This book contains a thorough and unique record of recent advances in the important scientific fields fluid–structure in

*250*
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*26MB*

*English*
*Pages 395
[381]*
*Year 2021*

- Author / Uploaded
- Marianna Braza
- Yannick Hoarau
- Yu Zhou
- Anthony D. Lucey
- Lixi Huang
- Georgios E. Stavroulakis

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- Mechanical Engineering

*Table of contents : PrefaceContentsSimulating the Dynamics of Primary Cilium in Pulsatile Flow by the Immersed Boundary-Lattice Boltzmann Method 1 Introduction 2 Mathematical Formulation and Numerical Method 3 Results and Discussion 3.1 Dynamics of Primary Cilium at Various Peak Reynolds Number 3.2 Effect of Womersley Number on the Cilium Dynamics 4 Conclusions ReferencesThe POD Analysis of Screech Tone in Low Mach Number Axisymmetric Supersonic Jet 1 Introduction 2 Computational Details 3 Proper Orthogonal Decomposition 4 Numerical Results and Analysis 4.1 Screech Tone's Frequency and Sound Pressure Level 4.2 POD Analysis of Fluctuating Velocity Field 5 Conclusion ReferencesDirect Numerical Simulations of Self-sustained Oscillations in Two-Dimensional Rectangular Cavity 1 Introduction 2 Numerical Simulations 2.1 Flow Configuration 2.2 Numerical Methods 3 Results and Analysis 3.1 Acoustic Field 3.2 Dynamic Mode Decomposition 3.3 Frequencies of Oscillation 4 Conclusion ReferencesEnergy Harvesting Using a Tensioned Membrane with a Spring-Mounted Trailing Edge in Axial Flow 1 Introduction 2 Experimental Design 3 Results 4 Conclusions ReferencesInteraction of Flow with a Surface-Mounted Flexible Fence 1 Introduction 2 Problem Description and Methodology 3 Results and Discussion ReferencesExperimental Study of a Passive Control of Airfoil Lift Using Bioinspired Feather Flap 1 Introduction 2 Experimental Details 3 Results and Discussion 4 Conclusions ReferenceTapered-Cantilever Based Fluid-Structure Interaction Modelling of the Human Soft Palate 1 Introduction 2 Methodology 3 Results and Discussion 4 Conclusions ReferencesBroadband Noise Absorber with Piezoelectric Shunting 1 Introduction 2 Theoretical Approach 3 Results and Discussion 4 Conclusions ReferencesSolid-Fluid Interaction in Path Instabilities of Sedimenting Flat Objects 1 Introduction 2 Some Examples of Co-existing States with Strong and Weak Solid-Fluid Interaction 3 Discussion and Conclusion ReferencesAerodynamic and Aero-acoustics Performance of Unsteady Kinematics Applied to a Rotor Operating at Low-Reynolds Number 1 Introduction 2 Test Case and Numerical Method 3 Modelling of the Unsteady Aerodynamic Performance 4 Aero-acoustic Performance 5 Conclusion ReferencesFree-End Mean Pressure Distribution for a Finite Cylinder: Effect of Aspect Ratio 1 Introduction 2 Experimental Approach 3 Results and Discussion 4 Conclusions ReferencesA Static Aeroelastic Analysis of an Active Winglet Concept for Aircraft Performances Improvement 1 Introduction 2 Models and Work Description 2.1 Aerodynamic and Structural Models 2.2 Work Description 3 Results 4 Conclusion ReferencesExperimental Study of the Effect of a Steady Perimetric Blowing at the Rear of a 3D Bluff Body on the Wake Dynamics and Drag Reduction 1 Introduction 2 Experimental Setup 3 Results 4 Conclusion ReferencesInfluence of Gap Width on Fluid–Structure Interaction for a Cylinder Cluster in Axial Flow 1 Introduction 2 Experimental Details 3 Results and Discussion 4 Conclusions ReferencesSkin-Friction Drag Reduction Using Micro-Grate Patterned Superhydrophobic Surface 1 Introduction 2 Experimental Details 3 Results and Discussion 4 Conclusions ReferencesSinuous and Varicose Modes in Turbulent Flow Through a Compliant Channel 1 Introduction 2 System Modelling 3 Results and Discussion 4 Conclusions ReferencesShape Optimization Considering the Stability of Fluid–Structure Interaction at Low Reynolds Numbers 1 Introduction 2 Numerical Methods 2.1 FSI Simulation 2.2 Calculation of Plunge-Damping Coefficient 3 Shape Optimization 3.1 Optimization Description 3.2 Results and Analysis 4 Conclusions ReferencesAerodynamic Sound Identification of Longitudinal Vortex System 1 Introduction 2 Experimental Approach 3 Numerical Approach 4 Results and Discussion 5 Conclusions ReferencesImpulsive Start-Up of a Deformable Flapping Wing at Different Angular Conditions 1 Introduction 2 Experimental Procedures 2.1 Setup 2.2 Data Processing 3 Results 4 Conclusion ReferencesThe Passive Separation Control of an Airfoil Using Self-Adaptive Flap 1 Introduction 2 Numerical Method 3 Results and Discussion 3.1 Flow Over a Naca0012 Airfoil 3.2 Flow Over a Naca0012 Airfoil with a Rigid Flap 3.3 Flow Over a Naca0012 Airfoil with a Flexible Flap 4 Conclusions ReferencesDesign of Blown Flap Configurations Based on a Multi-element Airfoil 1 Introduction 2 Aerodynamic Optimization of a Blown Flap Based on a Three-Element Airfoil 2.1 Optimization Settings 2.2 Optimization Results 3 Conclusion ReferencesAdded Masses of Cylinders of Different Shapes 1 Introduction 2 Experimental Details 3 Results and Discussion 4 Conclusions ReferencesRecognition Location Method of Sound Source Based on Rotating Microphones 1 Introduction 2 Theory 3 Numerical Simulation 4 Experimental Validation 5 Conclusion ReferencesPerformance Optimization of Microphone Array Beamforming Based on Multi-circular Ring Microphone Arrays Combination 1 Introduction 2 Theory 3 Simulation 4 Conclusion ReferencesThe Aeroacoustic Effect of Different Inter-Spaced Self-oscillating Passive Trailing Edge Flaplets 1 Introduction 2 Experimental Arrangement 3 Results 4 Conclusion ReferencesCircular Jet with Annular Backflow Using DBD Plasma Actuator 1 Introduction 2 Experimental Details 3 Results and Discussion 3.1 Initial Condition 3.2 Flow Structure 4 Conclusions ReferencesInvestigation of the Asymmetric Wake Mode of a Three-Dimensional Square-Back Bluff Body 1 Introduction 2 Experiment and Numerical Simulation Set up 3 Results 3.1 Mean Flow Field 3.2 Instantaneous Back Pressure and Side Aerodynamic Force 3.3 Instantaneous Flow Fields 3.4 Proper Orthogonal Decomposition Analysis 4 Conclusion ReferencesMechanisms of the Aerodynamic Improvement of an Airfoil Controlled by Sawtooth Plasma Actuator 1 Introduction 2 Experimental Details 3 Results and Discussion 4 Conclusions ReferencesAerodynamic Performance of a Sedan Under Wind-Bridge-Tunnel Road Condition 1 Introduction 2 Numerical Method 2.1 Geometric Model 2.2 Governing Equation 3 Computational Setup 4 Results and Discussions 5 Conclusions ReferencesVortex-Induced Vibration of a Circular Cylinder at High Reynolds Number 1 Introduction 2 Results and Discussion 3 Conclusions ReferencesNumerical Studying the Dynamic Stall of Reverse Flow Past a Wing 1 Introduction 2 Effects of Turbulence Models 3 Dynamic Stall Process 4 Conclusions ReferencesDrastic Changes of Turbulence in the Ignition Process of an n-Heptane/Air Mixture 1 Introduction 2 DNS of the Ignition Process of a Compressed n-Heptane/Air Mixture 3 Results ReferencesVisualization Observation of Two Phase Flow in Abrasive Supply Tube for Abrasive Injection Jet 1 Introduction 2 Experimental Apparatus and Method 3 Results and Discussion 3.1 Variation of Air Flow Rate in Abrasive Supply Tube 3.2 Flow Pattern and Velocity Distribution of Abrasive Particles 3.3 Frequency of Abrasive Dense Zone Formation at Different Positions 4 Conclusions ReferenceVortex Induced Vibrations With Bi-stable Springs 1 Introduction 2 Wake Oscillator Model (WOM) 3 Results from WOM Simulations 4 Theory: Predicting Lock-In Range for VIV 4.1 ``Equilibrium Constraint'' for VIV 4.2 Intersection of EC with Natural Frequency Curves 5 Results from CFD Simulations 6 Conclusion ReferencesImpact of Optimized Trailing Edge Shapes on Noise Generation 1 Introduction 2 Numerical Methodology 3 Results of the Optimization 4 Acoustic Evaluation 5 Summary and Outlook ReferencesCamber Setting of a Morphing Wing with Macro-acuator Feedback Control 1 Introduction 2 Large Scale Prototype for Morphing Flap Description 2.1 Technical Specifications 2.2 Proposed Solution 2.3 Actuation System: EMA 3 Modelling of the System and Feedback Control Design 4 Conclusion ReferencesA Hybrid Dual-Grid Level-Set Based Immersed Boundary Method for Study of Multi-phase Flows with Fluid–Structure Interactions 1 Introduction 2 Dual-Grid Level-Set Based Immersed Boundary Method 2.1 Implementation of BC at the Solid-Fluid Interface 2.2 Validation Test: Water Entry Problem 3 Conclusion ReferencesClosed-Loop Drag Reduction Over a D-Shaped Body Via Coanda Actuation 1 Introduction 2 Experimental Setup 3 Results 4 Conclusion ReferencesEffect of Mass Ratio on Inline Vortex Induced Vibrations at a Low Reynolds Number 1 Introduction 2 Computational Methodology 3 Results and Discussion 4 Conclusions ReferencesAnalysis of Turbulent Entrainment in Separating/Reattaching Flows 1 Introduction 2 Experimental Set-Up 3 Results and Discussion 4 Conclusions ReferencesDamped Oscillations of Spherical Pendulums 1 Introduction 2 Experimental Setup and Procedure 3 Results and Discussion 4 Conclusions ReferenceFlow Structures in the Initial Region of a Round Jet with Azimuthally Deformed Vortex Rings Utilizing a Sound Wave 1 Introduction 2 Experimental Apparatus and Methods 3 Experimental Results 4 Conclusions ReferenceStructure Generated Turbulence: Laminar Flow Through Metal Foam Replica 1 Introduction 2 Experimental Setup 3 Results and Discussion 4 Conclusions ReferencesDynamics of a Cambered A320 Wing by Means of SMA Morphing and Time-Resolved PIV at High Reynolds Number 1 Introduction 2 Prototype Description 3 Experimental Set-Up 4 Results 4.1 POD Analysis 4.2 Reconstruction from POD Modes 5 Conclusion ReferencesDesign and Experimental Validation of A320 Large Scale Morphing Flap Based on Electro-mechanical Actuators 1 Introduction 2 Design of Morphing Flap 2.1 Camber Control Principle, Specifications and Objectives 2.2 Actuation System Design 3 Preliminary Aerodynamic Results for the Fixed Configuration 3.1 Mean Pressure Measurements 3.2 Unsteady Pressure Measurements 4 Conclusion ReferencesManipulation of a Shock-Wave/Boundary-Layer Interaction in the Transonic Regime Around a Supercritical Morphing Wing 1 Introduction 2 Numerical setup 3 Results 3.1 Effect of Morphing on the Force Coefficients 3.2 Frequency Synchronization 3.3 Time-Averaged Force Coefficients at Various Actuation Frequencies 3.4 Comparison of Mean Velocity Profiles in the Wake 4 Conclusions ReferencesPredictive Numerical Study of Cambered Morphing A320 High-Lift Configuration Based on Electro-Mechanical Actuators 1 Introduction 2 Computational Methodology 3 Numerical Results 4 Conclusion ReferencesShape Control of Flexible Structures for Morphing Applications 1 Introduction 2 Formulation of the Problem 3 Numerical Examples and Discussion 4 Conclusions ReferencesContinuous Adjoint for Aerodynamic-Aeroacoustic Optimization Based on the Ffowcs Williams and Hawkings Analogy 1 Introduction 2 The CFD/FW-H Solver 3 The Continuous Adjoint Method 4 Verification of the Hybrid CFD/FW-H Solver 5 Optimization Results 6 Conclusions ReferencesOn Boundary Conditions for Compressible Flow Simulations 1 Introduction 2 Complex Mapping 2.1 Plane-Wave Solutions 3 Application Case: Hole-Tone Configuration 4 Conclusion ReferencesLarge-Eddy Simulation on Jet Mixing Enhancement Using Unsteady Minijets 1 Introduction 2 Numerical Method 3 Results and Discussion 4 Conclusion ReferencesMixing Characteristics of a Flapping Jet of Self-Excitation Due to a Flexible Film 1 Introduction 2 Experimental Description 3 Results and Discussion 4 Conclusion ReferencesFlow-Induced Vibration Characteristics of a Fix-Supported Elastic Wing 1 Introduction 2 Experiment Details 3 Results and Discussion 4 Conclusions ReferencesOn the Transient Effects Induced by Jet Actuation Over an Airfoil 1 Introduction 2 Experimental Details 3 Results and Discussion 3.1 Time-Averaged Control Effects 3.2 Transient Effects 4 Conclusion and Perspectives ReferencesArtificial Intelligence Control of a Turbulent Jet 1 Introduction 2 Experimental Details 3 Artificial Intelligence Control 3.1 Control Problem and Benchmark Actuations 3.2 Control Optimization Using Linear Genetic Programming 4 Results and Discussions 5 Conclusions ReferencesTurbulent Friction Drag Reduction: From Feedback to Predetermined, and Feedback Again 1 Introduction 2 Predetermined Control 2.1 Streamwise Traveling Wave 2.2 Uniform Blowing 3 Feedback Control Again 4 Toward the Future References*

Lecture Notes in Mechanical Engineering

Marianna Braza · Yannick Hoarau · Yu Zhou · Anthony D. Lucey · Lixi Huang · Georgios E. Stavroulakis Editors

Fluid-StructureSound Interactions and Control Proceedings of the 5th Symposium on Fluid-Structure-Sound Interactions and Control

Lecture Notes in Mechanical Engineering Series Editors Francisco Cavas-Martínez, Departamento de Estructuras, Universidad Politécnica de Cartagena, Cartagena, Murcia, Spain Fakher Chaari, National School of Engineers, University of Sfax, Sfax, Tunisia Francesco Gherardini, Dipartimento di Ingegneria, Università di Modena e Reggio Emilia, Modena, Italy Mohamed Haddar, National School of Engineers of Sfax (ENIS), Sfax, Tunisia Vitalii Ivanov, Department of Manufacturing Engineering Machine and Tools, Sumy State University, Sumy, Ukraine Young W. Kwon, Department of Manufacturing Engineering and Aerospace Engineering, Graduate School of Engineering and Applied Science, Monterey, CA, USA Justyna Trojanowska, Poznan University of Technology, Poznan, Poland

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Engineering Design Machinery and Machine Elements Mechanical Structures and Stress Analysis Automotive Engineering Engine Technology Aerospace Technology and Astronautics Nanotechnology and Microengineering Control, Robotics, Mechatronics MEMS Theoretical and Applied Mechanics Dynamical Systems, Control Fluid Mechanics Engineering Thermodynamics, Heat and Mass Transfer Manufacturing Precision Engineering, Instrumentation, Measurement Materials Engineering Tribology and Surface Technology

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More information about this series at http://www.springer.com/series/11236

Marianna Braza · Yannick Hoarau · Yu Zhou · Anthony D. Lucey · Lixi Huang · Georgios E. Stavroulakis Editors

Fluid-Structure-Sound Interactions and Control Proceedings of the 5th Symposium on Fluid-Structure-Sound Interactions and Control

Editors Marianna Braza Institut de Mécanique des Fluides de Toulouse UMR 5502 CNRS - INPT - UT3 Toulouse, France Yu Zhou Centre for Turbulence Control Harbin Institute of Technology (Shenzhen) Shenzhen, China Lixi Huang Department of Mechanical Engineering Zhejiang Institute of Research and Innovation The University of Hong Kong Hong Kong, China

Yannick Hoarau Laboratoire ICube CNRS UMR 7357 University of Strasbourg Strasbourg, France Anthony D. Lucey School of Civil and Mechanical Engineering Curtin University Perth, WA, Australia Georgios E. Stavroulakis School of Production Engineering and Management Technical University of Crete Chania, Greece

ISSN 2195-4356 ISSN 2195-4364 (electronic) Lecture Notes in Mechanical Engineering ISBN 978-981-33-4959-9 ISBN 978-981-33-4960-5 (eBook) https://doi.org/10.1007/978-981-33-4960-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 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 Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface

The present volume is a selection of peer-reviewed extended contributions after the 5th Symposium on Flow-Structure-Sound Interactions and Control (FSSIC) held from 27 to 30 August 2019 at the Minoa Palace Resort in Chania, Crete Island, Greece, www.smartwing.org/FSSIC2019. The symposium was attended by 125 participants amongst most renowned scientists in the field worldwide and comported three keynote and eight plenary lectures. The present volume largely focuses on advances in the theory, experiments, and numerical simulations of turbulence in the contexts of flow-induced vibration, noise and their control. This includes important practical areas of interaction, such as the aerodynamics of road and space vehicles, marine and civil engineering and nuclear reactors and biomedical science. One of the special features of this book is that it integrates acoustics with the study of flow-induced vibration, which is not common practice but is scientifically very helpful in understanding, simulating and controlling fluid–structure–sound interaction systems. This offers a broader view of the discipline from which readers will benefit greatly. Turbulence clearly has a significant impact on many such problems. On the other hand, new possibilities are emerging with the advent of various new science and technologies such as signal processing, flow visualisation and diagnostics, new functional materials, sensors and actuators, machine learning and artificial intelligence. These have enhanced interdisciplinary research activities, and it is in this context that the 5th Symposium on Fluid-Structure-Sound Interactions and Control (FSSIC) was organised. The meeting provided a forum for academics, scientists and engineers working in all related branches to exchange and share the latest progress, ideas and advances—having brought them together from both East and West to chart the frontiers of FSSIC. A general outcome was that the participants learned much from one another, and this meeting brought new research ideas and new interdisciplinary concepts in FSSIC field. The editors acknowledge the contribution of Dr. Abderahmane Marouf for the creation and maintenance of the FSSIC2019 symposium website as well as for the full papers final editing in the present volume. They acknowledge the contribution of Drs. Jan Vos and Dominique Charbonnier for the symposium logistics and express v

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Preface

warm thanks to the team of the Technical University of Crete and to the staff of Minoa Palace Resort for the local organisation.

Toulouse, France Strasbourg, France Shenzhen, China Perth, Australia Hong Kong, China Chania, Greece

Marianna Braza Yannick Hoarau Yu Zhou Anthony D. Lucey Lixi Huang Georgios E. Stavroulakis

Contents

Simulating the Dynamics of Primary Cilium in Pulsatile Flow by the Immersed Boundary-Lattice Boltzmann Method . . . . . . . . . . . . . . . Jingyu Cui, Yang Liu, Xiao Lanlan, and Chen Shuo

1

The POD Analysis of Screech Tone in Low Mach Number Axisymmetric Supersonic Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hu Li, Yong Luo, and Shuhai Zhang

9

Direct Numerical Simulations of Self-sustained Oscillations in Two-Dimensional Rectangular Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yong Luo, Hu Li, Shuaibin Han, and Shuhai Zhang

19

Energy Harvesting Using a Tensioned Membrane with a Spring-Mounted Trailing Edge in Axial Flow . . . . . . . . . . . . . . . . . . T. X. Chin, R. M. Howell, and A. D. Lucey

27

Interaction of Flow with a Surface-Mounted Flexible Fence . . . . . . . . . . . A. Tsipropoulos and E. Konstantinidis

33

Experimental Study of a Passive Control of Airfoil Lift Using Bioinspired Feather Flap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. J. Wang, Md. Mahbub Alam, and Yu Zhou

39

Tapered-Cantilever Based Fluid-Structure Interaction Modelling of the Human Soft Palate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. Cisonni, A. D. Lucey, and N. S. J. Elliott

45

Broadband Noise Absorber with Piezoelectric Shunting . . . . . . . . . . . . . . . Xiang Liu, Chunqi Wang, and Lixi Huang Solid-Fluid Interaction in Path Instabilities of Sedimenting Flat Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jan Dušek, Wei Zhou, and Marcin Chrust

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Aerodynamic and Aero-acoustics Performance of Unsteady Kinematics Applied to a Rotor Operating at Low-Reynolds Number . . . Nicolas Gourdain, Antonio Alguacil, and Thierry Jardin

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Free-End Mean Pressure Distribution for a Finite Cylinder: Effect of Aspect Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adam Beitel and David Sumner

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A Static Aeroelastic Analysis of an Active Winglet Concept for Aircraft Performances Improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Martin Delavenne, Bernard Barriety, Fabio Vetrano, Valérie Ferrand, and Michel Salaun

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Experimental Study of the Effect of a Steady Perimetric Blowing at the Rear of a 3D Bluff Body on the Wake Dynamics and Drag Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manuel Lorite-Díez, José Ignacio Jiménez-González, Carlos Martínez-Bazán, Luc Pastur, and Olivier Cadot

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Influence of Gap Width on Fluid–Structure Interaction for a Cylinder Cluster in Axial Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Wang, C. W. Wong, W. Xu, and Yu Zhou

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Skin-Friction Drag Reduction Using Micro-Grate Patterned Superhydrophobic Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zhang Bingfu, Tang Hui, and To Sandy

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Sinuous and Varicose Modes in Turbulent Flow Through a Compliant Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Konstantinos Tsigklifis and A. D. Lucey Shape Optimization Considering the Stability of Fluid–Structure Interaction at Low Reynolds Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 W. G. Chen, W. W. Zhang, and X. T. Li Aerodynamic Sound Identification of Longitudinal Vortex System . . . . . 113 Shigeru Ogawa, Hiroki Ura, Takehisa Takaishi, Hiroki Okada, Kota Samura, Harutaka Honda, and Kohei Suzuki Impulsive Start-Up of a Deformable Flapping Wing at Different Angular Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 Daniel Diaz, Thierry Jardin, Nicolas Gourdain, Frédéric Pons, and Laurent David The Passive Separation Control of an Airfoil Using Self-Adaptive Flap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Zhe Fang, Chunlin Gong, Alistair Revell, Gang Chen, Adrian Harwood, and Joseph O’Connor

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Design of Blown Flap Configurations Based on a Multi-element Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Yuhui Yin, Yufei Zhang, and Haixin Chen Added Masses of Cylinders of Different Shapes . . . . . . . . . . . . . . . . . . . . . . 139 Guanghao Chen, Md. Mahbub Alam, and Yu Zhou Recognition Location Method of Sound Source Based on Rotating Microphones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Xie Zheng, Xunnian Wang, Jun Zhang, Kun Zhao, Zhengwu Chen, Yong Wang, and Ben Huang Performance Optimization of Microphone Array Beamforming Based on Multi-circular Ring Microphone Arrays Combination . . . . . . . 153 Xunnian Wang, Xie Zheng, Jun Zhang, Kun Zhao, Zhengwu Chen, and Ben Huang The Aeroacoustic Effect of Different Inter-Spaced Self-oscillating Passive Trailing Edge Flaplets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Edward Talboys, Thomas F. Geyer, Florian Prüfer, and Christoph Brücker Circular Jet with Annular Backflow Using DBD Plasma Actuator . . . . . . 167 Norimasa Miyagi and Motoaki Kimura Investigation of the Asymmetric Wake Mode of a Three-Dimensional Square-Back Bluff Body . . . . . . . . . . . . . . . . . . . . . 173 Yajun Fan, Chao Xia, Diandian Ge, and Zhigang Yang Mechanisms of the Aerodynamic Improvement of an Airfoil Controlled by Sawtooth Plasma Actuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181 L. J. Wang, C. W. Wong, W. Q. Ma, and Yu Zhou Aerodynamic Performance of a Sedan Under Wind-Bridge-Tunnel Road Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Qianwen Zhang, Chuqi Su, and Yiping Wang Vortex-Induced Vibration of a Circular Cylinder at High Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193 Tulsi Ram Sahu, Gaurav Chopra, and Sanjay Mittal Numerical Studying the Dynamic Stall of Reverse Flow Past a Wing . . . 199 Biao Wang and Zhixiang Xiao Drastic Changes of Turbulence in the Ignition Process of an n-Heptane/Air Mixture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 Takashi Ishihara and Ryousuke Kuno Visualization Observation of Two Phase Flow in Abrasive Supply Tube for Abrasive Injection Jet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211 Y. Oguma, T. Takase, H. Quan, and G. Peng

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Vortex Induced Vibrations With Bi-stable Springs . . . . . . . . . . . . . . . . . . . . 217 Rameez Badhurshah, Rajneesh Bhardwaj, and Amitabh Bhattacharya Impact of Optimized Trailing Edge Shapes on Noise Generation . . . . . . . 223 F. Kramer, M. Fuchs, T. Knacke, C. Mockett, E. Özkaya, N. Gauger, and F. Thiele Camber Setting of a Morphing Wing with Macro-acuator Feedback Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 A. Giraud, Cédric Raibaudo, Martin Cronel, Philippe Mouyon, Ioav Ramos, and Carsten Doll A Hybrid Dual-Grid Level-Set Based Immersed Boundary Method for Study of Multi-phase Flows with Fluid–Structure Interactions . . . . . . 237 Sagar Mehta, Amitabh Bhattacharya, and Atul Sharma Closed-Loop Drag Reduction Over a D-Shaped Body Via Coanda Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243 Tamir Shaqarin, Philipp Oswald, Richard Semaan, and Bernd R. Noack Effect of Mass Ratio on Inline Vortex Induced Vibrations at a Low Reynolds Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249 Dániel Dorogi, László Baranyi, and E. Konstantinidis Analysis of Turbulent Entrainment in Separating/Reattaching Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255 Nicolas Mazellier, Francesco Stella, and Azeddine Kourta Damped Oscillations of Spherical Pendulums . . . . . . . . . . . . . . . . . . . . . . . . 261 Herricos Stapountzis, Ioanna Lichouna, Violetta Koumoukeli, and Margarita Stapountzi Flow Structures in the Initial Region of a Round Jet with Azimuthally Deformed Vortex Rings Utilizing a Sound Wave . . . . . . 267 Akinori Muramatsu and Kohei Tanaka Structure Generated Turbulence: Laminar Flow Through Metal Foam Replica . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 275 Chanhee Moon and Kyung Chun Kim Dynamics of a Cambered A320 Wing by Means of SMA Morphing and Time-Resolved PIV at High Reynolds Number . . . . . . . . . . . . . . . . . . . 283 Mateus Carvalho, Cédric Raibaudo, Sébastien Cazin, Moïse Marchal, G. Harran, Clément Nadal, J. F. Rouchon, and M. Braza Design and Experimental Validation of A320 Large Scale Morphing Flap Based on Electro-mechanical Actuators . . . . . . . . . . . . . . . 295 Y. Bmegaptche Tekap, A. Giraud, A. Marouf, A. Polo Domingez, G. Harran, M. Braza, and J. F. Rouchon

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Manipulation of a Shock-Wave/Boundary-Layer Interaction in the Transonic Regime Around a Supercritical Morphing Wing . . . . . . 305 J.-B. Tô, N. Bhardwaj, N. Simiriotis, A. Marouf, Y. Hoarau, J. C. R. Hunt, and M. Braza Predictive Numerical Study of Cambered Morphing A320 High-Lift Configuration Based on Electro-Mechanical Actuators . . . . . . 317 A. Marouf, N. Simiriotis, Y. Bmegaptche Tekap, J.-B. Tô, M. Braza, and Y. Hoarau Shape Control of Flexible Structures for Morphing Applications . . . . . . . 323 Georgios K. Tairidis, Aliki D. Muradova, and Georgios E. Stavroulakis Continuous Adjoint for Aerodynamic-Aeroacoustic Optimization Based on the Ffowcs Williams and Hawkings Analogy . . . . . . . . . . . . . . . . 329 M. Monfaredi, X. S. Trompoukis, K. T. Tsiakas, and K. C. Giannakoglou On Boundary Conditions for Compressible Flow Simulations . . . . . . . . . . 335 Javier Sierra, Vincenzo Citro, and David Fabre Large-Eddy Simulation on Jet Mixing Enhancement Using Unsteady Minijets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341 Yanyan Feng, Dewei Fan, Bernd R. Noack, Hong Hu, and Yu Zhou Mixing Characteristics of a Flapping Jet of Self-Excitation Due to a Flexible Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 M. Wu, M. Xu, and J. Mi Flow-Induced Vibration Characteristics of a Fix-Supported Elastic Wing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353 S. Peng, S. L. Tang, Md. Mahbub Alam, and Yu Zhou On the Transient Effects Induced by Jet Actuation Over an Airfoil . . . . . 359 Armando Carusone, Christophe Sicot, Jean-Paul Bonnet, and Jacques Borée Artificial Intelligence Control of a Turbulent Jet . . . . . . . . . . . . . . . . . . . . . . 365 Dewei Fan, Yu Zhou, and Bernd R. Noack Turbulent Friction Drag Reduction: From Feedback to Predetermined, and Feedback Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Koji Fukagata

Simulating the Dynamics of Primary Cilium in Pulsatile Flow by the Immersed Boundary-Lattice Boltzmann Method Jingyu Cui, Yang Liu, Xiao Lanlan, and Chen Shuo

Abstract In this study, the dynamics of primary cilium (PC) in a pulsatile blood flow is numerically studied. The two-way fluid-cilium interaction is handled by an explicit immersed boundary-lattice Boltzmann method with the cilium base being modeled as a nonlinear rotational spring (Resnick in Biophys J 109:18–25, 2015 [1]). The fluid-cilium interaction system is investigated at several pulsatile flow cases, which are obtained by varying the flow peak Reynolds numbers (Repeak ) and Womersley numbers (Wo). The cilium’s dynamics is observed to be closely related to the Repeak and Wo. Increasing the Repeak or decreasing the Wo results in an increase in cilium’s flapping amplitude, tip angular speed and maximum tensile stress. We also demonstrated that by reducing the Repeak or enhancing the Wo, one can shift the two-side flapping pattern of PC to a one-side one, making the stretch only occurs on one side. During the flapping process, the location of the maximum tensile stress is not always found at the basal region, instead, it is able to propagate from time to time within a certain distance to the base. Keywords Cilium dynamics · Fluid–structure interaction · Immersed boundary-lattice Boltzmann method · Pulsatile flow

1 Introduction Primary cilia are filament-like, immotile solitary protrusions from the apical surface of nearly every mammalian cell. Though being long considered as vestigial structures, J. Cui (B) · Y. Liu Research Centre for Fluid-Structure Interactions, Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong e-mail: [email protected] X. Lanlan School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, China C. Shuo School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_1

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they are recently demonstrated to play a crucial role in mechanosensation [2] through deflection in response to flow as is already observed in renal tubule cells [3], and impairment of cilia is correlated with the development of many diseases known as ciliopathies. The deflection of primary cilia is found to increase the intracellular calcium concentration. This process relies on the opening of PC2 cation channel which localizes to the primary cilia and is assumed to be stretch-activated [2]. The relationship between the opening of cation channel and the cilium deflection is yet to be elucidated. However, the stretch force on the cilium membrane along with other mechanical properties are still experimentally challenging to be measured due to the scales of the quantities involved. Numerical simulation would be an advantageous way to explore this fluid-cilium interaction system as much more detailed dynamic information can be obtained. Previous cantilevered Euler–Bernoulli beam model is proved to be incorrect for modelling cilium deflection, as the cilium base could experience some degree of rotation when subject to a fluid flow. The rotational-spring model that proposed by Resnick [1] can well match experimental measurements. The static Stokes flow considered in Resnick’s modelling, however, fails to reveal the transient and oscillatory nature of many biological flows, e.g. the blood and renal tubule flows. Moreover, the effect of fluid–structure interaction (FSI) is not well considered, which could significantly reduce the simulation accuracy. To remove these two drawbacks, in this study, Resnick’s rotational-spring model is integrated with an immersed boundary-lattice Boltzmann method (IB-LBM) to study the dynamics of primary cilia in pulsatile flow conditions. The FSI is considered in a fully coupled manner. Our physical model is illustrated in Fig. 1.

Fig. 1 The flow condition and the physical model considered (the pressure gradient waveform is reproduced using the data of McDonald [4])

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2 Mathematical Formulation and Numerical Method A BGK-lattice Boltzmann method with a D2Q9 lattice model and Guo et al.’s splitforcing scheme [5] is adopted to solve the fluid dynamics. The evolution equation is 1 eq f j (x, t) − f j (x, t) + f j t f j x + e j t, t + t − f j (x, t) = − τ

(1)

where j = 0, 1, . . . , 8 denotes the lattice space, f j is the density distribution function eq and f j its equilibrium value. τ is the dimensionless relaxation time, t the time interval, f j the forcing term which is related to the external force. The motion equation for a filament-like structure immersed in fluid is given by ρc

∂2 X ∂4 X ∂ ∂X = + F f l ui d T − K (s) b ∂t 2 ∂s ∂s ∂s 4

(2)

where X is the position of the cilium, s its Lagrangian coordinate, F f l ui d the hydrodynamic force, ρc and K b its linear density and bending rigidity, respectively. In our study, Eq. (2) is solved by an central finite difference method and the FSI is handled by a momentum exchange scheme-based immerse boundary method (IBM). For details of this version of IBM, interested readers are referred to Ref. [6]. Due to the attached rotational spring, every basal rotation induced by the fluid drag will generate a reverse bending moment at the basal end of cilium.

dX 2 L dX d2 X +α − k =0 ds 2 Kb ds ds

(3)

where L is the cilium length, k and α the rotational spring constants, respectively. The peak Reynolds number and Womersley number of the flow are defined as Repeak

2π f u0 D , Wo = D = υ υ

(4)

where u 0 is the maximum flow velocity, f the pulsatile flow frequency, D the vessel diameter.

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3 Results and Discussion 3.1 Dynamics of Primary Cilium at Various Peak Reynolds Number The dynamics of the cilium is studied by varying the Repeak at Wo = 0.6. Our results show that, after several cycles, the cilium steps into a periodic flapping pattern with its superposition of profiles in a cycle shown in Fig. 2. It is intuitive that the deflection amplitude at a higher Repeak is greater, as the corresponding flow drag also increases. Moreover, we observe that when the Repeak is lower than a critical value (see the case Repeak = 0.02), the cilium manages to flap only in the right-half domain. This one-side flapping results in the stretch of one side of the cilium while keeps the other side compressed during the entire deflection process. Cilium’s tip angular speed (TAS) is plotted in Fig. 3a, where the positive and negative values denote clockwise and anticlockwise deflections, respectively. In each cycle, the cilium is observed to first deflect clockwise at an increasing speed, then decelerate to zero before switching to an anticlockwise deflection. It is at this zeroangular-speed moment that the cilium reaches its right deflection limit. In the subsequent anticlockwise deflection, the cilium experiences an accelerating-decelerating recovery process before reaching its left deflection limit. In the rest period of the cycle, the cilium repeats the aforementioned deflection behavior but at a much lower amplitude due to the decreased pressure gradient. The fluctuation of TAS basically follows the applied pressure gradient waveform, except that the largest value is obtained during the first anticlockwise deflection process, instead of during the first clockwise deflection, where the largest pressure gradient is applied at a positive value. This may be due to the release of the bending energy that the cilium harvested during its first clockwise deflection process, where cilium’s largest deflection and bending energy is obtained. The fluctuation of the maximum curvature is plotted in Fig. 3b. The curvature of cilium can be considered proportional to its tensile stress as the cilium has a large

Fig. 2 Superposition of the cilium profile in a cardiac cycle at various Repeak (dashed green lines: clockwise deflections, solid blue lines: anticlockwise deflections, and solid red lines: tip trajectories)

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Fig. 3 Temporal fluctuation of the cilium’s TAS (a) and maximum cuvature (b) a typical case shows the relocation of MTS at Repeak = 0.4, Wo = 0.6 (c)

aspect ratio. Interestingly, in our simulations, the maximum tensile stress (MTS) is not always observed at the cilium base region as reported by Rydholm et al. [7]. Due to the pulsatile flow conditions, the location of the MTS could propagate from time to time during a cardiac cycle, though in most of the time it stays at the base. A case demonstrating this is shown in Fig. 3c, where relocation of the MTS within 0–45% of cilium length is observable. From Fig. 4, one can also see that when a primary cilium is subjected to a fluid flow with higher Repeak , its TAS and MTS both increase.

Fig. 4 Superposition of the cilium profile in a cardiac cycle at various Wo

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3.2 Effect of Womersley Number on the Cilium Dynamics Based on the vessel size we chose, simulations of cilium deflections in flow at various Wo were also performed at Repeak = 0.1. The superposition of cilium profile in a cardiac cycle are presented in Fig. 4, where we can see that as Wo increases the cilium deflection amplitude decreases. The one-side flapping model again can be observed when the Wo is large enough, e.g. Wo = 1.2. In this model, the cilium is unable to cross the centerline of the region, thus the flapping occurs only in the right half of the domain. It is also found that as the Wo increases, the amplitude of the TAS also increases while the deflection amplitude and maximum curvature decreases. The reason why such decrease occurs may be that the positive portion of the applied pressure gradient is larger than the negative portion in a cardiac cycle. The positive portion becomes even more dominant when Wo decreases, which brings a larger average drag force to the cilium and enables it to deflect more powerfully.

4 Conclusions In this study, an explicit IB-LBM is developed to study the dynamics of the primary cilium in pulsatile flows with the cilium base being modeled as a nonlinear rotational spring. It is found that the flapping pattern of primary cilium depends on both the Repeak and Wo. By reducing the Repeak or enhancing the Wo , the primary cilium will switch to a one-side flapping pattern from its original two-side one, making the stretch only happens on one side. When a primary cilium is subject to fluid flows with higher Repeak , its flapping amplitude, TAS and MTS all increase. In contrast, increasing the Wo reduces these quantities. Under pulsatile flow conditions, the MTS of the primary cilium is not always found at the cilium base region. In contrast, it could propagate periodically within a certain distance to the base.

References 1. Resnick A (2015) Mechanical properties of a primary cilium as measured by resonant oscillation. Biophys J 109(1):18–25 2. Praetorius HA, Spring KR (2003) Removal of the MDCK cell primary cilium abolishes flow sensing. J Memb Biol 191(1):69–76 3. Yoder BK (2007) Role of primary cilia in the pathogenesis of polycystic kidney disease. J Am Soc Nephrol 18(5):1381–1388 4. McDonald DA (1955) The relation of pulsatile pressure to flow in arteries. J Physiol 127(3):533 5. Guo Z, Zheng C, Shi B (2002) Discrete lattice effects on the forcing term in the lattice Boltzmann method, p 046308

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6. Niu XD, Shu C, Chew YT, Peng Y (2006) A momentum exchange-based immersed boundarylattice Boltzmann method for simulating incompressible viscous flows. Phys Lett A 354(3):173– 182 7. Rydholm S, Zwartz G, Kowalewski JM, Kamali-Zare P, Frisk T, Brismar H (2010) Mechanical properties of primary cilia regulate the response to fluid flow 298(5):F1096–F1102

The POD Analysis of Screech Tone in Low Mach Number Axisymmetric Supersonic Jet Hu Li, Yong Luo, and Shuhai Zhang

Abstract Direct numerical simulation of underexpanded supersonic circular cold jet at typical state issuing from sonic nozzle is carried out through solving axisymmetric Navier-Stokes equations directly. Near field screech tones of axisymmetric modes are investigated using POD analysis. The corresponding velocity field POD modes of the dominant coherent structures and the flow structures associated with screech tones are obtained respectively according to their energy and frequency. The energy variation along streamwise of the two kinds of flow structures and their spatial evolution are studied. Numerical results demonstrate that the interactions between shock-cell structures and jet shear layer occurring in the energy release sub-region of the screech-associated flow structures’ saturation region generate one or two kinds of axisymmetric A1 and A2 screech tone modes. Keywords Screech tone · Axisymmetric mode · Underexpanded supersonic jet · Proper orthogonal decomposition (POD)

1 Introduction As well known, imperfectly expanded supersonic jet could generate quasi-periodic shock-cell structures in its plume, which causes the radiation of two shock-associated noise components: broadband shock-associated noise and screech tones [1]. They are H. Li (B) · Y. Luo · S. Zhang State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China e-mail: [email protected] Y. Luo e-mail: [email protected] S. Zhang e-mail: [email protected] Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_2

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produced by the interaction between instability waves in the jet shear layer and shock cell structures in the jet core. In particular, screech tones have discrete frequencies and high intensity, which are known to be driven by an non-linear self-sustained acoustic feedback loop. Screech tones propagate primarily in the upstream direction, thus their amplitudes can be high enough to cause structural fatigue in nearby nozzle elements and control surfaces of the aircraft. Since Powell’s pioneering work [2, 3], lots of investigations on screech tone have been conducted via experiments and numerical approaches. Raman provided a concise historical perspective and summary of process in jet screech research during almost 50 years from Powell’s discovery [4, 5]. It is also well known that axisymmetric mode is the dominant screech mode in the supersonic jet at low mach numbers. In order to understand the acoustic feedback loop of screech tones, accurately locating their sound sources’ position is necessary. In authors’ previous work [6], axisymmetric A1 mode and A2 mode screech tones’ generation position are given through analyzing the dynamic evolution of their corresponding flow structures and acoustic field. The present work attempts to numerically investigate the sound generation mechanism of axisymmetric mode screech tone especially its sound source’s location based on Proper Orthogonal Decomposition (POD) of flow field data from the view of energy.

2 Computational Details Underexpanded supersonic circular cold jets are simulated by solving axisymmetric Navier-Stokes equations directly using fifth order finite difference weighted essentially non-oscillation (WENO) scheme, sixth order central finite difference scheme and third order Total Variation Diminishing (TVD) Runge-Kutta method for the discretization of spatial convection term, viscous term and temporal derivative respectively. The jet is assumed to be supplied by a convergent nozzle whose designed Mach number is therefore equal to 1. The thickness of nozzle is 0.2D (where D is nozzle diameter). The fully expanded jet Mach number is 1.19 and the Reynolds number is 6.216 × 105 . Thompson’s characteristic far field boundary conditions are applied at left boundary and upper boundary regions. At the downstream boundary region, the non-reflecting outflow boundary condition with buffer zone (stretched grids) is implemented. At the nozzle exit, the uniform inflow plane is recessed by six cells so as not to numerically restrict or influence the feedback loop. Initially, the whole computational domain except nozzle inlet is set to ambient flow conditions. The unsteady flow fields containing sound waves are obtained and the flow field data associated with screech tone is analyzed though proper orthogonal decomposition (POD) snapshot method [7].

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3 Proper Orthogonal Decomposition Proper orthogonal decomposition is an important tool that extracts and analyzes the coherent structures in turbulent flow [8]. In the POD analysis, characteristic decomposition of autocorrelation matrix R = U T U of fluctuating velocity field data snapshots U is executed, Rai = λi ai . The eigenvectors ai represents temporal POD modes, while spatial POD modes can be expressed as a linear combination of the products between fluctuating velocity field snapshots and temporal POD modes. The POD modes are sorted based on eigenvalues λi which represent their incompressible fluctuating kinetic energy content. It need to be point out that POD modes are usually paired. The mathematical expression of fluctuating velocity snapshots based on POD modes is as follows [9, 10], u (x, tk ) = ψ i (x) =

M

bi (tk ) ψ i (x) + ur es (x, t)

i=1 N

√1 λi

(1) ai (tk ) u (x, tk )

k=1

√ here ψ i are the spatial POD modes, bi = λi ai are the temporal POD modes, ur es is the residual. M is number of modes, M ≤ N , N is the total number of data snapshots series. The data are beginning to be recorded at fixed dimensionless time interval of Δt = 0.1 after the initial transients propagating out of the computational domain completely. Actually, 2048 instantaneous velocity fields are used to construct the data snapshots matrix U.

4 Numerical Results and Analysis 4.1 Screech Tone’s Frequency and Sound Pressure Level The time history of pressure signal is recorded at the selected monitor in the flowfield and later post-processing is to obtain spectral information using Fast Fourier Transformation techniques. Figure 1 displays the pressure signal’s spectral information (frequency and SPL) of the monitor located at the nozzle exit lip wall. The SPL shows that there are three spikes in the frequency spectrum range of larger than 5000 Hz. The second and third spikes correspond to the axisymmetric A1 and A2 mode screech tones respectively. And their values of frequency and SPL are shown in Table 1.

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Fig. 1 Spectral analysis of sound signal at the point [0.0,0.642] on the nozzle exit lip wall (M j = 1.19) Table 1 Spectral analysis of pressure signal at the point [0.0, 0.642] on the nozzle exit lip wall Modes Frequency (Hz) SPL (dB) A1 A2 B

6721 8637 5724

121 128 118

4.2 POD Analysis of Fluctuating Velocity Field The temporal POD modes ai (tk ) of 2D velocity flowfield of are shown in Fig. 2, including wavelengths, phase portrait and eigenvalues. The phase portrait demonstrates temporal correlations between modes of different orders and the eigenvalue characterizes each mode’s energy ratio. It is shown that the wavelengths of the first and second order modes are matched. The first two modes are also strongly correlated in time, producing a circle in their phase portrait. The matched wavelengths and temporal correlations indicate that the two modes represent a single oscillatory motion together. For the same reason, the fifth pair of modes also represent a oscillatory motion. However, there is no such temporal correction between the first and the third one. In addition, the first pair of modes have the highest energy content and the sum of their energy ratios is 37%. High energy ratio suggests that the structure represented by the first pair of modes is the dominant coherent flow structure in the jet.

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(a) First and second order (b) Eigenvalues (energy ratio) (c) Ninth and tenth order modes modes of POD modes

(d) Phase portrait between (e) Phase portrait between (f) Phase portrait between first and second order modes first and third order modes ninth and tenth order modes Fig. 2 Temporal POD modes and their eigenvalues of fluctuating velocity field (2D, M j = 1.19)

(a) Ninth order mode

(b) Tenth order mode

Fig. 3 FFT analysis of the fifth pair of temporal POD modes of fluctuating velocity field (2D, M j = 1.19)

Figure 3 displays the FFT analysis of the fifth pair of temporal POD modes. As can be seen in Fig. 3, the fifth pair of POD modes have a single absolutely dominant frequency (8660 Hz), which is close to that of axisymmetric A2 mode screech tone. It means that the fifth pair of POD modes represent the flow structures associated with screech tone of axisymmetric A2 mode. The first and fifth pairs of spatial POD modes of velocity field including both u and v components are shown in Fig. 4. The spatial evolution of such POD modes can

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(a) First order mode: u component

(b) First order mode: v component

(c) Second order mode: u component

(d) Second order mode: v component

(e) Ninth order mode: u component

(f) Ninth order mode: v component

(g) Tenth order mode: u component

(h) Tenth order mode: v component

Fig. 4 The first and fifth pairs of spatial POD modes of fluctuating velocity field (2D, M j = 1.19)

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be seen. Figure 4a–d show that the dominant coherent flow structure represented by the first pair of modes reach saturation state at the region of x/D > 4.0 in streamwise direction. Compared with the dominant coherent structures, the flow structures represented by the fifth pair of POD modes develop faster, which reach saturation state at the region of 2.0 < x/D < 4.0 along streamwise and then begin to decay rapidly (see details in Fig. 4e–h). In the upper left of the ninth and tenth order modes’ contours, there are some regular stripes radiating to the left side from the saturation region, which could be recognized as screech tone propagating towards upstream direction. It should be noted that the shock cell structures in jet potential core interact with the coherent structures in jet shear layer in this region to generate screech tones of A1 and A2 modes. Moreover, the energy ratio variations of dominant coherent structures and screechassociated flow structures along streamwise are investigated through based on POD analysis of velocity field’s slices in different axial position. Figure 5 displays the

Fig. 5 Eigenvalues’ variations along streamwise of the POD modes based on POD analysis of velocity field’s slices in different axial position (M j = 1.19)

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eigenvalues’ changes of relevant POD modes. At the streamwise position of x/D ≈ 3.16, the local maximum value point of eigenvalues’ summation of the second pair of modes precisely matches with the local minimum value point of eigenvalues’ summation of the first pair of modes. In other words, the dominant coherent structures undergo intensive energy release before the extreme point, while the flow structures associated with the second pair of POD modes undergo energy absorption. It indicates that there is energy transfer between the two kinds of structures. As can be seen from Fig. 4e–h, the flow structures associated with A2 mode screech tone is in a saturation state at such energy transfer zone before the extreme point. At the saturation state region, the corresponding fifth pair of POD modes have undergone the process of energy absorption and release successively. In the sub-region of energy release, there are two local minimum value points of their eigenvalues’ summation at the streamwise location of x/D ≈ 2.43 and x/D ≈ 3.25. It should be pointed out that the two key local minimum value points are the generation positions of axisymmetric A2 and A1 mode screech tones respectively as proposed by the work of Li [6].

5 Conclusion In this paper, direct numerical simulation of axisymmetric underexpanded supersonic cold jet issuing from sonic nozzle at jet Mach number of M j = 1.19 are carried out using high order accurate method. Axisymmetric A1 and A2 mode screech tones’ spectral information (frequency and SPL) are presented. Jet velocity field’s POD analysis are implemented, providing the POD modes corresponding to the dominant coherent flow structures and the flow structures associated with screech tone. The spatial evolution of the two kinds of flow structures is investigated. It is found that the screech-associated flow structures develop faster than the dominant flow structures, and reach saturation state more quickly but then decay rapidly. Their energy ratio variations along streamwise are also analyzed. The analysis results indicate that the screech-associated flow structures have undergone the process of energy absorption and release successively at the saturation region. The interactions between shock-cell structures in jet potential core and coherent structures in jet shear layer occurring in the energy release sub-region generate one or two kinds of axisymmetric (A1 and A2 ) screech tone modes.

References 1. 2. 3. 4.

Tam CKW (1995) Supersonic jet noise. Annu Rev Fluid Mech 27:17–43 Powell A (1953a) On the mechanism of choked jet noise. Proc Phys Soc London 66:1039–1056 Powell A (1953b) The noise of choked jets. J Acoust Soc Am 25:385–389 Raman G (1998) Advances in understanding supersonic jet screech: review and perspective. Prog Aerosp Sci 34:45–106

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5. Raman G (1999) Supersonic jet screech: half-century from Powell to the present. J Sound Vibr 225(3):543–571 6. Li H, Luo Y, Zhang SH (2019) Numerical study of shock- associated noise in axisymmetric supersonic jet. In: Zhou Y, Kimura M, Peng G, Lucey AD, Huang L (eds) Proceedings of the 4th symposium on fluid-structure-sound interactions and control (FSSIC2017). Fluid-StructureSound Interactions and Control. Springer Nature Singapore, pp 351–358. https://doi.org/10. 1007/978-981-10-7542-1 7. Sirovich L (1987) Turbulence and dynamics of coherent structures. Part I: coherent structures. Quart Appl Math 45(3):561–571 8. Lumley JL (1967) The structure of inhomogeneous turbulence flows. In: Yaglom AM, Tatarsky VI (eds.) Proceedings of atmospheric turbulence and radio wave propagation. Moscow, USSR: Nauka, pp. 166–178 (1967) 9. Edgington-Mitchell D, Oberleithner K, Honnery DR, Soria J (2014) Coherent structure and sound production in the helical mode of a screeching axisymmetric jet. J Fluid Mech 748:822– 847 10. Edgington-Mitchell D, Honnery DR, Soria J (2015) Multi-modal instability in the weakly underexpanded elliptic jet. AIAA J 53(9):2739–2749

Direct Numerical Simulations of Self-sustained Oscillations in Two-Dimensional Rectangular Cavity Yong Luo, Hu Li, Shuaibin Han, and Shuhai Zhang

Abstract Direct numerical simulations of self-sustained oscillations in two dimensional rectangular cavity are performed in both subsonic and supersonic flow. A fifth order weighted essentially non-oscillatory scheme (WENO) is used for the nonlinear term of the two-dimensional unsteady compressible Navier-Stokes equations. A third order Runge-Kutta method is used to discretize the time derivative. Different modes of the sound are distinguished by using dynamic mode decomposition (DMD) method. All the results show that the oscillating system would finally reach to the self-sustained state. Keywords Cavity · Aeroacoustics · DMD

1 Introduction Cavity is a typical configuration of fluid mechanics. There are many complex phenomena such as resonant tones, shear layer instabilities and complex wave interactions. In supersonic, there are also shock waves. The noise radiated by the flow past an open cavity has been studied for decades due to its important values both on theory and applications. The most important physical mechanism is the flow/acoustic resonance [1], described as follows: (i) Kelvin-Helmholtz instability excites an unstable shear layer and generates vortex, (ii) the shear layer moves downstream and imping on the back wall, which generates acoustic waves that propagate upwards, (iii) the acoustic waves interact with the leading edge fluids further excite the shear layer instabilities. These mean that the cavity oscillations is self-sustained and exists a feedback loop. The idea of such a feedback loop was known earlier for edge-tones in Powell’s work [2]. Through a series of experimental tests, Krishnamurty [3] discovered that the Y. Luo · H. Li · S. Han · S. Zhang (B) State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_3

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subsonic and supersonic flows past rectangular cavities would emit a strong acoustic radiation. Rossiter [1] identified a series oscillation modes with different discrete frequencies and gave a semi-empirical formula to predict the resonant frequencies. In this mechanism, the system is unstable and exists a stable limit cycle about an unstable equilibrium point. The nonlinearities play an important role when the perturbations grow in time, and finally saturate the system. By contrast, another mechanism proposed by Rowley et al. [4] is that the system is linearly stable, but lightly damped, and constantly excited by external disturbances. The oscillations would disappear when the external forcing were removed. In this paper, we try to identify the cavity oscillating mechanism for both the subsonic and supersonic flow using the direct numerical simulation.

