vision, Tsai’s two-step method is particularly popular. Instead of directly solving the standard collinearity equations (8.1), Tsai (1987) used a radial alignment constraint to obtain a linear least-squares solution for a subset of the calibration parameters, whereas other parameters including the radial distortion parameter are estimated by an iterative scheme. The camera calibration can be also carried out using a method developed by Heikkila (2000). Various methods for camera calibration and orientation in photogrammetry and computer vision are discussed in a book edited by Gruen and Huang (2001). In principle, these methods and open source software (such as OpenCV) can be adopted in PSP and TSP measurements. Here, no

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8 Image and Data Analysis Techniques

attempt is made to systematically survey and evaluate various camera calibration methods. To elucidate how to solve Eq. (8.1), we first discuss the DLT that can automatically provide initial values of the camera parameters and then describe an optimization method for more comprehensive calibration of camera.

8.1.2

Direct Linear Transformation

The Direct Linear Transformation (DLT), originally proposed by Abdel-Aziz and Karara (1971), is useful to determine approximate values of the camera parameters. Re-arranging the terms in the collinearity equations leads to the DLT equations L1 X þ L2 Y þ L3 Z þ L4
ðx þ dxÞðL9 X þ L10 Y þ L11 Z þ 1Þ ¼ 0, L5 X þ L6 Y þ L7 Z þ L8
ðy þ dyÞðL9 X þ L10 Y þ L11 Z þ 1Þ ¼ 0:

ð8:5Þ

The DLT parameters L1, . . ., L11 are related to the camera exterior and interior orientation parameters (ω, φ, κ, Xc, Yc, Zc) and (c, xp, yp). Unlike the standard collinearity equations (8.1), Eq. (8.5) is formally linear for the DLT parameters when the lens distortion terms dx and dy are neglected. In fact, the DLT is a linear treatment of what is essentially a nonlinear problem at the cost of introducing two additional parameters. The matrix form of the linear DLT equations for M targets is B L ¼ C, where L ¼ (L1, . . ., L11)T, C ¼ (x1, y1, . . ., xM, yM)T, and B is the 2M  11 configuration matrix that can be directly obtained from Eq. (8.5). Without using an initial guess, a least-squares solution for L is formally given by

1 L = BT B BT C: The camera parameters can be extracted from the DLT parameters from the following expressions (McGlone 1989) xp ¼ ðL1 L9 þ L2 L10 þ L3 L11 ÞL2 , yp ¼ ðL5 L9 þ L6 L10 þ L7 L11 ÞL2 , ffi q
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  c¼ L21 þ L22 þ L23 L2
x2p , φ ¼ sin
1 ðL9 LÞ, ω ¼ tan
1 ð
L10 =L11 Þ,

8.1 Geometric Calibration of Camera

205

κ ¼ cos
1 ðm11 = cos ðφÞÞ,
 m11 ¼ L xp L9
L1 =c,

1=2 , L ¼
L29 þ L210 þ L211 0 1 0 10 1 L1 L2 L3 L4 Xc B C B CB C @ Y c A ¼
@ L5 L6 L7 A @ L8 A: Zc L9 L10 L11 1 The DLT is widely used in both non-topographic photogrammetry and computer vision due to its simplicity. When dx and dy cannot be ignored, however, an iterative solution method is still needed and the DLT loses its simplicity. In general, the DLT gives fairly good values of the exterior orientation parameter and the principal distance, although it gives a poor estimate for the principal-point location (Cattafesta and Moore 1996). Therefore, the DLT is valuable, providing initial approximation for more accurate methods like an optimization method discussed below for comprehensive camera calibration.

8.1.3

Optimization Method

In order to develop a simple and robust method for comprehensive camera calibration, the singularity problem must be dealt with to solve the collinearity equations. Liu et al. (2000) proposed an optimization method based on the following insight. A strong correlation between the interior and exterior orientation parameters leads to the singularity of the normal equation matrix in the least-squares estimation for a complete set of the camera parameters. Therefore, to eliminate the singularity, leastsquares estimation is used for the exterior orientation parameters only, while the interior orientation and lens distortion parameters are calculated separately using an optimization scheme. This optimization method contains two separate but interacting procedures: resection for the exterior orientation parameters and optimization for the interior orientation and lens distortion parameters. When the image coordinates (x, y) are given in pixels, we express the collinearity equations (8.1) as f 1 ¼ Sh xn
xp þ dx þ cU=W ¼ 0, f 2 ¼ Sv yn
yp þ dy þ cV=W ¼ 0,

ð8:6Þ

where Sh and Sv are the horizontal and vertical pixel spacings (mm/pixel) of a sensor array, respectively, and U, V and W are the terms denoted in Eq. (8.1). In general, the vertical pixel spacing is fixed and known for a digital camera, but the effective horizontal spacing may be variable. Thus, an additional parameter, the pixel-

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8 Image and Data Analysis Techniques

spacing-aspect-ratio Sh/Sv, is introduced. The vector for the exterior orientation parameters and the vector for the interior orientation and lens distortion parameters in addition to the pixel-spacing-aspect-ratio are defined, i.e.,
T Πin ¼ c, xp , yp , K 1 , K 2 , P1 , P2 , Sh =Sv , Πex ¼ ðω, φ, κ, X c , Y c , Z c ÞT : For a given Πin, and a set of known points (targets) pn ¼ (xn, yn)T in the image plane and Pn ¼ (Xn, Yn, Zn)T in the object space, a solution for Πex in Eq. (8.6) can be found using an iterative least-squares method, referred to as resection in photogrammetry. The linearized collinearity equations for targets (n ¼ 1, 2, . . ., M ) are written as V ¼ Α ðΔΠex Þ
l,

ð8:7Þ

where ΔΠex is a correction term for the exterior orientation parameters, V is a 2M  1 residual vector, A is a 2M  6 configuration matrix, and l is a 2M  1 observation vector. The configuration matrix A and observation vector l in the linearized collinearity equations are 0

ð∂ f 1 =∂ Πex Þ1

1

C B B ð∂ f 2 =∂ Πex Þ1 C C B C ⋮ A¼B C B C B @ ð∂ f 1 =∂ Πex ÞM A ð∂ f 2 =∂ Πex ÞM

0

and

ð f 1 Þ1

1

C B B ð f 2 Þ1 C C B ⋮C l ¼
B C, B C B @ ð f 1 ÞM A ð f 2 ÞM

where ∂/∂ Πex is defined as (∂/∂ω, ∂/∂φ, ∂/∂κ, ∂/∂Xc, ∂/∂Yc, ∂/∂Zc) and the subscript denotes a target. The components of the vectors ∂ f1/∂ Πex and ∂ f2/∂ Πex are given by Liu et al. (2000). A least-squares solution to minimize the residuals V in Eq. (8.7) for the correction term is

1 ΔΠex = AT A AT l: In general, the 6  6 normal-equation-matrix (ATA) can be inverted without any singularity problem since the interior orientation and lens distortion parameters are not included in the least-squares estimation. To obtain such Πex that the correction term ΔΠex becomes zero, the Newton-Raphson iterative method is used to solve the nonlinear equation (ATA)
1ATl ¼ 0 for Πex. This approach converges over a considerable range of the initial values of Πex. Therefore, for a given vector Πin, the corresponding exterior orientation parameter vector Πex can be obtained, which is symbolically expressed as

8.1 Geometric Calibration of Camera

207

Πex ¼ RESECTIONðΠin Þ: At this stage, Πex is not necessarily correct unless Πin is accurate. Obviously, an extra condition is needed to obtain a correct Πin and the determination of Πin is coupled with the resection for Πex. An optimization scheme to obtain a correct Πin is described as follows. We notice that a correct Πin is intrinsically constant for a fixed camera/lens system, which is independent of the target locations pn ¼ (xn, yn)T in the image plane and Pn ¼ (Xn, Yn, Zn)T in the object space. Mathematically, Πin is an invariant under a transformation (pn, Pn) ° (pm, Pm) (m 6¼ n). Therefore, for a correct Πin, the parameters (c, xp, yp) are invariant under the transformation (pn, Pn) ° (pm, Pm) (m 6¼ n). In other words, for a correct Πin, the standard deviation of (c, xp, yp) calculated over all the targets from the collinearity equations should be zero, i.e., " #1=2 M
X
   2 std xp ¼ x p
x p =ð M
1Þ ¼ 0, n¼1

where std denotes the standard deviation and hi denotes the mean value. Furthermore, since std(xp)  0 is always valid, a correct Πin must correspond to the global minimum point of the function std(xp). Hence, the determination of a correct Πin becomes an optimization problem to seek such Πin that the objective function std(xp) is minimized, i.e.,
 std xp ! min : To solve this multiple-dimensional optimization problem, the sequential golden section search technique is used because of its robustness and simplicity. Since (c, xp, yp) are estimated from Eq. (8.1) for a given vector Πex, the optimization scheme for Πin is coupled with the resection scheme for Πex. Other appropriate objective functions can also be used; an obvious choice is the root-mean-square (RMS) deviation of the calculated object space coordinates of all the targets from the measured ones. In fact, it is found that std(xp) or std(yp) is equivalent to this RMS deviation in the optimization problem. The quantities std(xp) and std(yp) have a simple topological structure near the global minimum point, exhibiting a single “valley” structure in the parametric space (Liu et al. 2000). Generally, the topological structure of std(xp) or std(yp) depends on the three-dimensionality of a target field; stronger three-dimensionality of a target field produces a steeper “valley” in topology, leading to faster convergence in optimization. The topological structure of std(xp) or std(yp) can also be affected by random noise on the targets. Larger noise in images leads to a slower convergence rate and produces a larger error in optimization computation. Although the simple “valley” topological structure allows the convergence of optimization computation over a considerable range of the initial values, appropriate initial values are still

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8 Image and Data Analysis Techniques

Fig. 8.2 Step target plate for camera calibration

required to obtain a converged solution. The DLT can provide such initial values for the exterior orientation parameters (ω, φ, κ, Xc, Yc, Zc) and the principal distance c. Combined with the DLT, the optimization method allows rapid and comprehensive automatic camera calibration to obtain a total set of 14 camera parameters from a single image without requiring a guess of the initial values. The optimization method was used for calibrating a Hitachi CCD camera with a Sony zoom lens (12.5–75 mm focal length) and an 8 mm Cosmicar television lens. As shown in Fig. 8.2, a three-step target plate with a 2-in. step height provided a 3D target field for camera calibration, on which 54 circular retro-reflective targets of a 0.5-in. diameter spaced out 2 in. apart are placed. Figure 8.3 shows the principal distance given by the optimization method versus the zoom setting for the Sony zoom lens. Figures 8.4 and 8.5 show the principal-point location and radial distortion coefficient K1 as a function of the principal distance for the Sony zoom lens, respectively. The results given by the optimization method are in good agreement with measurements for the same lens using different optical methods and equipment in a laboratory (Burner 1995). The optimization method was also used to calibrate the same Hitachi CCD camera with an 8 mm Cosmicar television lens. Table 8.1 lists the calibration results given by the optimization method compared well with those obtained using optical equipment. In order to determine the interior orientation parameters accurately, a target field should fill up an image for camera calibration. In a large wind tunnel, however, a camera is often located far from a model such that a target field looks small in the image plane. In this case, a two-step approach is suggested that determines the interior and exterior orientation parameters separately. First, when a target plate is placed near a camera to produce a sufficiently large target field in the image plane, we can accurately determine the interior orientation parameters using the optimization method. Next, assuming that the determined interior orientation parameters are fixed for a locked camera setting, we obtain the exterior orientation parameters using the resection scheme from a target field placed in the measurement domain in a given wind-tunnel coordinate system.

Fig. 8.3 The principal distance as a function of zoom setting for a Sony zoom lens. (From Liu et al. 2000)

Fig. 8.4 The principal-point location as a function of the principal distance for a Sony zoom lens on a Hitachi camera. (From Liu et al. 2000)

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8 Image and Data Analysis Techniques

Fig. 8.5 The radial distortion coefficient as a function of the principal distance for a Sony zoom lens on a Hitachi camera. (From Liu et al. 2000)

8.2

Radiometric Calibration of Camera

Since PSP and TSP are based on radiometric measurements, a digital camera used for measurements should have a good linear response of the electrical output to the scene radiance. It is usually assumed that a scientific digital camera has a linear response to the scene radiance. However, there are many stages of image acquisition that may introduce nonlinearity; for example, video cameras often include some form of “gamma” mapping. It is needed to examine the linearity of the camera response. In addition, when the radiometric response function of a camera is known, the nonlinearity can be corrected. Here, a simple algorithm is described to determine the radiometric response function of a camera from a scene image taken in different exposures. First, we define I(x) as a linear radiometric response to the scene radiance and m[I(x)] as the measurement of I(x) by camera’s electronic circuitry that may produce a nonlinear electrical output. Actually, m[I(x)] is the brightness or gray level of an image, where x denotes the image coordinates. The nondimensional response function relating I(x) to m[I(x)] is defined by I ðxÞ=I max ¼ f ½ξðxÞ,

ð8:8Þ

Interior orientation Optimization Optical techniques

c (mm) 8.133 8.137

xp (mm)
0.156
0.168 yp (mm) 0.2014 0.2010

Sh/Sv 0.99238 0.99244

Table 8.1 Calibration for Hitachi CCD camera with 8 mm Cosmicar TV lens K1 (mm
2) 0.0026 0.0027

K2 (mm
4) 3.3  10
5 4.5  10
5

P1 (mm
1) 1.8  10
4 1.7  10
4

P2 (mm
1) 3  10
5 7  10
5

8.2 Radiometric Calibration of Camera 211

212

8 Image and Data Analysis Techniques

where ξ(x) ¼ m[I(x)]/m(Imax) is the nondimensional measurement of I(x) normalized by its maximum value m(Imax) and Imax is the maximum radiance in a scene. Recovery of f(ξ) is a task of the radiometric calibration of a camera. Two images of a scene are taken in two different exposures. According to the camera formula (Holst 1998), I(x) is proportional to an integration time tINT and inversely proportional to the square of the f-number F. Thus, we have the following functional equation for f(ξ), i.e., f ðξ1 Þ=f ðξ2 Þ ¼ R12 ,

ð8:9Þ

where the subscripts 1 and 2 denote the image 1 and image 2, and the factor R12 is defined as R12


 2 I max 2 t INT =F 1
 : ¼ I max 1 t INT =F 2 2

ð8:10Þ

Since m(Imax) corresponds to Imax, the boundary condition for f(ξ) is f (ξ ¼ 1) ¼ 1. We assume that f(ξ) can be expanded as f ðξÞ ¼

N X

cn ϕn ðξÞ,

ð8:11Þ

n¼0

where the base functions ϕn(ξ) are the Chebyshev functions. Note that other orthogonal functions and non-orthogonal functions like polynomials can also be used. Substitution of Eq. (8.11) to Eq. (8.9) leads to the following equations for the coefficients cn, i.e., N X

cn ½ϕn ðξ1 Þ
R12 ϕn ðξ2 Þ ¼ 0,

n¼0 N X

cn ϕn ð1Þ ¼ 1:

ð8:12Þ

n¼0

For selected M pixels in a scene image, Eq. (8.12) constitutes a system of M + 1 equations for the N + 1 unknowns cn (M  N ). For a given R12, a least-squares solution for cn can be found. In practice, since the factor R12 is not exactly known a priori, we use an approximate value of R12, i.e., R12


 2 mðI max 2 Þ t INT =F 1
 :  mðI max 1 Þ t INT =F 2 2

An iteration scheme can be used to give an improved value of R12.

8.3 Correction for Self-Illumination

213

Fig. 8.6 Two images of Mirror Lake of Yosemite (Ansel Adams 1935) taken by a Canon digital still camera (EOS D30) at different F-numbers: (a) F ¼ 4.0 and (b) F ¼ 5.6 for radiometric calibration of the camera

Figure 8.6 shows two images taken by a Cannon digital still camera (EOS D30) at the f-numbers of F ¼ 4.0 and F ¼ 5.6, where Ansel Adams’ photograph of Mirror Lake of Yosemite was used as a test scene providing a broad range of the gray levels for radiometric camera calibration. Figure 8.7 shows the radiometric response function of the camera retrieved from the two images, where six terms of the Chebyshev functions in Eq. (8.11) were used. The response function of the Canon digital still camera exhibits a nonlinear behavior; it is also different for the red, green, and blue (RGB) color channels.

8.3

Correction for Self-Illumination

The self-illumination of PSP and TSP results from the luminescent contribution to a point on a surface from all visible neighboring points; it becomes appreciable near a conjuncture of two surfaces and on a concave surface (Ruyten 1997a, b, 2001; Ruyten and Fisher 2001; Le Sant 2001b). Although the self-illumination can be suppressed to some extent by taking a ratio between a wind-on image and a wind-off image, it cannot be eliminated without considering the exchange of the radiative energy between neighboring surfaces, which may produce an error in data reduction of PSP and TSP. Therefore, we need to know how much the radiative energy leaves from an area element and travels toward another element.

8.3.1

View Factor

The geometric relations for this inter-surface interaction are known as view factors, configuration factors, shape factors, or angle factors (Modest 1993). We consider

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8 Image and Data Analysis Techniques

Fig. 8.7 Response functions of a Canon digital still camera (EOS D30) for the R, G, and B color channels obtained from radiometric calibration

diffuse surfaces that absorb and emit diffusely, and also reflect the radiative energy diffusely. The view factor dF dAi
dA j between two infinitesimal surface elements dAi and dAj, as shown in Fig. 8.8, is defined as a ratio between the diffuse energy leaving dAi directly toward and intercepted by dAj and the total diffuse energy leaving dAi, which is expressed as dF dAi
dA j ¼



 ni  X ij nj  X ij cos θi cos θ j dA ¼ dA j ,  2  4 j π Xij  π X ij 

ð8:13Þ

where ni (or nj) is the unit normal vector of dAi (or dAj), Xij is the position vector directing from dAi toward dAj, and θi (or θj) is the angle between the position vector Xij and the normal ni (or nj). The view factors leaving dAi directly toward the total surface Aj or leaving Aj toward dAi, or leaving Aj toward Ai can be similarly defined by integrating dF dAi
dA j (Modest 1993). The law of reciprocity is dAi dF dAi
dA j ¼ dA j dF dA j
dAi for these view factors. The view factor is a function of the geometric parameters. Methods for evaluating the view factors were discussed by Modest

8.3 Correction for Self-Illumination

215

Fig. 8.8 Radiative exchange between two surface elements

(1993) and a collection of the view factors for simple geometric configurations was complied by Howell (1982). For partially specular surfaces, the determination of the view factors is more complicated since the bidirectional reflectance distribution function (BRDF) of the paint must be known (Nicodemus et al. 1977; Asmail 1991).

8.3.2

Correction Scheme

The self-illumination correction is applied to an image intensity field denoted by I after it is mapped onto a model surface grid in the 3D object space. Because the image intensity is proportional to the luminescent energy flow rate, the image intensity Ii (the measured self-illuminated intensity) at an area element dAi is a ð0Þ sum of the local intrinsic intensity I i and integrated contributions from all neighboring elements, i.e., ð0Þ

I i ¼ I i þ ρwp λ2

N X

I j dF dA j
dAi dA j ,

ð8:14Þ

j¼1

where ρwp λ2 is the reflectivity of a wall-paint interface at the luminescent wavelength. ð0Þ In simulations, given a set of the intrinsic intensities I i , the image intensity Ii affected by the self-illumination can be obtained using a simple iteration scheme

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8 Image and Data Analysis Techniques

ðnþ1Þ

Ii

ð0Þ

¼ I i þ ρwp λ2

N X

ðnÞ

I j dF dA j
dAi dA j :

ð8:15Þ

j¼1

A more efficient Gauss-Seidel iteration scheme was used by Ruyten and Fisher (2001). In measurements, since the measured image intensity Ii is known in PSP and TSP images, an explicit relation is used to correct the self-illumination and recover ð0Þ the intrinsic intensity I i that is not affected by the self-illumination, i.e., ð0Þ

Ii

¼ I i
ρwp λ2

N X

I j dF dA j
dAi dA j :

ð8:16Þ

j¼1

The steps for correcting the self-illumination are: 1. 2. 3. 4. 5. 6.

Measure the reflectivity ρwp λ2 . Define a surface grid consisting of N surface elements dAi. Evaluate the view factors dF dA j
dAi . Map the image intensity Ii onto the surface grid. ð0Þ Calculate the intrinsic (corrected) intensity I i using Eq. (8.16). Calculate a ratio of the intrinsic (self-illumination-corrected) intensities and converting it to pressure or temperature.

8.3.3

Error Estimate

Ruyten and Fisher (2001) conducted a numerical simulation of correcting the selfillumination for a PSP test of the Alpha jet model and found that the error associated with the self-illumination in PSP measurements could reach several percentages of actual pressure. Here, we consider a simple but representative geometric configuration, a wedge-shaped conjunction of two infinitely large plates, as shown in Fig. 8.9; Fig. 8.9 Wedge-shaped conjunction of two plates

8.3 Correction for Self-Illumination

217

this case allows an analytical estimate of the error induced by the self-illumination. The image intensity at a location on the plate 1 is Z

ð0Þ

I 1 ¼ I 1 þ ρwp λ2

I 2 dF dA2
dA1 dA2 :

ð8:17Þ

plate2

Assuming that the image intensity at the plate 2 is homogeneous, by integrating the view factor for this configuration (Modest 1993), we obtain the image intensity at the plate 1 affected by the plate 2 ð0Þ

I 1  I 1 þ ε1 I 2 ,

ð8:18Þ

where the parameter ε1 ¼ ρwp λ2 ð1 þ cos αÞ=2 represents the combined effect of the angle α between the two plates and surface reflectivity. Clearly, the self-illumination   decreases from the maximum value at α ¼ 0 to zero at α ¼ 180 . A reciprocal relation gives the image intensity at the plate 2 ð0Þ

I 2  I 2 þ ε1 I 1 :

ð8:19Þ

When the parameter ε1 is small, the image intensity ratio at the plate 1 is  ð0Þ ð0Þ I 1 ref =I 1  I 1 ref =I 1 ð1 þ ε1 ε2 Þ: ð0Þ

ð0Þ

ð0Þ

ð8:20Þ

ð0Þ

The parameter ε2 ¼ I 2 ref =I 1 ref
I 2 =I 1 reflects a difference of the relative influence of the plate 2 on the plate 1 between the wind-off reference and wind-on conditions. Using the Stern–Volmer relation for PSP, we obtain an estimate for the pressure error associated with the self-illumination for a wedge configuration, i.e., j p
pð0Þ j ð0Þ

pref

 ε1 j ε2 j

! A pð0Þ þ , B pð0Þ

ð8:21Þ

ref

ð0Þ

where A and B are the Stern–Volmer coefficients, and p(0) and pref are, respectively, the intrinsic PSP-derived pressures in the wind-on and wind-off reference conditions that are not affected by the self-illumination. Similarly, using the Arrhenius relation for TSP, we have an estimate for the temperature error associated with the selfillumination for a wedge configuration, i.e., j T
T ð0Þ j R  ε1 j ε2 j , E nr T ð0Þ

ð8:22Þ

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8 Image and Data Analysis Techniques

where R is the universal gas constant, Enr is the activity energy of TSP, and T(0) is the intrinsic TSP-derived temperature that is not affected by the self-illumination.

8.3.4

Bidirectional Reflectance Distribution Function

The above discussions are based on the assumption that the luminescent paint surface is a diffuse surface or Lambertian surface. Nevertheless, a real paint surface is neither Lambertian nor specular. To characterize reflection on a general surface, the bidirectional reflectance distribution function (BRDF) was introduced by Nicodemus et al. (1977). As shown in Fig. 8.10, the incident radiance is generally a function of the incident direction defined by the incident polar angle and azimuthal angle (θi, φi), i.e., Li ¼ Li ðθi , φi Þ:

ð8:23Þ

The reflection radiance Lr(θi, φi; θr, φr) is quantitatively characterized by the BRDF f r ðθi , φi ; θr , φr Þ ¼ dLr ðθi , φi ; θr , φr Þ=dEi ðθi , φi Þ,

ð8:24Þ

where (θr, φr) defines the direction of reflection and the infinitesimal incident irradiance dEi(θi, φi) over a solid angle element dωi is

Fig. 8.10 Vectors of incident, reflecting, and viewing directions

8.3 Correction for Self-Illumination

dE i ðθi , φi Þ ¼ Li ðθi , φi Þ cos θi dωi :

219

ð8:25Þ

The BRDF has a unit of steradian
1. Here, the conventional radiometric notations L and E are used for radiance and irradiance, which are also applicable to the luminescent emission. The BRDF depends on a surface roughness distribution. For a perfectly diffuse surface where the reflection radiance is isotropic, i.e., Lr ¼ const., the BRDF is fr ¼ 1/π (Horn and Sjoberg 1979). For a general surface, the BRDF can be derived based on either the wave equation for electromagnetic waves or geometrical optics models (Beckmann and Spizzichino 1963; Torrance and Sparrow 1967; Nayar et al. 1991). Asmail (1991) gave a bibliographical review on the BRDF. From a viewpoint of application, empirical expressions for the scattered radiance from a rough surface are useful due to their simplicity (Cook and Torrance 1981; Haussecker 1999). An empirical model for a single light source is

 Lr ðX Þ ¼ ρa E a ðX Þ þ ρd E ls ðX Þ N T Ls þ ρs Els ðX Þp RT V ,

ð8:26Þ

where the first, second, and third terms are, respectively, the contributions from the ambient reflection, diffuse reflection, and specular reflection. In Eq. (8.26), ρa, ρd, and ρs are the empirical reflection coefficients for the ambient reflection, diffuse reflection, and specular reflection, respectively. As shown in Fig. 8.10, the vectors N, Ls, R, and V are, respectively, the unit normal vector of a surface, the unit vector directing the light source from the surface, the unit main directional vector of the specular reflection, and the unit viewing vector. Ea(X) and Els(X) are the irradiances for the ambient environment and light sources, respectively. The function p(RTV) is the directional distribution of the specular reflection, describing the spreading of scattered light. Phong (1975) gave a power function p(RTV) ¼ (RTV)n. In general, the main directional vector of the specular reflection, R, is a function of the incident direction of light
Ls. Although there are certain theories for predicting the specular direction R (Torrance and Sparrow 1967), R is not known for a general surface. The unknowns in Eq. (8.26), such as R, the reflection coefficients, and the parameters in p (RTV), have to be determined experimentally by calibration. Le Sant (2001b) measured the BRDF for the B1 PSP paint with talc using a BRDF calibration rig. As illustrated in Fig. 8.11, the BRDF calibration rig included a lamp for illumination and a spectrometer to measure the reflected light from a sample. The lamp emitted white light, enabling calibration of the BRDF in a visible range; the lamp moved from 0 at the vertical position to 60 . The zenith (or polar) angle of the spectrometer moved from 0 to 60 and the azimuth angle moved from 0 to 180 , where 180 was in the opposite direction of the emission. Figure 8.12 shows the measured BRDF for the B1 paint, which was nearly Lambertian when the zenith (or polar) angle of illumination was 10 , while specular reflection occurred when the zenith angle increased further. The maximum value was always achieved in the specular direction. The measured BRDF showed a superposition of diffuse reflection and specular reflection. A specular peak was observed at the zenith angle

220 Fig. 8.11 The zenith (or polar) and azimuth angles in the BRDF calibration rig. (From Le Sant 2001b)

8 Image and Data Analysis Techniques

zenith (spectrometer) zenith (illumination) 0°

180° 90°

90°

azimuth 0°

Fig. 8.12 The measured BRDF of the B1 paint at the illumination zenith angles of 10 , 20 , 30 , 40 , 50 , and 60 . (From Le Sant 2001b)

of 60 as well as a secondary peak at the azimuth angle of 90 . The value of the diffuse reflection factor depended on the zenith angle of illumination. Le Sant (2001b) was able to achieve a good fit to the measured BRDF using a modified Phong model (Phong 1975), as shown in Fig. 8.13, and the modeled BRDF captured the main features of the measured BRDF.

8.3 Correction for Self-Illumination

221

Fig. 8.13 The modeled BRDF of the B1 paint at the illumination zenith angles of 10 , 20 , 30 , 40 , 50 , and 60 using the modified Phong model. (From Le Sant 2001b) Fig. 8.14 Self-illumination in a corner coated with PSP. (From Le Sant 2001b)

Le Sant (2001b) also studied the self-illumination in a corner to validate a correction algorithm. The corner was painted with a Pyrene-based paint providing an image significantly affected by the self-illumination near the junction of the two plates, as shown in Fig. 8.14. Then, the left plate was covered with a black sheet, removing the effect of the self-illumination on the right plate, as shown in the right

222

8 Image and Data Analysis Techniques

Fig. 8.15 Self-illumination correction using the diffuse and Phong models. (From Le Sant 2001b)

image in Fig. 8.14. Figure 8.15 shows results before and after correcting the selfillumination based on the diffuse surface model and the Phong model. The selfillumination correction was effective; the self-illumination effect was reduced to 15% from about 40% near the junction. This paint behaved mostly like a diffuse paint such that the Phong model did not exhibit a significant improvement. Although the Phong model might improve the accuracy of correction for a surface with strong specular reflection, the computation time for the Phong model was much longer than that for the diffuse surface model.

8.4

Image Registration

The intensity-based method for PSP and TSP requires a ratio between the wind-on and wind-off images of a painted model. Since a model deforms due to the aerodynamic load, the wind-on image does not align with the wind-off image; therefore, these images have to be re-aligned before taking a ratio between these images. The image registration technique, developed by Bell and McLachlan (1993, 1996) and Donovan et al. (1993), is based on a transformation that maps the deformed wind-on image coordinates (xon, yon) onto the reference wind-off image coordinates (xoff, yoff). In order to register the images, some black fiducial targets are placed on a model. When the correspondence between the targets in the wind-off and wind-on images is established, a transformation between the wind-off and wind-on image coordinates of the targets can be expressed as

8.4 Image Registration

223

xoff ¼ yoff ¼

X X

aij φi ðxon Þφ j ðyon Þ, bij φi ðxon Þφ j ðyon Þ:

ð8:27Þ

The base functions φi(ξ) are either orthogonal functions (like the Chebyshev functions) or non-orthogonal power functions φi(x) ¼ xi used by Bell and McLachlan (1993, 1996) and Donovan et al. (1993). Given the image coordinates of the targets (fiducial markers) placed on a model, the unknown coefficients aij and bij can be determined using the least-squares method to match the targets between the wind-on and wind-off images. For image warping, one can also use a 2D perspective transform (Jähne 1999) a11 xon þ a12 yon þ a13 , a31 xon þ a32 yon þ 1 a x þ a22 yon þ a23 ¼ 21 on : a31 xon þ a32 yon þ 1

xoff ¼ yoff

ð8:28Þ

Although the perspective transform is nonlinear, it can be reduced to a linear transform using the homogeneous coordinates. The perspective transform is collinear that maps a line into another line and a rectangle into a quadrilateral. Therefore, Eq. (8.28) is more restricted than Eq. (8.27) for PSP and TSP applications. A comparative study of different image registration techniques was made by Venkatakrishnan (2003, 2004). Before the image registration technique is applied, targets (fiducial markers) must be identified and their centroid locations in images must be determined. The target centroid (xc, yc) is defined as xc ¼ yc ¼

XX XX

xi I ðxi , yi Þ= yi I ðxi , yi Þ=

XX XX

I ðxi , yi Þ, I ðxi , yi Þ,

ð8:29Þ

where I(xi, yi) is the gray level on an image. When a target contains only a few pixels and the target contrast is not high, the centroid calculation using the definition Eq. (8.29) may not be accurate. Another method for determining the target location is to maximize the correlation between the template f(x, y) and target scene I(x, y) (Rosenfeld and Kak 1982). The correlation coefficient CfI is defined as R f ðx þ x0 , y þ y0 ÞI ðx, yÞdxdy qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : CfI ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R 2 R 2 f ðx, yÞdxdy I ðx, yÞdxdy

ð8:30Þ

For the continuous functions f(x, y) and I(x, y), one can determine the location (x0, y0) of a target by maximizing CfI. However, it is found that for small targets in images, sub-pixel misalignment between the template and scene can significantly reduce the value of CfI even when the scene contains a perfect replica of the template.

224

8 Image and Data Analysis Techniques

To enhance the robustness of a localization scheme, Ruyten (2002) proposed an augmented template f ðx, yÞ ¼ f 0 ðx, yÞ þ f x Δ x þ f y Δ y, where f0(x, y) represented a conventional template and fx and fy are the partial derivatives of f(x, y). The additional shift parameters (Δ x, Δ y) allowed more robust and accurate determination of the target locations. In PSP and TSP measurements, operators can manually select targets and determine the correspondence between the wind-off and wind-on images. However, PSP and TSP measurements with multiple cameras in production wind tunnels may produce many images in a given test; thus, image registration becomes very laborintensive and time-consuming. It is nontrivial to automatically establish the pointcorrespondence between images taken by cameras with different viewing angles and positions. This problem is generally related to the epipolar geometry in which a point on a camera corresponds to a line on another camera (Faugeras 1993). Ruyten (1999) discussed the methodologies for automatic image registration including searching targets, labeling targets, and rejecting false targets. Unlike ad hoc techniques, the searching technique based on photogrammetric mapping is more rigorous. Once cameras are calibrated and the position and attitude of a tested model are approximately given by other techniques (such as accelerators and videogrammetric techniques), the targets in images can be found using photogrammetric mapping from the 3D object space to the image plane. Compared to the global methods of using a single transformation for the whole image, a local approach proposed by Shanmugasundaram and Samareh-Abolhassani (1995) divides an image domain into triangles connecting a set of targets based on the Delaunay triangulation (de Berg et al. 1998). For a triangle defined by the vertex vectors R1, R2, and R3, a point in the plane of the triangle can be described by a vector u1 R1 þ u2 R2 þ u3 R3 , where (u1, u2, u3) are referred to as the parametric (barocentric) coordinates and a constraint u1 + u2 + u3 ¼ 1 is imposed. When a wind-on pixel is identified inside a triangle and its parametric coordinates are given, the corresponding wind-off pixel can be determined by using the same parametric coordinates in the vertex vectors of the corresponding triangle in the wind-off image. Finally, the image intensity at that pixel is mapped from the wind-on image to the wind-off image. This approach is basically a linear interpolation assuming that the relative position of a point inside a triangle to the vertices is invariant under a transformation from the wind-on image to the wind-off image. Weaver et al. (1999) proposed a so-called Quantum Pixel Energy Distribution (QPED) algorithm that utilizes local surface features to calculate a pixel shift vector using a spatial correlation method. The local surface features could be targets,

8.5 Conversion to Pressure

225

pressure taps, and dots formed from aerosol mists in spraying on a basecoat. Similar to particle image velocimetry (PIV), the QPED algorithm can give a field of displacement vectors when the registration marks or features are dense enough. Based on a shift vector field, the wind-on image can be registered. Although the QPED algorithm is computationally intensive, it can provide local displacement vectors at certain locations to complement a global image registration technique. Kuzub et al. (2011) proposed a piecewise linear resection (PLR) method using a combination of natural feature and fiducial marker tracking. Although natural feature tracking was less accurate than fiducial marker tracking, the two motion vector sources could be combined, weighted, and segmented to produce a higher density motion gradient field. PLR was used to reduce wind tunnel model motion and deformation errors in the PSP application.

8.5

Conversion to Pressure

In PSP measurements, conversion of the luminescent intensity to pressure is complicated by the temperature effect of PSP especially when surface temperature distribution is not known. Empirically, a priori calibration relation between air pressure and the relative luminescent intensity is expressed by a polynomial  2 p I I ¼ C 1 ðT Þ þ C2 ðT Þ ref þ C3 ðT Þ ref : pref I I

ð8:31Þ

The experimentally determined coefficients C1, C2, and C3 in Eq. (8.31) can be expressed as a polynomial function of temperature. If the distribution of surface temperature is not given, a priori relation Eq. (8.31) cannot be directly applied to accurate conversion to pressure. To deal with this problem, a shortcut approach is in situ PSP calibration that directly correlates the luminescent intensity to pressure data from taps distributed on a model surface. In this case, the constant coefficients C1, C2, and C3 in Eq. (8.31) are determined using the least-squares method to achieve the best fit to pressure tap data over a certain range of pressures. Through in situ calibration, the effect of nonuniform surface temperature distribution is actually absorbed into a precision error of the least-squares estimation. When the temperature effect of PSP overwhelms a change of the luminescent intensity produced by pressure, in situ calibration has a large precision error. In addition, when pressure tap data do not cover a full pressure range on a surface, in situ PSP conversion may lead to a large bias error in data extrapolation outside a calibration range of pressures. A hybrid method between in situ and a priori methods is the so-called K-fit method developed by Woodmansee and Dutton (1998). Equation (8.31) is re-written as

226

8 Image and Data Analysis Techniques

   p I off I off 2 þ C 3 ðT Þ K I ¼ K P C 1 ðT Þ þ C2 ðT Þ K I , poff I I

ð8:32Þ

where Ioff ¼ I( poff, Toff) is the luminescent intensity in the wind-off condition, and KI ¼ Iref/Ioff and KP ¼ pref/poff are called the K-factors. The reference condition under which a priori calibration is made in a laboratory is generally different from the wind-off condition in a wind tunnel. While the factor KP ¼ pref/poff is known, the factor KI ¼ Iref/Ioff is generally not known and has to be determined since illumination condition and photodetector used in a laboratory may be different from those in a wind tunnel. Given the coefficients C1, C2, and C3 at a known temperature on an isothermal surface, KI can be determined using a single data point from pressure taps. When surface temperature data near a number of pressure taps are provided by other techniques like TSP and IR camera, a more accurate value of KI can be obtained using least-squares method. In the worst case where surface temperature distribution is totally unknown, assuming an average temperature over a surface, we are still able to estimate KI by fitting pressure tap data. Similar to in situ calibration, the effect of nonuniform temperature distribution is absorbed into a precision error of leastsquares estimation for KI. Bencic (1999) used a similarity variable of the luminescent intensity to scale the temperature effect of certain PSP, i.e.,  I ref  I  ¼ gðT Þ ref , I corr I

ð8:33Þ

where g(T ) was a function of temperature to be determined by a priori calibration. Under this similarity transformation, the calibration curves for the paint at different temperatures collapsed onto a single curve with the temperature-independent coefficients, i.e.,    2 p I  I  ¼ C1 þ C2 ref  þ C 3 ref  : pref I corr I corr

ð8:34Þ

In this case, instead of using a 2D calibration surface in a parametric space, only a single one-parameter relation Eq. (8.34) was used to convert the luminescent intensity ratio to pressure. Bencic (1999) found that this similarity was valid for a Ruthenium-based PSP used at NASA Glenn. In fact, as pointed out in Chap. 3, this similarity is a property of the so-called “ideal” PSP that obeys the following relations (Puklin et al. 1998; Coyle et al. 1999) I ðp, T Þ=I ðp, T ref Þ ¼ gðT Þ, I ref ðpref , T ref Þ I ðp , T Þ ¼ gðT Þ ref ref ref : I ðp, T ref Þ I ðp, T Þ

ð8:35Þ

8.6 Pressure Correction for Extrapolation to Low-Speed Data

227

Puklin et al. (1998) found that PtTFPP in FIB polymer was an “ideal” PSP over a certain range of temperatures. Note that this similarity is not the universal property of a general PSP.

8.6

Pressure Correction for Extrapolation to Low-Speed Data

PSP is particularly effective in high subsonic, transonic, and supersonic flow regimes. However, PSP measurement in low-speed flows is a challenging problem since a very small pressure change may not be sufficiently resolved by PSP. The major error sources, notably the temperature effect, image misalignment, and camera noise, must be minimized to obtain acceptable quantitative pressure data at low speeds. The resolution of PSP measurements is eventually limited by the photon shot noise of a digital camera. Liu (2003) proposed a pressure-correction method as an alternative to extrapolate low-speed pressure data. This method is able to obtain the incompressible pressure coefficient from PSP measurements at suitably higher Mach numbers (typically Mach 0.3–0.6) by removing the compressibility effect. It is noticed that there is a significant difference between the responses of the absolute pressure p and the pressure coefficient Cp to the freestream Mach number M1. The sensitivity of Cp to the Mach number for M 21 1 is estimated by SC p ¼

M 1 dCp  M 21 : C p dM 1

ð8:36Þ

In contrast, the sensitivity of pressure to the Mach number is approximately Sp
p1 ¼

M 1 d ð p
p1 Þ  2: ðp
p1 Þ dM 1

ð8:37Þ

For M 21 1, SCp is much smaller than Sp
p1 . For M1 ¼ 0.3 and dM1/M1 ¼ 10%, the relative change of the absolute pressure difference is d( p
p1)/( p
p1)  20%, while the relative change of Cp is only dCp/Cp  0.9%. Clearly, PSP can take advantage of the relative insensitivity of Cp to the Mach number to infer an approximate incompressible pressure coefficient distribution from data at suitably higher Mach numbers. Furthermore, the compressibility effect can be corrected using a pressure-correction method. In classical aerodynamics, the pressure-correction formulas were derived in order to extrapolate the pressure coefficient in subsonic compressible flows from the incompressible flow theory and low-speed pressure measurements. In contrast, for PSP applications, the pressure-correction formulas could be used to transform the compressible Cp to the corresponding incompressible Cpinc. The theoretical foundation for pressure correction in 2D potential flows is well established. The linearized

228

8 Image and Data Analysis Techniques

theory for subsonic compressible flow gives the Prandtl-Glauert rule (Anderson 1990) C p ¼ Cpinc =

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1
M 21 :

ð8:38Þ

The use of a hodograph solution of the nonlinear potential equation gives the Karman-Tsien rule (Anderson 1990) Cpinc

C p ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : M 21 C pinc 2 p ffiffiffiffiffiffiffiffiffiffi 1
M1 þ 2 2 1þ

ð8:39Þ

1
M 1

For PSP measurements on 2D airfoils at suitably high Mach numbers, both the Prandtl-Glauert rule and Karman-Tsien rule can be used to recover the incompressible pressure coefficient. Bell and Hand (1998) used the Prandtl-Glauert rule for the purpose of improving the image ratioing procedure of PSP to obtain a pseudo windoff pressure coefficient at a suitably low velocity. However, for complex 3D viscous flows such as separated flows, a general pressure-correction method is required. Liu (2003) developed an iterative pressure-correction method for 3D flows. For M 21 1, a pressure field can be generally expressed as a power series of M 21 . The pressure-correction formula for a general surface Z ¼ S(X, Y ) has a functional form composed of an incompressible term and a compressible correction term Cp  Cpinc þ M 21 F ½X, Y, SðX, Y Þ:

ð8:40Þ

Equation (8.40) is valid for not only potential flows, but also complex viscous flows over a 3D body. Because Cpinc ¼ Cpinc[X, Y, S(X, Y )] is a function of X and Y, we can, in principle, eliminate X in the correction function F[X, Y, S(X, Y )] by using Cpinc and Y. Therefore, since the correction function F[X, Y, S(X, Y )] is not specified yet, the equivalent form to Eq. (8.40) is
 C p  Cpinc þ M 21 F C pinc , Y :

ð8:41Þ

Equation (8.41) indicates that the pressure correction in 3D flows depends on not only Cpinc, but also one space coordinate Y. Note that the functional form of Eq. (8.41) remains valid after the coordinate Y is switched to another coordinate X. When Cp does not change along the coordinate Y, Eq. (8.41) is naturally reduced to the method for 2D and axisymmetrical flows. By writing F(Cpinc, Y) as a polynomial function, Eq. (8.41) becomes

8.6 Pressure Correction for Extrapolation to Low-Speed Data

Cp  C pinc þ M 21

N X

an ðY ÞCnpinc :

229

ð8:42Þ

n¼0

When the distributions of Cp and Cpinc are known along an intersection between the plane Y ¼ const. and the surface Z ¼ S(X, Y), the coefficients an(Y ) can be determined using the least-squares method. In wind tunnel measurements, pressure tap data in subsonic flow and the corresponding low-speed flow can be used to establish the relationship between Cp and Cpinc. However, this approach is not convenient for PSP measurements in wind tunnels since extra pressure tap data are required. Here, an iterative method is proposed to recover Cpinc from Cp data at two different subsonic Mach numbers M11 and M12. The biggest advantage of this method is that Cpinc can be directly obtained from two PSP images taken at M11 and M12 without use of additional pressure tap data. Denote Cp1 and Cp2 as the pressure coefficients at M11 and M12, respectively, and assume M11 < M12. Given the distributions of Cp1 and Cp2 along an intersection between the plane Y ¼ const. and surface Z ¼ S(X, Y), we need to solve the following equations to recover Cpinc and an(Y ) Cp1  Cpinc þ M 211

N X

an ðY ÞC npinc ,

n¼0

C p2  C pinc þ M 212

N X

an ðY ÞC npinc :

ð8:43Þ

n¼0

An iteration scheme for solving Eq. (8.43) is described below. 1. Give the initial distribution Cpinc(k) ¼ Cp1 (k ¼ 0) as a function of X along an intersection between Y ¼ const. and Z ¼ S(X, Y) in the object space (a row or column in the image plane). Here, k is the iteration index number. 2. By using the least-squares method, determine the coefficients an(k)(Y ) (n ¼ 0, 1. . ., N ) in a polynomial from a system of equations


N X  Cp2
C pincðkÞ =M 212 ¼ anðkÞ ðY ÞCnpincðkÞ : n¼0

3. To obtain the corrected value Cpinc(k + 1), substitute an(Y ) into

C pincðkþ1Þ  C p1
M 211

N X n¼0

anðkÞ ðY ÞCnpincðkÞ :

230

8 Image and Data Analysis Techniques

4. Go back to Step (2), replace Cpinc(k) by the corrected value Cpinc(k + 1) and iterate until the converged results Cpinc ¼ Lim C pincðkÞ and an ðY Þ ¼ Lim anðkÞ ðY Þ k!1

(n ¼ 0, 1, . . ., N ) are obtained. 5. Output the final Cpinc ¼ Cpinc[X, Y, S(X, Y )] and an(Y).

k!1

After processing for a large set of intersections, we can recover the distribution of Cpinc on the whole surface. Unlike the classical pressure-correction formulas for 2D flows, this iterative method is a nonlocal approach that has to be done along an intersection on a surface. The selection of the order N of a polynomial in Eq. (8.43) depends on the complexity of the Mach number effect on a pressure distribution along an intersection. For 2D flows and near-2D flows, N ¼ 2 is sufficient; for more complex flows, the order of a polynomial could be higher. The number of available data points on an intersection eventually limits the order of a polynomial. For PSP, data processing is typically done in the image plane rather than in a surface in the 3D object space. Therefore, for convenience, the pressure-correction method should be used in the image plane. The aforementioned analysis is made in an arbitrary object-space coordinate system (X, Y, Z) or a general non-orthogonal curvilinear coordinate system on a surface. Since there is a one-to-one projection mapping between the image plane (x, y) and the surface Z ¼ S(X, Y ), the iterative pressure correction method can be directly applied to rows or columns in PSP images. There are some limiting conditions for the application of the iterative pressurecorrection method. First, the two Mach numbers M11 and M12 should be lower than the critical Mach number at which flow becomes sonic at a certain point on a surface. Secondly, the pressure-correction method relies on the assumption that a surface pressure distribution does not have a drastic change due to the Reynolds number effect as the Mach number increases from M1 ¼ 0 to M11 and M12. When the Reynolds number effect on pressure overwhelms the effect of the Mach number, the pressure-correction method cannot produce correct results because the flow pattern has been qualitatively changed. This situation may happen on a high-lift model under certain testing conditions in certain flow separation regions that are particularly sensitive to the Reynolds number effect. Fortunately, there is a large class of flows in which the Reynolds number does not significantly affect a surface pressure distribution, such as attached flows and certain separated flows whose separation and re-attachment lines are fixed. For these flows, the pressure-correction method is applicable. The iterative pressure-correction method was validated for flows over a circular cylinder, sphere, prolate spheroid, transonic body, and delta wing (Liu 2003). Figure 8.16 shows the incompressible Cpinc distribution on a circular cylinder recovered by the iterative pressure-correction method along with the results obtained using the Prandtl-Glauert rule and Karman-Tsien rule. The iterative method produced excellent recovery of Cpinc given by the incompressible solution of potential flow over a cylinder (Lighthill 1954). The Karman-Tsien rule also gave a good correction, while the Prandtl-Glauert rule (a linearized method) was not accurate in the low-pressure region Cp ¼ [
3,
2]. The iterative method used the Cp

8.7 Generation of Deformed Surface Grid

231

2 Iterative method Karman-Tsien Prandtl-Glauert Incompressible solution

1

Cp

0

-1

-2

-3

Circle -4 0

1

2

3

theta (radian) Fig. 8.16 Pressure correction for a circular cylinder to recover the incompressible pressure coefficient. (From Liu 2003)

distributions at M11 ¼ 0.4 and M12 ¼ 0.6. The order of a polynomial was N ¼ 2 and the solution for Cpinc converged after 10 iterations. Both the Karman-Tsien rule and the Prandtl-Glauert rule used Cp at M1 ¼ 0.4 to recover Cpinc. Figure 8.17 shows the pressure correction for a prolate spheroid of a fineness ratio of 6 at AoA of 5.6 and zero ellipsoidal coordinate (Matthews 1953). The iterative method used Cp data at M11 ¼ 0.6 and M12 ¼ 0.8. Even though these Mach numbers are quite high, the iterative method still produced good results since the Mach numbers were less than the critical Mach number of 0.904 in this case. To examine the capability of the iterative pressure-correction method for complex vortical separated flows, it was also used to recover Cpinc on the upper surface of a 65 delta wing; the recovered Cpinc distributions showed a correct trend as the Mach number increases.

8.7

Generation of Deformed Surface Grid

For a more accurate representation of data, PSP and TSP results in images should be mapped onto a deformed surface grid of a model rather than a rigid surface grid when the model undergoes a large deformation in wind tunnel testing. Aeroelastic deformation data for a model can be obtained using the videogrammetric model

232

8 Image and Data Analysis Techniques 0.4

Prolate spheroid of fineness ratio 6

0.3

Cpinc, Iterative method Mach 0.0 Mach 0.6 Mach 0.8

Cp

0.2

0.1

AoA = 5.6 deg omega = 0 deg

0.0

-0.1

-0.2 0

10

20

30

40

50

Percent distance from nose Fig. 8.17 Pressure correction for a prolate spheroid to recover the incompressible pressure coefficient. (From Liu 2003)

deformation (VMD) measurement technique (Burner and Liu 2001; Liu et al. 2012; Le Sant 2004; Le Sant et al. 2005). Hence, PSP and TSP systems should be integrated with a VMD system for the fusion of pressure and temperature data with deformation data (Bell and Burner 1998; Liu et al. 1999; Gregory et al. 2009). In particular, Le Sant (2004) and Le Sant et al. (2005) used VMD data for image registration. There are two approaches to the integration of PSP/TSP with VMD. The first approach uses PSP/TSP simultaneously with VMD as a separate and independent system, while VMD provides deformation data for generating a deformed surface grid. The advantage of this approach is that the structure of a PSP/TSP system is not changed and PSP/TSP operation suffers no interference from VMD operation in large production wind tunnels. In contrast, the second approach uses the same camera for both PSP/TSP and VMD measurements at the same time; VMD software is integrated as an additional part of the PSP/TSP software package. Instead of a nearly normal view of a camera for pure PSP/TSP measurements, a combined system requires an oblique viewing angle of a camera to achieve good position sensitivity for VMD measurements. Usually, VMD gives wing deformation characterized by the twist and bending of a wing. When the local translation and twist are measured by VMD at different spanwise locations of a wing, a transformation of translation and rotation can be used

8.7 Generation of Deformed Surface Grid

233

to reconstruct a deformed surface grid of the wing. At a spanwise location Y, the deformed coordinate (X0, Y0, Z0) on a wing surface grid is locally related to the non-deformed grid coordinate (X, Y, Z ) by

X0

Z0

¼ RðY Þ

X Z

þ

T x ðY Þ T z ðY Þ

:

ð8:44Þ

The translation vector at a spanwise location Y of the wing is (Tx, Tz) and the rotational matrix is RðY Þ ¼

cos θtwist

sin θtwist


sin θtwist

cos θtwist

,

ð8:45Þ

where the twist θtwist is a function of the spanwise location Y. When the bending relative to the wingspan is small, the spanwise location does not change much, i.e., Y0  Y in an initial approximation, and the wing airfoil section remains the same. For a large bending, the improved estimation of the spanwise coordinate Y0 can be made by an iterative scheme. For illustration, we consider a wing with a NACA0012 airfoil section and assume that the spanwise distributions of twist and bending are given by θtwist ¼
5(Y/b)3, Tz ¼ 0.08 b(Y/b)3, and Tx ¼ 0, where b is the semi-span of the wing. Figure 8.18 shows a deformed surface grid generated using a transformation of translation and rotation.

Fig. 8.18 Generation of a deformed surface grid of a wing based on videogrammetric deformation measurements. (From Liu et al. 1999)

234

8.8 8.8.1

8 Image and Data Analysis Techniques

Noise Reduction Methods Phase Averaging

Unsteady PSP measurements at low speeds are challenging because the SNR of the PSP signal is insufficient to detect a surface pressure distribution. Surface pressure fluctuation associated with wind noise is on the order of one-tenth of the dynamic pressure of the airflow. At a flow velocity of 10 m/s, PSP needs to detect a surface pressure fluctuation associated with wind noise in the order of 10 Pa. Since the pressure sensitivity of a conventional PSP is about 1%/kPa, PSP data obtained at such low speeds are usually corrupted by image noise. Thus, it is necessary to improve the SNR by data processing. When a flow has a dominant frequency, phase averaging is a simple method to reduce the random noise. The SNR of PSP measurement at low speeds can be increased by averaging PSP luminescent intensity fields detected at the same phase of periodic pressure variation. Therefore, real-time phase detection from a trigger signal is essential to obtain accurate data. McGraw et al. (2006) proposed a phase detection method to measure a pressure variation on a 3D square cylinder, where a start point of the pressure variation in each cycle was detected and other phases were determined by a time delay from the start point. Gregory et al. (2006) measured a periodic pressure change in an acoustic resonance cavity using this phase-locked technique. Yorita et al. (2010a) applied band-pass filtering to pressure transducer data for removing random noise and zero-crossing point fluctuation. Therefore, the zero-crossing points of the filtered signal were determined at phases of 0 and 180 in one cycle as reference phases. Other phases were determined by using a time delay from each reference phase. Yorita et al. (2010b) and Asai and Yorita (2011) applied this method to unsteady PSP measurements on a flat plate surface around a square cylinder. By using a highspeed CMOS camera, unsteady PSP measurement and reference signal measurement were made simultaneously when an excitation light of PSP was operated in a continuous mode. Image acquisition of a high-speed camera was synchronized with a reference signal. The reference signal was filtered to remove random noise and obtain a clean waveform. With the phase information, the acquired PSP images were sorted into several phase bands. The sorted images were then ensembleaveraged for each phase band. This method required only a simple experimental setup and allowed for SNR enhancement by flexible image processing. Figure 8.19 shows the phase-averaged pressure fields on a flat plate surface around a square cylinder. The reference signal was provided by a pressure transducer at the center point of the lateral side. The unsteady pressure fields around the square cylinder were clearly visualized. A pair of high- and low-pressure regions appeared behind the square cylinder and traveled downstream, which were caused by the Karman vortex shedding from the cylinder. Singh et al. (2011) applied this method to measure a pressure field behind an oscillating fence actuator. Miozzi et al. (2016) applied phase-average based on a data-driven reference signal in time-resolved TSP

8.8 Noise Reduction Methods

235

Fig. 8.19 Phase-averaged pressure fields on the flat-plate surface around the square cylinder. (From Yorita et al. 2010b)

measurement on a cylinder in crossflow at subcritical Reynolds number. The signal, related to the vortex shedding periodicity, was extracted from the most regular time coefficient retained by the POD modes of temperature maps of the laminar separation bubble region.

8.8.2

FFT-Based Analysis

Spectral analysis based on the fast Fourier transform (FFT) was applied to unsteady PSP data to identify the dominant structures in surface pressure fields (Nakakita 2011, 2013; Crafton et al. 2017b; Noda et al. 2018; Ozawa et al. 2019). For a timedependent variable x(t), the Fourier transform of x(t) and the power spectrum (PS) of x(t) are written as, respectively, X ð f Þ ¼ F ½xðt Þ, Sxx ð f Þ ¼ jX ð f Þj2 ¼ X ð f ÞX ð f Þ, where * denotes the conjugation of a complex variable. Accordingly, for a time series xn ¼ x(nΔt) (n ¼ 1, 2, . . ., N ), the discrete Fourier transform of xn, and the PS of xn are given by, respectively, X ð f Þ ¼ FFTðxn Þ,

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8 Image and Data Analysis Techniques


 Sxx ð f Þ ¼ jX ð f Þj2 2=N 2 : To evaluate the correlation between the signals x(t) and y(t), the coherence is defined as   Sxy ð f Þ2 , Coh ð f Þ ¼ Sxx ð f ÞSyy ð f Þ 2

ð8:46Þ

where Sxy( f ) ¼ X( f )Y ( f ) is the cross-spectrum between x(t) and y(t), Sxx( f ) and Syy( f ) are the auto-spectra (power spectra) of x(t) and y(t), respectively. The coherent output power (COP) of x(t) is defined as COPð f Þ ¼ Sxx ð f ÞCoh2 ð f Þ:

ð8:47Þ

To reduce random noise, Nakakita (2011, 2013) applied the ensemble averaging to the cross-spectra and auto-spectra by dividing a large set of data into small subsets. When a long time series xn is divided into R segments, the power spectrum of the kth segment is denoted by Sxx, k( f ). The ensemble averaged power spectrum is hSxx it ¼

R 1X S ð f Þ, R k¼1 xx,k

ð8:48Þ

where hit denotes the average in a time domain. Thus, the ensemble-averaged coherence and COP are defined as, respectively,    Sxy ð f Þ 2  t  , Coh ð f Þ ¼ hSxx ð f Þit Syy ð f Þ t

ð8:49Þ

COPð f Þ ¼ hSxx ð f Þit Coh2 ð f Þ:

ð8:50Þ

2

and

When a pressure fluctuation and the photon shot noise in different segments are uncorrelated, the ensemble averaging reduces the random noise. Further, in addition to the temporal ensemble averaging, Ozawa et al. (2019) introduced the spatial ensemble averaging of the cross-spectra between neighboring pixels in a small region. The random noise was significantly reduced by the temporal and spatial ensemble averaging. Based on the spectral analysis, Noda et al. (2018) identified a small-amplitude pressure fluctuation due to the trailing edge noise on a NACA0012 airfoil by AA-PSP at the freestream velocities of 25 and 28 m/s. An elliptical illumination region near the trailing edge on the pressure side of the model was generated by a blue laser through a combination of collimating and cylindrical lenses. The

8.8 Noise Reduction Methods

237

luminescent intensity of PSP was captured by a 12-bit monochromatic high-speed CMOS camera. Pressure fluctuations associated with the trailing edge noise were measured by PSP, and 40,960 sequential images were recorded at 10 kfps. Using the signals from PSP, pressure transducers, and sound-level meter, the power spectra were calculated on the basis of full data FFT and ensemble averaging FFT. Furthermore, the COP for the dominant sound frequency was calculated using the signal from the sound-level meter. The sound-level meter and the transducers detected the same predominant frequency of 943.1 Hz in the discrete trailing edge noise. Figure 8.20 shows the power distribution of pressure fluctuation at approximately

Fig. 8.20 Power distribution on the pressure side of the NACA0012 airfoil at approximately 940 Hz obtained using (a) the full data FFT, (b) the ensemble-averaging FFT, and (c) the COP. (From Noda et al. 2018)

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8 Image and Data Analysis Techniques

940 Hz calculated using the three methods of data reduction: full data FFT, ensemble averaging FFT, and COP. The high-pressure fluctuation regions at about 940 Hz were identified by all the three methods.

8.8.3

Mode Decomposition Analysis

The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) can be used for de-noising of PSP and TSP data since noise is usually represented by higher-order modes. POD was used by Pastuhoff et al. (2013), Gordeyev et al. (2014), Peng et al. (2016b), Crafton et al. (2017a), Sugioka et al. (2019a), and Gößling et al. (2020) for de-noising of unsteady PSP data obtained in low-speed flows. Reconstruction based on some dominant POD modes yielded considerable improvement in the SNR, which was capable of extracting some characteristic behaviors of unsteady flow phenomena even below the noise floor. Ali et al. (2016) applied DMD to unsteady PSP data obtained in a rectangular acoustic cavity. Both DMD and POD were compared with phase averaging for data analysis. DMD and POD were robust techniques that can be applied to aperiodic or multi-frequency signals. Furthermore, DMD was better than POD in suppressing noise and effectively separating spectral energy when multiple acoustic excitation frequencies were present. Gößling et al. (2020) evaluated phase averaging, POD, DMD, and FFT for unsteady PSP measurements. DMD is identified to be very powerful in extracting pressure fluctuations and eliminating image noise, but FFT achieves comparable results in this application. The development of DMD was described by Schmid (2010). Further, DMD with a Kalman filter was discussed by Nonomura et al. (2018). An overview of modal analysis was given by Taira et al. (2017). Table 8.2 lists the noise reduction methods for low-speed PSP measurements and relevant references. Table 8.2 Noise reduction methods Methods Conditional image (phase) averaging

Pixel-by-pixel FFT Singular value decomposition (SVD), proper orthogonal decomposition (POD)

Dynamic mode decomposition (DMD) Coherent output power (COP) Kalman filter-based DMD (KFDMD) Cross spectral correlation (CSC)

References McGraw et al. (2006), Yorita et al. (2010a, b), Gordeyev et al. (2014), Singh et al. (2011), Davis et al. (2015) Nakakita (2007, 2011, 2013), Gößling et al. (2020) Pastuhoff et al. (2013), Gordeyev et al. (2014), Peng et al. (2016b), Roozeboom et al. (2016), Crafton et al. (2017a), Hiura et al. (2017), Wen et al. (2018), Sugioka et al. (2019a) Ali et al. (2016), Crafton et al. (2017a), Gößling et al. (2020) Noda et al. (2018), Nakakita & Ura (2020) Nonomura et al. (2018) Ozawa et al. (2019)

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239

The singular value decomposition (SVD) is one of the methods to find the POD modes. Consider a time sequence of N images (matrices) denoted by I(x, y, tk) with a size of m  n, where tk ¼ 1, 2, . . ., N. An image I(x, y, tk) at a given time is re-arranged into a column vector ak with the length of M ¼ m  n. Therefore, a data matrix is A ¼ [a1 a2. . .aN] with a size of M  N. SVD gives A = UΣV T ¼

S X

σ i ui vi T ,

ð8:51Þ

i¼1

where Σ = diag (σ 1, σ 2, . . ., σ S) is the diagonal matrix with S ¼ min (M, N), U = [u1 u2. . .uM] is the left matrix with a size of M  M, and V = [v1 v2. . .vN] is the right matrix with a size of N  N. The quantities σ k are the singular values of A with a descending order of σ 1  σ 2  ⋯  σ S  0. The left and right singular vectors are the orthonormal eigenvectors of AAT and ATA, respectively, (i.e., uiTuj ¼ δij and viTvj ¼ δij, where δij is the Kronecker delta). The left singular vectors uk (k ¼ 1, 2, . . ., S) of A represent the spatial modes or POD modes. The right singular vectors vk (k ¼ 1, 2, . . ., S) of A are the sequences of the temporal coefficients of the modes. A built-in Matlab function for SVD calculations is easy to use and reasonably fast. In addition to SVD, the snapshot method developed by Sirovich (1987) is widely used for extracting the POD modes. Pastuhoff et al. (2013) evaluated the fluctuating pressure field due to unsteady vortex shedding on the side of a square cylinder at the freestream velocities of 10–50 m/s. A 3D matrix of a size of 600  256  3000 was formed from the PSP images, where the first two dimensions were spatial and the third dimension temporal. SVD gave the left matrix U containing the first 3000 spatial singular vectors, each of length 153,600 corresponding to the number of pixels (600  256) in each image. The full left matrix V was given, where each temporal vector had the length of 3000 corresponding to the number of time steps. In this case, Σ was a 3000  3000 matrix. Figure 8.21 shows the spatial vectors uk and the frequency spectra of the temporal vectors vk at 50 m/s. It is noted that in Fig. 8.21a, the first and second modes correspond to the freestream and mechanical vibration, respectively. Thus, the second mode is removed (filtered out) to reconstruct the intensity fields. Figure 8.22 shows the PSP intensity fields at different times before and after filtering using SVD for the 50 m/s case. SVD resulted in a reduction of pixel noise of the order of two magnitudes, which made it possible to obtain the spatial form of flow structures as well as the shedding frequency. After a large set of POD modes is obtained from unsteady PSP data, a question is how to select a much smaller set of suitable POD nodes to faithfully reconstruct a time sequence of pressure fields. Traditionally, higher-energy POD modes are selected. However, such selection of the main POD modes for reconstruction is somewhat subjective particularly when the original data are noisy. Wen et al. (2018) proposed a data mining method based on compressed data fusion to extract clean signals from highly noisy unsteady PSP data obtained in low-speed flows. In this method, the fields reconstructed based on the POD modes are optimized to fit a sparse representation of scattered clean data (e.g., microphone data in their case).

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8 Image and Data Analysis Techniques

Fig. 8.21 (a) Magnitudes of the first 12 spatial vectors and (b) frequency spectra of the first four temporal vectors for the case of 50 m/s. (From Pastuhoff et al. 2013)

Fig. 8.22 Intensity fields at different times (a) before and (b) after filtering using SVD for the case of 50 m/s. (From Pastuhoff et al. 2013)

Then, high-quality reconstruction can be obtained using the optimized POD coefficients. This compressed data fusion approach was used to recover the unsteady pressure field on a flat plate induced by a cylinder wake flow at low speed. In essence, this method is a dynamic in situ calibration.

8.8.4

Heterodyne Method

Matsuda et al. (2013c) proposed another noise-reduction technique based on the heterodyne method. This measurement was realized by detecting the beat signal that

8.9 Image Deblurring

241

results from interference between a modulating illumination light source and a pressure fluctuation. By carefully adjusting the frequency of light and camera’s frame rate, the heterodyne-based method detected signals at the frequency of interest and eliminated noise signals at other frequencies. An advantage of this method is that one can use a camera with a considerably low frame rate. The effectiveness of the proposed method was demonstrated with a resonance tube. The pressure fluctuation distributions at the fundamental frequency (376.2 Hz) and the second and third harmonics (698.5 and 1032.7 Hz, respectively) were successfully obtained using the same camera frame rate (20 Hz). The measured values of the fluctuation were in good agreement with those obtained by a pressure transducer within experimental error. This method is a useful technique for measuring periodic unsteady phenomena, especially while expensive high-speed video cameras are not available.

8.9

Image Deblurring

In PSP measurements on a high-speed moving object such as rotorcraft blades with the two-gate lifetime method, image blurring associated with integration in a gating time (gate 2) could occur when a characteristic timescale of motion is close to the luminescent lifetime. The issue is particularly problematic near the leading and trailing edges of a moving object and regions with large surface pressure gradients, such as shock waves. To deal with this problem, Juliano et al. (2012), Gregory et al. (2014b), and Pandey and Gregory (2018) developed image-deblurring or imagedeconvolution techniques with a point-spread function modeled based on a lifetime decay of PSP and local velocity of an object. This problem belongs to a class of image deconvolution problems or the image restoration problems in image processing (Helstram 1967; Banham and Katsaggelos 1997; Oliveira et al. 2009). Mathematically, a blurred image B is expressed as a convolution of a latent (non-blurred) image L and a motion blur kernel K, i.e., B ¼ K  L þ N,

ð8:52Þ

where  is a convolution operator and N is unknown noise. In some applications where K is known, a simple image deconvolution method can be used to solve this problem for L from the blurred image B. However, when both L and K are unknown for a complex motion, this is an ill-posed problem. In this case, iterative methods are usually used to determine both L and K. Cho and Lee (2009) proposed a fast motion image deblurring method that had alternating optimization of L and K in an iterative process. In the latent image estimation and kernel estimation steps of the process, the optimization problems are expressed as, respectively,

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8 Image and Data Analysis Techniques

L0 ¼ arg min fkB
K  Lk þ ρL ðLÞg,

ð8:53Þ

K 0 ¼ arg min fkB
K  Lk þ ρK ðK Þg,

ð8:54Þ

L

K

where ρL(L ) and ρK(K ) are the regularization terms. Given a blurred image B and an assumed Gaussian kernel K, an initial estimate L0 of the latent image is obtained from Eq. (8.53) using a simple and fast deconvolution method with a Gaussian prior. Due to the characteristics of a Gaussian prior, L0 would contain smooth edges and noise in smooth regions. In the prediction step, a refined estimate L0 is obtained by restoring sharp edges and removing noise with efficient image filtering techniques. Then, L0 provides a good latent image needed for accurate kernel estimation in Eq. (8.54), and then an estimate K0 is used for Eq. (8.53) for further iterations. Juliano et al. (2012), Gregory et al. (2014b), and Pandey and Gregory (2018) used simple motion kernel models for deblurring of PSP images of rotating blades. A motion image deblurring algorithm was applied by Gregory et al. (2014b) to PSP data from a spinning disc operated at 269 Hz. Figure 8.23 shows wind-on images

Fig. 8.23 Gate 2 wind-on images of the tip corner of the painted blade edge spinning at 269 Hz: (a, b) original blurred images and (c, d) deblurred images. Images (b) and (d) have a truncated color bar to more clearly show exponential decay of the blur pattern. (From Gregory et al. 2014b)

8.10

Inverse Heat Transfer Methods

243

acquired from the open-ended gate 2 with a camera viewing from nearly directly overhead. The leading edge is at the bottom edge, with the PSP region moving downward and to the right. Figure 8.23a, b shows the effects of blurring on the blade edge and a registration marker, where extensive blurring is seen in the marker. Figure 8.23b, d shows the deblurred images. This deblurring technique was effective in recovering information at the blade edges when the amount of blurring is not too high.