2 Numerical Simulations 2.1 Flow Configuration The schematic diagram of the cavity configuration and the computational domain are shown in Fig. 1. The computational domain includes the near-field, a significant portion of the acoustic field, and the sponge zones (for subsonic cases). All variables are non-dimensionalized by the reference density ρ∞ , the reference temperature T∞ = 288.15K , the cavity depth D and the sound speed a∞ respectively. Here, the subscript ∞ represents the flow parameters at infinity. The simulations are initiated by free stream which will form a laminar boundary layer. We use about 260 thousands grids, the minimum grid spacing is 5 × 10−3 D.

2.2 Numerical Methods In the present work, the two-dimensional unsteady compressible Navier-Stokes equations without external forces are solved numerically. The fluid is assumed to be ideal gas. The dynamic viscosity coefficient is calculated by Sutherland’s formula. The

Fig. 1 Schematic diagram of 2-D open cavity configuration and computational domain

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Mach number M and the Reynolds number Re are constants related to specific computational cases. The ratio of specific heats and Prandtl number are maintained constant, with γ = 1.4 and Pr = 0.7, respectively. In this paper, for the governing equations, we use a fifth-order WENO scheme for the space convective terms, the sixth-order central difference schemes for the viscous terms, and the three-stage total variation diminishing (TVD) Runge-Kutta iterative method for time discretion. The techniques to improve the convergence to steady state [5, 6] are used to reduce the post shock oscillation. We use a nonlinear BC called sponge regions or sponge zones for subsonic cases to introduce artificial dissipation by adding the forcing term with a spatially varying damping coefficient to the right-hand-side of the governing equations [7].

3 Results and Analysis 3.1 Acoustic Field Figure 2 shows the numerical schlieren and their comparison with the experimental schlieren of Krishnamurty [3]. In these experiments [3], the cavity was made in a smooth flat plate and it has no solid wall in the width direction. The width of cavity is much larger than its length and depth, thus it approximates the two-dimensional model adequately. The flow in these experimental examples is laminar. The Mach numbers are 0.64, 0.7, 0.8 and 0.855. The ration of the length and the depth is L/D = 2. The comparison are satisfactory. There is only one wave that propagates upwards in the case of Mach number 0.64. Because the self-sustained oscillations is weak and the phases are close between the waves from the leading and trailing edge. In the cases of Mach numbers 0.7, 0.8 and 0.855, there are two waves with a clear phases difference. The frequencies of waves obtained from our DNS results agree well with the experimental frequencies for all four Mach numbers. Figure 3 contains the numerical schlieren and its comparison with the experimental schlieren [3] for a supersonic case with Mach number 1.38. The ration of the length and the depth is also L/D = 2. It can be noted that the acoustic waves are more complex in this case than those of the subsonic cases. Our DNS structures are visually similar with the experimental result.

3.2 Dynamic Mode Decomposition The dynamic mode decomposition (DMD) was proposed by Schmid [8] and is a powerful tool for analyzing the dynamics of nonlinear systems. The DMD modes decomposed from the flow data could identify the coherent structures. Figure 4 shows the DMD analysis results. Figure 4a is the eigenvalues of DMD, generally we only

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Fig. 2 Comparison of schlieren photographs with numerical schlieren from the DNS: a–d are schlieren photographs from Krishnamurty 1956s experiments [3], e–h are DNS results

Fig. 3 Supsonic cases, comparison of schlieren photographs with numerical schlieren from the DNS: a is the schlieren photograph from Krishnamurty 1956s [3] experiment, b is DNS result

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Fig. 4 DMD for M = 0.8, a is the eigenvalues distribution of DMD, b is the first DMD mode with St = 0.67, c is the second DMD mode with St = 1.34

Fig. 5 Strouhal numbers for peaks in spectra for different Mach numbers. Krishnamurty experiments’ results: •; Rowley et al. [9]’ results: ; the present DNS results: ; Rossiter’s semi-empirical formula: dashed line ( ) and solid line

need the first few modes since the other modes are very weakly in energy. Figure 4b is the first DMD mode with the frequency f 1 = 0.67. Figure 4c is the second DMD mode, which is the harmonic frequency of the first DMD mode since we have the frequency relation f 2 = 1.34 = 2 f 1 . We performed fast fourier transform (FFT) of the perturbation signals at the bottom of the cavity for the M = 0.8 case, the strouhal numbers for peaks in spectra is St = 0.67 = f 1 (see Fig. 5), therefore, Fig. 4b shows the dominant coherent structure of the cavity oscillations.

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Fig. 6 M = 0.6, a is the pressure perturbation signals at the bottom of the cavity with x = 0.5L, b is the STFT result of the pressure perturbation signals (17 contour levels)

3.3 Frequencies of Oscillation In Fig. 5, the frequency of the most energetic peak in the spectra for both the subsonic and the supersonic cases are compared to Rossiter’s semi-empirical formula [1], Krishnamurty’s experimental data [3] and Rowley’s results [9]. We can observe that the present DNS results match the experiments and Rossiter’s formula well. In Krishnamurty’s experiments [3], only one dominant mode and its harmonic were detected with laminar boundary layers upstream. However in Rowley’s results [9], two dominant modes (Rossiter mode 1 and Rossiter mode 2) can be observed. Figure 6a shows the pressure perturbation signals at the bottom of the cavity with x = 0.5L for the case of M = 0.6. Its short time fourier transform (STFT) [10] analysis result over a period of time is showed in Fig. 6b. Its vertical axis is the non-dimensional frequency. For Mach 0.6 in Rowley’s [9] results, the frequency of the dominant mode is St = 0.405, this frequency also exist in the initial period of our results. From Fig. 6b, we can note that the frequency of this mode is St = 0.408, and it is unstable. It decay in time and eventually disappear. In Fig. 17 of Rowley’s paper [9], the mode with less energy seems has tendency to disappear, unfortunately the calculating time may not long enough to let the system reach to the stable state.

4 Conclusion We use the DNS method to investigate the flow past a two-dimensional rectangular cavity for both the subsonic and the supersonic cases. The present results agree well with the experimental results and Rossiter’s semi-empirical formula. The most energetic modes of oscillation are extracted by the DMD method. We also use the STFT method to analysis the pressure perturbation signals at the bottom of the cavity. The result shows, the system would finally reach to a stable state and exists only one dominant mode, that means the oscillations are self-sustained and the system exists a stable limit cycle for the present DNS results.

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References 1. Rossiter JE (1964) Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aeronautical Research council Reports and Memoranda 3438 2. Powell A (1953) On edge tones and associated phenomena. Acta Acustica United with Acustica 3–1 3. Krishnamurty K (1956) Sound radiation from surface cutouts in high speed flow. PhD thesis, California Institute of Technology 4. Rowley CW, Williams DR, Colonius T, Murray RM, Macmynowski DG (2006) Linear models for control of cavity flow oscillations. J Fluid Mech 547:317–330 5. Zhang S, Shu C-W (2007) A new smoothness indicator for the WENO schemes and its effect on the convergence to steady state solution. J Sci Comput 31:273–305 6. Zhang S, Jiang S, Shu C-W (2011) Improvement of convergence to steady state solutions of Euler equations with the WENO schemes. J Sci Comput 47:216–238 7. Bodony D (2006) Analysis of sponge zones for computational fluid mechanics. J Comput Phys 212:681–702 8. Schmid P (2010) Dynamic mode decomposition of numerical and experimental data. J Fluid Mech 656:5–28 9. Rowley CW, Colonius T, Basu AJ (2002) On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J Fluid Mech 455:315–346 10. Nawab SH , Quatieri TF (1987) Short-time Fourier transform. Advanced topics in signal processing. Prentice-Hall, Inc.

Energy Harvesting Using a Tensioned Membrane with a Spring-Mounted Trailing Edge in Axial Flow T. X. Chin, R. M. Howell, and A. D. Lucey

Abstract We investigate experimentally an axial channel flow passing above and below a centrally placed, clamped-clamped tensioned membrane, where the trailingedge clamp is free to pivot about a hinge with a rotational spring stiffness. To the authors’ knowledge this is an unexplored fluid-structure system. For the range of parameters studied, the system is found to lose stability to flutter. The system is broadly governed by three parameters: the mount natural frequency, the nondimensional flow speed (stiffness ratio) and the mass ratio. It is found that the mass ratio does not have a significant effect on the flutter instability-onset flow-speed values. However, power-producing capabilities, with comparative efficiencies calculated relative to the available mean-flow kinetic-energy flux, show that mass ratio alone is not a unique determinant of efficiency. Maximum values of the comparative efficiency are found for a range of system properties. In energy-harvesting applications, these efficiencies might set the optimum design value for spring stiffness although the effect of energy take-off on the dynamics of the fluid-structure system would also need to be taken into account. Keywords Fluid-structure interaction · Axial flow · Flutter · Energy harvesting · Spring-mounted · Tensioned membranes

1 Introduction Herein we present a wind-tunnel-based experimental investigation that studies the fluid-structure interaction (FSl) of an axial channel flow passing above and below a centrally placed, clamped-clamped tensioned membrane, where the trailing-edge clamp is free to pivot about a hinge with a rotational spring stiffness; see Fig. 1. To the authors’ knowledge this is an unexplored FSI system. Of principal importance T. X. Chin · R. M. Howell (B) · A. D. Lucey Fluid Dynamics Research Group, School of Civil and Mechanical Engineering, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_4

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Fig. 1 Plane view of the fluid-structure system under consideration

is that the system loses stability to flutter at greatly lower flow speeds than that of a conventional flexible membrane fixed at both of its leading and trailing edges for which divergence instability would be the first, or critical, instability encountered with increasing applied flow speed [1]. The modification (from being fully clamped) of the trailing-edge constraint allows the system to take on some of the characteristics of a cantilevered-free flexible plate— a lifting surface—for which single-mode flutter is the critical instability for short plates (i.e. with low mass ratio). In such systems flutter is typically caused by irreversible energy transfer from the fluid flow to the structure due to phase differences between the pressure loading and the local plate velocity. However, long plates (those with high mass ratios) can also be destabilised by the fluid pressure coalescing two or more translational in vacuo modes of the structure and is often described as a Kelvin-Helmholtz mechanism; this mechanism also occurs for clamped-clamped flexible plates and membranes at flow speeds higher than those which yield divergence instability. We also remark that the constraint on the moving trailing edge that is imposed by the structural support breaks the system symmetry about the undisplaced position of the membrane that exists for the base (clamped-clamped) system. Destabilisation is of great interest for energy harvesting which can be readily achieved through an electro-mechanical system via rotation of the hinge at the trailing edge, analogous to the cantilever of [2] that is spring-mounted at its leading edge. Owing to the large deflections that are generated, the present system of energy extraction could be more effective than standard methods through deflection of piezoelectrics placed along the plate, for example see [3]. It also permits more flexible materials to be used (hence lowering the flow speed at which self-sustained oscillations occur) and directly yields rotation (albeit reciprocating) of a mechanical shaft while the fixing at the trailing-edge promotes two-dimensional deformations of the membrane even at high amplitudes of limit-cycle flutter motions. This paper serves to introduce the new FSI system and presents a preliminary investigation to determine the combination of system parameters best suited for energy harvesting.

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2 Experimental Design The wind tunnel is of cross-section 457 mm × 457 mm and capable of producing flow speeds ranging from U = 4 to 29 m/s with air density ρf = 1.2 kg/m3 . Herein, the membrane used is soft rubber (ρ = 1100 kg/m3 ) with a width of 360 mm, thicknesses h of 1.5 and 3 mm and lengths L of 600 and 800 mm. The membrane is mounted in the middle of the channel, as shown in Fig. 1a, to avoid wall effects by maintaining a sufficiently large channel height to membrane length ratio H/L. The slider feet of the rig, shown in Fig. 1b, are adjustable to allow the use of membranes of different L. Two springs are always attached between the back of the trailing edge pivot column to an adjustable rear arm which allows the setting of a pre-tension T to ensure that the pivot column was vertical before testing was initiated, see Fig. 1b. Thus, in each case studied the pre-tension was set to counter the dead weight of the membrane. Seven different linear springs were used for each set of results, with stiffness values in the range K = 98.9 to 1226.3 N/m. As seen in Fig. 1 these were fixed in a way that produces a moment about the slider-foot hinge to create the effect of a torsional spring stiffness κ for each spring. It is remarked that as the rigid bar attached to the membrane trailing edge rotates, the moment arm of the spring changes. However, this effect is small due to the selected geometry of the components and thus a constant κ was approximated. Each spring-membrane configuration therefore had its own particular √ angular frequency, = κ/Io , where Io is the combined mass moment of inertia of the pivot column and the membrane. In the experiments, for each value of , the applied flow speed was increased until self-starting motion occurred that saturated at finite amplitude at which the flow speed, Uc , the frequency f c and amplitude of rotation θc , where the deflection angle is then approximated by θ = θc | sin([2π f c ]t)|, were recorded, the latter two through the use of a camera. Thereafter, the flow speed was reduced to study the hysteresis behaviour of the system and the sub-critical flutter-instability onset speed although the findings presented below focus on the self-started limit-cycle flutter given its relevance to energy harvesting.

3 Results Results in Fig. 2 show how the main system characteristics vary with . Membrane lengths 600 mm and 800 mm are represented by the points • and respectively with membrane thicknesses 1.5 mm and 3 mm represented by filled and hollow markers respectively. The solid lines are best fits for all the data plotted. In [1], the non-dimensional scheme used L and U/L as reference length and time respectively. For a tensioned membrane, this gives the non-dimensional flow speed (or stiffness ratio) as M = ρf U 2 L/T which is plotted in Fig. 2a. The value of T was estimated through a moment balance that, in the absence of a flow, ensured that the membrane was horizontal, i.e. T balanced the moment due to the dead weight of the membrane, hence T ≈ ρhgL 2 /(2c) where c is the length of the pivot column. In

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Fig. 2 Effect of membrane/spring property variation on the fluid-structure interaction: Variation ¯ of (a) non-dimensional flow speed as a stiffness ratio M , (b) f¯c , (c) θc and (d) comparative with ¯ 0.22 ◦, 0.29 efficiency, η; L: 600 mm •, 800 mm ; h: filled 1.5 mm, hollow 3 mm; mass ratio, L: , 0.44 •, 0.58 . Best fit lines: —– all data, − − L = 600 mm, −· L = 800 mm

addition to this scheme, frequency related values were non-dimensionalised by the natural (in vacuo) frequency of the second mode of a flexible cantilever, ω2 , and so ¯ = /ω2 and f¯c = f c /ω2 . we have The system is also governed by the mass ratio L¯ = (ρf L)/(ρh) where the main effect of changing L¯ is upon inertial (added mass) effects in flutter of the system. Clearly, L¯ will change when L and h are varied and the value for each marker type is noted in the caption of Fig. 2, the range of values tested being between 0.22 and 0.58. The non-dimensional results in Fig. 2a show a reasonable collapse of the data for the different dimensional systems does occur and that L¯ does not have a significant ¯ the stiffness ratio effect on the flutter-onset M values. Thus, for a given value of , determines instability onset. This might be expected for this small range of L¯ values: as shown in [4] varying L¯ only has a significant effect when changing fluid (water to air) or material (rubber to glass). The values of U used to generate Fig. 2a are those at which self-starting instability appeared; values for the lower threshold of the hysteresis loop (not shown here) followed similar trends, the greatest flow-speed ¯ The approximate best-fit line in extent of the hysteresis loop occurring for low . Fig. 2a indicates a drop in instability-onset flow speed from the clamped-clamped ¯ → ∞ and a non-zero lower limit for ¯ →0 case that would be approached for corresponding approximately to a cantilever-free flexible plate. In Fig. 2b, c, it can

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¯ increased, then f¯c be seen that as the trailing-edge support stiffness, i.e. through , ¯ as might be anticipated on also increased whereas θc was a maximum for low physical grounds. For both membrane lengths, the unstable modes were similar to the fundamental in-vacuo mode of a membrane clamped at both its leading and trailing edges. It was observed that the thicker membranes have regular, large oscillations, whereas the thinner membranes have intermittent large oscillations with much higher frequency and lower amplitude surface vibrations. We propose that the instability mechanism of the dominant oscillation is the same in both cases, the thicker membrane steadier because it has more structural damping. The system’s overall ability to generate power is assessed through Fig. 2d. Power generation of the system is proportional to the power factor 2 θc2 (2π f c ); this is derived from the relationship of power output being equal to the product of moment and the rate of angular rotation of the pivot arm. The highest dimensional power factor (not shown here) was produced by the 3 mm thick, 600 mm long membrane ¯ As it is desirable to achieve high power factors for at a mid-range value of . low values of flow speed, comparative efficiencies, η, were therefore calculated, i.e. the power factor relative to the power available from the free stream, the latter calculated via the kinetic energy flux passing through the swept area of the membrane. ¯ for The resulting efficiencies are shown in Fig. 2d. Each case yields a value of which a maximum efficiency occurs. However, the non-dimensionalisation does not result in a single efficiency curve and this suggests that L¯ is not a unique parameter in the characterisation for power generation. However, at present it can be seen that the shorter, thinner membrane gives the highest efficiency. In energy-harvesting applications, such efficiencies might set the optimum design value for κ although the effect of energy take-off on the dynamics of the FSI system also needs to be taken into account.

4 Conclusions We have investigated experimentally in a wind tunnel an axial channel flow passing above and below a centrally placed, clamped-clamped tensioned membrane, where the trailing-edge clamp is free to pivot about a hinge with a rotational spring stiffness. For the range of parameters studied, the system is found to lose stability to flutter. The system behaviour appears to be governed by three parameters: the mount natural frequency, the non-dimensional flow speed (stiffness ratio) and the mass ratio. However, the characterisation of power-generating efficiency is not uniquely determined by the mass ratio but requires further geometric parameters to be taken into account. It is found that self-starting large-amplitude flutter motions set in at flow speeds far lower than those of a clamped-clamped system and that the mass ratio does not have a significant effect on flutter instability-onset values for the relatively short membranes studied herein. Comparative efficiencies of the system’s power-generating capabilities relative to the power available from the free stream have been deter-

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mined showing that maxima occur at finite values of the trailing-edge spring mount, suggesting that energy-harvesting applications of the system can be optimised. However, at present the effect of energy take-off on the dynamics of the FSI system has not yet been investigated. Future work will explore a greater range of system properties, especially geometric including the length of the pivot-column, and develop computational models of the system, initially a linear study to investigate instability onset, followed by a non-linear study that will incorporate flow separation and wake effects.

References 1. Pitman MW, Lucey AD (2009) On the direct determination of the eigenmodes of finite flowstructure systems. Proc Roy Soc A 465:257–281. https://doi.org/10.1098/rspa.2008.0258 2. Howell RM, Lucey AD (2015) Flutter of spring-mounted flexible plates in uniform flow. J Fluids Struc 59:370–393. https://doi.org/10.1016/j.jfluidstructs.2015.09.009 3. Piñeirua M, Michelin S, Vasic D, Doaré O (2016) Synchronized switch harvesting applied to piezoelectric flags. Smart Mater Struct 25:085004. https://doi.org/10.1088/0964-1726/25/8/ 085004 4. Tan BH, Lucey AD, Howell RM (2013) Aero-/hydro-elastic stability of flexible panels: prediction and control using localised spring support. J Sound Vib 332:7033–7054. https://doi.org/10. 1016/j.jsv.2013.08.012

Interaction of Flow with a Surface-Mounted Flexible Fence A. Tsipropoulos and E. Konstantinidis

Abstract The nominally two-dimensional flow over a surface-mounted flexible fence and its dynamical response were studied numerically by a finite-element method. The governing equations were solved using an arbitrary LagrangianEulerian method. The flow was resolved using URANS equations at a Reynolds number of 25000 based on the height of the fence, H . When the fence is fixed (nonvibrating), vortices form and separate from the edge in a two-step periodic process corresponding to a Strouhal number of 0.090. When the fence is flexible, its edge is deflected towards the flow direction and the flow unsteadiness induces periodic fluid loading causing the fence to vibrate at twice the frequency of vortex shedding. For a fence with a specific density of 7 and natural frequency of the first eigenmode adjusted to match the frequency of vortex shedding from the fixed fence, the average tip deflection is 0.144H while the standard deviation of tip displacement is 0.020H . Keywords Vortex shedding · Flow-induced vibration · CFD · Simulation · Finite-element method

1 Introduction The nominally two-dimensional flow over a surface-mounted fence has received considerable attention in the scholarly literature with reference to applications in the atmospheric boundary layer. Fences are often employed as windbreakers to create a sheltering effect [1]. For this configuration, the governing parameters are the Reynolds number and the ratio of the fence height to the height of the boundary layer at the same location. Another parameter whose influence has received attention is the porosity of the fence [2]. Interestingly, the full-scale windbreaker problem still poses challenges [3]. Early experimental studies concentrated on the development A. Tsipropoulos · E. Konstantinidis (B) Department of Mechanical Engineering, University of Western, Macedonia, Bakola and Sialvera, Kozani 50132, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_5

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of the mean flow behind the fence, which is characterized by a large recirculation bubble. However, there is rather scarce information on aspects of the flow such as the instability of the shear layer separating from the free edge, the roll-up into discrete large-scale vortices and eventual vortex shedding in the wake. Few numerical studies over fixed obstacles have provided information on the instantaneous twodimensional flow structures, which clearly show the unsteady nature of the flow for both laminar and turbulent regimes [4, 5]. Due to the inherent instability of the flow over a surface-mounted fence, unsteady fluid forces may set the fence into vibration if it is flexible. In this study, we investigate the interaction of the unsteady flow over a surface-mounted flexible fence and its induced dynamic motion by means of numerical simulations.

2 Problem Description and Methodology The geometry of the problem under consideration together with the computational mesh is schematically shown in Fig. 1a. A thin obstacle (fence) of height H and thickness 0.1H is mounted on a bottom solid floor. For a fence whose width normal to the flow is very large, the flow can be assumed as nominally two-dimensional. The computational domain is 15H long by 8H tall and the fence is placed at a distance 5H from the inlet boundary on the left side. The flow enters from the left side with uniform velocity U0 and exits from the right side. The thickness of the boundary layer that develops on the bottom floor at the location of the fence is very small compared to the fence height due to the small distance between the inlet and the fence. The fluid is modelled as Newtonian with density ρ f and dynamic viscosity μ f . From the point of view of fluid dynamics, the problem can be characterized by the Reynolds number, Re = ρ f U0 H/μ f . For all simulations reported here the Reynolds number is set at 2.5 × 104 . The fluid motion is governed by the continuity and

Fig. 1 a The geometry and computational mesh employed in the present study, and b detailed view of the mesh around the fence and bottom surface

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Navier–Stokes equations. Due to the turbulent nature of the flow being considered, the Unsteady Reynolds Averaged Navier–Stokes (URANS) equations with the standard k − turbulence model we employed to resolve the flow. The inlet flow is assumed to be turbulent with the k − parameters set at k0 = 0.005 m2 /s2 and 0 = 0.005 m2 /s3 . The flexible fence is modelled as an elastic solid with density, ρs , Young modulus of elasticity, E, as well as the Poisson’s ratio, ν. Two dimensionless parameters are required to describe the fluid-solid interaction. Here, we have employed the solid/fluid density ratio (or relative density) ρ ∗ = ρs /ρ f and the reduced velocity, defined as U ∗ = U0 / f n H where f n is the natural frequency of the first structural eigenmode. Given the material properties of the solid, the natural frequencies of the structure in vacuum were computed via eigenmode analysis using the finite-element code. Computational simulations were carried out using a finite-element method for the discretization of the governing equations. The arbitrary Lagrangian-Eulerian (ALE) method was employed to combine the flow dynamics using an Eulerian frame of reference and the solid dynamics using a Lagrangian description in a moving material frame. The numerical solution proceeded in an iterative mode where the fluid flow equations are initially solved, then the computed fluid forces are applied on the fluid-solid boundary to get the solid deformation, and finally the fluid velocities are imposed afresh based on the solid velocities on the fluid-solid interface until the solution converges. The computational mesh along with details around the obstacle and the bottom surface are shown in Fig. 1. The core of the mesh consists of trihedral elements but tetrahedral elements were used on the solid surfaces to resolve the hydrodynamic boundary layers with better accuracy (see Fig. 1b). A time step of 0.01 s was employed, which yields a Courant number of 0.16. The equations were integrated for a total time of 100 s, which is sufficient to establish a steady quasi-periodic state and to analyse the dynamic character of the fluid flow and solid deformation.

3 Results and Discussion The flow over a fixed fence was initially investigated as a reference case for comparison to cases where the fence is flexible and can respond to fluid forcing. Figure 2 shows distributions of instantaneous vorticity that clearly illustrate the periodic formation and shedding of large-scale vortices behind the fence. Detailed examination of the vorticity distributions shows that this periodic process involves two distinct steps: initially a large-scale negative vortex behind the free edge and a smaller positive vortex near its base (ground vortex) are formed. The upward movement of the positive ground vortex initiates separation of the oppositely-signed main vortex from the edge. As both vortices are convected downstream by the streamwise flow, the positive vortex entrains the negative which lifts off from the ground. The strength of oppositely-signed vortices diminishes with downstream distance due to cross-annihilation of vorticity. The two-step vortex-shedding process induces velocity fluctuations behind the fence with a rich spectral content. Spectra of the streamwise

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Fig. 2 Instantaneous distributions of planar vorticity (top row) and streamwise velocity magnitude (bottom row) around a fixed fence at three different instants over approximately half period of vortex shedding at Re = 2.5 × 104

velocity fluctuations contain several superharmonics of the main frequency of f v0 = 0.225 Hz, which yields a Strouhal number of S = f v0 H/U0 = 0.090. Simulations were subsequently carried out for a flexible fence with ρ ∗ = 7 at ∗ U = 11.1 where material properties of the solid fence were selected such that the natural frequency of the first structural eigenmode is equal to the frequency of vortex shedding from the fixed fence. Figure 3 shows distributions of instantaneous vorticity and streamwise velocity at three different instants over approximately half period of tip oscillation. The two-step process of vortex formation and shedding is once again evident with a large-scale negative vortex behind the edge and a smaller positive vortex near the fence base. The main negative vortex is now more compact while the smaller positive vortex near the ground occupies more space than in the fixed case (cf. Fig. 2). Furthermore, the positive ground vortex engulfs the negative main vortex during the lift-off process, which is more pronounced than for the static case. Figure 4 shows the time history of tip displacement ξ and corresponding spectra Sξ over the last 40 s of the simulation. The fence is deflected by the flow towards the flow direction. The tip oscillates back and forth from its average deflected position; the average deflection of the tip is 0.144H and the standard deviation of tip displacement amplitude is 0.020H . The tip oscillation is repeatable from cycle to cycle with a bi-frequency waveform resulting in two spectral peaks. The dominant peak occurs at twice the frequency of vortex shedding while the secondary peak occurs at the first super harmonic. Hence, the fence responds to periodic fluid loading by synchronization at twice the vortex shedding frequency when the Strouhal frequency is close to the primary structural eigenfrequency, possibly due to the dualstep periodic process of vortex shedding. This is a phenomenon akin to streamwise vortex-induced vibration of elastically-mounted circular cylinders where 1:2 subhar-

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Fig. 3 Instantaneous distributions of vorticity (top row) and velocity magnitude (bottom row) around a vibrating fence at three instants for ρ ∗ = 7 and U ∗ = 11.1

Fig. 4 Time history of the tip displacement (left plot) and the corresponding spectrum (right plot) for ρ ∗ = 7 and U ∗ = 11.1

monic synchronization also occurs [6]. Furthermore, the findings from the present study at Re = 2.5 × 104 are similar to a recent numerical study albeit at Re ≤ 800 [7], in particular the period doubling of the tip oscillation compared to the natural frequency. We have also considered the effect of varying the natural frequency of the structure f n by changing either the elasticity or the density of the solid fence. These simulations have shown that changes in the density do not substantially affect the average bending whereas the fence bends more towards the flow direction as the elasticity is increased. In addition, the standard deviation of tip displacement increases from 0.009H to 0.036H in the range 7.1 ≤ U ∗ ≤ 18.4, irrespectively of how f n is varied. More runs at higher U ∗ values are required to check if the response amplitude attains a peak as a function of U ∗ .

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References 1. Raine JK, Stevenson DC (1977) Wind protection by model fences in a simulated atmospheric boundary layer. J Wind Eng Ind Aerodyn 2(2):159–180 2. Perera MDAES (1981) Shelter behind two-dimensional solid and porous fences. J Wind Eng Ind Aerodyn 8(1-2):93–104 3. Liu B, Qu J, Zhang W, Tan L, Gao Y (2014) Numerical evaluation of the scale problem on the wind flow of a windbreak. Sci Rep 4:6619 4. Orellano A, Wengle H (2000) Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence. Eur J Mech B Fluids 9:765–788 5. Fragos VP, Psychoudaki SP, Malamataris NA (2007) Direct simulation of two-dimensional turbulent flow over a surface-mounted obstacle. Int J Numer Methods Fluids 55:985–1018 6. Konstantinidis E (2014) On the response and wake modes of a cylinder undergoing streamwise vortex-induced vibration. J Fluids Struct 45:256–262 7. Wang L, Lei C, Tian F-B (2018) Fluid–structure interaction of a flexible plate vertically fixed in a laminar boundary layer over a rigid wall. In: Lau TCW, Kelso RM (eds) Proceedings of 21st Australasian fluid mechanics conference, University of Adelaide, Adelaide, Australia

Experimental Study of a Passive Control of Airfoil Lift Using Bioinspired Feather Flap L. J. Wang, Md. Mahbub Alam, and Yu Zhou

Abstract This paper presents a systematic experimental investigation on a passive flow control of a NACA0012 airfoil using real feather flap which is installed on the pressure surface. The focus of the present study is to determine the major role of a real feather flap in the aerodynamic performance of a NACA0012 airfoil at small attack angles (α). The feather flap width w and its installation position x in are varied from 0.27c to 0.8c and from 0.0 to 0.2c, respectively, where x in is measured from the leading edge of the airfoil, and c is the chord length of the airfoil. Detailed Particle Image Velocimetry (PIV) measurements are conducted to understand the origin of the aerodynamic benefits introduced by the feather flap. When mounted on the pressure side, the feather flap is proved to be beneficial to improve the aerodynamic performance of the airfoil at small α (= −4° to 8°). The lift C L and lift-to-drag ratio C L /C D are enhanced by 186% and 72%, respectively, for w = 0.53c, x in = 0.2c at α = 2°. Time-averaged vorticity and streamwise velocity around the flapped airfoil weaken and decrease, respectively, compared with those around the plain airfoil, which are attributed to the increased C L and C L /C D . Keywords Low Reynolds airfoil · Passive control · Feather flap · Biomimetic

1 Introduction The inherent self-activated feathers on birds’ wings play role in bird flight, yielding a high efficiency (high lift-to-drag ratio), salient flying during landing and preying, or a sudden increase in attack angles of wings to sustain gusts. Inspired by the flight of certain birds, some biomimetic control methodologies for the flow over airfoils have been developed [1]. Bechert et al. [2] found that adaptive flexible flaps which mock the wing feathers produce good aerodynamic performances of airfoils by postponing L. J. Wang · Md. M. Alam (B) · Y. Zhou Center for Turbulence Control, Harbin Institute of Technology, Shenzhen, China e-mail: [email protected] Digital Engineering Laboratory of Offshore Equipment, Shenzhen, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_6

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the flow separation toward the trailing edge. Recently, a numerical systematic study [3] revealed that an optimal rigid flap can deliver a mean lift increase of about 20% on a NACA0020 airfoil at α = 20°. However, most researches focus on the lift enhancement of airfoil by using rigid and flexible flaps at post-stall angles. No research has been done using real feathers which are flexible, could interact more vigorously with the flow than rigid artificial flaps. Furthermore, not much attention has been paid at small positive α or at small negative α. The objectives of the present experimental study are to (i) explore the effect of real feather flaps on the lift and aerodynamic efficiency of at small α, (ii) explore the optimum configuration by changing the width and installation position of flap systematically, and (iii) shed some light on the physical mechanism determining the lift enhancement by real feather flaps.

2 Experimental Details Experiments were carried out in a wind tunnel with a test section of 0.3 × 0.3 m2 in cross-section and 2.0 m in length. A NACA0012 airfoil with chord length c (= 150 mm) and span length b (= 260 mm) was vertically mounted between the two end plates through pitching pivots (Fig. 1a). The spanwise length of the constructed feather flap was 0.85b. The flap width was changed as w = 0.27c, 0.53c and 0.8c composed by one, two and three rows of feathers, respectively. With the leading edges of feather flap and airfoil as the references, the flaps installed at four different locations, i.e., x in = 0.0, 0.05c, 0.1c and 0.2c (Fig. 1b). The freestream velocity U ∞ was 4 m/s, corresponding to Re = 3.8 × 104 based on c. The fluid forces were measured by a load cell mounted at the bottom end of the pitching pivot. PIV Circular scale

Pivoted rod

Support screw rod

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y

260 mm

300 mm

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z 45 mm

x

y z

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NACA 0012 Flow

Leading edge

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x in

w

Fig. 1 a Sketch of force measurement setup, and b airfoil model with further flap with w = 0.27c attached on suction surface at x in = 0.2c

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technique was used to measure the flow field over the pressure side of the airfoil with and without feather flaps at different α.

3 Results and Discussion Figure 2 presents the dependence of lift C L and drag C D on w and x in when the flap is placed on the pressure side. While C L is zero at α = 0° for the plain airfoil (without flap, baseline), it with the flap is positive at α = −4° to 0° except for w = 0.27c and 0.8c at x in = 0.0. The use of the flap decreases the zero-lift α by more than 4° at x in ≥ 0.1c. The maximum lift enhancement is about 186% for w = 0.53c, x in = 0.2c, at α = 2°, and the maximum C L (= 0.88) obtained in this case approaches to the maximum C L (= 0.9) of the plain airfoil. At the same x in (e.g. x in = 0.0), the C L at α < 5° increases as w increases from 0.27c to 0.53c and drops with a further increase in w to 0.8c. This trend is the same with x in = 0.2c (Fig. 2c) and different with x in = 0.1c (Fig. 2b). On the other hand, a higher C L enhancement (α < 5°–8°) and a larger α range of enhanced C L are achieved at a higher x in . The observation suggests that birds can get a positive lift around α = 0° (even at negative α) by manipulating their feathers. Moreover, the modified stall angle α stall moves forwards to 8º from the natural one (11°) under the effect of the flap, except for the case of w = 0.53c and x in = 0.1c where α stall = 10°. That means the pressure-side feather flap makes α stall appearing in advance, and this effect is almost independent on w and x in . With the purpose of estimating the overall aerodynamic performance improved by the flap, C L /C D is presented in Fig. 2d–f as a function of x in , w and α. A higher C L /C D than that

Fig. 2 Dependence of a, b, c lift C L and d, e, f lift-to-drag C L /C D on flap width w and its position x in on pressure surface

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for the plain airfoil is obtained at −4° < α < 3° for all flap configurations. However, the flap aggravates the aerodynamic performance compared with the baseline for α > 3° due to the decrease and increase of modified C L and C D , respectively. The maximum enhancement in C L /C D is obtained at α ≈ 0° for x in = 0.2c and w = 0.53c. The C L /C D increment at α = 2° is 70% for the same x in and w. The effect of w on C L /C D is almost the same as that on C L , especially in the range of α < 6° (Fig. 2a–c). Figure 3 shows ωz * contours around the plain airfoil (baseline) and the flapped airfoil with w = 0.27c and 0.53c at x in = 0.2c. The region covered by the flap is hatched. The solid and dashed lines represent the positive and negative vorticities, respectively. As expected, the ωz * is negative on the pressure side of the airfoil. Consider the case of α = 2° first. The maximum magnitude of ωz * (= 32.5) of the plain airfoil persists around x = 0.4c (Fig. 3a). However, there are two maxima of ωz * of the flapped airfoil before and after x = 0.4c, respectively. The former maximum ωz * (= 30.0 and 27.5 for w = 0.27c and 0.53c, respectively) is smaller than the baseline ωz * while the latter maximum ωz * (= 36.0 and 34.0 for w = 0.27c and 0.53c, respectively) is larger (Fig. 3a–c). However, both maxima of the flapped airfoil in the case of α = 6º are larger than that of the plain airfoil (Fig. 3d–f). The decrease in ωz * in the case of α = 2° before in x in = 0.4c results from an obstruction effect by the flap on the flow. On the other hand, the increase after x in = 0.4c can be attributed to the disturbance by feather tips creating more vorticity. The flap for α = 6° makes more remarkable modifications to the vorticities beyond x in = 0.4c than that for α = 2°. The vorticities near the trailing edge are however much smaller for the flapped airfoil than for the plain airfoil. Considering that the trailing edge vortex having the counterclockwise rotation creates an upward flow and hence degrades the lift force on the airfoil, this is one reason why the lift enhancement occurs for the flapped airfoil compared to the plain airfoil. This also explains the increase of lift with the increase of w from 0.27c to 0.53c at x in = 0.2c (Fig. 2c). The isocontours of U* in Fig. 4 show that the flow in the vicinity of the airfoil keeps almost static (or “dead”) for a larger area in the case of flapped airfoil than the plain airfoil (Fig. 4a, d; b, c and e, f), which leads to a generation of a high pressure on the lower surface of the airfoil, hence a higher lift. The dead flow region enlarges

Fig. 3 Isocontours of time-averaged vorticity. a, b, c α = 2° and d, e, f α = 6°. a, d plain airfoil. b, e flapped airfoil with w = 0.27c, x in = 0.2c. c, f flapped airfoil with w = 0.53c, x in = 0.2c. The contour increment and cutoff level are 2.5 and ± 2.5, respectively

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Fig. 4 Isocontours of time-averaged streamwise velocity. a, b, c α = 2° and d, e, f α = 6°. a, d plain airfoil. b, e flapped airfoil with w = 0.27c, x in = 0.2c. c, f flapped airfoil with w = 0.53c, x in = 0.2c. The contour increment is 0.04

with w and α (Fig. 4b, c and e, f), that is a reason for the wider flap to produce a higher lift increase at specific x in and α (Fig. 4b, c). The magnitude of maximum U* is connected to drag force, an increase in the magnitude of maximum U* corresponds to an increased drag [4]. As shown in Fig. 4, the magnitudes of maximum U* in the range of 0.4 < x/c < 0.7 of the flapped airfoil are larger than that of the plain airfoil. The flap engenders a slower recovery of U* as can be seen from U* = 0.72 at x/c = 1.1, 1.32 and 1.5 (predicted value) for the baseline, w = 0.27c and w = 0.53c, respectively, for α = 2° (Fig. 4a–c).

4 Conclusions The optimum configuration of the pressure side flap is x in = 0.2c and w = 0.53c, resulting in maximum enhancements of 186% in C L and 70% in C L /C D at α = 2°. The enhancements of C L and C L /C D at small α are attributed to (1) the increase in leading-edge vorticities (generating lift) and the decrease in trailing edge vorticities (generating downforce) and (2) the larger dead flow region in the vicinity of the flapped airfoil pressure surface, leading to a generation of a high pressure. Acknowledgements The authors wish to acknowledge the support given to them from NSFC through Grants 11672096, 11632006 and 12002110 and from the Research Grant Council of the Shenzhen Government through grants JCYJ20170811152808282 and JCYJ20180306171921088.

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Reference 1. Bechert DW, Bruse M, Hage W, Meyer R (1997) Biological surfaces and their technological application-laboratory and flight experiments on drag reduction and separation control. AIAA paper, 1960 2. Bechert DW, Hage W, Meyer R (2006) Self-actuating flaps on bird- and aircraft-wings. In: Flow phenomena in nature: inspiration, learning and applications 2 (design and nature), WIT Transactions on State-of-the-art in Science and Engineering, vol 4, pp 435–446 3. Rosti ME, Omidyeganeh M, Pinelli A (2018) Passive control of the flow around unsteady aerofoils using a self-activated deployable flap. J Turbul 19(3):204–228 4. Roshko A (1954) On the drag and vortex shedding frequency of two-dimensional bluff bodies. NACA Technical Note, pp 1954–3169

Tapered-Cantilever Based Fluid-Structure Interaction Modelling of the Human Soft Palate J. Cisonni, A. D. Lucey, and N. S. J. Elliott

Abstract Most simplified and anatomically-derived models of the flow-induced motion of the soft palate during snoring and sleep apnoea adopt homogeneous material properties. In this study, a fluid-structure interaction model based on a flexible cantilever axially mounted in a straight channel flow is used to represent the uvulopalatal system in snoring conditions. Numerical simulations with tapered cantilevers were performed to investigate the effect of material inhomogeneity on the dynamics of the soft palate. Increasing the degree of tapering of the cantilever is shown to decrease the flow speed required to initiate flutter instability. With a free end more than twice thinner than the clamped end, a tapered cantilever can become even more unstable than the equivalent uniform cantilever with the same total mass. However, the frequency of oscillation of a tapered cantilever always remain higher than the equivalent uniform cantilever. Keywords Flutter instability · Soft palate · Tapered cantilever

1 Introduction Flow-induced flutter of the soft-palate tissues is a common source of snoring and can be an indicator of sleep apnoea, a serious condition [7]. Despite the intricate shape of the soft palate and the uvula extending from it, as well as the surrounding nasopharyngeal airway passage, physical models based on simplified geometries have been proposed to understand the pathogenesis of these widespread breathing disorders [1, 5]. By representing the soft palate as a sprung mass or a flexible cantilever, these lowcomplexity fluid-structure interaction (FSI) models have allowed prediction of the critical flow speed required to initiate palatal flutter and the vibration frequency. More J. Cisonni (B) · A. D. Lucey · N. S. J. Elliott School of Civil and Mechanical Engineering, Curtin University, Perth, Australia e-mail: [email protected] N. S. J. Elliott School of Physiotherapy and Exercise Science, Curtin University, Perth, Australia © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_7

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complex models based on three-dimensional realistic geometries reconstructed from computed tomography images of human airways have been employed to provide patient-specific data exploitable in a clinical context [8]. Hitherto, most simplified and anatomically-derived models used homogeneous material properties. However, experimental analyses suggest that the biomechanical properties of the tissues can vary significantly across the palate, particularly from hard palate to uvula [3]. Moreover, the inhomogeneity of the soft palate can be a crucial factor in the palatal deformation and displacement, potentially leading to airway closure [2]. This study focuses on the effect of inhomogeneous structural properties on the dynamics of the soft palate. A simplified FSI model relevant to the uvulo-palatal system in snoring conditions is employed to characterise the flow-induced flutter instability for increasing degrees of inhomogeneity.

2 Methodology The soft palate is approximated by a flexible cantilever clamped to a rigid wall representing the hard palate. The surrounding airways are simplified to a straight channel at the centre of which the cantilever is axially mounted. The physical properties of the FSI system are detailed in Fig. 1a. The viscous flow with mean inlet velocity U is governed by the two-dimensional Navier–Stokes and continuity equations. The cantilever is modelled as an infinitely-thin beam of constant density ρSP , Young’s modulus E and Poisson’s ratio ν, governed by the geometrically non-linear onedimensional Kirchoff–Love beam equation. As shown in Fig. 1b, its thickness h SP is therefore used as a control parameter to produce variations along of the its length specific mass m SP = ρSP h SP and flexural rigidity B = Eh 3SP / 12 1 − ν 2 . The open-source finite-element library oomph-lib [6] is used to formulate the problem following a similar approach to that employed by Cisonni et al. [4]. The

Fig. 1 Description of the simplified FSI model of soft palate: a parameters of the flexible cantilever immersed in viscous channel flow and b cantilever thickness profile representing soft-palate (SP) properties variations from hard palate (HP) to uvula tip (UT)

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flexible cantilever is modelled as a one-dimensional elastic Kirchhoff-Love beam, allowing for geometric non-linearity. It is spatially discretised using two-node Hermite beam elements and time stepping for the solid is done with a Newmark scheme. The two-dimensional incompressible Navier-Stokes and continuity equations are employed to model the viscous flow. The fluid domain is spatially discretised using nine-node quadrilateral Taylor-Hood elements with adaptive mesh refinement capabilities and time stepping for the fluid is done with a second-order backward differentiation formula scheme. The FSI problem is discretised monolithically and the solution to the non-linear system of equations is obtained by employing NewtonRaphson method and the SuperLU direct linear solver within the Newton iteration. The critical velocity Ucrit required to obtain self-sustained palatal-flutter is determined from the linear stability analysis of the FSI system through time-marching simulations. A base case including a uniform cantilever of thickness h SP = 0.96 mm is used as a reference to elucidate the influence of the tapering amplitude (h UT / h HP ) of the cantilever on the characteristics of its Mode-2 neutral stability.

3 Results and Discussion The gradual decrease in thickness of the one-dimensional beam from its clamped end to its free end effectively decreases the local specific mass and increases the local flexibility of the cantilever. Indeed, anatomical observations show that the soft palate is relatively stiff towards its anterior edge, partially because it is tethered to the hard palate and along its sides. The stiffness of the tissues is reported to be reduced towards the posterior edge from which the narrower uvula extends and is laterally unconstrained [3]. As shown in Fig. 2a, when the cantilever becomes increasingly lighter and more flexible towards the uvula tip, the critical velocity is significantly reduced, indicating that palatal flutter can occur more easily. Clearly, this might be expected since thinning the cantilever must reduce its overall stiffness. However, this effect of tapering exceeds that due simply to material reduction. This is seen by examining the critical velocity for an equivalent uniform cantilever with identical total mass in Fig. 2a. The comparison between the two models shows that the tapered cantilever is slightly more stable than the corresponding uniform cantilever for thickness ratios between 0.8 and 1, but more unstable for lower thickness ratios, particularly when h UT / h HP < 0.5. However, as shown in Fig. 2b, the quasi-linear decrease in oscillation frequency with decreasing thickness ratio is more rapid for a uniform-cantilever based model than for a tapered-cantilever based model. Thus, the oscillation frequency predicted with a uniform-cantilever based model could more easily fall below the range of snoring frequencies (20–320 Hz) if the beam becomes very thin. On the other hand, the decrease in frequency for the tapered-cantilever based model remains limited, even for relatively large tampering amplitudes. Over the range of thickness ratios considered, both tapered and equivalent uniform cantilevers become unstable with mode 2, as shown in Fig. 3. For the equivalent

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Fig. 2 Comparison of critical a velocity and b frequency between tapered-cantilever based FSI model of soft palate with decreasing uvula-tip thickness h UT and constant hard-palate thickness h HP = 0.96 mm, and a model based on equivalent cantilever of uniform thickness (h SP = (h HP + h UT ) /2)

Fig. 3 Comparison of neutral-stability mode shapes between tapered-cantilever based FSI model of soft palate for different uvula-tip thickness h UT and constant hard-palate thickness h HP = 0.96 mm, and a model based on equivalent cantilever of uniform thickness (h SP = (h HP + h UT ) /2). Axial coordinates x1 are scaled with the length of the flexible cantilever L SP and transverse coordinates x2 are scaled with the maximum deflection

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uniform cantilevers, the mode shape remains similar for all the decreasing values of thickness ratio. For the tapered cantilever, however, the deformation of the lighter and more flexible free-end becomes more prominent than that of the clamped upstream part as the thickness ratio decreases. This predicted oscillation-shape aligns more closely to the soft-palate deformation occurring predominantly towards the uvula.

4 Conclusions The linear stability analysis of tapered cantilevers in channel flow has been used to investigate the effect of structural inhomogeneity on the dynamics of the soft palate. With a free end increasingly thinner than the clamped end, tapered cantilevers become increasingly more unstable. They also require lower flow speed to initiate flutter instability and oscillate at higher frequencies than equivalent uniform cantilevers with the same total mass. Increasing the degree of tapering of a cantilever can be used to replicate more accurately the flow-loaded dynamics of the soft palate. Simplified FSI models based on inhomogeneous cantilevers appear to be more suitable to describe and analyse the uvulo-palatal system in snoring conditions. Acknowledgements This work was supported by resources provided by The Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia.

References 1. Aurégan Y, Depollier C (1995) Snoring: Linear stability analysis and in-vitro experiments. J Sound Vib 188:39–54. https://doi.org/10.1006/jsvi.1995.0577 2. Berry DA, Moon JB, Kuehn DP (1999) A finite element model of the soft palate. Cleft Palate Craniofac J 36:217–223. https://doi.org/10.1597/1545-1569_1999_036_0217_afemot_2. 3.co_2 3. Birch MJ, Srodon PD (2009) Biomechanical properties of the human soft palate. Cleft Palate Craniofac J 46:268–274. https://doi.org/10.1597/08-012.1 4. Cisonni J, Lucey AD, Elliott NSJ, Heil M (2017) The stability of a flexible cantilever in viscous channel flow. J Sound Vib 396:186–202. https://doi.org/10.1016/j.jsv.2017.02.045 5. Huang L, Quinn SJ, Ellis PD, Ffowcs Williams JE (1995) Biomechanics of snoring. Endeavour 19:96–100. https://doi.org/10.1121/1.412411 6. Heil M, Hazel AL (2006) oomph-lib—an object-oriented multi-physics finite-element library. In:Schäfer M, Bungartz HJ (eds) Fluid-structure interaction. Springer, pp 19–49 7. Maimon N, Hanly PJ (2010) Does snoring intensity correlate with the severity of obstructive sleep apnea? J Clin Sleep Med 6:475–478 8. Pirnar J, Dolenc-Grošelj L, Fajdiga I, Žun I (2015) Computational fluid-structure interaction simulation of airflow in the human upper airway. J Biomech 48:3685–3691. https://doi.org/10. 1016/j.jbiomech.2015.08.017

Broadband Noise Absorber with Piezoelectric Shunting Xiang Liu, Chunqi Wang, and Lixi Huang

Abstract Many efforts have been devoted to enhance the sound absorption performance of a micro-perforated panel (MPP) absorber, which usually consists of an MPP fitted in front of a backing wall or cavity. Among them, one possible way is to employ the panel vibration of the MPP to achieve extra sound absorption through the structure-acoustic coupling. Previous study has shown that the extra absorption can be effectively improved by attaching a shunted piezoelectric ceramic (PZT). The present work aims to explore the interaction mechanism between the shunted PZT and the perforated panel, and then a strategy is developed to construct multiple electrical resonances at desired frequencies for wide absorption bandwidth with parallel multiple resonance shunt circuit. The experiments show that the electrical resonance can be controlled precisely by adjusting the circuit parameters and agree well with the theoretical model, which makes it achievable to enhance MPP resonance at different frequencies and widen the absorption bandwidth. Keywords Sound absorption · Electro-mechanical coupling · Tunable reactance

1 Introduction Micro-perforated panel (MPP) is an attractive alternative to traditional porous sound absorption materials. However, its absorption capability is usually not enough since significant absorption occurs mainly around its resonance frequencies. Many efforts have been made to further improve or optimize its acoustic performance [1–5]. For better low frequency absorption performance, one alternative way is to employ the panel vibration of the MPP to achieve additional sound absorption through structureacoustic coupling [6]. Aiming for tunable and enhanced absorption performance, X. Liu · L. Huang Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China X. Liu · C. Wang (B) · L. Huang Lab of Aerodynamics and Acoustics, HKU-Zhejiang Institute of Research and Innovation, Hangzhou 311305, Zhejiang, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_8

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Chang et al. [7] propose to attach a passively shunted piezoelectric ceramic (PZT) to the flexible perforated panel. Results show that the absorption peak due to structural vibration can be conveniently adjusted by tuning the shunt circuit, and at the same time the absorption bandwidth is increased because of the additional shunt damping. The work in [7] focuses on the sound absorption coefficients by the coupling of the flexible panel vibration and a simple RL shunt circuit with a single electrical resonance. A thorough analysis on the interaction between the shunted PZT and the perforated panel is not addressed, though it is crucial for extending the shunt absorption to wide bandwidth with more complicated multiple resonance shunt circuit. In the present work, the interaction mechanism between the shunted PZT and the perforated panel is investigated, and then a strategy is developed to construct multiple electrical resonances at desired frequencies for wide absorption bandwidth with parallel multiple. A finite element (FE) model is established for the analysis of the fully coupled system consisting of the structural vibration of the flexible panel, the sound field, the acoustic dissipation of the MPP, the PZT and the shunt circuit. The FE model is validated by comparing the predicted sound absorption coefficients and the experimentally measured data using an impedance tube. Numerical analysis shows that the shunted PZT may increase or decrease the vibration of the structure in different situations, and the current in every branch of circuit dissipates sound energy in a different manner. A design strategy is then proposed to create more resonances with the parallel branches circuit to widen the absorption band at any desired frequency range, which can work in the surroundings with several changeable tonal noise peaks.