8.10

Inverse Heat Transfer Methods

The analytical and numerical inverse transfer methods were developed to calculate heat flux distributions on a model using a time sequence of TSP images (Liu et al. 2010, 2018; Cai et al. 2011, 2018a, b). It is assumed that a model is in thermal equilibrium with the ambient conditions at t ¼ 0. In other words, the initial temperature of a model including both the insulating layer and base is assumed to be the ambient temperature Tin (the initial temperature) before a run. Under this condition, an analytical transient solution of the one-dimensional (1D) timedependent heat conduction equation for the surface heat flux has been obtained for a thin polymer (TSP or TSP/insulator) on a semi-infinite base and a finite base (Liu et al. 2010, 2018). For constant thermal properties of materials, the heat flux at the polymer surface on a semi-infinite base is given by a convolution-type solution, i.e.,
Z t k p 1
ε2 W ðt
τ, εÞ dθps ðτÞ pffiffiffiffiffiffiffiffiffiffi qs ðt Þ ¼ pffiffiffiffiffiffiffi dτ, πap dτ t
τ 0

ð8:55Þ

where θps(t) ¼ T(t, L )
Tin is the temperature change at the polymer surface from the ambient temperature, L is the polymer layer thickness, and 2 W ðt, εÞ ¼ pffiffiffi π

Z

1 0


 exp
ξ2 dξ
pffiffiffiffiffiffi : 1 þ ε2
2ε cos 2Lξ= ap t

ð8:56Þ

The parameter ε in Eq. (8.55) is defined as ε ¼ ð1
εÞ=ð1 þ εÞ , where ε ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi kp ρp cp =kb ρb cb , kp, cp, and ρp are the thermal conductivity, specific heat, and density of the polymer, respectively, kb, cb, and ρb are the thermal conductivity, specific heat, and density of the base material, respectively, and ap ¼ kp/cpρp is the thermal diffusivity of the polymer. For ε ¼ 0 , Eq. (8.55) recovers the classical solution for a semi-infinite base since W ðt, 0Þ ¼ 1. This means that the function W ðt, εÞ represents the effect of the polymer layer (or TSP itself) on the determination of heat flux, which depends on ε, ap, and L. The discrete form of Eq. (8.55) for actual calculation of heat flux is

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8 Image and Data Analysis Techniques


 n k p 1
ε2 X θps ðt i Þ
θps ðt i
1 Þ pffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qs ðt n Þ ffi pffiffiffiffiffiffiffi πap t n
t i þ t n
t i
1 i¼1    W ðt n
t i Þ þ W ðt n
t i
1 Þ :

ð8:57Þ

Equation (8.57) is considered as a generalization of the Cook-Felderman method (Cook and Felderman 1970) for a combination of a polymer layer and a semi-infinite base of any material. For ε ¼ 0, Eq. (8.57) recovers the Cook-Felderman method for a semi-infinite base since W ðt, 0Þ ¼ 1 . Equation (8.57) is easy to implement in applications. Further, for a polymer layer on a finite base, the function of W ðt, εÞ in Eq. (8.55) can be expressed as a generalized form by incorporating the effect of the finite thickness of the base into account (Liu et al. 2018). The inverse heat transfer methods have been applied to various cases in aerothermodynamic testing (Liu et al. 2018, 2019a, b, c; Liu and Risius 2019). The Cook-Felderman method was used to calculate the heat flux from a time sequence of TSP images under the assumption that a polymer layer (TSP plus basecoat) can be treated as a semi-infinite base in a short runtime (Ozawa et al. 2015; Laurence et al. 2019). However, a TSP layer on a finite base is considered as a two-layer structure rather than a semi-infinite base; the thermal properties of such a two-layer structure are not exactly known a priori. A practical solution is to model a combination of a polymer layer and a base as an equivalent semi-finite base where the effective thermal penetration parameter ηp ¼ ρpcpkp is determined by in situ calibration. Risius et al. (2017) proposed an in situ calibration method based on data obtained from a heat-flux sensor at a selected location. Further, the in situ calibration method was generalized by Liu and Risius (2019) based on the analytical inverse heat transfer solution for a finite base, and applied to TSP images obtained on a wedge in a high-enthalpy hypersonic wind tunnel. The thermal penetration parameter ηp was determined by in situ calibration using data obtained by a reliable heat flux sensor at a reference location. In TSP measurements, the analytical inverse heat transfer methods using constant thermal properties are reasonably accurate when a surface temperature change is smaller than 10 K in a short runtime. However, when a surface temperature change is sufficiently large in high-enthalpy hypersonic flows, the effect of temperaturedependent thermal properties of a polymer layer should be considered in heat flux calculation. To consider the temperature-dependent thermal properties of materials, numerical inverse heat transfer methods were developed by Cai et al. (2011, 2018a, b) for TSP measurements. A simple method was developed by Liu et al. (2019a) for correcting the effect of the temperature-dependent thermal diffusivity on TSP heat flux measurements. A relation between the heat flux obtained using the constant thermal diffusivity and the heat flux obtained using the temperaturedependent diffusivity was derived based on an analysis of the nonlinear heat conduction equation. The nondimensional correction factor was introduced and modeled as an approximate function of measured surface temperature for monotonically increasing heat flux histories typically occurring in short-duration hypersonic

8.10

Inverse Heat Transfer Methods

245

tunnels, which was determined in situ using known data at several selected locations. The corrected heat flux field was obtained by multiplying the correction factor field with the heat flux field obtained using the analytical inverse heat transfer method for constant thermal properties. The 1D inverse heat transfer method, Eq. (8.55), is able to give reasonable results when it is applied to a 3D model in tests in a short-duration wind tunnel, and the recovered heat flux at a point on a surface can be intuitively considered as a certain averaged value in a neighborhood of that point. Equation (8.55) ignores the lateral heat conduction effect on a 3D body that could be significant at certain locations where the spatial gradient of heat flux is large. This situation could occur near shockwave/boundary-layer interaction, boundary-layer transition, flow separation, and strong vortex/wall interaction. Further improvement should be made by correcting the lateral heat conduction effect. Based on an analogy between the 1D and 3D solutions of the heat conduction equation, a convolution-type integral equation with a Gaussian filter (kernel) was given as a model for correcting the lateral heat conduction effect (Liu et al. 2011). In this equation, a heat flux field obtained by using the 1D method is actually a Gaussian-filtered (spatially averaged) heat flux field in a 3D case. This physical meaning is clear and intuitive. This equation is mathematically equivalent to that in the classical image deconvolution problem or image restoration problem. Therefore, to extract the true heat flux field by solving this integral equation, the adaptive total variation regularization method can be used directly. A two-step method was proposed by Liu et al. (2011) to calculate heat flux fields from a time sequence of surface temperature images. The 1D inverse method is first used to calculate the heat flux one point by one point on a surface, and then an image deconvolution method is applied to heat flux images obtained using the 1D inverse method as a field approach to correct the lateral heat conduction effect.

Chapter 9

Applications of PSP

This chapter describes PSP measurements in various flows in a range of facilities. Both intensity-based and lifetime-based PSP measurements in high subsonic, transonic, and supersonic flows are first described since PSP is a more effective technique in these flows. Then, unsteady pressure measurements using fast PSPs (porous PSPs) are discussed, which reveal oscillating shock waves interacting with boundary layers in transonic flows and supersonic impinging jet resonant modes. PSP measurements on blunt bodies, rocket models, circular cone, and scramjet nozzle in high-enthalpy hypersonic and shock tunnels using fast PSPs reveal complex shock-wave/boundary-layer interactions, shock-body interactions, and boundary-layer separations. PSP results in low-speed flows where a change in air pressure is very small are obtained when the temperature effect of PSP is carefully compensated and noise-reduction techniques are applied. PSP measurements on rotating blades can be made using the single-shot two-gate lifetime method, as demonstrated in several examples here. Porous PSP is a unique technique for surface pressure measurements in low-pressure flows, and the examples include a low-density impinging jet and wings in the Mars wind tunnel. Other PSP applications include measurements in cryogenic wind tunnels, sonic impinging jets, flight testing, and acoustic resonance box.

9.1

Subsonic, Transonic, and Supersonic Wind Tunnels

PSP measurements are more feasible in high subsonic, transonic, and supersonic flows. Surface pressure measurements on various aerodynamic models with PSPs have been conducted in large production wind tunnels at the NASA Research Centers (Langley, Ames and Glenn), the Boeing Company, AEDC, and WrightPatterson Air Force Research Laboratory in the USA (McLachlan and Bell 1995; McLachlan et al. 1995; Bell et al. 2001; Crites 1993; Morris et al. 1993a; Morris and Donovan 1994; Crites and Benne 1995; Dowgwillo et al. 1996; Sellers 1998a, b, © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_9

247

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9 Applications of PSP

2000, 2009; Crafton et al. 2013, 2018; Woike et al. 2017). PSP has been extensively used in wind tunnels at TsAGI in Russia (Bykov et al. 1992, 1993, 1997; Troyanovsky et al. 1993; Mosharov et al. 1997), British Aerospace and DERA in the UK (Davies et al. 1995; Holmes 1998), DLR in Germany (Engler 1995; Engler and Klein 1997a, b; Engler et al. 1991, 1992, 2001a, b; Yorita et al. 2014), ONERA in France (Lyonnet et al. 1997), and JAXA in Japan (Asai 1999; Shimbo et al. 2000; Nakakita et al. 2006). Besides applications of PSP in external aerodynamic flows, PSP has been used to study supersonic internal flows with complex shock wave structures in turbomachinery (Cler et al. 1996; Lepicovsky 1998; Lepicovsky et al. 1997; Taghavi et al. 1999; Lepicovsky and Bencic 2002). This section describes typical intensity-based and lifetime-based PSP measurements in subsonic, transonic, and supersonic flows.

9.1.1

Intensity-Based Measurements

Engler et al. (2001b) and Klein et al. (2005) measured surface pressure fields and aerodynamic loads on an AerMacchi M-346 advanced trainer aircraft model at AoAs from
4 to 36 and the angles of sideslip from
13 to 13 over a Mach number range of 0.6–0.95. Experiments were conducted in the industrial wind tunnel with a 1.8 m  1.8 m test section at DNW-HST in Amsterdam, the Netherlands. The AerMacchi M-346 advanced trainer aircraft model had a 1.2-m length and a 1.0-m span. Figure 9.1 shows a surface grid and a painted model with exchangeable flaps, air brakes, rudders, and ailerons. Since a total of 19 configurations were tested, 20 additional model parts were painted besides the basic model. All the parts of the complex model were illuminated and captured by CCD cameras placed around it in order to measure the aerodynamic effects at high AoAs and angles of sideslip for maneuvers influenced by flaps, air brakes, rudders, and ailerons. To overcome the problems of shadows and inhomogeneous illumination for excitation, pyrene-based

Fig. 9.1 The AerMacchi M-346 advanced trainer aircraft model: (a) surface grid and (b) PSP-coated model. (From Engler et al. 2001b)

9.1 Subsonic, Transonic, and Supersonic Wind Tunnels

249

Fig. 9.2 PSP system including twin-CCD-camera units, fiber optics illuminators, computers for data/image acquisition. (From Engler et al. 2001b)

two-luminophore PSP was employed. Since this PSP had a weak temperature dependency, the error due to the temperature effect could be reduced. As shown in Fig. 9.2, at each of four observation directions, a UV light source is connected to four 20-m long optic fibers; thus, a total of 16 fiber optics heads connected with four UV light sources illuminated the whole model from all the four directions. Eight cooled 12-bit CCD cameras were used for image acquisition. At each observation direction, a twin-CCD-camera unit with different filters was used to acquire in parallel the pressure signal at 450–550 nm (blue) and the reference signal at 600–650 nm (red). Figure 9.2 shows twin-CCD-camera units and illuminator heads installed on the wall of the test section. The use of the twin-CCD-camera unit eliminated the need of a filter-shifting device which could not take account of the unsteadiness of the light sources. As PSP was integrated into a standard wind tunnel measurement system, accurate and rapid acquisition and transmission of data became an important issue to decrease the wind tunnel run time. An automatic trigger and data exchange system were used. After the acquisition of a set of “blue” and “red” images by the four twin-CCDcamera units (eight CCD cameras), a TTL ready signal from the PSP system was sent to the wind tunnel control/data system, and the flow parameters and model attitudes were adjusted and recorded for next run. After the above process was completed, a TTL trigger signal from the tunnel control/data system activated all the cameras and lights for new PSP measurements.

250 Fig. 9.3 The pressure coefficient (Cp) distributions along the lines on the upper surface on the model for the clean configuration at Mach 0.6 and the angle of attack of 14 . (From Engler et al. 2001b)

9 Applications of PSP Cp 0 0.

-1 -1.5 -2

Cp

600

700

800 x 900

700

800 x 900

700

800 x 900

0 0.

-1 1.5 -2

Fig. 9.4 The pressure coefficient (Cp) distributions along the lines on the upper surface on the model for the configuration with the positive and negative ailerons at Mach 0.6 and the angle of attack of 14 . (From Engler et al. 2001b)

600

Cp 0 0.5 -1 -1.5 -2

600

0 Cp -0.5 -1 -1.5 -2

600

700

800

x

900

Figures 9.3 and 9.4 show the distributions of the pressure coefficient Cp on the upper surface of the model for the clean configuration and the configuration with positive and negative ailerons at Mach 0.6 and AoA of 14 . It can be seen that the pressure distribution is significantly altered from one configuration to another. The pressure distributions along the lines on the wings indicate a symmetrical pressure field with respect to the model centerline for the clean wing configuration, in contrast to the asymmetric one for the configuration with the positive and negative ailerons. Figure 9.5 shows a typical pressure field mapped onto a surface grid of the model. From the 3D PSP data on the model surface, Engler et al. (2001b) calculated the

9.1 Subsonic, Transonic, and Supersonic Wind Tunnels

251

Fig. 9.5 Typical pressure distribution mapped onto a surface grid of the model. (From Engler et al. 2001b)

coefficients of the normal force, pitching moment, rolling moment, wing root torsion moment, outboard droop hinge moment, and horizontal tail normal force. The aerodynamic force and moment coefficients obtained from PSP were in agreement with balance measurements at Mach 0.95 on the configuration with the leading edge droop set to zero. Nakakita et al. (2006) described an intensity-based PSP system used in the JAXA Transonic Wind Tunnel (JTWT1). JTWT1 is a closed-circuit and continuous-flow wind tunnel with a 2 m  2 m test section. PSP consisted of PtTFPP as a probe molecule and poly(IBM-co-TFEM) as a polymer binder, which had a pressure sensitivity of 0.85%/kPa. TSP was Ru(phen) as a probe molecule in polyurethane as a gas impermeable polymer binder. Figure 9.6 shows the PSP measurement setup at JTWT1. There were three sets of CCD cameras and illumination units in the upper and side windows. The side measurement system consisted of both the left and right units. Because an aircraft model was painted using PSP and TSP symmetrically, the upper system measured both the PSP and TSP sides at the same time; however, the side system needed two sets of CCD cameras and illumination units to measure the PSP and TSP sides at the same time. The illumination light sources were 300-W Xenon lamps to excite PSP and TSP. The output light was transmitted to an illumination light head through a light guide used to handle the light transmission easily. The illumination light head was a lens system with which the PSP-painted model could be illuminated uniformly. CCD cameras were used to detect the luminescent intensity from PSP and TSP. To increase the SNR, slow-scan and cooled interline 14-bit CCD cameras with microlens (Hamamatsu, ORCA-II-ERW) were used, where the spatial resolution was 1344  1024 pixels. The camera had more than 50% quantum efficiency at PSP

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Fig. 9.6 Components of the JAXA practical PSP measurement system. (From Nakakita et al. 2006) Fig. 9.7 ONERA M5 model and pressure tap lines (Line-1 and Line-2), where PSP and TSP are coated on the port and starboard sides, respectively. (From Nakakita et al. 2006)

and TSP luminescence wavelengths. Optical filters (Asahi spectra) were installed in the front of the illumination light head (illumination filter) and CCD cameras (luminescent filter). The illumination filter had a transmission band of 400–550 nm, corresponding to the absorption wavelength of the probe molecules of PSP and TSP. The luminescent filter had a transmission band of 590–710 nm, corresponding to the luminescent wavelength of PSP and TSP. The ONERA M5 model was used as a standard model for PSP validation experiments at JTWT1, where the model had a wingspan of 0.982 m and a fuselage length of 1.058 m. Figure 9.7 shows the PSP/TSP-painted ONERA M5 model. Starboard and port sides were coated with PSP and TSP respectively; hence a correction for any temperature dependence of the PSP paint could be applied, given, of course, that the flow field was symmetrical. The layer thicknesses were 50–100 μm for both PSP and TSP. There were 133 pressure taps on the whole model, and pressure data were obtained with three Scanivalve pressure scanners.

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253

Fig. 9.8 PSP results on the ONERA M5 model (M ¼ 0.84, α ¼ 0.6 , q ¼ 31.1 kPa, Ps ¼ 62.9 kPa): (a) the pressure coefficient (Cp) distribution (left-hand side in upper figure, right-hand side in lower figure), (b) temperature distribution (left-hand side in upper figure, right-hand side in lower figure), (c, d) comparisons between PSP and pressure tap data at Line-1 and Line-2, respectively. (From Nakakita et al. 2006)

Figure 9.8 shows the example of the PSP results at Mach 0.84. The data for the upper surface and lower surface were acquired in different runs. Figure 9.8a shows the surface pressure distribution. On the wing, a complex flow field with a multiple shock wave system is observed. It is also recognized that the low-pressure region on the wing extends to the fuselage. The temperature distribution in Fig. 9.8b shows a variation over several degrees, which is too large to assume uniform temperature. Thus, the temperature compensation using TSP is important for practical wind tunnel tests. Figure 9.8c, d shows comparisons of PSP data with pressure tap data on line-1 and line-2 marked in Fig. 9.7. PSP results were obtained using a priori calibration and a hybrid method combining a priori and in situ calibrations. The PSP results given by the hybrid calibration method are in good agreement with pressure tap data on both the upper and lower surfaces. However, on the lower surface, the data given by a priori calibration method deviate from pressure tap data.

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Fig. 9.9 PSP luminescent lifetime decay and gated times of a CCD camera: (a) two-gate method and (b) three-gate method

9.1.2

Lifetime-Based Measurements

The multiple-gate method can be used for lifetime-based PSP measurements. As illustrated in Fig. 9.9a, after PSP is excited by pulsed light, two integrated luminescent intensities I1 and I2 are acquired by a gateable digital camera (CCD or CMOS) in the gate times Δt1 and Δt2 during PSP luminescence decay. By calibration, the intensity ratio I1/I2 can be expressed as a function of pressure and temperature. For a fixed temperature, pressure can be calculated from I1/I2. As illustrated in Fig. 9.9b, to obtain both pressure and temperature, three gated luminescent intensities I1, I2, and I3 are acquired in gate 1, gate 2, and gate 3 of a digital camera. Two gated intensity ratios I1/I2 and I1/I3 constitute two simultaneous independent equations of pressure and temperature. Therefore, pressure and temperature can be determined. A lifetimebased system was developed by Mitsuo et al. (2006a) to measure simultaneously pressure and temperature based on a dependency of the luminescent lifetime of PSP on both pressure and temperature. They showed that pressure and temperature fields could be reconstructed from three gated intensity images acquired with a CCD camera. The system was composed of a low-noise CCD camera and LED illuminators that evenly excite a PSP-painted model. The camera had an intensity resolution of 14 bit and a sensor size of 1334  1024 pixels. Either blue or UV LED illuminator was used as excitation light source at the emission peak of 460 or 395 nm, respectively. Lifetime-based PSP calibration is illustrated in Fig. 9.10a. A PSP coupon was set in a pressure- and temperature-controlled chamber. PSP was excited by LED illuminators, and the luminescence of PSP was detected by a CCD camera. The master trigger source to the camera and LED illuminator was a pulse generator. Figure 9.10b shows a lifetime imaging system set for PSP calibration. The calibration surfaces for I1/I2 and I1/I3 are shown in Fig. 9.11, which can be expressed as polynomial functions of pressure and temperature.

9.1 Subsonic, Transonic, and Supersonic Wind Tunnels

255

Fig. 9.10 Lifetime imaging system: (a) design of the system and (b) a multi-gated camera and LED illuminators. (From Mitsuo et al. 2006a)

Fig. 9.11 PSP calibration surfaces: (a) I1/I2 and (b) I1/I3. (From Mitsuo et al. 2006a)

To evaluate the performance of the lifetime-based system in wind tunnel testing, Mitsuo et al. (2006b) measured surface pressure and temperature fields on a 70 delta wing at Mach 0.55. The test was conducted in the 0.2 m  0.2 m Supersonic Wind Tunnel at JAXA. The delta wing model with the sharp leading edges was made of aluminum, which had a root chord of 100 mm. The top surface of the model was coated with a white basecoat and then PtTFPP-based PSP using an airbrush. The model was strut-mounted at the center of the test section at AoA of 20 . The PSP-painted delta wing was illuminated by UV-LED illuminators through an optical window. The PSP luminescence was detected by a gateable CCD camera. The emission filter for PSP was a band-pass filter (650  20 nm), which was mounted in the front of the camera lens. Figure 9.12 shows the gated PSP images I1, I2, and I3 acquired in three gate times of the CCD camera. The luminescent image I1 is considerably different from I2 and I3, which is insensitive to pressure and temperature. In contrast, complicated patterns associated with pressure and temperature are observed in the images I2 and I3. Pressure and temperature images were obtained from the ratio images I1/I2 and

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9 Applications of PSP

Fig. 9.12 Gated PSP luminescent lifetime images: (a) I1, (b) I2, and (c) I3. (From Mitsuo et al. 2006a)

Fig. 9.13 Multi-gated PSP lifetime measurements on the delta wing at M ¼ 0.55, Pt ¼ 100 kPa, and AoA ¼ 20 : (a) pressure and (b) temperature. (From Mitsuo et al. 2006a)

I1/I3 by using the two calibration surfaces in Fig. 9.11. Figure 9.13 shows surface pressure and temperature fields on the delta wing at Mach (M) 0.55 and a total pressure (Pt) of 60 kPa. The low-pressure regions induced by the leading-edge vortices can be seen in the pressure field. The model temperature measured by a thermocouple was approximately equal to that given by the lifetime imaging system. Mébarki and Benmeddour (2016) conducted PSP measurements on a moving store in the NRC 1.5 m pressurized blowdown wind tunnel in Ottawa, Canada. This tunnel can run for 10–100 s depending on the flow conditions. The typical mode of operation of the tunnel is the continuous pitch sweep mode, where the model AoA (pitch) or roll angle is varied while the wind tunnel flow parameters are held constant. The pitch sweep mode of operation permits the collection of more data points in a single run. In this case, PSP measurement should be performed on a continuously moving model, if the exposure time can be reduced to less than a few milliseconds. Therefore, the lifetime-based method is suitable for this type of application. The model was a 40%-scale model of a GBU-38 store mounted on a straight sting. The fins had the maximum thickness of 2.3 mm near the center body, and slanted leading edges and sides. As shown in Fig. 9.14, only the upper surfaces of the store horizontal fins were painted with PSP. Six markers were placed on the top

9.1 Subsonic, Transonic, and Supersonic Wind Tunnels

257

Fig. 9.14 Store fins coated with PSP and markers used for image resection. (From Mébarki and Benmeddour 2016)

surfaces of the fins for image resection, which were 0.1 mm thick retroreflective circular tapes. The store center body was not painted with PSP to eliminate the selfillumination between the normal surfaces. The commercial Unifib PSP (ISSI, Inc.) was used, containing porphyrin as a probe luminophore in a fluorinated polymer (FIB) mixed with scattering agents. It emits at 650 nm and its luminescence lifetime varies from 80 μs in vacuum to about 10 μs at atmospheric pressure. The Zyla 5.5 camera equipped with a 5.5 Megapixel scientific CMOS sensor was selected for this experiment because of its high resolution and frame rate, and low read-out noise and short inter-framing times. The camera and 3 UV-LED lamps equipped with a 40 -angle UV lens were mounted in the plenum of the test section, viewing the model through 3-in. diameter ceiling windows. To increase the amount of light collected by the camera, 3  3 pixel binning was applied, reducing the resolution of the camera to 850  720 pixels. To separate the excitation light and the luminescent emission, the filter (Omega 415WB100) on the light source and the filter (Andover 630-FG-07) on the camera were used. For each excitation light pulse, two gated intensity images I1 and I2 were acquired in the rising and decaying stages of the luminescent response of PSP to a pulse excitation, respectively. The image ratio R ¼ I1/I2 formed a data point in a run. When the data point frequency was 24.5 Hz, there were 650 data points in a 26.5 s run. At the lowest pitch rate of 3 /s, this corresponded to a pitch interval of 0.12 between two data points. In the wind-off reference condition at the same temperature (Tref ¼ T ), the image ratio is denoted by Rref. For the Unifib PSP, the ratio of ratios R/Rref is a function of the normalized pressure p/pref, but it is independent of

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9 Applications of PSP

temperature. This implies that Rref and R have the same temperature dependency. Such an “ideal PSP” can be used to obtain more accurate pressure data by eliminating the temperature effect. The images R and Rref were mapped onto the model surface mesh in the 3D object space by the image resection, and pressure conversion and correction were carried out on the mesh. In addition, mapping PSP data onto the surface mesh is necessary for comparison with CFD data. Mébarki and Benmeddour (2016) investigated the effect of continuously sweeping through a model incidence range by comparing the PSP sweeping data with the pitch step data obtained at the same condition. When the sweeping motion was too fast, the PSP response time lagged, and the pressure field included information from the previous pitch angles particularly in the regions of high-pressure gradients near the leading edge of the fins. It was found that at a pitch rate of 3 /s, the pressure coefficient error caused by continuously sweeping was about 0.03, which was acceptable. Therefore, a comparison between PSP and CFD data was performed only using PSP data collected at a pitch rate of 3 /s. To improve the quality of PSP data, temporal averaging (averaging several data points together around a pitch angle of interest) was applied. Temporal averaged data over 8 images were used in comparison with the CFD data. Figure 9.15 shows the pressure coefficient (Cp) images obtained by PSP and CFD for three AoAs at Mach 1, where in situ calibration is applied by using the CFD data at one location. The Cp distributions are extracted at the spanwise locations of 48 mm marked as white straight lines in the center-right panel of Fig. 9.15. Comparisons between PSP and CFD data are presented in Fig. 9.16 at AoA of 10 for different Mach numbers. A lifetime-based system developed by Arnold Engineering Development Center (AEDC) represents the state-of-the-art of PSP measurements in a large production wind tunnel (Sellers 2009). Figure 9.17 is a layout of the AEDC PSP system. PSP is excited by 40 LED units (10 LED units per wall), which illuminate at a wavelength of 464 nm. The LED units were pulsed on for 30 μs every 600 μs, for a 5% duty cycle, using a Berkley Nucleonics Corporation 555 digital delay generator. The luminescence was measured with eight 12-bit CoolSNAP K4 interline transfer cameras with a spatial resolution of 2048  2048 pixels. The interline transfer technology provides accurate and repeatable exposure times necessary for the repeated experimental conditions required for the lifetime technique. The cameras also have a unique capability to accumulate the charge from thousands of individual pulses on the CCD before readout. The camera gating is controlled with the delay generator to maintain the temporal relationship between the LED pulse and camera exposure. The luminescent light emitted by the paint is passed to the camera detector through a narrow-band-pass filter centered at 650 nm with a full width at half maximum of 40 nm. Two gated images are acquired for each LED pulse. An intensity ratio between the gate 1 and gate 2 is a function of pressure. The PSP data acquisition system set the delay generator for gate 1 to pulse the LEDs for 30 μs and acquire a 30-μs image during the LED pulse for a predetermined number of pulses. Once the image acquisition for gate 1 was complete, the delay generator was set for gate 2 to pulse the LEDs for 30 μs and acquire a 30-μs image 5 μs after the LED pulse ended. The number of pulses for each gate was set to provide the brightest

Fig. 9.15 Comparisons of the pressure coefficient fields between CFD prediction and PSP measurements at Mach 1. (From Mébarki and Benmeddour 2016)

Fig. 9.16 Comparisons of the pressure coefficient distributions between CFD prediction and PSP measurements for AoA ¼ 10 at the spanwise locations Y ¼ 48 mm (upper white line on fin 1 in the center-right panel of Fig. 9.15) and Y ¼
48 mm (lower white line on fin 2 in the center-right panel of Fig. 9.15). Line at X ¼ 938 mm on fin 1 indicates where the offset was computed in in situ calibration. (From Mébarki and Benmeddour 2016)

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9 Applications of PSP

Fig. 9.17 AEDC 8-camera PSP system: lifetime cameras and LED lights. (From Marvin Sellers of Arnold Engineering Development Center (AEDC)) Fig. 9.18 The PSP-coated FAVOR model in AEDC Propulsion Wind Tunnel 16T. (From Marvin Sellers of Arnold Engineering Development Center (AEDC))

image possible, without saturation, for each test condition. The images for all eight cameras were acquired simultaneously. The Facility Aerodynamics Validation and Operations Research (FAVOR) model was tested as a standard check model in the AEDC Propulsion Wind Tunnel (PWT) 16T that is a closed-loop, continuous-flow, variable-density tunnel capable of being operated at Mach numbers from 0.06 to 1.60. The test article was a 5% scale model of the F-111 with new wings having a NACA 64-210 profile, a fixed sweep angle of 35 , and a span of 1.22 m. Figure 9.18 shows the PSP-coated FAVOR model in AEDC PWT 16T. The PSP contained PtTFPP as a probe luminophore and the FIB7 polymer as a binder. Figure 9.19 shows the pressure coefficient distributions on the

9.2 Unsteady Measurements

261

Fig. 9.19 The pressure coefficient distributions on the upper and lower surfaces of the FAVOR model at an angle of attack of 10 and Mach 0.8. (From Marvin Sellers of Arnold Engineering Development Center (AEDC))

upper and lower surfaces of the FAVOR model at AoA of 10 and Mach 0.8. Good agreements are achieved between the PSP data and pressure tap data at different Mach numbers and AoAs. In addition, the integrated forces and moments calculated from PSP data are consistent with force balance measurements.

9.2 9.2.1

Unsteady Measurements Transonic Wing Buffeting

Sugioka et al. (2018a) studied transonic buffeting phenomena on a swept wing using fast PSP. PSP measurements were conducted on an 80%-scaled NASA Common Research Model (CRM) in the JAXA Transonic Wind Tunnel (JTWT1) at a Mach number of M ¼ 0.85 and a chord Reynolds number of Re ¼ 1.54  106. The angle of attack was varied between 2.82 and 6.52 . In the experiment, a test section equipped with perforated walls and optical windows was used. Figure 9.20a shows the CRM installed in the JTWT1 test section. The mean aerodynamic chord was 0.15 m, and the full span length was 1.27 m. The CRM was composed primarily of stainless steel. Fast PC-PSP with low surface roughness was made for the experiment. For every 0.5 g of ester polymer, 9.5 g of titanium-oxide particles (rutile type), 0.04 g of dispersant, and 30 mL of toluene were mixed, and the mixture was stirred for 1 day. The composite was applied to the model using a spray gun, and the binder surface

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9 Applications of PSP

Fig. 9.20 (a) The 80%-scaled CRM installed in the test section and (b) schematic of the PSP system in JTWT1. (From Sugioka et al. 2018a)

was then polished to reduce surface roughness. PtTFPP dissolved in toluene was sprayed and adsorbed onto the pre-coated binder surface. Figure 9.20b illustrates the PSP measurement system in JTWT1, which consists of two UV-LED illuminators as excitation light sources and a high-speed camera (Phantom V1211) as a detector with a 35-mm lens and a band-pass optical filter (590–710 nm). The camera frame rate was set to 2000 fps. The time-averaged pressure, local Mach number, and RMS pressure fluctuations were evaluated to understand the general flow fields on the CRM wing. Figure 9.21 shows these quantities measured at AoA (α) ¼ 2.82 (under cruise condition), 4.68 , 6.00 , and 6.52 (under off-design conditions). Figure 9.22 shows profiles of the local Mach number along η ¼ 0.4 and 0.6, where η is the spanwise coordinate normalized by the half-span length. Figure 9.21 clearly shows the details of the timeaveraged pressure distributions and areas with large pressure fluctuations under both cruise and off-design conditions. The shock wave at about η ¼ 0.4 moves upstream, and the pressure fluctuation amplitude at the shock foot increases as AoA increases. At α ¼ 2.82 , the flow and shock wave appear stable. In addition, the RMS fluctuation of the pressure coefficient, Cprms, is small over the entire wing. At α ¼ 4.68 , the shock begins oscillating on the main wing. Under this condition, a narrow band with a high Cprms appears outboard wing (η > 0.4). The value of Cprms in the narrow band is approximately 0.1. The band corresponds to the shock foot location, indicating that the shock in the mid-span region starts to oscillate. At α ¼ 6.00 , the high-Cprms band appears thicker compared to that at α ¼ 4.68 . At α ¼ 6.52 , the value of Cprms on the wing is much larger than that at α ¼ 6.00 particularly at η ¼ 0.5–0.7, indicating separation induced by shock oscillation. The distributions of the pressure coefficient fluctuation at sequential times for α ¼ 6.52 are shown in Fig. 9.23 as a typical case, where an interval between the images is 0.5 ms. Buffet cells are observed at the outboard wing at 0 and 0.5 ms for α ¼ 6.52 . A large upstream shock movement occurs at the inboard wing (t ¼ 0–1.5 ms) and propagates slowly in the outboard direction (t ¼ 2.0–4.0 ms).

9.2 Unsteady Measurements

263

Fig. 9.21 Time-averaged pressure coefficient (Cp), local Mach number (Mloc), and RMS pressure coefficient fluctuation (Cprms) distributions on the CRM wing obtained using PSP at M ¼ 0.85 and Re ¼ 1.54  106. (From Sugioka et al. 2018a)

Fig. 9.22 Local Mach number profiles calculated from surface pressure at two spanwise locations: (a) η ¼ 0.40 and (b) η ¼ 0.60 (M ¼ 0.85, Re ¼ 1.54  106). (From Sugioka et al. 2018a)

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9 Applications of PSP

Fig. 9.23 Time-series of the pressure coefficient fluctuation distributions obtained using PSP at α ¼ 6.52 (M ¼ 0.85, Re ¼ 1.54  106). (From Sugioka et al. 2018a)

The spectral analysis results are obtained from time-resolved PSP measurements. The Strouhal number (St) is used to characterize the pressure fluctuation frequency, where the representative length of St is the mean chord length of 0.15 m. The characteristic frequencies are identified from the power spectral density (PSD) profiles and coherence spectra. Figure 9.24 shows the PSD profiles on the lines of η ¼ 0.3, 0.4, and 0.6 for α ¼ 6.52 . It is indicated that the shock wave oscillates with a large amplitude at low frequency (St < 0.1). This low-frequency component corresponds to the intermittent shock oscillation observed in the time-series pressure distribution (see Fig. 9.23). There are two types of shock oscillation, which have different frequencies and origins. The first is a pressure perturbation with the bump Strouhal number of St ~ 0.31, which originates at the mid-span wing (η > 0.4). The second is shock oscillation with the Strouhal number of St ~ 0.09, which is generated at the inboard wing (η < 0.4). Figure 9.25 shows the coherence and phase-shift maps for the pressure fluctuations at the bump Strouhal number (St ¼ 0.31, f ¼ 582 Hz). The coherence maps in Fig. 9.25 show that there is a high level of coherence along the shock foot and near the trailing edge at η ¼ 0.6, and the pressure perturbation at St ¼ 0.31 is propagated in the direction from inboard to outboard. It is found that the component with the bump Strouhal number also exists at higher AoAs. Note that for α ¼ 6.52 , the dominant component at the bump Strouhal number does not appear in the PSD profiles. It is noted that a similar PC-PSP was used in unsteady surface pressure measurements in fin-shock-wave/boundary-layer interaction (Mears et al. 2020).

9.2 Unsteady Measurements

265

Fig. 9.24 Power spectral density (PSD) profiles at α ¼ 6.52 in the chordwise direction along lines at (a) η ¼ 0.30, (b) η ¼ 0.40, and (c) η ¼ 0.60 (M ¼ 0.85, Re ¼ 1.54  106). (From Sugioka et al. 2018a)

9.2.2

Unsteady Pressure on Rocket Fairing Model

Nakakita et al. (2012) conducted unsteady PSP measurements on a rocket faring model at Mach 0.7–0.85 and AoAs from
2 to +5 in the JAXA Transonic Wind Tunnel (JTWT1). Figure 9.26a shows the rocket faring model installed in the test section of JTWT1. The cylindrical fuselage diameter of the model was 0.213 m and the total model length was 1.125 m. The model was made of A5052 aluminum alloy. The front part of the model was coated with AA-PSP, as shown in the yellow part in Fig. 9.26a. There were 55 pressure taps to measure steady pressure distribution and 22 kulite pressure transducers to measure unsteady pressure; they were installed at the opposite side of the model. On the top of the cone part of the model, the 142-μmhigh roughness strip was set at x ¼ 78.8 mm to make the boundary layer turbulent. Luminophore in AA-PSP used in the experiment was [Ru(dpp)3]Cl2, which was directly absorbed on the porous AA layer of the model. Figure 9.26b shows a schematic of the unsteady PSP system in JTWT1. A highspeed camera and a laser illumination device were installed at the ceiling of JTWT1. The high-power laser main body was located outside of the wind tunnel chamber, and laser light was guided to the test section ceiling through an optical fiber with

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Fig. 9.25 Coherence (upper) and phase shift (lower) at St ¼ 0.31 at α ¼ 6.52 . The reference point is a point (pixel) with the maximum of Cprms value along a line at η ¼ 0.6 (M ¼ 0.85, Re ¼ 1.54  106). (From Sugioka et al. 2018a)

Fig. 9.26 (a) AA-PSP-coated rocket fairing model and circular laser illumination area on the top and (b) PSP system. (From Nakakita et al. 2012)

15-m length and 0.8-mm core diameter. An illumination collimator was installed at the end of the optical fiber. Laser light illuminated the AA-PSP-coated model through a 10 cm square optical window at the ceiling of the test section. The high-

9.2 Unsteady Measurements

267

Fig. 9.27 Unsteady PSP data in the area around the shoulder between the cone and cylindrical part of the model. (From Nakakita et al. 2012)

Fig. 9.28 Time-averaged pressure coefficient distributions in comparison with kulite pressure transducer data at Mach 0.8: (a) AoA ¼ 0 and (b) AoA ¼ 4 . (From Nakakita et al. 2012)

speed camera was the Phantom V7.3 CMOS high-speed 14-bit camera. The spatial resolution was 400  400 pixels at a frame rate of 5 kfps with a 0.198 ms exposure time. The 7 W high-power blue laser diode (450–455 nm) was used as an illumination light source for AA-PSP. A circular laser illumination area with a diameter of about 150 mm was selected around a junction between the cone and cylindrical section, which is shown as a white circle in Fig. 9.26a. Unsteady PSP measurements were made only in the laser-illuminated area by the camera, as shown in Fig. 9.27. The time-averaged pressure distribution was produced by averaging unsteady PSP images and applying in situ calibration. Figure 9.28 shows the time-averaged pressure coefficient distributions in the centerline at Mach 0.8 and AoAs of 0 and 4 in comparison with the kulite pressure transducer data. Figure 9.29 shows the surface pressure field with the sketched flow

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Fig. 9.29 Unsteady PSP data and the sketched flow structures at Mach 0.8 and AoA ¼ 0 . (From Nakakita et al. 2012)

structures revealed by Schlieren visualization at Mach 0.8 and AoA of 0 . The flow on the cone is subsonic and it is accelerated at the juncture between the cone and the cylindrical part, which is called the shoulder. The flow downstream of the shoulder becomes supersonic due to the expansion fan and the pressure was low there. In the case of Mach 0.8, shock wave and lambda shock wave, which are related to separation induced by shock-wave/boundary-layer interaction, are observed in a small supersonic region. Pressure in the separation region gradually increases. There is flow re-attachment downstream of the cylinder part, which was outside of the unsteady PSP measurement area. Fast-Fourier Transformation (FFT) was applied to time-series unsteady PSP results to investigate spectral structures of the unsteady phenomena around the rocket faring model. Figure 9.30 shows the fields of the power spectrum density (PSD) of the pressure coefficient at three frequency bands and PSD distributions at three locations near the kulite pressure transducers at Mach 0.8 and AoA of 4 . The PSD distributions obtained from unsteady PSP data are in good agreement with those obtained from the kulite pressure transducers.

9.2.3

Oscillating Shock Wave in Transonic Flow

Merienne et al. (2015) used fast-PSP to study the interaction between an oscillating shock wave and a separated boundary layer in a transonic channel flow. Experiments were conducted in the S8Ch wind tunnel of the ONERA Meudon Center on a setup made of a rectilinear upper wall and a lower wall equipped with a contour profile (bump), as shown in Fig. 9.31. This facility is a continuous transonic wind tunnel having a test section with a height of 100 mm and a span of 120 mm. The shape of the bump was designed to induce strong interaction between a boundary layer and a

9.2 Unsteady Measurements

269

Fig. 9.30 Fields of PSD of the pressure coefficient at three frequencies (left panel), and PSD distributions compared with the kulite data at three locations (right panel) at Mach 0.8 and AoA ¼ 4 . (From Nakakita et al. 2012)

shock on the rear part of the bump. The stagnation conditions were ambient pressure and temperature. The unit Reynolds number was about 1.4  107/m and the nominal Mach number was 1.45. Nearly sinusoidal pressure perturbations were introduced at the downstream end of the channel by a periodic variation of the second throat section using a rotating elliptical shaft. This system caused forced oscillations of the shock wave at a known adjustable frequency. The shaft rotation frequency was set at 15 Hz, and the shock oscillation was induced at a frequency of 30 Hz. An Al-Mg alloy insert (including part of the bump) with a length of 160 mm and a width of 120 mm was designed and manufactured. This insert was anodized. Luminophore, [Ru(dpp)3]Cl2, was adsorbed at the AA surface by a dipping process in a solution containing the dye. The PSP measurement system used a continuous light source filtered in the UV range. Images were acquired using a 12-bit high-speed

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Fig. 9.31 Schematic of the wind-tunnel test section. (From Merienne et al. 2015)

Fig. 9.32 Experimental setup in the wind-tunnel test section. (From Merienne et al. 2015)

camera (Phantom V7.1) with a spatial resolution of 800  600 pixels. A high-pass filter (>600 nm) was placed in the front of the camera lens. The setup in the wind tunnel is shown in Fig. 9.32. Two optical fibers located on the test section roof allowed illumination of AA-PSP. The camera was placed outside the wind tunnel in a top view position. The physical spatial resolution achieved in these conditions of the field of view was 0.2 mm for a pixel. In the test, the acquisition rate was set at

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Fig. 9.33 Time-averaged (left panel) and RMS (right panel) PSP images without shock oscillation induced by a rotating elliptical shaft. (From Merienne et al. 2015)

Fig. 9.34 Time-averaged (left panel) and RMS (right panel) PSP images with shock oscillation induced by a rotating elliptical shaft. (From Merienne et al. 2015)

300 Hz to have a maximum of intensity on the images according to the shock oscillation frequency (30 Hz) with an exposure time of 2 ms. Figure 9.33 shows the time-averaged surface pressure field and RMS pressure fluctuation field when the shaft is locked and the shock is steady. When the shaft is rotating, as shown in Fig. 9.34, the shock footprint on the averaged image is enlarged so that the shock-wave oscillation area is clearly visible on the corresponding RMS pressure fluctuation field. The power spectral densities (PSDs) were computed on signals provided by the kulite sensors and data extracted on PSP images. Results at several locations are presented in Fig. 9.35. The PSDs obtained from PSP and kulite sensors are in reasonable agreement.

9.2.4

Impinging Jet Resonant Modes

Davis et al. (2015) measured supersonic impinging jet resonant modes using fast PSP. Measurements were performed on a high-speed impinging jet facility with a nearly ideally expanded Mach 1.5 axisymmetric converging-diverging nozzle with a throat diameter of 25.4 mm. Figure 9.36 shows a schematic of the impinging jet setup and PSP system. The nozzle exit was mounted flush with an acrylic lift plate

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Fig. 9.35 Comparisons of PSDs between kulite sensors and PSP at the locations indicated in the PSP image. (From Merienne et al. 2015)

with a diameter of 15Dj, where Dj is the nozzle exit diameter. The acrylic lift plate allows a camera and light source to be mounted directly behind to image the impingement region. An aluminum insert of a diameter of 5.85Dj was used as the impingement surface and was flush mounted with two unsteady kulite pressure transducers at the radial locations r/Dj ¼ 0 and 1. Tests were conducted over a range of impingement heights (h/Dj), particularly for two critical heights of h/Dj ¼ 4 and 4.5 at which the helical and axisymmetrical resonant modes occurred, respectively. The aluminum insert on the impingement surface was painted with a porous fast PC-PSP (a commercial formulation). Both the binder and luminophore layers of the sprayable formulation were hand-sprayed using an air spray gun. PSP was illuminated using a high-power pulsed LED light source emitting at 400 nm. The paint was imaged using a 14-bit cooled CCD camera with a spatial resolution of 1600  1200 pixels. A long-pass (>600 nm) optical filter was attached to the camera

9.2 Unsteady Measurements

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Fig. 9.36 Experimental setup for PSP measurements in the impinging jet. The surface-mounted kulite signal is band-passed about the impingement tone and fed to a delay generator to generate trigger signals for the LED light source and CCD camera. The LED light source and camera are mounted behind the acrylic lift plate on opposing sides. (From Davis et al. 2015)

lens to eliminate light from the LEDs. Due to the presence of the nozzle and stagnation chamber, the camera viewed the impingement surface obliquely. To focus the entire surface, a Scheimpflug mount was attached to the camera. The processed images were then de-warped using a dot pattern calibration plate. The images obtained were phase-locked using the unsteady pressure transducer at r/ Dj ¼ 1 on the impingement surface. The raw signal from the pressure transducer was band-pass-filtered using a high-pass/low-pass filter. The band-passed signal was used as an input to a digital delay generator to generate a trigger signal for the LED light source. The light source is able to pulse every cycle. The time-averaged pressure coefficient field obtained from PSP measurements is presented in Fig. 9.37a, where the computed intensity ratio was calibrated using the average pressure from the two absolute kulite transducers. Also shown in Fig. 9.37b is a pressure profile extracted along a radial line marked in Fig. 9.37a compared with independent conventional static pressure measurements on the impingement surface. In the region of high pressure at the jet stagnation point, the measured pressure recovers about 85% of the jet total pressure. The average pressure then drops rapidly from the stagnation point to recover to atmospheric at r/Dj  1. In addition to the time-averaged pressure field, the pressure fluctuation fields exhibited very interesting resonant modes. The symmetric mode was observed at a nozzle to plate spacing of h/Dj ¼ 4.5. The power spectral density obtained from the unsteady pressure transducer located on the impingement surface at r/Dj ¼ 1 indicated that there was a single dominant peak at f ¼ 6.3 kHz. The peak in the surface pressure was indicative of strong, coherent periodic structures, providing a clean band-passed signal to obtain phase-locked results. Figure 9.38 shows the phaselocked pressure fluctuation fields on the impingement plate for phases of ϕ ¼ 0 and ϕ ¼ 180 . To correlate these fields obtained from PSP with the jet flow structures,

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Fig. 9.37 Time-averaged pressure coefficient field on the impingement surface: (a) PSP results, and (b) extracted pressure profile compared with static pressure sensor measurements. (From Davis et al. 2015)

Fig. 9.38 Phase-averaged results at h/Dj ¼ 4.5 and f ¼ 6.3 kHz: (a) Schlieren at ϕ ¼ 0 , (b) Schlieren at ϕ ¼ 180 , (c) PSP at ϕ ¼ 0 , and (d) PSP at ϕ ¼ 180 , linking the flow field with surface pressure for the axisymmetric mode. In (c) and (d), the red and blue contours represent regions of higher and lower intensities, respectively. (From Davis et al. 2015)

9.2 Unsteady Measurements

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phase-averaged Schlieren images at the same phases are shown directly above. In Fig. 9.38, concentric rings in the PSP-derived pressure fields are associated with the impingement of the vortical structures in the jet column identified in the companion Schlieren images. The PSP images for phases of ϕ ¼ 0 and ϕ ¼ 180 are out of phase. This unsteady pressure pattern is a result of the impingement and the outward radial propagation of the periodic large-scale structures associated with the impingement tone. The pressure fluctuations persist for several jet diameters away from the stagnation point, indicating that the structures remain coherent in the wall jet. These features are not revealed in the time-averaged pressure fields. In another case, for a nozzle to plate spacing of h/Dj ¼ 4, especially complex flow structures were observed. The power spectral density for an unsteady pressure transducer located at r/Dj ¼ 1 on the impingement surface showed the existence of the dominant peaks at f1 ¼ 7.1 kHz and f2 ¼ 4.3 kHz. The spectral features were sensitive to some factors depending on the lift plate size and somewhat arbitrary parameters. Results for f1 ¼ 7.1 kHz are first discussed. Figure 9.39 shows the phaseaveraged PSP and corresponding Schlieren images for two phases of ϕ ¼ 0 and

Fig. 9.39 Phase-averaged results at h/Dj ¼ 4.0 and f ¼ 7.1 kHz: (a) Schlieren at ϕ ¼ 0 , (b) Schlieren at ϕ ¼ 180 , (c) PSP at ϕ ¼ 0 , and (d) PSP at ϕ ¼ 180 , linking the flow field with surface pressure for the axisymmetric mode. (From Davis et al. 2015)

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ϕ ¼ 180 for f1 ¼ 7.1 kHz. The phase-averaged Schlieren images indicate that the mode clearly appears to be dominantly axisymmetric. The phase-averaged PSP results at these phases show the visible concentric rings that were used to identify the axisymmetric mode. The intensity distribution has large deviations from the ideal axisymmetric mode. This could be due to the interaction of the axisymmetrical mode at f1 ¼ 7.1 kHz with the helical mode at f2 ¼ 4.3 kHz. For f2 ¼ 4.3 kHz, as shown in Fig. 9.40, the phase-averaged Schlieren and PSP images exhibit the helical mode features. The annular rings associated with the vortical structures in the shear layer are no longer visible. Rather, large radial displacement resulting in a sinuous jet column structure is observed. Images at intermediate phases reveal that this is indeed a helical mode. The differences between the axisymmetric modes are even more apparent in the phase-averaged PSP images in Fig. 9.40. The opposing regions of higher and lower intensity rotate with increasing phase. The alternating regions of pressure on the impingement surface are associated with the large-scale radial displacement of the jet column due to the spiral motion of the vortical structures observed in the Schlieren images.

Fig. 9.40 Phase-averaged results at h/Dj ¼ 4.0 and f ¼ 4.3 kHz: (a) Schlieren at ϕ ¼ 0 , (b) Schlieren at ϕ ¼ 180 , (c) PSP at ϕ ¼ 0 , and (d) PSP at ϕ ¼ 180 , linking the flow field with surface pressure for the axisymmetric mode. (From Davis et al. 2015)

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Fig. 9.41 Helical mode shape obtained from PSP at h/Dj ¼ 4 and f ¼ 5.8 kHz. (From Davis et al. 2015)

To demonstrate a cleaner helical mode, an additional case for h/Dj ¼ 4 was considered, where a single tone at f ¼ 5.8 kHz was observed in the spectra, which was attributed to random initial conditions that set this particular instability mode. The PSP results for an arbitrary phase at this frequency are shown in Fig. 9.41, revealing clearly a helical mode at this condition.

9.3

Hypersonic and Shock Wind Tunnels

PSP application in high-enthalpy hypersonic facilities is difficult since a large temperature increase on a model would cause the overwhelming temperature effect of PSP. In addition, since hypersonic wind tunnels are usually short-duration tunnels, fast PSP is required to achieve a short response time. PSP measurements in high-enthalpy hypersonic facilities are usually combined with surface temperature measurements with TSP or IR thermography for correcting the temperature effect of PSP. Efforts have been made on the application of PSP in hypersonic facilities. Kegelman et al. (1993) conducted PSP measurements on a 1/6-scale Pegasus launch vehicle model and a shock/boundary-layer interaction model in the NASA Langley Mach 6 High Reynolds Number Tunnel. Troyanovsky et al. (1993) carried out PSP visualization in shock/body interaction in a Mach 8 shock tube with a duration of 0.1 s. Borovoy et al. (1995) measured surface pressure distribution on a cylinder at Mach 6 in a shock wind tunnel with a duration of 40 ms. Jules et al. (1995) used PSP to study shock-wave/boundary-layer interaction over a flat-plate/conical-fin configuration at Mach 6. Hubner et al. (1997, 1999, 2000, 2001) measured surface pressure distributions on a wedge and an elliptic cone at Mach 7.5 in the Calspan hypersonic shock tunnel with a run-time of 7–8 ms. Buck (1994) discussed simultaneous temperature and pressure measurements on dyed ceramic models using luminescent materials in hypersonic wind tunnels. Nakakita et al. (2000) and Nakakita and Asai (2002) used AA-PSP to measure surface pressure fields on the expansion corner and

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compression corner models at Mach 10 in the JAXA Middle Scale Shock Tunnel with a duration of 30 ms. Watkins et al. (2009) conducted lifetime-based PSP and TSP measurements on the aftbody of a capsule vehicle in the NASA LaRC 31-in. Mach 10 wind-tunnel facility. Yang et al. (2012a, b, c) measured pressure fields using AA-PSP on a truncated cone model and a double ramp model at Mach 5. Peng et al. (2020) measured surface pressure and temperature fields in hypersonic shock/ body interaction between bodies in close proximity at Mach 6 using PSP and TSP.

9.3.1

Blunt Bodies

Watkins et al. (2009) used PSP and TSP to visualize and quantify surface interactions of reaction control system (RCS) jets on the aftbody of capsule reentry vehicle models: an Apollo-like configuration and an early Orion crew module configuration. Tests were performed in the NASA LaRC 31-in. Mach 10 wind-tunnel facility. The test section has a 0.75 m  0.45 m tempered-glass window for optical experimental techniques. A test model was protected from the flow until the operating condition was reached. Then, the model was injected to the tunnel centerline in approximately 0.55 s from the backside of the test section using a hydraulic injection system. Freestream Reynolds numbers obtained in this tunnel varied from 1.5  106 to 6.5  106/m, and the average Mach number was 9.58  0.2. The models were constructed with a steel fore-body heat shield and plastic/ ceramic nanocomposite aftbodies. Two distinct aftbody shapes were studied. The first shape mimicked an Apollo-era design that had no protrusions, whereas the second shape was based on an early NASA Orion design. Because the nanocomposite material used for the aftbodies is an insulating material, the model for PSP was coated with an additional thin layer of copper (~635 μm thick) to dissipate heat and provide a surface with near-uniform temperature. The models with a diameter of 127 mm were set at AoA of 24 . Each RCS jet had a 685-μm-diameter throat and an exit area to throat ratio of 22.5. The RCS jet chamber pressures were set at either 1725 or 3450 kPa before injection so that the jet was firing as the model was injected into the tunnel. PSP was PtTFPP as a probe luminophore in a copolymer FEM. Before application to the model, the surface was first cleaned and degreased using acetone. After drying, a white acrylic primer was applied to the surface as a basecoat to enhance the adhesion of the FEM top coat as well as to enhance scattering of the luminescent intensity back to the camera. TSP was Ru(bpy) in a commercially available clear urethane sealant. The two-gate lifetime method was used to collect all PSP data to minimize the slight inconsistencies in sting positioning as well as the significant differences in reference temperature and pressure. Illumination was provided using four LED arrays with a center wavelength of 400 nm, which were pulsed for 30 μs at a rate of 1667 Hz to acquire all data. Images were acquired using an interline transfer camera that was modified to allow “on chip” accumulation of multiple images. TSP data were acquired using a standard intensity-based method. In this mode, the LED

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arrays were run in a continuous fashion and images were acquired using a non-interline transfer camera. The reference image was acquired by injecting the model into the test section before tunnel operation. The model was then retracted into the model box, and the tunnel started. Once tunnel conditions stabilized, the model was reinjected and data collection began. Figure 9.42 shows PSP results from the Apollo configuration with the yaw RCS jet at several Reynolds numbers and jet blowing pressures. It is noted that the noise

Fig. 9.42 PSP results from the Apollo configuration at increasing Reynolds number (Re) and different RCS yaw jet blowing pressure (Pj). (From Watkins et al. 2009)

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Fig. 9.43 Representative heating images recovered using TSP on the Apollo configuration at Re ¼ 0.56  106 and yaw jet blowing pressure of 3450 kPa. The location of the thin crack is also depicted. (From Watkins et al. 2009)

in the data is mostly due to the photon shot noise as the pressure regime being investigated is approaching the practical limit of the PSP formulation. The effects of the jet on the surface pressure fields are clearly visible in all the cases, with the greatest effects occurring at the highest Reynolds number and the higher ratio between the jet pressure and the stagnation-point pressure (Pj/PT,2). These data show that there is an increase in surface pressure due to increasing the jet pressure, but this effect is very small. Figure 9.43 shows several normalized heat transfer coefficient maps calculated at various times during a run, where Ch is the convective heat transfer coefficient, ChFR is the convective heat transfer coefficient calculated using the method of Fay and Riddell, β is the substrate thermal product, and βREF is the approximate substrate thermal product. The effects of the adiabatic expansion of the gas as the actual jet exit are visualized as dark color, corresponding to low temperature. Yang et al. (2012a) measured surface pressure distributions on a truncated cone at Mach 5 using AA-PSP. PSP measurements were conducted in an intermediate blowdown hypersonic tunnel having a test time of 7.5 s. The tunnel mainly consists of a high-pressure vessel, vacuum tank, electric heater, axisymmetric nozzle, test section, and auxiliary systems such as pumping, pressure supply, and water cooling system. The Mach 5 contoured nozzle was used. The gas temperature was raised from ambient to 700 K to avoid condensation in the test section. Unit Reynolds number ranging from 4.5  106 to 16.5  106/m was obtained by varying the supply pressure and heater temperature. The tunnel test section was a free-jet type with an

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axisymmetric nozzle exit of 152 mm diameter. Two 195 mm diameter quartz windows were used on the sides of the wind tunnel test section to provide optical access for flow visualization. The test model was a 30 apex truncated cone followed by a cylinder portion. The cone was truncated by means of removing the tip from the nose (50% of the nose cone length, i.e., 29 mm). This model was fabricated from aluminum alloy 6061, which was anodized efficiently for the PSP application. The anodized model was dipped into the dye solution to obtain a uniform luminescent coating after posttreatment. The dye solution was [Ru (dpp)3]2+ diluted in dichloromethane solvent with a concentration of 0.3  10
3 mol/L. The truncated cone model was supported using a sting mounted on the arc, which allowed for the variation of the angles of incidence. A pair of LED panels with a peak wavelength of 470 nm was used as the excitation light source. Each LED panel comprised 13  10 LEDs. The LED panel was placed on each side of the test section to provide more uniform illumination on the surface of the model. A 12-bit LaVision Image Intense CCD camera was used for image acquisition. A combination of an orange long-pass filter (>550 nm) and an IR rejection filter (400 nm) was placed on the intensifier to detect the luminescence. Figure 9.49 shows a time sequence of surface pressure fields measured by using the two AA-PSP plates, where the time interval between two successive images is 10 μs. The upper images show the results of the PSP sample 1, and the lower images show those of the PSP sample 2. The pore depths of the samples 1 and 2 were 2.2 and 10.7 μm, respectively. The pore diameters of the samples 1 and 2 were 168 and 20 nm, respectively. The response times of the samples 1 and 2 were 0.36 and

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287

Fig. 9.48 Schematic of the experimental setup for shock tube tests. (From Numata et al. 2017)

Fig. 9.49 Time sequence of surface pressure fields induced by shock-wave interactions with a circular cylinder measured by using the AA-PSP sample 1 (upper half images) and the AA-PSP sample 2 (lower half images). (a) t ¼ 0 (μs), (b) t ¼ 10 (μs), (c) t ¼ 20 (μs), (d) t ¼ 30 (μs), (e) t ¼ 40 (μs), (f) t ¼ 50 (μs), and (g) t ¼ 60 (μs). (From Numata et al. 2017)

10.3 μs, respectively. In these images, the photon shot noise effect on the PSP images is visible due to low emission intensities. The luminescent intensity of the sample 1 is lower than that of the sample 2. However, it is noted that the images obtained on the sample 1 are much sharper than those on the sample 2, indicating

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that the sample 1 has a shorter response time than the sample 2. In these figures, a shock wave propagates from left to right. As shown in Fig. 9.49a–d, when the shock wave is passing around the cylinder, a curved high-pressure region is formed in the front of the circular cylinder. In Fig. 9.49c–f, the shock wave continues to propagate downstream and diffract behind the cylinder. Also, a low-pressure region was formed behind the cylinder. In addition, using the same ultrafast AA-PSP, Numata et al. (2015) and Numata and Ohtani (2018) measured sonic-boom-induced wall pressure fields generated by free-flight projectiles and pressure fields on free-flight projectiles in a ballistic range, respectively. Quinn and Kontis (2013) used TLC-PSP to measure transient pressure fields during a shock diffraction process. The change in pressure due to the shock wave and the induced vortex were captured.

9.3.4

Scramjet Nozzle

Hirschen et al. (2009) measured surface pressure fields on a single expansion ramp nozzle at a freestream Mach number of 7 in the hypersonic wind tunnel H2K at DLR in Cologne. This facility is a blowdown wind tunnel with test durations of up to 30 s, depending on the flow conditions. In the experiment, the total pressure was 2.1 MPa, the freestream pressure was 515 Pa, the total temperature was 650 K, and the freestream unit Reynolds number was 8  106. The model was a single expansion ramp nozzle with a total length of 200 mm and a total width of 80 mm, as shown in Fig. 9.50a, where fourteen pressure taps were located along the centerline of the ramp. Figure 9.50b shows the entire model installed in the wind tunnel (flow is from left to right). The model was held by a vertical strut mounted onto the side of the model and connected to it by an adapter to attain a certain separation between the strut and the model. This separation prevented the shock originating at the strut leading edge from perturbing the nozzle flow field. The angles of attack and yaw were set at 0 . The exhaust gas (nozzle internal flow) was supplied to the nozzle

Fig. 9.50 The single expansion ramp nozzle: (a) model in the wind tunnel and (b) side view of the nozzle model connected to a forebody. (From Hirschen et al. 2009)

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plenum by a pipe connected on the centerline on top of the settling chamber, through which the test gas was injected. Two-luminophore PSP developed by DLR was applied to the ramp surface, as shown in Fig. 9.50a. UV excitation on PSP was provided by a flash lamp operating at 20 Hz, and the luminescent emissions of the pressure-dependent and pressureindependent luminophores of the paint were at 450–550 and 600–650 nm, respectively. Two cooled PCO CCD cameras with a 12-bit intensity resolution and exposure times of 1.7 s were used for image acquisition. Hence, at 20 Hz, the luminescence arising from about 34 flash lamp pulses was cumulatively stored on the CCD chips, leading to an averaging of the pressure levels over this time interval. By using filters in the front of the cameras, one camera captured only the pressuresensitive signal, and the other only the reference pressure-insensitive signal. Calibration of the PSP system was carried out in situ in the wind tunnel on separate samples in a calibration chamber where both temperature and pressure were varied. The temperature on the model surface in the H2K wind tunnel was measured before, during, and after the experiment using an IR camera. An overview of the PSP setup is shown in Fig. 9.51. Figure 9.52a shows the normalized surface pressure distribution obtained by PSP for a freestream unit Reynolds number of Re ¼ 8  106 and a nozzle pressure ratio of 500. The positions of pressure taps on the left, center, and right lines and the characteristic lines of the expansion fan are also indicated in Fig. 9.52a. Here the nozzle pressure ratio is defined as a ratio between the nozzle total pressure and the freestream pressure. Figure 9.52b compares PSP data along the centerline with pressure tap data. Figure 9.53 shows the normalized surface pressure distributions on the surface of the single expansion ramp for nozzle pressure ratios of 250 and 375 at Re ¼ 8  106. It is found that the normalized surface pressure distributions (normalized to the nozzle total pressure) for different nozzle pressure ratios are almost invariant. Furthermore, the normalized surface pressure distributions are approximately the same at different freestream Reynolds numbers. Therefore, PSP Fig. 9.51 Schematic of the setup for PSP in the hypersonic wind tunnel H2K. (From Hirschen et al. 2009)

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Fig. 9.52 PSP measurement results at Mach 7 for a freestream Reynolds number of Re ¼ 8  106 and a nozzle pressure ratio of 500: (a) normalized surface pressure field and (b) normalized surface pressure distribution along the centerline. (From Hirschen et al. 2009)

Fig. 9.53 Normalized surface pressure fields at Mach 7 for a freestream Reynolds number of Re ¼ 8  106 and the nozzle pressure ratios of (a) 250 and (b) 375. (From Hirschen et al. 2009)

measurements reveal the interesting similarity of the surface pressure distributions on the expansion ramp surface in a parametric domain of the nozzle total pressures and freestream Reynolds numbers.

9.3.5

Hypersonic Boundary-Layer Separation

Running et al. (2019) conducted unsteady PSP measurements on a blunt 7 -halfangle circular cone at high AoAs at Mach 6 to identify lee-side crossflow-induced boundary-layer separation. Based on the previous studies, it was observed that a line of local minimum RMS pressure fluctuations corresponded to a line of separation on the lee side of a cone. Therefore, unsteady PSP measurement provides a feasible way to identify separation lines. Measurements were conducted in the pulsed arc-heated

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hypersonic wind tunnel (ACT-1) at the University of Notre Dame. ACT-1 is a conventional-noise tunnel that can produce hot or cold flow at Mach numbers of 4.5, 6, and 9. Data were collected at Mach 6 under cold (arc-off) conditions with a total temperature of 293 K and a total pressure of 500 kPa for a test time of about 0.5 s. A 7 -half-angle circular cone model consisted of an interchangeable nosetip (with 0.5- or 1.5-mm radius) and a frustum with a base radius of 25 mm. The entire length of the model with a 0.5- or 1.5-mm-radius nosetip was 199.5 or 191.4 mm. The nosetips were manufactured out of steel, while the frustum was made from 6061 aluminum for anodization purposes. The frustum with AA-PSP started at a distance of 75 mm from the tip of the cone, and ended at the base. AA-PSP was made to measure fluctuating surface pressures. Great care was taken to control the pore depth of the AA layer since it greatly affected the frequency response of the PSP. The final model had a pore depth of 8 μm and an average pore diameter of 24 nm. Bathophen ruthenium (RuDPP) was used as a probe luminophore. Two 10-W blue lasers (440–449 nm) were used as an illumination light source for the AA-PSP. The AA-PSP model was imaged with a high-speed 12-bit monochrome camera (Photron FAST CAM SA1.1) at 20,000 fps, which provided a sufficient SNR to detect small surface pressure changes on the model. Figure 9.54 shows a schematic of the experimental setup for PSP measurements in ACT-1. Figure 9.55 shows the time-averaged pressure field mapped to the x–y and x–ϕ coordinates for a test conducted at AoA of 9.8 with the 1.5-mm radius nosetip, where ϕ is the azimuthal angle along a windward ray. The azimuthal pressure gradient is favorable from the leading edges until ϕ ¼ 160 ; the pressure rises from there to the leeward ray. Figure 9.56 shows the corresponding RMS pressure fluctuation field, where the separation lines are indicated at the minimum value of RMS pressure fluctuation. The locations of the separation lines depended on AoA.

Fig. 9.54 Schematic of the experimental setup for the AA-PSP measurements in ACT-1. (From Running et al. 2019)

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Fig. 9.55 Time-averaged pressure field mapped to (a) the x–y and (b) x–ϕ coordinates for a test conducted at AoA of 9.8 with the 1.5-mm radius nosetip. (From Running et al. 2019)

9.4

Low-Speed Flows

PSP measurements in low-speed flows are challenging, where a change in pressure is very small. The major error sources, notably the temperature effect, image misalignment, and camera noise, must be minimized to obtain acceptable quantitative pressure results at low speeds. It is realized that PSP measurements at low speeds require accuracy of 0.1% over a pressure range of 80–100 kPa. This accuracy is difficult to achieve using a typical PSP with a temperature sensitivity of about 1%/ K because a temperature change of 0.1 K could produce an error as large as a required pressure resolution. Furthermore, the accuracy of PSP is further reduced

9.4 Low-Speed Flows

293

Fig. 9.56 RMS pressure fluctuation field mapped to (a) the x–y and (b) x–ϕ coordinates for a test conducted at AoA of 9.8 with the 1.5-mm radius nosetip, where the separation lines are indicated by lines. (From Running et al. 2019)

due to the camera noise and variation of the excitation intensity during a test run. The most common procedure to deal with the temperature effect is the application of in situ calibration to correlate the luminescent intensity to pressure tap data. In this case, the temperature-induced error is absorbed into an overall fitting error in in situ calibration. Even though some systematic errors are removed, it is impossible for this procedure alone to reduce the error to a level equivalent to that caused by a temperature change of 0.1 K on a nonuniform thermal surface in wind tunnel testing. After investigating low-speed PSP measurements in large production wind tunnels at NASA Ames, Bell et al. (1998) pointed out that the most significant errors were due to the temperature effect of PSP and model motion. Therefore, a solution is the combined use of in situ calibration with a temperature-insensitive PSP. An illumination field should be measured in order to correct both the spatial and temporal excitation variations on a surface. Furthermore, a large number of images

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should be averaged to reduce camera noise. Brown et al. (1997) and Brown (2000) made baseline PSP measurements on a NACA0012 airfoil at low speeds (less than 50 m/s). The experiments systematically identified the major error sources affecting PSP measurements at low speeds and developed the practical procedures for minimizing these errors. After considerable efforts were made to reduce the errors, reasonably good pressure results were obtained at speeds as low as 10 m/s. PSP measurements on delta wings, swept wings, and car models at low speeds were performed by Engler et al. (2001a) at ONERA and DLR to identify the major error sources and evaluate the performance of different PSPs. Measurements were made on a delta wing in the ONERA low-speed research wind tunnel and on swept wings in the Low-Speed-Wind-Tunnel (LSWT) of Daimler-Chrysler Aerospace at Bremen in German. Other researchers also measured pressure distributions on delta wings at low speeds (Morris 1995; Shimbo et al. 1997; Le Sant 2001a; Verhaagen et al. 1995). Engler et al. (2001a) and Aider et al. (2001) measured pressure distributions on car models at low speeds in the ENSMA T4P low-speed wind tunnel at Poitiers in France and in the Daimler Benz wind tunnel at Sindelfingen in Germany. In addition, Torgerson et al. (1996) conducted PSP experiments in a low-speed impinging jet to determine the limiting pressure difference that can be resolved using a laser-scanning system combining an optical chopper or acousticoptic modulator with a lock-in amplifier.