2 Theoretical Approach Figure 1 shows the two-dimensional configuration of the theoretical model. The flexible panel bonded with a shunted PZT is clamped at one end of the impedance tube and backed with a rigid cavity. The structural vibration is governed by

Fig. 1 Configuration of the smart absorber

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Fig. 2 Configuration of the smart absorber

Ds (1 + j × ξ )∇ 4 w + ρs

∂ 2w = pduct − pcav ∂t 2

(1)

in which Ds , ξ , ρs , w denote flexural rigid, loss factor, structure surface density, and normal displacement respectively. Sound pressure in the duct side and back cavity side are represented with pduct and pcav . The PZT can be regarded as a voltage source connected with intrinsic capacitor C0 and resistance R0 in series as shown in the electrical part of Fig. 2. The PZT is governed by the following equation,

T D E ε d = dt sE T S

(2)

where D,S, ε, s, E, T, d are electrical displacement, strain, permittivity, elastic compliance, electric field strength, stress, and piezoelectric effect matrix. A plane acoustic wave is incident on the flexible panel. The vibration response of the flexible panel bonded with the shunted PZT are solved. The lumped parameter circuit model schematic is shown in Fig. 2. The coupling matrixes [s d ε] in Fig. 2 are coefficient matrixes in the Eq. 2.

3 Results and Discussion Firstly, a series resistor-inductor (RL) single resonance circuit is connected to a PZT-5J patch, to resonate with the capacitor C0 in the PZT. The capacitance of the 64.5 mm × 14.5 mm × 0.42 mm PZT patch is about 33nF. In the experiment, this PZT is attached to a panel absorber and tested in a 100 mm × 100 mm cross section impedance tube with two B&K 1/2 in. microphones according to ISO 10534-2. Figure 3a shows the predicted and experimentally measured absorption coefficients. The natural resonance frequency of opened shunted PZT system is about 330 Hz. The predicted results are in good agreement with the experimental results. The numerical result indicates that the energy is mainly dissipated by the volume displacement of the first mode, as shown in Fig. 3b. By a large number of experiments, it’s found that when the electrical and mechanical resonance frequencies ( f E L E and f M E ) get close,

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(b)

Fig. 3 a Predicted and experimental results; b modal shape of the flexible MPP

the vibration velocity caused by mechanical resonance is still significant at f E L E , and lead to an add-up voltage in the voltage source of the PZT model. In this case, a relatively large resistance can get more partial voltage at the f M E and dramatically improve the mechanical resonance absorption, since the big capacitance from C0 and inductance from the circuit will get much partial voltage at f M E but don’t dissipate energy, then a bigger resistance can grab more voltage from them and dissipate. By appropriately designing the resistance, the structural vibration can be enhanced with a low resistance and when the resistance is too large, the over-damped acoustic phenomenon will happen at certain frequencies. For broadband absorption, multiple parallel branches are added in the shunt circuit, f il as shown in Fig. 4a. In each branch, the first two elements Cn and L n work as a LC filter to adjust frequency response of circuit. The other elements Rn and L tun n are

Fig. 4 a Schematic of parallel reactance circuit; b gain-phase function of the first two electrical resonances; c the predicted total reactance of entire circuit model

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Fig. 5 a Sound absorption on panel; b multiple electrical resonances on MPPA; c mean vibration velocity; d voltage response on PZT; e the current intensity flowing through R2

designed to dissipate energy and resonate with C0 in the PZT. Firstly, two electrical resonances are implemented to test the feasibility of multi-resonance. Figure 4b shows Gain-Phase function of the first two electrical resonances. The two peaks of Gain function correspond to the electrical resonances. In Fig. 4c, the calculated total reactance of C0 and shunt circuit goes through zero from negative to positive twice to generate two electrical resonances, which suggests that the designed circuit can control total reactance to zero at any desired frequencies. When the shunted PZT is bonded to the MPP, two more absorption peaks due to electrical resonances appear apart from the original mechanical resonance absorption peak, as shown in Fig. 5a, b. Figure 5c shows the mean vibration velocity of the MPP. Two smaller velocity peaks appear near the mechanical resonance frequency, which can be explained by the voltage response on two poles of PZT patch in Fig. 5d. The relatively small resistance results in a huge current intensity in the total circuit and big voltage value on two poles of PZT. This big voltage will increase the vibration of PZT, and accordingly, make the plate vibrate. So the relative velocity between air particles and MPP increase to dissipate more energy. The intensity of the current flowing through the resistor R2 in the 2nd branch is shown in Fig. 5e. By the LC filter in the 2nd branch, the current I2 is small at the first electrical resonance and mechanical resonance, while becomes huge at second electrical resonance. Thus, the vibration of MPP is increased to improve MPP’s Helmholtz effect. Meanwhile, part of the energy is also dissipated by resistance.

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4 Conclusions The coupling mechanism between shunted PZT and panel type absorber is studied to widen the absorption bandwidth. The finite element calculation results have a good agreement with experiments. Based on these results, the multiple branch circuit can create electrical resonances at any desired frequencies, and improve the Helmholtz dissipation of MPPA. The working principle of the multiple branch circuit is clearly analyzed. Therefore, the designed controllable smart broadband multi-resonance absorber can be applied to the noise environment with several different and even changing tonal noise peaks, such as fan noise or flow duct noise. Acknowledgements This project is supported by National Natural Science Foundation of China (Grant No. 51775467).

References 1. Wang C, Huang L (2011) On the acoustic properties of parallel arrangement of multiple microperforated panel absorbers with different cavity depths. J Acoust Soc Am 130(1):208–218 2. Zhang Y, Chan YJ, Huang L (2014) Thin broadband noise absorption through acoustic reactance control by electro-mechanical coupling without sensor. J Acoust Soc Am 135(5):2738–2745 3. Wang C, Cheng L, Pan J, Yu G (2010) Sound absorption of a micro-perforated panel backed by an irregular-shaped cavity. J Acoust Soc Am 127(1):238–246 4. Wang C, Huang L, Zhang Y (2014) Oblique incidence sound absorption of parallel arrangement of multiple micro-perforated panel absorbers in a periodic pattern. J Sound Vib 333(25):6828– 6842 5. Wang C, Choy YS (2015) Investigation of a compound perforated panel absorber with backing cavities partially filled with polymer materials. J Vib Acoust Trans ASME 137(4):044501 6. Lee YY, Lee EWM, Ng CF (2005) Sound absorption of a finite flexible micro-perforated panel backed by an air cavity. J Sound Vib 287(1–2):227–243 7. Chang D, Liu B, Li X (2010) An electromechanical low frequency panel sound absorber. J Acoust Soc Am. 128(2):639–645

Solid-Fluid Interaction in Path Instabilities of Sedimenting Flat Objects Jan Dušek, Wei Zhou, and Marcin Chrust

Abstract As soon as particles, freely falling or ascending under the action of gravity, buoyancy and hydrodynamic forces, reach Reynolds numbers exceeding values of the order of one hundred, path instabilities arise yielding non vertical, mostly oscillating, trajectories. In this paper we focus on the behavior of flat undeformable solid spheroids. Direct numerical simulations of their fall (ascension) in a quiescent ambient Newtonian fluid reveal the existence of regimes characterized by strong and weak interaction between the fluid and the solid body motion resulting, respectively, in strongly oscillating or almost straight trajectories. In many cases these regimes even co-exist for the same problem parameters. Mathematically, this makes their prediction dependent on initial conditions and, physically, this may result in a strong sensitivity of solid-fluid systems to external perturbations. Keywords Solid-fluid interaction · Path instabilities · Oblate spheroids

1 Introduction Path instabilities considerably change the behavior both of individual sedimenting particles and of a whole multi-particle system. At the scale of a single particle, this leads to a multitude of non-trivial regimes. These effects are especially striking for particles falling vertically in laminar regime (spheres, flat axisymmetric bodies, oblate spheroids, cylinders, etc.). At large scales of sedimenting systems of a large number of particles, the path instabilities have been recognized to cause clustering in dilute systems leading to otherwise unpredicted increase of sedimenting velocities [1]. Both, the single particle and multi-particle systems depend on the intensity of the effective coupling between the wake and the degrees of freedom of the solid body.

J. Dušek (B) · W. Zhou · M. Chrust Institut ICube—Equipe de Mécanique des Fluides, Université de Strasbourg, 2, rue Boussingault, 67000 Strasbourg, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_9

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The latter results in regimes with strong and weak response of the body dynamics to that of the fluid flow. The earliest relatively exhaustive parametric study of path instabilities dates back to early 2000s [2] and concerned homogenous spherical bodies (considered also in Ref. [1]). However, homogeneous spheres appear to be too perfect to present as rich dynamics as flat objects [3]. Strongly and weakly oscillating trajectories were found in direct numerical simulations of infinitely flat disks [4] and flat cylinders of large diameter/height aspect ratios [5]. At the same time, the strongly and weakly interacting modes were predicted for flat cylinders by linear analysis by Tchoufag et al. [6] who introduced the terminology of, respectively, ‘solid’ and ‘fluid’ modes. A detailed parametric study was presented recently for oblate spheroids of aspect ratio χ = d/a, where d is the equatorial diameter and a the length of the symmetry axis, varying from infinity to one [7]. It benefits from a specifically designed numerical method [4] based on spectral—spectral-element spatial discretization combined with a domain decomposition using a dynamic sub-domain reconnection based on the spherical harmonic expansion yielding a highly accurate and highly efficient solver. Among other results, the investigation revealed many cases of co-existence of solid and fluid modes. This co-existence considerably influences the transition scenario. The latter is parameterized by three parameters obtained by non-dimensionalizing the flow equations coupled with solid body motion equations. In addition to the aspect ratio characterizing the shape of spheroids (assumed to be homogeneous), two more parameters were defined in Ref. [7]. The relative inertia of the body and of the surrounding fluid is determined by the non-dimensionalized mass m ∗ = m/(ρd 3 ) where m is the mass of the spheroid, d its diameter and ρ the fluid density. The third parameter is the Reynolds number G = U d/ν based on the velocity scale U given by the effective acceleration due to gravity and buoyancy U = (m ∗ − V /d 3 )gd (ν being the kinematic viscosity of the fluid and V the volume of the body) called Galileo number. In the investigated parameter domain, the average vertical asymptotic velocities non-dimensionalized by this velocity scale lie between one and two which means that the asymptotic Reynolds numbers can be roughly estimated to be situated between once and twice the Galileo number. The three-parameter domain investigated in Ref. [7] is delimited by χ ≥ 1.1 (almost spheres to infinitely flat spheroids), m ∗ ≤ 5 (at m ∗ = 5, the behavior is expected to be qualitatively similar to any larger m ∗ ) and 30 ≤ G ≤ 300. The lowest instability threshold was found for the infinitely flat spheroid of m ∗ = 2 at G = 35. The investigation was limited to G ≤ 300. As a consequence, not all regimes become chaotic, however, most thresholds delimiting individual regimes become almost independent of the Galileo number at this limit. The mentioned paper [7] evidences significant sub-critical effects resulting in many cases of co-existence of multiple stable states. Mostly, the coexisting states are characterized by strong and weak solid-fluid interaction. No place was available to discuss and illustrate their differences. In the present paper we select three qualitatively very different examples of co-existing fluid and solid states and show the impact of the different solid—fluid interactions on the wake and trajectory of the falling body.

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2 Some Examples of Co-existing States with Strong and Weak Solid-Fluid Interaction Three examples for three different aspect ratios of spheroids are considered in what follows. The first one concerns very flat spheroids of aspect ratio 10 of m ∗ = 0.25 at Galileo number: 115 (see Fig. 1). Note that, unlike in Fig. 2 of Ref. [7], both regimes are situated exactly at the same point of the parameter space. The critical Galileo number for the loss of stability of the steady vertical trajectory is 91 for the same aspect ratio independently of of m ∗ for m ∗ < 0.3. ‘Light’ spheroids obey the sphere-like scenario with a regular (steady) primary bifurcation. As can be seen, the fluid mode is characterized by a very small amplitude of oscillation of the spheroid axis as compared to the solid mode. In agreement with the sphere-like scenario, the trajectory is actually oblique oscillating, albeit with a very slight mean inclination of only 0.3◦ with respect to the vertical. In contrast, the extent of vorticity iso-surfaces taken at the same level of ±0.7 is comparable and the maximum (situated between 0.5 and 2 d downstream of the body center) is of the same order, respectively, 2.7 and 6.9, for the fluid and the solid mode. In the fluid mode, the wake structures as practically the same as that of a fixed body with significant streamwise vorticity due to the vortex shedding but with negligible response of the body. In the solid mode, the response of the body to the wake oscillation is very strong. It further enhances the wake vorticity and, consequently, the drag, leading to a reduction of mean settling velocity by 14%.

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In Fig. 2, coexisting solid and fluid modes for spheroids of aspect ratios 3 and 1.1 are illustrated. The kinograms are represented with equal scales of vertical and horizontal axes. The body is on the scale. In Fig. 2a the fluid mode is a slightly oscillating periodic exactly vertical fall unlike that of Fig. 1a. The co-existing solid mode yields an oblique trajectory with the spheroid rotating over edge (tumbling regime). This regime is characteristic for rather massive (m ∗ ≥ 1) bodies. To select one of the two modes, appropriate initial condition must be imposed. (E.g., with small and large angular velocity of rotation.) A similar situation occurs for the almost spherical shape in Fig. 2b. The trajectory of the fluid mode (represented in the first two figures at left in terms of a kinogram of a short section of motion and a global picture of the path of the body center) is very close to vertical with almost no oscillation of the body. However, if the trajectory of the spheroid center is represented in strongly enlarged horizontal scales, the trajectory appears to be genuinely non-vertical, three-dimensional and chaotic. In contrast, the solid mode presents significant (amplitude of inclination 53◦ ), strictly periodic oscillations (the direction of the symmetry axis is visualized as a red dotted line) and the trajectory is planar. Again, the strong solid-fluid interaction enhances the drag by about 10%.

3 Discussion and Conclusion Apart from the already mentioned dependence of the trajectories on the the initial conditions, the level of external perturbations plays also an important role in the selection of the attractor. The solid modes are, generally, more stable than the fluid ones, which means that the fluid modes can be difficult to observe experimentally if only the motion of the body is registered. This may lead to discrepancies between experimental observations, linear theory and numerical simulations. Flat spheroids present the three characteristic regimes evidenced experimentally already by Field et al. [9], called “periodic” or “flutter”, “intermittent” and “tumbling”. The numerical study [7] showed that the robust flutter, intermittent and tumbling regimes ‘spill over’ below the threshold of primary instability of the steady vertical state. The co-existence of solid and fluid unsteady modes illustrated in Fig. 2a characterizes the scenario for large non-dimensionalized masses and that illustrated in Fig. 1 dominates the region of light spheroids. Experimental observations would tend to overlook the fluid modes while progressive tracking of bifurcations starting from the steady vertical regime might reveal the solid modes only after the fluid ones become unstable. This can yield completely different pictures of the scenario, namely erroneous predictions of the threshold of instability of the vertical trajectories. E.g. observations of a significant upward shift of the threshold of path instability of flat cylinders characterized by a small inertia, were due to the fact that the small oscillations of fluid modes could not be distinguished from experimental noise (see [5]). Similarly, it can be expected, that experiments with more massive bodies will underpredict the instability thresholds.

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Almost spherical spheroids (χ = 1.1) present qualitatively the same scenario as spheres [8] overlapped, for light particles (m ∗ < 0.25, i.e. density ratio < 0.5), with the robust solid zig-zagging mode (flutter) represented in Fig. 2b. In an experiment, only this regime would be seen for light imperfect spheres. This might be a possible explanation of the surprising observations reported in Ref. [10].

References 1. Uhlmann M, Doychev T (2014) Sedimentation of a dilute suspension of rigid spheres at intermediate Galileo numbers: the effect of clustering upon the particle motion. J Fluid Mech 752:310–348 2. Jenny M, Dušek J, Bouchet G (2004) Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid. J Fluid Mech 508:201–239 3. Ern P, Risso F, Fabre D, Magnaudet J (2011) Wake-induced oscillatory paths of bodies freely rising of falling in fluids. Ann Rev Fluid Mech 44:97–121 4. Chrust M, Bouchet G, Dušek J (2013) Numerical simulation of the dynamics of freely falling discs. Phys Fluids 25:044102 5. Chrust M, Bouchet G, Dušek J (2014) Effect of solid body degrees of freedom on the path instabilities of freely falling or rising flat cylinders. J Fluids Struct 47:55–70 6. Tchoufag J, Fabre D, Magnaudet J (2014) Global linear stability analysis of the wake and path of buoyancy-driven disks and thin cylinders. J Fluid Mech 740:278–311 7. Zhou W, Chrust M, Dušek J (2017) Path instabilities of oblate spheroids. J Fluid Mech 883:445– 468 8. Zhou W, Dušek J (2015) Chaotic states and order in the chaos of the paths of freely falling and ascending spheres. Int J Multiphase Flow 75:205–223 9. Field SB, Klaus M, Moore MG (1997) Chaotic dynamics of falling disks. Nature 388:252–254 10. Horowitz M, Williamson CHK (2010) The effect of Reynolds number on the dynamics and wakes of freely rising and falling spheres. J Fluid Mech 651:251–294

Aerodynamic and Aero-acoustics Performance of Unsteady Kinematics Applied to a Rotor Operating at Low-Reynolds Number Nicolas Gourdain, Antonio Alguacil, and Thierry Jardin

Abstract Micro air vehicles with vertical take-off and landing capabilities are used for a large panel of missions (rescue, recognition, etc.). However, the aerodynamic performance of the propeller is usually lower than with classical large rotors, due to increased viscous drag and flow separation. This paper explores the possibility to increase the rotor performance by taking advantage of the flow unsteadiness, with unsteady forced motions (pitching, flapping and surging). Both flapping and surging have the potential to improve the rotor thrust. Keywords LBM · LES · Unsteady kinematics · Aero-acoustics

1 Introduction Major efforts have been done to improve the rotor performance by optimising the blade design, under steady flow conditions. However, the possibility to increase the rotor performance by taking advantage of unsteady flows has received less attention. Typically, the thrust coefficient could be written as a function of the three possible solid rotation angles and their corresponding angular velocities (known as pitching, flapping and surging). This concept was previously investigated on a micro-scale rotor, sometimes by coupling both flapping and pitching motions [1, 2]. The objective of the present work is thus to study the influence of unsteady kinematics on the performance of a rotor operating at low Reynolds number. The numerical prediction of such unsteady flows (leading edge vortex, massive separation) remains challenging and the unsteady displacement of the blade require adapted numerical methods. To address these difficulties, the present work relies on the use of Large-Eddy Simulation (LES) performed with a Lattice-Boltzmann Method (LBM). The influence of flapping, pitching and surging on the aerodynamic and acoustic performance is investigated. N. Gourdain (B) · A. Alguacil · T. Jardin ISAE-SUPAERO, University of Toulouse, Toulouse 31400, France e-mail: [email protected] Department of Aerodynamics, Energetics and Propulsion, Toulouse, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_10

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2 Test Case and Numerical Method The test case is a 2-bladed rotor operating in hover, for which the main characteristics are reported in Table 1. The angle of attack of the airfoil is α0 = 15◦ . Numerical simulations rely on LES performed with a LBM flow solver [3], which already demonstrated its capability to predict the flow for such rotors [4]. A hierarchical grid refinement is used with 5 grid levels, leading to a total number of grid points for the mesh of 143.5 × 106 . The dimension of the first cell in the direction normal to the wall is y + ≈ 50. An overview of the flow field and the rotor performance predictions are shown in Fig. 1. An aero-elastic flow solver was previously validated to simulate unsteady motions [5] as pitching angle α (around the spanwise axis), flapping angle β (around the blade hinge, perpendicular to the spanwise axis) and surging angle ω (around the rotor axis, corresponding to a variation of the rotation speed Ω).

3 Modelling of the Unsteady Aerodynamic Performance Numerical simulations were previously performed [5] and used to derive an analytical model to evaluate the performance of unsteady kinematics (rotation combined with pitching, flapping or surging). The torque and thrust coefficients, C Q and C T , are Q.Ω T defined as C T = 1 ρ(Ω.D) 1 2 π D 2 and C Q = 3 5 (T and Q are time-averaged 2×16 2×32 ρΩ π D thrust and torque, respectively). The forced motion model is based on a periodic motion that is superimposed to the main rotation of the blade, with an angular velocity defined as q˙ = −Ωm qmax cos (Ωm t), where Ωm is the motion pulsation and qmax the amplitude of the motion. The modelling of unsteady motion effects on C T relies on a decomposition with three terms: a steady term (I ) depending on the geometric blade angle α0 , an unsteady term (I I ) related to the flow angle dα f induced by the forced motion (estimated with the thin airfoil theory [6]) and an unsteady term (I I I ) depending on the unsteady rotation speed Ω f (flapping and surging adds a component to the rotation speed, but not pitching). Finally, the modelling of C T writes: C T f (t) = [C T (α0 ) + C T (dα f , t − τ f )] × Ω 2f /Ω R2 I

Table 1 Characteristics of the rotor test case Number of blades Rotation rate Ω R Rotor diameter, D Blade chord, C Reynolds number, Re

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Fig. 1 a instantaneous Q-criterion flow field coloured with streamwise velocity (LES-LBM) and b thrust coefficient C T with respect to the torque coefficient C Q

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Fig. 2 Variation of the thrust coefficient C T compared to the pure rotation case (note: the model does not converge for amplitude of flapping larger than 0.11 rad)

with τ f a time-lag. The value of the thrust coefficient C T (α0 + dα f ) is then interpolated from the steady performance shown in Fig. 1b. The influence of two parameters are investigated: the motion pulsation and the maximum amplitude. The results for the thrust coefficient is shown in Fig. 2 and the results for the figure of merit, defined 3/2 as C T /C Q , is shown in Fig. 3. The results are expressed as a difference with those obtained for the pure rotation case (C T = 0.023, FoM = 0.62). The information provided by the model can be summarised as follow: (a) an increase of the frequency or amplitude increases the thrust, (b) surging and flapping are good candidates to improve the thrust and (c) surging is able to increase the figure of merit.

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Fig. 3 Variation of the figure of merit compared to the pure rotation case (note: the model does not converge for amplitude of flapping larger than 0.11 rad)

4 Aero-acoustic Performance The impact of unsteady kinematics on the rotor noise is estimated by analyzing the LES-LBM results. The chosen parameters are those associated to an increase of the thrust (i.e. high pulsation and amplitude), with Ω f = 3Ω R and qmax = 0.17, 0.09 and 0.23 (rad) for pitching, flapping and surging, respectively. The flow fields coloured with time-averaged pressure fluctuations are shown in Fig. 4. For the pure rotation case, the pressure fluctuations are located in the vicinity of the rotor tip. The unsteady kinematics is responsible for an increase of the pressure fluctuations at the wall. Pressure signals are then recorded at x = 6.R from the rotor center, in the rotor plane, which is sufficient to avoid hydrodynamics perturbations. The instantaneous pressure field and a Discrete Fourier Transform are shown in Fig. 5a, b.

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Fig. 4 Root mean square of the pressure fluctuations on the suction side wall: a pure rotation, b rotation + pitching, c rotation + flapping and d rotation + surging

The frequency f˜ is normalized by 2π/Ω R , with Ω R the rotor pulsation. The blade passing frequency (BPF) is f˜B P F = 2 and the frequency associated to flapping, pitching and surging is f˜ck = 3. These frequencies interact, leading to the emergence of new harmonics f˜i = k1 f˜B P F ± k2 f˜ck , with k1 and k2 integers. Aerodynamic and acoustic performances are shown in Fig. 5c. As expected, the unsteady kinematics leads to an increase of the total noise (more than 15 dB for surging) due to the increase of the flow unsteadiness on the blade wall.

5 Conclusion Numerical simulation, based on LES-LBM, have been performed to investigate the influence of compound kinematics, as pitching, flapping and surging (combined with rotation). The different forced motions superimposed to the rotation have a significant influence on the rotor performance: pitching, flapping and surging lead to an increase of the thrust coefficient (up to more than 40% with surging), at the

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Fig. 5 a Instantaneous flow field coloured with pressure (pure rotation) and b Discrete Fourier Transform of a pressure signal registered at x = 6R (dashed line) and c sound pressure level with respect to the thrust coefficient C T

price of a penalty on the torque that partially balance the advantage on the thrust. Among these forced motions, surging and flapping are the most promising candidates. However, a significant work is still required to reduce the overcost in terms of noise to improve these compound kinematics. Perspectives to this work include the study of more complex motions, considering a combination of many angular velocities. Such unsteady kinematics can be optimized with global or local algorithms. For example, a gradient descent algorithm with adjoint equations could be used to estimate the performance sensitivity to the different motions. Acknowledgements Numerical simulations have been performed thanks to the resources provided by the Federal University of Toulouse (under projects CALMIP p1425 and p17014) and GENCI (project A0042A07178). These supports are greatly acknowledged. Special thanks to Jonas Latt, for his support on Palabos and to Michael Bauerheim for helpful discussions.

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References 1. Wu J, Wang D, Zhang Y (2015) Aerodynamic analysis of a flapping rotary wing at a low Reynolds number. AIAA J 53:2951–2966 2. Chen L, Wu J, Zhou C, Hsu SJ, Cheng B (2018) Unsteady aerodynamics of a pitching-flappingperturbed revolving wing at low Reynolds number. Phys Fluids 30(5):051903 3. Lallemand P, Luo LS (2000) Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys Rev E 61(6):6546–6562 4. Gourdain N, Singh D, Jardin T, Prothin S (2017) Analysis of the turbulent wake generated by a micro-air vehicle hovering near the ground with a Lattice Boltzmann Method. J Am Helicopter Soc 64(2):1–15 5. Alguacil A, Jardin T and Gourdain N (2020) Fluid-structure interactions and unsteady kinematics of a Low-Reynolds-Number Rotor. AIAA J 58(2):955–967 6. Osborne C (1973) Unsteady thin-airfoil theory for subsonic flow. AIAA J 11(2):205–209

Free-End Mean Pressure Distribution for a Finite Cylinder: Effect of Aspect Ratio Adam Beitel and David Sumner

Abstract The mean pressure distribution on the free end of a surface-mounted finiteheight cylinder was studied experimentally at a Reynolds number of Re = 6.5 × 104 and a relative boundary layer thickness of δ/D = 0.6. The cylinder aspect ratio was varied from AR = 0.5 to 11 in increments of 0.5 to study the changes that occurred in the mean pressure distribution. The contribution of the free-end pressure distribution to the mean normal force was also obtained. With an increase in aspect ratio, the pair of eye-like spots on upstream half of the free end disappears, the region of adverse pressure gradient in front of the reattachment line becomes stronger and moves farther downstream, and a prominent enclosed region of higher pressure develops near the trailing edge. The pressure contribution to the mean normal force increases with AR to reach a constant value of C N,P ≈ 0.78 for AR ≥ 6.5. This behaviour contrasts that of the total normal force C N , which tends to decrease in value for AR ≥ 6.5 due to an increased contribution of the wall shear stress acting on the sides of the cylinder. Keywords Finite cylinder · Pressure distribution · Normal force

1 Introduction The characteristics of the mean recirculation zone above the free end of a surfacemounted finite-height cylinder (Fig. 1) are sensitive to the cylinder’s aspect ratio AR = H/D (for height H and diameter D) [1, 2]. The thickness of the mean recirculation zone, the locations of the arch vortex centre and its end points within this zone, and the positions of the mean reattachment line and near-surface critical points, are known to vary with AR [3]. Studies reporting surface flow visualization and mean pressure distribution measurements on the free end illustrate a complex dependency on AR and the relative thickness of the boundary layer δ/D on the ground plane [3]. A. Beitel · D. Sumner (B) Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N 5A9, Canada e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_11

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Fig. 1 Schematic of the flow around a surface-mounted finite-height cylinder partially immersed in a flat-plate boundary layer (where U(z) is the boundary layer velocity profile) showing the mean normal force F N . Details of the free-end coordinate system (r,θ) are shown in the inset

The free-end mean pressure distribution is the main contributor to the mean normal force F N experienced by a finite cylinder [4], an essential aspect of the overall wind loading of cylindrical structures (such as grain bins and oil storage tanks) [5, 6], and is important in the understanding of the convective heat and mass transfer properties of surface-mounted cylindrical components (such as electronic components on circuit boards) [7]. Flow about the free end of a finite cylinder has also been associated with “end-cell induced vibration” [8]. Most studies reporting free-end pressure distributions for finite cylinders have been made for very-low aspect ratios of AR ≤ 2 [1]. There are limited published data on the sensitivity of the mean normal force coefficient C N = 8F N /(q∞ πD2 ) (for freestream dynamic pressure q∞ , and normalization with the surface area of the free end) to AR. In the present study, the mean free-end pressure distribution for a finite cylinder is obtained experimentally for a wide range of aspect ratio.

2 Experimental Approach Experiments were conducted in a low-speed wind tunnel with finite cylinders of 0.5 ≤ AR ≤ 11 (the AR was varied in increments of 0.5) at a Reynolds number of Re = 6.5 × 104 and with δ/D = 0.6. The experimental set-up was similar to [4] where the critical aspect ratio was identified as AR ≈ 2 ± 0.5. The free end was instrumented

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with 15 static pressure taps arranged in an S-shaped pattern similar to [2]. Each finite cylinder was rotated in θ through 360° in increments of 1° to obtain the mean pressure distribution, P(r,θ ) (for radial position r). Data are presented using the dimensionless mean pressure coefficient C P = (P − P∞ )/q∞ (for freestream static pressure P∞ ). The pressures were measured by two Scanivalve ZOC17IP/8px DeltaP differential pressure scanners. Integrating C P (r,θ ) gives the mean normal force coefficient based on pressure, C N,P .

3 Results and Discussion Examples of the mean C P distributions (shown as contour lines of constant C P ) for selected aspect ratios are shown in Fig. 2. For all aspect ratios, the pressure coefficients on the entire free-end surface are always negative, indicating an upward-directed (+z direction) positive normal force coefficient (due to pressure) is experienced. For most aspect ratios, the same general features of the mean C P distribution are observed, but the locations and relative sizes of these features change with AR. The C P distribution for the cylinder of AR = 0.5, which is well below the critical aspect ratio, and is the only cylinder that is fully immersed in the boundary layer (δ/D = 0.6), is unique. The lowest (most negative) pressure coefficients are always found on the upstream half of the surface beneath the mean recirculation zone and the mushroom vortex. For 1 ≤ AR ≤ 5, a pair of “eye-like spots” appears within this region, located towards the sides of the cylinder; these spots are occasionally seen in published surface flow visualization studies and broadly correspond to the termination points of the mushroom vortex located within the mean recirculation zone [1]. Higher (less negative) pressure coefficients are always found on the downstream half of the free-end surface behind the reattachment line; as the AR is increased, a localized enclosed region of higher pressure develops upstream of the trailing edge; this region is particularly prominent at the highest aspect ratios tested in the present study. In the central part of the free end, beginning near the centre of the cylinder and extending downstream to the approximate location of the reattachment line, there is a concentrated band of closely spaced contour lines that denotes a region of adverse pressure gradient. This gradient becomes stronger as the aspect ratio increases. The C P distribution becomes relatively insensitive to aspect ratio for AR ≥ 7. The C P values as a whole tend to become more negative with an increase in AR, which indicates an increase in the upward-directed (+z direction) normal force coefficient with AR. Mean normal force coefficient data (Fig. 3) show that the pressure contribution (C N,P ) to the normal force increases with AR but a nearly constant value of C N,P ≈ 0.78 is attained for AR ≥ 6.5. In contrast, the total normal force coefficient (from both the pressure and shear stress contributions) (C N ) data from [4], from direct measurement with a force balance, attain a maximum of C N ≈ 0.87 for 2.5 ≤ AR ≤ 6.5 but then progressively decrease with increasing AR. This behaviour in C N is attributed to the greater influence of downward-directed (−z direction) wall

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Fig. 2 Selected mean pressure distributions on the free end of the finite cylinder (showing contour lines of constant mean pressure coefficient, C P ) (flow from top to bottom)

shear stress on the cylinder’s side surfaces at higher AR. For these cylinders, the rear surface experiences a predominantly downward-directed near-wake flow, and the cross-stream vortices within the upper and lower near wake are much weaker compared to lower aspect ratios [4]; these features of the local flow field are thought to be responsible for the greater downward-directed shear force.

4 Conclusions Mean pressure measurements on the free end of a finite cylinder, at Re = 6.5 × 104 and with δ/D = 0.6, show that the C P distribution and its contribution to the normal

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Fig. 3 Mean normal force coefficient data for a surface-mounted finite-height cylinder, Re = 6.5 × 104 , δ/D = 0.6. Open symbols: normal force coefficient based on pressure (C N,P ), obtained by integrating the free-end mean pressure distributions. Solid symbols: total normal force coefficient (C N ) data, measured directly using a force balance, from [4]. Dashed lines: piecewise straight-line curve fits used to identify trends in the behaviour of C N and C N,P data with AR

force are sensitive to the cylinder’s aspect ratio. As the aspect ratio increases, the pair of eye-like spots on upstream half of the free end disappears, the region of adverse pressure gradient in front of the reattachment line becomes stronger and moves farther downstream, and a prominent enclosed region of higher pressure develops near the trailing edge. A unique C P distribution is found for shortest cylinder of AR = 0.5, which is well below the critical aspect ratio of AR ≈ 2 ± 0.5, but is also the only cylinder in the study that is completely immersed in the flat-plate boundary layer on the ground plane. Although the C P distribution and C N,P become relatively insensitive to aspect ratio for AR ≥ 7, the wall shear stress contribution to the normal force, acting on the sides of the cylinder, acts to reduce the total normal force coefficient with further increases in AR for AR ≥ 6.5.

References 1. Sumner D (2013) Flow above the free end of a surface-mounted finite-height circular cylinder: a review. J Fluids Struct 43:41–63 2. Tsutsui T (2012) Flow around a cylindrical structure mounted in a plane turbulent boundary layer. J Wind Eng Ind Aerodyn 104:239–247 3. Sumner D, Rostamy N, Bergstrom DJ, Bugg JD (2017) Influence of aspect ratio on the mean flow field of a surface-mounted finite-height square prism. Int J Heat Fluid Flow 65:1–20 4. Beitel A, Heng H, Sumner D (2019) The effect of aspect ratio on the aerodynamic forces and bending moment for a surface-mounted finite-height cylinder. J Wind Eng Ind Aerodyn 186:201–213 5. Macdonald PA, Kwok KCS, Holmes JD (1988) Wind loads on circular storage bins, silos and tanks. 1. Point pressure measurements on isolated structures. J Wind Eng Ind Aerodyn 31(2– 3):165–188 (1988)

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6. Uematsu Y, Moteki T, Hongo T (2008) Model of wind pressure field on circular flat roofs and its application to load estimation. J Wind Eng Ind Aerodyn 96:1003–1014 7. Rödiger T, Knauss H, Gaisbauer U, Krämer E (2007) Pressure and heat flux measurements on the surface of a low-aspect-ratio circular cylinder mounted on a ground plate. In: Tropea C et al (eds) New Research in Numerical and Experimental Fluid Mechanics VI, NNFM 96. Springer, Berlin, pp 121–128 8. Kitagawa T, Fujino Y, Kimura K, Mizuno Y (2002) Wind pressures measurement on end-cellinduced vibration of a cantilevered circular cylinder. J Wind Eng Ind Aerodyn 90:395–405

A Static Aeroelastic Analysis of an Active Winglet Concept for Aircraft Performances Improvement Martin Delavenne, Bernard Barriety, Fabio Vetrano, Valérie Ferrand, and Michel Salaun

Abstract Winglets appeared on aircraft few decades ago (Whitcomb in A design approach and selected wind-tunnel results at high subsonic speeds of wing-tip mounted winglet, 1976 [1]). They have demonstrated their efficiency to decrease the induced drag. However, their design is still a trade-off between structural penalties, high-speed and low-speed aerodynamic performances. Therefore, as fixed devices, they are suboptimal in off-design conditions. The active winglet concept studied in this work may cope with this issue and improve performances in a wider range of operational conditions. CFD/CSM computations are performed and show that the flexibility of the wing must be taken into account to evaluate the impact of active winglets. Besides, a far-field drag decomposition tool is used to highlight the effect of the device on drag physical components. Keywords CFD/CSM · Winglets · Far-field decomposition · Static aeroelasticity

1 Introduction In the early 70s, winglets were introduced on aircraft to limit the wing tip vortices and decrease lift-induced drag. More recently a lot of efforts were put on engines consumption and noise. But it seems that the current aircraft configuration is approaching its limits: improvements are lower and more expensive to reach. Multi-disciplinary researches on active configurations, adjustable to flight conditions, have been ontrend for several years [2, 3]). It is shown that such configurations may enable to M. Delavenne (B) · V. Ferrand ISAE-SUPAERO, Université de Toulouse, Toulouse, France e-mail: [email protected] M. Delavenne · B. Barriety · F. Vetrano Airbus Operations SAS, 316 Route de Bayonne, Toulouse, France M. Salaun ICA, Université de Toulouse, ISAE-SUPAERO, MINES ALBI, UPS, INSA, CNRS, Toulouse, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_12

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Fig. 1 Wing main parameters definition: Twist is positive nose up; cant is positive for upward deflections

save up to 10% of block-fuel. Active winglet concept, patented by Airbus [4], aims to control the wing shape by a quasi-static actuation of the winglets during the flight to minimize the drag. Some researches already analyzed similar devices using only CFD computations on rigid structures [5] and showed that up to 2% of fuel can be saved. This study aims to analyse the impact of winglet deflection on steady aerodynamic performances and on wing shape. High-fidelity coupled CFD (Computational Fluid Dynamics) and CSM (Computational Structural Mechanics) are considered to compute the static aeroelastic equilibrium. Here, only the cant angle of the winglet can change. The impact of this deflection on drag components will be assessed using a far-field decomposition tool (Fig. 1).

2 Models and Work Description 2.1 Aerodynamic and Structural Models XRF1 model, an Airbus provided industrial research test-case, representing a long range wide body aircraft, is considered. High-fidelity methods are used to assess as precisely as possible both steady aerodynamic performances and static structural displacements. TAU solver is considered to solve RANS equations (Reynolds Average Navier-Stokes). Unstructured meshes for the different winglet configurations are generated and are composed of about 20 million nodes. The Menter-SST (Shear Stress Transport) turbulence model is used [6]. This solver is coupled with Nastran to compute structural displacements resulting from the aerodynamic loading. A 350,000◦ of freedom finite elements model of the aircraft is considered.

2.2 Work Description First on Fig. 2, rigid and flexible polars are generated and compared for 3 different cant angle (δ) configurations and various angle of attack at cruise condition. It enables to assess the impact of flexibility on active winglet benefits. Then on Fig. 3, the stiffness of the wing is adjusted to analyse the impact of the wing deformation on

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Fig. 2 XRF1 polars for rigid and flexible case Fig. 3 Aircraft drag evolution expressed as fraction of the minimum drag and function of cant angle and wing stiffness

the sensitivity of the performances to the cant angle of the winglet. Five winglet cant angles are considered and three different wing stiffness are compared: the reference which correspond to the initial finite elements model, a more rigid wing and a more flexible one. A far-field drag analysis is performed. It enables to segregate the physical components of the drag to refine the analysis. This analysis relies on the work [7] and considers only the momentum equation to compute forces. The drag components are divided into a reversible part, the induced drag, and an irreversible part, the combination of wave and viscous drags.

3 Results Polar curves presented on Fig. 2 highlight the added-value of CFD/CSM simulations regarding to rigid CFD to assess the efficiency of the active winglet. This preliminary analysis shows that the device is only useful when the stiffness is introduced. Indeed,

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for rigid case, the 0◦ configuration is always better than the others while for flexible case, at low angle of attack, the 45◦ configuration is the most interesting. However, considering wing stiffness leads to a decrease in the efficiency of the device: at iso-Cl the drag difference between extreme configurations is reduced by 20%. This diminution of the drag sensitivity to cant angle as wing stiffness decreases is also illustrated on Fig. 3. It shows that for the stiffest wing (−20% bending displacement w.r.t. reference), drag variation reaches 1.75% while it is reduced to 0.55% and 0.3% for the reference and the more flexible case (+13% bending displacement) respectively. To understand this behaviour, the correlation between the local change in angle of attack on the winglet (Δαwinglet ) and the variation of wing twist (θwing ) should be considered: (1) Δαwinglet = sin−1 (sin(θwing ) ∗ cos(δ)) This correlation weakens as cant angle increases (in absolute value). Therefore, the winglet will be more loaded for higher cant angles. Analysing more into the details the drag decomposition into physical components (wave, viscous and induced drag) highlights antagonist effects amplified or damped by the wing flexibility (see Fig. 4). For “rigid” case, induced drag (Fig. 4c) reaches a minimum for δ = 0◦ . For that stiffness, wing twist sensitivity to cant angle is limited (Fig. 4d), thus the lift distribution will be more external due to maximal span for the extended winglet position, which is advantageous for induced drag. On the contrary, for more flexible cases, the minimum of induced drag is shifted toward positive deflections. This behaviour originated from wing distortion effects that are amplified with flexibility and lead to competitive effects. When the winglet is extended, maximum span effect is counterbalanced by the wing twist diminution that impacts wing and winglet loading (1) with a detrimental effect on induced drag. When the winglet is folded toward positive or negative directions, its loading increases but the projected span is reduced. Thus, it exists a position for which the span effect is still advantageous while the twist effect is not detrimental enough. This tends to smooth the induced drag evolution as function of cant angle. Regarding wave and viscous drag (Fig. 4a, b), they raise rapidly as deflection increases. This is common for all wing stiffness configurations and is the result of a flow acceleration at the junction between the wing and the winglet that locally reinforces the shock [8]. Consequently, for more flexible cases, the gains on the induced drag—already damped by flexible effects— are lowered by the losses on viscous and wave drag, leading to a diminution of the sensitivity of the total drag to the cant angle.

4 Conclusion An active winglet is analysed using high-fidelity CFD/CSM computations. It is highlighted that the flexibility of the wing plays a significant role reducing by 25% the efficiency of the device. Three different wing stiffness are studied and show that

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Fig. 4 Drag breakdown and delta wing twist for three different wing stiffness, results expressed as fraction of the minimum drag and initial wing twist

the sensitivity of total drag to winglet cant angle decreases with flexibility. This behaviour originates from the competition between the span effect on one hand and wing distorsion and winglet loading effects on the other hand, combined with viscous and wave drag evolutions. Static aeroalastic effects plays a major role modifying the wing and winglet loading. Future works will include flutter consideration as well as an analysis of other configurations to test the generality of the results.

References 1. Whitcomb RT (1976) A design approach and selected wind-tunnel results at high subsonic speeds of wing-tip mounted winglet. NASA Technical note 2. Vasista S, Tong L, Wong KC (2012) Realization of morphing wings: a multidisciplinary challenge. J Aircr 49(1):11–28 3. Barbarino S, Bilgen O, Ajaj RM et al (2011) A review of morphing aircraft. J Intell Mater Syst Struct 22:823–877

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4. Barriety B, Aircraft with active control of the warping of its wings. Airbus Operations SAS. In: US patent 6827314B2 5. Cooper JE, Chekkal I, Cheung R et al (2015) Design of a morphing wingtip. J Aircr 52(5):1394– 1403 6. Menter FR (1994) Two-equations eddy-viscosity turbulence models for engineering applications. AIAA J 32(8):1598–1605 7. Meheut M, Bailly D (2008) Drag-breakdown methods from wake measurements. AIAA J 46(4):847–862 8. de Mattos BS, Macedo AP, da Silva Filho DH (2003) Consideration about winglet design. In: AIAA, 21st applied aerodynamics conference

Experimental Study of the Effect of a Steady Perimetric Blowing at the Rear of a 3D Bluff Body on the Wake Dynamics and Drag Reduction Manuel Lorite-Díez, José Ignacio Jiménez-González, Carlos Martínez-Bazán, Luc Pastur, and Olivier Cadot Abstract In a perspective of active flow control of the bistable wake of a squareback Ahmed body, we show that the steady blowing through a perimetric slit at the rear of the body is not equivalent to a material rear perimetric cavity, the latter being able to suppress the bistable dynamics and symmetrize the wake flow, while the former cannot achieve any of these two features, indicating that steady perimetric blowing is not able to control the symmetric unstable steady solution of the system. Keywords Aerodynamics of 3D bluff bodies · Bistable dynamics · Drag reduction · Wake flow manipulation

1 Introduction Ahmed-like bluff bodies are prototype models for ground vehicles commonly used for academic research on aerodynamics performance [1]. Three-dimensional rectangular blunt bodies are known to exhibit bistable dynamics involving two reflectional symmetry-breaking wake flows, depending on the body base aspect ratio, Reynolds number and ground clearance, among other parameters [2–4]. These wake topologies break the reflectional symmetry, being the wake deflected on one or the other side with respect to the symmetry plane, yielding permanent side loading on the body, with sudden reversals of the lateral force and increase of the drag [2]. M. Lorite-Díez · J. I. Jiménez-González · C. Martínez-Bazán Departamento de Ingeniería Mecánica y Minera, Universidad de Jaén, Campus las Lagunillas, 23071 Jaén, Spain L. Pastur (B) Institute of Mechanical Sciences and Industrial Applications, ENSTA-Paris, Institut Polytechnique de Paris, 828 Bd des Maréchaux, 91120 Palaiseau, France e-mail: [email protected] O. Cadot School of Engineering, University of Liverpool, Liverpool L69 3GH, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_13

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The use of a perimetric rear cavity at the back of the body suppresses the bistable dynamics and achieves a drag reduction of up to 9%, by stabilizing the (presumably) symmetric steady wake flow [5, 6]. In an active flow control perspective, it would therefore be beneficial to design a fluidic equivalent of the material cavity. It is tempting to achieve this goal by steadily blowing air through a perimetric slit at the back of the body. Base blowing can suppress the periodic shedding at the wake behind axisymmetric bodies [7, 8]. It has been implemented in several experiments for open-loop and closed-loop control applications of the square-back Ahmed body wake flow [9, 10]. In these experiments, however, the unforced wake flow was either symmetric in the horizontal plane and only steadily deflected vertically [9, 10], or, when the flow was actually bistable in the horizontal plane, the control was shown to promote left/right transitions of the wake flow, only slightly decreasing the drag [10]. As a result, it could not be proved whether such a perimetric blowing actuator could stabilize or not the symmetric wake flow, associated with the lowest drag. The present contribution is aimed to experimentally address this question.

2 Experimental Setup A schematic view of the experimental set-up is shown in Fig. 1. A ground plate is placed in an Eiffel-type wind tunnel to form a 3/4 open jet facility, which provides a uniform stream of velocity U∞ = 20 m/s, density ρ and dynamic viscosity μ. The turbulence intensity is smaller than 0.3% and the homogeneity of the velocity over the 390 × 400 mm2 test section is about 0.4%. The Ahmed-like square-back model is = 291 mm-long, w = 97.25 mm-wide and h = 72 mm-high. For this study, the ground clearance was set at c/ h = 0.278.

Fig. 1 a Sketch of the experimental setup with the body rear blowing system. b Picture of the body showing the feeding tubes for air blowing. c The back of the body with the pressure taps A, B, C, D

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Air blowing at the rear of the body is supplied through an additional frame of depth d/ h = 0.417 whose internal cavity is pressurized by injecting a steady controlled flow rate Q b of air through internal tubes, as shown in Fig. 1b. This cavity is closed by a rear plate whose dimensions are adjusted such as to let a 2 mm-thick perimetric slit opened at the back of the body (s/ h = 0.028), through which the rear base flow is discharged into the wake with velocity Ub . The injected air flow rate Q b is precisely controlled with a digital mass flow meter. The bleed coefficient is defined as Cq = Q b /U∞ wh. The origin of the direct trihedral cartesian coordinate system (x, y, z) is placed at the center of the body base, being x the streamwise direction, z the direction normal to the ground and y the side direction. The characteristic length, velocity, pressure, 2 /2 and h/U∞ , respectively. The Reynolds number and time scales are h, U∞ , ρU∞ 5 Re = ρU∞ h/μ is set to 10 . The body base pressure is measured at probes A, B, C and D in Fig. 1c, using a Scanivalve ZOC22 pressure scanner sampling at 100 Hz per channel over 250 s. The instantaneous pressure coefficient is defined as 2 , c p (y, z, t) = 2 ( p(y, z, t) − p∞ ) /ρU∞

where p∞ denotes the reference static pressure at the inlet of the test section. The instantaneous base drag coefficient is calculated as cb (t) = −

c p (M, t)/4,

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and the wake of the horizon asymmetry is evaluated by means of the gradients tal g y ≈ h (c p (B, t) − c p (A, t)) + (c p (D, t) − c p (C, t)) /2Δy and vertical gz ≈ h (c p (A, t) − c p (C, t)) + (c p (B, t) − c p (D, t)) /2Δz base pressure coefficients, with Δy = y B − y A and Δz = z C − z A . Additionally, the drag force is measured through a multi-axial AMTI-MC3A load cell, while the recirculation bubble length L r is estimated on the mean flow-fields obtained from PIV measurements in either the symmetric vertical plane or the horizontal mid-plane, using a dual pulse laser (Nd:YAG, 2 × 135 mJ, 4 ns) synchronized with a FlowSense 77 EO 4Mpx CCD camera.

3 Results The first configuration we consider is the four-slit (4S) configuration. The sensitivity map of Fig. 2a shows that the perimetric steady blowing neither suppresses the wake asymmetry nor its bistability, for any value of the blowing coefficient Cq . Henceforth, the instantaneous wake flow remains either deflected to the left (gˆ y = −0.13) or to the right (gˆ y = +0.13) despite the blowing, with a higher probability for the later to occur at large Cq due to the blowing imperfect homogeneity. Meanwhile, the

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Fig. 2 a Probability distributions of the horizontal g y and vertical gz non-dimensional pressure gradients as the blowing coefficient Cq is increased (sensitivity map). White to black indicates unfrequent to frequent occurrences, respectively. The most probable values of g y and gz are gˆ y ≈ ±0.13 and gˆ z ≈ 0.03, respectively. The slight changes of g y are presumably due to blowing nonuniformities. b Evolution of the relative variations of the time-averaged drag coefficient C x , timeaveraged base drag Cb and the recirculation bubble length L r with Cq

vertical gradient remains constant to gˆ z ≈ 0.03. However, as depicted in Fig. 2b, the rear blowing has an impact on the time-averaged drag C x , which is reduced by 3% for Cq ≈ 6.6 × 10−3 , when the recirculation bubble is the most elongated. As also shown in Fig. 2b, both the base drag Cb and the inverse of the recirculation length 1/L r follow the same trend as the drag force. These correlated trends indicate that the rear-blowing first elongates the recirculating bubble, causing a pressure recovery at the base of the body as a consequence of the reduction of the bubble curvature and the associated pressure gradients, resulting in drag reduction, at small and moderate blowing flow rates [11]. In this regime, the rear-blowing therefore behaves like a steady base-bleeding actuation on the wake flow [12]. Meanwhile, the flow structure is smoothly adjusting to the new recirculation length, without significant modification, as shown in Fig. 3a, b. For larger blowing flow rates beyond the optimal value Cq , the bubble length decreases when increasing the blowing rate Cq , resulting in a base pressure decrease and consequently a drag increase. In this flow regime, the rear-blowing does not behave anymore like a base-bleed but instead contributes to the turbulent mixing in the shear layers. As an interesting result, the body symmetry-preserving blowing of the four-slit configuration does not force the wake flow to recover its instantaneous symmetry. One may wonder whether this result remains true for any symmetric steady blowing configuration, namely the left and right (LR) blowing configuration, and, to a less extent, the top and bottom (TB) blowing configuration. The sensitivity map of Fig. 3c, d show that none of these two configurations can suppress the bi-stable dynamics of the wake flow. This also means that a symmetric steady blowing configuration at the rear of the body does not have the authority to stabilize the unstable symmetric wake flow solution.

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4 Conclusion Symmetric perimetric blowing with moderate flow rates at the rear of the bluff body has a beneficial impact on the drag, promoting an effective base-bleeding effect. However, unlike uniform base-bleeding, perimetric blowing is much easier to implement on real vehicles, offering new perspectives for practical applications. Interestingly, steady, perimetric blowing could not suppress the bi-stable dynamics of the wake flow, indicating that this actuator has no authority on the unstable symmetric wake flow. Acknowledgements This work has been partially supported by the Spanish MINECO, MEDC and European Funds under project DPI2017-89746-R, José Castillejo Grant CAS18/00379 and Fellowship FPU 014/02945.

References 1. 2. 3. 4. 5. 6.

Choi H, Lee J, Park H (2014) Ann Rev Fluid Mech 46:441 Grandemange M, Gohlke M, Cadot O (2013) J Fluid Mech 722:51 Grandemange M, Gohlke M, Cadot O (2013) Phys Fluids 25:095103 Volpe R, Devinant P, Kourta A (2015) Exp Fluids 56:99 Evrard A, Cadot O, Herbert V, Ricot D, Vigneron R, Délery J (2016) J Fluids Struct 61:99 Sanmiguel-Rojas E, Jiménez-González JI, Bohorquez P, Pawlak G, Martínez-Bazán C (2011) Phys Fluids 23:114103 7. Sevilla A, Martínez-Bazán C (2004) Phys Fluids 16:3460

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8. Bohorquez P, Sanmiguel-Rojas E, Sevilla A, Jiménez-González JI, Martínez-Bazán C (2011) J Fluid Mech 676:110 9. Barros D, Borée J, Noack BR, Spohn A, Ruiz T (2016) J Fluid Mech 805:422 10. Li R, Barros D, Borée J, Cadot O, Noack BR, Cordier L (2016) Exp Fluids 57:158 11. Bearman PW (1967) The aero Quart, vol. XVIII 207 12. Bearman PW (1967) Aero Quar 18(3):207–224 13. Li R, Bore J, Noack BR, Cordier L, Harambat F (2019) Phys Rev F 4(3):034604

Influence of Gap Width on Fluid–Structure Interaction for a Cylinder Cluster in Axial Flow P. Wang, C. W. Wong, W. Xu, and Yu Zhou

Abstract This work aims to experimentally investigate the effect of gap width P* (= P/D, where D is the cylinder diameter) on the fluid–structure interaction for a symmetrically-arranged cylinder cluster in turbulent axial flow. The cylinder cluster comprised of an elastic cylinder which is centrally located between two non-vibrating cylinders and may vibrate freely in the transverse direction. The P* varies from ∞ (an isolated cylinder) to 1.28. Simultaneously measurements of the cylinder vibration and the velocity field adjacent to the elastic cylinder are performed at the freestream velocity U ∞ ranging from 0.19 to 2.14 m/s. Two distinct regions, viz., RI and RII , are identified at P* ≥ 1.57 and P* < 1.57, respectively, based on the root-mean-square vibration amplitude Arms * (Arms * = Arms /D) of the elastic cylinder. It is found that the dynamics of large-scale structures between cylinders resulting from the unstable shear layer around the elastic and the non-vibrating cylinders mainly contribute to the transformation from RI to RII . Keywords Axial fluid-induced vibration · Fluid–structure interaction · Elastic cylinder · Gap width

1 Introduction The dynamics of cylinder clusters in the turbulent axial flow have been extensively studied due to its importance in engineering applications, such as nuclear reactors and heat exchangers. Fuel elements in cluster are subjected to the unsteady lateral forces resulting from the loading of high momentum, unsteady and axial-flowing coolant, therefore inducing large lateral vibrations. The dynamics of fuel elements or cylinders in cluster have been investigated both experimentally and numerically P. Wang · C. W. Wong (B) · W. Xu · Y. Zhou Center for Turbulence Control, Harbin Institute of Technology, Shenzhen, China e-mail: [email protected] C. W. Wong · W. Xu · Y. Zhou Shenzhen Digital Engineering Laboratory of Offshore Equipment, Harbin Institute of Technology, Shenzhen, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_14

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[1–4]. Most studies concerned on the fluid-elastic instabilities of an isolated cylinder or cylinder cluster, however, the physics for the interaction between the deformed elastic cylinder and the surrounding flow are still not clear. It has been found that the large-scale vortex structures between two cylinders generate the flow instability and pressure perturbance on the cylinder wall [5], thus producing large vibration of the cylinders. This work aims to study the dynamics of an elastic cylinder in a cluster at various gap width in the turbulent axial flow. The fluid–structure interaction is investigated through detailed analysis of the simultaneously measured flow field in between the cylinders and the vibration of the elastic cylinder.

2 Experimental Details Experiments were carried out in a closed-loop vertical water tunnel at Harbin Institute of Technology, Shenzhen, P.R. China. The test section was 2.0 m high with a square cross-section of 0.3 × 0.3 m2 . Figure 1a shows a schematic of the experimental setup and the definitions of coordinates (x, y, z), with the origin defined at the centre of the elastic cylinder, following the right-hand system. The flow velocity U ∞ was 0.19– 2.14 m/s or U (= U ∞ L(mf / EI)1/2 , where L, mf and EI, are cylinder length, added mass of fluid per unit length and cylinder flexural rigidity, respectively) = 0.64–6.98. An elastic cylinder was fixed between two rigid (or non-vibrating) cylinders along the x-direction using airfoil-shaped supporting structures. The elastic cylinder was made of room-temperature vulcanizing silicone and had a L, D and E of 605.0 mm, 14.0 mm and 2.78 MPa, respectively. This cylinder is identical to that used in [6]. Two hollowed circular cylinder (hereafter called rigid cylinder) made of Fluoro-Ethylene Polymer (FEP) and each one had a L and D of 605.0 and 14.0 mm, respectively, were installed symmetrically on both sides of the elastic cylinder. The refractive index of FEP (1.338) is similar to that of water (1.333), so that the optical distortion of the recorded images in the particle image velocimetry PIV measurements was minimized

Fig. 1 a Schematic of the water tunnel and b synchronized PIV–LDV measurements

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and can be neglected. A custom-made NI LabVIEW program was used to initiate and control both the laser Doppler vibrometer LDV and PIV systems for data acquisition (Fig. 1b). The sampling frequency was set at 200 Hz and the sampling time was set at 10 s. Note that the vibration of the cylinder and its adjacent flow field were all measured at the mid span of the elastic cylinder. The root-mean-square vibration amplitude Arms and the flow fluctuation between the cylinders were measured and analyzed at P* varying from ∞ (an isolated cylinder) to 1.28).

3 Results and Discussion Figure 2 shows the dependence of the root-mean-square vibration amplitude Arms * (Arms * = Arms /D) of the elastic cylinder on U at various P* in y- and z- directions. At U = 6.98 (Fig. 2a), the Arms * of elastic cylinder in the y-direction increases slightly with decreasing P* from ∞ (an isolated cylinder) to 1.57, while the Arms * exhibits a mild reduction in the z-direction. In fact, the axial mean flow velocity between the two adjacent cylinders becomes small as P* approaches to 1.57, causing the

Fig. 2 a RMS value of vibration of elastic cylinder at U = 6.98 in y- and z-directions; Dependence of Arms * on U in b y- and c z-direction

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reduction in the mean acceleration of fluid between the cylinders, and as a result, the Arms * in the z-direction is decreased. At P* < 1.57, the Arms * of the elastic cylinder in both y- and z-directions increases significantly with decreasing P* . Two distinct regions, RI and RII , at P* ≥ 1.57 and P* < 1.57, respectively, are identified based on the Arms * of the elastic cylinder. On the other hand, the Ayrms * (the subscript y denotes the y-direction) and Az-rms * (the subscript z denotes the z-direction) of elastic cylinder increase approximately linearly with increasing U at any given P* (Fig. 2b, c). The Arms * of the elastic cylinder in y direction is always larger than its counterpart in the z direction given the same P* . It has been found that the buckling and flutter instabilities do not appear at P* ≥ 1.43 for any given U in the experiments. However, given U is sufficiently large, the buckling phenomenon would occur at P* < 1.43 (not shown). Figure 3a, b shows the variation of the urms * (= urms /U ∞ ) and U/U ∞ (where U denotes the mean flow velocity) between the two cylinders in x–z plane at U = 6.98. In general, at P* = 1.71 and 1.57, the minimum urms * is found at the midpoint between the cylinders, and urms * increases rapidly to the maximum value near the cylinder wall (Fig. 3a). Note that the minimum and maximum values of urms * at P* = 1.57 is similar to those at P* = 1.71. At P* < 1.57 (RII ), the urms * at the midpoint between the cylinders is appreciably increased with decreasing P* , due to the enhanced instability of shear layer around the elastic cylinder, which is supported later by the PIV data. In other word, the instability of the shear layer of the elastic cylinder, particularly in the z-direction, enhances the flow velocity fluctuations between the cylinders, therefore increasing the Arms * of elastic cylinder. Note that the maximum U/U ∞ between the cylinders decreases with decreasing P* (Fig. 3b). Figure 4a, b presents the instantaneous vorticity contours ωy * (= ωy D/U m , where U m is the flow velocity in the centre line of flow field between cylinders) in the x–z plane at the mid span of the cylinder. At U = 6.98 and P* = 1.71 (Fig. 4b), the large-scale eddy structures are randomly distributed, moving along the wall of the elastic cylinder. Perhaps, there exist some interactions of some small-scale structures in between the cylinders. The movement of large-scale eddy structures close to the

Fig. 3 Variation of the a urms * and b U/U ∞ between two cylinders in x–z plane at U = 6.98 under various P*

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Fig. 4 Contours of instantaneous vorticity in x–z plane at U = 6.98; a P* = 1.43; b P* = 1.71

wall and the limited interactions of some small-scale structures can be considered as the main flow characteristic of RI . However, at P* = 1.43 (RII ) and U = 6.98 (Fig. 4a), the large-scale eddy structures would separate from both the left and the right walls and interact with other eddy-structures from the opposite wall. The separated large-scale eddy structures from the cylinder wall and the shear layer thickness are closely connected; these eddy structures propagate in the crosswise direction, thus increasing the shear layer thickness around the elastic cylinder. Furthermore, the energetic motion of the flow structures between the cylinders would in-turn enhance the instability of the shear-layer around the elastic cylinder. As a result, the Arms * of the cylinder is significantly increased and the transformation takes place from RI to RII with decreasing P* .

4 Conclusions 1. At various gap width P* , the dynamics of the elastic cylinder can be divided into two regions, viz., RI and RII (the minimum resolution of the gap ratio P* is about

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0.07), depending on the rapid change of the gradient of the root-mean-square vibration amplitude Arms * of the elastic cylinder. 2. The dynamics of the large eddy-structures and their possible interactions in the immediate vicinity of the cylinder wall plays an important role in the determination of RI and RII . With reducing P* , the instability of the shear layer around the elastic cylinder cause the separation of the large eddy-structures from the cylinder wall, enhancing the fluid-to-fluid and/or fluid-to-structure interactions and thus leading the transformation from RI to RII. Acknowledgements Authors wish to acknowledge support from the NSFC through grants 11502060, 11632006, 51935005 and U1613226, and from the Research Grants Council of the Shenzhen Government through grants JCYJ20160531193045101, JCYJ20150513151706565 and JCYJ20160531193220561.

References 1. Liu ZG, Liu Y, Lu J (2012) Numerical simulation of the fluid–structure interaction for an elastic cylinder subjected to tubular fluid flow. Comput Fluids 56:192–202 2. Païdoussis MP (1979) The dynamics of clusters of flexible cylinders in axial flow: theory and experiments. J Sound Vib 65:391–417 3. Païdoussis MP, Gagnon JO (1984) Experiments on vibration of clusters of cylinders in axial flow: modal and spectral characteristics. J Sound Vib 96:341–352 4. Gagnon JO, Païdoussis MP (1994) Fluid coupling characteristics and vibration of cylinder clusters in axial flow. Part I: Theory. J Fluids Struct 8 :257–291 5. Moerloose LD, Aerts P, Ridder JD, Vierendeels J, Degroote J (2018) Numerical investigation of large-scale vortex in carry of cylinders in axial flow. J Fluids Struct 78:277–298 6. Wang P, Wong CW, Zhou Y (2019) Turbulent intensity effect on axial-flow-induced cylinder vibration in the presence of a neighboring cylinder. J Fluids Struct 85:77–93

Skin-Friction Drag Reduction Using Micro-Grate Patterned Superhydrophobic Surface Zhang Bingfu, Tang Hui, and To Sandy

Abstract This study investigates experimentally the drag reduction of the micrograte patterned superhydrophobic (SHPO) surface compared with its smooth flat counterpart in turbulent boundary layer flow. Two SHPO surfaces were examined, with the same air fraction but different grate spacings. Both surfaces were fabricated using ultra-precision machining techniques. A dedicated, high resolution skinfriction balance was developed to measure the drag reduction in a water tunnel at the Reynolds number Reτ , based on the friction velocity uτ , of about 500. Significant drag reductions of 41% and 34% were obtained by the two surfaces. It is found that neither the air fraction or the static contact angle can predict the reduction in drag. Further, we show that the shape of the gas–liquid interface between grates may have a pronounced effect on the drag reduction. Keywords High-resolution skin-friction balance · Superhydrophobic surface · Drag reduction

1 Introduction The emerging development of microfluidic devices such as bioMEMS, chips, and micro-pumps has resulted in an increased need to reduce skin friction drag in such devices. Superhydrophobic (SHPO) surfaces are composed of micro/nano size structures on hydrophobic material and have strong water repellent capacity. Air pockets Z. Bingfu (B) Institute for Turbulence-Noise-Vibration Interactions and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, China e-mail: [email protected] Z. Bingfu · T. Sandy State Key Laboratory of Ultra-Precision Machining Technology, Department of Industrial and System Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong T. Hui Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Hong Kong © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_15

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can be entrapped in the micro-grooves when the surface is submerged in water. The SHPO surface has a great potential for drag reduction due to the presence of an air layer on the surface, which acts as a lubricant for the outer water flow and hence reduces friction drag. For example, Henoch et al. [1] experimentally studied the drag reduction of a SHPO surface with nano-grass, and obtained an impressive drag reduction of about 50 and 20% in laminar and turbulent flow regimes respectively. Drag reduction using SHPO surfaces has been given more and more attention, with a variety of surface patterns investigated, including grates, cylindrical or square posts, micro-nano hierarchical structures, and random or rough surface structures. The effectiveness of SHPO surface in drag reduction in turbulent boundary layer (TBL) remains in the debate due to the greatly scattered experimental data. Take the micro-grate patterned SHPO surface as an example. In a channel flow with the bottom wall replaced by a SHPO surface, Daniello et al. [2] obtained a maximum drag reduction of about 27% with an air fraction f a = 50%. Here f a is evaluated as f a = g/p, where g and p are the gap and spacing between two neighboring grates, respectively. However, using a much larger air fraction (f a = 80%), Woolford et al. [3] achieved a much smaller drag reduction of only 11%. In another experiment, with an even larger air fraction (f a = 95%), Park et al. [4] attained a greatly higher drag reduction, reaching up to 75%. Such large scattering is probably associated with the systematic error resulted from the indirect drag measurement, and the loss of plastron on SHPO surface, which leads to an underestimation of the drag reduction. On the other hand, a large number of numerical studies have been carried out on the turbulent drag reduction of SHPO surfaces, especially with the micro-grates (e.g. Rastegari and Akhavan [5]). These studies call for a more complete experimental data base for the validation of the computational fluid dynamics (CFD) codes. This work aims to address the above-mentioned issues through an experimental study on the drag reduction of SHPO surfaces with longitudinal micro-grates based on particle image velocimetry (PIV) and high-resolution skin-friction measurements, and to provide experimental data for the validation of the CFD codes.

2 Experimental Details The micro-grate patterned SHPO surfaces were fabricated on 80 mm × 80 mm flat COC (cyclic olefin copolymer) sheets using ultra-precision machining techniques. Two different surfaces were manufactured, denoted as SHPO#1 and SHPO#2 , with p = 60 μm and 100 μm, g = 30 μm and 50 μm, respectively, resulting in the same f a of 50%. The normalized gaps g+ based on the viscous length scale of SHPO#1 and SHPO#2 surfaces are 0.36 and 0.64, respectively. The grate depth d of these surfaces is 37.3 μm. One smooth surface of the same size was made using the same material, which was used to produce data for comparison purpose. The smooth surface has a static contact angle θ of 94° (Fig. 1), whereas the two SHPO surfaces have almost the same θ of 152°, indicating good hydrophobic properties.

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Fig. 1 a Surface topology of the SHPO surface. b Schematic of geometry of the SHPO surface. Static contact angles of water droplets on c flat and d SHPO#1 surfaces

Fig. 2 Schematic of experimental setup in water tunnel test section

Experiments on drag reduction using patterned SHPO surface were conducted in a closed-loop water tunnel with a test section of 0.3 m (width) × 0.6 m (height) × 2.4 m (length). A flat plate of 1.8 m × 0.29 m × 0.02 m was suspended horizontally in the tunnel test section by six steel bars, which were connected to a rigid frame fixed directly to the ground (Fig. 2). Two arrays of cylindrical roughness elements aligned in spanwise direction were arranged at 0.16 m from the plate leading edge to generate a fully developed boundary layer. A floating element force balance was developed to measure the skin friction drag of the test surfaces. The balance was accurate to 10–4 N based on calibration results (not shown), resulting in an uncertainty of approximately 1% of the drag force. The test plate was installed on the vertical frame of the balance and was placed in the rectangular hole of the flat plate, with the test surface flush with that of the flat plate and the micro-grates aligned in streamwise direction. The right-handed Cartesian coordinate system (x, y, z) is defined in Fig. 2, with the origin o at the center of the test surface. The distance between the plate leading edge and the test surface center L c is 1.26 m. A Dantec two-dimensional time-resolved PIV system was used to measure the boundary layer in the (x, z) plane of y = 0. The instantaneous velocity components in the x and z directions are designated as U and W, which can be decomposed as U = U + u and W = W + w, respectively, where overbar denotes time-averaging, and u and w are the fluctuating velocity components. The uncertainties in U and W are about 1% of the free-stream velocity U ∞ . A total of 4000 images were captured for each case. Measurements were conducted at U ∞ =

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0.33 m/s. The status of air layer over SHPO surfaces was monitored using a camera. The plastron was observed to sustain without any loss for at least 20 min for all the drag reduction test cases, which is longer than needed to complete the tests.

3 Results and Discussion The skin-friction drag on the test surfaces is determined by F = F z l h /l v , where F z is the force measured by the load cell, lh and l v are arms of the horizontal bar and vertical frame of the balance. The drag coefficient is evaluated by C f = 2F/ρU 2∞ A, where ρ is the water density and A is the surface area, and the drag reduction is quantified by DR ≡ (C f0 − C f )/C f0 . Here the subscript ‘0 ’ denotes quantities measured over the smooth surface. The C f of SHPO#1 and SHPO#2 surface are 0.0027 and 0.0031, resulting in DR of 41% and 34%, as compared with that (0.0047) of the smooth surface, respectively. Table 1 lists the boundary layer thickness δ B , momentum thickness θ, viscous length scale δ v , Reτ based on δ B and uτ , Reθ based on U ∞ and θ, and wall shear stress τ w . Figure 3 shows the normalized mean streamwise velocity profiles over the baseline and the two SHPO surfaces. The logarithmic part collapses onto the classical logarithmic law, which is indicated by the solid line and can be expressed as +

U0 =

1 ln z+ 0 + B0 κ

(1)

with κ = 0.41 and B0 = 5.0. The superscript ‘+ ’ indicates normalization by uτ and/or δ v . Based on the fit of the logarithmic profile (z+ 0 = 80–200) using the Clauser method, the uτ 0 is estimated to be about 0.0161 m/s, which agrees well with that (0.160 m/s) measured by the friction balance (Table 1). On the other hand, for each SHPO surface, the velocity profile exhibits an upward shift as compared with the baseline case, with the shifting magnitude increasing with the amount of DR. The SHPO#1 and SHPO#2 have nearly the same θ (152°) and f a (50%), but the former leads to substantial larger DR (41%) than that (34%) of the latter. Following the meniscus deformation analysis by Rastegari and Akhavan [5], the protrusion angle (θ p ) and the maximum meniscus bending depth (hp ) may be written as Table 1 TBL flow parameters at U ∞ = 0.33 m/s (L c based Reynolds number ReL = 4.1 × 105 ) Sample

δ B (mm)

θ (mm)

uτ (m s−1 )

δ ν (μm)

Reτ

Reθ

τ w (kg m−1 s−2 )

Smooth

35.6

3.75

0.0160

63.1

564

1225

0.256

SHPO#1

37.7

3.99

0.0122

82.5

455

1304

0.149

SHPO#2

37.3

3.98

0.0130

77.7

480

1300

0.169

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Fig. 3 Mean streamwise velocity profiles for SHPO and baseline surfaces scaled by their own inner units, measured at the center (x + = 0 and y+ = 0) of the surface. The solid line represents the + classical law of the wall for the baseline surface U0 = ln z+ 0 /0.41 + 5

, 2

(2)

g hp = 2k 2 − 4 − k2 .

(3)

θp = arctan √

k

1−(k/2)

where k = P g/σ is the non-dimensional curvature of the interface, P is the Laplace pressure across the interface and is estimated by the static pressure at the surface (≈400 Pa), and σ is the surface tension. The dependence of the liquid–air interface shape on g and P could be supported by the measurement results from Tsai et al. [6] with g = 12 μm. The θ p and hp are calculated to be about 15° and 1.2 μm at P of 4500 pa, respectively, which are consistent to their microscope measured meniscus data. Given the same depth beneath the water, the gas pressures of the two SHPO surfaces are equal. However, the difference in the shape of the meniscus would result in different air volumes inside the grooves of the two surfaces. The θ p and hp of SHPO#2 are about 15° and 1.7 μm from Eqs. (2) and (3), respectively, which are higher than those (9° and 0.6 μm) of SHPO#1 . It is inferred that the shape of the interface on the gap between the grates may have a great effect on the drag reduction.

4 Conclusions An experimental study has been conducted on the skin friction drag reduction using micro-grates patterned SHPO surfaces in turbulent flow in a water tunnel. Two SHPO

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surfaces, with different surface geometries, were fabricated using the ultra-precision machining technique. The surfaces have good hydrophobic property, with a static contact angle of water droplets reaching about 152°. A dedicated, high-resolution skin-friction balance was developed in measuring the friction drag of the surfaces. The two surfaces produced significant drag reductions by 41 and 34%, though with the same f a and θ, indicating that neither f a or θ alone can predict the reduction in drag. It is found that the higher drag reduction may be ascribed to smaller deformation of the meniscus.

References 1. Henoch C, Krupenkin TN, Kolodner P, Taylor JA, Hodes MS, Lyons AM, Peguero C, Breuer K (2006) Turbulent drag reduction using superhydrophobic surfaces. In: 3rd AIAA flow control conference, AIAA paper No. 2006-3192, California, U.S. 2. Daniello RJ, Waterhouse NE, Rothstein JP (2009) Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21:085103 3. Woolford B, Prince J, Maynes D, Webb BW (2009) Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys Fluids 21:085106 4. Park H, Sun GY, Kim CJ (2014) Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J Fluid Mech 747:722–734 5. Rastegari A, Akhavan R (2018) The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets. J Fluid Mech 838:68–104 6. Tsai P, Peters AM, Pirat C, Wessling M, Lammertink RGH, Lohse D (2009) Quantifying effective slip length over micropatterned hydrophobic surfaces. Phys Fluids 21:112002

Sinuous and Varicose Modes in Turbulent Flow Through a Compliant Channel Konstantinos Tsigklifis and A. D. Lucey

Abstract We study the stability of two-dimensional fully-developed turbulent flow through a channel having spring-backed compliant walls. We decompose the FSI system into sinuous (symmetric disturbances relative to channel centre-line) and varicose (anti-symmetric) modes to assess the effect of wall compliance and structural damping on the stability of the flow-induced wall-based instabilities, Travelling Wave Flutter (TWF) and Divergence. The results show that varicose TWF and Divergence instabilities are more unstable than their sinuous counterparts. Varicose TWF, with long wavelength and high wavespeed, is the critical instability for a system with low levels of structural damping. Sinuous and varicose Divergence instabilities have similar wave characteristics and originate from a downstream propagating, downstream-stable hydrodynamic mode branch found in turbulent rigid-wall channel flow. The onset of Divergence is largely insensitive to the effect of structural damping. Finally, larger amplitudes of fluctuating wall shear stress occur for instabilities that feature larger amplitudes of vertical-disturbance wall velocity. Keywords Turbulent channel flow · Compliant wall · Varicose and sinuous modes

1 Introduction Theoretical work has been conducted on the stability of potential [1], steady laminar flow [2] and pulsatile laminar flow [3] through a flexible channel. Across these flow regimes there are many biomedical and microfluidic applications ranging from flows through the arteries to lab-on-a-chip technology. The underlying FSI system exhibits a plethora of instability branches. In the present work we investigate the spatial stability of steady turbulent channel flow through a compliant channel by decomposing the K. Tsigklifis (B) · A. D. Lucey Fluid Dynamics Research Group, School of Civil and Mechanical Engineering, Curtin University, Perth, WA 6845, Australia e-mail: [email protected] A. D. Lucey e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_16

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Fig. 1 a Decomposition of the full problem into sinuous and varicose modes. b Schematic of mean turbulent flow (bulk flow speed U B∗ ) through a compliant channel (sinuous mode shown)

stability problem to its sinuous (symmetric) and varicose (antisymmetric) parts—see Fig. 1—with a focus on the ensuing dispersion diagrams. These then lead to the generation of neutral-stability maps for the different instability branches corresponding to sinuous and varicose modes.

2 System Modelling The fully-developed steady mean turbulent channel flow is modelled and determined through the RANS equations using the Boussinesq hypothesis for the Reynolds stresses with the eddy viscosity calculated by solving the standard one-equation Spalart-Allmaras model (see [4]). Using a standard wave-type approximation, the organised flow disturbances are modelled using the modified Orr-Sommerfeld equation with additional terms to account for the effect of turbulent Reynolds stresses on the evolution of the organised disturbances. We implement a two degrees of freedom (2-DOF) compliant-wall model that allows both vertical and axial displacements of the wall interface through the isotropic Kirchhoff plate equation with dashpottype damping and a uniformly distributed spring foundation that adds stiffness only through the vertical component of wall displacements [4]. Flow and structure are fully coupled by imposing normal and tangential force balances and continuity of velocity at the two flow-wall interfaces. Finally, we couch the system as a boundary-value ˆ The wavenumber eigenvalues type generalized eigenvalue problem, Aqˆ = iα B q. α = αr + iαi define the spatial asymptotic stability; thus, for given real circular frequency ωr , the fully coupled linearised FSI system will be spatially stable if αi > 0,

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and unstable if αi < 0. The spatial stability analysis then reveals the different sinuous and varicose instability branches that exist and their wave characteristics following the methods of Ashpis and Reshotko [5]. The vertical and axial stiffness of the channel-wall model are characterised by 1/2 the dimensionless free-wave speed of the vertical motion, CV = (4Ks Bs )1/4 /Ms = ∗ ∗ ∗ ∗4 2 ∗2 ∗4 1/4 (4K E h L /(12(1 − ν )ρs νl )) , and by the ratio of the vertical to axial freewave speeds, RVA = CV /CA = (K ∗ h ∗ (1 − ν 2 )/(3E ∗ ))1/4 , where CA = (As /Ms )1/2 is the dimensionless free-wave speed of axial motion [4]. Ks , Bs , Ms , As are respectively the dimensionless spring-foundation stiffness, flexural rigidity, wall inertia and in-plane stiffness, made dimensionless through the average velocity of the steady turbulent channel flow, U B∗ , the half channel height, L ∗ and the kinematic viscosity of the fluid νl∗ . K ∗ , E ∗ , h ∗ , ρs∗ are respectively the spring foundation stiffness, elastic modulus, thickness and density of the compliant walls while ν is the material Poisson ratio.

3 Results and Discussion We focus on fluid-loaded wall waves, in particular the instabilities of Travelling Wave Flutter (TWF) and Divergence modes whose main characteristics are described in [3]. Figure 2a, b (sinuous and varicose modes respectively) are dispersion diagrams from the spatial stability analysis showing the variation of complex wavenumber (αi against αr ) with increasing real wavefrequency ωr as shown by the direction of the black arrows for each of the branch families. For clarity, we have not plotted the hydrodynamic modes, nor the axial wall modes. The compliant-wall properties are those of the relatively stiff walls used in [3], of steady and pulsatile laminar flow but with a low level (d = 1% of critical) of structural damping included. Results for two bulk Reynolds numbers, ReB = U B∗ L ∗ /νl∗ = 8555 and ReB = 11901 are shown in each of (a) and (b). The lower value is the critical ReB for the onset of sinuous TWF in (a) that is about to dip into the fourth quadrant (where αr > 0 and αi < 0), the higher is the critical value for sinuous Divergence onset in (a) that is about to dip into the fourth quadrant. Each of these sinuous instabilities feature the trajectory of the mode from the first quadrant, αr > 0 and αi > 0, into the fourth quadrant and therefore the classification of [5] indicates that they would appear as amplifying waves downstream of a (driver) source of excitation with downstream-directed phase speed, c = ωr /αr . A comparison of Fig. 1a, b shows that varicose TWF and divergence modes become unstable at lower Reynolds numbers than their sinuous counterparts. In addition, the trajectory of the sinuous TWF mode is replaced in the varicose case by a downstream-of-the-driver, downstream-propagating wall-based TWF instability branch originally located in the fourth quadrant. This varicose TWF mode is first unstable for low wavenumbers at ωr = 0.013 with very high phase speeds c ≈ 10 for ReB = 8555 and c ≈ 13 for ReB = 11,901 and can readily be stabilised by structural damping. Sinuous and varicose Divergence branches both originate from a

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Fig. 2 Dispersion diagrams (in the αr -αi plane) for turbulent-flow-loaded compliant-wall waves: variation of complex wavenumber with increasing wave frequency (the direction of black arrows) of a sinuous and b varicose modes. Dashed, solid and dash-dotted lines correspond to TWF, Divergence and (vertical) structural-mode branches, respectively. Red lines at ReB = 8555 and green lines at ReB = 11,901. For clarity the hydrodynamic and axial modes are not included. Wall-structure parameters: CV = 15180, RVA = 0.12, d = 1% critical damping

downstream-propagating, downstream-stable hydrodynamic-mode branch (not plotted) in the first quadrant which exists within the corresponding rigid-walled system. Wall compliance permits this mode to become unstable at a finite wavenumber with a wavespeed c ≈ 0.83 for sinuous disturbances, while for varicose disturbances the most unstable mode has a wavespeed c ≈ 0.9 at ReB = 11,901. From results such as those above, we construct the neutral-stability diagram presented as Fig. 3. This indicates the onset-values of the bulk Reynolds number, ReB , and associated wavenumber, αr , for sinuous and varicose TWF and Divergence instabilities. Curves for both elastic (d = 0) and with a low level of structural damping (d = 1% of critical) are included to illustrate the effect of damping on instabilityonset values of ReB . It is seen that the FSI system is less stable for both TWF and Divergence instabilities when varicose disturbances occur as compared with sinuous perturbations. In addition, structural damping has a strong stabilizing effect on both

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Fig. 3 Neutral-stability curves giving the Bulk Reynolds number, ReB , and mode wavenumber, αr , at instability onset for TWF and Divergence instabilities, with and without structural damping (d), for sinuous (thick lines) and varicose (thin lines) modes in fully-developed turbulent flow through a compliant channel. Inset figures show eigenfunctions, for the modes at the points indicated in the ReB -αr plane. The eigenfunctions comprise the normalised real part of the organised disturbance velocity (uˆ x and uˆ y respectively being axial and wall-normal directions) across the channel. Wallstructure parameters: CV = 15180, RVA = 0.12

sinuous and varicose TWF instabilities. By contrast, structural damping only has a very small destabilizing effect on both sinuous and varicose Divergence instabilities. Clearly, Fig. 3 shows that (varicose) TWF is the critical mode for instability onset in the FSI system; however, higher values of structural damping could further stabilise the TWF modes until (varicose) Divergence yields the critical instability as ReB is increased. The insets in Fig. 3 show the normalised real part of the organised disturbance velocity eigenfunctions across the channel for the critical conditions of sinuous and varicose TWF and Divergence (at the ReB -αr coordinate indicated by markers). The sinuous TWF instability is seen to generate larger fluctuating wall shear stress amplitudes mainly due to the relatively larger vertical disturbance velocity amplitudes at the wall-flow interface when compared to those of the sinuous Divergence instability. The opposite is seen for the varicose TWF and Divergence instabilities, with the wall shear stress amplitudes and the vertical velocity amplitudes on the wall being larger for Divergence. Finally, comparing sinuous and varicose TWF eigenfunctions, it can be inferred that sinuous modes generate larger fluctuating wall shear stress and disturbance velocity amplitudes at the compliant wall whereas for Divergence these quantities are higher for varicose modes.

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4 Conclusions We have studied the time-asymptotic spatial stability of steady turbulent flow through a compliant channel considering separately the sinuous and varicose modes of the organised disturbance oscillations. We identified sinuous and varicose TWF and Divergence instability mode branches which appear as downstream-travelling downstream amplified waves. From dispersion diagrams we have generated the map of instability onset for the system in the Reynolds-number—wavenumber plane. The sinuous TWF instability appears as a very fast wave that is very sensitive to the stabilising effect of structural damping; its mode branch is similar to that of flutter in inviscid fluid-conveying FSI systems [6]. Varicose TWF appears as a lowwavenumber instability which is stabilised by structural damping. Both the sinuous and varicose Divergence modes become unstable at finite wavenumber and are very slightly destabilised by structural damping. Finally, higher disturbance wall shear stress amplitudes appear in sinuous TWF and varicose Divergence modes relative to those developed in the varicose TWF and sinuous Divergence. These higher levels appear to arise from larger vertical disturbance velocity amplitudes of the compliantwall.

References 1. Burke MA, Lucey AD, Howell RM, Elliott NSJ (2014) Stability of a flexible insert in one wall of an inviscid channel flow. J Fluids Struct 48:435–450. https://doi.org/10.1016/j.jfluidstructs. 2014.03.012 2. Davies C, Carpenter PW (1997) Instabilities in a plane channel flow between compliant walls. J Fluid Mech 352:205–243. https://doi.org/10.1017/S0022112097007313 3. Tsigklifis K, Lucey AD (2017) Asymptotic stability and transient growth in pulsatile Poiseuille flow through a compliant channel. J Fluid Mech 820:370–399. https://doi.org/10.1017/jfm.2017. 163 4. Tsigklifis K, Lucey AD (2018) Instability of a compliant channel conveying steady and pulsatile turbulent flows. In: Lau TCW, Kelso RM (eds) Proceedings of the 21st Australasian fluid mechanics conference, Adelaide, 10–13 Dec 2018. ISBN 978-0-646-59784-3 5. Ashpis DE, Reshotko E (1990) The vibrating ribbon problem revisited. J Fluid Mech 213:531– 547. https://doi.org/10.1017/S0022112090002439 6. De Langre E, Ouvrard AE (1999) Absolute and convective bending instabilities in fluidconveying pipes. J Fluid Struct 13:663–680. https://doi.org/10.1006/jfls.1999.0230

Shape Optimization Considering the Stability of Fluid–Structure Interaction at Low Reynolds Numbers W. G. Chen, W. W. Zhang, and X. T. Li

Abstract This work employed shape optimization to enhance the stability of the flow past a single-degree-of-fredom transversely vibrating cylinder at subcritical Reynolds numbers (Re < 47). Dynamic derivative is used as the optimization objective. To improve the calculation efficiency, a surrogate model is constructed to replace the numerical simulation in the optimization process. Research shows that through the shape optimization, vortex-induced vibration is successfully suppressed at design conditions and the stability of the fluid–structure interaction system is remarkably improved. Keywords Shape optimization · Fluid–structure interaction · Stability

1 Introduction Traditional aerodynamic optimization mainly aim at aerodynamic performance like the drag or lift [1–3]. However, the shape optimization about the stability of the flow past a circular cylinder at low-Reynolds numbers has rarely been studied. Vortex-induced vibration (VIV) is a hot research topic in the field of fluid–structure interaction (FSI). The critical Reynolds number Recr of the flow past a fixed circular cylinder is about 47 [4]. Cossu and Morino [5] and Mittal et al. [6] found that VIV can still appear when Re < Recr. By using the reduced order model (ROM), Li et al. [7] precisely predicted the stability envelope of the cylinder with single-degree-of-freedom (SDOF) transverse vibration as illustrated in Fig. 1. Dynamic derivative of the cylinder can be obtained by forced oscillation method for sufficient large mass ratio at a known structural frequency [8–10]. As a parameter related to dynamic stability, dynamic derivative is adopted as the optimization objective to improve the FSI stability of the SDOF transversely vibrating cylinder. Shape optimization does not require additional structure and energy injection compared to active controls [11–13]. W. G. Chen (B) · W. W. Zhang · X. T. Li School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_17

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Fig. 1 Stability envelope of a SDOF transversely vibrating cylinder, m ∗ = 50

In this paper, shape optimization will be used to improve the stability of SDOF elastically-supported cylinder system at subcritical Re. Dynamic derivative is considered as the optimization objective. The stability boundary after optimization is obtained by the ROM-based FSI model.

2 Numerical Methods 2.1 FSI Simulation For 2-D laminar flow problem, unsteady Navier–Stokes equations are employed. The finite volume method with the standard central scheme is utilized to solve the Navier– Stokes equations. The time marching method is a dual time-stepping technique. For more details on computational fluid dynamics (CFD), the reader can refer to the work of Jiang [14]. The grid motion is accomplished by the radial basis function interpolation [15]. As illustrated in Fig. 2, we adopt the hybrid unstructured grids with 11,704 nodes. The size of the computational domain is 60D × 40D (D is the diameter of the cylinder).

2.2 Calculation of Plunge-Damping Coefficient In this study, the SDOF plunging motion of cylinder is studied, so the dynamic derivative only refers to plunge-damping derivative. The form of the forced harmonic plunging motion is given as: h(t) = h m sin kt

(1)

where h m is the amplitude of vibration, and k = 2π/U ∗ is the reduced frequency.

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Fig. 2 a Hybrid grid, b close-up view of the hybrid grid

Referring to the work of Zhang et al. [10], the integral form of the plunge-damping derivative Clh˙ can be expressed as: 1 Clh˙ = π hm

t s +T

Cl (t) cos ktdt

(2)

ts

where Cl (t) is the lift coefficient at time t, ts represents an arbitrary moment after a . periodic flow is obtained, T is the period of forced oscillation cycle and T = 2π k

3 Shape Optimization 3.1 Optimization Description Plunging damping coefficient Clh˙ is selected as the goal for optimization. The maximum thickness of the optimized shape can’t be less than the initial value. The class-shape function transformation (CST) technique [16] is used to parameterize the circular section. To improve the optimization efficiency, RBF (radial-basis function) model [17] is used to construct the surrogated madel of Clh˙ with respect to shape parameters. As a heuristic optimization algorithm, differential evolution algorithm (DE) [3] is adopted as optimization algorithm in this research.

3.2 Results and Analysis As shown in Fig. 2, we carry out shape optimization at Re = 22 and U ∗ = 9.45. The initial value of Clh˙ is equal to 2.60. Symmetrical shape is investigated here. And the

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number of design variables is eight. The Clh˙ varies from 2.86 to −4.30 through 500 iterations. Figure 3 displays the optimized shape compared to the original one. The position of maximum thickness is closer to back end position through optimization. As shown in Fig. 4, the stability envelopes are obtained by the ROM-based FSI model. Through optimum design, the critical Reynolds number of the FSI system is increased from 20 to 24, and the instability range of the system is also reduced. We carry out a second optimization at Re = 26 and U ∗ = 8.40. Figure 5 displays the secondly optimized shape. Figure 6 shows the stability envelope of Fig. 3 Optimized shape compared to the original one

Fig. 4 Optimized stability envelope compared to the original one

Fig. 5 Shapes before and after the optimization

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Fig. 6 Stability envelopes before and after optimal design

the second optimization. The critical Reynolds number of the system is increased to 27. Therefore, the instability region is remarkablely reduced by using of shape optimization.

4 Conclusions In this work, we adopt the shape optimization method to enhance the FSI stability at subcritical Reynolds numbers. Plunge-damping derivative calculated by forced oscillation method is adopted as the optimization objective. Through shape optimization, the FSI system of a SDOF transversely vibrating cylinder turns to be stable at design states. The critical Reynolds number of VIV is increased from 20 to 27. Meanwhile, the instability region is remarkablely reduced by using of shape optimization.

References 1. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Ann Arbor 6(2):126–137 2. Peter JEV, Dwight RP (2010) Numerical sensitivity analysis for aerodynamic optimization: a survey of approaches. Comput Fluids 39(3):373–391 3. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359 4. Williamson CHK, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36(1):413–455 5. Cossu C, Morino L (2000) On the instability of a spring-mounted circular cylinder in a viscous flow at low Reynolds Numbers. J Fluids Struct 14(2):183–196 6. Mittal S, Singh S (2005) Vortex-induced vibrations at subcritical Re. J Fluid Mech 534(534):185–194 7. Li X, Zhang W, Jiang Y, Ye Z (2015) Stability analysis of flow past anelastically-suspended circular cylinder. Chin J Theor Appl Mech 47(5):874

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8. Da Ronch A, Vallespin D, Ghoreyshi M et al (2012) Evaluation of dynamic derivatives using computational fluid dynamics. AIAA J 50(2):470–484 9. Liu X, Liu W, Zhao Y (2015) Unsteady vibration aerodynamic modeling and evaluation of dynamic derivatives using computational fluid dynamics. Math Prob Eng 10. Zhang W, Yiming G, Yilang LIU (2018) Abnormal changes of dynamic derivatives at low reduced frequencies. Chin J Aeronaut 31(7):1428–1436 11. Chen WL, Xin DB, Xu F et al (2013) Suppression of vortex-induced vibration of a circular cylinder using suction-based flow control. J Fluids Struct 42(4):25–39 12. Du L, Sun X (2015) Suppression of vortex-induced vibration using the rotary oscillation of a cylinder. Phys Fluids 27(2):195–2023 13. Huera-Huarte FJ (2017) Suppression of vortex-induced vibration in low mass-damping circular cylinders using wire meshes. Marine Struct 55:200–213 14. Jiang Y (2013) Numerical solution of Navier–Stokes equations on generalized mesh and its applications. NWPU, Xi’an, China (Ph. D. thesis) 15. Boer AD, Schoot MSVD, Bijl H (2007) Mesh deformation based on radial basis function interpolation. Comput Struct 85(11):784–795 16. Kulfan B, Bussoletti J (2006) “Fundamental” parameteric geometry representations for aircraft component shapes. In: Aiaa Paper, pp 1–45 17. Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257

Aerodynamic Sound Identification of Longitudinal Vortex System Shigeru Ogawa, Hiroki Ura, Takehisa Takaishi, Hiroki Okada, Kota Samura, Harutaka Honda, and Kohei Suzuki

Abstract Longitudinal vortex generated around automobiles and airplanes is reproduced by a delta wing with attack angle of 15°, which was merged in the uniform flow at 10 m/s. The paper aims to clarify the sound source of the longitudinal vortex system. The beamforming technique was applied to identify the sound sources of the vortex system in the JAXA (Japan Aerospace Exploration Agency) wind tunnel. To verify the simulation model used, aerodynamic sound in the far field was compared with measured one. Estimated sound agrees quite well with measured one. To clarify aerodynamic sound generation mechanism, sound source distribution and vortex structure were numerically investigated. As a result, following findings were obtained. (1) Dominant sound source was experimentally observed by beamforming technique at the apex of the longitudinal vortex system. (2) Numerical analysis clarified sound source distributions of derivatives of surface pressure fluctuations, which were caused by the strongest unsteady motions of the vortices at the apex of the vortex system. Keywords Aerodynamic sound · Longitudinal vortex · Beamforming · CFD

1 Introduction Longitudinal vortices generated around automobiles and airplanes are regarded as one of the most dominant aerodynamic noise sources. There have been so many studies to reveal the generation mechanism of aerodynamic noise produced by longitudinal vortex. However, it has not yet been clarified that how the longitudinal vortex system has been generated and how this system produces the aerodynamic noise. The present paper aims to reproduce the longitudinal vortex with a simple delta wing model, and to identify noise sources by beamforming technique as well as to S. Ogawa (B) · H. Okada · K. Samura · H. Honda · K. Suzuki National Institute of Technology, Kure College, 2-2-11 Agaminami, Kure, Japan e-mail: [email protected] H. Ura · T. Takaishi Japan Aerospace Exploration Agency, 6-13-1, Osawa, Mitaka, Tokyo, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_18

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clarify aerodynamic sound generation mechanism numerically. The sound induced by turbulence in an unbounded fluid is generally called aerodynamic sound. With respect to aerodynamic sound, Lighthill [1] transformed the Navier–Stokes and continuity equations to form an exact, inhomogeneous wave equation whose source terms are important only within the turbulent region. Lighthill equation is expressed in Eq. (1). 2 ∂ 2 Ti j 1 ∂2 2 c − ∇ (ρ − ρ ) = , 0 0 ∂xi x j c02 ∂t 2 Ti j = ρvi v j + ( p − p0 ) − c02 (ρ − ρ0 ) δi j − σi j .

(1)

where T ij is Lighthill stress tensor, the term ρvi vj Reynolds stress, and the speed of sound c0 in a medium of uniform mean density ρ 0 and pressure p0 . At low Mach number M 1, the acoustic efficiency of the surface dipoles exceeds the efficiency of the volume quadrupoles by a large factor ~O (1/M 2 ) [2, 3]. Therefore, dipole sound caused by solid bodies is supposed to be dominant in this study. Dipole sources are expressed as Lighthill-Curle equation [2] as Eq. (2) for acoustic compact. This equation means that sound pressure pf in the far field emitted from solid bodies are expressed in terms of time derivative of solid surface pressure fluctuations p f (x, t) =

1 xi 4π c0 x 2

ni

|x| |x| ∂p 1 xi ∂ Fi (t − (t − )d S = ) . ∂t c0 4π c0 x 2 ∂t c0

(2)

Fi = pi d SHere indicates the summation of the forces the obstacle acts on the fluid. That is, unsteady motions of vortices apply forces on the obstacle and time derivative of the reaction forces from the obstacle is the dipole sound source. Most practical problems of sound generation by flow involve moving boundaries and moving sources interacting with such boundaries. Ffowcs Williams and Hawkings applied Lighthill’s equation to moving sound sources with control surfaces. FW-H equation reduces to Lighthill-Curle Eq. (2) if the control surface is stationary. For high Reynolds number flow at low Mach number, Howe [3] introduces the vortex sound equation shown in Eq. (4) with total enthalpy B defined as

dp 1 2 + v , ρ 2 − ∇ 2 B = div(ω × v).

B=

1 ∂2 c02 ∂t 2

(3)

(4)

As Lighthill equation, the right hand means sound source including vorticity, which explicitly shows that vorticity ω is the sound source. In case of acoustic compact, far-field acoustic pressure emitted from dipole source [4] is also given as

Aerodynamic Sound Identification of Longitudinal Vortex System

p f (x, t) =

ρ0 xi 4π c0 |x|2

|x| ∂ ) · ∇φi dy, (ω × v)(y, t − ∂t c0

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(5)

where ∅i is velocity potential which satisfies Laplace equation ∇ 2 ∅i and would be produced by translational motion of the body at unit speed in the i direction [3]. Here this factor indicates the acoustic radiation efficiency. It therefore follows that aerodynamic sound is generated by unsteady motions of the vortex, and acoustic radiation efficiency increases especially when there exists the vortex near an obstacle.

2 Experimental Approach The experiment was conducted in the JAXA wind tunnel. The delta wing with L = 0.8 m × 0.8 m was immersed in the uniform flow U = 10 m/s in the test section (2 m × 2 m) of the wind tunnel. Reynolds number is 5.3 × 105 for L = 0.8 m, U = 10 m/s. The microphone array [5] consists of 96 microphones (B&K Type 4939), which was installed in the anechoic chamber 1.5 m away from the delta wing as shown in Fig. 1. The beamforming technique [5] was applied to identify the noise sources of the longitudinal vortex. Figure 2 indicates sound pressure distribution on the wing. For the frequency range from 0.5 to 5 kHz in interest, the apex of the longitudinal vortex is considered dominant sound sources. Regarding sound characteristics the authors’ previous study [6] also clarified dipole characteristics of broadband sound, increasing in proportion to 6.2 power of the flow velocity. Fig. 1 Experimental arrangement of microphone array and far field microphone installed inside the anechoic chamber

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Fig. 2 Sound sources of longitudinal vortex system measured by microphone array at U = 10 m/s with angle of attack α = 15°

3 Numerical Approach CFD was employed to analytically investigate the structure of the longitudinal vortex. The study uses the software STAR-CCM + with software V11.06.011. In the simulation, numerical delta wing model has apex angles of 90° just as in flow experiment. Numerical unsteady analysis was conducted for sound calculation. This layer of cells is necessary to simulate flow field accurately. The prism layer mesh [7] is defined in terms of its thickness, the number of cell layers, and the size distribution of the layers. To calculate the flow filed in the longitudinal vortex with higher accuracy, the thickness of prism layer was decided so that wall Y + [7] is less than 1.4 across the wing surface. The total thickness of prism layer is 1 mm with 10–15 layers while mesh size is 0.5 mm for longitudinal vortex region and especially 0.3 mm for the apex region with 0.005 mm for the region closest to the model surface for higher resolution. As a result, the total number of meshes amounts to 125 million. Time step is 0.1 ms to simulate the largest maximum frequency 5 kHz. Figure 3 visualized the longitudinal vortex, which shows the highest velocity at the apex. To verify the simulation model used, aerodynamic sound in the far field was compared with measured one. Sound estimated by FW-H equation [3] agrees quite well with measured one obtained by integrating spatially sound pressure distribution with the microphone array as shown in Fig. 4.

4 Results and Discussion To clarify aerodynamic sound generation mechanism, sound source distribution and vortex structure were numerically investigated. Figure 5 shows distributions of time

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Fig. 3 Longitudinal vortex system visualized by streamlines around the delta wing. The apex of the vortex has maximal velocity

Fig. 4 Comparison between measured aerodynamic sound and estimated one by FW-H method in the far field

Measured

Estimated

Fig. 5 Time derivative of surface pressure fluctuations with maximal values at the apex

derivatives of surface pressure fluctuations [or dipole sound source in Eq. (2)] which have the highest values for all the frequencies. This shows the same tendency as the sound source distributions obtained experimentally in Fig. 2. Figure 6 shows the vortex structures in time series (μs) in the section A. Clockwise vortex (blue color)

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Fig. 6 Unsteady motions of the vortices around the apex of the delta wing in the section A at 10 m/s

induces counterclockwise vortex (red color), which results in a pair of vortices. Figures 7 and 8 show the unsteadiness of the strength of the vortices in the each section. It is found that the strength of the vortex is the highest at the section A and Fig. 7 Clockwise vorticity has maximum at the apex and decreasing in the axial direction

A B C D

Fig. 8 Counterclockwise vorticity is weaker than clockwise one at each section

A B C D

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decreases in flow direction B, C, and D and that stronger clockwise vortex generates weaker counterclockwise one. Based on these analyses, mechanism of aerodynamic sound is considered that the vortices formed at the apex of the wing with vehement unsteadiness of vortex motion induce sound wave efficiently. For M = 0.03 1 at U = 10 m/s, the radiation is accordingly dominated by the dipole. It seems that this great increase in acoustic radiation efficiency brought about by surface dipoles on the wing occurs especially when vorticity strongly interacts with the apex from Eq. (5).

5 Conclusions To identify the sound source of the longitudinal vortex system, the study was conducted experimentally and numerically. As a result, following findings were obtained. (1) Dominant sound source was experimentally observed by beamforming technique at the apex of the longitudinal vortex system. (2) Numerical analysis clarified maximal sound source at the apex of the vortex system from distributions of derivatives of surface pressure fluctuations. Therefore it follows that dominant sound source at the apex is generated by the strongest unsteady motions of the vortices and the highest acoustic radiation efficiency.

References 1. Lighthill MJ (1952) On sound generated aerodynamically I. General theory. Proc R Soc London A 211:564–587 2. Curle N (1955) The influence of solid boundaries upon aerodynamic sound. Proc R Soc London A 231:505–514 3. Howe MS (1998) Acoustics of fluid-structure interactions. Cambridge University Press, Cambridge 4. Takaishi T, Ikeda M, Kato C (2004) Method of evaluating dipole sound source in a finite computational domain. J Acoustic Soc Am 116(3):1427–1435 5. Johnson DH, Dudgeon DE (1993) Array signal processing—concepts and techniques. Prentice Hall (1993) 6. Ogawa S, Ura H, Takaishi T, Okada T, Samura K, Honda H, Suzuki K (2018) Noise source identification of aerodynamic sound radiated from longitudinal vortex generated around the leading edge of a delta wing by beamforming technique. In: Proceedings of the 38th symposium on fluid dynamic noise (in Japanese) 7. Ogawa S, Takeda J, Yano K (2016) Aerodynamic sound radiated from longitudinal and transverse vortex systems generated around the leading edge of delta wings. Open J Fluid Dyn 6(2):101–118

Impulsive Start-Up of a Deformable Flapping Wing at Different Angular Conditions Daniel Diaz, Thierry Jardin, Nicolas Gourdain, Frédéric Pons, and Laurent David

Abstract This paper aims at evaluating the influence of the initial rotation on a flapping deformable wing. Scanning PIV techniques are used to obtain the instantaneous volumic velocity fields, which allow the computation of the pressure field and calculation of the forces generated by the wing. The experiments were performed with a flat deformable wing, in order to also see the influence of the wing flexibility on the lift production. Comparing our results to those obtained in previous studies at different Reynolds number (Percin and van Oudheusden in Exp Fluids 56(2):1–19 (2015), [1, Diaz et al., in Comparison between start-up and established flow conditions in deformable flapping wings, pp 2035–2050, (2018), 2]), it was shown how the typical vortical structures that are generated around a flapping wing (Jardin et al., in J Fluid Mech 702:102–125, (2012), [3]) remain stronger, less chaotic and more compact for a longer period of time for a low Reynolds number. The present work further focuses on the role of the initial direction of rotation in this case of study. Keywords Flapping flight · Deformable wings · Applied PIV

1 Introduction Devices that mimic hummingbirds and dragonflies flight agility would revolutionize the way micro–air vehicles are conceived, presenting an alternative to the conventional fixed and rotatory wing concepts. Whereas previous studies on flapping wings accelerated from rest have extensively provided data of the flow field and force generation characteristics of both translating-pitching plates and revolving wings at constant angle of attack [4, 5], a relatively small amount of them have been compared with experiments of revolving-pitching flapping wings [1, 2]. D. Diaz (B) · F. Pons · L. David Institut Pprime, CNRS, Université de Poitiers, ENSMA, Poitiers, France e-mail: [email protected] D. Diaz · T. Jardin · N. Gourdain ISAE-Supaero, University of Toulouse, Toulouse, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_19

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The detection of important features of the flapping motion has been the key for the better understanding of this type of flight. It is well-known that wing rotation is an essential feature for hovering insects [6, 7]. Thanks to their ability to actively rotate their wings, they can alter both the magnitude and the direction of the force generated. Another interesting feature is the effect of wing flexibility in flapping flight. Although the benefits of flexibility have been not well specified, some evidence points out that wing deformation enhance thrust and lift production [8, 9]. In addition, as previously presented, it has also been established how for low Reynolds number the vortical structures remain stronger, more organized and slightly less-segmented for a longer period of time [2]. However, it was also stated that the initial direction of rotation may also have an influence in the results obtained. Therefore, the present work will focus on evaluating the effects of changing the initial direction of rotation.