9.4.1

Ground Vehicle Models

Gouterman et al. (2004) used dual-luminophore PSP to measure surface pressure fields on a car model in low-speed flows. They formulated PtTFPL and MgTFPP in the FIB polymer and optimized their relative concentrations. PtTFPL was used as a pressure-sensitive component (PSP) emitting at about 740 nm and MgTFPP was used as a temperature-sensitive component (TSP) emitting at about 650 nm. The FIB polymer has a smaller temperature dependency than other commonly used polymers and most importantly has the same temperature dependency at vacuum and atmospheric pressure. These attributes allow for a simple correction of the temperature effect of PSP. This PSP was tested in the NRC IAR 2 m  3 m low-speed continuous atmospheric wind tunnel, equipped with a ground board used for automotive testing. A simplified automobile model was used, which had the general form of a notchback passenger car but without wheels. It was made of mahogany, with some aluminum parts. The model dimensions were: length ¼ 533.4 mm, width ¼ 203.2 mm, and height ¼ 101.6 mm. Figure 9.57 shows a photograph of the painted model in the test section. The excitation for the dual-luminophore PSP was provided by two air-cooled LED lamps with a band-pass color filter absorbing all wavelengths above 600 nm. The dual-luminophore emission was collected with two Peltier-cooled 12-bit Photometrics CCD cameras with a spatial resolution of 512  512 pixels. One camera was used to record the PSP emission with a color filter transmitting from 720 to

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Fig. 9.57 Photograph of the PSP-coated model in the wind tunnel. (From Gouterman et al. 2004)

1050 nm, while the second camera recorded the TSP emission using a band-pass filter centered on 650 nm. The two CCD cameras, located on the same tripod at a distance of approximately 2.5 m away from the model, acquired pressure and temperature images simultaneously. An average of 32 images was acquired for every run condition using an exposure time of 3 s per image to reduce the noise level. After every run, the wind-off images were acquired at the same conditions and later used as the reference. TSP measurements indicated that the model side appeared slightly hotter than the top surface. This temperature difference between the top and the side led to an error on the PSP data. Thus, the in situ calibration was performed using pressure tap data at the centerline station, and applied to the whole image. As shown in Fig. 9.58, the pressure coefficient fields at the freestream velocity of 94 m/s for several yaw angles were obtained based on the ratio of ratios, PSP-intensity-ratio/TSP-intensity-ratio, and the parameter PSPcorr, defined by Gouterman et al. (2004) for correction of the temperature effect. The PSP-derived pressure coefficient distribution along the centerline is compared in Fig. 9.59 with discrete pressure tap measurements obtained at the freestream velocity of 94 m/s and the yaw angle of 20 . The results confirm the performance of the ratio of ratios method and the parameter PSPcorr method. Yamashita et al. (2007) used PSP to measure surface pressure fields on a simplified car model (Ahmed model). A commercial two-luminophore PSP was used. Similar to the PSP used by Gouterman et al. (2004), the ratio of ratios between the pressure-sensitive component and reference component of this PSP was largely independent of temperature in a temperature range around 20  C. Therefore, the temperature effect of PSP was minimized in low-speed measurements. It was found that more accurate pressure measurements could be made by using the wind-off image acquired immediately after shutting down the tunnel in the image ratioing

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Fig. 9.58 The PSP-derived pressure coefficient fields at 94 m/s for three yaw angles:
20 , 0 , and 20 (from top to bottom), based on the ratio-of-ratios method (left panel) and the parameter PSPcorr method (right panel). Flow direction is from right to left. (From Gouterman et al. 2004)

Fig. 9.59 Comparison between PSP and pressure tap data along the centerline, where PSP data were obtained based on the ratio-of-ratios method and the parameter PSPcorr method. (From Gouterman et al. 2004)

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Fig. 9.60 (a) The pressure field and (b) corresponding surface oil visualization image on the Ahmed model for the yaw angle of 0 . (From Yamashita et al. 2007)

Fig. 9.61 (a) The pressure field and (b) corresponding surface oil visualization image on the Ahmed model for the yaw angle of 20 . (From Yamashita et al. 2007)

procedure. Since the thermal pattern in the after-run wind-off image was approximately the same as that in the wind-on image, the temperature effect of PSP was more effectively eliminated by the image ratioing procedure. Figures 9.60 and 9.61 show the pressure fields and corresponding surface oil visualization images on the Ahmed model for the yaw angles of 0 and 20 , respectively. The flow velocity was 50 m/s. The PSP results capture complicated pressure structures over the Ahmed model, which correspond to skin friction structures in surface oil visualization. At the yaw angle of 0 , a suction peak and a separation bubble are visualized near the front part of the model and a horse-shoe vortex can be seen along the edge of the slant. For the yaw angle of 20 , a complicated vortex structure, similar to the leadingedge separation of a delta wing, can be seen on the right-hand side of the model. Similar to the case of the yaw angle of 0 , a low-pressure region at the front part of the model is caused by flow separation at the left-hand side of the model, suggesting that a vortex is shed downstream from this point.

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9.4.2

9 Applications of PSP

Rugby Ball

Seo et al. (2010) measured surface pressure fields on a rugby ball model using PSP to evaluate the aerodynamic force on a non-spinning rugby ball. There was a lace (seam) on the surface of the rugby ball. The AoA (α) is the angle between the longitudinal axis of the ball and the wind direction. The lace angle (σ) gives the angular position of the lace. With the longitudinal axis perpendicular to the wind direction (α ¼ 90 ), the lace angle σ is defined as 0 if the lace is situated facing the wind, and it is 90 when it is situated on the right and 270 when on the left. When the lace is at the back, away from the wind, it is 180 . A 30% scaled model of a rugby ball was tested, which was made of aluminum to reduce a temperature gradient on it. There were four channels on the surface representing the seams on the surface of a ball. Two semi-ellipsoids made of aluminum were joined together by screws. The shape of the semi-ellipsoid was based on caliper measurements on a ball. Figure 9.62 shows a picture of the experimental setup of the ball model at α ¼ 60 and σ ¼ 60 . PSP used in experiments was PtTFPP as a probe luminophore in the FIB polymer binder. Figure 9.63 shows the pressure coefficient fields on the ball at α ¼ 90 for different lace angles at a wind speed of 50 m/s, indicating the dependence of the pressure field on the lace angle. It was found that the seam of the ball is the trigger for initiating low pressure when the seam is situated around σ ¼ 60 from the stagnation point. Figure 9.64 shows the dependence of the pressure field on AoA at the lace angle of σ ¼ 60 .

Fig. 9.62 The scaled model of a rugby ball at α ¼ 60 and σ ¼ 60 : (a) front view and (b) back view. (From Seo et al. 2010)

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Fig. 9.63 The pressure coefficient fields on a rugby ball model at α ¼ 90 : (a) model without seam, (b) σ ¼ 0 , (c) σ ¼ 30 , and (d) σ ¼ 60 . (From Seo et al. 2010)

9.4.3

Unsteady Pressure Fluctuation on Slat as Noise Source

Nakakita (2007, 2010) developed a fast PSP technique to measure unsteady pressure fields at low-speed flows. Nakakita and Ura (2020) conducted unsteady PSP measurements on a slat in a wing model and identified surface pressure fluctuations on the slat as a noise source by correlating PSP data with microphone measurements. Measurements were made on an OTOMO model at 50 m/s in a range of AoAs from 6 to 12 in the JAXA 2 m  2 m Low-Speed Wind Tunnel (LWT2). The OTOMO model was a half-span model designed for fundamental research of aeroacoustic noise generated by high-lift devices, which had a 0.6-m chord and a 1.35-m halfspan length. Its main wing was a straight wing with an aspect ratio of 4.5. In wind tunnel testing, the slat-deployed configuration was used, and only the slat was painted with PSP. Figure 9.65a illustrates the PSP measurement system that consisted of three violet-LED units and a high-speed camera. To cover a frequency range of slat aeroacoustic noise up to 2 kHz, the frame rate of the camera was 10 kHz

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9 Applications of PSP

Fig. 9.64 The pressure coefficient fields on a rugby ball model at σ ¼ 60 : (a) α ¼ 0 , (b) α ¼ 30 , and (c) α ¼ 60 . (From Seo et al. 2010)

and the exposure time was 99 μs. Figure 9.57b shows the OTOMO model with the illuminated PSP-painted slat. Three LED units were not strong enough to generate PSP luminescence for the whole painted surface, so that the unsteady PSP measurement area was divided into the upper and lower regions. A microphone was installed on the tunnel wall just below the optical window for the unsteady PSP measurement system, as shown in Fig. 9.65b.

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Fig. 9.65 Unsteady PSP and microphone correlation measurement system: (a) schematic of the model and PSP setup and (b) photos of the PSP system, microphone, and LED-illuminated PSP-coated slat. (From Nakakita and Ura 2020) Fig. 9.66 Spectrum of far-field noise of the OTOMO slat at 50 m/s and AoA of 14 . (From Nakakita and Ura 2020)

Figure 9.66 shows the sound spectral characteristics at the OTOMO slat cove obtained in previous measurements. It is indicated that there are multiple tone peaks at 940, 1330, and 1770 Hz in addition to the high-frequency trailing-edge tone and broadband noise. The multiple tone peaks were not harmonics, which could be related to feedback phenomena around the slat. The source of these distinct tone peaks could be identified by unsteady PSP measurements correlated with microphone measurements. To evaluate the correlation between unsteady PSP data and microphone data, the coherence is defined as

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Sxy ð f Þ 2 Coh ð f Þ ¼ , Sxx ð f ÞSyy ð f Þ 2

where x and y demote unsteady PSP data at a location and microphone data, respectively, Sxy( f ) is the cross-spectrum between x and y, Sxx( f ) and Syy( f ) are the auto-spectra of x and y, respectively. The significance of the coherence is that it provides a measure to correlate detected acoustic noise in space with surface pressure fluctuation. The effective strength of a noise source is given by the coherent output power (COP) defined as COPð f Þ ¼ Sxx ð f ÞCoh2 ð f Þ: Figure 9.67 shows the unsteady pressure power maps, Sxy( f ), at 940  20 Hz on the OTOMO slat at 50 m/s for different AoAs. Strong unsteady pressure fluctuation is located near the re-attachment point in the chordwise direction and distributed from the wing root to tip for all the AoAs. Although there were some large pressure fluctuation regions, it is not easy to identify clearly an acoustic noise source from the unsteady pressure fluctuation power maps alone. Figure 9.68 shows the corresponding maps of the coherence. Higher coherence values are concentrated in smaller and narrower regions, indicating that unsteady pressure fluctuation captured by PSP was highly correlated with acoustic noise measured by the microphone. The region with the high coherence value is considered as an acoustic noise source. It is

Fig. 9.67 Unsteady pressure power maps at 940  20 Hz on the OTOMO slat at 50 m/s in different AoAs. (From Nakakita and Ura 2020)

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Fig. 9.68 Coherence maps at 940  20 Hz on the OTOMO slat at 50 m/s in different AoAs. (From Nakakita and Ura 2020)

also observed that the noise source generally moves from the wing root to tip as AoA increases. Figure 9.69 shows the corresponding maps of COP, indicating the strength of the noise source.

9.5

Rotating Machinery

PSP is a feasible technique for measuring surface pressure fields on high-speed rotating blades in turbomachinery where conventional techniques are particularly difficult to use. Using a laser-scanning system, Burns and Sullivan (1995) measured the pressure distributions on a small wooden propeller at a rotational speed of 3120 rpm and a TRW Hartzell propeller at a rotational speed of 2360 rpm. Further, using an improved laser-scanning system, Liu et al. (1997a), Torgerson (1997), Torgerson et al. (1998), and Liu et al. (2002) performed PSP measurements on rotor blades in a high-speed axial flow compressor and an Allied Signal F109 turbofan engine. The formation of a shock was measured as an abrupt increase in the pressure distributions at the speeds of 17,000 and 17,800 rpm. As the rotational speed increased, the shock became stronger and its location moved downstream. PSP measurements with a digital camera on high-speed rotating blades have some problems to be solved, such as limited optical access to the entire surface of blades,

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Fig. 9.69 Coherence output power maps at 940  20 Hz on the OTOMO slat at 50 m/s in different AoAs. (From Nakakita and Ura 2020)

very short light duration for sufficient illumination, weak luminescence, and quantitative measurements without standard instrumentation for in situ calibration of PSP. Mosharov et al. (1997) obtained surface pressure distributions on propellers using a CCD camera system with a pulsed light source. PSP measurements on helicopter rotor and propeller blades were carried out at TsAGI (Bykov et al. 1997; Bosnykov et al. 1997; Kuzmin et al. 1998; Mosharov et al. 1997, 2005; Kulesh et al. 2006) and NASA Ames (Schairer et al. 1998b). Navarra et al. (1998) obtained pressure images on a rotor blade using an ICCD camera system. Hubner et al. (1996) suggested a lifetime imaging method for PSP measurements on a rotating object based on detecting the luminescent decay traces of a rotating painted surface on a CCD camera. Using a CCD camera system, Bencic (1997, 1998) conducted full-field PSP and TSP measurements on rotating blades of a 24-in. diameter scale-model fan in the NASA Glenn 9  15 ft low-speed wind tunnel at rotational speeds as high as 9500 rpm. Klein et al. (2013) conducted PSP measurements on rotating propeller blades using the lifetime-based method. Watkins et al. (2016) measured global surface pressures on rotor blades in simulated forward flight in the NASA Langley 14  22 ft subsonic tunnel. After correcting the temperature effect on PSP, the results agreed both qualitatively and quantitatively with pressure transducer measurements. Sato et al. (2019) conducted lifetime-based PSP measurements on a rotating blade in low-Reynolds-number condition for the Mars helicopter. The PSP results indicated that a leading-edge vortex was generated, covering a large

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part of the blade. Wartzek et al. (2016) conducted PSP measurements in the setup including the compressor stage and the distortion generator and compared the experimental data with the corresponding CFD results. Zimmermann et al. (2019) discussed the feasibility of PSP measurement in in the bearing clearance of aerostatic bearings.

9.5.1

Rotating Compressor Blades

Pastuhoff et al. (2016) measured pressure fields on the blades of a radial compressor rotating at speeds up to 50 krpm using a lifetime-based laser-scanning PSP system. A schematic of the setup and a photograph are shown in Figs. 9.70 and 9.71, respectively. The compressor under investigation was a Rotrex C30-74 supercharger with an aluminum impeller with seven primary and seven splitter blades, which was driven by a 45 kW electric motor. The compressor inlet with a 51 mm diameter was open to the atmosphere and the outlet was connected to a plastic hose with a Pitot tube (to measure the stagnation pressure), a rotary ball valve to control the mass flow and a turbine mass flow meter. An optical blade passage sensor was mounted in the

Fig. 9.70 Lifetime-based laser-scanning system for PSP measurements on compressor blades. (From Pastuhoff et al. 2016)

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Fig. 9.71 Photograph of the experimental setup with (a) compressor, (b) diode laser, (c) scanning galvanic mirrors, (d) dichroic mirror, (e) lens, (f) long-pass filter, (g) photomultiplier tube, and (h) blade passage sensor. (From Pastuhoff et al. 2016)

compressor to measure the impeller rotation rate and phase, whereas a thermographic camera was used to measure the impeller surface temperature. The seven primary blades of the compressor impeller were coated with PC-PSP consisting of two layers, a ceramic undercoat and a PtTFPP sensor layer. To collect the emitted light from the PSP, a photo-multiplier tube was placed centered on the rotational axis of the compressor behind a 590 nm long-pass filter and a focusing lens. Excitation light was provided by a 405-nm diode laser that could be used as a pulsed laser or a modulated laser up to 100 MHz. The laser beam was led into the same optical path as the acquisition system by a long-pass (505 nm cutoff) dichroic mirror mounted between the compressor and the focusing lens. The laser spot was guided to a point on the impeller surface through two scanning galvanic mirrors. Control of the laser pulse and the galvanic mirrors, as well as acquisition of the photomultiplier tube and the blade passage sensor, was provided via a computer. The laser-scanning system was programmed to scan a rectangular area of 401  401 points covering the surface of the impeller. The output signal from the photomultiplier was fed through an amplifier before sampling. The signal of the photomultiplier tube that was proportional to the luminescent intensity of PSP after laser pulse was fitted by an exponential decaying function, and the luminescent lifetime was determined, which was converted to pressure by using a calibration relation. Figure 9.72 shows the surface pressure fields obtained using the scanning-laser measurements for the five cases with rotational speeds of 10, 20, 30, 40, and 50 krpm. Furthermore, the pressure profiles along the chord of each individual

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Fig. 9.72 Surface pressure fields on the impeller blades (upper panel) from scanning measurements for cases 6, 7, 3, 8, and 9 with rotational speeds of 10, 20, 30, 40, and 50 krpm, respectively. The lower panel shows the pressure profiles along the chord, defined in case 6 as c ¼ 2π/7, of the blade at half the blade radius, gray lines show the distribution from the seven individual blades, black line their average. (From Pastuhoff et al. 2016)

blade at half the radius along with the mean of the seven distributions (black line) are also shown. As can be clearly observed, the pressure increases almost linearly across the blades and the gradient increases as the rotational speed increases. Peng et al. (2017) used a single-shot lifetime-based PSP/TSP system to measure surface pressure and temperature fields on rotating blades in turbocharger compressors. PSP was PtTFPP as a probe luminophore in a polymer-ceramic (PC) binder. The PC binder was a mixture of high concentration of ceramic particles with a small amount of polymer to physically hold the ceramic particles to the surface. The luminophore mixture was applied onto the porous surface of the binder, which interacted immediately with oxygen, resulting in a frequency response over 6 kHz. TSP was Ru(dpp) as a temperature sensor in an oxygen-impermeable automobile clearcoat (Dupont ChromClear) as a binder. The combination of PSP/TSP allowed simultaneous lifetime-based measurements and excitation by the same light source. Two turbocharger compressors with different size were tested, and they are referred to as “TC1” and “TC2.” As shown in Fig. 9.73, each compressor had a total of six main blades with one blade applied with TSP and two other blades applied with PSP. One of the PSP blades served as a backup, since the PSP was more susceptible to mechanical damage and chemical contamination than the TSP. The measurement system for the turbocharger test is shown in Fig. 9.74. A laser beam was produced by a 532-nm Nd:YAG laser, which was first expanded by a concave lens and then passed through an optical diffuser to improve the uniformity of the illumination field. The illumination covered the entire compressor disk to provide excitation for both PSP and TSP blades. The luminescent signals were collected by a CCD camera (PCO. 1600) through a long-focus lens (200 mm/f4, Nikon). A longpass filter (>600 nm) was installed before the lens to exclude the excitation light. The timing of the system was controlled by a digital pulse/delay generator. A picture

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Fig. 9.73 Turbocharger compressor blades coated with PSP and TSP. (From Peng et al. 2017)

Fig. 9.74 Single-shot lifetime-based system for PSP and TSP measurements on turbocharger compressor. (From Peng et al. 2017)

of the TC1 compressor after installation on the test facility is shown on the bottom right in Fig. 9.74. The two-gate method for a single laser pulse was used for luminescent lifetime measurements. The data processing procedures included four steps: image transformation, image deblurring, image registration, and temperature correction. A deblurring algorithm of Juliano et al. (2012) was used to process the images, and the motion blur was reduced significantly. Figure 9.75 shows the instantaneous fields of the normalized temperature change ΔT/Tref on the TC1 compressor blade at four different rotation speeds. It is clear that the temperature generally increased during the tests, and the amount of temperature rise increased with rotation speed. Obviously, for such strong and complex temperature variations on the blade, a pixel-by-pixel temperature correction on the PSP data was definitely necessary to obtain reasonable pressure results. Figure 9.76 shows the corresponding fields of the normalized pressure p/pref measured by PSP after

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Fig. 9.75 TC1 blade temperature fields at (a) 20,000 rpm, (b) 40,000 rpm, (c) 60,000 rpm, and (d) 80,000 rpm. (From Peng et al. 2017)

Fig. 9.76 TC1 blade temperature-corrected pressure fields at (a) 20,000 rpm, (b) 40,000 rpm, (c) 60,000 rpm, and (d) 80,000 rpm. (From Peng et al. 2017)

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temperature correction. Generally, a streamwise pressure gradient existed on the blade with reduced pressure near the leading edge and increased pressure downstream due to compression. This streamwise pressure gradient increased with rotation speed. Also, a radial pressure gradient can be observed in all cases near the leading edge with the minimum pressure appearing at the tip. This is also reasonable considering that the relative flow velocity reached the maximum at the tip. The general trends of the temperature and pressure fields in TC2 compressor were similar to those of the TC1 compressor.

9.5.2

Helicopter Blades

A single-shot lifetime-based PSP method was developed by Juliano et al. (2011), Disotell et al. (2014, 2016), and Weiss et al. (2017b) for applications requiring highpressure sensitivity on a moving model such as a rotor blade. This method is based on a single pulse of high-energy excitation light and a double-frame (two-gate) exposure on an interline transfer CCD camera for recording luminescent lifetime. Small pressures can be measured on an aperiodic-moving surface where phase averaging is not applicable. This method was demonstrated on a 0.126 m diameter propeller rotating at 70 Hz, and pressure data were acquired within a single pulse of excitation light energy, with no image averaging required. Watkins et al. (2012) applied the single-shot lifetime-based PSP method to measure pressure fields on rotating blades of the U.S. Army General Rotor Model System in the 14-by-22-Foot Subsonic Tunnel at NASA Langley. Preliminary results show that the PSP results agreed both qualitatively and quantitatively with pressure transducer data. Disotell et al. (2014, 2016) used the single-shot lifetime-based PSP method to measure unsteady pressure fields on an articulated model helicopter rotor to simulate forward flight conditions. The experiments were conducted in the Battelle Subsonic Wind Tunnel Facility at the Ohio State University. The Eiffel wind tunnel is capable of producing flow speeds up to 45 m/s in the test section that is 0.9 m high, 1.5 m wide, and 2.9 m long. A schematic of the setup and instrumentation is shown in Fig. 9.77. Optical equipment was installed on a platform above the ceiling window. Illumination was provided by a pulsed Nd:YAG laser (532 nm wavelength, 200 mJ/ pulse) with a maximum repetition rate of 15 Hz. The laser beam was expanded by a spherical divergent lens (
50 mm focal length), and the resulting light volume was smoothed by a glass diffuser. Luminescence emitted from PSP (wavelength peak at 650 nm) was recorded by a 14-bit scientific-grade CCD camera. Two optical longpass filters (>590 nm) were attached in the front of the camera to reject the excitation light. The interline transfer architecture of the camera allowed double-exposure images to be acquired in quick succession. The timing system was triggered by a once-per-revolution signal provided by the output of a motor speed controller. A pulse/delay generator received an exposure trigger from the camera to flash the laser. PtTFPP in PC was chosen as PSP for these unsteady tests due to its high sensitivity, ease of application to the blade, and its enhanced frequency response.

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Fig. 9.77 Schematic of the helicopter setup and PSP/TSP measurement system in the wind tunnel. (From Disotell et al. 2014)

Since PtTFPP in PC exhibit a relatively high degree of temperature sensitivity of about 3%/K, the temperature effects can entirely overwhelm the PSP signal, especially when a pressure change on the blade is small. To correct for the temperature effect, TSP was applied to a second blade on the main rotor. Ru(bpy) in DuPont ChromaClear served as TSP. A white screen layer of spray paint was applied to the blade before PSP and TSP application. The ratio-of-ratios of the two-gated intensities were used for lifetime measurements. A hobby helicopter was mounted on a stand in the test section by fastening the fuselage skids to a bracket as shown in Fig. 9.77. The main rotor consisted of two untwisted, rectangular blades with a radius of 12.8 cm. Figure 9.78 illustrates the blade azimuthal angle (ψ) convention and rotor disk quadrants. The longer blades had limited the maximum tip speed in hover to 40 m/s, which would have challenged the pressure response limit of PSP. Figure 9.79 shows the single-shot temperature and pressure fields measured by TSP and PSP and normalized by ambient temperature and pressure, where the pressure fields are temperature-corrected. The pressure field indicates the expected trend of suction near the leading edge of the blade. The blade pressure distribution in hover gives a reference for comparison with forward flight conditions. Figure 9.80 shows the single-shot pressure fields for an advancing blade (ψ ¼ 95 ) and retreating blade (ψ ¼ 270 ) for the advance ratio of 0.15. The collective and longitudinal cyclic pitches on the blade were 10 and 2.5 , respectively. The PSP results clearly show the qualitative difference in the surface pressure fields between the two sides of the rotor disk. The advancing blade exhibits higher suction (lower pressure) compared with the hover case due to the larger relative freestream velocity to the blade. On the retreating side, the freestream velocity relative to the blade is oriented in the opposite

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Fig. 9.78 Blade azimuthal angle convention and rotor disk quadrants. (From Disotell et al. 2014)

Fig. 9.79 Single-shot fields of (a) temperature and (b) pressure on the hovering blade, where x and y are the chordwise and radial coordinates, respectively, and cmax and R are the maximum chord and radius of the blade, respectively. (From Disotell et al. 2014)

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Fig. 9.80 Single-shot pressure fields on the advancing (upper panel) and retreating (lower panel) blades for the advance ratio of 0.15, where x and y are the chordwise and radial coordinates, respectively, and cmax and R are the maximum chord and radius of the blade, respectively. (From Disotell et al. 2014)

direction to the linear velocity of the blade. Because of the lower dynamic pressure seen by the retreating blade, the maximum pressure change decreased compared to the hover case.

9.6 9.6.1

Low-Pressure Flows PSP Properties at Low Pressure

Niimi et al. (2005) investigated the feasibility of PSP measurements in low-pressure flows and rarefied gas flows. Three types of PSP, PtOEP/GP197, PtTFPP/poly (TMSP), and Bath-Ru/AA, were tested in pressures lower than 150 Pa to examine their fundamental properties, such as pressure/temperature sensitivity and time response of luminescence. Figure 9.81 shows the experimental apparatus for tests. PSP samples were set inside a vacuum chamber evacuated by a rotary pump or a turbomolecular pump. Pure oxygen gas was supplied into the chamber where pressure was monitored by a capacitance manometer and was kept at 0.01–151 Pa. Using a Peltier thermocontroller and a thermocouple, the temperature of a PSP sample was controlled at a constant (293–305 K). A xenon-arc lamp with a bandpass filter was used as an excitation light source, and the light was transmitted via an optical fiber to illuminate the sample in the vacuum chamber. The band-pass filters

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Fig. 9.81 Experimental setup for PSP measurements in a low-pressure range. (From Niimi et al. 2005)

Fig. 9.82 Calibration results for PtOEP/GP197, Bath-Ru/AA, and PtTFPP/poly(TMSP) in a low-pressure range: (a) the Stern–Volmer plots and (b) zoomed-in view of the data. (From Niimi et al. 2005)

were used to cover the absorption spectra of the luminophores. The luminescence was filtered by a long-pass filter (>600 nm) to eliminate the light from the xenon lamp and was detected by a CCD camera with an image intensifier. The optical system was covered with a black curtain to shut out stray light from outside the system. A converging nozzle could be attached at the supply port of the oxygen gas to carry out the experiments for a supersonic free jet impinging on a solid surface using the same vacuum chamber. Figure 9.82 shows the Stern–Volmer plots for PtOEP/GP197, Bath-Ru/AA, and PtTFPP/poly(TMSP) in a pressure ranges of 1.0  10
2–151 Pa. The surface temperature of each sample was kept at 300 K (at 293 K for PtOEP/GP197). The reference pressure pref of each datum was set at the lower limit of the pressure range. As indicated in Fig. 9.82, the luminescent intensity of PtOEP/GP197 exhibits a very

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Fig. 9.83 Temperature effect on the Stern–Volmer plots for (a) Bath-Ru/AA and (b) PtTFPP/ poly(TMSP) in a low-pressure range. (From Niimi et al. 2005)

weak pressure sensitivity in a range of pressures below 150 Pa. The result is attributed to insufficient gas permeability of the polymer GP197 used as a binder, so that oxygen molecules almost never diffuse into the binder and quench the luminescence of PtOEP. Thus, PtOEP/GP197 is not suitable for pressure measurement in low pressure below 150 Pa. The luminescent intensity ratio Iref/I for BathRu/AA depends linearly on the pressure ratio p/pref when pressure is above 20 Pa, while the nonlinear dependency appears when pressure is below 20 Pa. This nonlinearity is probably caused by the adsorption of oxygen molecules on the AA surface. The relatively high-pressure sensitivity of Bath-Ru/AA even in low-pressure conditions seems to be due to the fact that the Bath-Ru molecules adsorbed on the AA surface interact directly with oxygen molecules. PtTFPP/poly (TMSP) exhibits the highest pressure sensitivity among the three PSPs and good linearity of the Stern–Volmer plot over the entire pressure range. Also, the absolute luminescent intensity of PtTFPP/poly(TMSP) is the highest. Such good properties are due to the large free volume of poly(TMSP) so that oxygen molecules can permeate more easily through the polymer matrix. Figure 9.83 shows the temperature dependency of the luminescent intensity of Bath-Ru/AA and PtTFPP/poly (TMSP) for several low-pressure conditions, where the reference luminescent intensity I300 is the intensity at 300 K. The results indicate that the higher the pressure, the larger the temperature sensitivity (i.e., the slope). Because the temperature dependency of the luminescent intensity is not negligibly small, correction for the surface temperature effect is required for precise pressure measurements using PSP. As an application of PSP to low-density gas flows, the pressure distribution on a solid surface on which a supersonic free jet impinged was measured using PtTFPP/ poly(TMSP). In the experiment, a converging nozzle was attached at the supply port of oxygen gas and the temperature of the solid surface was kept at 300 K. The nozzle diameter was 0.3 mm, the impinging angle was 60 , and the distance from the nozzle exit to the surface was 2 mm. The source pressure of the jet and the background pressure in the chamber were set at 53.9 kPa and 133.8 Pa (pressure ratio is 403), respectively. A typical raw image on the surface on which the jet impinged is shown

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9 Applications of PSP

Fig. 9.84 Pressure distributions on a solid surface on which a supersonic jet impinged obtained using PtTFPP/poly(TMSP) in a low-pressure range: (a) typical PSP image and pressure field and (b) pressure distribution along the projected centerline of the impinging jet at different background pressures. (From Niimi et al. 2005)

in the upper part of Fig. 9.84a, and the pressure distribution calculated from the Stern–Volmer relation is shown in the lower part. A distinct image of the pressure distribution could be obtained, although a local change of surface temperature caused by the jet impingement was not compensated for. In the same geometrical condition, the luminescent intensity distributions were imaged for various background pressures PB (133.8, 80.2, 50.9, and 31.2 Pa). The surface pressure distributions along the projection line of the centerline of the impinging jet are shown in Fig. 9.84b. The horizontal axis of Fig. 9.84b is the distance normalized by the whole length of the projection line shown in Fig. 9.84a, and the origin is placed downstream. As shown in Fig. 9.84b, pressure far from the nozzle exit is close to the background pressure in every case. The results indicate the feasibility of a quantitative measurement technique of surface pressure using PtTFPP/poly(TMSP) in a low-pressure range.

9.6.2

Measurements in the Mars Wind Tunnel

Anyoji et al. (2009, 2010, 2011, 2015) measured surface pressure fields on an aluminum flat plate with a blunt leading edge at low speeds in the Mars wind tunnel (MWT) at Tohoku University. The plate had a chord length of 50 mm, a thickness 2.5 mm, and a span length 100 mm. The MWT is a low-density wind tunnel that can produce a subsonic flow at low pressures for aerodynamic measurements of low-Reynolds number wings of flight vehicles for Mars exploration. The MWT is composed of a vacuum chamber, an induction-type wind tunnel, and a buffer tank, as shown in Fig. 9.85a. The induction-type wind tunnel is located inside the vacuum chamber where the pressure condition of the Martian atmosphere can be simulated.

9.6 Low-Pressure Flows

317

Fig. 9.85 (a) The Mars wind tunnel (MWT) at Tohoku University and (b) setup for PSP measurements. (From Anyoji et al. 2015)

The test section of the MWT is 100 mm wide and 150 mm high. The upper and lower walls diverge downstream to compensate for the development of wall boundary layers. The test gas is dry air in usual tests, but can be replaced with carbon dioxide. This wind tunnel is driven by a multiple-nozzle supersonic ejector located downstream of the test section. Ejection of high-pressure gas from the ejector induces the flow in the test section. The gas inside the vacuum chamber is exhausted to the buffer tank through a connecting flexible pipe. During the test time, pressure in the vacuum chamber is kept constant by controlling a butterfly valve placed in the flexible pipe. Measuring pressure fields on an airfoil in low-pressure conditions is crucial to understand the aerodynamic characteristics of the airfoil for flight on Mars. In low-pressure conditions, a thin airfoil usually has higher aerodynamic performance than that of a thick airfoil. Since it is difficult to install conventional pressure sensors due to limitations of model construction, PSP is particularly suitable for thin airfoil models. PSP used for measurements in the MWT was PdTFPP as a probe luminophore in poly(TMSP) as a binder. The composition of this PSP is PdTFPP (4.8 mg), poly(TMSP) (0.16 g), and toluene (20 mL). The absorption and emission peaks are approximately 407 and 670 nm, respectively. This PSP has a good pressure sensitivity under low-pressure conditions (as low as 1 kPa). Figure 9.85b illustrates the setup for PSP measurements in the MWT. The optical equipment was placed outside the vacuum chamber and measurements were made through an optical window on the top of the vacuum chamber. PSP was excited by a UV LED unit with a peak wavelength of 395 nm. A band-pass filter (400  50 nm) was placed in the front of the light source to remove undesirable near-infrared radiation. The luminescence from PSP was captured by a thermoelectrically cooled 12-bit CCD camera (Hamamatsu C4742-95-12ER) with an optical band-pass filter (670  20 nm). Figure 9.86 shows the pressure coefficient (Cp) fields and the Cp distributions along the centerline of the flat panel at AoA of 0 for the total pressures of 10 kPa (Re ¼ 3.2  104) and 1 kPa (Re ¼ 3.4  103), where Re is the Reynolds number based on the plate length. The Mach number was set at around 0.3. In processing of

318

9 Applications of PSP

Fig. 9.86 The pressure coefficient fields and profiles along the centerline of the flat plate model at AoA of 0 for two different Reynolds numbers: (a) Re ¼ 3.2  104 and (b) Re ¼ 3.4  103. (From Anyoji et al. 2015)

PSP images, the wind-on image was obtained by averaging eight images and was normalized by the wind-off image. The temperature change on the test plate during the test time was 0.02 and 1.04 K at chamber pressures of 1 and 10 kPa, respectively. The effects of the temperature changes on the pressure sensitivity were 0.482 and 2.15%/K at 1 and 10 kPa, respectively, indicating that the variations of the pressure coefficient Cp due to the temperature change were 0.0045 at 1 kPa and 0.67 at 10 kPa. The pressure results with and without both temperature correction and in situ calibration are compared in Fig. 9.86. In such a low-Reynolds-number flow around a

9.6 Low-Pressure Flows

319

Fig. 9.87 The pressure coefficient fields and profiles along the centerline of the flat plate model at AoA of 0 as the Reynolds number increases: (a) Re ¼ 4.9  103 (Ret ¼ 245), (b) Re ¼ 6.1  103 (Ret ¼ 305), (c) Re ¼ 1.1  104 (Ret ¼ 550), (d) Re ¼ 2.0  104 (Ret ¼ 1000) and (e) Re ¼ 4.1  104 (Ret ¼ 2050). (From Anyoji et al. 2011)

flat plate with a blunt leading edge, the flow separates at the leading edge and reattaches to the surface after the transition, forming a laminar separation bubble. The low-pressure regions around the leading edge observed in Fig. 9.86 indicate the presence of the laminar separation bubble. The transition location can be identified as the point where the surface pressure begins to rapidly recover. The re-attachment location can be defined as the location downstream of the transition point at which a rapid decrease in the rate of the pressure recovery is observed. The estimated reattachment locations are approximately at x/c ¼ 0.22 for Re ¼ 3.2  104 and x/c ¼ 0.21 for Re ¼ 3.4  103. Figure 9.87 shows the development of the pressure field on the flat plate as the Reynolds number increases from 4.9  103 to 4.1  104 at zero AoA. The reattachment length is strongly dependent on the Reynolds number. There is a peak around the Reynolds number based on the plate thickness from Ret ¼ 300–500. Anyoji et al. (2011) reported PSP results on a NACA0012-34 airfoil and a circular arc airfoil. Nose et al. (2011) measured pressure fields on the Ishii wing that was used by JAXA for a Mars aircraft in the MWT. Ishiwaki et al. (2017) measured pressure fields on a delta wing in the MWT. Inspired by the features of bird and insect wings, Mangeol et al. (2017) measured pressure fields on flat plates with serrated leading edges at a low Reynolds number. Figure 9.88 shows the pressure coefficient fields on a serrated flat plate at Mach 0.46 and Re ¼ 11,000. It is found that the plate with short-wavelength serrations underperforms in terms of the lift-todrag ratio under all the conditions compared to the baseline case, while the plate with large-wavelength serrations slightly outperforms it at around the stall angle.