2 Experimental Procedures 2.1 Setup The experimental tests were performed in a water tank made of Altuglas with an octagonal section and dimensions of 1 m × 1 m × 1.5 m. The wing is attached at its root by a pivot joint, allowing the rotation along the spanwise axis. This enables the modification of the angle of attack. At the same time, the pivot joint is fixed into a vertical axis (perpendicular to the spanwise axis), allowing the flapping motion (Fig. 1). The tests were conducted using a PET (Polyethylene Terephthalate) flat-flexible wing with sharp edges and a thickness of 0.125 mm. The flapping motion to mimic corresponds to a wing with a 1 cm chord and 4 cm span, flapping in the air at a Reynolds number of 1000 and a frequency of 10.18 Hz. However, as the experiments are carried out in water (reducing the velocity and increasing the dimension for a better visualization) the Reynolds similitude was calculated, keeping also the same nondimensional stroke amplitude (flapping amplitude/chord). This results in a wing with 6 cm chord and 24 cm span performing a flapping period of 51.4 s. At the start (ψ

1: Revolution motion engine 2: Worm Gear Screw 3: Revolution Axis 4: Angle of attack rotation engine 5: Pulley System 6: Wing

Fig. 1 Illustration of the flapping angles (left) and the assembly allowing the rotating and revolving motion of the wing (right)

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Case

α0

α˙ 0

Description

1

0°

Counterclockwise

Current study

2

45◦

No rotation

Current study

3

90◦

Clockwise

Test performed in [2]

= −60°) or end (ψ = 60°) of the upstroke/downstroke, the wing is subjected to both rotating and accelerating/decelerating motions. After the supination or pronation, the airfoil undergoes a constant velocity revolution phase with a fixed angle of attack of 45 degrees. This same configuration was used by Diaz et al. in [2], as well as the procedure for the PIV acquisition. These previous experiments, started from an angle of attack of 90°, while now cases starting from 0° and 45° are tested (Table 1).

2.2 Data Processing Velocity Fields Computation. The calculation of the velocity fields from scanning PIV measurements is performed by sub-pixel correlation using a code developed internally with SLIP library [10]. The correlation is carried out using the FTEE (fluid trajectory evaluation based on an ensemble-averaged cross-correlation) method [11] with two passes over the volumes of 32 * 32 * 16 pixels, with a 50% overlapping rate. Pressure Calculation. The pressure distribution is obtained by spatially integrating its gradient derived from the velocity flow field [12]. Force Estimation. Thanks to the determination of the velocity and acceleration fields by Time Resolved Particle Image Velocimetry (TR-PIV), the application of the complete momentum equation approach is possible [13].

3 Results Temporal evolution of the flow structures for the different cases has been calculated and it is shown in the following figures (all the 2D images of this section correspond to the 75% wingspan plane). The well-defined and coherent vortical structures characteristic of this motion [3] are found: leading edge vortex (LEV), tip vortex (TP) and trailing edge vortex (TEV). Overall, the structures found for all cases are almost the same. This verifies the statement of Diaz et al. in [2], that the vortical structures remain stronger, more organized and slightly less-segmented for a longer period of time for low Reynolds number cases, no matter the direction of the initial rotation of the wing.

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Fig. 2 Temporal evolution of contours of non-dimensional out-of-plane vorticity (wz c/Vt ). First, second and third rows show case 1, 2 and 3 respectively

However, some features can be distinguished between the three cases. First, the counterclockwise rotation of the wing shows the rapid formation of strong TEVs compared to the other two cases. This is shown in Fig. 2, having sooner detachment of contours of vorticity (corresponding with the TEVs) for the counterclockwise rotation case. In addition, the detachment of the initial LEV also occurs sooner for case 1 and 2 (ψ = −40°), matching with the vorticity contours of Fig. 2. On the other hand, the TV generated is more robust for case 3. Due to this, the spanwise flow (see Fig. 3) coming from the root to the tip of the wing, is undermined with the flow generated by the TV for case 3, while for the other cases the spanwise flow is stronger. Finally, Fig. 4 shows the evolution of the lift production for the first flapping period. Two main features can be distinguished in this graph. First, the curve for case 3 (no initial rotation) does not show the initial peak of lift production as the other two cases, meaning that this increase in force comes from the initial rotation of the wing. Then, it can also be seen how for case 1 the force increases more rapidly than in case 3, but then it also drops faster. This is related to the sooner formation and detachment of the LEV in case 1, as previously discussed in Fig. 2.

4 Conclusion The influence of initial rotation in a deformable flat flapping wing was established with this work. It has been shown how depending on the initial direction of rotation the TEVs are generated more rapidly. In addition, it also affects the formation and

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Fig. 3 Temporal evolution of contours of non-dimensional spanwise velocity (Vz /Vt ). First, second and third rows show case 1, 2 and 3 respectively

CL Comparison 1,0 Case1 Case2 Case3

0,8

CL

0,6

0,4 0,2 0,0

-0,2

-60

-50

-40

-30

-20

-10

0

ψ (°)

10

20

30

40

50

60

Fig. 4 Lift production evolution for the three cases studied

detachment of the initial LEV, having a direct impact on the initial force peak generated by the wing. Also, the strength of the TV is altered, changing the spanwise flow along the wing. Acknowledgements This project has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement No. 769237, HOMER (Holistic Optical Metrology for Aero-Elastic Research). It is also included in the CPER FEDER project of the Region Nouvelle Aquitaine.

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References 1. Percin M, van Oudheusden BW (2015) Three-dimensional flow structures and unsteady forces on pitching and surging revolving flat plates. Exp Fluids 56(2):1–19 2. Diaz D, Jardin T, Pons F, David L (2018) Comparison between start-up and established flow conditions in deformable flapping wings. In: 19th international symposium on applications of laser and imaging techniques to fluid mechanics, Lisbon, pp 2035–2050 3. Jardin T, Farcy A, David L (2012) Three-dimensional effects in hovering flapping flight. J Fluid Mech 702:102–125 4. Kim D, Gharib M (2010) Experimental study of three-dimensional vortex structures in translating and rotating plates. Exp Fluids 49(1):329–339 5. Ozen CA, Rockwell D (2012) Flow structure on a rotating plate. Exp Fluids 52(1):207–223 6. Dickinson MH (1994) The effects of wing rotation on unsteady aerodynamic performance at low Reynolds numbers. J Exp Biol 175:45–64 7. Sane SP, Dickinson MH (2002) The effects of wing rotation and a revised quasi-steady model of flapping flight. J Exp Biol 205:1087–1096 8. Heathcote S, Wang Z, Gursul I (2008) Effect of spanwise flexibility on flapping wing propulsion. J Fluids Struct 24(2):183–199 9. Gorpalakrishnan P, Tafti DK (2010) Effect of wing flexibility on lift and thrust production in flapping flight. AIAA J 48(5):865–877 10. Tremblais B, David L, Arrivault D, Dombre J, Thomas L, Chatellier L (2010) Logical standard library for image processing, Licence CECILL DL 03685-01, APP IDDN.FR.001.300034.000. S.P.2010.000.21000 11. Jeon YJ, Chatellier L, Beaudoin A, David L (2015) Least-square reconstruction of instantaneous pressure field around a body based on a directly acquired material acceleration in time-resolved PIV. In: 11th international symposium on PIV, Santa Barbara 12. Jeon YJ, Gomit G, Earl T, Chatellier L, David L (2018) Pressure field reconstruction from TR-PIV measurements. Exp Fluids 59:27 13. David L, Jardin T, Farcy A (2009) On the non-intrusive evaluation of fluid forces with the momentum equation approach. Meas Sci Technol 20(9):1–11

The Passive Separation Control of an Airfoil Using Self-Adaptive Flap Zhe Fang, Chunlin Gong, Alistair Revell, Gang Chen, Adrian Harwood, and Joseph O’Connor

Abstract The control of boundary layer separation, to bring about performance enhancements on air/water vehicles, has been a very active research area in recent years. In this paper, the passive separation control of a Naca0012 airfoil via a rigid/flexible flap at Reynolds number Re = 1000 is investigated. The effects of the flap configurations (length, attachment position, deployment angle and material properties) on the airfoil aerodynamic performance which is quantified by mean lift and mean drag are investigated. Compared to the clean Naca0012 airfoil case, via the passive separation control of flap with optimal configuration, the mean lift coefficient is improved by 13.51%, and the mean drag coefficient is decreased by 3.67%. Keywords Passive separation control · Flap · Lattice Boltzmann · Immersed boundary · Finite element

1 Introduction The manipulation of fluid flows and the control of boundary-layer separation, to bring about performance enhancements on air/water vehicles, has been a very active research area in the fluid mechanics community. Because the fluid mechanisms behind the boundary-layer separation is very complicated, it is worthwhile to analyze and emulate efficient flying mechanisms observed in nature, in the form of swimming and flying animals, as they have evolved for millions of years and reached a high level Z. Fang · C. Gong (B) Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an, Shaanxi, China e-mail: [email protected] A. Revell · A. Harwood · J. O’Connor School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, UK G. Chen State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xian Jiaotong University, Xi’an, Shaanxi, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_20

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of adaptation. Carruthers et al. [1] observed that birds would pop-up there feathers when the flow separation started to develop on the upper side of their wings, these small flexible coverts could counteract backflow and prevent an abrupt breakdown in lift. And this self-adjusting mechanism has been interpreted as a biological high-lift device assuming that a delay in flow separation results in higher lift at lower flight speeds [1]. This paper numerically investigates the influence of various hairy flaps located on the upper surface of a Naca0012 airfoil, the Reynolds number defined by chord-length of airfoil is Re = 1000. The fluid motion is obtained by solving the lattice Boltzmann equation. The dynamics of the hairy flaps are calculated using the finite element method (FEM), and the interaction between fluid and structure is handled using the immersed boundary method (IBM). Aerodynamic performance is quantified by the mean drag and the mean lift of Naca0012 airfoil. And the influence of the flap configurations on the aerodynamic performance is investigated.

2 Numerical Method As an explicit time-advancement method, the lattice Boltzmann method has been proven to be a viable and efficient substitute for Navier–Stokes solver and put into use in many fluid-flow simulations. The Boltzmann equation for incompressible viscous flow is: ∂f + e · ∇x f + F · ∇e f = f ∂t

(1)

where f is the distribution function of the particles located at spatial coordinate x and time t with velocity e. The force term F accounts for any external force applied to the fluid, f represents the collision operator which includes a non-linear distribution function term f . The immersed boundary method uses independent grids to discretize the fluid and structure separately. The fluid is discretized by a set of Eulerian points, which are the fixed, regular Cartesian lattice points, while the boundary of the structure immersed in the fluid is discretized by a set of markers, which are called Lagrangian points [2]. The predicted velocity u* simulated by the fluid in the absence of the structure is interpolated onto the embedded geometry of the obstacle, G, discretized using Lagrangian marker points with coordinates Xk : U∗ Xk , t n = u∗

(2)

The nonlinear dynamic finite element method is introduced as the structural solver to obtain the dynamic response of flexible flaps, the kinetic equation of flexible flap can be written as:

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0.45

Fig. 1 Averaged lift coefficient over six oscillations with period T

⎯Cl-Present ⎯Cl-Falagkaris et al. ⎯Cl-Johnson and Tezduyar

0.44

⎯Cl

0.43

0.42

0.41

0.4

0.39 0.0

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T

0.6

¨ ˙ MX(t) + CX(t) + Fint (X) − Fext (t) = 0

0.8

1.0

(3)

˙ and X ¨ represent the flap displacement, velocity and acceleration, respecwhere X, X tively. M and C are the mass and damping matrices of flap. Fint represents the internal force of flap, and it is a nonlinear function of the displacement X. Fext (t) represents the external forces such as the fluid force and gravity acting on the flap.

3 Results and Discussion 3.1 Flow Over a Naca0012 Airfoil The first case studies the unsteady flow around a Naca0012 airfoil at Re = 1000 and AoA = 10°, which has been investigated extensively in the literature. The Strouhal number St is defined as St = f D c/U ∞ , where f D is the shedding frequency, c is the chord length of airfoil, U ∞ is the free stream velocity. In the present case, the computed Strouhal number is 0.8417, which is about 2.2% smaller than the value of 0.861 reported by Falagkaris et al. [3] and the value of 0.86 reported by Johnson and Tezduyar [4]. The time-averaged lift coefficient over the last six periods is compared with the reported values in [3, 4] in Fig. 1. It can be seen that the present results agree well with these two references.

3.2 Flow Over a Naca0012 Airfoil with a Rigid Flap Figure 2 shows a Naca0012 airfoil with one rigid flap clamped on the suction side. Its length is L, the deployment angle between flap and airfoil upper surface is θ, and the distance from the leading edge to the fixed end of flap measured along the chord c is P. Here we define two dimensionless parameters: the length ratio L* = L/c and the position ratio P* = P/c. As a preliminary calculation, the deployment angle θ is fixed at 90°

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Fig. 2 Configuration of a Naca0012 at AoA = 10° with a flap attached on its upper surface

L

c

θ

P

Figure 3a, b show the mean lift coefficients and mean drag coefficients of Naca0012 airfoil together with rigid flap in different test cases, respectively. For comparison, the results of the clean airfoil case are also included. From these two figures, it can be seen that for a rigid flap of a certain length, the closer it is to the trailing edge of airfoil, the higher the overall mean lift coefficient and the smaller the overall mean drag coefficient. When the length of flap increases, if the flap is not too close to the trailing edge (P* = 0.5, 0.6), the overall mean lift coefficient decreases and the overall mean drag coefficient increases. If the flap is close to the trailing edge (P* = 0.7, 0.8, 0.9), the overall mean lift coefficient increases first and then decreases. Analogously, the overall mean drag coefficient decreases first and then increases. When L* = 0.1 and P* = 0.9, the airfoil with a rigid flap achieves its best aerodynamic performance (highest lift coefficient and smallest drag coefficient), and its performance is better than the clean airfoil. Focusing on this case, we continue to investigate the effects of deployment angles. It can be seen from Fig. 4 that when the deployment angle θ increases, the mean lift coefficient increases and mean drag coefficient decreases. At θ = 90°, the airfoil and flap achieve maximum mean lift coefficient and minimum mean drag coefficient. 0.5

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Fig. 4 The mean lift and drag coefficients of airfoil together with rigid flap in different cases

3.3 Flow Over a Naca0012 Airfoil with a Flexible Flap Finally, focusing on the case L* = 0.1, P* = 0.9, θ = 90°, we replace the rigid flap with a flexible flap and change its material properties. The root of flexible flap is clamped on airfoil surface in order to keep the deployment angle θ constant. Here we define two dimensionless parameters to describe the material properties of flexible flap: the bending coefficient K = EI/ (ρ f U ∞ 2 L 3 ) and the mass ratio M* = ρ s h/ρ f L, where E is the Young’s modulus of flap, I is its second moment of area, h is flap thickness, ρ s is flap density and ρ f is fluid density chosen as ρ f = 1.225 kg/m3 . Figure 5a, b show the mean lift coefficients and mean drag coefficients of Naca0012 airfoil together with flexible flap in different test cases, respectively. From these two figures, it can be seen when the flap bending coefficient K is very small, the airfoil with lighter flap (M* is smaller) has higher overall mean lift coefficient, for the flap with M* = 5, the overall mean lift coefficient is higher than that in rigid flap case, while for the flap with M* = 50, the overall mean lift coefficient is much smaller than that in rigid flap case, even smaller than that in clean airfoil case. When K = 0.08 and M* = 15, the airfoil with a flexible flap achieves its optimal aerodynamic performance. 0.17

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4 Conclusions We numerically investigate the effects of a flap on the aerodynamic performance of a Naca0012 airfoil. For rigid flap, the results show that when the flap has length ratio L* = 0.1, position ratio P* = 0.9 and deployment angle θ = 90°, the airfoil with flap achieves optimal aerodynamic performance. For flexible flap, the results show that when the flap has bending coefficient K = 0.08 and mass ratio M* = 15, the airfoil with flap achieves optimal aerodynamic performance. Compared to the clean airfoil case, the mean lift coefficient of this optimal case is improved about 13.51%, and the mean drag coefficient is decreased about 3.67%. Acknowledgements The present work was partially supported by the Fundamental Research Funds for the Central Universities of Northwestern Polytechnical University, NSFC Foundation (Grant No.1167225, No.11511130053) and the Natural Science Foundation of Shaanxi Provence (No.2016JM1007).

References 1. Carruthers AC, Thomas ALR, Taylor GK (2007) Automatic aeroelastic devices in the wings of a Steppe Eagle Aquila nipalensis. J Exp Biol 210(23):4136–4149 2. Peskin CS (1972) Flow patterns around heart valves: A numerical method. J Comput Phys 10(2):252–271 3. Falagkaris EJ, Ingram DM, Viola IM, Markakis K (2017) PROTEUS: a coupled iterative forcecorrection immersed-boundary multi-domain cascaded lattice Boltzmann solver. Comput Math Appl 74(10):2348–2368 4. Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119(1):73–94

Design of Blown Flap Configurations Based on a Multi-element Airfoil Yuhui Yin, Yufei Zhang, and Haixin Chen

Abstract In this study, a new configuration of an internally blown flap based on a multi-element airfoil for the high lift device of an amphibious aircraft is proposed and discussed. To explore the potential of current configuration, a differential evolution algorithm is employed. The optimization results show that current internally blown flap can gain the same lift enhancement with less energy consumption. The stall performance is also enhanced compared with traditional simple hinge blown flaps. The result of a parametric analysis of design parameters proves the robustness of the configuration which contributes to the employment of dual objective optimization. After the optimization design, the response to jet momentum coefficients is analyzed and the result shows that there exist two critical momentum coefficients that separate the lift vs. jet momentum curve into three segments and each segment corresponds to different flow separation phenomena. The circulation control rule for a multi-element airfoil with inserted energy if different and more complicated. Keywords Internally blown flap · Multi-element airfoil · Aerodynamic design · Coanda effect

1 Introduction Amphibians, as an important type of STOL airplanes which can take off and land on both land and water, have several specific demands for high-lift devices [1]. When working on water, to fulfill the requirements of wave resistance and structural strength, the lift coefficient should be quite large and the working angle of attack is smaller than ordinary planes, which leads to the application of powered lift systems. Specifically, internally blown systems have high efficiency on lift increasing and are often adopted. The internal flow system sets internal ducts and nozzles in proper positions to eject high-speed air onto flaps or trailing edges to augment the lift. The requisite Y. Yin · Y. Zhang (B) · H. Chen Tsinghua University, 100084 Beijing, People’s Republic of China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_21

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lift coefficient can be achieved at a smaller angle of attack, making it suitable for amphibious aircraft or other STOL aircraft. The US-2 amphibious aircraft, as an example, has practically applied internally blown flaps. The jet slots are set near the leading edges of flaps. In addition, the slipstream of propellers also contributes to high-capacity lift. As a result, the maximum lift coefficient of the aircraft can reach 7.0, which is almost twice as much as the Boeing 737 high-lift devices [2]. Inspired by existing configurations and results, an internally blown flap based on a multi-element airfoil is proposed and discussed in the present study. There are three motivations for this application. (1) Compared with a simple hinge flap, a multielement airfoil enables a larger design space. The positions and deflection angles of slats, flaps and spoilers can all be altered, which helps to seek configurations with larger lifts and better stall performance with less jet energy consumption. (2) Multielement airfoils have been widely used as high-lift devices in most transport aircraft. Designs based on multi-element airfoils can be easily applied to former aircraft with less cost. (3) Based on multi-element airfoils, with carefully designed rotating axes and sliding rails, high-lift devices could have two configurations for both powered and unpowered conditions, which can help amphibious aircraft save fuel when taking off or landing on airfield runway. The present study is to explore the potential of an internally blown flap based on a multi-element airfoil. Maximum lift coefficients and stall angles of five different jet momentum coefficients are evaluated, and the flow features are analyzed. Parametric analysis using a one-factor-at-a-time approach is conducted for the five optimized individuals to test the affecting factors of these configurations. The variation of the jet momentum coefficient is further studied, and the result reveals a novel pattern of flow separation control at a large jet momentum coefficient.

2 Aerodynamic Optimization of a Blown Flap Based on a Three-Element Airfoil An aerodynamic optimization consists of reliable evaluation of the performance and effective optimizing algorithm. A open source Reynolds-averaged Navier–Stokes solver, CFL3D version 6.7 [3], is used to calculate the flow field. The Spalart– Allmaras turbulence model with curvature correction is adopted. Two public cases, GTRI dual radius CC airfoil and three-element airfoil 30P30N, are computed for the validation. The results illustrate that the present turbulence model, and flow solver have the validity to assess the force coefficients of airfoils with internal jet flow and high lift devices. The following study takes the same turbulence model and solver settings. To measure the strength of inserted jet flow, two coefficients are adopted. The jet momentum coefficient is defined by Eq. (1).

Design of Blown Flap Configurations Based …

Cμ =

135

m˙ j V j 1 ρ V2 S 2 ∞ ∞ ref

(1)

where m˙ j is the jet mass flow rate, V j is the jet velocity, ρ∞ and V∞ are the free stream density and velocity, and Sr e f is the reference area. Besides the momentum, the energy consumption is also important. Assuming the process to be a expansion from a high-pressure cavity, the power coefficient is defined by Eq. (2) [4]. Pc, j

m˙ j c p T01 = ηj

P02 P01

(γ −1)/γ

3 − 1 / 0.5ρ∞ V∞ Sr e f

(2)

where cp is the constant-pressure specific heat, T 01 is the free stream total temperature, ηj is the pump efficiency assumed to be 0.85, P01 is the free stream total pressure, and P02 is the total pressure at the outlet of the high-pressure cavity. After the definition of measurement, an internally blown flap based on a threeelement airfoil in the present study is demonstrated in detail. The sketch of the blown flap is shown in Fig. 1. The flap is used as a Coanda surface. The jet nozzle can be located at the trailing edge of the main wing right under the spoiler and moves simultaneously when the spoiler rotates. The flexible nozzle is connected with a high-pressure cavity located in the main wing. Figure 1b shows a possible structure, a retractable nozzle which can retract during the cruising stage. The baseline airfoil used in this study is 30P30N [5]. The height of the slot is 0.002C. One simplification used in the following studies is that the inner flow of the nozzle is neglected. The inlet boundary is set at the nozzle surface. This simplification is acceptable for lift computations compared with airfoils having a jet plenum chamber.

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(a) Parameters near the slat

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Fig. 2 Sketch of the seven optimization parameters

Fig. 3 Grid sketch of 30P30N

2.1 Optimization Settings In order to ensure the performance at low angles, dual objective optimizations are performed. The lift coefficients at α = 0° and α = 16° are simultaneously optimized for the maximum. To assess the lift increasing effect at different injected energy, five optimizations are set at momentum coefficients ranging from 0.025 to 0.125. Seven optimization variables including the deflection of the spoiler are optimized, these variables are displayed in Fig. 2. The grid domain size is [−150C, 150C] in x direction and [−120C, 120C] in y direction. The total grid cell number is 124 thousands. The grid sketch is shown in Fig. 3.

2.2 Optimization Results After the optimization converged to a static Pareto front, the configuration which has the same “marginal effect” of lift coefficient at α = 16° and at α = 0° is selected. Specifically, the individual that is located at the tangent point of the Pareto front and a straight line with a slope of −1.0. The force coefficients of five optimizations are

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Table 1 Optimization results for different momentum coefficients 0.025

0.050

0.075

0.100

CL at 0°

Cμ

Original 2.18

3.23

4.82

5.65

6.33

6.93

CD at 0°

0.048

0.098

0.080

0.090

0.11

0.13 53.31

L/D

0.125

45.42

32.96

60.25

62.78

57.55

CL at 16°

3.89

4.99

5.80

6.44

6.95

7.31

CD at 16°

0.081

0.14

0.15

0.16

0.19

0.21

35.64

38.67

40.25

36.58

34.81

L/D

48.02

7 7

6 CL

CL

6

5

Rigid droop-nose [5] Flexible droop-nose [5] Current config. 0.04

0.06 C

(a) CL vs. Cμ

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0.2 Pc,j

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Fig. 4 Comparison of the present configuration with the Coanda flaps [6]

shown in Table 1. The results indicate the feasibility of current configurations. The comparison of the present configuration with the traditional Coanda flaps [6] is shown in Fig. 3. The variation of C L with C μ is shown in Fig. 3a. The present configuration attains a higher lift at a small jet momentum coefficient, but then the Coanda flaps take the lead. The Coanda flaps have narrower slots, which leads to higher jet speed and higher energy consumption. Consequently, the present configuration has a significant advantage if considering the performance at a certain jet power coefficient, as shown in Fig. 3b. The result indicates that the present configuration is valid and suitable to satisfy the demand of the STOL airplane with less energy consumption. Mach number contours and streamlines of typical configurations at α = 16° optimized different C μ are shown in Fig. 4. Large curvature of streamlines and pneumatic flap phenomena can be observed and there is no flow separation because of the Coanda effect Fig. 5.

3 Conclusion An internal blown flap based on a three-element airfoil is proposed and discussed. The concept is aimed at the development of STOL aircraft such as amphibious

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(b) Optimized at Cμ=0.075 (c) Optimized at Cμ=0.125

Fig. 5 Mach number contours and streamlines for three optimal individuals

aircraft that require a high lift coefficient. Several dual objective optimizations are conducted to explore the potential of the configuration at different injected energies. The objectives are to maximize the lift coefficients at two different angles of attack. Five optimal solutions are obtained after the optimizations. The optimal solutions differ from the original three-element airfoil in many aspects. On the geometrical aspect, the slats of the optimal solutions are far from the main wing, and the flaps are close; conversely, the flap can deflect to a very large angle, and the spoiler deflection plays an important role in increasing lift and robustness. Compared with previous blown flap configurations, the optimal configuration reaches the same lift with less energy consumption. The advantage is more significant at small C μ . In addition, the jet slot is wider, which is beneficial for structural strength. The results above indicate validity and high efficiency.

References 1. Dathe I, Deleo M (1989) Hydrodynamic characteristics of seaplanes as affected by hull shape parameters. AIAA paper 1989-1540 2. Obert E (2009) Aerodynamic design of transport aircraft, Delft University, Part 5.2 3. “CFL3D Version 6 Home Page”, https://cfl3d.larc.nasa.gov/ 4. Xu H, Qiao C, Yang H (2018) Active circulation control on the blunt trailing edge wind turbine airfoil. AIAA J 56(2):554–570 5. Spaid F, Lynch F (1996) High Reynolds number, multi-element airfoil flowfield measurements. AIAA Paper 1996-682 6. Burnazzi M, Radespiel R (2014) Design of a droopnose configuration for a coanda active flap application. J Aircraft 51(5):1567–1579

Added Masses of Cylinders of Different Shapes Guanghao Chen, Md. Mahbub Alam, and Yu Zhou

Abstract This paper presents an experimental investigation on added masses of cylinders of different shapes including circular, square and rectangular cross sections in water and paraffin oil. The dependence of added mass on cylinder attack angle θ (= 0°–90°) is also paid attention to. The added mass is estimated from the shift of the oscillation frequencies of the cylinder in water or paraffin oil from that in the air (vacuum). It is found that added mass is dependent on both cylinder shape and orientation but is independent of the fluid medium. For circular cylinder, the added mass is equal to the mass of fluid displaced by the cylinder. Yet it declines from θ = 0° to 45° for the square cylinder and grows monotonically from θ = 0° to 90° for the rectangular cylinder. The rectangular cylinder has a smaller and greater added mass than the circular cylinder for θ ≤ 15° and θ > 15°, respectively. Also, the square cylinder undergoes large added mass compared to the circular cylinder for all θ values. Keywords Added mass · Square cylinder · Circular cylinder · Rectangular cylinder

1 Introduction Added mass of column structures is a crucial parameter in the study of fluid–structureinteractions. Brennen [1] deduced that the added mass of the circular cylinder in potential flows is equal to the mass of the fluid displaced by the cylinder. The added mass coefficient, defined by the ratio of added mass and displaced fluid, can be modeled as the mass of some volume of fluid moving with the object. Vikestad et al. [2] performed an experiment with a lightly damped elastically mounted rigid G. Chen · Md. M. Alam (B) · Y. Zhou Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology, Shenzhen, China e-mail: [email protected] Digital Engineering Laboratory of Offshore Equipment, Shenzhen, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_22

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Fig. 1 Experimental setup and cylinder cross-sections

cylinder subjected to a constant flow with and without external disturbance. They found that the added mass coefficient for circular cylinder is 1.04. The external harmonic disturbance has an influence, albeit weak, on the added mass. One can easily perceive that the flow disturbance by a towing square cylinder is higher than that by a circular cylinder. Does it not mean the added mass coefficient is dependent on the body shape? The added mass coefficient for square cylinder in potential flow estimated to be approximately 1.188 [3, 4]. Is it independent of its moving orientations? Another example, a flat plate with its width parallel to the flow will have much less disturbance than the plate with its width normal to the flow. Again, are the added mass coefficients are the same for both orientations? What about the added mass for a cylinder in different fluid properties (such as water and chemical oil)? The objective of the work is to examine whether the added mass coefficient is dependent on the cylinder shape and orientation and fluid properties. Circular, square and rectangular cylinders are considered with the attack angle (θ ) varying from 0° and 90° (Fig. 1). Experiments were conducted in two fluid mediums, water and paraffin oil which have distinct densities and viscosities.

2 Experimental Details The experiment is conducted in a fluid tank of 1.2 × 0.6 × 0.5 m in dimensions, with 0.5-m dimension being the height. A cylinder is vertically mounted on two parallel rails with air bearing, so that the cylinder can feely slide along the rails without tilting in x- and y-direction, guaranteeing its movement in the x-direction only (Fig. 1). In

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order to make the cylinder an oscillator, two springs are used, so that the cylinder can oscillate freely when an initial displacement is given. The cylinder cross-sections considered are shown in Fig. 1. The cylinders, each 550 mm in length, were hollow, made of acrylic, with a 2 mm wall thickness. The characteristic dimensions of the three cylinders were the same, D = 40 mm. The smaller side (thickness) of the rectangular cylinder was 10 mm. The actual natural frequency f 0 of a cylinder system is measured from the free vibration, generated by giving an initial displacement, of the cylinder in air. The response of the cylinder was measured using a laser vibrometer with a resolution of 0.05 µm. When the cylinder is partially submerged in a fluid, the cylinder will have a new natural frequency f w , which again can be obtained from the free vibration of the cylinder. The added mass ma is estimated from the change in the natural frequencies as m a = ( f 0 / f w )2 − 1 m

(1)

where m is the cylinder mass. The added mass is normalized as m a∗ = m a /m f

(2)

where mf is mass of fluid displaced by the cylinder.

3 Results and Discussion Figure 2 illustrates normalized frequency ratio f * (= f w /f 0 ) as a function of θ for the three cylinders in water (Fig. 2a) and oil (Fig. 2b). For the circular cylinder, f * = 0.921 in water and 0.937 in oil, naturally independent of θ. For the square cylinder, the f * grows as θ increases from 0° to 45° and declines for a further increase in θ.

Fig. 2 Dependence of f* on θ for different cylinders in a water and b paraffin oil. The cylinder cross-sections represent orientations of the cylinders

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The f * distribution is symmetric about θ = 45°, as expected. On the other hand, for the rectangular cylinder, f * being the largest (= 0.989, in water) at θ = 0° decreases to 0.878 (in water) at θ = 90°. That is, the rectangular cylinder with the longest dimension along the oscillation yields a largest f * , and that with the smallest dimension corresponds to the smallest f * . Though qualitatively similar observations are made for both water and oil, the magnitude of f * is larger in oil than in water for the same configurations. Applying Eqs. (1) and (2), m a∗ was calculated and the results are presented in Fig. 3. Interestingly, though f * differs between water and oil (Fig. 2), m a∗ does not differ much between two fluid mediums. The m a∗ for the circular cylinder is 1.045 in water and 1.038 in oil. For the square cylinder, m a∗ = 1.52 at θ = 0°, higher than that for the circular cylinder. It declining with θ reaches a minimum of 1.20, then bounces back to its previous value with a further increase in θ to 90°. The m a∗ for the rectangular cylinder behaves differently, increasing from m a∗ = 0.55 to 4.90 (in water) when θ is varied from 0° to 90°. Overall, it can thus be concluded that m a∗ is sensitive to cylinder cross-section and cylinder orientation but not to fluid properties. The magnitudes of added mass for square and rectangular cylinders are not equal to their displaced fluid mass anymore.

Fig. 3 m* a versus different θ for all test cylinders. The cylinder cross-sections represent orientations of the cylinders

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4 Conclusions An experimental investigation is conducted on the added masses of circular, square and rectangular cylinders oscillating in water and paraffin oil. The light is shed on the dependence of added mass on the cylinder orientation θ varied from 0° to 90°. The fluid medium has no influence on the added mass. m a∗ is highly sensitive to θ for square and rectangular cylinders. For square cylinder, the m a∗ declines from 1.52 at θ = 0° to a minimum of 1.20 at θ = 45°, followed by an increase upto θ = 90°. The m a∗ for rectangular cylinder however monotonically increases from 0.55 to 4.90 when θ is increased 0° from to 90°. The m a∗ is smaller for the rectangular cylinder at θ ≤ 15° than for the circular cylinder while larger for θ > 15°. That for the square cylinder is large at all 0° compared to the circular cylinder case.

References 1. Brennen CE (1982) A review of added mass and fluid inertial forces. Report CR82.010, Naval Civil Engineering Laboratory, Port Hueneme, California 2. Vikestad K, Vandiver JK, Larsen CM (2000) Added mass and oscillation frequency for a circular cylinder subjected to vortex-induced vibrations and external disturbance. J Fluids Struct 14:1071–1088 3. Kyeong HJ, Myung JJ (2017) Added mass estimation of square sections coupled with a liquid using finite element method. Nuclear Eng Technol 49:234–244 4. Blevins RD (1979) Formulas for natural frequency and mode shapes. Van Nostrand Reinhold, New York

Recognition Location Method of Sound Source Based on Rotating Microphones Xie Zheng, Xunnian Wang, Jun Zhang, Kun Zhao, Zhengwu Chen, Yong Wang, and Ben Huang

Abstract Microphone arrays have been widely used in sound source localization in recent decades. Traditional static microphone arrays need to use a large number of microphones, which leads to high cost. In order to solve this problem, this paper introduces a method of sound source localization based on rotating microphones. Compared with the static microphone array, the method proposed in this work can accurately locate sound source with a small number of rotating microphones. For validation, the main theories and methods are introduced. Accordingly, numerical simulations were conducted to show the characteristics of source location results. At last, tests were conducted in an anechoic chamber and the good performance of this method was validated with the experimental data. Theoretical analysis, simulations and experimental results show that by rotating the microphone array, it can accurately locate the sound source with a small number of microphones. Keywords Sound source localization · Rotating microphone

1 Introduction Sound source localization based on microphone array using beamforming algorithm [1–3] is a powerful analysis tool for analyzing the mechanism of sound production, which can show the distribution of Sound Pressure Level(SPL) in detail and provide guidance for noise reduction.

X. Zheng (B) · J. Zhang · K. Zhao · Z. Chen · Y. Wang · B. Huang Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, People’s Republic of China e-mail: [email protected] X. Zheng · X. Wang State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, People’s Republic of China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_23

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The conventional sound source localization approach using a static array requires a large number of microphones to increase the resolution, which can be an obstacle in the practical engineering. This paper introduces a method for source location based on a rotating microphone array [4]. Compared with the conventional approach with the same number of microphones, the new method with the rotating array is expected to more accurately locate the sound sources. For validation, this paper begins with a theoretical analysis to establish the corresponding data process algorithm. Accordingly, numerical simulation was conducted to show the characteristics of source location results. At last, tests were conducted in an anechoic chamber and the good performance of this method was validated with the experimental data.

2 Theory Figure 1 is a schematic that shows a rotating microphone X m = (Rm cos(m + m T ), Rm sin(m + m T ), 0), a sound source X 0 = (R0 cos 0 , R0 sin 0 , H0 ) and a scan point X = (R0 cos 0 + R cos , R0 sin 0 + R sin , H0 ). Assume the sound source is a single frequency signal, which can be written as: pe (τe ) = p0 exp(iω0 τe ). The sound signal propagation from the sound source to the rotating microphone is the same as that of a stationary microphone, so, the reconstructed signal of the scan point is: P(X, τ ) = p0 exp(iω0 τ )

exp(iω0 L m /c) L m , exp(iω0 L m /c) L m

(1)

in which: L m = |X 0 − X m | , L m = |X. − X m | .

Fig. 1 Schematic of a rotating microphone

(2)

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Fourier transform of Eq. (1): p0 F(X, ω) = lim l→+∞ 2l

l −l

exp(iω0 τ ) exp(iω0 L m /c) L m dτ, exp(iωτ ) exp(iω0 L m /c) L m

(3)

when the following conditions are satisfied: R0 Rm m Rm R 2 1, c R + Rm2 + H02 0 R02 + Rm2 + H02

R02

Rm R0 1 1 R 2 + 2R R0 , 1, 2 2 2 2 R02 + Rm2 + H02 + Rm + H0

(4)

(5)

then: ω Rm R F(X, ω0 ) ≈ p0 · J0 ( ), 2 2 2 c R0 + Rm + H0 + R 2 + 2R R0 cos( − 0 )

(6)

It can be found from Eq. (6) that when R = 0, the scan point coincides with the sound source point, and the amplitude of F(X, ω0 ) is equal to the amplitude of the sound source. When the scan point deviates from the sound source position, R = 0, the amplitude of F(X, ω0 ) is less than p0 . By processing all the scan points, the sound source can be accurately identified and located.

3 Numerical Simulation Figures 2a, 3 and 4a are the initial positions of different rotating microphone arrays and the sound source. Figures 2b, 3 and 4b are the corresponding sound sources location maps of different rotating arrays, respectively. The simulation results show that: a rotating microphone can locate the sound sources; at the same rotation radius, a microphone work equivalent to multiple microphones; the performance can be improved by adding some microphones at certain rotation radii.

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(a)

Rotating microphone

(b)

Source location

Fig. 2 1 Microphone

(a)

Rotating microphones

(b) Fig. 3 3 Microphones

Source location

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Fig. 4 3 Rings

Fig. 5 Rotating microphone array

4 Experimental Validation In order to validate the theoretical analysis and simulation results, a rotating microphone array device (Figs. 5 and 6) was built. Two speakers were used as sound sources in the experiments, the coordinates of sound sources were (0.28, −0.05, 1.1 m) and (−0.1, −0.05, 1.1 m), The distance between the plane of sound sources and the rotation plane of microphones was

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Fig. 6 Microphone array

(a) Microphone 3

(b) Microphones 1, 2, 3

(c) Microphones 3, 6, 9, 12

(d) Microphones 1-12

Fig. 7 Results of real sound source localization at 3996 Hz

1.1 m. The sound frequencies were selected at 3996 and 5996, respectively. The rotation speed of the microphone array frame was 4 turns per second. The sound source location were measured using different rotating microphones, and the results of Figs. 7 and 8 were obtained. The experimental results are consistent with the results of numerical simulation, and the result show that a rotating microphone can locate two sound sources at the same time.

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(a) Microphone 3

(b) Microphones 1, 2, 3

(c) Microphones 3, 6, 9, 12

(d) Microphones 1-12

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Fig. 8 Results of real sound source localization at 5996 Hz

5 Conclusion Rotating microphone array is a innovative approach for sound source localization, first proposed by Cigada [4], which is an improved measurement method based on the traditional beamforming method. In this paper, the signal processing of a single rotating microphone is established by theoretical analysis. Furthermore, simulation and experimental studies were carried out, and the results show that: 1. The sound source can be accurately located by a rotating microphone array, even if the array has only one rotating microphone. 2. Compared with Cigada’s [4] method and other beamforming methods, since there is no delay and sum of signals in the process of a single rotating microphone signal, the method in this work is essentially different from the beamforming algorithm. In other words, sound source localization using a single rotating microphone is a novel approach, which can significantly reduce the number of microphones in sound source localization. 3. Increasing microphones at the same rotation radius of the rotating microphone array hardly improve the array performance. However, if adding microphones at specific rotation radii, the maximum side lobe level of the array can be significantly increased.

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References 1. Johnson DH, Dudgeon DE (1993) Array signal processing: concepts and techniques 2. Dougherty RP (2002) Beamforming in acoustic testing: aeroacoustic measurements. Springer, Berlin 3. Michel U (2006) History of acoustic beamforming. In: Berlin beamforming conferences, Berlin, p 17 4. Cigada A, Lurati M, Ripamonti F, Vanali M (2008) Moving microphone arrays to reduce spatial aliasing in the beamforming technique: theoretical background and numerical investigation. J Acoust Soc Am 124:3648–3658 Dec.

Performance Optimization of Microphone Array Beamforming Based on Multi-circular Ring Microphone Arrays Combination Xunnian Wang, Xie Zheng, Jun Zhang, Kun Zhao, Zhengwu Chen, and Ben Huang Abstract In this paper, a fast method of microphone array optimization is proposed. Firstly, the theoretical analysis of a single circular ring microphone array was carried out, and the beamforming function was obtained, which can be expressed by the Bessel function. Then, via analysing the properties of Bessel function, the sidelobes distribution of the circular ring array beamforming was achieved, the resolution and the dynamic range were determined. Accordingly, based on the combination of several circular ring arrays, the sidelobes of the large array were reduced, and the beamforming optimization was realized. Finally, proposed method was validated by numerical simulation, and the numerical simulations are consistent with theoretical analysis. Keywords Microphone array · Optimization · Bessel function

1 Introduction Microphone array beamforming, as a powerful sound source imaging tool, is widely used to locate the noise source and analyze the noise generation mechanism [1–3]. Generally, two main parameters for evaluating array performance, i.e. the beam width and the maximum side lobe level [2, 4], are determined primarily by the microphone layout and the number of microphones.

X. Wang · X. Zheng (B) State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang 621000, People’s Republic of China e-mail: [email protected] X. Wang e-mail: [email protected] X. Zheng · J. Zhang · K. Zhao · Z. Chen · B. Huang Key Laboratory of Aerodynamic Noise Control, China Aerodynamics Research and Development Center, Mianyang 621000, People’s Republic of China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_24

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In particular, a good microphone array layout can significantly improve the array performance. In order to optimize the array layout, many different array patterns have been proposed. In the early days, the rectangular, the circular ring, the X-shape and the spiral array patterns [1, 2, 5] were proposed. Then the multi-armed spiral array pattern [2, 6] based on parametric distribution was developed. Recently, Sarradj [4, 7] developed a parametric optimization method based on the point spread function (PSF) of a circular continuous aperture. In this paper, based on the beamforming of a circular ring array, an array optimization method of multiple circular-ring-arrays combination is proposed.

2 Theory Figure 1 shows the schematic of a sound source x0 , a scan point x, and a circular ring microphone array. Microphones are evenly distributed on the X-Y plane. Assume the sound source is a single frequency signal, which can be expressed as: σ(t) = p0 exp(iωt). The beamforming of the scan point x can be written as: p(x, τ ) = p0 exp(iωτ ) ·

Fig. 1 Circular ring microphone array

Fig. 2 Circular ring continuous array

mic 1 exp(iωlm /c) lm · mic m=1 exp(iωlm /c) lm

(1)

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where lm and lm are the distances from xm to x0 and x, respectively. When mic approaches to infinity, as shown in Fig. 2, Eq. (1) can be described as: 1 p(x, τ ) = p0 exp(iωτ ) · 2π

2π 0

exp(iωlθ /c) lθ · dθ exp(iωlθ /c) lθ

(2)

If h 20 is much greater than r02 , rm2 , r 2 , Eq. (2) can be simplified as: ⎞

⎛ ωrrm

⎠ p(x, τ ) = p0 exp(iωτ )J0 ⎝ 2 2 2 2 c r0 + rm + r + h 0 + 2rr0 cos(ϕ − ϕ0 )

(3)

where J0 (·) is the zero-order Bessel function. It should be noted that although the circular ring array is assumed to have an infinite number of microphones, in fact, when the number of microphones meets the following equation, increasing the number of microphones does not change the result. 1 ωrrm mic > 3.5 c r02 + rm2 + r 2 + h 20 + 2rr0 cos(ϕ − ϕ0 ) π

(4)

For a large array consisting of two circular ring arrays, the sound pressure level (SPL) of the beamforming results can be written as: S P L(X ) = 20 log 10|1/2 · [J0 (X ) + J0 (a X )]|

(5)

ωrrm1 X= 2 c r02 + rm1 + r 2 + h 20 + 2rr0 cos(ϕ − ϕ0 )

(6)

2 r02 + rm1 + r 2 + h 20 + 2rr0 cos(ϕ − ϕ0 ) rm2 a= = const 2 r02 + rm2 + r 2 + h 20 + 2rr0 cos(ϕ − ϕ0 ) rm1

(7)

where the parameter X is proportional to the variable r , and a is a constant. As illustrated in Fig. 3, the maximum side lobe levels of single circular ring arrays with different radii are both equal to 7.899 dB. After testing the parameter a, the maximum side lobe level of the large array reaches its peak value, which is shown in Fig. 4. Further research results indicate that the performance of the large array can be improved by adding a series of circular rings with appropriate radii. I.e., the PSF of a large array composed of N circular rings can be written as:

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Fig. 3 Single circular ring

Fig. 4 Two circular rings

W Nα (X ) =

N 1 J0 (α j X ) N j=1

(8)

where α j is the parameter obtained from the radius of the j-th ring, selecting a series of suitable α j , then the large array can be optimized. For example, the PSF can be expressed as: N 1 β J0 (β j−1 X ) (9) W N (X ) = N j=1 As shown in Fig. 5a–c, the SPL outputs of the arrays composed with 3, 4 and 5 circular rings are optimized, respectively. Another way to optimize the large array composed of multiple circular ring arrays is to use the following form of PSF functions. For example, for 2, 4, 8, 16 circular rings:

Performance Optimization of Microphone Array Beamforming . . .

(a) N = 3, β = 0.653

(b) N = 4, β = 0.645

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(c) N = 5, β = 0.695

Fig. 5 Array optimization results obtained from Eq. (9)

(a) Four circular rings

(b) Eight circular rings

(c) Sixteen circular rings

Fig. 6 Array optimization results obtained from Eqs. (11)–(13)

W2 (X ) = 1/2 · [J0 (X ) + J0 (a X )], 0 < a < 1

(10)

W4 (X ) = 1/2 · [W2 (X ) + W2 (bX )], 0 < b < 1

(11)

W8 (X ) = 1/2 · [W4 (X ) + W4 (cX )], 0 < c < 1

(12)

W16 (X ) = 1/2 · [W8 (X ) + W8 (d X )], 0 < d < 1

(13)

When a = 0.591, b = 0.54, c = 0.365, d = 0.4525, the optimal combinations of 2, 4, 8, 16 circular rings are obtained, which are shown in Figs. 4 and 6. It can been seen from Figs. 3–6 that increasing the number of circular rings with specific radii can improve the dynamic range of the entire array, and the main lobe width is simultaneously widened. One way to reduce the width of the main lobe is to increase larger radii of circular rings, i.e. select the parameters a = 1/0.591 = 1.692, b = 1/0.54 = 1.852, c = 1/0.365 = 2.740, d = 1/0.4525 = 2.210. It should be noted that the above array optimization method is an optimization for variable X ∈ (0, ∞). If the scan surface is limited to a certain range, i.e., X ∈ (0, X 0 ), then there are more excellent combinations of circular ring arrays.

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c (a) 23 microphones (b) 60 microphones (c) 60 microphones (d) 60 microphones Fig. 7 Schematic diagram of array and sound source

(a) 23 microphones

(b) 60 microphones

(c) 60 microphones

(d) 60 microphones

Fig. 8 PSF diagram of different arrays

3 Simulation In order to validate the effectiveness of the method, the simulation were performed by four different microphone arrays. The relative positions of the sound source and the microphones are shown in Fig. 7, the number of microphones in Fig. 7 are 23, 60, 60, 60, respectively. The frequency of the sound source is 2,000 Hz. The beamforming results are shown in Fig. 8. The contrast between Fig. 8a, b show that when the number of microphones in a circular ring array reaches a certain value, the PSF map of the circular ring array remains the same. √ 7 2000 · 12 + 12 · 1 = 22.01 mic > √ 2 340 02 + 1 + 2 + 4 + 0 Figure 8b–d indicate that the dynamic range of microphone array can be increased obviously by increasing the number of the circular rings in the array.

4 Conclusion In this paper, a new method of array optimization is proposed and the effectiveness of the method is confirmed by simulations. The results show that:

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1. For a single circular ring array, when the number of microphones reaches a certain value, adding microphones can not improve array performance, 2. Increasing the number of circular ring arrays with specific radii can improve the dynamic range of the entire array.

References 1. Johnson DH, Dudgeon DE (1993) Array signal processing: concepts and techniques 2. Underbrink J (2002) Aeroacoustic phased array testing in low speed wind tunnels. In: Mueller T (ed) Beamforming In Aeroacoustic Measurements. Springer, Heidelberg, Berlin 3. Michel U (2006) History of acoustic beamforming. In: Berlin beamforming conferences, Berlin, p 17 4. Sarradj E (2016) A generic approach to synthesize optimal array microphone arrangements. In: Berlin beamforming conferences, Berlin, p 12 5. Nordborg A, Wedemann J, Willenbrinlk L (2000) Optimum array array microphone configuration. In: Inter-noise 2000 6. Hald J, Christensen JJ (2002) A class of optimal broadband phased array geometries designed for easy construction. In: Inter-noise 2002 7. Sarradj E (2015) Optimal planar microphone array arrangements. Nurnberg, p 4

The Aeroacoustic Effect of Different Inter-Spaced Self-oscillating Passive Trailing Edge Flaplets Edward Talboys, Thomas F. Geyer, Florian Prüfer, and Christoph Brücker

Abstract An aeroacoustic investigating looking into the effect of changing the interspacing of passive self-oscillating trailing edge flaplets has been carried out using a NACA 0012 aerofoil. Clear differences can be observed between each of the different cases. Where a reduction in low frequency noise, an increase in high frequency noise and a reduction in turbulence intensity in the wake can be seen for each case. As the inter-spacing is reduced, the differences become more prominent, when compared to the reference aerofoil. Keywords Passive oscillators · Aeroacoustics · Trailing edge flaplets · Fluid structure interaction

1 Introduction Bio-mimicking is a topic of increasing interest within the aeroacoustic community, where many different strategies have been tested and implemented in order to reduce perceived noise levels from either aircraft, wind turbines or compressors; to name a few examples. Many of these strategies are inspired from the well-known ‘silent’ flight of the owl [1]. In the present study, a novel configuration of a flexible trailing edge is used, consisting of an array of individual elastic flaplets mimicking the tips of bird feathers aligned along the span of the wing. This type of trailing edge modification with arrays of individual mechanical oscillators in the form of elastic flaps has thus far only been studied by the authors [2–6].

E. Talboys (B) · C. Brücker City, University of London, London EC1V 0HB, UK e-mail: [email protected] T. F. Geyer · F. Prüfer Brandenburg Institute of Technology Cottbus–Senftenberg, Cottbus 03046, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_25

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2 Experimental Arrangement The aerofoil used in the current study was a NACA 0012 symmetric aerofoil, with a chord length of 0.19 m and a span width of 0.28 m. The aerofoil was 3D printed in two halves such that the flaplets could be adhered on the centre plane of the aerofoil and extended out of the trailing edge of the aerofoil, as seen in Fig. 1. The flaplet arrays were laser cut from a 180 µm thick polyester film. For the present study, the inter-spacing (s) between flaplets was altered in accordance to the specification in Table 1. Acoustic and hot wire anemometry (HWA) took place in the small aeroacoustic open jet wind tunnel [7] at the Brandenburg University of Technology in Cottbus, with a setup similar to that used in [8] and in [6], where a full description of the experimental set-up can be seen. For the present study, all measurements were taken at a constant chord based Reynolds number Re = 200,000 with a varying geometric angle of attack, αg , from αg = 0◦ to 15◦ .