320

9 Applications of PSP

Fig. 9.88 The pressure coefficient fields on a serrated flat plate at Mach 0.46 and Re ¼ 11,000: (a) α ¼ 4 and (b) α ¼ 6 (left) and α ¼ 7 (right). (From Mangeol et al. 2017)

9.7 9.7.1

Other Topics Cryogenic Wind Tunnels

PSP measurements were made in cryogenic wind tunnels where the oxygen concentration in the working nitrogen gas is extremely low and the temperature is as low as 90 K (Asai et al. 1997a; Upchurch et al. 1998; Egami et al. 2006). The development of cryogenic PSP formulations was motivated by the needs for global pressure measurement techniques in large-scale pressurized cryogenic wind tunnels such as the National Transonic Facility (NTF) at NASA Langley and the European

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321

Transonic Wind Tunnel (ETW) in Cologne, Germany. Asai et al. (1997a) developed AA-PSP and measured surface pressure distributions on a 14% thick circular-arc bump model in a small cryogenic wind tunnel in JAXA. PSP data were in good agreement with pressure tap data at 100 K over a range of the Mach numbers of 0.75–0.84. However, the methodology of coating on an AA surface cannot be applied to stainless steel models typically used in cryogenic wind tunnels. Upchurch et al. (1998) developed a polymer-based cryogenic PSP that could be applicable to all types of surfaces including stainless steel. This paint was successfully demonstrated in pressure measurements on an airfoil in the 0.3-m cryogenic tunnel at NASA Langley. Asai et al. (2000, 2002) also presented a polymer-based cryogenic PSP formulation applied to cryogenic wind tunnels and short-duration shock tunnels, which was based on a polymer Poly(TMSP) having very high gas permeability. This PSP can be dissolved into a solvent and applied using an airbrush to any model surface including stainless steel, in contrast to AA-PSP which is applicable to aluminum or aluminum alloy. Watkins et al. (2012) conducted intensity-based PSP measurements on a swept wing model at cryogenic conditions in NTF and identified some issues in their measurements. Yorita et al. (2018) used a lifetimebased PSP system to measure surface pressure fields on a swept wing in ETW. Asai et al. (2000, 2002) described the application of poly(TMSP)-based PSP and AA-PSP data to a circular-arc bump model and a delta wing model in the JAXA 0.1m transonic cryogenic wind tunnel. The tunnel was operated by controlling both liquid nitrogen injection and gaseous nitrogen exhaust. A small amount of air was injected just downstream of the test section, and the oxygen concentration was varied from near zero to 2000 ppm by adjusting the flow rate of injected air. The model was viewed through a 70-mm diameter window on the opposite sidewall. For intensitybased measurements, a 300-W xenon lamp with a band-pass filter (400  50 nm) was used for illumination. A dichroic mirror (550 nm) was used to separate the luminescent emission of PSP from the excitation light. A 14-bit cooled CCD digital camera with a band-pass filter (650  20 nm) placed before the lens was used for luminescence measurements. The aluminum bump model was a 14% circular arc with a chord length of 50 mm. The bump model was equipped with 16 pressure taps at the mid-span, as shown in Fig. 9.89a. The poly(TMSP)-PSP were coated in two 8-mm wide strips on the surface using an airbrush, while the other two strips were anodized to make AA-PSP. Figure 9.89b shows the surface pressure distribution obtained using in situ calibration on the bump model at Mach 0.82 and a total temperature of 100 K, where the image at Mach 0.4 was used as a reference image since the tunnel could not run below that speed. The PSP-derived pressure data are in good agreement with pressure tap data. It was found that the use of a priori calibration did not produce results consistent with pressure tap data because the slope of a priori calibration curve was twice as large as that of the in situ calibration curve. Also, PSP measurement on a delta wing model at Mach 0.75 and the total temperature of 100 K clearly visualized the primary and secondary separations generated by the leading-edge vortices. Furthermore, Kojima et al. (2006) examined the feasibility of the lifetime-based method to measure the pressure distribution on

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9 Applications of PSP

Fig. 9.89 (a) Circular-arc bump model and (b) pressure coefficient distributions given by PSP and pressure taps at Mach 0.82 and total temperature of 100 K. (From Asai et al. 2002)

the same circular-arc bump model in the JAXA 0.1-m transonic cryogenic wind tunnel. Yorita et al. (2018) conducted lifetime-based PSP measurements on a swept wing of a full-span airplane model in ETW at cryogenic conditions. A two-gate lifetimebased method was applied to deal with the issues caused by the model deformation between wind-on and reference conditions. The cryogenic PSP used in tests was PtTFPP as a probe luminophore in poly(TMSP) as a polymer binder. PSP was carefully applied to the surface of the model. After masking the non-painted area and cleaning the model surface by a suitable solvent, target markers were applied on the model metal surface using a black pen. The screw holes were filled with filler material and also masked using a black pen. After these preparations, the PSP was directly sprayed onto the model surface without a primer and basecoat layer to avoid interaction between different layers. The thickness of the paint was below 5 μm, and the roughness of the paint was approximately 0.15–0.3 μm. After coating, the model was kept in the model preparation room with normal room air for one night. The model was transported to a temperature-variable room filled with dried air the next morning. After a short inspection, the model was transported to the nitrogen-filled test section of the wind tunnel. A UV-LED unit with a 405-nm peak was developed for cryogenic wind tunnel tests, which could be externally operated in either pulsed or constant modes. The LED head and control electronics were designed to fit into a heated cylindrical temperature protection housing to protect the equipment from cold nitrogen gas. An optical band-pass filter (385  35 nm) was attached in the front of the LEDs. Additionally, a cylindrical lens was installed in the front of the optical filter to improve the illumination distribution on the model wing surface. The LED unit was installed at an optical window of the top wall, which was located exactly opposite of the port side of the upper wing surface. A CCD camera (PCO4000, PCO) with an optical band-pass filter (650  50 nm) was installed in another

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323

temperature protection housing. This camera had a capability of multi exposure accumulation on the sensor using an external control signal. The lens was equipped with remote focus and aperture controls to adjust for the large model position changes during the test. The camera unit was installed in an optical window downstream of the LED position and observed the model surface at a slightly tilted angle. For PSP measurements in nitrogen gas flow in ETW, pure oxygen gas was injected into the flow downstream of the test section. Due to the closed cycle setup of the wind tunnel, oxygen was evenly distributed in nitrogen by the time it reached the inlet of the test section. Liquid nitrogen was continuously injected into the wind tunnel to keep the flow temperature constant. Therefore, a continuous oxygen injection was also needed with manual adjustment of the injection rate for each test condition. This manual operation caused a time-dependent oxygen concentration of 1000 ppm with variations of up to 50 ppm during an image acquisition period. Figure 9.90 shows the pressure fields on the upper surface of the swept wing at four different test conditions. The Mach number was 0.85 for all data points and the Reynolds numbers were varied by changing the flow temperature and pressure. The

Fig. 9.90 PSP-derived pressure fields on the upper surface of the swept wing model at different test conditions in ETW: (a) Condition 1: Re ¼ 6.4  106, Ttot ¼ 296 K, (b) Condition 2: Re ¼ 25.0  106, Ttot ¼ 164 K, (c) Condition 3: Re ¼ 25.0  106, Ttot ¼ 115 K, and (d) Condition 4: Re ¼ 42.5  106, Ttot ¼ 115 K. (From Yorita et al. 2018)

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9 Applications of PSP

Fig. 9.91 PSP in situ calibration results using pressure tap data in ETW: (a) Condition 1: Re ¼ 6.4  106, Ttot ¼ 296 K, (b) Condition 2: Re ¼ 25.0  106, Ttot ¼ 164 K, (c) Condition 3: Re ¼ 25.0  106, Ttot ¼ 115 K, and (d) Condition 4: Re ¼ 42.5  106, Ttot ¼ 115 K. (From Yorita et al. 2018)

flow direction is from the top of the figure. The white or black dots and lines on the model surface indicate the uncoated areas (e.g., pressure holes, screw holes, and model joint part). The pressure distributions associated with complex shock structures are successfully visualized near the leading edge. A secondary shock structure is also visible in the middle part of the wing. The SNR of PSP data decreases with decreasing temperature, which is a result of the reduction of the pressure sensitivity of PSP. However, even during the lowest temperature condition, the SNR of PSP data is still sufficiently high to distinguish the main structures in the pressure distribution. Figure 9.91 shows the PSP in situ calibration results using pressure tap data at four different test conditions. The ratio-of-ratios values of PSP are compared with the measured pressure tap values in these plots. The data in Fig. 9.91 follow a linear calibration relation. These plots indicate that all PSP data obtained at four test conditions show a good correlation with pressure tap data. The RMS error of the pressure coefficient at the highest Reynolds number condition is about 0.036.

9.7 Other Topics

9.7.2

325

Subsonic and Sonic Impinging Jets

Subsonic and sonic impinging jets have complex flow structures on a simple geometrical configuration, which provide a good testing case for applying PSP and TSP complemented with other global flow diagnostic tools such as Schlieren flow visualization and PIV (Crafton et al. 1999, 2006a, b; Li et al. 2020b). Crafton et al. (1999, 2006a, b) studied subsonic jets and sonic under-expanded jets impinging on a flat plate at an oblique incidence angle from a converging nozzle. Results were obtained on two geometric configurations at the impingement angles of 10 and 20 and the impingement distances of 3.8 and 4.5 nozzle exit diameters, respectively. The jet exit velocity was varied from Mach 0.3 to Mach 1.0. PSP was used to measure surface pressure fields, and TSP to measure surface temperature fields and heat transfer coefficient on the impingement surface. Figure 9.92 shows the impinging jet setup and PSP/TSP measurement system. The jet facility consisted of a cylindrical settling chamber (5 in. in diameter and 12 in. in length) with a 1.5-in. radial inlet and a 5-mm diameter nozzle with a 15 convergence angle. The settling chamber was instrumented with a J-type thermocouple to monitor the total temperature of the jet; the total pressure was set using a regulator and monitored using a Heise pressure gauge with 0.2 psi resolution. Compressed air was supplied to the nozzle from an air compressor system. The impingement plate was an 8-in. high, 12-in. long, and 1.5-in. thick aluminum plate. The normalized geometric impingement distance (H/D) and the impingement angle (θ) were varied independently to produce multiple impingement configurations. The impingement angles of 20 and 10 were tested, where 90 corresponded to normal impingement. The geometric impingement distance (H ) was four jet diameters. The coordinate system (S, Y) on the impingement plate was defined in such a way that the origin coincided with the geometric impingement point, the S-coordinate was along the surface of the impingement plate in the mainstream direction, and the Y-coordinate was along the surface of the impingement plate in the cross-mainstream direction. In experiments, Ru(dpp) in RTV was used as PSP and Ru(bpy) in model airplane dope was used as TSP. PSP and TSP, coated on the surface of the impingement plate, were excited by a blue LED array at 460 nm. The luminescent emission, filtered using a long-pass optical filter (>570 nm) to eliminate the excitation light, was detected using a 16-bit Photometrics CCD camera. A ratio between the flow-on and flow-off reference images was converted to pressure or temperature using a priori calibration relations. The temperature distribution on the impingement surface in a sonic jet is shown in Fig. 9.93 for H/D ¼ 3.8, θ ¼ 10 , and p0/pa ¼ 2.7, where pa is the atmospheric pressure. The surface temperature variation is less than 0.5 K from the region outside of the influence of the jet to any location inside the region of jet impingement. This temperature difference would result in an error of about 0.1 psi in PSP measurements if the temperature effect of PSP was not corrected. Figure 9.94 shows the pressure field obtained using PSP for H/D ¼ 3.8, θ ¼ 10 , and p0/pa ¼ 2.7. The pressure pattern associated with shock cells in the sonic jet was clearly visualized. An insight

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9 Applications of PSP

Fig. 9.92 Schematic of (a) an obliquely impinging jet test facility and (b) PSP/TSP measurement system. (From Crafton et al. 1999, 2006a)

into the multi-peak pressure distribution was gained by Schlieren flow visualization. Pressure on the impingement plate varied by more than 8 psi, suggesting that the temperature-induced PSP measurement error was less than 3% of the full range of pressure. Figure 9.95 shows a composite representation of the streamwise pressure distribution and Schlieren image for the sonic jet impinging at 10 . The locations of the shock waves correspond to the pressure peaks on the impingement surface. Figure 9.96 shows the streamwise pressure distributions along the axis of symmetry for different total pressures ( p0/pa) of the jet at the impingement angles of 10 and 20 . The subsonic pressure distributions show a single pressure peak at the stagnation point. This peak pressure location changed with the impingement angle. The first pressure peak in the multi-peak pressure distribution of the sonic impinging jet coincided with the single peak in the subsonic pressure distribution. The first

9.7 Other Topics

327 301

po/pa 2.71 H/D 3.8 12 T 10o

300.8

10

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8

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300

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299

Temperature [K]

Fig. 9.93 Temperature distribution on the impingement surface of an impinging sonic jet. (From Crafton et al. 1999) 19

po/pa 2.71 14 H/D 3.8 12 T 10o

18 17

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10 8

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Fig. 9.94 Pressure distribution on the impingement surface of an impinging sonic jet. (From Crafton et al. 1999)

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9 Applications of PSP

Fig. 9.95 Composite representation of the streamwise surface pressure distribution with the corresponding Schlieren image of an impinging sonic jet. (From Crafton et al. 1999)

pressure peak corresponded to the stagnation point. In these cases, the first pressure peak location (the stagnation point) was always found somewhere upstream (toward the nozzle) of the geometric impingement point. In fact, the deviation of the stagnation point from the geometric impingement point is an intrinsic property of the non-orthogonal viscous stagnation flow (Dorrepaal 1986; Liu 1992). This deviation decreases to zero as the impingement angle approaches to 90 . Crafton et al. (1999, 2006a) discussed the correlation between the peak pressure location and the geometric impingement point, which was related to the impingement distance H and the impingement angle θ. A model for the location of the maximum pressure was sought based on the exact solution of the Navier-Stokes equations given by Dorrepaal (1986) and Liu (1992) for a non-orthogonal stagnation flow. This model fitted the experimental data well.

9.7.3

Flight Tests

McLachlan et al. (1992), using PtOEP in silicone resin, measured surface pressure fields on a fin attached to the underside of an F-104 fighter jet in flight. A selfcontained data acquisition system was installed inside the fin, which consisted of an

9.7 Other Topics

329

19

T = 10, H/D = 3.8

Pres sure [psi a]

18

po/pa 1.07 po/pa 1.14 po/pa 1.27

17

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15 14 13 12 -4

0

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T = 20, H/D = 4.5

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18

po/pa 1.07 po/pa 1.14

17

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po/pa 2.10

po/pa 1.55 po/pa 2.71

15 14 13 12 -4

0

4

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16

S/D Fig. 9.96 Streamwise pressure distributions along the axis of symmetry of an impinging sonic jet for different total pressures ( p0/pa) of the jet at the impingement angles of 10 (upper panel) and 20 (lower panel). (From Crafton et al. 1999)

8-bit digital video camera and a UV lamp triggered remotely to excite PSP. PSP was applied to a Plexiglas panel mounted flush with the fin. The luminescent emission from PSP was transmitted through the Plexiglas into the fin and subsequently recorded by the video camera. Two tests were conducted at night at the Mach

330

9 Applications of PSP

numbers of 1.0–1.6 at altitudes between 30,000 and 33,000 ft. Pressure taps mounted on the fin were used for PSP in situ calibration. Results showed a favorable comparison to pressure tap data at Mach numbers greater than 1.3, and an accuracy of about 0.24 psi was reported. Houck et al. (1996) performed flight tests using PSP on a Navy A-6 Intruder, where PSP was painted on an Mk76 practice bomb. The data acquisition system consisted of a battery-operated strobe light for excitation that was synchronized with a Nikon 50-mm film camera used to measure the luminescent emission. This system was self-contained and mounted onto a bomb rack adjacent to the practice bomb. Three night flights were flown at altitudes between 5000 and 10,000 ft at the Mach numbers of 0.4–0.82. After the flights, negative films were developed and digitized by projecting them onto a 14-bit CCD camera. No in situ calibration was done so that only qualitative results were presented and the temperature effect was unable to be accounted for. Using a similar film camera system, Fuentes and Abitt (1996) measured pressure fields on a Clark-Y airfoil mounted underneath the wing of a Cessna 152 aircraft. In general, issues associated with film developing and processing make film-based systems more difficult for quantitative measurements. Using a portable 2D phase-based laser-scanning lifetime system, Lachendro et al. (1998, 2000) conducted in-flight PSP measurements on a wing of a Raytheon Beechjet 400A aircraft at two flight conditions: (1) 31,000 ft and Mach 0.75, and (2) 21,000 ft and Mach 0.69. For in-flight PSP measurements, a lifetime-based or phase-based technique is more suitable because this technique does not require a reference signal used in conventional intensity-based systems, and therefore it is not affected by the wing and fuselage deformation. The lifetime-based technique is also insensitive to the ambient light from the Moon and stars. A compact laser-scanning system was specially designed for phase-based PSP and TSP measurements at large distances. Ru(dpp) PSP and three PtTFPP PSPs in different binders were used for in-flight tests. As illustrated in Fig. 9.97, the strips were wrapped around the leading edge and positioned streamwise to the trailing edge. Pressure data in the above flight conditions were available from a flight test previously conducted by Mitsubishi Heavy Industries (MHI). Since this aircraft was a derivative of the Mitsubishidesigned Diamond II, it had been extensively studied in flight and wind tunnel testing (Shimbo et al. 1999). For the other three flight tests, as shown in Fig. 9.97, the painted strips were placed at 31%, 55%, and 85% spans that corresponded to the locations in the MHI flight test. At each location, PSP and TSP strips were placed side by side. Lachendro et al. (1998) and Lachendro (2000) found a considerable temperature variation across the wing chord that was caused by wing fuel tanks warmed by moving fuel and relatively cooled stringers. They had to use a simple heat transfer model to estimate the mean temperature on the wing in the flight conditions. The chordwise pressure distributions were obtained at 31%, 55%, and 85% span. Figure 9.98 shows the pressure coefficient Cp given by PSP at 21,000 ft and Mach 0.69 compared to the existing MHI fight test data. The distribution of Cp was calculated from a priori calibration relation of PSP using the mean wing temperature of
5  C which was estimated based on a heat transfer model. It is noted that the first data point near the leading edge in the MHI flight test data is likely erroneous and it could

9.7 Other Topics

331

Fig. 9.97 PSP and TSP installation for flight tests. (From Lachendro 2000)

be disregarded. Near the trailing edge after x/c ¼ 0.75, the PSP data are significantly lower than the MHI flight test data. This is because the mean temperature of
5  C used for PSP data reduction over the whole wing section could lead to an underestimated value of Cp at the thin trailing edge that was actually colder than the middle portion of the wing. Egami et al. (2013a) reported a feasibility test for in-flight pressure measurement using PSP applied to a pylon surface of the VFW614 ATTAS aircraft. Three PSP measurement methods used in the test were “intensity method with LED-array,” “intensity method with Electro Luminescence (EL) foil,” and “image-based lifetime method.” The intensity method with LED-array is the most conventional method in wind tunnel testing. The image-based lifetime method is now popularly used in steady and unsteady PSP measurements in various applications. In contrast, the intensity method with Electro Luminescence (EL) foil is novel; here an EL foil is

332

9 Applications of PSP

-1.4 °

-1.2

PSP T=-5 C MHI Flight Test Data

-1.0 -0.8 -0.6 Cp

-0.4 -0.2 0.0 0.2 0.0 0.4

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0.6 0.8 Fig. 9.98 The distribution of the pressure coefficient (Cp) obtained using Ru(dpp)-based PSP at the altitude of 21,000 ft and Mach 0.69 compared with the MHI flight test data. (From Lachendro 2000)

Fig. 9.99 Application of the EL foil, pressure sensor, and PSP on the pylon: (a) before PSP application and (b) after PSP application. (From Egami et al. 2013a)

used as a light source. The EL foil is glued to the airplane surface and PSP is applied to the upper surface of the EL foil. PSP is illuminated from the underside by the EL foil that can excite PSP very effectively since the EL foil and PSP are directly in contact. Thus, much higher luminescent intensity from PSP is achieved by excitation using the EL foil. Equipment for PSP and IR thermography system was set up to fulfill the requirements of the flight test and certification in the ATTAS aircraft. The EL foil was applied to the pylon of the ATTAS aircraft using a strong double-sided tape, as shown in Fig. 9.99a. The power cable was connected between the EL foil and the EL converter inside the cabin through a hole in the lower fuselage. Furthermore, a

9.7 Other Topics

333

pressure sensor was installed at the center of the region of interest on the pylon without EL foil and its pneumatic connection into the cabin was also realized, as seen in Fig. 9.99b. PtTFPP-based PSP, including nanoTiO2 for the intensity enhancement, was applied to the pylon using an airbrush. One half of the PSP was applied directly to the pylon surface, and another half was applied to the EL foil, as shown in Fig. 9.99b. The emission light from the PSP was measured by a CCD-camera which was installed inside the cabin in front of a window. At the same time, the temperature distribution on the PSP layer surface was observed by the IR camera. Figure 9.100 shows the pressure distributions on the pylon surface measured by the intensity-based method with the LED-array as a light source. A run image was taken at Mach 0.56 and the side slip angle β ¼ 0 , and reference images were obtained at no-wind condition on the ground, Mach 0.21, and Mach 0.23. The resulting images show slightly different patterns depending on the applied reference image. The influence of the temperature distribution on the pylon is still visible, although the temperature correction has already been applied to the results. The PSP results differ from pressure tap data with an offset of 0.8 – 6.2 kPa. These values correspond to a temperature decrease of 1–7.8  C. The pressure distributions along the A–A0 line in Fig. 9.100a are compared in Fig. 9.101 with the offset correction. All plots exhibit a very similar tendency, where a pressure increase is observed in the chordwise direction. It indicates that PSP itself works well in the flight test. The major difficulty comes from temperature changes. The lifetime-based method gives the same results as those given by the intensity-based method using the LED-array. For the intensity-based method using the EL foil in this flight test, the EL foil could provide 25% more excitation light than the LED light source at a distance of 2 m between the CCD camera and the area covered with PSP. This is a benefit of an EL foil in the flight test. On the other hand, the difference in the local adhesion property between the EL foil, filter, and protecting layers generated a big temperature difference on the layer, which made the temperature correction difficult in this flight test. Sugioka et al. (2019b) conducted in-flight PSP measurements to visualize the location of a shock wave on the main wing surface of the JAXA Flying-Test-Bed “Hisho.” The “Hisho” is an experimental airplane based on the Cessna Citation Sovereign (Model 680). The maximum flight Mach number and altitude of Hisho are 0.80 and approximately 47,000 ft, respectively. The aircraft flew at both subsonic and transonic speeds at the flight altitudes between 25,000 and 45,000 ft. A lifetime imaging system was set up onto the cabin of the experimental aircraft, and PSP images were acquired under trim flight conditions. PSP was PtTFPP as a probe luminophore and HFIPM as a polymer binder. Urethane paint was used as a white base coat. Urethane paint and PSP were coated onto aircraft films, not directly onto the wing surface. The size of a film was approximately 300 mm  210 mm. In preparing the PSP film sheets, a white basecoat was first formed on films. After the coating had dried, black fiducial markers were attached. A thin film of HFIPM prevented interaction between the white basecoat and PSP active layer. Finally, PSP was applied using a spray gun. The PSP films were placed at y/(b/2) ¼ 33–40% in the

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9 Applications of PSP

Fig. 9.100 Pressure distributions at Mach 0.56, β ¼ 0 and Alt ¼ 21,000 ft, calculated using various reference images: (a) reference on ground before the flight test, (b) reference at Mach 0.21, Alt ¼ 5000 ft, (c) reference at Mach 0.23, Alt ¼ 10,000 ft, (d) reference at Mach 0.21, Alt ¼ 6000 ft, and (e) reference on ground after the flight test. (From Egami et al. 2013a)

spanwise direction and x/c ¼ 10–70% in the chordwise direction, where b and c are the span and chord lengths, respectively. Figure 9.102 shows an image of the PSP films on the wing. The lifetime imaging system consisted of a CCD camera and a UV LED light. A 35-mm lens and a long-pass optical filter (>580 nm) were placed in front of the camera, and a low-pass optical filter (590 nm) was mounted to separate the excitation light from the paint luminescence. Phase locking techniques were used to record time-resolved pressure-sensitive paint data. The pulsing of the LED array was synchronized with pressure fluctuation measured by the kulite pressure transducer through the gating function on a triggered oscilloscope. A variable delay was added to oscilloscope’s TTL pulse with a pulse/delay generator. Phase-locked time

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Fig. 9.108 PSP-derived pressure fields for the (1, 1, 0) mode at 145.4 dB and 1286 Hz at three phases: (a) 0 , (b) 90 , and (c) 180 . (From Gregory et al. 2006)

histories were recorded by varying the delay throughout the oscillation cycle. Thus, this system made phase-averaged measurements of unsteady pressure fields. The frequency of the driving signal was adjusted such that a maximum pressure amplitude was obtained near the resonant frequency for the mode characterized by (nx, ny, nz) ¼ (1, 1, 0), where nx, ny, and nz are the mode numbers in the x, y, and z directions, respectively. The tuned driving frequency was 1286 Hz at the predicted resonance frequency. Figure 9.108 shows the PSP-derived pressure fields at three phases separated by 90 within an oscillation cycle. Figure 9.108a, c shows the antinode pressure fields at their maxima and minima, while a nearly uniform pressure across the cavity is shown in Fig. 9.108b. Figure 9.109a shows the pressure contour plot of PSP data for the (1, 1, 0) mode shape at a sound pressure level of 145.4 dB, which represents one phase-averaged point within an oscillation period, at the condition when the antinode pressure is nearly maximum. The pressure distribution compares favorably with the general distribution from the linear theory, as shown in Fig. 9.109b. There are some minor differences between the PSP data and the theoretical solution, which may be attributed to nonlinear effects at high sound pressure levels in these tests. Disotell and Gregory (2011) developed a single-shot lifetime PSP system capable of measuring high-frequency acoustic fields with nonperiodic, acoustic-level pressure changes. PSP consisted of PtTFPP as a pressure sensor and a polymer/ceramic matrix binder, which was applied to a back wall inside an acoustic resonance cavity

9.7 Other Topics

343

Fig. 9.109 Pressure contour plots for the (1, 1, 0) mode shape at 145.4 dB and 1286 Hz: (a) PSP data and (b) the analytical solution, where pressure is expressed in Pascal. (From Gregory et al. 2006)

Fig. 9.110 Single-shot PSP-derived pressure fields for the (1, 1, 0) mode at 145.4 dB and 1302 Hz at three phases: (a) 0 , (b) 90 , and (c) 180 . (From Disotell and Gregory 2011)

that was duplicated from the design of Gregory et al. (2006). The lifetime technique was based on two gated intensity images acquired in the luminescent response of PSP excited by a single pulse of light, which afforded the ability to capture instantaneous pressure fields. Figure 9.110 shows single-shot PSP results at three

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9 Applications of PSP

Fig. 9.111 Comparisons of the decomposed mode shapes (2, 1, 0) (upper panel) and (1, 2, 0) (lower panel). (From Ali et al. 2016)

phases at the same sound pressure level and resonant mode studied by Gregory et al. (2006). Ali et al. (2016) conducted PSP measurements of acoustic pressure fields in a rectangular cavity driven by two speakers. A high-speed camera was used to generate a continuous time record of acoustic pressure fluctuations with PSP. DMD and POD were used to extract the spatial modes of pressure fields. Figure 9.111 shows the mode shapes corresponding to the simultaneous excitation of PSP in the resonance box. The top and bottom rows of the figure show mode shapes (2, 1, 0) and (1, 2, 0), respectively. The theoretical mode shapes are given in Fig. 9.111a, d. The results from POD are given in Fig. 9.111b, e. As shown in Fig. 9.111c, f, DMD is better than POD at suppressing noise and at effectively separating spectral energy when multiple acoustic excitation frequencies are present.

Chapter 10

Applications of TSP

This chapter describes TSP measurements in various flows, in particular hypersonic flows. TSP application is first demonstrated in a small shock tube that is commonly available in universities to study complex shock-induced flow over a wall-mounted cylinder. TSP measurements on a circular cone, an inlet ramp, the AGARD HB-2 standard model, and single and double fins in hypersonic wind tunnels are described. Then, TSP measurements on a circular cone in a quiet Mach-6 Ludwieg tube are discussed for quantitative heat flux calculation from TSP data and correction of the lateral heat conduction effect. TSP is used as a global diagnostic tool for boundarylayer transition detection on various models. Heat flux measurements in a sonic impinging jet are described as an example of TSP application to general heat transfer problems.

10.1

Small Shock Tube

Ozawa (2016) and Ozawa and Laurence (2018) conducted transient TSP measurements in a small shock tube facility at the Tokyo Metropolitan University. As shown in Fig. 10.1, this facility is a convergent type of shock tube with a total length of 9 m and an inner tube diameter of 100 mm. A circular-shaped tube is transformed into an octagon-shaped tube, and four removable test windows in the test section are available for optical measurements. Using TSP, Ozawa (2016) measured the aerothermodynamic characteristics of a transient boundary layer on the tube wall generated by a traveling incident shock and a reflected shock, particularly shock-wave/ boundary-layer interaction, transition front, streamwise streaky structures, and turbulence. Further, Ozawa and Laurence (2018) studied the shock-induced flow over a wallmounted cylinder in the shock tube. The circular cylinder was mounted at the centerpoint of a flat plate, which was taken as the origin of the coordinate system. The axis of the cylinder was normal to the flat-plate surface (see Fig. 10.1). The © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_10

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Fig. 10.1 Schematic of (a) the shock tube, (b) transition piece, and (c) flat-plate test article; photographs of (d) the circular cylinder, (e) the flat plate with a TSP coating, and (f) a mounted thermocouple. (From Ozawa and Laurence 2018)

diameter of the cylinder was 3 mm. In general, a range of flow conditions are achievable in a shock tube through varying the driver/driven tube pressures and gas compositions, and potentially the temperatures. Here, both the sections were unheated, and air was used as both the driver and driven gas, leaving the driver pressure, p4, and the driven pressure, p1, as the two parameters that could be varied. The shock and post-shock Mach numbers were fixed, and the post-shock unit Reynolds number was varied. This was achieved by varying p4 and p1 individually while keeping the ratio p4/p1 fixed at a value of 130. Three conditions were explored, denoted by Condition A ( p4 ¼ 650 kPa, p1 ¼ 5 kPa), Condition B ( p4 ¼ 520 kPa, p1 ¼ 4 kPa), and Condition C ( p4 ¼ 390 kPa, p1 ¼ 3 kPa). According to the one-dimensional inviscid flow theory for this pressure ratio and choice of gas, the predicted incident shock speed was us ¼ 965 m/s (Ms ¼ 2.8), the reflected shock speed was ur ¼ 404 m/s (Mr ¼ 2.0 relative to the post-incident-shock flow), and a useful test time was approximately 1.0 ms at the upstream end of the test section. Here, the subscripts s and r denote the incident shock and the reflected shock wave, respectively. TSP was Ru(phen) as a temperature sensor in an ethanol-soluble polyamidebased polymer as a binder. TSP was applied directly to the PU base layer using a spray gun. The thickness of the applied TSP layer estimated using a film thickness meter was about 1.5 μm. The circular cylinder was painted black to minimize reflections; it was attached to the flat plate following the application of the TSP layer. The optical setup for TSP measurements is shown in Fig. 10.2. Two LED light sources (about 462 nm) equipped with lenses were used to provide continuous illumination for TSP for a duration of 1 s during each run to minimize photodegradation of TSP. A 12-bit high-speed camera (Phantom v2011) was employed as a detector. A frame rate of 180 kfps with an exposure time of 3.86 μs

10.1

Small Shock Tube

347

Fig. 10.2 Schematic of optical setup for TSP measurement and installation of the flat-plate test article with a circular cylinder. (From Ozawa and Laurence 2018)

was typically used, which allowed a visualization area of 384  204 pixels corresponding to a physical area of 44.2 mm  23.5 mm. A band-pass filter (560–640 nm) was placed in the front of the camera, allowing detection of the TSP luminescence at 580 nm with a transmission ratio of more than 90%. Figure 10.3 shows a sequence of time-resolved Schlieren images and TSP-derived heat flux fields in Condition A for a 15-mm-high cylinder with a height-to-radius ratio of h/r ¼ 10, where h and r are the height and radius of the cylinder, respectively. Here the heat flux fields are calculated using the analytical inverse heat transfer solution (see Eq. (8.55)). As various sequences were recorded in different experiments, the experimental times were synchronized by means of pressure measurements. Schlieren sequences with both vertical and horizontal knife-edge orientations are shown: the former reveals the presence of the bow shock upstream of the cylinder more readily, while the latter provides improved visualization of the wake phenomena as well as the upstream boundary-layer structures. At t ¼ 0.006 ms, the incident shock is visible ahead of the cylinder between x/r ¼ 7 and 5 in Schlieren images, and a corresponding increase in heat flux is observed extending to the left of the shock in TSP visualization. During the subsequent three time steps (t ¼ 0.028 ms to t ¼ 0.111 ms), the heat flux distributions show a region of enhanced heating spreading radially outwards from the cylinder as the bow shock develops ahead of the cylinder in Schlieren images. The bow shock

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Fig. 10.3 Sequences of Schlieren images and TSP-derived heat flux fields for Condition A with h/ r ¼ 10: (a, b) the vertical and horizontal density gradients visualized by Schlieren photography; (c) the instantaneous heat flux. The experimental times from the top panel to bottom panel are t ¼ 0.006, 0.028, 0.044, 0.111, 0.183, 0.228, 0.317, and 0.667 ms. (From Ozawa and Laurence 2018)

appears particularly strong in the vertical knife-edge images during this development for the cylinder with the large aspect ratio and the relatively thin laminar boundary layer. The thickening of the upstream boundary layer during this period is evidenced by a decrease in heat flux in the undisturbed region of the flow.