3 Results Figure 2 shows the sound pressure levels for each of the different flaplet geometries at different geometric angles of attack. At αg = 0◦ (Fig. 2a), all cases show a clear tonal peak between 0.6 and 0.8 kHz, with no real discernible difference between the cases. In the low frequency range, a clear reduction can be seen for all of the flaplet cases and is particularly evident in the small spacing case. This low frequency effect has been seen in previous studies [6] and has been attributed to a modification of the

Fig. 1 Photograph of NACA 0012 aerofoil with the trailing edge flaplets attached Table 1 Flaplet properties and naming convention used within the current study Configuration Length (L) (mm) Width (W) (mm) Interspacing (s) Eigen frequency name (mm) ( f ) (Hz) Large Medium Small

20 20 20

5 5 5

7 3 1

111 104 107

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Fig. 2 12th Octave band acoustic spectra at the three different geometric angles of attack. L p is the sound pressure level normalised with 20 µPa

large scale structures in the flow. In the mid-frequency range (0.9–2 kHz) a reduction can also be seen, prior to a noise level increase at frequencies beyond this point. As the angle increases to αg = 10◦ , there is a stark difference between the medium spacing and the rest. A large tonal peak is present at 0.7 kHz and is not observed amongst the other cases. This is believed to be due to the flaplets, at this testing condition and this specific geometry, damping the non-linear instabilities within the boundary layer sufficiently enough to cause the formation of a laminar separation bubble on the pressure side of the aerofoil, a necessary feature required for tonal noise. The decrease at low frequencies and the increase at the higher frequencies are also observed. A similar trend can also be seen at αg = 15◦ . It can be clearly seen across all the angles, that as the inter-spacing is increased, any differences that have been observed tend towards the reference case. This is thought to be due to the flaplets acting as a ‘filter’ for large scale structures. This effect, coupled with the previously observed shear-layer stabilisation [5], leads to a low frequency noise reduction and a scattering of the noise to higher frequencies. Wake profiles were taken from a set distance, 0.25c, downstream of the aerofoil solid trailing edge. Such that the results for the reference and flaplet aerofoils can be compared, the normalisation proposed by Wygnanski et al. [9] has been used. Figure 3a–e show that the streamwise velocity component for all cases and at all three test angles collapse well on to each other, and at αg = 0◦ , onto the theoretical solution [9] (Fig. 3a). Positive values of ξ indicate the suction side of the aerofoil, therefore it can be seen that, as the angle of attack increases, the deficit profile becomes positively skewed due to the thickening of the boundary layer on the suction side of the aerofoil

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Fig. 3 Normalised wake profile measurements. a–e Streamwise velocity component normalised using the formulation proposed by Wygnanski et al. [9] and b–f v component turbulence intensity, normalised with respect to the maxima of the reference cases. Note that the theoretical solution [9] is only plotted in (a) as ( )

at increasing angles. Figure 3b–f show the turbulence intensity in the v velocity component normalised with the respective reference maxima. At αg = 0◦ , there is little difference between the three flaplet cases, but they are significantly reduced compared to the reference case. At αg = 10◦ , all three cases are still reduced in comparison to the reference case, with the small spaced case lower than both other cases. Further increasing the angle shows a clear difference between all cases, where there is a clear and distinct level of reduction dependent on the spacing. This further shows that the large scale structures are less present with decreasing flaplet interspacing. Figure 4 shows the turbulence spectra from the pressure side of the aerofoil. At αg = 0◦ , multiple peaks can be seen for all cases within the same frequency range where the tonal noise component is observed in Fig. 2a. As αg is increased to 10◦ , the reference case shows none of these multiple tones but rather one clear distinct peak followed by subsequent harmonics. This dominant peak can also be observed within the acoustic spectra at this frequency. The large spaced flaplets show a similar peak, but it is much reduced with a few small peaks at the tonal noise frequency seen in Fig. 4a. The most interesting observation is at the medium spacing, where a clear singular peak is observed. The frequency at which this peak occurs is in agreement with the tonal noise seen in Fig. 2b and the conclusion of sufficient instability damping. When the spacing is further reduced, it can be seen

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Fig. 4 v turbulence spectra from the pressure side of the aerofoil at 0.25c behind the solid trailing edge. Each spectra is offset by 12.5 dB from each other, for clarity

that the singular peak of the medium spaced flaplets and the dominant peak of the reference and large spaced flaplets has been damped out and a series of multiple, smaller peaks are present. Here it can be concluded that the small spacing damps out the instabilities more extensively than the medium spacing, overcoming some sort of threshold that prevents the formation of the laminar separation bubble, hence tonal noise. At the highest test angle, αg = 15◦ (Fig. 4c), the dominant peak observed for the reference case at αg = 10◦ is seen in all cases. But crucially, as the spacing is reduced, the peak reduces in amplitude and almost completely for the small spacing.

4 Conclusion The effect on the inter-spacing of self-oscillating trailing edge flaplets has been investigated using both a 56 microphone array and hot-wire anemometry wake measurements. A low frequency reduction and a high frequency noise increase are seen in all of the flaplet cases when compared to the reference case. Both of these noise level differences increase in magnitude as the flaplet inter-spacing is reduced, showing that the flaplets could be acting as some sort of a large structure filter. The turbulence intensity wake profiles also agree with this finding, as it can be seen that as the inter-spacing is reduced, the maximum turbulence intensity also reduces.

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Acknowledgements The position of Professor Christoph Brücker is co-funded by BAE SYSTEMS and the Royal Academy of Engineering (Research Chair no. RCSRF1617\4\11) and travel funding for Mr. E. Talboys was provided by The Worshipful Company of Scientific Instrument Makers (WCSIM), both of which are gratefully acknowledged.

References 1. Graham R (1934) The silent flight of owls. Aeronaut J 38(286):837–843 2. Kamps L et al (2016) Vortex shedding noise of a cylinder with hairy flaps. J Sound Vib 388:69– 84 3. Kamps L et al Airfoil self noise reduction at low Reynolds numbers using a passive flexible trailing edge. In: 23rd AIAA/CEAS aeroacoustics conference, no June, Reston, Virginia. American Institute of Aeronautics and Astronautics, pp 1–10, June 2017 4. Geyer TF et al (2019) Vortex shedding and modal behavior of a circular cylinder equipped with flexible flaps. Acta Acust United Acust 105:210–219 5. Talboys E, Brücker C (2018) Upstream shear-layer stabilisation via self-oscillating trailing edge flaplets. Exp Fluids 59:145 6. Talboys E et al (2019) An aeroacoustic investigation into the effect of self-oscillating trailing edge flaplets. J Fluids Struct 1–13 7. Sarradj E et al (2009) Acoustic and aerodynamic design and characterization of a small-scale aeroacoustic wind tunnel. Appl Acoust 70(8):1073–1080 8. Geyer TF et al (2010) Measurement of the noise generation at the trailing edge of porous airfoils. Exp Fluids 48:291–308 9. Wygnanski I et al (1986) On the large-scale structures in two-dimensional, small-deficit, turbulent wakes. J Fluid Mech 168:31

Circular Jet with Annular Backflow Using DBD Plasma Actuator Norimasa Miyagi and Motoaki Kimura

Abstract In this study, the influence of the direction of the backward plasma-induced flow generated by a plasma actuator (PA) on the jet flow was investigated. In the case of the backflow PA, the centerline velocity was increased by the contraction of the main flow near the nozzle exit due to the influence of the backflow. Additionally, the fluctuation of the jet boundary layer became stronger as the duty ratio was increased. From these factors, it is considered that the backflow by the plasma induced flow effectively works on the diffusion of the jet structure. Keywords Jet · Mixing · Plasma actuator · Flow control

1 Introduction Jets are essentially unstable because of the presence of a free shear layer, and as a result, their flow structure is extremely complex. Recent studies have examined fluid control techniques using plasma actuators (PAs) based on atmospheric pressure dielectric barrier discharge (DBD) [1, 2]. The present authors have previously applied PAs with the diffusive mixing control of circular jets [3, 4]. One of the present authors has applied a PA to the flame stabilization of premixed combustion [5]. With plasma actuation applied just before the combustion gas blowing, it was possible to obtain flame holding even when a floating flame was generated by the gas flow velocity without plasma actuation. Two mechanisms can be considered for this flame holding mechanism. One is the radicalization of combustible gas by plasma generation, and the other is the influence of the plasma-induced flow. The influence of this flow has not yet been sufficiently discussed in the literature. N. Miyagi (B) Nihon University Junior College, Narashinodai 7-24-1, Funabashi City, Chiba 2748501, Japan e-mail: [email protected] M. Kimura College of Science and Technology, Nihon University, Kanda-Surugadai 1-8-14, Chiyoda-ku, Tokyo 1018308, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_26

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Fig. 1 Schematics of the coaxial backward flow PA used in this study

In the present study, the jet diffusion mechanism was investigated using a coaxial dielectric barrier discharge PA in a low-Reynolds-number flow (Re = 1000). A coaxial PA was installed at the nozzle exit to promote mixing. In a conventional PA [6, 7], because it is necessary to ground the covered electrode that receives the unequal electric field on the downstream side of the exposed electrode, the plasma generation position is within the nozzle pipe line. In the new type coaxial PA (see Fig. 1), the exposed plasma-generating electrode is placed at the nozzle exit, and the ionized layer with the covered electrode is placed upstream from the plasma generation position. In this way, the electrodes are arranged to produce a backward induced flow. In this study, the velocity distribution and fluctuation were measured using hotwire velocity probe to determine the influence of the direction of the induced flow on the diffusion of the jet.

2 Experimental Details Figure 1 shows a schematic of the PAs used to generate backward flows. As shown in the figure, a ring-shaped electrode (exposed electrode) and a cylindrical electrode (covered electrode) are attached to a cylindrical dielectric body composed of a machinable glass ceramic (MACOR, Corning, Inc.). An alternating voltage is applied to the actuator to generate a dielectric barrier discharge and induce a flow as a result of the plasma discharged inside the cylindrical nozzle. A ceramic plate is installed around the outer circumference of the covered electrode in this PA to act as an insulating layer. A non-uniform electric field can be generated by grounding the exposed electrode and applying an alternating voltage to the dielectric coated electrode. Even with this electrode arrangement, a backflow can be induced. Figure 2 shows the experimental apparatus, and Table 1 lists the experimental conditions. For the purpose of the diffusion control of the jet, a cylindrical PA was attached to the nozzle exit. In this experiment, the flow velocity was set to V 0 = 1.54 m/s, corresponding to a Reynolds number of almost 1000 based on the jet velocity and the nozzle exit diameter (d = 10 mm). The initial fluctuation frequency is f n = 75 Hz when the actuator is off, and the driving frequency of the PA was set

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based on this initial frequency. Plasma generation was carried out with a relatively low power under stable plasma generating conditions. The duty ratio was varied from 0%, corresponding to the actuator not being driven, to 100%, which corresponds to continuous driving. A hot-wire anemometer was used to measure the flow velocity. The hot-wire anemometer uses a single I-type wire probe (wire diameter: 5 µm, sensing length: 1 mm), and the electric signals were passed through a constanttemperature anemometer (CTA) circuit and a linearizer. The calibration of the hotwire anemometer was performed in the constant-velocity region at the nozzle exit. The signal from the hot-wire anemometer was passed through a low-pass filter (LPF; cut off frequency: 3 kHz) to remove electric noise, observed with an oscilloscope or fast Fourier transform (FFT) analyzer, and recorded as digital data by a data acquisition device (sampling rate: 10,000 sample/s). Data analysis was performed on a personal computer (PC). The coordinate system was defined with the origin set at the center of the nozzle exit, and the x- and r-directions were defined as the streamwise and radial directions, respectively. The hot-wire probe was made to traverse the radial direction with the

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hot wire oriented parallel to the circumferential direction. Because an I-type probe was used, the velocity distribution is given by the velocity without being divided into components. Within the scope of this experiment, the streamwise velocity is considered to be prominent. The plasma generation position corresponds to the position of the exposed electrode. The position of the electrode was x = −2 mm in this case. To avoid an electrical short, the hot-wire probe measurement was carried out at a distance of 5 mm or more from the plasma generation position. Therefore, in this experiment, the effect of suction due to backflow cannot be detected.

3 Results and Discussion 3.1 Initial Condition Figure 3 shows the velocity profiles near the nozzle exit (at x/d = 0.5) using the backward type PA at different duty ratios. When the PA was switched on, the center velocity was increased by the contraction of the main flow near the nozzle exit as a result of the influence of the backflow. The fluctuation of the jet boundary layer also became strong. These effects increased as the duty ratio was increased.

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3.2 Flow Structure Figure 4a, b shows the time-averaged velocity distribution and the distribution of the centerline velocity fluctuation along the central axis. With the induced backflow, the centerline velocity was increased by the contraction of the main flow near the nozzle exit as a result of the influence of the backflow. In comparison with the case when the PA was off, the centerline velocity decay occurred earlier for all considered duty ratios. Near x/d = 4.0, the centerline velocity showed attenuation, and diffusion was promoted. In the case of plasma actuator was ON, even when the duty ratio and the ejection velocity were high, the centerline velocity attenuated immediately after jetting and reduced to the bulk velocity at x/d = 3. Figure 4b shows the distribution of the centerline velocity fluctuation. The first peak is the initial fluctuation due to acoustic resonance, and the second peak is influenced by the developed shear layer. The fluctuation is gradually amplified until the shear layer reaches the center axis. Therefore, the structure of the jet can be estimated to be the initial region of the potential core up to the second peak and the fully developed region after the peak. With the induced backflow, the velocity fluctuation along the centerline rapidly became strong, if the duty ratio is 50% or more. The peaks of the fluctuation distributions showed similar tendencies to those with the corresponding duty ratios in the case of induced forward flow [7]. However, because the velocity fluctuation rapidly increased, the position of the peak approached the nozzle exit with the backflow. The backflow at the nozzle exit was considered to be strongly involved in the velocity fluctuation applied to the shear layer of the jet. 1.5

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4 Conclusions A backflow DBD PA was applied to jet diffusion control, and the duty ratio and intermittency of the plasma-induced backward flow were varied. 1. In the case of the backflow PA, the center velocity was increased by the contraction of the main flow near the nozzle exit because of the influence of the back flow. Additionally, the fluctuation of the jet boundary layer became stronger with increasing duty ratio. 2. With the induced backflow, the velocity had increased by the main flow construction at the nozzle exit. And the shear layer grew rapidly because of the influence of backflow, and it disturbed to the centerline velocity.

References 1. Corke TC, Enloe CL, Wilkinson SP (2010) Dielectric barrier discharge plasma actuators for flow control. Annu Rev Fluid Mech 42:505–529 2. Moreau E (2007) Airflow control by non-thermal plasma actuators. J Phys D Appl Phys 40(3):605–636 3. Kimura M, Asakura J, Onishi M, Sayou K, Miyagi N (2013) Jet diffusion control by using a coaxial type DBD plasma actuator, ICJWSF2013. In: Proceedings of ICJWSF2013 4th international conference on jets, wakes and separated flow, 79, No 806, pp 2041–2052 4. Miyagi N, Ueki H, Kimura M (2015) Diffusion control in circular jet using coaxial type DBD plasma actuator. In: ASME/JSME/KSME 2015 joint fluids engineering conference. https://doi. org/10.1115/ajkfluids2015-14711 5. Kanai S, Tsuchida H, Yoshida K, Akimoto M, Kimura M (2017) Flame control in combustion nozzle using a coaxial type DBD plasma actuator. In: FSSICS2017, 4th symposium on fluid structure and sound interaction conference 6. Miyagi N, Kimura M (2017) Jet diffusion control using plasma actuators—influence of plasmainduced flow instability on jet diffusion. In: ICJWSF2017, 6th international conference of jet, wake and separated flow 7. Miyagi N, Kimura M (2018) Jet diffusion control using plasma actuators. In: Fluid-structuresound interactions and control proceedings of the 4th symposium on fluid-structure-sound, pp 155–160

Investigation of the Asymmetric Wake Mode of a Three-Dimensional Square-Back Bluff Body Yajun Fan, Chao Xia, Diandian Ge, and Zhigang Yang

Abstract This paper reports a detailed investigation of the asymmetric wake mode behind a three-dimensional square-back bluff body using both experimental measurement and numerical simulation at ReH = U 0 H/v = 9.2 × 104 (where U 0 is free-stream velocity, H is the height of body and v viscosity). The analyses of the instantaneous back pressure, velocity field as well as the side aerodynamic force suggest that the near-wake is dominated by a random displacement of the wake between two preferred reflectional-symmetry-breaking (RSB) locations. Utilizing the proper orthogonal decomposition (POD), three dynamic modes of unsteady wake are identified: the bi-stable behavior or RSB characterized by a long time-scale, the global oscillation leading to vortex shedding at St H = 0.154 and the periodic pumping at St H = 0.07. The reconstruction of the velocity field is analyzed, revealing a mutual connection between different coherent structures. Keywords Bluff body · Bi-stable · Unsteady wake · POD

1 Introduction Over the past three decades, more and more investigations have carried out on the three-dimensional bluff body, such as the square-back Ahmed body. The mean flow over this geometry has been investigated clearly, it presents a pair of symmetrical reverse vortex structures on the horizontal section. On the vertical section, it shows a static symmetry-breaking mode resulting from the existence of ground [1, 2].

Y. Fan · C. Xia (B) · D. Ge · Z. Yang Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management Systems, Shanghai 201804, China e-mail: [email protected] Shanghai Automotive Wind Tunnel Center, Tongji University, Shanghai 201804, China Z. Yang Beijing Aeronautical Science and Technology Research Institute, Beijing, 102211, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_27

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Through experimental investigation on a square-back model base with a base ratio of one, Duell and George [3] detected the existence of a periodic pumping mode of the wake. Besides, a high frequency mode was also observed and explained as vortex shedding from the mixing layers. Similar results were also obtained by Khalighi et al. [4] in experimental and numerical investigations using a different square-back geometry with an aspect ratio of 1.4. Recently, Grandemange et al. [1] found experimentally that the unsteady wake of square-back Ahmed body presents bi-stable states randomly switching at a time scale about 1000H/U 0 (where U 0 is free-stream velocity, H the height of the model), which is much larger than that of a typical vortex shedding. These asymmetric states crucially depend on the ground proximity and aspect ratios [5] and could alter the base pressure distribution and dynamics. There are great difficulties in detecting bi-stable behavior through numerical simulation because of the long time scale characteristic of bi-stability. Lucas et al. [2] conducted numerical simulation over the flat back Ahmed model using LBM method to investigate bi-stable behavior. However, only one state was observed. Although many works were devoted to the study of unsteady wake of a three-dimensional bluff body, the interaction between different flow structures is still not clear. Moreover, it is still a great challenge to study this bi-stable switching by numerical simulations. In the present work, the unsteady wake over a 1/4 scale square-back Ahmed body is investigated by wind tunnel testing including pressure measurement and PIV measurement. In addition, we use the improved delayed detached eddy simulation (IDDES) to capture the bi-stable wake behavior at long time scales. Proper orthogonal decomposition (POD) is also applied to extract coherent flow structures in the wake.

2 Experiment and Numerical Simulation Set up The experimental campaigns took place in an open-jet, close-loop, low speed wind tunnel.The 1/4 scale square back Ahmed body is placed over a raised floor, which was used to control boundary layer thickness, as shown in Fig. 1a. The blockage ratio is less than 6%. In this paper, superscript asterisk ‘*’ denotes normalization by the height of model. Experiments were carried out at U 0 = 20 m/s corresponding to ReH = 9.2 × 104 . A cartography of the pressure field of 25 points distributed at the rear of the body was obtained by means of piezoresistive pressure sensor, pressure

Fig. 1 a Experimental setup; b The ones of the 2D PIV planes; c Positions of the pressure taps; d Grids distribution in symmetry plane z* = 0.67

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data were sampled at 50 Hz for 600 s. PIV measurement was performed in the z* = 0.67 plane with a sample frequency of 1.25 Hz. The time-dependent IDDES (based on SST model) [6] is a hybrid RANS-LES model, which combines the advantages of the delayed detached-eddy simulation (DDES) and the wall-modelled large eddy simulation (WMLES). The size of computational domain is 40L × 9.4H × 5H. The boundary conditions are specified as following: velocity inlet for the inlet; pressure outlet for the outlet, non-slip wall condition for the Ahmed body and the stationary ground; symmetry for the rest boundaries. The Reynolds number is 9.2 × 104 based on the height of the Ahmed body, which is the same as experimental setting. The total number of cells is 10.5 million and the Courant number (Co) fulfills Co < 1 for most grids. Figure 1(d) shows the grids distribution with high symmetry at lateral direction.

3 Results 3.1 Mean Flow Field The time-averaged flow fields of the z* = 0.67 plane are presented in Fig. 2 for both experiment and numerical simulation results. The mean streamwise and spanwise velocity distribution of numerical simulation are in good agreement with those obtained by experiment apart from small difference in the location of the free stagnation point. It’s located at x* = 1.49 downstream of model base for numerical simulation which is consistent with the results obtained by Grandemange et al. [1].

Fig. 2 Time-averaged flow field of z* = 0.67 plane: a the streamwise velocity U*; b the spanwise velocity V*

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Fig. 3 Bi-stable behaviour of the pressure field and side force: a excerpt of the C p evolution; b related PDF; c Time history of the side force signals from simulation

3.2 Instantaneous Back Pressure and Side Aerodynamic Force The high RMS value of the C p field is mainly derived from the bi-stable behavior of the pressure field, which was already observed by Grandemange et al. [1] and Volpe et al. [7] Further evidence is provided in Fig. 3a which reports the temporal evolution of the synchronized measurements of two piezoelectric transducers, located at symmetric points as shown in Fig. 1c. As can be seen, the pressure coefficient of the two taps continuously switches between two well-defined levels. This is even more obvious when the probability density functions (PDFs) computed on the whole acquisition time interval are plotted, as shown in Fig. 3b, since the pressure data distribute as a bimodal statistical function. In addition, Fig. 3c shows the change of side force signals of numerical simulation from T* = 0 to T* = 5200. The value of Cs is fluctuated from about 0.02 to −0.02 (−0.02 to 0.02) greatly during 611–694 and 2861–2917, which is a strong evidence of the switch from one state to another.

3.3 Instantaneous Flow Fields The instantaneous flow fields of the z* = 0.67 plane at three representative moments are presented in Fig. 4 both for the experiment and simulation. It is obvious that the

Fig. 4 Instantaneous velocity field in z* = 0.67 plane

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vortex structure on the one side is larger than another side which may lead to vortex shedding at time T1 and T3. These represent the asymmetrical wake topology in the bi-stable behavior. The wake is almost symmetrical during the switching process such as the instantaneous flow field at time T2.

3.4 Proper Orthogonal Decomposition Analysis Turbulent kinetic energy contribution POD was applied to extract the coherent structures from the turbulent wake field. The first four POD modes occupy 24.7, 3.8, 3.6, and 3.0% of the energy respectively for experiment. However, the first four POD modes occupy 10.8, 1.8, 1.5, and 1.4% respectively for simulation. The fact that the energy contribution of the first mode is far higher than others indicates the dominant role of the first mode in the wake. Mode and spectrum analysis The first four modes represented by u-direction velocity are shown in Fig. 5 only for numerical results. The first unsteady mode is anti-symmetrical and shows large-scale motions in the shear layers, dominated by the U velocity component. The power spectrum of the time series of each mode’s energy coefficient is displayed at the right side of the mode figure. Then, the spectrum associated with the first mode decreases with a -2 law for very low frequencies, this indicates that the first order mode reflects the horizontally asymmetric bi-stable behavior which confirms the findings of Grandemange [1]. The U velocity component

Fig. 5 The U velocity component contour of modes 1–4 in the z* = 0.67 plane and normalized power spectra of the mode coefficient, mode1-4

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Fig. 6 Low-order phase-averaged vorticity field overlapped with the velocity streamlines

of the second mode is also anti-symmetric and the sign is arranged in the streamwise, which is similar to the third mode with a π/2 phase shift. Both the second and the third mode’s spectrum shows peak at St H = 0.154, corresponding to the global oscillation in the lateral direction. The Mode 4 spectrum shows a peak at a reduced frequency of St H = 0.07, which corresponds to the wake pumping. The reconstructed flow field Figure 6 shows the reconstructed flow field by a low-order phase-averaged vorticity field with the first fourth modes, revealing three significant features in the wake. Firstly, the vortex structures exhibit obvious asymmetry which is not similar to the symmetry exhibited by the time-averaged flow field, and large vortex structure appears alternately at the left or right side. Meanwhile the wake exhibits the characteristics of left and right oscillation, which is corresponding to a peak frequency of St H = 0.154. Further, this oscillation leads to vortex shedding as shown in the instantaneous flow field. In addition, the wake exhibits periodic pumping in the streamwise direction corresponding to a peak frequency of St H = 0.07.

4 Conclusion Wind tunnel experiment and IDDES numerical simulation have been conducted to detect the asymmetric wake mode behind a three-dimensional square-back bluff body. The unsteady wake is dominated by three distinct flow patterns, consisting of bi-stable behavior, global oscillation and pumping. Bi-stability is a long-term scale flow phenomenon, which exhibits a random displacement of the wake between two preferred off-center locations. The global oscillation appears as a wobble of the wake in the horizontal directions, which causes vortex shedding at the strouhal number of 0.154. The pumping is characterized by the expansion and contraction of the size of the wake, corresponding to a peak strouhal number of 0.07. The three unsteady flow structures in the wake region are coupled with each other. When the bi-stable behavior occurs, the wake pattern is asymmetrical in the horizontal direction, that is, the left/right side of wake exhibits the large vortex structure, while the other side appears the discrete vortex shedding. Meanwhile, the recirculation region is in an extended state of wake pumping.

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References 1. Grandemange M, Gohlke M, Cadot O (2013) Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J Fluid Mechan 722(5):51–84 2. Lucas JM, Cadot O, Herbert V et al (2017) A numerical investigation of the asymmetric wake mode of a squareback Ahmed body—effect of a base cavity. J Fluid Mech 831:675–697 3. Duell EG, George AR (1999) Experimental study of a ground vehicle body unsteady near wake. SAE Trans 108(6; Part 1):1589–1602 4. Khalighi B, Zhang S, Koromilas C, Balkanyi S, Bernal LP, Iaccarino G, Moin P (2001) Experimental and computational study of unsteady wake flow behind a bluff body with a drag reduction device. Technical report, SAE technical paper 5. Grandemange M, Gohlke M, Cadot O (2013) Bi-stability in the turbulent wake past parallelepiped bodies with various aspect ratios and wall effects. Phys Fluids 095103 6. Gritskevich MS, Garbaruk AV (2012) Development of DDES and IDDES formulations for the k-omega shear stress transport model. Flow Turbulence Combust 88:431–449 7. Volpe RPD, Kourta A (2015) Experimental characterization of the unsteady natural wake of the full-scale square back Ahmed body: flow bi-stability and spectral analysis. Exp Fluids (2015)

Mechanisms of the Aerodynamic Improvement of an Airfoil Controlled by Sawtooth Plasma Actuator L. J. Wang, C. W. Wong, W. Q. Ma, and Yu Zhou

Abstract This work aims to investigate the control mechanism of aerodynamic performance enhancement of a NACA 0015 airfoil with a sawtooth dielectric barrier discharge (DBD) plasma actuator at a Reynolds number Re of 7.7 × 104 . A parametric study on the non-dimensionalized burst frequency F + (= f b c/U ∞ , where f b , c and U ∞ are the burst frequency, airfoil chord length and the free-stream velocity, respectively) and duty cycle (DC) is conducted at a post-stalled angle-of-attack α = 16°. The timeaveraged lift coefficient C L is maximized at F + = 0.6, DC = 5% or 50%. At F + = 0.6 and DC = 5%, the enhanced momentum transfer and the movement of plasmainduced large-scale vortex structures over the suction side of the airfoil attribute to the lift augmentation. While in the case of F + = 0.6 and DC = 50%, the laminarto-turbulent transition takes place near the leading-edge of the airfoil, thus forming turbulent boundary layer, which is linked with more momentum near wall that delays flow separation. Keywords NACA 0015 airfoil · Plasma actuation · Flow separation control

1 Introduction Dielectric barrier discharge (DBD) plasma actuator is a state-of-the-art and promising technique for flow separation control [1]. Our research group developed and applied a sawtooth DBD plasma actuator (hereafter called sawtooth plasma actuator), which generates larger jet velocity than the “traditional” linear DBD plasma actuator under the same power consumption, on a NACA 0015 airfoil. This sawtooth plasma actuator could also produce the near-wall streamwise vortices in the trough region of the sawtooth electrode, which led to the delay of stall angle α stall of this airfoil by 5° L. J. Wang · C. W. Wong · W. Q. Ma · Y. Zhou Center for Turbulence Control, Harbin Institute of Technology, Shenzhen, China L. J. Wang · C. W. Wong (B) · Y. Zhou Shenzhen Digital Engineering Laboratory of Offshore Equipment, Harbin Institute of Technology, Shenzhen, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_28

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and the increase of the maximum lift coefficient C Lmax by 9% under the steady actuation [2]. The C Lmax was increased by 27.5% when the sawtooth plasma actuator was operated in the burst mode [3]. The present investigation aims to explore the underlying physical mechanisms for the improved aerodynamic performance of the airfoil controlled by the sawtooth plasma actuator under the burst-mode actuation.

2 Experimental Details Experiments are conducted at a chord-Reynolds number Re of 7.7 × 104 . A sawtooth plasma actuator which is originally developed at our Research Institute comprised of two copper sawtooth electrodes separated by a PMMA material (Fig. 1b). The actuator was installed at 0.02c (where c denotes airfoil chord) downstream from the leading-edge and on the suction side of the airfoil, covering the central 0.6b (where b denotes the airfoil span). The applied sinusoidal waveform is fixed at a voltage V a = 15 kV and frequency f = 11 kHz. The duty cycle (DC) is varied from 1% to 100% (steady mode), while the non-dimensional burst frequency F + (= f b c/U ∞ , where f b and U ∞ are the burst frequency and the free-stream velocity, respectively) is varied from 0.3 to 9.0. The time-averaged lift force F L is measured directly with a unidirectional load cell (Interface SM-50 N, S type) mounted at the bottom end of the pitching pivot. The flow fluctuation frequency in the shear layer are extracted through FFT analysis of the hotwire-measured streamwise velocity fluctuations at the mid-span of the airfoil. Particle image velocimetry (PIV) measurements are performed to capture the flow-field over the suction side of the airfoil in the x–y planes, that aligned with the peak-to-peak (P–P) and trough-to-trough (T–T) of the sawtooth (Fig. 1c), thus providing an insight into the underlying mechanisms behind the aerodynamic improvement.

Fig. 1 a Wind tunnel setup for the force measurement; b Schematic of the sawtooth plasma actuator; c Examples of discharge filaments formed by the sawtooth DBD plasma actuators

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3 Results and Discussion There are two ΔC L (= C L,unsteady − C L,off , where the C L is lift coefficient and the subscripts unsteady and off denote the burst-modulated actuation and the plasma-off, respectively) peaks, 0.46 and 0.41, at DC = 5 and 50%, respectively, when F + = 0.6 and the angle-of-attack α = 16º (Fig. 2a). The ΔC L reduces as F + > 0.6 at Re = 7.7 × 104 . Under the optimum control conditions (i.e., F + = 0.6, DC = 5% or 50%), the power spectrum density (PSD) of the streamwise fluctuating velocity u in the shear layer of the airfoil is analyzed at a fixed measurement location, i.e., (x/c, y/c) = (0.6, 0.15). Note that all data were measured in the plane parallel to the tip of the sawtooth electrode. Without control (Fig. 3a), the hot-wire measurement point is far away from the vortex shedding (as confirmed with the smoke-flow visualization, not shown), therefore no peak can be observed in the baseline case. At F + = 0.6 and DC = 5% (Fig. 3b), there is a prominent peak at 18 Hz, corresponding to the natural vortex shedding frequency of the airfoil wake. At F + = 0.6 and DC = 50% (Fig. 3c), in addition to the frequency peak at 18 Hz, there also exits the second harmonics of the peak at 36 Hz, suggesting that the vortex structures generated above the airfoil

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Fig. 3 Power spectrum density (PSD) of the streamwise fluctuating velocity u in the shear layer of airfoil a without control, b with control, F + = 0.6, DC = 5% and c with control, F + = 0.6, DC = 50%. Measurement point at x/c = 0.6 and y/c = 0.15

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surface is broken at high DC levels [4]. These ‘broken’ vortex structures convey highspeed flow and entrain large momentum near suction surface of airfoil periodically, resulting in the delay of flow separation and lift increase. Detailed PIV measurements are then performed for these two optimum control conditions. Figure 2b shows the streamwise distribution of the normalized maximum TKE max in the P-P plane for each control case. The normalized 2 T K E (= 0.75(u 2 + v 2 )/0.5U∞ , where u and v are the root-mean-square velocities, respectively) is calculated spatially along the x- and y- directions over the xy measurement plane, hence the TKE max along the y-direction is sought at each x-position. For the case of DC = 5%, the TKE max peak appears at 0.12c which associated with the vortex structures induced by the sawtooth plasma actuator (as confirmed by our PIV data, Fig. 4). The generation and the movement of these vortices are expected to increase the lift force on the airfoil. On the other hand, the TKE max peak in the case of DC = 50% shrinks drastically due to the shear layer attachment on the suction surface up to 0.7c while the vortex shedding occurs at x/c > 0.7 (not-shown). It is expected that at a low DC level (5%) the fluctuating velocities generated by the actuator is large, so producing large TKE and enhancing the momentum transfer from the outer flow into the boundary layer over the airfoil. On the other hand, at DC = 50% the laminar-to-turbulent transition takes place as the result of the plasma actuation. It is proposed that the turbulent boundary layer is formed over the suction surface of the airfoil, causing large momentum near wall and delaying flow separation.

Fig. 4 Non-dimensional phase-averaged spanwise vorticity ω*z (= ωz c/U ∞ ) in P-P plane under the unsteady actuation (F + = 0.6, DC = 5%)

Mechanisms of the Aerodynamic Improvement …

y/c

y/c 0.025

a)

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x/c

0.025

v

b)

x/c

v

Fig. 5 Temporal evolution of the normal velocity v along streamwise direction at y/c = 0.025. a F + = 0.6, DC = 5%; b F + = 0.6, DC = 50% (in P-P plane)

Figure 4 shows the temporal development of the non-dimensional phase-averaged spanwise vorticity ω*z (=ωz c/U ∞ ) at F + = 0.6 and DC = 5%. Note that different phase angles, i.e. 0, 7π/10, 14π/10 and 19π/10, are presented here. Under the burstmodulated actuation, there are two periodic processes of the shear layer evolution in each cycle, the first one is the emergence and development of the shear layer and the second one is the vortex shedding over the suction surface. The vortex structures which initially found near the leading-edge of the airfoil contain large momentum and remain close to the airfoil surface when propagating downstream of the airfoil. It is the fact that the low-pressure region around these vortex structures which enhances the C L . In order to characterize the spatial-temporal dynamics of the flow, the evolution of the normal velocity v is extracted along a line at y/c = 0.025 (Fig. 5). At F + = 0.6, DC = 5%, the vortex structures are found in the immediate vicinity of the suction surface of the airfoil. These structures gradually convect to the downstream and bring the high kinetic energy to the airfoil surface along their path, encouraging momentum entrainment into the separation region. The advection of vortex structures is indicated by time-varied v amplitude (streaks in v contour). When the DC is increased to 50%, the amplitude of v increases significantly compared to that at DC = 5%, implying that the near-wall flow is more turbulent. It is therefore the flow momentum exchange from above the airfoil surface is enhanced.

4 Conclusions Experimental investigation is performed to study the effect of F + and DC of the plasma actuation on the lift enhancement of a NACA 0015 airfoil and the underlying mechanisms behind the aerodynamic improvement under the brust-mode actuation.

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At F + = 0.6 and DC = 5%, the enhanced momentum transfer and the movement of plasma-induced vortex structures over the suction side of the airfoil attribute to the lift augmentation. While in the case of F + = 0.6 and DC = 50%, the plasma actuation enhances the laminar-to-turbulent transition near the leading-edge of the airfoil, forming turbulent boundary layer which is associated with large momentum exchange near wall that allows delay of flow separation and increase in C L . Meanwhile the shedding of vortices near the trailing-edge of the airfoil partially contributes to the rise of lift force on the airfoil. Acknowledgements Authors wish to acknowledge support from the National Natural Science Foundation of China through grants 11502060, 11632006, 91752109, 51935005, 12002110 and 91952204, and from the Research Grants Council of the Shenzhen Government through grant JCYJ20160531193045101.

References 1. Corke TC, Enloe CL, Wilkinson SP (2010) Dielectric barrier discharge plasma actuators for flow control. Annu Rev Fluid Mech 42:505–529 2. Wang LJ, Wong CW, Lu ZY, Wu Z, Zhou Y (2017) Novel sawtooth dielectric barrier discharge plasma actuator for flow separation control. AIAAJ 55(4):1405–1416 3. Wang LJ, Wong CW, Fu XD, Zhou Y (2018–1062) Influence of burst-modulated frequency on sawtooth DBD plasma actuator for flow separation control. AIAA Paper 4. Sato M, Aono H, Yakeno A, Nonomura T, Fujii K, Okada K, Asada K (2015) Multifactorial effects of operating conditions of DBD plasma actuator on laminar-separated-flow control. AIAAJ 53(9):2544–2559

Aerodynamic Performance of a Sedan Under Wind-Bridge-Tunnel Road Condition Qianwen Zhang, Chuqi Su, and Yiping Wang

Abstract Due to the complexity of the wind environment around bridge-tunnel section in canyon, the flow field around vehicle is complex and changeable. In this paper, the processes of a sedan pulling out of a two-way four-lane tunnel and passing through the pylon area under canyon wind condition were simulated numerically using the dynamic mesh technique. The results showed that canyon wind and the terrain topography have a significant effect on the aerodynamic performance of the vehicle. Keywords Unsteady aerodynamics · Canyon wind · Bridge-tunnel section

1 Introduction With the development of economic and city traffic, a great deal of bridges and tunnels are constructed in mountainous highways [1]. Due to the unique topography, geology, climate, altitude and other factors in mountain areas, the strong unsteady crosswind, often called canyon wind, has a great impact on vehicle performance and safety [2– 4]. Here, the focus was put on the aerodynamic performance of a sedan pulling out of a two-way four-lane tunnel and passing through the pylon area, thus providing guidance for improving the crosswind stability of vehicles.

Q. Zhang · C. Su · Y. Wang (B) Hubei Key Laboratory of Advanced Technology for Automotive Components, Wuhan University of Technology, Wuhan 430070, China e-mail: [email protected] Hubei Collaborative Innovation Center for Automotive Components Technology, Wuhan University of Technology, Wuhan 430070, China Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Wuhan 430070, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_29

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a) Canyon model

b) Mountain-bridge-tunnel model

c) Passenger car model

Fig. 1 Mountain-bridge-tunnel-sedan model

a) The cross-section of tunnel

b) The location of sedan in tunnel

Fig. 2 Dimensions of tunnel and illustration of vehicle location

2 Numerical Method 2.1 Geometric Model A typical bridge-tunnel connection section in western China around Beipanjiang bridge is selected as a subject for study. The terrain and geomorphology are constructed by extracting the contour map from the geographic information system (GIS) with its area 1425 m * 404 m (see Fig. 1). The bridge used in current research is a twin tower three-span cable-stayed bridge. A common two-way four-lane straight tunnel is chosen, ignoring the wind turbine and other equipment inside the tunnel. The sedan, is a simplified passenger car, which located inside the tunnel, 3.2 m away from the side wall and 29.09 m away from the exit of the tunnel (see Figs. 1 and 2).

2.2 Governing Equation Numerical simulations for vehicle aerodynamic were performed using a pressurebased solver in FLUENT, which is based on the finite volume method. Considering the real conditions of this study and the computational accuracy and effectiveness, a three-dimensional, incompressible, unsteady, RNG k-ε two-equation turbulent model is utilized in this study [5]. The turbulence eddy viscosity could be computed as a function of turbulence kinetic energy k and turbulence dissipation rate ε:

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Fig. 3 Boundary condition of computational domain

Gk ∂k ∂k k 2 ∂k ∂ αk ν+Cμ + = + uj −ε ∂t ∂x j ∂ xi ε ∂x j ρ 2 1 ∂ε k 2 ∂ε ε ∂ ∂ε ∗ ε αε ν+Cμ + C1ε G k − C2ε + uj = ∂t ∂x j ∂ xi ε ∂x j ρ k k

(1)

(2)

in which α k = α ε = 1.39 is the turbulent Prandtl number in the k equation and the ε equation, C μ = 0.0845, C 1ε = 1.42, C 2ε = 1.68, η0 = 4.38, β = 0.012.

3 Computational Setup A simplified computational domain is established to enclose the canyon-bridgetunnel model. The length, width and height of the computational domain are 1425 m × 404 m × 540.695 m. The outline features of the real canyon terrain are retained as the bottom of the computational domain (See Fig. 3). The inlet and outlet boundaries are set to pressure outlet (relative pressure p = 0). The speed of the sedan is 30 m/s, and the crosswind was perpendicular to the moving direction of the sedan.

4 Results and Discussions As shown in Fig. 4, the aerodynamic loads of the sedan in the process of pulling out of the tunnel and passing through the bridge tower are plotted. It can be seen from Fig. 4a that when a sedan runs out of tunnel, the drag force increases sharply near the exit of the tunnel. And then, it generally maintained a downward trend until t = 3 s, in spite of some fluctuations. When the sedan comes to the pylon area, the drag force fluctuates greatly because of complex canyon wind and topography. In Fig. 4(b) and 4(c), the variation of lateral force and yaw moment is similar and followed the same trend, which increase significantly in the crosswind and decrease greatly due to the shielding effect of the bridge tower.

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a) Drag force

b)Lateral force

c)Yaw moment

Fig. 4 Aerodynamic forces and moment

The instantaneous velocity distributions at the x–y section (z = 0.6 m) are displayed in Fig. 5, which capture the change of the flow field of the sedan pulling out of the tunnel and enters in the crosswind. T = 0 s, the sedan is located in the tunnel. At this time, the crosswind does not affect the car, and the lateral force and yaw moment are almost zero. The velocity distribution of the flow field around the car is almost symmetrical. However, when the car pulls out of the tunnel, the velocity distribution turns asymmetric due to the complex canyon wind. The effect of terrain on the flow field around the vehicle is shown in Fig. 6. The complex canyon wind produced a huge eddy near the tunnel exit, acting on the left side of the car body and made the negative lateral force and yaw moment. As the sedan moves far away from the tunnel, the influence of the vortex on the vehicle is reduced. The instantaneous displacement and the velocity distributions of the sedan in the process of driving into and out of the bridge tower area are shown in Fig. 7. At 4.2 s, half of the sedan was sheltered from bridge tower. The flow field in the front of the sedan was symmetrical, while the velocity distribution in the rear of the car was asymmetrical at this time. The opposite trend can be found in the process of driving out of the pylon area at t = 4.55 s. At approximately 5.5 s, the sedan was completely

Tunnel

a) t=0.8s

Tunnel

b)t=0.975s

Fig. 5 Snapshot of velocity magnitude (Z = 0.6 m)

Tunnel

c)t=1.1s

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b)t=1.5s

c)t=2s

Fig. 6 Snapshot of streamlines

Tower

Tower

a) t=4.2s

b)t=4.35s

Tower

c)t=4.55s

d)t=5.5s

e)t=6s

Fig. 7 Snapshot of velocity magnitude at x–y section (Z = 0.6 m)

immersed in the canyon wind, the impact of the bridge pylon was decreased and the lateral force and yaw moment were constantly increased. It also can be seen that the car has a significant sideslip in the crosswind.

5 Conclusions The aerodynamic performance of a sedan driving in the canyon-bridge-tunnel section is revealed by numerical simulation. The drag force, lateral force and yaw moment of the sedan increased obviously when it comes out of the tunnel in the crosswind. When the sedan is pulled out of the tunnel, the complex canyon wind affected by the terrain formed a huge eddy at the tunnel exit. The lateral force opposite to the direction of the incoming flow acted on the left side of the car and produced an unexpected change. When the sedan passing by the pylon area, the aerodynamic loads also changed sharply due to the shielding effects of the tower and the complex topography. In this complex road condition, the sedan deviates from the original path. It is worth mentioning that the road condition has a great impact on the vehicle’s crosswind sensitivity and driving stability.

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Acknowledgements The research was supported by the National Natural Science Foundation of China (Grant No. 51775395) and China Scholarship Council (CSC No.201906950068).

References 1. Rabani M, Faghih AK (2015) Numerical analysis of airflow around a passenger train entering the tunnel. Tunn Undergr Space Technol 45:203–213 2. Carbonne L, Winkler N, Gunilla Efraimsson KTH. Use of full coupling of aerodynamics and vehicle dynamics for numerical simulation of the crosswind stability of ground vehicles, SAE, 2016-01-8148 3. Li LI, Guang-Sheng DU, Liu ZG, et al (2010) The transient aerodynamic characteristics around vans running into a road tunnel. J Hydrodyn Ser B 22(2):283–288 4. Winkler N, Drugge L, Trigell AS et al (2016) Coupling aerodynamics to vehicle dynamics in transient crosswinds including a driver model. Comput Fluids 138:26–34 5. Wang JY, Hu XJ (2012) Application of RNG k-ε turbulence model on numerical simulation in vehicle external flow field. Appl Mech Mater 170–173:3324–3328

Vortex-Induced Vibration of a Circular Cylinder at High Reynolds Number Tulsi Ram Sahu, Gaurav Chopra, and Sanjay Mittal

Abstract Large-eddy simulation (LES) of vortex-induced vibration (VIV) of a low mass ratio (m ∗ = 10) circular cylinder in the critical flow regime is carried out. In this regime, the boundary layer transitions from a laminar to turbulent state. Weakening of vortex shedding and reduction of drag is observed. The amplitude of cross-flow and in-line oscillations of the cylinder towards the end of the critical regime is small compared to that in the sub-critical flow. Keywords Vortex-induced vibration · Turbulent flow · Large-eddy simulation

1 Introduction A bluff body placed in a fluid stream sheds vortices of alternating sign. This causes fluctuating forces on the structure. If the body is allowed to move, these forces may lead to its vibration. This type of oscillation of the body is often called as vortexinduced vibration (VIV) [1]. VIV is undesirable in many engineering applications since these self-excited oscillations can lead to fatigue failure of the structure [2]. Several experimental and numerical studies for VIV of a circular cylinder have been carried out in the past at low- and moderate- Reynolds number (Re < 30,000) [3]. Recently, a few experimental studies have been conducted for high Reynolds number O(105 ) [4–6]. A systematic high Reynolds number numerical study is expensive and challenging. Flow past a stationary cylinder is characterized into four regimes based on the state of the boundary layer [7]: (1) sub-critical, (2) critical, (3) supercritical, and (4) transcritical. In the critical regime, the boundary layer transitions from laminar to turbulent

T. R. Sahu · G. Chopra · S. Mittal (B) Department of Aerospace Engineering, Indian Institute of Technology Kanpur, Kanpur, UP 208016, India e-mail: [email protected] URL: http://home.iitk.ac.in/∼smittal/ © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_30

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state. This leads to a very sharp reduction in drag with Reynolds number. This phenomenon is known as drag crisis. Details of this phenomenon can be found in [8–10]. In the present study, we address the VIV response of an elastically mounted cylinder during drag crisis. To this extent we present aerodynamic forces, the amplitude and frequency response, vortex-shedding frequency, and mode of vortex shedding at the following Reynolds numbers: (1) Re = 5.0 × 104 (sub-critical), (2) Re = 1.5 × 105 (critical) and (3) Re = 3.0 × 105 (supercritical). The fluid flow is governed by the incompressible Navier-Stokes equations in primitive variables form. A stabilized space-time finite element formulation is utilized to solve the governing equations [11]. The Streamline-Upwind/Petrov-Galerkin (SUPG) and PSPG (pressure-stabilizing/Petrov-Galerkin) are employed for stabilizations of numerical technique [11]. Large-eddy simulation is employed to solve Navier-Stokes equations. The Sigma model [10] is implemented to model the effects of the sub-grid scales in the flow. A circular cylinder of diameter D and span length 0.5D is mounted on elastic support. The support is modelled via linear spring and damper. The motion of the body is governed by the following equation: ˙ + ¨ + 4π ζ Y Y U∗

2π U∗

2 Y=

2CF π m∗

(1)

Here, Y represents the normalized displacement of the body, ζ the structural damping ratio and CF the instantaneous force coefficients for the body. The cylinder can vibrate in-line and transverse to the flow. Therefore, Y is the generalized displacement and consists of two degrees of freedom. Similarly CF represents the generalized force coefficient. The reduced velocity of the system, U ∗ is defined as U/ f n D where f n is the natural frequency of the oscillator. Another parameter of interest is the frequency ratio, f ∗ , the ratio of the frequency of the body vibration to the natural frequency of the oscillator. The mass ratio m ∗ is the ratio of the mass of the body to the mass of the fluid displaced by it. For the present computations m ∗ = 10 and U ∗ = 5 are considered. To encourage high amplitude of oscillation, ζ is set to zero.

2 Results and Discussion Figure 1 shows the time-averaged drag force coefficient (C d ) of the vibrating cylinder with Re. Results of flow past a stationary cylinder from previous studies are also shown for the reference. The present computations capture the phenomenon of drag crisis. Interestingly, the r ms of lift coefficient (Clr ms ) decreases while vortex shedding frequency (St) increases with Re in the regime of drag crisis, as shown in Fig. 2a. The decrease in Clr ms during the drag crisis indicates weakening of vortex shedding in this regime. In Fig. 2b, the variation of time-averaged lift force coefficient (C l )

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1.5

— Cd

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3D-VIV (present) Chopra et al. (2017) Weisselberger (1921) Schewe (1983) Achenbach (1971)

0.5

Lehmkhul et al. (2014) 0.0 4 2x10

5x10

4

5

5

2x10

1x10

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3x10 4x10

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Fig. 1 Flow past a stationary and oscillating cylinder: variation of the mean drag coefficient with Re. Hollow symbols denote data from earlier studies for the stationary case while filled symbols represent data for the present VIV case (a) 2.5

0.20

(b) 0.6

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0.5 0.0 4 5.0x10

—

-Cl

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0.17 5 3.0x10

0.0 4 5.0x10

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3.0x10

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Fig. 2 VIV of a cylinder: variation of the a r.m.s. value of the lift coefficient (Clr ms ) and Strouhal number (St) coefficients and b mean lift (C¯l ) coefficient with Re

with Re is also shown. A non-zero C l is observed at Re = 1.5 × 105 (critical). It occurs due to the asymmetric boundary layer transition. Flow on the upper surface becomes critical, whereas, flow on the lower surface remains sub-critical. Further, at Re = 3.0 × 105 the boundary layer on both the upper and lower surface becomes critical, which results in zero value of C l . The VIV response in the drag crisis regime is very interesting. The trajectory of the vibrating cylinder in the (X, Y ) plane for three values of Reynolds numbers is shown in Fig. 3. The trajectories are more or less elliptic for Re = 1.5 × 105 and 3.0 × 105 . This indicates that the in-line oscillation frequency is close to that of the cross-flow. As seen from Fig. 5(b) the values of f ∗ for cross-flow and in-line oscillations are close to each other. The 2S mode of vortex shedding is observed for all three Re. As seen from Fig. 4a– c, two vortices of opposite signs, marked V1 and V2 in the instantaneous pressure iso-contours, are shed during one cycle of oscillation. This suggests that at U ∗ = 5, the system is on initial branch of the lock-in state. In the study of Williamson and Govardhan [1], the VIV response of a cylinder in lock-in regime is characterized into three branches with respect to reduced flow speed, namely initial branch, lower

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0.4

0.4

0.4

0.0 -0.4 -0.8

Y/D

(c) 0.8

Y/D

(b) 0.8

Y/D

(a) 0.8

0.0 -0.4

-0.1

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-0.8 -0.4

0.1

0.0

-0.2

X/D

0.0

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0.4

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-0.1

X/D

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X/D

Fig. 3 VIV of a cylinder: (X, Y) trajectories at a Re = 5.0 × 104 , b Re = 1.5 × 105 , and c Re = 3.0 × 105 . (a) 2S

(b) 2S

V1 V2

(c)2S

V1

V2

V2

V1

Fig. 4 VIV of a cylinder: instantaneous pressure iso-contours a Re = 5.0 × 104 b Re = 1.5 × 105 and c Re = 3.0 × 105 at an instant when the displacement of the cylinder is maximum (a) 0.8

(b) 1.00

0.4 0.2 0.0 4 5.0x10

0.95

A*y

f*

A*

0.6

A*x

f*y f*x

0.90

5

1.5x10

Re

5

3.0x10

0.85 4 5.0x10

1.5x10

5

3.0x10

5

Re

Fig. 5 VIV of a cylinder: variation of a normalized amplitude of cylinder oscillation, A∗ and b frequency ratio, f ∗ with Re

branch, and upper branch. The initial branch is associated with 2S mode of vortex shedding while the upper and lower branch comprise 2P mode [1]. Figure 5 shows the variation of cross-flow as well as in-line amplitude and frequency response with Re. The amplitude of cross-stream oscillation reduces significantly beyond the critical regime. This is manifestation of weakening of vortex shedding during drag crisis. The amplitude of oscillation is relatively large, specially in the in-line direction at Re = 1.5 × 105 . The large amplitude, in both cross-flow and in-line oscillation of the cylinder, is associated with synchronization/lock-in, wherein the vibration frequency is close to the natural frequency of the system. This phenomenon is clear from Fig. 5b where both the frequency ratios f y∗ and f x∗ are close to unity.

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3 Conclusions Vortex-induced vibration (VIV) of an elastically mounted cylinder in the regime of drag crisis is studied. In this regime, the drag coefficient reduces rapidly with increase in Re. Three-dimensional computations have been carried out using a stabilized finite element method. Sigma subgrid-scale model is employed for large-eddy simulations. The present computations capture the phenomenon of drag crisis very well. The computations show that the vortex shedding weakens during the drag crisis. This leads to decrease in the amplitude of cross-stream oscillation of cylinder. The phenomenon of lock-in is observed for both cross-flow and in-line motion of the cylinder. The lock-in is associated with 2S mode of vortex shedding. Acknowledgements Computations were carried out at HPC facility at Indian Institute of Technology Kanpur.

References 1. Williamson CHK, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36:413–455. https://doi.org/10.1146/annurev.fluid.36.050802.122128 2. Amman OH, Von Kármán T, Woodruff GB (1941) The failure of the Tacoma Narrows bridge. Technical report, Washington, DC http://resolver.caltech.edu/CaltechAUTHORS:20140512105559175 3. Williamson CHK, Govardhan R (2008) A brief review of recent results in vortex-induced vibrations. J Wind Eng Ind Aerodyn 96:713–735. https://doi.org/10.1016/j.jweia.2007.06.019 4. Dahl J, Hover F, Triantafyllou M, Oakley O (2010) Dual resonance in vortex-induced vibrations at subcritical and supercritical Renolds numbers. J Fluid Mech 643:395–424. https://doi.org/ 10.1017/S0022112009992060 5. Raghavan K, Bernitsas MM (2011) Experimental investigation of Reynolds number effect on vortex induced vibration of rigid circular cylinder on elastic supports. Ocean Eng 38(5–6):719– 731. https://doi.org/10.1016/j.oceaneng.2010.09.003 6. Narendran K, Murali K, Sundar V (2015) Vortex-induced vibrations of elastically mounted circular cylinder at Re of the O(105 ). J Fluids Struct 54:503–521. https://doi.org/10.1016/j. jfluidstructs.2014.12.006 7. Achenbach E (1968) Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 106 . J Fluid Mech 34(4):625–639. https://doi.org/10.1017/ S0022112068002120 8. Mittal S, Behara S (2011) Transition of the boundary layer on a circular cylinder in the presence of a trip. J Fluids Struct 27(5-6):702–715. https://doi.org/10.1016/j.jfluidstructs.2011.03.017 9. Singh SP, Mittal S (2005) Flow past a cylinder: shear layer instability and drag crisis. Int J Numer Meth Fluids. 47(1):75–98. https://doi.org/10.1002/fld.807 10. Chopra G, Mittal S (2017) The intermittent nature of the laminar separation bubble on a cylinder in uniform flow. Comput Fluids 142:118–127. https://doi.org/10.1016/j.compfluid. 2016.06.017 11. Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95(2):221–242. https://doi.org/10.1016/0045-7825(92)90141-6

Numerical Studying the Dynamic Stall of Reverse Flow Past a Wing Biao Wang and Zhixiang Xiao

Abstract The delayed detached-eddy simulation with adaptive coefficient (DDESAC) and original DDES method are applied to simulate the dynamic stall of the reverse flow past a finite-span wing with NACA0012 airfoil. The numerical results match the measurements well. DDES-AC performs better than the original DDES, especially for the second dynamic stall. Keywords DDES-AC · Dynamic stall · Reverse flow

1 Introduction The dynamic stall of rotors has an important effect on the aerodynamic performance of the helicopter. At the same time, the dynamic stall often leads to unsteady loads and vibrations. In fact, for the high-speed helicopter, its rotor partly works in the reverse flow state. It means that the traditional trailing edge is indeed the leading edge. The reverse dynamic stall is so different from that of forward flow. Then, it is required to deeply study the reverse flow at dynamic stall. Dynamic stall of reverse flow was experimentally and numerically studied for the aerodynamic and dynamic characteristics of a UH-60A operating at high advance ratios [1–3]. Wang et al. [4] applied improved delayed detached eddy simulation (IDDES) to simulate the reverse flow and effectively control the reverse flow by undulating leading edge. Compared to a large number of studies on the oscillating wing at forward state [5–9], fewer preliminary researches on the dynamic stall of reverse flow can be found. Lind et al. [10–13] experimentally measured the static reverse flow about the unsteady aerodynamic loads, Reynolds number effects, vortex shedding and mean aerodynamic forces. On the basis of static flow, they [14] also investigated the dynamic stall at reverse state. Hodara et al. [15] applied the hybrid method to simulate the pitching oscillating motion past the reverse NACA-0012 airfoil. Both B. Wang · Z. Xiao (B) School of Aerospace Engineering, Tsinghua University, Beijing 100084, China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_31

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experimental and computational results reveal that the flow separation at the sharp leading edge can lead to the early formation of a dynamic-stall vortex. Here, the dynamic stall of reverse flow past the finite-span wing is simulated by DDES-AC (adaptive coefficient) and original DDES. The dynamic stall is hoped to be explored.

2 Effects of Turbulence Models The pitching oscillation motion is simulated by our in-house code, called as Unsteady NavIer-STockes solver (UNITs). It is a finite volume solver and has been successfully validated and applied to simulate the oscillating forward flows past a wing [16]. DDES model is an advanced DES-type models, reducing the computational cost when predicting the unsteady turbulent flows at high Reynolds number. DDES-AC overcomes the excessive protection for the boundary layer by DDES. Owing to the effective reduction of the modelled eddy viscosity, the shear layer instability obtained by using DDES-AC is observed to be much more upstream [16]. To some extent, DDES-AC alleviates the “grey area” problem. This model and its detailed formulations can be found in our previous work [16]. Here, we will focus on the dynamic stall of reverse flow. The measurements by Lind et al. [14] are used to compare with present computational results. The Mach number is 0.1 and the Reynolds number based on the chord length is Re = 3.3 × 105 . The rotating center is at three-quarter chord (x/C = 0.75). The angle of attack (AoA) is determined by α = 8.9° + 9.9°sin(2kt) with reduced frequency k of 0.16. In the present simulations, 6000 steps in a pitching period are adopted to reduce the phase-averaged errors and to be adepquate for the vortex shedding frequencies. The computational grid is a C-type one, shown in Fig. 1. The far-field boundary is 20C (chord). The first cell height near the wall is 5 × 10−5 C to guarantee their y+ less than 1.0. Owing to the maximum AoA of 18.8°, the neaarly isotropic grids on the leeward side are clustered approximate 0.5C over the airfoil to capture the small-scale structures. The spanwise length is 2C with equal interval of 250 cells. Then, the total grid cells are 14 million.

Fig. 1 Near-field grids and comparison of the phase-averaged aerodynamic forces

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The original DDES and DDES-AC models are applied to simulate the dynamic stall of reverse flow. Figure 1 presents the comparisons of forces in a pitching cycle, which are phase-averaged for five cycles, among the measurements, DDES and DDES-AC. DDES overestimates the peak of C L (5.8%), and cannot capture the second peak of C L . DDES-AC decrease the difference of CL between the measurements and simulations, especially in the first and second stall process. For the coefficients of CD , DDES and DDES-AC performs similar. Accordingly, DDES-AC performs better. To demonstrate the difference between the two models, the instantaneous flow fields, such as Q criterion, spanwise vorticity and streamlines at different phases are presented in Fig. 2. When the upstroke AoA is 13.7° (Fig. 2a, b), both DDES-AC and DDES models capture the strong primary dynamic stall vortex (PDSV). When the upstroke AoA is 18.6°, nearly equal to the maximum AoA, the PDSV by DDES-AC begins to breakdown, which causes the decrease of lift. However, PDSV by DDES has not broken yet, and its strength is still very large. After the first dynamic stall (the downstroke AoA is 16.5°), the TEV becomes so large that the PDSV does not shed from the surface for DDES. But for DDES-AC, the TEV is already completely shedding from the surface and the SDSV forms. The SDSV by DDES-AC is not as large as the PDSV by DDES at the moment, so that the lift by DDES is also larger than that of by DDES-AC.

(a) Spanwise averaged Cp

(b) Spanwise averaged spanwise vorticity and streamline Fig. 2 Comparison of Cp and Spanwise vorticity

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When the downstroke AoA is 13.7°, the SDSV evolves to the downstream of the wing. The SDSV by DDES-AC is more downstream than that by DDES. At the same time, the former one is closer to the upper surface of the wing than the latter one and the flow speed in the SDSV region by DDES-AC is larger than that by DDES. Both of these factors lead to lower pressure on upper surface and larger lift. In summary, the breakdown and shedding of PDSV by DDES is delayed, which causes the late generation or diminishing of SDSV. At the same time, the SDSV by DDES-AC is closer to the wall than that by DDES. The strong “grey area” of DDES is the reason for the vanishing of second dynamic stall. The shear layer instability from the sharp leading edge by DDES is too downstream, which causes the phase hysteresis to be larger. Fortunately, DDES-AC improves the prediction capability from the “grey area” problem [15], and then the numerical dynamic process is closer to the measurements than DDES.

3 Dynamic Stall Process In this section, the dynamic stall of reverse flow is briefly discussed. It generally behaves similar with that of forward flow. For both the reverse and forward flows, the large-scale dynamic stall vortex forms and convects over the upper wing, which leads to the nonlinear loads. Differently, two dynamic stalls, whose mechanisms are very different, in one pitching cycle can be observed for the reverse flow. The first dynamic stall occurs in the pitching up process near the maximum AoA, whose mechanism is similar with the static stall. When AoA increases, the leadingedge vortex sheds from the sharp leading edge over the whole upper surface, resulting in a significant decrease of lift coefficients. Conversely, the second dynamic stall occurs in the pitching down process, with decrease of AoA. It is mainly caused by the SDSV. Three snapshots of SDSV in the pitching down process are shown in the Fig. 3. At the AoA of 18.3°, a new leadingedge vortex (SDSV) can be observed near the leading edge. The above PDSV is far away from the wing surface, and a TEV is generated at the trailing edge. The flow over the wing is dominated by the vortex near the trailing edge. When the AoA is

Fig. 3 Development and evolution PDSV and SDSV at five phases

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decreased to 16.5°, the TEV sheds from the wing surface and the leading-edge vortex mentioned above evolves to 30%C. The large-scale vortices and massive separation lead to small lift. As the AoA is further decrease to 8.9°, the SDSV evolves to the trailing edge and will shed from the wing surface to the wake. Then the second dynamic stall happens and the lift becomes smaller. The development speed of SDSV is slower than the oscillating speed, leading to the rapid decrease of vortex lift. This is the main reason for the second dynamic stall.

4 Conclusions The dynamic stall of reverse flow past a finite-span wing is simulated by DDES-AC and DDES models. Owing to reduction of the “grey area” from the shear layer to fully developed turbulence, DDES-AC performs better than the original DDES. The mechanism of two dynamic stalls in one pitching cycle is different. The primary dynamic stall is the same with static stall. The development speed of SDSV is slower than the oscillating speed, leading to the second dynamic stall. Acknowledgements The authors would like to thank the National Natural Science Foundation of China (Grant Nos. 91441202, 91852113 and 11772174) and the National Key Research and Development Program of China (Grant No. 2019YFA0405302 and 2016YFA0401200), and express our gratitude to Tsinghua National Laboratory for Information Science and Technology for computation resources.

References 1. Datta A, Yeo H, Norman TR (2013) Experimental investigation and fundamental understanding of a full-scale slowed rotor at high advance ratios. J Am Helicopter Soc 58(2):1–17 2. Potsdam M, Datta A, Jayaraman B (2016) Computational investigation and fundamental understanding of a slowedUH-60A rotor at high advance ratios. J Am Helicopter Soc 61(2):1–17 3. Potsdam M, Yeo H, Ormiston RA (2013) Performance and loads predictions of a slowed UH-60A rotor at high advance ratios. In: 39th European rotorcraft forum 4. Wang B, Liu J, Li QB, Yang YJ, Xiao ZX (2019) Numerical studies of reverse flows controlled by undulating leading edge. Sci China Phys Mech Astron 62(7):974712 5. Corke TC, Thomas FO (2015) Dynamic stall in pitching airfoils: aerodynamic damping and compressibility effects. Annu Rev Fluid Mech 47:479–505 6. Costes M, Richez F, Pape AL, Gavériaux R (2015) Numerical investigation of threedimensional effects during dynamic stall. Aerosp Sci Technol 47:216–237 7. Visbal MR (2011) Numerical investigation of deep dynamic stall of a plunging airfoil. AIAA Journal 49(10):2152–2170 8. Akbari MH, Price SJ (2003) Simulation of dynamic stall for a NACA 0012 airfoil using a vortex method. J Fluids Struct 17(6):855–874 9. Carr LW (2009) Progress in analysis and prediction of dynamic stall. J Aircraft 25(1):6–17 10. Lind AH, Jones A (2016) Unsteady airloads on static airfoils through high angles of attack and in reverse flow. J Fluids Struct 63:259–279

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11. Lind AH, Smith LR, Milluzzo JI et al (2016) Reynolds number effects on rotor blade sections in reverse flow. J Aircraft 53(5):1248–1260 12. Lind AH, Jones AR (2015) Vortex shedding from airfoils in reverse flow. AIAA J 53(9):2621– 2633 13. Lind AH, Lefebvre JN, Jones AR (2014) Time-averaged aerodynamics of sharp and blunt trailing-edge static airfoils in reverse flow. AIAA J 52(12):2751–2764 14. Lind AH, Jones AR (2016) Unsteady aerodynamics of reverse flow dynamic stall on an oscillating blade section. Phys Fluids 28(7):1–17 15. Hodara J, Lind AH, Jones AR, Smith MJ (2016) Collaborative investigation of the aerodynamic behavior of airfoils in reverse flow. J Am Helicopter Soc 61(3):1–15 16. Liu J, Zhu WQ, Xiao ZX, Sun HS, Huang Y, Liu ZT (2018) DDES with adaptive coefficient for stalled flows past a wind turbine airfoil. Energy 161:846–858

Drastic Changes of Turbulence in the Ignition Process of an n-Heptane/Air Mixture Takashi Ishihara and Ryousuke Kuno

Abstract Two-dimensional turbulent combustion with rapid temperature and pressure growth in the ignition process of a homogeneous n-heptane/air mixture is studied by high-resolution direct numerical simulations (DNSs) of the flow field of the mixture with up to 20482 grid points. The DNSs show that the turbulent flow mixes the temperature field so that it affects on the ignition delay. The DNSs show also that the rapid temperature and pressure growth due to the heat release at ignition makes drastic changes in the turbulent velocity field, especially in its compressible component, and causes pressure oscillations in some cases. Keywords Turbulence · Ignition process · Pressure oscillations · n-heptane/air mixture · DNS

1 Introduction In recent years, environmental and energy issues have been a topic of high interest. For combustion engines, it is required to improve the thermal efficiency and reduce the environmental load. In this context, Homogeneous Charge Compression Ignition (HCCI) engine is expected to satisfy these requirements. However, it is still difficult to control its self-ignition process in turbulent combustion. An understanding of the physics of the autoignition process of premixed gases in turbulent flow in HCCI engines is important for the control of the autoignition process. With the recent development of supercomputers, the understanding of combustion physics by the use of direct numerical simulations (DNSs) of turbulent combustion has been advanced (e.g. see Ref. [1]). However, in general, the DNS of turbulent combustion is difficult because in turbulent combustion, phenomena of significantly T. Ishihara (B) Okayama University, Okayama 700-8530, Japan e-mail: [email protected] R. Kuno Nagoya University, Nagoya 464-8603, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_32

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different time scale and spatial scale as well as a great amount of chemical reactions are mixed. Therefore, not all combustion phenomena have been realized by the DNSs. We developed a direct numerical calculation (DNS) code of the ignition process of an n-heptane/air premixed gas and used it to investigate the role of turbulence in the auto-ignition process. As a result, we found that the mixing of temperature field by turbulent flow affects the progress of low temperature oxidation reaction, and as a consequence, turbulence works to delay the average self-ignition time. However, in these numerical simulations, computations beyond the end of the main ignition were difficult (all of the computations diverged at the time of main ignition). Recently, we improved the code by using a new parallel solver for high-resolution differential scheme and checked the convergence of the numerical solutions by changing space and time steps. As a result, although the area size of the previous computation was as small as 4 mm, it became possible to expand it to 16 mm and to calculate efficiently in the improved code. Using the newly developed code, we investigate the turbulence intensity dependency of n-heptane self-ignition process. We found that, when the size of the calculation area is large and the initial turbulence intensity is weak, a pressure-vibration phenomenon due to the generation of pressure wave at the time of auto-ignition was realized by the our DNS. In this paper, we report how turbulence is greatly modified by the ignition process by investigating the compressible and incompressible components of the energy spectra.

2 DNS of the Ignition Process of a Compressed n-Heptane/Air Mixture N-heptane is one of the primary components of gasoline. One of the important characteristics of the auto-ignition process of an n-heptane/air mixture is the low temperature oxidation reaction accompanied by heat release before ignition. Since the number of chemical species and reactions is huge, the large-scale three-dimensional DNS using a detailed reaction mechanism of the n-heptane/air mixture is still challenging. In our DNS, full compressible Navier-Stokes, total energy, species and mass continuity equations are numerically solved under periodic boundary condition in a two-dimensional space. We adopt a reduced chemical mechanism which was developed by Tsurushima [2] to well reproduce the low-temperature oxidation process of the n-heptane air mixture. Chemkin Thermodynamic Database was used to calculate enthalpy, entropy, and volume specific heat of each chemical species. We set the initial pressure of 4.0 MPa, the equivalence ratio of 0.5, the average temperature of 780 K, and the temperature fluctuation RMS of 9.4 K. We used random incompressible flow fields as the initial velocity fluctuations, for which we set amplitude and spectrum (and integral length scale). We used an eighth-order compact difference scheme for spatial derivatives [3] and a fourth-order Runge-Kutta method for time integration, in which the terms related to

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Fig. 1 A comparison of the contour plots of heat release rate at t = 0.42 ms: (Left) 8th-order central difference scheme with 2562 grid points, (right) 8th-order compact difference scheme with 5122 grid points. The size of the computational domain is 4 mm × 4 mm. We have confirmed that almost the same result as the right is obtained by the computation using 8th-order compact difference scheme with 10242 grid points

the chemical reactions were implicitly treated [4]. To eliminate numerical instability occurring in high wavenumber modes, we used an eighth-order implicit low-pass filter [5]. In a series of our DNSs, we have compared the numerical results obtained by an eighth-order central difference scheme with those by an eighth-order compact difference scheme by changing the number of grid points. Then, we have confirmed that the convergence of the numerical solutions is obtained by increasing the number of grid points in the eighth-order compact difference scheme and have found that the grid size should be as small as 7.2 × 10−3 mm [6]. (Figure 1 shows a sample of the numerical convergence.) Recently, we could improve the DNS code by using an efficient parallel algorithm [7] for the calculation of the eighth-order compact difference. As a result, we could increase the number of grid points to perform DNS in larger domain sizes. In addition, by adjusting time steps manually at the ignition time, we could simulate beyond the ignition time. To see the parameter dependence of the results, we conducted DNSs with different domain sizes (L) from 4 mm to 16 mm and different amplitudes of the initial velocity fluctuations (u ) from 4 to 16 m/s. The number of grid points for the largest domain (L = 16 mm) is 20482 .

3 Results Figure 2 shows a typical time history of spatial average temperature. The ignition delay is defined as the time during which the spatial average of the temperature rise 400 K above the average initial temperature. The ignition delay depends on both the

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Fig. 2 Typical time history of spatial average temperature

velocity and temperature fields. We confirmed that the dependence is not inconsistent with previous studies (e.g., [8–10]). In the case of L = 16mm (large domain) and u = 4m/s (small velocity fluctuation), we observed pressure oscillations due to propagating pressure waves after the ignition at t ∼ 0.7ms. The propagating pressure waves in our DNS are strongly affected by the periodic boundary condition. However, it was suggested that the properties of the pressure oscillations observed in our DNS agree well with those observed in experiments in the literature [11]. Figure 3 shows the time evolution of the incompressible and compressible components of the energy spectrum in this case. As observed in Fig. 3, initially the energy spectrum is dominated by incompressible component, while, after the ignition, the energy spectrum is dominated by compressible component not only at low wavenumbers but also at high wavenumbers. In this case, we observed steep-fronted pressure waves after ignition.

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Initially the turbulence mixes the temperature field which plays a key role in reactions. Then, rapid heat release reactions at ignition makes drastic changes in the turbulent velocity field, especially in its compressible component, and causes pressure oscillations in some cases, depending on flow and temperature conditions. Acknowledgements This study used the computational resources of the K computer provided by the RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (project IDs: hp170264 and hp180226).

References 1. Chen JH, Choudhary A, de Supinski B, DeVries M, Hawkes ER, Klasky S, Liao WK, Ma KL, Mellor-Crummey J, Podhorszki N, Sankaran R, Shende S, Yoo CS (2009) Terascale direct numerical simulations of turbulent combustion using S3D, Comput Sci Discov 2:015001 2. Tsurushima T (2009) A new skeletal PRF kinetic model for HCCI combustion. Proc Combust Inst 32:2835–2841 3. Lele SK (1992) Compact finite difference schemes with spectral-like resolution. J Comput Phys 103:16–42 4. Kennedy CA, Carpenter MH (2003) Additive Runge-Kutta schemes for convection- diffusionreaction equations. Appl Numer Math 44:139–181 5. Shang JS (1999) High-order compact-difference schemes for time-dependent Maxwell equations. J Comput Phys 153:312–333 6. Kuno R, Ishihara T (2018) Direct numerical simulation of compressible turbulence with reactions and rapid temperature growth. In: Proceedings of 15th international conference on flow dynamics, Nov 7–9, Sendai, pp 800–801 7. Mattor N, Williams TJ, Hewett DW (1995) Algorithm for solving tridiagonal matrix problems in parallel. Parallel Comput 21:1769–1782 8. Yoo CS, Lu T, Chen JH, Law CK (2011) Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature inhomogeneities at constant volume: parametric study. Combust Flame 158:1727–1741 9. Luong MB, Yu GH, Lu T, Chung SH, Yoo CS (2015) Direct numerical simulations of ignition of a lean n-heptane/air mixture with temperature and composition inhomogeneities relevant to HCCI and SCCI combustion. Combust Flame 162:4566–4585 10. Saito N, Minamoto Y, Yenerdag B, Shimura M, Tanahashi M (2018) Effects of turbulence on ignition of methane-air and n-heptane-air fully premixed mixtures. Combust Sci Technol 190:452–470 11. Vressner A, Lundin A, Christensen M, Tunestål P, Johansson B (2003) Pressure oscillations during rapid HCCI combustion. In: SAE Paper No. 2003-01-3217

Visualization Observation of Two Phase Flow in Abrasive Supply Tube for Abrasive Injection Jet Y. Oguma, T. Takase, H. Quan, and G. Peng

Abstract Abrasive injection jets (AIJs) are widely used for industrial cutting. It is known that flow pulsation will occur in AIJ with increase of the mass flowrate of abrasive particle supply. Due to the flow pulsation the cutting surface of workpiece becomes rough and the cutting performance of AIJs drops. Previous works reveal that flow pulsation of AIJ is closely related to the fluctuations of abrasive supply to nozzle head. In this work, high-speed camera observation of two-phase flow in abrasive supply tube is conducted using a model abrasive supply system. A straight tube is connected horizontally to a suction chamber and 80 mesh garnet is supplied to by using a sealed abrasive supply chamber. With increases of the mass flow rate of abrasive particles and the distance from the inlet of abrasive supply tube, distinct zones of abrasive particle concentration (dense zone) are observed in the abrasive supply tube. Image analysis reveals that the velocity abrasive particles in dense zones at downstream is faster than that in dense regions at upstream. Thus, dense zones combine while flow downstream along the supply tube. Keywords Abrasive water jet · Gas-solids two-phase flow · PIV

1 Introduction Abrasive injection jets (AIJs) are widely used for industrial cutting, and their cutting capability has been investigated extensively from different viewpoints [1, 2]. It is known that flow pulsation will appear in AIJ when the mass flowrate of abrasive particle supply increases to a certain amount [3, 4]. Due to the jet flow pulsation, the cutting surface of workpiece becomes rough, and the quality of cutting drops Y. Oguma (B) · T. Takase · H. Quan · G. Peng College of Engineering, Nihon University, 1 Nakagawara, Tokusada, Tamura-Machi, Koriyama, Fukushima, Japan e-mail: [email protected] H. Quan College of Energy and Power Engineering, Lanzhou University of Technology, No. 287 Langongping Road, Qilihe District, Lanzhou, Gansu, People’s Republic of China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_33

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also. Previous works reveal that flow pulsation of AIJ is closely related to the fluctuations of abrasive supply to nozzle head [5]. However, the mechanism of abrasive transportation fluctuation occurring in the abrasive supply tube is still unclear. In this work, observation and PIV of air–solid-particle two-phase flow in abrasive supply tube are conducted by using a simplified model abrasive supply system in order to clarify the motion of abrasive particles in the abrasive supply tube of AIJs.

2 Experimental Apparatus and Method Figure 1 shows the model abrasive supply system used to observe the motion of abrasive particles in the tube. A straight antistatic polyurethane tube is connected from a sealed supply chamber to a suction chamber. The abrasive particles adopted is Garnet #80 (ρ a = 4070 kg/m3 ) whose diameter is about 150–180 µm. Mass flow rate of abrasive particles is adjusted in the range of M a = 20–217 g/min. The pressure in the suction chamber is set to 81 kPa. The two-phase flow of abrasive particles and air in the supply tube is photographed using a high speed CMOS camera together with a halogen light source. The position of camera observation is arranged within the range of x = 500–4000 mm. The instantaneous velocity component of x, y is defined as u, v respectively.The photographing frame rate of camera is set at 2000 and 10,000 fps for abrasive particles flow photography and PIV respectively, and the exposure time is 2.0, 1.25 µs. The observation area is 56 × 15 mm. At each observation position, the number of taken images of flow observation and PIV of the abrasive is 20,000 and 5000, respectively. The PIV analysis is carried out using

Fig. 1 Experimental set up of simplified model for abrasive supply system used in AIJs

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Fig. 2 Variation of air flow rate Qair in the abrasive supply tube with the abrasive mass flow rate M a

the direct cross correlation method incorporating sub-pixel analysis by Gaussian distribution [6].

3 Results and Discussion 3.1 Variation of Air Flow Rate in Abrasive Supply Tube Figure 2 shows the variation in air flow rate Qair in the abrasive supply tube with the abrasive mass flow rate Ma . The Qair measured under the condition without abrasive particle supply (M a = 0 g/min) is 30 L/min. The Qair monotonously decreases when M a < 70 g/min and then becomes almost a constant when M a ≥ 70 g/min.

3.2 Flow Pattern and Velocity Distribution of Abrasive Particles Figure 3 shows an example of the instantaneous velocity vectors of abrasive particle overlaid on sequential photographs of two-phase flow in abrasive supply tube taken by high speed CMOS camera. Since the light source is set at the opposite side of High speed CMOS camera, abrasive particles appear to be black in the images. As shown in the figure a distinct zone of abrasive particle concentrated, which is called dense zone, is formed in the tube and it moves downstream sequentially. In addition, abrasive particles scatter at upstream and downstream side of the dense zone and relative sparse zone can be seen in front of dense zone. The instantaneous velocity vectors is calculated by image correlation analysis and its magnitude is defined by V = (u2 + v2 )1/2 . The velocity in abrasive dense zone keeps almost uniform in the y direction, but the velocity in abrasive sparse zone is slower than that in abrasive dense zone and varies in the y direction.

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Fig. 3 Instantaneous velocity vector distributions of abrasive particles around the position of x = 4000 mm when M a = 106 g/min

Figure 4 shows one-pixel images and velocity of abrasive particle arranged in time series. These one pixel images were picked out from a series photographs of a highspeed video file at a prescribed position as shown in Fig. 3 by the yellow line (one

Fig. 4 One-pixel images of abrasive motion and particle velocities at different x coordinates arranged in time series when: a M a = 20 g/min, b 106 g/min, c 217 g/min

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pixel width in the flow direction). The black bands in the image represent the period of dense zone passing through the prescribed position, and the white bands represent the period that sparse zone of abrasive passing through the position. The velocity V of abrasive particles are averaged the velocity vectors on yellow line in Fig. 3. In the case of (a), no dense zone of abrasive particles can be confirmed at each observation position and the abrasive are transported uniformly. The V are fluctuated over time. In Fig. 4b, c black bands of dense zone of abrasive particles can be confirmed and fluctuations in abrasive transportation are demonstrated. The V in dense zones is larger than that in sparse zones and the V in dense zones at downstream of the abrasive supply tube is larger than that in dense zones at upstream. The fluctuation of V in sparse zones decreases with increase of M a . The velocity in each dense zone has fluctuations due to the friction and the fluctuation due to interaction between abrasive particles. As a result, it is considered that dense zones merge gradually to form a large pulsating flow. In addition, since the velocity in sparse zone between dense zones of abrasive particles is far smaller than that in dense zones, the pressure gradient in the abrasive supply tube is not constant and it is considered that the pressure at upstream side of dense zones increases.

3.3 Frequency of Abrasive Dense Zone Formation at Different Positions Figure 5 shows the frequency f Dense of abrasive dense zone appearing at different positions from the sealed supply chamber. When Ma is 106–217 g/min, the frequency of dense zone tends to have a peak at x = 500 mm and then decreases gradually with the distance x. However, when M a = 41, 71 g/min the frequency of dense zone appearing shows a peak at x = 1000 mm around. Fig. 5 Frequencies of abrasive dense zone formation along the tube under different abrasive mass flow rate M a conditions

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According to the results in Figs. 2 and 5, the air flow rate is constant under the condition in M a ≥ 70 g/min which the generation frequency of dense zone is high. In other words, it is considered that the abrasive dense zone is sequentially formed in the abrasives supply tube with the increase of the M a and the Qair decreases.

4 Conclusions Observation and PIV of air–solid-particle two-phase flow in abrasive supply tube are conducted by using a simplified model abrasive supply system in order to clarify the motion of abrasive particles in the abrasive supply tube of AIJs. The main conclusions are given as follows. (1) When the distance from the inlet of abrasive supply tube increases to a certain value distinct zones of abrasive particle concentration occur. (2) The velocity of abrasive in dense zones is larger than that in sparse zones. The velocity of abrasive in dense zones decreases in the stream direction along the tube. (3) The frequency of dense abrasive zone appearing shows a maximum at x = 500 mm when the M a is 106–217 g/min, and then decreases gradually with the distance from the inlet.

Reference 1. Summers DA (1995) Water Jetting Technology, E & FN Spons 2. Momber AW, Kovacevic K (1998) Principles of abrasive water jet machining. Springer, Berlin 3. Geskin ES (1993) Technology of waterjet machining and manufacturing process for the year 2000 and beyond. In: Proceedings of International Symposium. Water Jet Technology, 10th Anniversary of WJTSJ, pp 53–86 4. Shimizu S, Aihara Y, Hiraoka Y (2000) Drilling Capabilities and high speed photograhic observations of abrasive water jets. J Jet Flow Eng 17(1):4–9 (in Japanese) 5. Shimizu S, Ishikawa T, Saito A, Peng G (2009) Pulsation of abrasive injection jet. In: Proceedings of 2009 American WJTA conference and expo, Paper 2-H, pp 59–62 6. Raffel M, Willert C, Wereley S, Kompenhans J (2007) Particle image velocity a practical guide, Springer, Berlin, pp 138–139

Vortex Induced Vibrations With Bi-stable Springs Rameez Badhurshah, Rajneesh Bhardwaj, and Amitabh Bhattacharya

Abstract We report characteristics of Vortex Induced Vibration (VIV) for a cylinder attached to a bi-stable spring, which, unlike linear springs, has two potential wells. We use a Wake Oscillator Model (WOM) as well as an in-house CFD code to study this problem. For small inter-well separation, we observe a widening of the range of reduced velocities over which lock-in occurs. To explain this result, we formulate a theory based on the kinetic energy budget of the cylinder, which balances the rate of energy production and energy dissipation. For harmonic oscillations and large mass ratio, the theory suggests the existence of a universal relationship between the amplitude and frequency of the structure during the lock-in, which we term as the Equilibrium Constraint. Preliminary CFD simulations support the existence of the Equilibrium Constraint. Keywords Fluid-structure interaction · Wake oscillator model · Bistable springs · Vortex shedding

1 Introduction Experiments on VIV of mono-stable non-linear softening as well as bi-stable springs [1, 2] indicate that the non-linearity in springs can cause lock-in to occur over a larger range of reduced velocities compared to linear springs. Bistable spring exhibit double-well force potential, during the transition from one stable state to other, larger amplitudes may exist over a broad frequency bandwidth. However, researchers have not been able to clearly attribute a reason for the increase in the range of lock-in when R. Badhurshah · R. Bhardwaj · A. Bhattacharya (B) Department of Mechanical Engineering, IIT Bombay, Mumbai, India e-mail: [email protected] R. Badhurshah e-mail: [email protected] R. Bhardwaj e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_34

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the elastic structure exhibits bi-stability. In this work, we focus on characterizing VIV of a cylinder attached to bi-stable springs. Unlike linear springs, the elastic potential energy of bi-stable springs is characterized by two stable minimas separated by a nondimensional distance proportional to β. In the presence of VIV, the bi-stable cylinder may undergo single-well, double-well or intermittent oscillations, depending on the initial displacement and fluid forcing. We propose a theoretical model, based on the balance of production and dissipation of energy, to explain how bi-stability in springs leads to a wider lock-in regime. We then show results from two types of numerical simulations to verify the proposed theory. First, a lower-order model, namely Wake Oscillator Model (WOM), is used to study the effect of bistable springs on VIV of cylinder [3]. We next use CFD simulations based on Immersed Boundary Method (IBM) to study the problem at Reynolds number of 150 and a high solid-to-fluid mass ratio of 20.

2 Wake Oscillator Model (WOM) The Wake Oscillator Model (WOM) [3] is a widely used 2 degree-of-freedom model for VIV around a cylinder attached to springs. The model generates a time series (in time T ) for the transverse displacement Y (T ) and the fluid lift force coefficient C L (T ) of a cylinder with mass m undergoing VIV in the presence of a uniform flow velocity U . The important dimensional scales in this problem are the angular frequency of vortex shedding f = 2π f vs , diameter of the cylinder D, density of the fluid ρ, and RMS (Root mean squared) value of lift force for stationary cylinder, C L0 . Here f vs is the vortex shedding frequency of a stationary cylinder. The non-dimensional displacement, time, cylinder mass and lift force are given as y = Y/D, and t = T f , μ = m/(ρ D 2 ) and q = 2C L (t)/C L0 respectively. The governing equations for y(t) and q(t) in the WOM for a general spring are : du s γ y˙ + = Mq y¨ + 2ξ δ + μ dy

(1)

q¨ + (q 2 − 1)q˙ + q = A y¨

(2)

Here u s (y) = Us (Y )/(D 2 m2f ) is the non-dimensional spring potential, and Us (Y ) is the dimensional spring potential, given by: Us (Y ) =

1

KY2 for Linear Spring −k1 Y 2 + k3 Y 4 for Bi-stable Spring 2

(3)

where K is the linear spring constant, while k1 and k3 are the spring constants of the bi-stable spring [4]. The location of the stable points for the bistable spring are Y0 = ±(k1 /(2k3 ))1/2 , and the linearized spring constant at these stable points is given as K = −4 k1 . The non-dimensional separation of the stable points is β = |YD0 | .

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The √ characteristic natural frequency (s ) the spring mass system is given as s = K /m. The terms, A, M, and γ are various parametric and coupling constants. rs , while the nonThe non-dimensional structural damping is represented by ξ = 2m s rf dimensional fluid damping is given by γ = f ρ D . In Eq. 1, δ = s / f is reduced angular frequency, while M = C L0 /(16π 2 St 2 μ) is the lift coefficient. Here μ = m/(ρπ D 2 ) is the mass ratio and St = f vs D/U is the characteristic Strouhal number for vortex shedding.

3 Results from WOM Simulations We have performed simulations of the WOM at a mass ratio of μ = 20 for linear and bi-stable springs, for a range of reduced velocity Ur = 2πU/(s D). Since we were quite interested in exploring the nature of double well oscillations for VIV with bistable springs, therefore we initiate all simulations with a large initial displacement y(0). We observe that (Fig. 1a), for VIV with linear spring, the maximum amplitude of oscillation, a0 , is large only over a limited range of reduced velocity (4.5 < Ur < 6.5), whereas, for bi-stable spring, the oscillations can be large over a much wider range of reduced velocity, especially for β 1 (e.g. lock-in range is 2 < Ur < 15 for β = 0.05). To understand the widening of lock-in range in the presence of bistable springs, we present a theory, which invokes a new “Equilibrium Constraint” via the kinetic energy equation of the cylinder and lock-in of the fluid with the structure.

4 Theory: Predicting Lock-In Range for VIV 4.1 “Equilibrium Constraint” for VIV We assume that during high amplitude oscillations, the fluid locks in with the structure, which is a good assumption for high mass ratios. During lock-in, the structure and the wake both undergo harmonic oscillations y(t) = y0 + a0 cos(ωt) and q = q0 cos(ωt + ψ) respectively, where ψ is the phase lag between the displacement and lift force, while ω is the non-dimensional structure frequency. Starting with the structure equation (Eq. 1), and applying zero external damping (i.e. ξ = 0), we then multiply both sides of the structure equation with y˙ and average over an oscillation cycle to obtain the following expression, which is essentially the average budget of the kinetic energy equation of the cylinder : γ μ

a0 ω = M q0 (a0 , ω) sin ψ(a0 , ω)

(4)

The above equation is termed as “Equilibrium Constraint” (EC), since it represents a balance of energy production rate (on the RHS) and dissipation rate (on the LHS).

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Here we have assumed the existence of a functional form q0 (a0 , ω) and ψ(a0 , ω) for the amplitude of the wake variable and the phase lag. These functions are obtained from the WOM by using the data from simulating one-way coupled wake equation (Eq. 2), in which y = a0 sin(ωt) is imposed, and a0 , ω are varied over a range of values. The EC may be denoted as P(a0 , ω) = 0, where P(a0 , ω) is the difference of the LHS and RHS of Eq. 4. Interestingly, the EC is independent of the type of spring used, since the parameters of the spring potential are not present in Eq. 4.

4.2 Intersection of EC with Natural Frequency Curves For the discussion in this paragraph, we will denote natural frequency of the springmass system in vacuum as n , and the non-dimensional natural frequency as ωn = n / f . For large mass ratio, during lock-in, we expect the solid to oscillate with its natural frequency ω = ωn . Thus, the existence of the EC P(a0 , ω) = 0 implies that, for any given reduced velocity Ur , obtaining the natural frequency ωn allows us to in turn specify a0 . For the linear spring, it is easy to show that ωn = 1/(St · Ur ). For bi-stable springs, it can be shown that ωn = Fn∗ (a0 /β)/(St · Ur ), where Fn∗ (x) captures the dependence of the natural frequency on the maximum amplitude of oscillation [5]. Using simulations of the spring-mass system in vaccum, we are able to obtain the following fit for Fn∗ (x): Fn∗ (x)

=

1 −√0.5x 2 − 10x 4 for 0 < x√< 0.6 x 2 − 1.6 for x > 2

√

2−1

(5)

The two different ranges above correspond to single√well oscillations (x = a0 /β < √ 2 − 1) and double-well oscillations (x = a0 /β > 2). Fig. 1b, c shows the intersection points of the EC with the natural frequency curves for VIV with linear and a bi-stable spring (β = 0.05) respectively. It is clear that, due to the form of the natural frequency curves, VIV with bistable springs leads to a larger range of Ur over which lock-in can occur, thus explaining the results from our WOM simulations. Fig. 1a shows good qualitative agreement between the a0 versus Ur curves predicted by the above theory with the results from WOM simulation.

5 Results from CFD Simulations We numerically simulate VIV of a cylinder attached to linear as well as bi-stable springs using an in-house CFD code based on immersed boundary method (IBM). The length and width of the computational domain is 65D × 40D with 257 × 257 nodes. The cylinder is allowed to only move in the spanwise (y) direction. Nonuniform grid with minimum grid size 0.025D was used to perform the simulations.

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Fig. 1 a Plots of a0 vs Ur for VIV with linear spring (red) and bi-stable spring with β = 0.05 (blue). Plots are from WOM (dashed) and theory (solid). b Plot for estimating amplitude for a given Ur for VIV of cylinder attached with linear spring at lock-in condition. Solid (red) curve shows the zero isocontour for P(a0 , ω) = Cγ a0 ω − Mq0 (a0 , ω) sin ψ(ω, a0 ), referred as the EC. The dashed blue lines are the natural frequency curves ωn = 1/(St · Ur ) for the linear springs. c Schematic plot for estimating a0 for a given Ur for VIV of cylinder attached with bi-stable spring during lockin (β = 0.05). The dashed (magenta) and dotted (blue) lines shows the natural frequency curves ωn = Fn∗ (a0 /β)(StUr )−1 for single well and double well oscillations respectively 1.15 1.1 1.05

0.7 St.Ur * = n

Linear Bistable

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Fig. 2 Figure shows lock-in of structure frequency with either natural frequency or structure frequency using CFD simulations (left) and a0 versus ω (right)

Similar to the results from the WOM simulations, we observe a widening of the lock-in range in the presence of bi-stable springs here. Figure 2 (left) shows a lock-in plot, where ω/ωn has been plotted against Ur∗ = 2πU/(n D). Here ω is the structure frequency. The data points on the lock-in plot for bi-stable and linear springs collapse here. The lock-in with natural frequency of the spring occurs over 4.2 < Ur∗ < 6.5; the structure appears to lock-in with the fluid outside this range. Figure 2 (right) shows a0 plotted against ω for simulations with bi-stable and linear springs. Again, the data points appear to show a collapse, supporting the existence of an Equilibrium Constraint curve.

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6 Conclusion In this work, we have shown that during VIV of a cylinder, the presence of a bistable spring can lead to a widening of lock-in regime. To explain this effect, we have presented a theory, in which the average kinetic energy equation of the cylinder has been used. The theory implies the existence of a universal Equilibrium Constraint between the amplitude and frequency of oscillation, which appears to be supported by CFD simulations. The theory developed here may be used to understand the effect of other types of non-linear springs on VIV of bluff bodies.

References 1. Williamson CHK, Govardhan R (2004) Vortex-induced vibrations. Annu Rev Fluid Mech 36:413–455 2. Zhang LB, Abdelkefi A, Dai HL, Naseer R, Wang L (2017) Design and experimental analysis of broadband energy harvesting from vortex-induced vibrations. J Sound Vib 408:210–219 3. Facchinetti ML, De Langre E, Biolley F (2004) Coupling of structure and wake oscillators in vortex-induced vibrations. J Fluids Struct 19:123–140 4. Harne RL, Wang KW (2013) A review of the recent research on vibration energy harvesting via bistable systems. Smart Mater Struct 22:023001 5. Mackowski AW, Williamson CHK (2013) An experimental investigation of vortex-induced vibration with nonlinear restoring forces. Phys Fluids 25(8):087101

Impact of Optimized Trailing Edge Shapes on Noise Generation F. Kramer, M. Fuchs, T. Knacke, C. Mockett, E. Özkaya, N. Gauger, and F. Thiele

Abstract A realistic transonic airfoil at landing speed is optimized for lift achieving a lift increase of 10.4% with minimal changes to the shape. This is realized by a Gurney type flap deformation of the trailing edge. For an efficient process, the optimization uses sensitivity maps generated by an adjoint unsteady RANS flow solver. Using scale-resolving DDES simulations, the lift-only optimized airfoil shape produces around 4 dB more noise than the base shape. The noise is evaluated using a simplification of Curle’s equation. Keywords Optimization · Airfoil · Noise · Sensitivity

1 Introduction Optimized for selected flight states such as cruise, take-off and landing, current wing design on commercial aircraft requires mechanical parts to realize these configurations. This limits the achievable shapes and enforces compromises on the design. Extensive research has been conducted during the last decade to implement deforming morphing wing structures to overcome this limitation [1]. The work in the present paper was conducted within the framework of the EU project “Smart Morphing and Sensing” which combines shape memory alloys for low frequency deformations with distributed piezoelectric fiber actuators for high frequency actuations [2, 5]. The main contribution of the present work is to numerically identify the most efficient placement for such actuators. For an adjoint solver, the costs for the sensitivity evaluation are independent of the number of control faces. It is therefore very efficient for distributed controls [3, 4]. In this paper, such an adjoint solver is applied to F. Kramer (B) · M. Fuchs · T. Knacke · C. Mockett · F. Thiele CFD Software E+F GmbH, Wolzogenstr. 4, 14163 Berlin, Germany e-mail: [email protected] E. Özkaya · N. Gauger Chair for Scientific Computing, TU Kaiserslautern, Kaiserslautern, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_35

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a realistic commercial airfoil closely matching the experimental campaign [2]. The resulting sensitivity maps are used to optimize the shape for lift and thus used to identify efficient locations for the low frequency actuation by a quasi steady approach. The presented optimization approach aims at rapid turnaround times. The focus of the present paper is to quantify the influence of the optimized shape on noise radiation which is a very important side effect to be considered. With the airfoil being placed in a channel, a simplified version of Curle’s equation is presented to evaluate the noise radiation without the need for a complex FWH outside its scope.

2 Numerical Methodology The low frequency deformation is modeled by quasi-steady simulations within a domain matched to the wind tunnel of the corresponding experiments. The computational domain in Fig. 1 demonstrates the total dimensions of the channel L x = 7.7m and L y = 0.712m whereas the chord length of the airfoil is c = 0.7m. Throughout this paper, values are kept dimensional for direct comparison with the experiments. The mesh was generated and morphed using ANSA from BETA CAE Systems and is based on an airfoil geometry provided by the “Institut de Mécanique des Fluides de Toulouse” (IMFT). The angle of attack is fixed to Ao A = 10◦ . For the unsteady RANS lift optimization, the mesh is 2D, consists of 196,000 cells and preserves y + < 1 on most of the airfoil surface. In accordance with the experiments, the Reynolds number is Re = cu in /ν = 106 and the Mach number Ma = u in /a = 0.065 where c = 0.7m is the chord length, u in = 21.5m/s the inflow velocity and a the speed of sound. For the k −ω turbulence model, a turbulent intensity of T U = 0.01 and viscosity ratio of ν/νt = 1 are applied as inflow conditions. All simulations in this study are compressible. The in-house flow solver CFDFlux is a block-structured Finite Volume code solving the Navier–Stokes equations on a co-located grid and with second order accuracy in time and space. It uses a fully-implicit scheme and a pressure-based algorithm with a numerically advanced Rhie and Chow interpolation suitable for sensitive applications such as aeroacoustics. A hybrid wall boundary condition blends smoothly between a low and a high Reynolds boundary condition, relaxing common constraints on the near wall mesh. However, the mesh in the present investigation is designed to resolve the boundary layer with a low Reynolds boundary condition. The sensitivities are calculated by deriving an adjoint solver from the primal solver by discrete adjoint code transformation using software Tapenade [6]. The accuracy of

Fig. 1 Computational domain

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the adjoint solver was verified by comparing with Finite Differences at selected locations. Excessive memory demands of the adjoint solver being caused by storing flow solutions forward in time are avoided by using a two-level checkpointing approach which carefully balances disk and memory usage in a hybrid storage scheme. The noise investigation is performed using DDES on an extruded mesh with L z = 0.4m using 80 cells in the spanwise direction (total mesh size is 15.6 million cells). The spanwise domain extent was chosen to allow decorrelation between the spanwise periodic boundary conditions. However, the flow still features correlated turbulent structures in the wake of the airfoil.

3 Results of the Optimization The optimization was performed for a total of 60 cycles. The corresponding shapes at cycle 21 and 60 are shown in Fig. 2 along with the baseline case. Although the overall shape changed only slightly, the lift increased by 10.6 and 18.0% respectively. This is achieved by mainly two distinctive features: The upper surface moves upwards keeping the flow better attached, and the trailing edge is deformed downwards similar to a Gurney flap increasing the overall circulation. The enlarged view in Fig. 2 (right) demonstrates this Gurney flap type deformation of the trailing edge. The constraints employed during the deformation of the airfoil are designed to preserve an acceptable surface grid. During the progress of the optimization however, the volume grid deforms beyond what can be considered a reasonable grid. Therefore, cycle 21 was picked as optimized shape for the acoustic evaluation featuring a significant lift increase and small overall deformation while satisfying a reasonable grid quality. However, the grid quality is not comparable to a mesh specifically designed for the final shape. The influence of this slightly degraded grid quality and the influence of finer meshes on the following investigation could not be quantified.

Fig. 2 Deformation of the airfoil during optimization. Cycle 21 (red) and 60 (green). Rear part (left), enlarged view on trailing edge (right)

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4 Acoustic Evaluation Compared to common acoustic evaluations of airfoils, the boundary conditions are very close to the airfoil producing massive reflections. Far-field prediction methods are generally not applicable in such setups. However, in order to approximate sound radiation into the far-field, we use the loading noise source term of Curle’s equation. Applying far-field assumptions and neglecting retarded time and rigid body motion leads to Eq. (1), where a0 is the ambient speed of sound, xi the observer position, yi the position of the emitting surface element, n i its unit normal vector, R the distance between observer and surface element, and S the rigid surface. For low Mach and Strouhal numbers, this simplified equation produces reasonably good results compared to a full-featured FWH solution. pload ∼ =

1 4πa0

(xi − yi )n i dp dS R2 dt

(1)

The narrow-band spectrum of an observer vertically below the airfoil at a distance of 100m is shown in Fig. 3. The baseline airfoil shape produces a strong peak around 150 Hz and two harmonic peaks around 450 and 900 Hz. The optimized shape is approximately 8 dB louder at the first two peaks but 11 dB quieter at the third peak. Integrating the spectra for multiple observers around the lower arc, the directivity of the overall sound pressure level in Fig. 4 shows that the optimized shape is around 4 dB louder than the base shape over the whole lower arc. This outcome can be expected for an airfoil which produces more than 10% more lift. How much the

Fig. 3 Narrow-band spectra of the base and the optimized shape for an observer at a distance of 100 m below the airfoil (ϑ = 90◦ )

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Fig. 4 Directivity for the lower arc at a distance of 100m. ϑ = 0◦ is parallel to the mean flow

channel walls influence the result could not be quantified in this study but a similar result is very likely. The objectives lift and noise are therefore somewhat opposing which stresses the need to incorporate noise constraints directly into the optimization.

5 Summary and Outlook The realistic airfoil shape which was optimized for lift only by using sensitivity maps from an adjoint solver produces 10.4% more lift than the base shape. At the same moment, it increases the noise by approximately 4 dB for all lower arc observers. From these findings it can be inferred that the optimization should incorporate noise as objective or at least constraints to keep/reduce noise while increasing the lift. Additionally, this investigation will be extended to an even more realistic multielement airfoil in free flight which would remove the bias from reflections and channel modes present in the current study. Acknowledgements This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 723402 “Smart Morphing and Sensing”.

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References 1. Barbarino S, Bilgen O, Ajaj RM, Friswell M, Inman D (2011) A review of morphing aircraft. J Intell Mater Syst Struct 22(9):823–877 2. Jodin G, Motta V, Scheller J, Duhayon E, Döll C, Rouchon JF, Braza M (2017) Dyamics of a hybrid morphing wing with active open loop vibrating trailing edge by Time-Resolved PIV and force measures. J Fluids Struct 74:263–290 3. Lyu Z, Martins JRRA (2014) Aerodynamic shape optimization of an adaptive morphing trailing edge wing. In: Proceedings of the 15th AIAA/ISSMO multidisciplinary analysis and optimization conference, Atlanta, GA, June 2014, AIAA, pp 2014–3275 4. Nemili A, Özkaya E, Gauger NR, Kramer F, Thiele F (2016) Discrete adjoint based optimal active control of separation on a realistic high-lift configuration. In Dillmann A, Heller G, Krämer E (eds) New results in numerical and experimental fluid mechanics X, pp 237–246. Springer International Publishing, Cham 5. Scheller J, Jodin G, Rizzo KJ, Duhayon E, Rouchon JF, Triantafyllou MS, Braza M (2016) A combined smart-materials approach for next-generation airfoils. Solid State Phenom 251:106– 112 6. Hascoet L, Pascual V (2013) The Tapenade automatic differentiation tool: principles, model, and specification. ACM Trans Math Softw 39(3). https://doi.org/10.1145/2450153.2450158

Camber Setting of a Morphing Wing with Macro-acuator Feedback Control A. Giraud, Cédric Raibaudo, Martin Cronel, Philippe Mouyon, Ioav Ramos, and Carsten Doll

Abstract This paper relates the camber control of a morphing flap actuated by a macro-actuator composed by five electromechanical actuators. Controlling the camber of the flap could provide fuel consumption by reaching specific aerodynamic profiles. Due to their reliability, electromechanical actuators are used for the macroactuator. They are located and integrated to resist to realistic aerodynamic forces. Their control is determinant to ensure the flap mission. Based on a simplified model using Lagrange principle leading to macro-actuator feedback control, the strategy deals with the interconnection of the five electromechanical actuators. Flow simulations are computed around the flap to have more pressure distribution data. Finally, feedback control simulations are provided. Keywords Camber control · Morphing flap · Electromechanical actuation · Feedback control · Aerodynamic force · Flow computation

A. Giraud (B) · M. Cronel · I. Ramos NOVATEM, Toulouse, France e-mail: [email protected] M. Cronel e-mail: [email protected] I. Ramos e-mail: [email protected] C. Raibaudo · P. Mouyon · C. Doll ONERA, Toulouse, France e-mail: [email protected] P. Mouyon e-mail: [email protected] C. Doll e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_36

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1 Introduction In the context of an energy efficiency improvement, especially within more electrical aircrafts, the morphing of structure could provide many benefits [1]. The shape of morphing structures can be optimized to improve their aerodynamic performance [2]. For instance, adaptive morphing flap could reduce aircraft fuel consumption thanks to a shape adaptation to flight conditions. Reducing fuel consumption is a high environmental and economic challenge: 2% of CO2 emissions were due to civil aviation in 2008 [3] and 1 kg of fuel saved represents a 1000$ savings [4]. The work presented in this article is a part of a European project called Smart Morphing and Sensing (SMS), which is a multi-disciplinary upstream project that employs intelligent electro-active actuators that will modify the lifting structure of an aircraft and to obtain the optimum shape with respect to the aerodynamic performance (high lift and low drag). This paper focuses on a specific part of the projet, the design, control and test of a Large Scale (LS) prototype. The LS prototypes will be fully equipped with both integrated sensors and actuators for use in laboratory and windtunnel experiments. The overall goal of this prototype is the design of a flap for shape optimization of realistic full-scale aero structures, in order to increase the aerodynamic performance of the smart wing in a realistic scenario both in terms of aerodynamic loads and structural constraints. The feasibility of this principle has been proved in [5] where Shape Memory Alloy (SMA) actuators were used to control the camber of a small flap. Indeed, SMA actuators properties are particularly suitable for slow motion in high force conditions [6]. However, SMA actuation is not as reliable as electromechanical actuation. Electromechanical actuators (EMA) have many applications in aircrafts [7, 8] and even as primary flight control actuator if reliability is ensured [9] That is why we propose here to focus on an electromechanical actuation for the morphing flap, which as been well detailed in [10], and especially on the camber control of the flap through its actuation system control. The specifications and the designed flap description are first described and the control strategy with flow computations and feedback control simulations are detailed in the second part of the article.