10.1

Small Shock Tube

349

Fig. 10.4 Instantaneous heat flux fields overlaid with main features from Schlieren images: (a) t ¼ 0.111 ms and (b) t ¼ 0.317 ms. (From Ozawa and Laurence 2018)

The heat flux field at t ¼ 0.111 ms is reproduced in the upper plot of Fig. 10.4a with some key visualized Schlieren features. The leading edge of the bow shock has propagated upstream to x/r ¼ 5.0, whereas the increase in heat flux has already extended as far as x/r ¼ 6.7. Clearly, the influence of the unsteady shock-wave/ boundary-layer interaction (SWBLI) on the wall heating extends upstream of the generating shock; the upstream surface region over which the heat flux is affected by the SWBLI is referred to as the “interaction zone.” A number of curved, streak-like features are present in the heat flux distribution around and upstream of the cylinder in this TSP image. These streaks resemble the turbulent features seen in previous measurements of the undisturbed flat-plate boundary layer (Ozawa 2016). By t ¼ 0.111 ms, the SWLBLI ahead of the cylinder is inducing the laminar-to-turbulent boundary-layer transition immediately downstream of the interaction. In Fig. 10.4a, a fan-shaped region of increased heating with curved sides extending downstream of the cylinder can be seen. Schlieren images reveal a shear layer being shed from either

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Applications of TSP

side of the rear of the cylinder, with associated separation shocks. The distance between the two shear layers reaches a minimum at the neck region lying at around x/ r ¼ 5, from which point recompression waves are generated. The spatial relationship between these waves and the fan-shaped region is illustrated in Fig. 10.4a. Just upstream of the recompression wave, a notable decrease in heat flux is observed; the heat flux then increases directly behind the recompression to reach a maximum level a short distance downstream. In Fig. 10.4b at t ¼ 0.317 ms, the global heat flux level has decreased compared to that in Fig. 10.4a. At this time, the turbulent boundary layer thickness has grown, and the decreasing temperature gradient near the wall thus results in smaller heat fluxes throughout the flow field. The effect of the SWTBLI on the upstream flow field at this time can be delineated by changes in direction of the streaks in TSP image. A notable feature in the heat flux distribution is a narrow, bow-shaped structure ahead of the cylinder (x/r ¼ 3.0), which probably reveals the presence of horseshoe vortices.

10.2

Hypersonic Wind Tunnels

Surface heat flux distributions on a waverider model at Mach 10 were measured by Liu et al. (1994b, 1995b) using EuTTA-dope TSP in the Hypervelocity Wind Tunnel No. 9 that uses pure nitrogen as the working fluid at the Naval Surface Warfare Center. The waverider model had an overall length of 39 in., a span of 16.2 in., and a base height of 6.8 in. The experiment was run at a freestream Mach number of 10, an average total pressure of 1300 psia, and an average total temperature of 1840  C. The wind tunnel run time was 2.3 s. The AoA of the model was set at 10 . The discrete Fourier law was used as a simple heat transfer model to calculate heat flux from a time sequence of TSP images. From surface heat flux fields, the laminar-turbulent transition was identified, and the movement of the transition line toward the leading edge was observed when the surface temperature increased with time. Heat flux histories obtained by TSP at selected locations were in agreement with data obtained by thermocouples. Kurits and Lewis (2009) further discussed TSP heat flux measurements in long-duration hypersonic flows in the Tunnel No. 9. Surface heat flux fields on a 25 /55 indented cone model were obtained by Hubner et al. (2002) using Ru-phen TSP in the 48-in. hypersonic shock tunnel (HST) and the LENS I tunnel facilities at the Calspan-University of Buffalo Research Center. The indented cone model had a back diameter of 0.262 m. The model was fitted with a sharp-nose cap (0.194 m long) or a blunt-nose cap (6.4 mm radius). Nominal test conditions are the Mach numbers of 9.5–11.1 and the unit Reynolds numbers of 140,000 and 300,000/m with run times less than 10 ms. TSP was applied over a white polyurethane insulating layer, and both were sprayed using conventional aerosol/airbrush equipment. The nominal TSP thickness and insulator thickness were 5–10 and 100–150 μm, respectively. TSP and an insulating layer were applied to 50% of the model for the HST tests and 25% of the model for the LENS I

10.2

Hypersonic Wind Tunnels

351

tests. A fast CCD camera system was used to acquire TSP images at 100–5000 fps, depending on the duration of a test run, the desired sampling rate, and the ability to effectively detect the emission from TSP in short exposures. Surface heat flux fields for the model with the sharp-nose cap at Mach 9.6 and Re ¼ 270,000/m in the LENS I tests showed a stabilized axisymmetric pattern associated with the separated and shock/boundary-layer interaction regions. The centerline heat flux distributions obtained by TSP were in agreement with heat-flux gauge measurements. The relative error of TSP measurements was about 15%. Hubner et al. (2001) also measured temperature distributions on an elliptic cone lifting body in short-duration hypersonic flows. Fast-responding TSP was used in the High-Enthalpy Shock Tunnel Göttingen (HEG) of DLR. HEG is a large reflected-shock wind tunnel that uses a free piston to generate the driver conditions necessary to reproduce realistic hypersonic flows in a wide range of flow conditions (Hannemann 2003; Hannemann and Martinez Schramm 2007; Martinez Schramm et al. 2004, 2017; Risius et al. 2017). Like all facilities of its type, HEG has a test duration of a few milliseconds (550 nm) was used to acquire TSP images. A typical under-expanded jet was considered, where the preheated base temperature was 45  C, the total pressure was 29 psia (200 kPa), the jet exit Mach number

10.5

Impinging Jet Heat Transfer

395

Fig. 10.54 The characteristic quantities as a function of time at the location of the maximum value and the reference location for the preheated base temperature of 45  C: (a) surface temperature, (b) heat flux, and (c) Nusselt number. (From Liu et al. 2019b)

was one, and the Reynolds number based on the nozzle diameter was 1.86  105. When a jet impinges on the surface of a preheated finite plate, the surface temperature change θps ¼ Tps  Tin is a function of time, where Tin is an initial surface temperature of the plate. Figure 10.53a shows three typical fields of θps at t ¼ 1, 3, and 5 s. The heat flux fields were calculated by applying the generalized form of Eq. (8.55) to a time sequence of surface temperature images, as shown in Fig. 10.53b. To describe the time-dependent behavior of heat transfer fields, characteristic temperatures and heat fluxes were taken at the position of the maximum temperature change and a reference location marked in Fig. 10.52b. The characteristic temperature change and heat flux at these positions are shown in Figs. 10.54a, b as a function of time, which decay with time due to heat convection to the flow. An intriguing question is whether time-dependent surface temperature could exhibit certain self-similarity. A normalized surface temperature change is introduced, i.e.,

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Fig. 10.55 The normalized surface temperature distributions across the origin at different times in Case 1, (a) profiles in the x-axis and (b) profiles in the y-axis for the preheated base temperature of 45  C. (From Liu et al. 2019b)

Fig. 10.56 The normalized surface heat transfer distributions across the origin at different times, (a) profiles in the x-axis and (b) profiles in the y-axis for the preheated base temperature of 45  C. (From Liu et al. 2019b)

b θps ðx=DÞ ¼

θps ðx, t Þ  θps ðxref , t Þ  , max θps ðx, t Þ  θps ðxref , t Þ

where xref/D ¼ (10.4, 0) is the reference location, and θps(xref, t) is a value at the reference location. The quantities at the reference location θps(xref, t) and max|θps(x, t)  θps(xref, t)| as a function of time are shown in Fig. 10.54a. Figure 10.55 shows normalized surface temperature profiles (b θps -profiles) in the x-axis and y-axis across the origin at different times in the span of 1–7 s. Interestingly, all the data collapse and the profiles become largely time-invariant. This indicates that the b θps -fields are approximately self-similar.

10.5

Impinging Jet Heat Transfer

397

Fig. 10.57 The normalized fields: (a) surface temperature, (b) heat flux, and (c) Nusselt number, where the circular mark indicates the reference location for the preheated base temperature of 45  C. (From Liu et al. 2019b)

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Similarly, a normalized heat flux field is defined as b qs ðx=DÞ ¼

qs ðx, t Þ  qs ðxref , t Þ , max jqs ðx, t Þ  qs ðxref , t Þj

where qs(xref, t) and max|qs(x, t)  qs(xref, t)| as a function of time are shown in Fig. 10.54b. As shown in Fig. 10.56, normalized heat flux profiles (b qs-profiles) in the x-axis and y-axis at different times collapse as well. The b qs -fields are approximately qs -field represent self-similar. Further, time-averaged b θps -field and b D E the more universal heat transfer distributions. Figure 10.57a, b shows the b θps -field and hb qs i T T

field, respectively, where h•iT is the time-averaging operator. Conventionally, the Nusselt number is used for impinging jet heat transfer, which is defined as Nu ¼

qs ðx, t Þ hD D ¼ , kf kf T ps ðx, t Þ  T aw

where h is a convective heat transfer coefficient, kf is the thermal conductivity of the fluid (e.g., air), D is a nozzle exit diameter, and Taw is an adiabatic wall temperature as a reference value for scaling. Here, Taw was experimentally determined from measured time histories of the surface temperature and heat flux at different locations. In a qs  Tps plot, data over a time span of 1–7 s at five randomly selected locations collapse into a near-linear curve. Therefore, extrapolating these data via the linear regression gives a value of Tps at qs ¼ 0, which is just an experimentally determined adiabatic wall temperature Taw ¼ 317.9 K in this case. The time history of Nu at the location of the maximum heat transfer is shown in Fig. 10.54c, indicating that max(Nu) changes with time much more gradually than its counterparts in the temperature and heat flux after a transient stage of the impinging jet. The normalized Nu profiles by max(Nu) in the x-axis and y-axis at different times collapse. A normalized time-averaged Nusselt number field, hNuiT/ max (Nu), is shown in Fig. 10.57c. Although hNuiT/ max (Nu) still has visible pattern associated with the impinging jet, its spatial variation is much smaller and its distribution is much more uniform compared to the corresponding normalized temperature change and heat flux fields. In this sense, the Nu-fields exhibit selfsimilarity.

Chapter 11

Extended Applications of PSP and TSP

This chapter describes extended applications of PSP and TSP to other problems. Based on the mass transfer analogy, PSP as an oxygen sensor provides a global method to determine the film cooling effectiveness on various gas turbines surfaces such as flat plate, blade surface, blade tip, endwall, and leading and trailing edges. Unsteady film cooling measurements with fast PSP are described. Skin friction is related to surface temperature, scalar concentration, and surface pressure, and the exact relations between skin friction and these quantities can be derived from the fundamental equations of fluid mechanics. Therefore, a skin friction field can be determined as an inverse problem from surface flow visualizations using TSP and PSP. Extraction of skin friction fields from TSP and PSP visualizations is demonstrated in three examples: water flow over a circular cylinder, dual colliding impinging nitrogen jets, and square junction flow. PSP can be adapted as a planar oxygen optode for global measurement of free oxygen distribution across the sediment-water interface, as demonstrated in two examples. Other applications include pressuresensitive particles for simultaneous pressure and velocity measurements, oxygen distributions in fuel cells, and thermographic phosphors to measure surface temperature fields on a piston and on a cylinder side wall of an engine.

11.1

Film Cooling Measurement Using PSP

11.1.1 Mass Transfer Analogy In gas turbines, a large difference in temperature between hot gas and blade surface results in a very significant thermal load. Advanced cooling technologies are required, including both internal cooling and external cooling of blades. Film cooling of the turbine blade is achieved by discharging coolant into the hot mainstream flow through holes drilled into internal ducts to form a cold buffer gas film, with which the blade material is protected from the hot combustion gases. Coolant © The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5_11

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Fig. 11.1 Measurement of film cooling effectiveness using (a) the heat transfer method and (b) the mass transfer method. (From Han and Rallabandi 2010)

could be a foreign gas or a mixture of a foreign gas and air. Extensive experimental studies have been made to determine the film cooling effectiveness on various surfaces such as flat plate, blade surface, blade tip, endwall, and leading and trailing edges (Han and Rallabandi 2010). The film cooling effectiveness is defined as η¼

T1  Tf , T1  TC

ð11:1Þ

where T1 is the mainstream (freestream) temperature, Tf is the film temperature, and TC is the coolant temperature. When blade material with very low conductivity is used, Tf is approximately the adiabatic wall temperature Taw. Figure 11.1a shows a typical configuration for film cooling, where a protective coolant is injected into hot mainstream. The global temperature measurement methods (IR cameras, thermochromic liquid crystals and TSP) can be used to measure surface temperature fields brought about by the temperature difference between mainstream and coolant, from which the film cooling effectiveness can be estimated. Models (blades, vanes, flat plates, etc.) are typically made of a very low heat-conducting material so that the surface is nearly adiabatic and thus the surface temperature is approximately equal to the film temperature. The cooling effectiveness in this case is referred to as the adiabatic effectiveness. When the surface temperatures are measured and the mainstream and coolant temperatures are known, the film cooling effectiveness can be directly estimated using Eq. (11.1). However, since there is no perfect adiabatic wall in reality, heat conduction into a substrate will always exists. The underlying assumption of an adiabatic wall is no longer a good approximation in regions near holes and thin edges. As a result, the application of the thermal methods could lead to significant errors in these regions. To avoid the conduction-related issues in the thermal methods, the mass transfer analogy can be used to infer the film cooling effectiveness based on mass transfer visualization on a non-penetrable surface. In this perspective, PSP as an oxygen sensor provides a useful global diagnostic tool for film cooling measurement. The PSP technique applied to film cooling was proposed by Zhang and Fox (1999) and Zhang and Jaiswal (2001), and applied to various facilities (Ahn et al. 2006, 2007;

11.1

Film Cooling Measurement Using PSP

401

Chen et al. 2015; Natsui et al. 2016; Shiau et al. 2018; Wilhelm and Schiffer 2019). A systematical review on this topic was given by Han and Rallabandi (2010). The mass transfer analogous case for film cooling is illustrated in Fig. 11.1b, where the mainstream has the gas concentration C1 and the coolant gas discharged through holes has the tracer concentration CC. The governing equation and boundary conditions for the heat transfer problem of film cooling are mathematically the same as those in the corresponding mass transfer problem. The normalized temperature and gas concentration distributions have the same solution, when the turbulent Lewis number LeT ¼ (εT + α)/(εM + D) is one, where εT and εM are the turbulent thermal and mass diffusivities, respectively, and α and D are the thermal and mass diffusivities, respectively. Therefore, the film cooling effectiveness can be expressed in terms of the concentrations, i.e., η¼

T f  T 1 T aw  T 1 C w  C1   , TC  T1 TC  T1 CC  C1

ð11:2Þ

where C1 is the mainstream gas concentration, CC is the coolant gas concentration, and Cw is the gas concentration at the non-penetrable surface. Equation (11.2) presents a mass transfer analogy to the heat transfer problem for film cooling.

11.1.2 Determining Film Cooling Effectiveness In experiments, a selected foreign gas (such as nitrogen and CO2) is injected through the film cooling holes to simulate the coolant-to-mainstream density ratio effect, which reduces the local concentration of oxygen near the wall in film cooling regions. This change in the concentration of oxygen can be detected by PSP. Equation (11.2) is re-written in a suitable form for PSP measurements, i.e., η

CO2 ,fg Cw  C 1 C O2 ,fg  C O2 ,air ¼ ¼1 , CC  C 1 C O2 ,C  CO2 ,air CO2 ,air

ð11:3Þ

where CO2 ,fg is the oxygen concentration when a foreign gas is injected, C O2 ,air is the oxygen concentration in the mainstream air flow, and C O2 ,C is the oxygen concentration in the coolant (a foreign gas) that is zero. Further, by considering the mole fractions and molecular weights of air mixed with a foreign gas, Eq. (11.3) is expressed in terms of the partial pressure of oxygen, i.e.,

1 pO2 ,air =pO2 ,R W fg η1 1þ 1 , W air pO2 ,fg =pO2 ,R

ð11:4Þ

where pO2 ,air, pO2 ,fg, and pO2 ,R are the partial pressures of oxygen in the pure air flow, air flow mixed with a foreign gas, and flow-off reference condition, respectively, and Wfg and Wair are local effective molecular weights of a foreign gas and air,

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respectively. In a special case where the molecular weight of a foreign gas is similar to that of air (e.g., nitrogen injection), Eq. (11.4) becomes η1

pO2 ,fg =pO2 ,R : pO2 ,air =pO2 ,R

ð11:5Þ

  A PSP calibration relation is generally given by I=I R ¼ f pO2 =pO2 ,R , where the I and IR are the luminescent intensities of PSP at the flow-on and flow-off conditions, respectively, after the dark current is subtracted. Therefore, the relevant quantities in Eq. (11.4) are given by   pO2 ,fg =pO2 ,R ¼ f 1 I fg =I R ,

pO2 ,air =pO2 ,R ¼ f 1 ðI air =I R Þ,

ð11:6Þ

where Iair, Ifg, and IR are the luminescent intensities of PSP in the pure air flow, air flow mixed with a foreign gas, and flow-off reference condition, respectively. To estimate the film cooling effectiveness, PSP images Iair, Ifg, and IR should be obtained in addition to the dark current image. Various examples of film cooling measurements using PSP were summarized by Han and Rallabandi (2010). Recent research has been focused on unsteady PSP film cooling measurements (Zhou et al. 2018a, b, 2019; Cai et al. 2018a, b).

11.1.3 Circular, Shaped, and Sand-Dune-Inspired Holes Zhou et al. (2018a) measured, using fast PC-PSP, the unsteady film cooling effectiveness behind three types of holes: circular hole, shaped hole, and sand-duneinspired hole. In their experiment, CO2 gas was discharged as a coolant from a single injection hole at an inclination angle of 35 . The blowing ratio (M), which is defined as the mass flux ratio of jet to cross flow, was varied from 0.40 to 1.40. The test models were made of a hard-plastic material and manufactured with a rapid prototyping machine. Figure 11.2 shows a schematic of the selected film cooling configurations: a circular hole, a shaped hole, and a Barchan dune-shaped injection compound (BDSIC) hole. A circular hole with a diameter (D) of 8.0 mm is the baseline configuration, which has an injection angle of 35 and an entry length of 5D. As shown in Fig. 11.2b, a laidback, fan-shaped hole opens 10 in the spanwise directions and 10 laidback toward the surface. In a BDSIC hole in Fig. 11.2c, the dune shell is 2.9D wide and 4.3D long in the streamwise direction from the dune leading edge to the horns. The film cooling experiments were conducted in a low-speed, suction-type wind tunnel with a 500 mm  90 mm optically transparent test section. Figure 11.3 shows the experimental setup for PSP film cooling measurements. The test plate was mounted flush along the bottom wall of the test section. A large-volume plenum chamber (150 mm  200 mm  180 mm) was installed underneath the test model for

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Film Cooling Measurement Using PSP

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Fig. 11.2 Schematic of (a) circular hole, (b) shaped hole, and (c) BDSIC film cooling configuration, where D is the diameter of coolant hole. (From Zhou et al. 2018a)

a stable and constant supply of coolant. PSP was PtTFPP as a probe luminophore in a polymer-ceramic binder. PSP was coated in the region of interest downstream of the holes. A high-power UV LED light with a wavelength of 390 nm was used as the excitation source for PSP. A high-speed CMOS camera with a band-pass filter (650  50 nm) was used to detect the luminescent emission of PSP at 500 fps. Measurements were conducted in isothermal conditions with a constant environmental temperature of 22  C. Figure 11.4 shows the measured mean cooling effectiveness and standard deviation (STD) fields for the circular hole at blowing ratios (M ) of 0.4, 0.9, and 1.4. The ensemble-averaged effectiveness results were obtained from a sequence of 15,000 instantaneous PSP images. At a blowing ratio of 0.4, the coolant stream injected from the circular hole spread downstream over the surface, and the effective cooling

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Fig. 11.3 Experimental setup used for PSP film cooling measurements. (From Zhou et al. 2018a)

reach approximately 5D downstream but disappeared suddenly due to the insufficient momentum and limited volume of the coolant gas at this low blowing ratio. The corresponding STD field exhibits much higher fluctuations along the coolant shear layer boundary where the coolant interacted intensively with the adjacent mainstream. Two strips with relatively high fluctuations are observed at the lateral edges of the circular hole, starting from around the leading edge to approximately 2D downstream. In contrast, the center region with higher cooling effectiveness has smaller fluctuations. As the blowing ratio increased to 0.9, the region with high effectiveness becomes narrower. The coolant jet separates from the test plate immediately after its injection, but it re-attaches approximately 2.5D downstream. In the corresponding STD field, two strips with significantly high fluctuations are found to spread laterally behind the coolant hole, which is related to the unsteady behaviors associated with jet separation and reattachment. Further increasing the blowing ratio to 1.4, the jet stream completely separates from the surface and penetrates into the cross-flow, leading to poor film cooling effectiveness on the surface. Figure 11.5 shows the measured ensemble-averaged effectiveness and STD fields for the shaped hole at various blowing ratios. The film cooling effectiveness values for the shaped hole are much higher than those for the circular hole, especially at relatively high blowing ratios. Due to jet diffusion along the lateral and laidback directions, a high-momentum jet would remain on the surface rather than separating the cross-flow. In the STD fields for a blowing ratio of 0.4, a high-fluctuation region

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Fig. 11.4 Measured film cooling effectiveness fields: (a) ensemble-averaged effectiveness and (b) STD distributions for the circular hole as a baseline case at various blowing ratios. (From Zhou et al. 2018a)

near the exit of the shaped hole is observed. In the cases with blowing ratios of 0.9 and 1.4, greatly intensified fluctuations are observed in the sides of the shaped holes, which are caused by the unsteady coolant shedding as it interacted with the crossflow. Figure 11.6 shows the measured mean effectiveness and STD fields for the BDSIC configuration at various blowing ratios. Compared with the circular and shaped holes, the film cooling effectiveness distributions for the BDSIC configuration exhibit wider and more uniform spreading of the coolant. Due to BDSIC’s special design, the coolant stream impinges on the inner surface of the dune shell and then discharges tangentially into the cross-flow, which significantly improves the film cooling performance. The STD fields have much smaller values than those for the circular and shaped holes at blowing ratios of 0.9 and 1.4, except in the narrow shear flow regions extending from the dune horns.

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Fig. 11.5 Measured film cooling effectiveness fields: (a) ensemble-averaged effectiveness and (b) STD distributions for the shaped hole at various blowing ratios. (From Zhou et al. 2018a)

11.2

Skin Friction Diagnostics Using PSP and TSP

11.2.1 Basic Relations Global skin friction diagnostics methods based on surface flow visualizations were discussed by Liu (2013, 2019) from a unified perspective. There are the fundamental relations between skin friction and other measurable surface quantities (e.g., temperature, scalar density, and pressure in TSP/PSP measurements), which can be derived from the relevant governing equations in fluid mechanics. Since these relations can be re-cast into a generic form of the optical flow equation in the image plane, skin friction fields can be extracted from TSP/PSP images as an inverse problem. The discussions given by Liu (2019) are recapitulated in this section. For a curved surface, the exact relations between skin friction and other measurable surface quantities were derived by Chen et al. (2019) by applying the methods of differential geometry to the governing partial differential equations in fluid

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Fig. 11.6 Measured film cooling effectiveness fields: (a) ensemble-averaged effectiveness and (b) STD distributions for the BDSIC configuration at various blowing ratios. (From Zhou et al. 2018a)

mechanics. For generality, these relations are projected onto the image plane by the orthographical transformation and written in a generic form, i.e., G þ τ  ∇g ¼ 0,

ð11:7Þ

where τ is a skin friction vector, g is a measurable quantity, and G is a source term to be modeled or approximated. Equation (11.7) represents a formal balance between ∇g projected on a skin friction vector τ and the source term G. The quantities g and G are defined differently, as described below, depending on specific surface visualization techniques used in experiments.

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Heat Transfer Visualization with TSP Global heat-transfer-based skin friction measurement methods are particularly relevant to global surface temperature measurements with TSP (Liu and Woodiga 2011; Miozzi et al. 2016, 2019; Capone et al. 2015). In this case, for a flat surface where the effect of the surface curvature is zero, the quantities g and G are defined as G ¼  μfQ and g ¼ Tw, where Tw is the surface (wall) temperature, and the source term on a surface is given by " #
   3 1 ∂ μ ∂Φ ∂ T 2 þa :  a∇ qw þ fQ ¼ k ∂t ρc ∂x3 w ∂ðx3 Þ3

ð11:8Þ

w

In Eq. (11.8), ρ, c, μ and a ¼ k/ρc are the density, specific heat, dynamic viscosity, and thermal diffusivity, respectively, Φ is the dissipation function, and qw ¼  k [∂T/∂x3]w is the surface heat flux that is positive when heat enters into fluid from a surface. The subscript w in the variables and operators denotes the quantities on a wall. Here, the coordinates on the surface are denoted by (x1, x2) and the wall-normal coordinate is denoted by x3. The term (∂/∂t  a∇2)qw in Eq. (11.8) is interpreted as a source term in a formal diffusion process of the heat flux on a surface. To extract a skin friction field from a surface temperature field, fQ should be modeled. In TSP measurement on a preheated or precooled body, a TSP layer coated on a thin basecoat on a body is considered as a composite polymer layer. A heuristic model is f Q ¼ γ ðT ref  T w Þ, where γ is an empirical heat transfer coefficient, Tw is the TSP surface temperature, and Tref is a reference temperature selected for a specific experimental arrangement (for example, temperature in a heated or cooled body). This model was used in global skin friction diagnostics using TSP (Liu and Woodiga 2011; Miozzi et al. 2016, 2019; Capone et al. 2015). Note that Lemarechal et al. (2021b) inferred skin friction based on TSP measurements using an explicit relation between skin friction and heat flux in roughness-triggered boundary layer in water.

Mass Transfer Visualization with PSP According to Liu et al. (2014, 2015), the relation between skin friction and surface scalar concentration can be derived from the binary mass diffusion equation with a source term, i.e., ∂ϕ1 =∂t þ u  ∇ϕ1 ¼ D12 ∇2 ϕ1 þ Qs , where ϕ1 ¼ ρ1/ρ is the relative concentration (density) of the species 1, ρ ¼ ρ1 + ρ2 is the total density of the binary gas (a mixture of species 1 and 2), D12 is the diffusivity

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Skin Friction Diagnostics Using PSP and TSP

409

of a binary system, and Qs is the source term. For binary mass transfer visualization with PSP, G ¼  μfM and g ¼ ϕ1, where the source term on a surface is written as fM

" #    3 ∂ ϕ1 ∂Qs ∂ 2  D12 ∇ m_ 1w þ ¼ þ D12 , D12 ρ ∂t ∂x3 w ∂ðx3 Þ3 1




ð11:9Þ

w

and m_ 1w ¼ D212ρ½∂ϕ1 =∂x3 w is the surface diffusive flux of species 1. The term ∂=∂t  D12 ∇ m_ 1w in Eq. (11.9) is interpreted as a source term in a formal diffusion process of mass flux on a surface. How to model fM depends on a specific measurement technique for species. For mass transfer visualization with PSP, a model for fM is given by   f M ¼ ρw γ m ϕ1w  ϕ1,00 , where ϕ1w and ϕ1, 00 are the values of ϕ1 at the gas-PSP interface and the PSP-solid interface, respectively, γ m ¼ 2D1p/h is a coefficient, D1p is the diffusivity of the species 1 in the polymer, and h is the PSP coating thickness.

Pressure Visualization with PSP The relation between skin friction vector and surface pressure can be derived from the Navier-Stokes equations in a general surface coordinate system (Liu et al. 2016; Chen et al. 2019). For surface pressure measurement with PSP, G ¼  μfΩ and g ¼ p, where a source term fΩ is expressed as   ∂Ω  μωw  K  ωw þ μθ ðωw  nÞ  ∇θw , fΩ ¼ μ ∂n w

ð11:10Þ

where Ω = |ω|2/2 is the enstrophy, ∂/∂n is the derivative along the wall-normal direction, ω ¼ ∇  u is the vorticity, K is the surface curvature tensor, θ = ∇  u is the dilation rate, μ is the dynamic viscosity, μθ is the longitudinal viscosity, and n is the unit normal vector of the surface. The subscript w in the variables and operators denotes the quantities on a wall. In Eq. (11.10), the first term μ[∂Ω/∂n]w is the boundary enstrophy flux (BEF), and the second term is interpreted as a curvatureinduced contribution. The term ωw  K  ωw in Eq. (11.10) is formally interpreted as the interaction between the surface curvature and the vorticity on a surface. The third term is interpreted as a contribution induced by the temporal-spatial change of the fluid density on the surface. When the Reynolds number is sufficiently large, the second term related to the surface curvature could be neglected. At a wall, the third term related to the compressibility could be neglected. Therefore, for a flat surface, fΩ is just the BEF.

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11.2.2 Variational Method Theoretically, a skin friction field can be determined by solving Eq. (11.7) as an optical flow problem (Liu and Shen 2008). By minimizing the following functional with a smoothness regularization term in an image domain D Z

Z  ðG þ τ  ∇gÞ dx1 dx2 þ α j∇τ1 j2 þ j∇τ2 j2 dx1 dx2 , 2

J ðτ Þ ¼ D

ð11:11Þ

D

the Euler-Lagrange equations are obtained, i.e., ½G þ τ  ∇g∇g  α ∇2 τ ¼ 0,

ð11:12Þ

where α is a Lagrange multiplier, and ∇ ¼ ∂/∂ xi and ∇2 ¼ ∂2/∂ xi∂ xi (i ¼ 1, 2) are the gradient operator and Laplace operator in the image plane, respectively. Given G and g, Eq. (11.12) can be solved numerically for τ ¼ (τ1, τ2) with the Neumann condition ∂τ/∂n ¼ 0 imposed on a domain boundary ∂D. Since Eq. (11.7) is valid instantaneously, unsteady skin friction fields can be extracted from unsteady surface temperature, pressure, and scalar measurements. In an error analysis, the substitution of the decompositions g ¼ g0 + δ g, G ¼ G0 + δ G, and τ ¼ τ 0 + δτ to Eq. (11.12) yields an error propagation equation, where δ g, δ G, and δτ are errors, and g0, G0, and τ 0 are the non-perturbed fields that exactly satisfy Eq. (11.7). A formal estimate of the relative skin friction error (δτ)N ¼ δτ  ΝT is (Liu 2013)
   ðδτ ÞN δG τ0 α 2 ðδτ ÞN ∇ ¼   δN T þ , kτ 0 k k∇g0 k kτ 0 k kτ 0 k kτ 0 k k∇g0 k2

ð11:13Þ

where kτ 0k is a mean value of skin friction, and NT ¼ ∇ g0/k∇g0k is the unit normal vector to an iso-value line g0 ¼ constant. The first term in the right-hand side (RHS) of Eq. (11.13) is the contribution from the elemental error in measurement of G. The second term is the contribution from the elemental error in measurement of the surface gradient of the relative intensity. The third term is the contribution from the artificial diffusion of (δτ)N associated with the Lagrange multiplier. Since the first term in the RHS of Eq. (11.13) is proportional to k∇g0k1, the relative error (δτ)N/ kτ 0k increases as k∇g0k decreases. The third term is proportional to αk∇g0k2, indicating that the Lagrange multiplier α must be sufficiently small to reduce the error particularly when k∇g0k is small.

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Skin Friction Diagnostics Using PSP and TSP

411

11.2.3 TSP-Derived Skin Friction Fields in Water Flow Miozzi et al. (2016) conducted TSP measurements on a circular cylinder in the cavitation tunnel at CEIMM (CNR-INM, formerly INSEAN at Rome, Italy), which is a closed-loop water tunnel having a 1:5.96 contraction nozzle and a 600 mm  600 mm test section. Freestream turbulence intensity and flow uniformity at the channel centerline are 1.5% and 0.4%, respectively. Figure 11.7 shows the experimental setup at the CEIMM cavitation tunnel, where UV LED lamps illuminate the TSP-coated cylinder in cross-flow, and a fast camera records images from the cylinder surface at the TSP emission wavelength (615 nm). A hollow aluminum cylinder model was used in experiments, and the cylinder diameter, length, and thickness were 36, 600, and 13.5 mm, respectively. The experiments were conducted at freestream velocity ranging from 2 to 4 m/s. The Reynolds numbers, based on the cylinder diameter and water kinematic viscosity at 25  C, ranged from 72,000 to 144,000. The cylinder was uniformly heated up by running hot water through its hollow core. TSP was coated on a white basecoat on the cylinder surface, and thus surface temperature signatures generated by flow structures were clearly visualized.

Fig. 11.7 Experimental setup at CEIMM cavitation tunnel, where UV LED lamps light up the TSP-coated cylinder in cross-flow and a fast camera records pictures from the cylinder surface at the TSP emission wavelength (615 nm). (From Miozzi et al. 2016)

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Fig. 11.8 Surface temperature field mapped onto the surface mesh of the cylinder, where the viewing position of the camera and the coordinate system are indicated. (From Miozzi et al. 2016)

A time sequence of TSP images was obtained at 1000 fps by using the CMOS camera, and temperature data on the cylinder surface were quantitatively extracted from TSP images using a TSP calibration relation. Figure 11.8 shows a surface temperature field mapped on the surface mesh of the cylinder. Figure 11.9a shows the time-averaged surface temperature image of the mid-section of the cylinder. From this surface temperature field, a skin friction field is extracted by solving the Euler-Lagrange equation, Eq. (11.12), where G ¼  μfQ and g ¼ Tw. For a heated cylinder in water flow, a model fQ ¼ γ(Tref  Tw) is used, where Tref is the body temperature of the heated cylinder, and γ is an empirical heat transfer coefficient (treated as a constant in this case). Figure 11.9b shows the extracted skin friction topology, indicating that the primary laminar flow  separation occurs at the angular position ϕ  80 and re-attachment due to transition  occurs at ϕ  95 such that a separation bubble forms. The secondary separation  occurs immediately after the re-attachment at ϕ  100 . The re-attachment and

11.2

Skin Friction Diagnostics Using PSP and TSP

413

Fig. 11.9 (a) Time-averaged surface temperature image and (b) extracted time-averaged skin friction lines. Text arrows identify the laminar separation line and the secondary turbulent re-attachment/separation sequence. Markers exactly replicate the same positions in both maps to facilitate comparison. (From Miozzi et al. 2016)

secondary separation lines are so close that they could not be clearly distinguished in surface temperature images without this image processing. Quantitative results of relative skin friction distribution along the cylinder circumference were obtained by taking the spatial average of skin friction in the spanwise direction. Figure 11.10 shows comparisons between measurement data, CFD data, and Schlichting’s solution for the laminar boundary layer (Rizzetta and Visbal 2009; Olson et al. 2015; Achenbach 1968; Schlichting 1979). All data are normalized by their maximum. The analytical solution deviates from the other data just after the maximum of skin friction is reached, while all the other profiles collapse quite well across a large part of the laminar region. Downstream of the laminar  separation line (|τ x| ¼ 0 at ϕ  80 ), the TSP-derived relative skin friction profile captures the re-attachment and secondary separation lines (here defined as the zero crossings of the main streamwise component magnitude |τ x|). Further, it is found that the re-attachment and secondary separation lines drift downstream and upstream at the vortex-shedding frequency. The unsteady high-spatial-resolution data allow a deeper analysis of the evolution of the re-attachment and secondary separation, revealing critical features in phase averaged skin friction fields (Miozzi et al. 2016).

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Fig. 11.10 Comparison of time-averaged skin-friction distributions between TSP-derived and previous data: TSP data (continuous line), Rizzetta and Visbal (2009) (circle), Olson et al. (2015) (square), Achenbach (1968) (triangle), and Schlichting (1979) ( ). (From Miozzi et al. 2016)

11.2.4 PSP-Derived Skin Friction Fields in Dual Colliding Impinging Nitrogen Jets To examine the capability of mass-transfer-based skin friction diagnostics, Liu et al. (2014) conducted PSP visualizations in dual colliding impinging nitrogen jets. Figure 11.11 shows an experimental setup. Two nitrogen jets impinged on a wall toward each other from two straight tubes with an inner diameter of 5.18 mm at an impingement angle of 30 . The nozzle-to-surface distance was 29.5 mm and the separation between the exit centers of the two tubes along the x-axis was 80 mm. The offset between the two tubes in the y-axis was adjusted to generate different flow patterns. The nitrogen jet exit velocity was 4.14 m/s. For surface mass-transfer visualization with PSP, Eq. (11.7) is re-written for the measured luminescent intensity when the flow is isothermal. The luminescent emission of PSP is related to the relative oxygen density ρ2 (the species 2) by the Stern–Volmer relation. The Stern–Volmer relation is expressed as I ref =I ¼ A þ Bðρ2 =ρ2ref Þ, ρ2 ¼ ðρ2ref =BÞðI ref =I Þ  Aρ2ref =B, where I and Iref are the luminescent intensities of PSP in the wind-on and wind-off reference conditions, respectively, A ¼ (1 + Kρ2ref)1 and B ¼ Kρ2refA are the Stern– Volmer coefficients for aerodynamics applications, and ρ2ref is the value of ρ2 at the wind-off reference condition. When nitrogen is added in flow for surface masstransfer visualization with PSP, the relative density of nitrogen (the species 1) in PSP

11.2

Skin Friction Diagnostics Using PSP and TSP

415

Fig. 11.11 Experimental setup for dual colliding impinging jets: (a) side view and (b) top view. (From Liu et al. 2014)

is ρ1 ¼ 1  ρ2. In this case, in the Euler-Lagrange equation Eq. (11.12), g ¼ Iref/I is the normalized image intensity, and G  g  Iref/I00 is the source term, where I00 is the luminescent intensity of PSP that corresponds to ρ1, 00 at the PSP-solid interface. For PSP in flow added with nitrogen, G < 0 since the concentration of nitrogen at the PSP-solid interface is smaller such that I > I00. Figure 11.12 shows the normalized PSP intensity ratio images (I/Iref) in the dual colliding impinging jets with the offsets of 0, 4, 7.5, and 11.5 mm, respectively. Skin friction fields are extracted from these images by solving Eq. (11.12). Skin friction lines are shown in Fig. 11.13. As shown in Fig. 11.13a, the impingement regions of the two head-on jets are merged such that there is only one node near the middle and the merged jet is bifurcated and deflected in the vertical direction (y-axis). When the two jets are offset by 4 mm, as visualized in Fig. 11.13b, two wall-jets are deflected at the inclination angle of about 25 relative to the y-axis. Two nodes associated with

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the impinging jets are clearly separated and a saddle occurs between them. As the offset is increased to 7.5 and 11.5 mm, the separation between the two nodes is enlarged while the saddle remains at the center between them, as shown in Fig. 11.13c, d.

11.2.5 PSP-Derived Skin Friction Field in Junction Flow Liu et al. (2016) studied the feasibility of extracting a skin friction field from a surface pressure field when a BEF field is given in a junction flow over a square cylinder. PSP measurements were conducted in the Tohoku-University Basic Aerodynamics Research Wind Tunnel. This is a suction-type wind tunnel that has a test section of a 300 mm width, a 300 mm height, and a 760 mm length. In junction flow measurements, the test model was a 3D square cylinder that had a 40 mm  40 mm cross-section and 100 mm height, as shown in Fig. 11.14. The test model was vertically mounted on a flat plate, which could be rotated by a turntable. PSP measurements were conducted mainly on the floor around the model. The freestream velocity was set at 50 m/s in PSP measurement. The incident angle relative to the freestream was set at 0 degrees for the square cylinder. The Reynolds number based on the model length was ReD ¼ 1.3  105 for the square cylinder. The local

Fig. 11.12 PSP intensity ratio images of the dual colliding impinging jets with the offsets of (a) 0, (b) 4, (c) 7.5, and (d) 11.5 mm. (From Liu et al. 2014)

11.2

Skin Friction Diagnostics Using PSP and TSP

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Fig. 11.13 Skin friction lines of the dual colliding impinging jets with the offsets of (a) 0, (b) 4, (c) 7.5, and (d) 11.5 mm. (From Liu et al. 2014) Flat plate

H 100 mm

Turn table (PSP)

230 mm W 40 mm

D 40 mm

Fig. 11.14 Schematic of the junction flow over a cylinder on a flat plate. (From Liu et al. 2016)

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Fig. 11.15 PSP and GLOF visualizations in the junction flow over a square cylinder: (a) normalized surface pressure filed obtained from PSP and (b) GLOF image. (From Liu et al. 2016)

Fig. 11.16 Skin friction and BEF fields in the junction flow over a square cylinder: (a) skin friction lines extracted from GLOF images and (b) BEF field. (From Liu et al. 2016)

Reynolds number in the boundary layer was Rex ¼ 7.8  105 for the location of the front of the cylinder at 230 mm from the flat-plate leading edge. It was confirmed by hot-wire measurement that the incoming boundary layer was laminar. Figure 11.15a shows a normalized surface pressure field obtained from PSP measurements in this junction flow. For comparison, global luminescent oil-film (GLOF) skin friction diagnostics were conducted at the same test conditions, where perylene-mixed silicone oil was used. The working principles of GLOF skin friction measurements are described by Liu et al. (2008) and Liu (2013, 2019). Figure 11.15b shows a typical GLOF image in the junction flow. Figure 11.16a shows skin friction lines extracted from GLOF images. From this extracted skin friction field and the surface pressure field obtained

11.3

Planar Oxygen Optode

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Fig. 11.17 Skin friction field extracted from the surface pressure field and BEF field in the junction flow over a square cylinder: (a) skin friction vectors and (b) skin friction lines. (From Liu et al. 2016)

using PSP, a BEF field (a fΩ-field) is reconstructed using the relation fΩ ¼ μ1τ  ∇ p. Figure 11.16b shows the BEF field reconstructed from PSP and GLOF measurements, where some subtle features are marked, particularly nulls corresponding to isolated critical points in a skin friction field. Then, from the surface pressure field and BEF field, a skin friction field is extracted by solving Eq. (11.12). Figure 11.17 shows extracted skin friction vectors and lines, which are in good agreement with the results extracted from GLOF images. The relative error in the whole measurement domain is less than 7%. Figure 11.17b shows the interesting skin friction topology on the floor surface. A saddle S1 is located upstream of the square cylinder, from which the primary necklaced separation line originated. In addition, attachment lines originated from the sides of the cylinder. The primary separation and attachment lines associated with a single large horseshoe vortex forming in the front of the cylinder. Behind the cylinder, a combination of a saddle (S2) and two spiraling sink nodes (foci) N1 and N2 are observed, which are the time-averaged on-wall footprints of the shedding wake structures.

11.3

Planar Oxygen Optode

The O2 distribution across the sediment-water interface and the benthic O2 exchange rate are key measures in benthic biogeochemistry and chemical oceanography. PSP can be adapted as a planar oxygen optode for global measurement of free oxygen distribution across the sediment-water interface. O2 images in aquatic sediments are

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Fig. 11.18 Schematic of the experimental setup. The planar optode is fixed between the sample sediment and the front window of the aquarium. The optics part is kept in the dark box. (From Oguri et al. 2006)

obtained by immobilizing O2 quenchable luminophore on a transparent support foil and placing them in sediments along the side of glass aquaria. Under excitation light applied from the outside, the emitted O2 sensitive luminescence of the foil is detected by a CCD camera. The approach makes it possible to resolve real-time temporal O2 dynamics. Planar optodes were first developed by Glud et al. (1996, 1999) and applied to various problems that were reviewed by Santner et al. (2015). For high-precision measurements in O2 depleted aquatic environments, Oguri et al. (2006) developed a planar optode system based on PtOEP and Ru(dpp)3Cl2 as oxygen sensing luminophores. Planar optodes were attached to the internal part of the front glass window of an aquarium that had an overall size of 150 mm  150 mm  10 mm and the front glass window was removable for the easy exchange of optode and sample. As shown in Fig. 11.18, the optics consisted of an excitation light source, a dichroic mirror that deflected the excitation light and guided it through the front window and a band-pass filter. Two light sources were used for excitation of the two respective luminophores. The one for PtOEP optodes consisted of 100 UV-LEDs (central wavelength of 375 nm), while the one for Ru (dpp)3Cl2 optodes consisted of 48 blue-LEDs (central wavelength of 470 nm). The dichroic mirror had a threshold of reflection/transparency between 520 and 550 nm. Band-pass filters were placed in the front of a macro-lens in order to eliminate residual nonluminescent light. For PtOEP sensors, a red filter was applied, while a red-orange filter was used for Ru(dpp)3Cl2 optodes. A multi-gateable 14-bit CCD camera was used for lifetime measurements. The image size was 1344  1024 pixels.

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Planar Oxygen Optode

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Fig. 11.19 (a) Luminescence lifetimes and (b) Stern–Volmer plots obtained from the PtOEP and Ru(dpp)3Cl2 planar optode films in seawater. (From Oguri et al. 2006)

For the preparation of PtOEP optodes, 546 mg of PtOEP and 10 g of polystyrene pellets were dissolved in 200 mL of toluene. This solution kept stable for an extensive period when stored in the refrigerator and was used as a stock solution. For the optode film fabrication, the stock solution was diluted to 50% by adding toluene and a sample was spread onto a 100 μm thick polyethylene terephthalate film using a Pasteur pipette. Subsequently, the toluene was allowed to evaporate by keeping the film at room temperature for 8 h. To eliminate any potential scattering effects on the luminescent signal and to avoid potential harmful UV-effects on biological samples, the sensor was covered by a 20 μm thick layer of black silicone elastomer. For the preparation of Ru(dpp)3Cl2 optodes, 50 mg of Ru(dpp)3Cl2 and 10 g of polystyrene pellet were dissolved in 200 mL of dichloromethane solvent. This stock solution was as stable as the aforementioned one, and prior to sensor fabrication, it was diluted to 50% by dichloromethane. The procedures for coating, drying, black silicon covering, and annealing were identical for the two sensors. For planar optode calibration, the sample seawater was collected and put in the aquarium attached with the planar optode film inside. Then, the seawater was flushed with a mixture of air/N2 gas, regulated by a valve system interactively controlled by continuously recording O2 concentration using a microelectrode sensor. At least three images at three different O2 saturation values were obtained to establish the relationship between the lifetime and O2 concentration. Because the sensor performance, especially luminescence lifetime, was changed by temperature, the calibration and further O2 imaging were carried out under the same temperature. The calibration results of the luminescent lifetime for the two planar optode sensors are presented in Fig. 11.19. The results indicate the higher dynamic range of low O2 concentrations of the PtOEP sensor. However, the sensitivity of the PtOEP sensor was gradually saturated with increasing O2 concentration, while the Ru(dpp)3Cl2 sensor had an almost linear O2 response.

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Figure 11.20 shows the O2 images obtained at the sediment-water interface of two aquaria as acquired by the two planar sensors. The images indicate the better SNR of the PtOEP-based system. The high quality of the PtOEP-derived images can also be visualized by following the O2 concentration in a non-stirred and a non-air-bubbled water face overlying an O2 consuming sediment. Figure 11.21 shows plumes of water with different O2 concentrations moved around by convection driven by evaporation and small thermal gradients at two different times. These images reflect the O2 dynamics during sediment settling and following plume dynamics in the water at every 5 min for a total of 6 h. Franke et al. (2006) applied planar oxygen optodes in a wave tank to study the influence of oxygenated pore-water flow and diffusive transport on the degradation of labile particular organic matter (POM: Ulva lactuca pieces) embedded in permeable sediment. The wave tank was filled with natural sandy sediment (median grain size 180 μm, porosity 35.2%, permeability 13.0  1012 m2) and artificial seawater (salinity 32). Sediment surface topography was created by sinusoidal waves generated at the upstream end of the wave tank using a wave paddle, as shown in Fig. 11.22a. In particular, propagating ripples were produced by adjusting the water level to a height of 19 cm above the sediment surface and the wave amplitude of 7 cm, a wavelength of 70 cm, and a frequency of 1.25 Hz. With these settings, root mean square value of the horizontal flow velocity directly above the sediment was 0.12 m/s. Two-dimensional O2 distributions were measured with a semi-transparent planar oxygen optode (14 cm wide and 10 cm high) glued to the wave tank wall by transparent silicone. The sensing layer (30 μm thick) in the optode was made from a solution containing 10 mg of PtPFPP, 490 mg polystyrene, 3 mL chloroform, and 330 mg titanium dioxide (TiO2) particles. O2 images were recorded using the luminescence lifetime imaging system. The accuracy of oxygen readings was between 2% air saturation (AS) and 7% AS in the regions of 0–10% AS and 75–100% AS, respectively. The images (640  480 pixels) covered an area of 80 mm  60 mm on the wall. The O2 images were superimposed with the sediment surface images recorded synchronously using a second CCD camera mounted on the other side of the wave tank channel, as shown in Fig. 11.22b. Steady-state O2 distributions maintained under long-term advective conditions were similar in all experiments, as shown in Fig. 11.23a, c, d. Characteristic undulating patterns of oxygen-rich pore water developed under ripple troughs and oxygen-depleted pore-water upwelling zones formed under ripple crests. Oxygen penetration was enhanced under ripple troughs (0.5–2.4 cm), and strong vertical and horizontal oxygen gradients developed. When diffusive conditions lasted for more than 4 h, oxygen was completely consumed in deeper sediment layers and its penetration was limited to the top layer (0.5–0.7 cm). Under these conditions, typical O2 distribution is shown in Fig. 11.23b. It is demonstrated in Fig. 11.23c, d that steady local zones of reduced oxygen concentrations developed at the locations of the Ulva lactuca discs as well as in the sediment downstream the discs. This was

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Fig. 11.20 Comparison between two O2 images in low oxygen concentrations: (a) image by the Ru (dpp)3Cl2 planar optode film with blue-LED excitation and (b) image by the PtOEP optode with UV-LED excitation. (From Oguri et al. 2006)

caused by the enhanced oxygen consumption at the Ulva lactuca discs, which compared in magnitude to the advective oxygen supply. In contrast, no such oxygen-reduced zones were observed in the surrounding sediment, where the oxygen consumption was relatively low.

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Fig. 11.21 O2 concentration images in the aquarium: (a) image taken at 7:00 and (b) image taken at 8:00 on June 30, 2004. (From Oguri et al. 2006)

11.4

Other Topics

11.4.1 Pressure-Sensitive Particles A question is whether PSP can be adapted for pressure measurement in 3D flow. Abe et al. (2004) developed a method for visualizing a spatial distribution of oxygen using particles coated with pressure-sensitive dye. At the same time, pressure-

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Fig. 11.22 The experimental wave tank setup. (a) Overview with locations of circular pieces of Ulva lactuca placed in the sediment in front of the semi-transparent planar O2 optode, preferably under ripple troughs (WP: wave paddle, AB: artificial beach). (b) Cross-section of the wave tank showing the setup for the simultaneous sediment surface and oxygen imaging. (From Franke et al. 2006)

sensitive particles (PS-particles) could be used as tracking particles in PIV for simultaneous pressure and velocity measurements. Porous micro-balloons in airflow PIV experiments, known as God Balls, were used. These micro-balloons, which have porous outer shells, were made of silicon dioxide. They are typically 0.5–25 μm in diameter (average 13 μm). The true density was 2.1 g/m3, and the bulk density is 0.22–0.40 g/m3, making these particles suitable for seeding into the gas flow. The pressure-sensitive dye was [Ru(bpy)32+]Cl2. The PS-particles were prepared as follows. A solution was prepared by mixing 0.10 g of [Ru(bpy)32+]Cl2 in 100 mL of ethyl alcohol (concentration: 0.0013 mol/L). The micro-balloon particles were then soaked in the solution by immersing 0.50 g of God Balls in 3.5 mL of solution. The sediment was extracted and dried. The pressure-sensitive dye infiltrated into porous holes of the God Balls. The intensity-based method for a single-luminophore sensor cannot be used in this case since no reference image is available in 3D flow. Therefore, the two-gate lifetime method was adopted. For calibration, PS-articles were scattered on a transparent glass plate to simulate particles floating in space. The relation between the two-gated intensity ratio and the oxygen fraction was obtained through this calibration experiment. Measurements of the oxygen distribution in a jet with PS-particles were conducted as a demonstration of the proposed method. The test section was filled with natural air, which was fitted with a jet nozzle with a 5-mm

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Fig. 11.23 O2 distributions maintained during the long-term degradation experiments under advection (oxic) and diffusion (anoxic) conditions, respectively. Panels a, c, and d show typical steady-state oxygen distributions under advective conditions. Panel b shows a typical steady-state oxygen distribution during long-term diffusive conditions. Circles show the positions of Ulva lactuca discs, black horizontal lines mark the sediment surface, and the arrows indicate the approximate streamlines of the pore water flow. (From Franke et al. 2006)

diameter. The nozzle was connected to the particle reservoir and nitrogen tank. The pulsed laser was applied as a laser sheet that was directed into the test section. The laser and CCD camera were synchronized by an external trigger signal produced by a pulse generator. When the laser pulse was generated at the end of the first frame, the luminescence peak image was captured at the first gated frame as a reference. Then after that, the second frame started to capture the gated image of decaying luminescence depending on the oxygen concentration. Figure 11.24 shows the two gated images IB and IA. These two images were used to determine the intensity ratio IB/IA for converting the image of the oxygen concentration by using the calibration relation. Figure 11.25 shows the oxygen density distribution obtained by the two-gate lifetime method. The estimated error was about 20%. Note that the results given by Abe et al. (2004) were just the oxygen density distributions rather than pressure distributions, but their study demonstrated the potential of the technique. Kimura et al. (2006) made polystyrene microspheres emitting both the oxygensensitive platinum porphyrin (PtOEP) luminescence and the pressure-insensitive silicon porphyrin (SiOEP) luminescence. Imaging of PS-particles in air suspensions of varying oxygen concentrations was performed in an aerosol jet. The entire plume of PS-particles was illuminated by two LED arrays, and intensity images were captured with a CCD camera. PS-particles flowed from the nozzle tip entrained

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427

Fig. 11.24 Two gated luminescent intensity images captured in the jet demonstration. (From Abe et al. 2004)

with carrier gases of varying oxygen concentrations. The entire plume of PS-particles was illuminated using two LED arrays. Two images were taken with a CCD camera through 580 and 650 nm filters. Figure 11.26 shows the ratios of the images at different oxygen concentrations.

11.4.2 Fuel Cells Inukai et al. (2008) used PSP for direct visualization of oxygen distribution in operating fuel cells. Fuel cells are devices that produce electric power by means of the chemical reaction of oxygen and fuels (usually hydrogen) as a cleaner energy source. The chemical reactions are nonhomogeneous throughout the reaction field and not well understood. A central issue in fuel cell research is the measurement of the parameters, including oxygen distribution to determine the performance of cell operation. PSP, PtTFPP in poly(1-trimethylsilyl-1-propyne) (pTMSP), was used as a thin water-insoluble dye film for oxygen visualization. Figure 11.27a schematically shows the structure of the polymer electrolyte membrane fuel cell (PEMFC) for oxygen visualization. As shown in Fig. 11.27b, the dye PSP film was coated on the oxygen channel of the separator or on a 10 mm thick plate fabricated specially of transparent polyacrylate resin. Figure 11.27c shows a photograph of the cell used in oxygen measurements. During cell operation, illumination for PSP was provided by a 407-nm laser. The laser beam was diffused, expanded, and distributed uniformly onto the separator. The emission from the dye film through the transparent separator was filtered (>600 nm), and images were captured by a CCD camera. A schematic of the imaging system is shown in Fig. 11.27d for measuring the oxygen partial pressure in a PEMFC.

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Fig. 11.25 Oxygen density distribution obtained by the two-gate lifetime method. (From Abe et al. 2004)

Fig. 11.26 PS-particle plume at different oxygen concentrations. (From Kimura et al. 2006)

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Fig. 11.27 (a) Schematic of the oxygen visualization cell, (b) transparent separator with current collectors of gold-plated metal ribs, (c) a PEMFC cell, and (d) schematic diagram of the oxygenimaging system using a dye film on transparent polyacrylate resin. Note that imaging area ¼ 10 cm  10 cm, channel width ¼ 2 mm, channel depth ¼ 1 mm, rib width ¼ 1 mm. Current collectors were separated into five sections, as outlined in red in (b). (From Inukai et al. 2008)

Figure 11.28 shows steady-state images of the oxygen partial pressures along the gas-flow channel in an operating fuel cell for overall oxygen utilizations (U O2 ) of 0%, 33%, 55%, 77%, and 90% (current density ¼ 0, 92, 153, 214, and 245 mA/cm2, respectively). One hundred and twenty-eight images were successively accumulated, and were subsequently averaged at each set of conditions. The error in the experiments was estimated to be 2% by statistical analysis of the repeated runs. As the oxygen utilization was increased (due to increasing current density), the oxygen partial pressures clearly decreased. As shown in each frame of Fig. 11.28, oxygen utilization also decreased gradually from the entrance to the exit. Figure 11.29 shows the changes in the oxygen partial pressure along the channel at various current densities (JG) and U O2 values, which were obtained directly by the visualization method (white symbols) and by calculation from the sectional currents at the five current collectors (filled red symbols). The oxygen partial pressures decreased monotonically along the channel. The oxygen partial pressures calculated from the sectional currents are higher than those measured by the visualization method. This is because that the actual distribution of water and the rate of water transport into/out of the membrane were unknown and not included in the calculations.

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Fig. 11.28 Oxygen partial pressure distributions visualized in an operating PEMFC. Cell temperature ¼ 70  C, relative humidity ¼ 50% (air and H2), air flow ¼ 500 mL/min, H2 flow ¼ 500 mL/ min, current density ¼ (a) 0, (b) 292, (c) 153, (d) 214, (e) 245, and (f) 0 mA/cm2, oxygen utilization ¼ (a) 0%, (b) 33%, (c) 55%, (d) 77%, (e) 90%, and (f) 0%. (From Inukai et al. 2008)

11.4.3 Phosphor Thermometry Someya et al. (2013) used thermographic phosphor to measure surface temperature fields on a piston and a sidewall in a cylinder of an engine under the condition of combustion. The commercially available Y2O2S:EuSm was calcined to flat quartz windows in the engine without any binding materials. A side window was set in the sidewall of a cylinder and a piston window was installed in the piston head. The diameter of the side window was 24 mm and the phosphor-coated region was 18 mm in diameter. The diameter of the piston window was 70 mm and the phosphor-coated region was 50 mm in diameter. The Y2O2S:EuSm layer on the quartz window had an average thickness of 2.5 μm. Since the thin Y2O2S:EuSm coated quartz window was transparent, intense light from combustion flames passing through the film made it impossible to directly measure the wall temperature during combustion. Therefore, an additional opaque thin film was formed by evaporating aluminum to protect and fix the phosphor material. It was less than 100 nm thick. The emission spectrum of Y2O2S:EuSm excited at 355 nm exhibited peaks at 625 and 705 nm. The emission intensity decreases with increasing temperature. Instead of the two-color method, the lifetime-based method was adopted by

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Fig. 11.29 Oxygen partial pressures measured by visualization (open symbols) and calculated from the current density (filled red symbols) for a PEMFC. (From Inukai et al. 2008)

acquiring sequential four images in a time period of 100 μs during the luminescent decay. Figure 11.30a, b shows the experimental setups for measuring the temperatures of the side window and the piston window, respectively. The engine had a fourvalve pent-roof cylinder head and a flat piston. Surface temperature measurements of a single-cylinder optical engine were performed using a high-speed camera without an image intensifier. An optical crank angle encoder allowed the camera and the laser to be synchronized relative to the engine cycle. The phosphor was obliquely illuminated by a pulsed Nd:YAG laser (355 nm) through a diffusion plate. The pulse repetition rate was 12.5 Hz. The high-speed camera (Photron Fastcam SA-X) was positioned in the front of the glass window with an optical high-pass filter that transmitted light with wavelengths over 560 nm. The camera started to record images 10 μs after excitation to cut off fluorescence and noise generated by the excitation light. The camera has an image depth of 12 bits and a spatial resolution of 512  378 at 40,000 fps. Four sequential images captured after each trigger were used to estimate the surface temperature distribution. Figure 11.31 shows instantaneous temperature distributions of the piston window for the 250–2000th cycles. The spatial resolution of temperature measurement was 410 μm. The contour lines represent intervals of 3  C. A hot spot was located where the flames directly made contact. The piston window and hot spot temperatures gradually increased. The heat of the piston was released to the piston sleeve only

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Fig. 11.30 Schematic of the experimental setup for surface temperature measurements: (a) a sidewall and (b) a piston in a cylinder of an engine. (From Someya et al. 2013)

Fig. 11.31 Measured temperature distributions on the piston window for the case of combustion at 250th, 500th, 1000th, 1500th, and 2000th cycle after starting to fire the engine. (From Someya et al. 2013)

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through the piston-ring because the piston itself had no passive cooling system in the experimental engine. The position with the highest temperature varied with time because the shape of the spreading flames and the position where the flames impinged differed in each cycle. The temperature continued to increase in the transient process after the commencement of firing. The temperature range and the temperature gradient increased for 2000 cycles.

Appendix A: Chemistry

Luminophores Here, we describe luminophores used as sensor probes for PSP and TSP. In general, the luminophores (sensor probes) absorb photons of shorter wavelengths and emit photons (luminescence) of longer wavelengths (lower frequency or energy) (Lakowicz 1983; Banwell and McCash 1994). Luminescence is classified into two types: fluorescence from the excited singlet state and phosphorescence from the excited triplet state. Phosphorescence generally has a larger Stokes shift and a longer luminescence lifetime than fluorescence. The intensity and lifetime of phosphorescence vary depending on the oxygen concentration and temperature quenching, while those of fluorescence vary only with thermal quenching. Therefore, phosphorescent and fluorescent emitters are mainly used as luminophores for PSP and TSP, respectively. However, there are some exceptions, such as pyrene and pyrene derivatives emitting excimer fluorescence for PSP and lanthanide complexes emitting phosphorescence for TSP.

PSPs As a luminophore for PSP, porphyrin derivatives (Pt2+, Pd2+), transition metal complexes (Ru2+, Os2+), cyclometalated complexes (Ir3+), and polycyclic aromatic hydrocarbons (pyrene and perylene derivative) have been commonly employed. All metalloporphyrins, transition-metal, and cyclometalated complexes are a combination of organic compounds (called ligands) and certain metals. Polycyclic aromatic hydrocarbons consist mostly of carbon, hydrogen, oxygen, or nitrogen, and some other elements. Comparing representative luminophores, platinum porphyrin (PtTFPP), ruthenium complex (Ru(dpp)32+), and pyrene derivative (PBA), PtTFPP

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 T. Liu et al., Pressure and Temperature Sensitive Paints, Experimental Fluid Mechanics, https://doi.org/10.1007/978-3-030-68056-5

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has the longest luminescence lifetime (
15 μs) at atmospheric pressure and room temperature, followed by Ru(dpp)32+ (
500 ns) and PBA (~50 ns). The difference in luminescence lifetime could affect the time response of PSP (see Chap. 7). The chemical details of luminophores as an oxygen probe are reviewed by Wolfbeis (1991), Amao (2003), Takeuchi and Amao (2005), Quaranta et al. (2012), and Wang and Wolfbeis (2014, 2016).

Porphyrin Derivatives Porphyrin derivatives are used as an oxygen sensor (Gouterman 1997). They are mainly used in combination with polymer binders. There are two types of porphyrins: metalloporphyrins and free-base porphyrins with and without central metal, respectively. Some of the porphyrin derivatives are highly sensitive to oxygen; they are generally stable compounds with a long lifetime, but some of them have low luminescent intensity at atmospheric pressure depending on the metal in the center.

Metalloporphyrins Pt and Pd are commonly used as the central metals of metalloporphyrins for PSP. In near-atmospheric pressure and room temperature conditions, porphyrins whose central metal is Pt are used. Platinum octaethylporphyrin (PtOEP) is one of the first luminophores used for wind tunnel studies (Gouterman 1997). PtOEP can be excited by visible light; it emits red light, having good pressure sensitivity. Pt fluorinated porphyrin, platinum tetrakis(pentafluorophenyl)porphine (PtTFPP) has been developed to achieve higher photostability of platinum porphyrins. As the electron-withdrawing character of the perfluorophenyl substituents of PtTFPP strongly raises the redox potentials and reduces the electron density of the porphyrin ring, PtTFPP is stable against photo-oxidation and photo-reduction (Lee and Okura 1997; Amao 2003). PtTFPP is one of the most widely used luminophores for PSP due to its high-pressure sensitivity and photostability. Platinum tetra (pentafluorophenyl)porpholactone (PtTFPL) has similar properties to PtTFPP. It has a red-shifted phosphorescent emission wavelength of 733 nm (Khalil et al. 2002, 2004), which enables a combination of PtTFPL with TSP and reference dyes that emit light at around 600–650 nm. Pd-porphyrins are also employed as a luminophore for PSP; they have a longer luminescent lifetime than Pt. Pd-based PSPs have lower pressure sensitivity and luminescent intensity near atmospheric pressure than Pt-based ones. Therefore, Pdporphyrin-based PSPs are often used in low pressure or low oxygen concentration conditions. Pt- and Pd-porphyrins can be dissolved in many organic solvents, such as toluene, dichloromethane, ethanol, and methanol, and can be embedded into various types of polymers, including siloxanes, acetylene polymers, and fluoropolymers. On the other hand, Pt and Pd tetrakis (4-carboxyphenyl) porphyrin (PtTCPP and

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PdTCPP) with a carboxyl group can be chemisorbed on anodized aluminum substrates (Kameda et al. 2004; Takeuchi and Amao 2005).

Free-Base Porphyrins Free-base porphyrins have a shorter luminescent lifetime and weaker pressure sensitivity than metalloporphyrins. However, they also show lower temperature effects and faster time response than metalloporphyrins such as PtTFPP. These can be advantages under some test conditions. H2TFPP can be immobilized in polymers, and H2TCPP with carboxyl group can be chemisorbed on anodized aluminum substrates (Amao et al. 1999a; Kameda et al. 2004; Takeuchi and Amao 2005).

Transition Metal Polypyridyl Complexes Among transition metal, polypyridyl complexes, ruthenium(II) (Ru2+) and osmium (Os2+) polypyridyl complexes are widely used for both PSP and TSP (Demas and DeGraff 1991; Demas et al. 1977, 1999; Bacon and Demas 1987; Carraway et al. 1991a, b; Sacksteder et al. 1993; Xu et al. 1994, 1996; Klimant and Wolfbeis 1995; Amao 2003; Takeuchi and Amao 2005). While Ru2+ polypyridyl complexes have absorption and emission peaks around 460 and 610 nm, respectively, Os2+ complexes have intense red absorptions and emit phosphorescence around 730 nm (Xu et al. 1996). Generally, these complexes are quite photostable, and many of them have a very intense emission at low temperatures, and they can be used for cryogenic measurements. On the other side, they are mostly inorganic salts and are insoluble in common nonpolar solvents such as toluene and hexane. Therefore, the polymers that can incorporate these dyes are limited. Poly(DMS) is one of the possible polymers for Ru2+ and Os2+ complexes. Xu et al. (1996) reported various oxygen sensors with various Ru2+ and Os2+ complexes immobilized in poly(DMS) film. Also, they are well physically adsorbed on anodized aluminum substrates and form AA-PSP. Ruthenium complex-based AA-PSPs are often used for unsteady and cryogenic measurements. Ru(dpp)32+, known as Bathophen-ruthenium, shows good pressure sensitivity on AA, silicone, or silica-gel, but exhibits a relatively hightemperature dependency. Ru(bpy)32+ also is used as a PSP with silica-gel (Burns 1995).

Cyclometalated Iridium and Complexes Cyclometalated iridium complexes such as Ir(ppy)3 are widely used as organic EL light-emitting dyes due to their high luminescent intensity and photostability (Amao et al. 2001; Amao 2003; Gao et al. 2002; Borisov and Klimant 2007; Fischer et al. 2009; Wang and Wolfbeis 2014). Many iridium complexes have been developed, exhibiting a wide color range of luminescence from blue to red, whereas Ru(dpp)32+

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and PtTFPP emit red light. Therefore, iridium complexes that emit blue or green light are possibly combined with TSP and reference dyes that emit red or green light. Iridium tris(2-phenylpyridine anion) (Ir(ppy)3), a typical iridium complex, is soluble in organic polymers, displaying strong green light (512 nm) with high quantum efficiency (Amao et al. 2001; Amao 2003). Ir(ppy)3 in the styrene-TFEM-copolymer film has outstanding sensitivity for oxygen (Amao et al. 2001). Mak et al. (2009) also reported the high sensitivity of Ir(ppy-NPh2)3 immobilized in the ethylcellulose matrix on changes of oxygen partial pressure.

Polycyclic Aromatic Compounds Polycyclic aromatic compounds mainly consist of carbon and hydrogen. As a luminophore for PSP, pyrene and pyrene derivatives are well employed (Fonov et al. 1998; Mébarki 1998; Engler et al. 2002; Le Sant and Merienne 2005; Kameda et al. 2004; Klein et al. 2005; Basu et al. 2003, 2005, 2009; Basu and Rajam 2004). They offer a wide variety of synthetic transformations to obtain many new compounds with potential pressure sensitivity. The basic luminophore, pyrene, absorbs UV light (
340 nm) and emits blue light. Pyrene emits monomer luminescence around 400 nm alone and excimer luminescence around 480 nm when two molecules are in close proximity. The luminescence of pyrene of excimer state is called excimer fluorescence. Pyrene exhibits low-temperature dependency and high-pressure sensitivity. As the temperature increases, the luminescent intensity from the monomer peak increases, and that of the excimer peak decreases. Therefore, the wavelength range between the monomer and excimer peaks provides almost zero temperature sensitivity. On the other side, pyrene suffers from photodegradation and sublimation. It causes changes in the luminescent intensity and spectral distribution (Mébarki 1998; Basu et al. 2003, 2009). The photodegradation and sublimation of pyrene can be improved by adding appropriate side chains to the pyrene. In general, it is quite challenging to predict the influence of any substituents on the pressure sensitivity of pyrene molecules. Pyrene and pyrene derivatives applied to an anodized aluminum substrate show highpressure sensitivity. They show only small pressure sensitivity in the polymer matrix, except for silicone resins. Engler et al. (2002) reported that pyrene derivatives showed high-pressure sensitivity in poly(DMS). Basu et al. (2009) developed a stable PSP formulation in which pyrene was covalently bonded to the polymer binder to prevent degradation. It showed high-pressure sensitivity of 0.7%/kPa and low-temperature sensitivity of