2 Large Scale Prototype for Morphing Flap Description 2.1 Technical Specifications Based on an Airbus commercial aircraft, this section deals with the morphing flap design. The flap profile has been adapted from industrial specifications: 1 m chord and 2 m span. A chordwise loading is specified, equivalent to 1200 daN/m2 of aerodynamic upward forces. An idea of the force distribution is represented in Fig. 1. Only the shape of the flap is adapted to flight conditions, with a morphing profile.

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Fig. 1 Aerodynamic force distribution

The flap profile evolves between two extreme shapes, a high cambered shape and a low cambered shape, as presented in Fig. 2. The proposed solution is detailed below.

2.2 Proposed Solution In order to reach the desired profile, the flap is divided into 6 parts connected with five hinges (Fig. 3). The locations of hinges are determined by optimization, for SMA actuators [11]. Actually, the SMA actuators appear as a smarter way to articulated the flap, but they remain hard to control, to integrate and are not as reliable as EMA. The optimization results with SMA are used for EMA in order to provide a comparison between the two solutions in the future. Then, EMA provide linear forces, using leverage around hinges. A block of five EMA (one for each hinge) forms a macro actuator. To ensure the shape in realistic fligth conditions, four macro-actuators are needed along the flap span, as described in Fig. 4 (the fourth macro actuator is hidden under the wing skin on the figure).

2.3 Actuation System: EMA The EMA design is well documented in [10] and mainly consists in a permanent magnet motor connected to a screw nut through a gearbox as presented in Figs. 5 and 6. The EMA are located to respect the right leverages and to manage space: the macro-actuator (Fig. 7) cannot be larger than 50cm. Indeed, the 2m span flap requires four macro-actuators.

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Fig. 4 Morphing flap with 4 macro-actuators

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Fig. 5 The EMA

Fig. 6 Detailed view of the EMA Fig. 7 The macro-actuator

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3 Modelling of the System and Feedback Control Design From the mechanical draft, a dynamical model of the camber actuation is designed using MATLAB and Simulink. The morphing wing is simplified as 5 strands, connected by pivots around parallel axis. The overall model is presented in Fig. 8. Each strand k is defined by its mass m k , length lk , centre of gravity G k , inertia Jk and articular parameter qk (corresponding to angles expressed in the global referential). Hypotheses are chosen for this simplified model: rotations are considered two dimensional and around parallel axis, strands non-deformable and pivots perfect. The description of the dynamical equilibrium of the system is therefore performed using the Lagrange principle: M(q)q¨ + N (q, q) ˙ q˙ = Fg (q) + Fa (q) + (q)

(1)

with Fg (q) moment of the gravitational force, Fa (q) moment of aerodynamical forces, (q) moment applied by the actuators at the pivot, M(q) inertia matrix and N (q, q) ˙ gyroscopic effects, here neglected due to the slow motion of the morphing wing. A proper knowledge of the aerodynamical forces and moments Fa applied on the morphing wing is crucial and could be challenging. A simulation of the flow over the morphing wing is used here to obtain the pressure distribution for different cambers. Details of the simulation can be found in the SMS project. Minimal and maximal cambers of the wing are presented in Fig. 9. Contributions of the pressure for extrados (wing’s top) and intrados (wing’s bottom) are separated. Positions of the articulations are brought back to the mean line of the wing (obtained as the mean position between extrados and intrados). Forces and moments applied on each articulation, and their center of pressure are eventually obtained from the pressure distribution. A

Fig. 8 Scheme of the simplified morphing wing used for the Simulink simulation

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Fig. 9 Results of the flow simulation for different cambers of the wing, here a minimal and b maximal angles tested

more complete database of simulations will be available soon with a bigger camber deformation for the large scale wing, in order to improve the aerodynamical model. The simplified model of Fig. 8 is then used to design feedback controllers. An objective of angular morphing is fixed by the global flows and pilot demands parameters. The closed-loop control goal is to achieve this objective with precision and speed as in [12]. A proportional-integral-derivative (PID) regulator is first considered as a reference closed-loop controller in order to achieve the performances previously detailed. Preliminary results of the feedback control of the structure are presented on Fig. 10. The full skeleton shows a global convergence of the complete system. Targets of the joint angles are partially or totally reached by the controller. For the next steps of the present study, the full model will be improved by more mechanical and aerodynamical informations. Some specificities of the system could perturb the proper control, like the hysteresis behavior of the EMA and saturations of actuators. A consideration of these phenomena and a more sophisticated approach of the feedback control synthesis will also be considered in order to counter these difficulties.

Fig. 10 Results of the feedback control simulation to achieve target skeleton. a Skeleton evolution w.r.t. time, b evolution of joint angles (full line) compared to the targets (dotted), c aerodynamic torques applied on the joints

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4 Conclusion The full control of the camber was performed by a multidisciplinary approach between mechanics, electronics and automatic science. It allows a global integration of the control in order to fit the camber with specific profiles, allowing a decrease of the drag and, therefore, the fuel consumption.

References 1. Barbarino S, Bilgen O, Ajaj RM, Friswell MI, Inman DJ (2011) A review of morphing aircraft. J intell Mater Syst Struct 22(9):823–877 2. Lyu Z, Martins JRRA (2015) Aerodynamic shape optimization of an adaptive morphing trailing-edge wing. J Aircr 52(6):1951–1970 3. Roboam X, Sareni B, De Andrade A (2012) More electricity in the air: toward optimized electrical networks embedded in more-electrical aircraft. IEEE ind Electron Mag 6(4):6–17 4. Boglietti A, Cavagnino A, Tenconi A, Vaschetto S, di Torino P (2009) The safety critical electric machines and drives in the more electric aircraft: a survey. In: Industrial electronics, 2009. IECON’09. 35th Annual conference of IEEE. IEEE, pap 2587–2594 5. Jodin G, Scheller J, Duhayon E, Rouchon JF, Braza M (2017) Implementation of a hybrid electro-active actuated morphing wing in wind tunnel. In: Solid state phenomena, vol 260. Trans Tech Publications, pp 85–91 6. Jani JM, Leary M, Subic A, Gibson MA (2014) A review of shape memory alloy research, applications and opportunities. Mater Design (1980-2015) 56:1078–1113 7. Gerada C, Bradley KJ (2008) Integrated PM machine design for an aircraft EMA. IEEE Trans Ind Electron 55(9):3300–3306 8. Ziegler N, Matt D, Jac J, Martire T, Enrici P (2007) High force linear actuator for an aeronautical application. association with a fault tolerant converter. In: International Aegean conference on electrical machines and power electronics, 2007. ACEMP’07. IEEE, pp 76–80 9. Giraud A, Ramos I, Nogarede B (2019) An innovative short-circuit tolerant machine for an aeronautical electromechanical actuator. In: More electrical aircraft (MEA 2019), Toulouse 10. Giraud A, Cronel M, Ramos I, Nogarede B (2018) Camber actuation of an articulated wing with electromechanical actuators. In: IUTAM symposium on critical flow dynamics involving moving/deformable structures with design applications, Santorini, Grece. IUTAM 11. Jodin G, Tekap YB, Saucray J-M, Rouchon J-F, Triantafyllou M, Braza M (2018) Optimized design of real-scale a320 morphing high-lift flap with shape memory alloys and innovative skin. Smart Mater Struct 27(11), 115005 (2018) 12. Pierre B, Jean-Pierre R (1993) Analyse et régulation des processus industriels: régulation continue, vol 1. Editions Technip

A Hybrid Dual-Grid Level-Set Based Immersed Boundary Method for Study of Multi-phase Flows with Fluid–Structure Interactions Sagar Mehta, Amitabh Bhattacharya, and Atul Sharma

Abstract A hybrid Dual-Grid Level Set based Immersed Boundary Method (DGLSIBM) for CFD simulation of multiphase flow over a moving immersed body is presented. It aims to provide a relatively simpler yet efficient algorithm to develop and implement for computational analysis of fluid-solid interactions involving welldefined movement of solid structures in three-dimensions. The boundary conditions at the interface of fluid and moving solid are applied directly onto the discrete equations based on the properties of level-sets used to define the interfaces, thus making it easier to implement the scheme numerically, and avoiding case-by-case geometric approach used in Cut-cell or Ghost-Cell Immersed Boundary Method algorithms. The method is validated against data from literature for standard test cases; one such case of water entry of sphere is illustrated. Keywords Level-set method · Immersed boundary method · Multiphase flows · Fluid structure interaction · Moving boundary problem

1 Introduction Several accurate and efficient techniques exist for numerical simulation of multiphase flows and fluid-structure interaction. Any numerical method that attempts to solve such problems should be able to capture the flow physics at the three-phase liquid-solid-gas interface robustly and accurately, even when both interfaces are moving. The traditional Immersed Boundary Methods (IBMs) have proved to be successful in such class of problems to a great extent. The first IBM [1] for simulating fluidstructure interaction in single-phase fluid flow used the non-boundary fitted approach, where submerged solid surface is represented by connected points. The interaction between the fluid, discretized on the Eulerian grid, is accomplished by distributing the nodal forces and interpolating the velocities through an approximated Dirac S. Mehta (B) · A. Bhattacharya · A. Sharma Indian Institute of Technology Bombay, Mumbai, India e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_37

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delta function. However, this method was limited to single-phase fluid-structure interactions involving flexible solids, until [2]. At the same time, variants of immersed boundary method emerged, such as Direct Forcing IBM, Cut-Cell Method, and Ghost cell Method, mentioned in the review [3]. These methods can be applied to both flexible and rigid solids but cannot be easily extended to flows involving moving 3-phase contact lines. In the present work, a hybrid DGLSIBM method is proposed to provide a relatively simpler and easy to implement alternative compared to other standard IBMs.

2 Dual-Grid Level-Set Based Immersed Boundary Method Formally, the computational domain D is divided into fluid F and solid S regions, so that D = F ∪ S (Fig. 1). The various phases can be represented in terms of Level Set x , t) and φ f ( x , t) defined as a smooth signed normal distance function (LS) fields φs ( measured from the solid-fluid and fluid-fluid (liquid-gas) interface respectively. Both the solid and fluid motion is described by a common velocity field u( x , t). x , t) and dynamic viscosity field μ f ( x , t) vary discontinThe fluid density field ρ f ( uously across the liquid-gas interfaces, which make contact angle θc with respect to x ∈ D, while φ f , ρ f and the solid surface (Fig. 1). Note that φs and u are defined for ∀ x ∈ F only. Also, ns and n f are defined as the normal vectors μ f are defined for ∀ x |φ f (x ,t)=0 respectively. pointing towards solid for ∀ x |φs (x ,t)=0 and towards liquid for ∀ The governing equations for the class of problems represented by above schematic are (1) Navier-Stokes equations (Eqs. 1–2) for incompressible multi-phase fluid flow and (2) Level-set equations (Eqs. 3–4) for interface tracking [4]. with body force G Note that, in this work, the velocity of the solid is prescribed for solid-fluid interface, Fig. 1 Schematic of computational domain and spatial discretization

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and hence the algorithm is applicable to one-way coupled FSI problems in the present form. ∇ u = 0

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properties are x , t) = H φ f ρl + 1 − H φ f ρg and μ f ( x , t) =

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2.1 Implementation of BC at the Solid-Fluid Interface The major contribution of the present work lies in the hybrid, yet simplistic, way the boundary conditions at the solid-fluid interface is implemented deriving from the concepts of ghost-cell IBM and properties of LS functions. Let ψ( x , t) be a generic field, representing any flow property or the level-set function. The boundary conditions that are applied at non-diffused solid-fluid interface (∀ x |φs (x ,t)=0 ) for u, p and φ f are: s u = U −∇ p · nˆ s = ρ f

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∇φ f · nˆ s = − cos(θc )

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At any given time t, for a ghost cell center (▲) xg , the gradient of φs is used to find a unit vector nˆ s xg normal to the solid-fluid interface ∂F. By definition, dg = φs |x=x g is the normal distance of xg from the interface. An image point (˛) x f inside the fluid domain is then that it lies at a distance δ = 2 from the found, such ∂F interface i.e. x f = xg − dg + δ nˆ s xg . In contrast to the case-by-case Ghostcell IBM, if the radius of curvature of ∂F is higher than 2 , it is guaranteed that x f is surrounded by only “fluid” cell centers in the present method. This allows a decoupled linear interpolation from these “fluid” cells to obtain ψ x f at the image point. However, for multi-phase fluid, there arises two different situations as below: Case “A” In this case, the fluid phase at xg is the same as the fluid phase at x f . In such a situation (Fig. 2a), a unique value of ψ at xg can be obtained via linear extrapolation from values of ψ at ∂F and x f . First, the “boundary intercept” point xo , where xo , t) or Neumann condition Dirichlet condition ψ∂F = ψo (

∂ψ ∂n

= γo ( xo , t) is defined, is located at the intersection of ∂F and xg − x f as xo = xg − dg nˆ s xg . Then, the Dirichlet boundary condition (Eq. 6) is applied as ψ xg , t = ψ x f , t +

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Fig. 2 Schematic for interface BC implementation in a Case “A” b Case “B” with staircase profile representation (blue-dotted line)

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Case “B” In this case, the fluid phase at xg is different from the fluid phase at x f , because of which there will be discontinuities in the value of velocity gradient and pressure between xg and x f . Due to this sharp jump, the algorithm for “Case A” is not suitable for implementing the boundary conditions. For this case, first the boundary ∂F is effectively represented as a staircase shape (Fig. 2b), and each normal-component direction is denoted as cˆα . Then, the procedure for “Case A” φ x and δ (α) = is carried out using nˆ s xg = cˆα thus giving dg(α) = (α)s( g ) φs x f −φs (xg ) − dg(α) , ∀α. The final value of ψ at xg is thus a weighted sum of all ψ (α) given as (α) ψ xg , t = ψ cˆα · nˆ s xg

(11)

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2.2 Validation Test: Water Entry Problem Various grid independence tests have been performed and module-based verifications obtained by comparison with variety of problems. One such problem comprising of a domain containing air and water and a sphere which falls from its initial position slightly above the surface of water (Fig. 3a) characterised by Table 1 is illustrated here. The results are validated against one of the benchmark cases with similar inputs found in the works of [5] as represented in Fig. 3b.

Fig. 3 a Schematic [5] for the water entry problem. b Comparison of results for drag coefficient over the dimensionless depth (z/D) measured from initial water surface (z = 0)

242 Table 1 Input characteristics for water entry problem

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The top wall BC was kept as outflow while the rest treated as walls. The grid used was 448 * 448 * 576 with CFL condition set as 0.6. As illustrated in Fig. 3b, the results show excellent agreement with the literature and hence demonstrates no significant loss of accuracy by use of level sets for solidfluid interface and consequent force estimations in the fluid flow even with such a moderate grid size and CFL criteria. Moreover, the simplified calculation for ghost cell properties applied in the present calculations avoids a lot of geometric and iterative calculations used in most of the contemporary IBMs thus suggesting reduced computational efforts.

3 Conclusion It can be observed from the validation results against a standard test case as shown that the new hybrid technique is capable to efficiently handle multiphase FSI problems using a relatively simpler alternate approach using level set functions with IBM.

References 1. Peskin CS (1972) Flow patterns around heart valves: a numerical method. J Comput Phys 10:220–252 2. Yang J, Stern F (2009) Sharp interface immersed-boundary/level set method for wave body interactions. J Comput Phys 228:6590–6616 3. Mittal R (2005) Iaccarino, G: Immersed boundary methods. Annu Rev Fluid Mech 37:239–261 4. Gada VH, Sharma A (2011) On a novel dual-grid level-set method for two-phase flow simulation. Numer Heat Transfer Part B 59:26–57 5. Abraham J, Gorman J, Reseghetti F, Sparrow E, Stark J, Shepard T (2014) Modeling and numerical simulation of the forces acting on a sphere during early-water entry. Ocean Eng 76:1–9

Closed-Loop Drag Reduction Over a D-Shaped Body Via Coanda Actuation Tamir Shaqarin, Philipp Oswald, Richard Semaan, and Bernd R. Noack

Abstract Up to 40% drag reduction was achieved for a D-shaped cylinder in an experiment with robust model-based closed-loop control. The flow is actuated with on-off jet slots blowing in the stream-wise direction over the top and bottom edge. These jets are deflected inward with Coanda surfaces, thus realizing drag reduction by aerodynamic boat tailing. The flow state is monitored with pressure sensors at the trailing surface. The pressure fluctuation level is found to be closely related to drag. A starting point for control design is an optimized open-loop control, with a Strouhal number of 0.33 and duty cycle of 50%. Successful closed-loop drag reduction was achieved, in terms of a improving output stability and enhancing performance in term of settling time. Keywords D-shaped body · Closed-loop control · Flow control · Drag reduction

1 Introduction In the last decades, the closed-loop control of bluff bodies has been actively investigated [1]. The control of bluff bodies is tackled mainly using two approaches: separation control and wake control. Separation control is widely used on airfoils, humps and, circular cylinders [4]. Recently, the D-shape has served as a benchT. Shaqarin (B) Department of Mechanical Engineering, Tafila Technical University, Tafila 66110, Jordan e-mail: [email protected] P. Oswald · R. Semaan Institut für Strömungsmechanik, Technische Universität Braunschweig, Hermann-Blenk-Straße 37, 38108 Braunschweig, Germany B. R. Noack Center for Turbulence Control, Harbin Institute of Technology, Shenzhen, Room 312, Building C, University Town, Xili, Shenzhen 518058, People’s Republic of China Institut für Strömungsmechanik und Technische Akustik (ISTA), Technische Universität Berlin, Müller-Breslau Straße 8, 10623 Berlin, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_38

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mark plant for wake control and stabilization. Pastoor et al. [3] examined adaptive slope-seeking and phase control for the purpose of drag reduction on the same bluff body and achieved a 40% increase in base pressure and 15% drag reduction. Stalnov et al. [7] developed an opposition control on a D-shaped body with the aid of a proportional-integral controller. Their control approach resulted in a mitigation of bluff-body wake unsteadiness and a concomitant drag reduction. Dalla Longa et al. [2] reported a theory revealing that drag reduction can be achieved by manipulating wake flow fluctuations. The proposed controller successfully attenuates base pressure fluctuations, increasing the base pressure by 38%. This work presents an experimental study that addresses the drag reduction on a 2D D-shaped body using pulsed Coanda blowing. This study experimentally validated the strong correlation between drag coefficient (Cd ) and the wake fluctuations as reported by Dalla Longa et al. [2]. This fact facilitates the real-time closed-loop drag reduction dramatically since the computation of the Cd is slower than the direct measurement of the pressure fluctuation using, for instance, microphones.

2 Experimental Setup Experiments were conducted in the LNB (low noise wind-tunnel for low-Reynoldsnumbers at Technische Universität Braunschweig). The wind tunnel is a continuous, room-circulation, and atmospheric Eiffel type tunnel. The dimensions of the closed test section are 1500, 600 and, 400 mm in the streamwise, transverse, and spanwise directions, respectively. The maximum freestream velocity U∞ is approximately 20 m/s with a turbulence level along the vertical symmetry axis of the test section less than 0.1% measured at U∞ = 10 m/s. The dimensions of the D-shaped model depicted in Fig. 1 are L = 190.6 mm, H = 52 mm, and W = 400 mm for chord length, body height, and width. The model is mounted on both spanwise sides of the test section to avoid extra blockage and to ease the mounting of actuators and sensors inside the model. The Reynolds number based on the height of the D-shaped body is defined as Re H = U∞ H/ν, where ν is the kinematic viscosity of the air at ambient conditions. The drag coefficient computation is based on the pressure distribution in the wake, which is measured by two parallel pressure rakes, as depicted by Fig. 1. The first rake consists of 22 Pitot tubes for the total pressure measurements, and the second rake has 5 Prandtl tubes for total and static pressure measurements. The streamwise distance between the rake and the base of the D-shaped model is 130 mm. This distance is large enough to avoid measurements in the recirculation region in the near wake of the body. A dedicated temperature-compensated pressure measurement system (DTC Initium) is used to collect pressure data for the rake and the pressure taps around the model, accompanied by an ESP-64HD 64 channels pressure scanner. Moreover, the model is equipped with 5 microphones (type: TOM-1545P-R) evenly spaced in the normal direction along the midspan at the model base.

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Fig. 1 The D-shaped body with the coanda flap and the pressure rake

Eight fast switching, on-off, solenoid valves (Festo, MHJ9-QS-4-MF) are installed in the D-shaped body, four valves are responsible for the actuation on the upper slit, and the other four valves are responsible for the actuation on the lower slit on the trailing edges of the body. The actuators are manipulated via a square wave signal where the frequency ( f ) and duty cycle (DC) of the valves are adjustable. The velocity ratio and Strouhal number are defined respectively as: VR =

Uj fH , St H = U∞ U∞

The closed-loop controller was implemented on a high performance Arduino Due, 32-bit ARM core, microcontroller board. The control system consists of two loops, one is the Arduino microcontroller and the other is the realtime data acquisition system, both are synchronized with each other.

3 Results Initially, a square wave signal is sent to the actuator with a 50% duty cycle and a frequency ranging from 60 to 400 Hz. These tests were carried out for U∞ = 16 m/s (Re H = ∼55,000) and U j = 75 m/s, resulting in a velocity ratio of V R = 4.7. The sampling frequency is 2 kHz, the microphones signals are filtered by an 8th order low-pass filter with cut-off frequency of 80 Hz. The objective of the low-pass filter design is to preserve, the natural shedding frequency (65–70) Hz and to minimize the noise contamination of the switching valves ( f >100 Hz). Figure 2a clearly shows the effect of the actuation frequency on the associated drag reduction. Drag is reduced significantly at two frequency ranges away from the natural shedding frequency and its harmonics; at approximately St = ∼0.33 and ∼1.3. At these Strouhal numbers,

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the drag is reduced by ∼40%. For forthcoming tests, the actuating frequency was fixed to St = 0.33. The effect of a duty cycle at St = 0.33 is depicted in Fig. 2b. The drag is reduced effectively in the DC range (0–50%), and after 50% duty cycle there is no further decrease in the drag. Actuation with 50% DC at this specific frequency (ΔCd = −40%) appears to be better than continuous blowing (ΔCd = −35%). Surprisingly, actuation with DC = 20% appears to have a similar effect on the drag associated with continuous blowing. The figure indicates a monotonic relation between the actuation duty cycle up to 50% DC and the reduction in drag. Figure 3a shows one open-loop test at U∞ = 16 m/s. The test consists of three phases: base flow (0–4s), followed by pulsed actuated flow with St = 0.33 and 50% DC (4–8s) and finally, continuous blowing (8–10s). The resultant mean drag coefficient are Cd = 0.82, 0.47 and 0.54, respectively. The microphone signal (s) is clearly shown to be highly contaminated by the actuation frequency. On the contrary, the fluctuation level of the filtered signal is undeniably shown to decrease in the pulsed actuation case. This is also confirmed by the continuous blowing case (where no actuator frequency is involved), as the fluctuation level decreases, and almost identical for both filtered and unfiltered microphone signals. The figure at the bottom shows that the fluctuation level is lowered by ∼50% in comparison to the base flow, which is correlated with the ∼40% drag reduction. The transients from the non-actuated to actuated flow can assist the modeling from the input to output. A first-order model is used to capture the transient response. Consequently, a black-box model is identified describing the dynamic relationship between the duty cycle (DC) and the percentage reduction of the fluctuation level (). G(S) =

−0.5 0.1S + 1

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where S is the Laplace operator. Having the model (1), the robust H∞ controller design methodology presented thoroughly in Shaqarin et al. [5, 6] is easily followed. The designed controller was discretized to be implemented in the microcontroller in

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its digital form. The closed-loop response of the H∞ controller is depicted in Fig. 3b. The feedback signal to the controller is (( − base )/base ), where the commanded reference is a 50% reduction of the fluctuation level compared to the base flow. The figure clearly shows that the controller was successful in regulating the fluctuation level as commanded, with much less oscillation compared to the openloop control case. The controller improved the time domain specifications, as for instance, the settling time of the response is faster by 50% than the open-loop one.

4 Conclusion The influence of periodic forcing via Coanda blowing on the drag of a 2D D-shaped body is investigated. Pulsed jets with variable frequency and duty cycle are blown at the top & bottom Coanda surfaces on the model trailing edge. Open-loop tests have shown that actuation with St = 0.33, 1.3 can reduce the drag by ∼40%. Moreover, actuation at these frequencies was found more efficient than continuous blowing in terms of reduced drag and energy injected. This study proved experimentally the strong correlation between drag coefficient (Cd ) and the wake fluctuations as reported by Dalla Longa et al. [2]. The pressure fluctuation level is decreased by ∼50% in comparison to the base flow, which is correlated with the ∼40% drag reduction.

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References 1. Brunton SL, Noack BR (2015) Closed-loop turbulence control: progress and challenges. Appl. Mech. Rev. 67(5), article 050801 1–48 2. Dalla Longa L, Morgans AS, Dahan JA (2017) Reducing the pressure drag of a d-shaped bluff body using linear feedback control. Theor Comput Fluid Dyn 31(5–6):567–577 3. Pastoor M, Henning L, Noack., BR, King R, Tadmor G (2008) Feedback shear layer control for bluff body drag reduction. J Fluid Mech 608:161–196 4. Siegel SG, Cohen K, McLaughlin T (2006) Numerical simulations of a feedback-controlled circular cylinder wake. AIAA J 44(6):1266–1276 5. Shaqarin T, Noack BR, Morzynski M (2018) The need for prediction in feedback control of a mixing layer. Fluid Dyn Res 50(6):065514 6. Shaqarin T, Al-Rawajfeh AE, Hajaya MG, Alshabatat N, Noack BR (2019) Model-based robust H∞ control of a granulation process using Smith predictor with Reference updating. J Process Control 77(C):38–47 7. Stalnov O, Fono I, Seifert A (2011) Closed-loop bluff-body wake stabilization via fluidic excitation. Theor Comput Fluid Dyn 25(1–4):209–219

Effect of Mass Ratio on Inline Vortex Induced Vibrations at a Low Reynolds Number Dániel Dorogi, László Baranyi, and E. Konstantinidis

Abstract In this two-dimensional numerical study, vortex-induced vibration of a circular cylinder is analyzed using an in-house code. Mass ratios of m ∗ = 2 and 10 are investigated at Reynolds number Re = 100. For both m ∗ values a single excitation region is identified with a peak amplitude value of 0.22% of the cylinder diameter. For a system without external damping the magnitude of the streamwise fluid force was found to be zero where the vibration frequency passes through the natural frequency in vacuum. Across the same point the phase angle between displacement and streamwise fluid force changes by 180◦ . Keywords Low Reynolds numbers · Mass ratio · Vortex-induced vibration

1 Introduction One fundamental aspect of fluid-structure interaction is vortex-induced vibration (VIV). The periodic shedding of vortices in the wake of a flexible bluff body or an elastically supported rigid body leads to cross-flow vibrations. The non-linear nature of this flow phenomenon makes it very complex [1] and so the majority of studies analyze simplified configurations of a rigid cylinder elastically mounted on springs where the body can undergo only a single-degree-of-freedom motion D. Dorogi (B) · L. Baranyi Department of Fluid and Heat Engineering, University of Miskolc, 3515 Miskolc-Egyetemváros, Miskolc, Hungary e-mail: [email protected] URL: http://geik.uni-miskolc.hu/intezetek/EVG/ L. Baranyi e-mail: [email protected] E. Konstantinidis Department of Mechanical Engineering, University of Western Macedonia, Bakola and Sialvera, 50132 Kozani, Greece e-mail: [email protected] URL: http://mech.uowm.gr/index.php/en/ © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_39

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(in either transverse or streamwise direction). While transverse studies are more typical, streamwise motion also plays a role, and the excitation source comes from vortex shedding in the wake for both configurations; related studies can shed more light on the fluid-structure interactions [2]. Two excitation regions were identified in streamwise VIV by the early experimental studies of King [3]. The first branch occurs below the reduced velocity value of U A∗ = U∞ /( f n,a D) = 2.5, where U∞ is the free stream velocity, f n,a is the natural frequency of the structure in still fluid and D is the cylinder diameter. This excitation region is associated with symmetrical shedding of vortices simultaneously from both sides of the cylinder. The second branch occurs at U A∗ > 2.5 and is associated with shedding of oppositely-signed vortices alternately from each side of the cylinder. However, Bourguet and Lo Jacono [4] found a single peak of inline response at a Reynolds number of 100 in their numerical study. In addition to the reduced velocity value, mass ratio m ∗ and the structural damping coefficient ζ have been shown to have an effect on streamwise cylinder response. Aguirre [5] concluded from his experiments that the mass ratio did not affect the normalized oscillation amplitude, while the normalized response frequency was not influenced by the stiffness of the mechanical system. In this study, vortex-induced vibration of an elastically supported circular cylinder allowed to move only in inline direction is investigated by means of numerical simulations. The main objective of this study is to investigate the effects of mass ratio on the streamwise response of the cylinder.

2 Computational Methodology In this study two-dimensional incompressible Newtonian constant property fluid flow around a circular cylinder free to vibrate only inline with the free stream is investigated using an in-house CFD approach. Two components of the Navier-Stokes equations, continuity equation and pressure Poisson equation govern the fluid flow and Newton’s second law is used to compute the instantaneous cylinder displacement, velocity and acceleration. The physical domain of the computations is enclosed between two concentric circles; R1 and R2 are the dimensionless radius of the cylinder and outer surface, respectively. Both on R1 and R2 Dirichlet-type boundary conditions (BCs) are applied for the two velocity components and Neumann-type boundary condition is used for fluid pressure. In order to satisfy these BCs accurately, boundary-fitted coordinates are applied, that is, the physical domain is transformed into a computational domain. Using appropriate mapping functions (as suggested by Baranyi [6]) the grid on the computational domain is equidistant, while the mesh is fine nearby the cylinder and coarse in the far field. The transformed governing equations with the mapped BCs are solved using an in-house code based on finite difference method (see Baranyi [6] and Dorogi and Baranyi [7] for details). Independence studies were carried out before the system-

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atic computations. Then, the results obtained (for stationary and oscillating cylinder cases) are validated against the literature data; good agreements were found. The results of independence studies and comparisons were published in [6–8]. Due to the lack of space these are not repeated here.

3 Results and Discussion In this study inline vortex-induced vibration of a circular cylinder is investigated at the Reynolds number of Re = U∞ D/ν = 100, where U∞ is the free stream velocity, D is the cylinder diameter and ν is the kinematic viscosity of the fluid. Systematic computations are carried out at the reduced velocity range of U ∗ = U∞ /( f n D) = 2 − 4.5 and mass ratio values of m ∗ = 2 and 10 using zero structural damping ζ = 0. Here f n is the natural frequency of the body in vacuum. Figure 1a and b show the normalized oscillation amplitude A∗ = A/D and vibration frequency f ∗ = f D/U∞ against reduced velocity, respectively. It can be seen that, the response shows one peak where the oscillation amplitude reaches 0.22% of the cylinder diameter for both m ∗ values. This finding is comparable with that of [4]; they identified a peak amplitude of approximately 0.002 at U ∗ = 3 and m ∗ = 40/π . In the excitation range A∗ increases monotonically until its peak value beyond which it decreases (see Fig. 1a). The vibration frequency behaves contrary: f ∗ decreases until its minimum value and then it shows to increase (see Fig. 1b). The minimum value in f ∗ and the peak in A∗ are identified at the same U ∗ value; these values remain almost the same for both m ∗ = 2 and 10. However, location of the peak response depends strongly on the mass ratio; it shifts to higher reduced velocity values by increasing m ∗ . (a) 0.0025

m∗ = 2 m∗ = 10

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Fig. 2 Magnitudes of fluid forces in inline (a) and transverse (b) directions (C x and C y , respectively) against reduced velocity U ∗ for mass ratio values of m ∗ = 2 and 10 at Re = 100 and ζ = 0

In Fig. 2a and b the magnitude of the unsteady inline C x and transverse C y fluid force components are shown against U ∗ for m ∗ = 2 and 10. Similar tendencies can be seen in both force coefficients: they increase gradually with U ∗ reaching a peak level approximately near the point where peak amplitudes of cylinder oscillation appear (see Fig. 1a). Then, a steep decrease of the force coefficients within a narrow range of U ∗ is observed, which is followed by a gradual increase at the high end of U ∗ values. It is very interesting to note that at U ∗ = 3.0504, where the vibration frequency coincides with the natural frequency of the body in vacuum, C x tends to zero (see Fig. 2a). This point is indicated by a vertical line on the right plot of Fig. 1. Note that the oscillation amplitude is low but non-zero at U ∗ = 3.0504. Thus, a question arises how inline fluid force with approximately zero magnitude (C x ∼ = 0) can result in finite oscillation amplitude. Careful investigations are carried out in the vicinity of U ∗ = 3.0504. It was found that a superharmonic frequency component with very low intensity remains in the spectra of the unsteady inline fluid force. It can be seen that where the vibration frequency passes through the natural frequency in vacuum, the phase angle between cylinder displacement and inline fluid force changes abruptly. For undamped vibrations, = 0◦ and 180◦ are the only theoretically possible values. Figure 3 shows against U ∗ for m ∗ = 2 and 10. It can be seen that changes steeply at around U ∗ = 3.0504. In a thin reduced velocity range phase angle attains intermediate values (between 0◦ and 180◦ ) which illustrates that inline fluid force is nonharmonic in this domain.

4 Conclusions In this two-dimensional numerical study inline vortex-induced vibration of a circular cylinder is investigated using an in-house code. The Reynolds number and the

Effect of Mass Ratio on Inline Vortex Induced . . . Fig. 3 Phase angle between cylinder displacement and inline fluid force against reduced velocity U ∗ for m ∗ = 2 and 10 at Re = 100 and ζ = 0

253 180

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structural damping coefficient are fixed at Re = 100 and ζ = 0, respectively. Mass ratio values of m ∗ = 2 and 10 are considered, while reduced velocity is varied in the range of U ∗ = 2 and 4.5. An excitation region with a peak amplitude value of 0.22% of the cylinder diameter is found in this study. Although the peak response seems to be independent from the mass ratio, the location of it shifts to higher U ∗ values with increasing m ∗ . At the point where the vibration frequency f is identical with the natural frequency of the body in vacuum f n , the magnitude of inline fluid force tends to zero. At the same location phase angle between cylinder displacement and inline fluid force changes steeply from 0◦ to 180◦ . The steep change of phase angle in the vicinity of f = f n can be explained by the nonharmonic behavior of inline fluid force. Further work is underway to study the problem for more values of mass ratio and Reynolds number. Acknowledgements The research was supported by the EFOP-3.6.1-16-00011 “Younger and Renewing University—Innovative Knowledge City—institutional development of the University of Miskolc aiming at intelligent specialisation” project implemented in the framework of the Széchenyi 2020 program. The realization of this project is supported by the European Union, co-financed by the European Social Fund.

References 1. Sarpkaya T (2004) A critical review of the intrinsic nature of vortex-induced vibrations. J Fluids Struct 19:389–447 2. Konstantinidis E (2014) On the response and wake modes of a cylinder undergoing streamwise vortex-induced vibration. J Fluids Struct 45:256–262 3. King R (1977) A review of vortex shedding research and its application. Ocean Eng 4:141–171 4. Bourguet R, Lo Jacono D (2015) In-line flow-induced vibrations of a rotating cylinder. J Fluid Mech 781:127–165 5. Aguirre J (1977) Flow-induced in-line vibrations of a circular cylinder, Ph.D. thesis, Imperial College of Science and Technology 6. Baranyi L (2008) Numerical simulation of flow around an orbiting cylinder at different ellipticity values. J Fluids Struct 24:883–906

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7. Dorogi D, Baranyi L (2018) Numerical simulation of a freely vibrating circular cylinder with different natural frequencies. Ocean Eng 158:196–207 8. Dorogi D, Baranyi L (2019) Occurrence of orbital cylinder motion for flow around freely vibrating circular in uniform stream. J Fluids Struct 87:228–246

Analysis of Turbulent Entrainment in Separating/Reattaching Flows Nicolas Mazellier, Francesco Stella, and Azeddine Kourta

Abstract In this work, we report the experimental investigation of a canonical separating/reattaching shear-layer controlled via a synthetic jet. A mean energy budget, applied on a control surface, is performed to characterize the effect of the forcing. Using a sudden expansion model, the head loss coefficient is inferred independently of the control surface dimensions. It is found that the mean energy loss coefficient scales with mass entrainment. Keywords Flow separation · Turbulent entrainment · Head loss

1 Introduction Separating/reattaching flows are one important source of aerodynamic losses in many industrial flows, one common example being the large shape drag of bluff bodies. Separation control techniques aiming at reducing such detrimental effects have received great attention during the past decades. In this respect, one common approach has tried to modify the pressure distribution induced by separation by acting on the characteristic length scale of the flow L R (usually measured as the streamwise length of the recirculation region) [1]. Periodic actuators, such as pulsed or synthetic jets, have proven particularly effective at tuning L R [2]. However, the understanding of the physical mechanisms at play is still incomplete, which makes it difficult, if not impossible, to extrapolate results to real life applications. Recent studies proposed an attractive framework to tackle this issue by considering turbulent entrainment as the quantity scaling the main features of the flow. The simplicity of these entrainmentbased flow descriptions might pave the way to new separation control strategies. Berk et al. [3] investigated the effect of synthetic jets on the separated flow over a backward-facing step. They showed that the mean recirculation length scales linearly with the momentum flux induced by the forcing. Stella et al. [4] studied the scaling N. Mazellier (B) · F. Stella · A. Kourta University of Orléans, INSA-CVL, PRISME, EA 4229, 45072 Orléans, France e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_40

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of a prototype separating/reattaching flow over a descending ramp by focussing on mass entrainment through the boundaries of the separated shear-layers. In a recent work, [5] they modeled the mean recirculation region as a steady elongated vortex, whose characteristics relate to the mean entrainment of mass through the separation line. Anyway, their work does not provide connection between mass entrainment and loads and/or energy losses, which are more appropriate targets for flow control. To tackle this issue, this study proposes to investigate the possible relationship between mean mass entrainment and head loss in a diffuser-like flow.

2 Experimental Set-Up Experiments are carried out on a 25◦ , salient-edge descending ramp, spanning a step height h = 100 mm (see Fig. 1). The ramp is installed in the S1 wind tunnel of the PRISME Laboratory, at University of Orléans, France. Details on the experimental model and facility are reported in [5]. For all experiments, the freestream velocity was set to U∞ = 20 ms−1 . The separated flow that originates at the upper edge of the ramp is manipulated with a spanwise synthetic jet, ejected through 1 mm wide slot, 2 mm downstream of the upper edge of the ramp. The jets are operated at dimensionless frequencies St A = f A h/U∞ ∈ [0.1; 1] (with f A being the forcing frequency), and 2 ) ≤ 0.03 (where w is the width of the at momentum coefficients Cμ = 2wU 2j /(hU∞ slot and U j is the peak velocity of the jet). The flow is investigated mainly by Particle Image Velocimetry (PIV) and wall-pressure measurements. In this work, the analysis is restricted to the mean flow. In the remainder of the paper, all variables are reported in dimensionless form, indicated with the symbol , using h and U∞ as normalization parameters.

Fig. 1 Sketch of the ramp model. The recirculation region is identified by the shaded area. The field of view of PIV measurement is visualized by a gray rectangle

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3 Results and Discussion Here, we focus on 3 typical configurations: (i) the baseline (i.e., no forcing), (ii) the case featured by the smallest recirculation region and (iii) the case leading to the lowest pressure drag, which are achieved by tuning both forcing frequency and momentum coefficient. These cases are depicted in Fig. 2a–c, respectively, which show the region covered by the mean recirculation region. It is worth noticing that, based on a simple vortex model, Stella et al. [5] evidenced a linear relationship between L R and the mean mass flux entrained through the separation line. Accordingly, in the following, the mean recirculation length will be used as a surrogate of mass entrainment, our objective being to relate the latter to energy losses. Let us introduce a closed control surface S (see Fig. 2d) on which the energy budget is calculated using PIV data. This surface is build such that it encompasses the entire mean recirculation region, the outlet section being located at the streamwise position of the baseline reattachment point. The upper and lower boundaries coincide with a streamline and with the ramp wall, respectively. Accordingly, the flow rate crossing the control surface is

h 1

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Fig. 2 Backward flow probability for the baseline (a), the smallest bubble (b) and the lowest pressure drag (c) cases. Black lines indicate the mean separation line. d Schematic of the control volume on which the energy budget is calculated

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⎡ ΔH =

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2 with Fr = U∞ / (gh) being the Froude number, g indicating the gravity acceleration, and P the normalized mean pressure. The latter is inferred by integrating the mean momentum transport equation along the wall-normal direction. One arising issue, then, is the choice of h 1 (h 2 being dependent on h 1 ). Introducing the pressure loss coefficient ξ such that ΔH = ξ Fr/2 and following the expression of head loss in a sudden expansion, also referred as Borda formula, it comes

h1 2 , ξ =κ 1− h2

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where the constant κ is only dependent on the forcing conditions. As emphasized in Fig. 3, this expression is well supported by the data. The comparison between the energy loss, related to κ, and the mass entrainment, characterized by L R , is provided in Fig. 4 for the three tested cases. 0.6 0.4 0.2 0 0.05

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0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.5

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Fig. 4 Relationship between head loss and recirculation length scale. Baseline case: blue circle; smallest recirculation case: red square; lowest pressure drag: black triangle. The dash line represents a power law fit κ = A(L R )α

The results plotted in Fig. 3 reveal that the mean head loss constant scales with the mean recirculation length scale. Our data are well fitted by a power law relationship κ = A(L R )α , with A ≈ 0.8 and α ≈ 0.4. This confirms that mean mass entrainment is a key parameter in the understanding and the control of separating/reattaching shear layers.

4 Conclusions A canonical mean separating/reattaching flow undergoing perturbations by means of synthetic jet is studied via Particle Image Velocimetry, which is used to infer both mean mass entrainment through the mean separation line and mean head loss within the recirculation region. It is found that the energy loss coefficient scales with the mean recirculation length emphasizing the role of mass entrainment. This outcome might be of great value for the design of efficient control strategies in the future. Acknowledgements This work was supported by the French National Research Agency (ANR) through the Investissements d’Avenir program, under the Labex CAPRYSSES Project (ANR-11LABX-0006-01).

References 1. Chun KB, Sung HJ (1996) Control of turbulent separated flow over a backward-facing step by local forcing. Exp Fluids 21:417–426 2. Sigurdson LW (1995) The structure and control of a turbulent reattaching flow. J Fluid Mech 298:139–165

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3. Berk T, Medjnoun T, Ganapathisubramani B (2017) Entrainment effects in periodic forcing of the flow over a backward-facing step. Phys Rev Fluids 2(7):074605 4. Stella F, Mazellier N, Kourta A (2017) Scaling of separated shear layers: an investigation of mass entrainment. J Fluid Mech 826:851–887 5. Stella F, Mazellier N, Kourta A (2018) Mass entrainment-based model for separating flows. Phys Rev Fluids 3:114702

Damped Oscillations of Spherical Pendulums Herricos Stapountzis, Ioanna Lichouna, Violetta Koumoukeli, and Margarita Stapountzi

Abstract The damped oscillations of a spherical pendulum in planar motion is examined in a wind tunnel. Angular deflections and accelerations are measured for various wind speeds and their influence on the periods of oscillation and the time to complete pendulum rest are presented. Keywords Pendulum motion · Damped oscillations · Unsteady loading

1 Introduction The scientific interest in the kinematics and dynamics of pendulum motions dates back to centuries and it is still active in a diverse range of engineering and physical problems. Due to its simplicity, the ideal pendulum with a piece of string conveniently lends itself for both theoretical and experimental educational purposes, in fact nowadays quantitative experimental study may be accomplished with a smartphone. However, when it comes to real cases such as those involving finite size and number of masses (e.g. multiple pendulums), connecting elements (ropes, rods, oil riser pipes, legs), fluid–structure interaction (FSI), the detailed analysis becomes quite complicated [1–4]. Examples, with combinations of the above, could be the coupled dynamics of a cluster of parachutes to a payload where a pendulum like swinging motion has been observed during descent, pendulum suspension to reduce fluid sloshing during an earthquake, wing flutter, walking (bipedal locomotion of leg) simulated as pendulum in biomechanics, crane dynamics, vertical axis wind turbine stability and autorotation and horizontal axis wind turbine load alleviation. In the present paper we examine the damped planar oscillations of a spherical pendulum in a wind tunnel under large initial angular deflections along the wind. H. Stapountzis (B) · I. Lichouna · V. Koumoukeli Mechanical Engineering Department, University of Thessaly, 383 34 Volos, Greece e-mail: [email protected] M. Stapountzi FORTH Institute of Molecular Biology and Biotechnology, 700 13 Heraklion, Greece © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_41

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The objective is to find how variations in the wind tunnel speed affect the period of oscillation and the time it takes for the pendulum to come to rest. Due to the unsteady motion of the sphere both the drag and added mass coefficients keep changing from start to end of the oscillation. It is anticipated therefore that the findings from this work would be helpful when attempting to model this specific pendulum motion either by using engineering models (e.g. involving Morison’s equation) or in more elaborate CFD simulations.

2 Experimental Setup and Procedure A spherical pendulum was allowed to perform oscillations in a wind tunnel, the heavy sphere (M = 7.5 kg, D = 0.115 m diameter) moving on a plane parallel to the mean free stream of speed U0 (0 < U0 < 15.47 m/s). The low friction cylindrical hinge (journal type of bearing) was mounted on the ceiling of the wind tunnel and was connected to the sphere by means of a lightweight rod. The equivalent pendulum length was L = 0.47 m and the initial angle of release MAX = O (65°). The pendulum was equipped with a KISTLER type one component accelerometer and with a small LED type light in order to monitor the instantaneous tangential acceleration and position of the pendulum center by video recording during the damped oscillations after the moment of release. The signal from the accelerometer (raw value in Volts) is the algebraic (±) magnitude of the tangential acceleration, that is, the magnitude of the acceleration vector felt by the accelerometer was tangential to the circular path of the accelerometer itself fixed to the pendulum.

3 Results and Discussion The accelerometer samples were more than 70,000 at a sampling rate of 200 Hz, while the videos were taken at frame rates of 50 and 240 fps leading to acceleration aT resolutions better than 0.004 m2 /s. Figure 1 is a time record of the instantaneous deflection angle (t) in degrees of the pendulum for the maximum wind tunnel speed U0 = 15.47 m/s and in still air, U0 = 0 m/s. The results shown were obtained from video analysis. The time taken from the initiation of the oscillation to complete rest, TREST , is almost halved with high wind speed in comparison to the no flow condition, while the rate of decay of the successive ± peaks in (t) deviates from the linear behavior noticed for U0 = 0 m/s. Due to the overwhelming effect of the gravity forces compared to the aerodynamic forces for the range of wind tunnel speeds used, there is no sign of loss of stability, the oscillations always die out. There is good agreement between the video and accelerometer results for the absolute value of aT as Fig. 2 indicates, meaning that the accelerometer calibration was satisfactory.

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Fig. 1 Pendulum angular deflection for various wind tunnel speeds

Fig. 2 Absolute value of the tangential acceleration from video, accelerometer

The frequency of oscillation fo was computed from spectral analysis of the accelerometer and video signals, the corresponding values being very close. Figure 3 shows that the frequency fo increases by about 4% when the wind tunnel speed is raised from zero to 15.47 m/s. More detailed effects of the wind tunnel speed on the period of oscillation TP (=1/fo ) and the time for the pendulum to come to rest, TREST , are presented in the legend of Fig. 4. It is concluded that as the wind tunnel speed increases both the period of oscillation TP and the time to rest TREST decrease. The damping ratio of oscillations is here defined as ζ = [1 + (2π/ln(i /i+1 )2 ]−0.5 . For at least thirty periods of oscillation, t/TP < 30, Fig. 4 indicates that the damping ratio ζ increases both with the wind tunnel speed U0 and with t/TP . At larger values of

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Fig. 3 Effect of wind tunnel speed on oscillation frequency

Fig. 4 Effect of wind tunnel speed on the damping ratio ζ

t/TP the rate of increase of ζ has a stronger dependence on the tunnel speed, however the errors in the computation of ζ become gradually bigger due to the diminishing values of the angular deflections i . The higher levels of damping ζ with U0 are consistent with the pendulum reaching the rest stage gradually sooner. Introducing the time varying Keulegan—Carpenter number KC = UMAX-REL TP /D the data of Fig. 4 may be plotted in a different form in Fig. 5. UMAX-REL is defined as the maximum speed of the sphere center relative to the wind and due to the unsteady motion it keeps changing at every cycle of the damped oscillation. Its value was calculated from analysis of the video recordings. Figure 5 clearly demonstrates that under constant values of the dimensionless time t/TP , ζ increases both with the local KC number as well as with the wind tunnel speed. The rate of increase of the damping ratio is more profound at higher speeds U0 . For constant wind speed, ζ increases with time t/TP , but decreases as the local KC number increases.

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Fig. 5 Effect of Keulegan–Carpenter number on the damping ratio ζ

4 Conclusions The damped oscillations of the freely swinging planar spherical pendulum in a wind tunnel were monitored by video recordings and accelerometer measurements, the results by using the two methods being in good agreement. It was found that the behavior of the pendulum was affected by increases in the wind speed U0 in many ways: The time it takes to come to rest TREST decreases; The period of oscillation TP decreases; The damping ratio ζ increases; For constant values of the time t/TP the damping ratio ζ increases as the local value of the Keulegan-Carpenter number increases.

Reference 1. Moe G, Verley RLP (1980) Hydrodynamic damping of offshore structures in waves and currents. In: 12th offshore technology conference OTC 3798, pp 37–44 2. Sarpkaya T (2010) Wave forces on offshore structures. CUP 3. Gomes JMP (2012) FSI-induced oscillation of flexible structures in uniform flows. Ph.D. thesis, Universität Erlangen-Nürnberg, p 35 4. Neill D, Livelybrooks D, Donnelly RJ (2007) A pendulum experiment on added mass and the principle of equivalence. Am J Phys 75:226–229

Flow Structures in the Initial Region of a Round Jet with Azimuthally Deformed Vortex Rings Utilizing a Sound Wave Akinori Muramatsu and Kohei Tanaka

Abstract Vortex ring is formed and breaks down through wavy deformation in the initial region of a round jet. We attempted to deform a vortex ring of the round jet azimuthally and wavily using synthetic jets. The synthetic jets are generated at the side of a round nozzle by a sound wave. From flow visualization of the excited jet, it is found that the vortex ring is azimuthally and wavily deformed by the synthetic jets and the deformed shape is determined by the number of synthetic jets. Outflows from the jet column appear between the synthetic jets. From the results by a PIV, the velocity and pressure of outflows are large and low. The velocity in the jet column is fluctuated largely and periodically. The separated flow formed by the synthetic jets are similar to the side jets in a helium gas jet. Keywords Jet · Synthetic jet · Side jets · Flow visualization · 3D imaging · PIV

1 Introduction Jets are simple shear flows but also widely used in industrial fields. The spatial development process of a round jet strongly depends on vortex rings and streamwise vortices in the initial region. Vortex rings are generated near the nozzle exit and break down via wavy deformation in the azimuthal direction in the near field. The streamwise vortices are concerned with the wavy deformation of the vortex ring [1]. Moreover, the azimuthal and wavy deformation of the vortex ring is also related to the formation of side jets [2, 3]. We attempted to deform a vortex ring azimuthally and wavily by synthetic jets to investigate relation between deformation of the vortex ring and the formation of the side jets. The flow structure of the round jet adding the synthetic jets was examined by experiments. The cross-sections of the jet was A. Muramatsu (B) College of Science and Technology, Nihon University, Funabashi, Chiba, Japan e-mail: [email protected] K. Tanaka Graduate School of Science and Technology, Nihon University, Funabashi, Chiba, Japan © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_42

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visualized using a PLMS (planar laser Mie scattering). The velocity, vorticity, and pressure fields were measured using a PIV.

2 Experimental Apparatus and Methods Figure 1 shows experimental apparatus for flow visualization. A round nozzle has small holes in the side, as shown in Fig. 2. The exit diameter of the nozzle D0 is 12 mm and the diameter of the holes is 2 mm. The number of the holes is respectively three, four, five, and six. The holes are connected to a loudspeaker through vinyl tubes.

Fig. 1 Experimental apparatus for flow visualization

Fig. 2 A round nozzle with six holes and two visualized sections

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A sine wave is input to the loudspeaker, so that synthetic jets are generated from the holes. Air is vertically issued from the nozzle into the still air. A jet Reynolds number Re is defined by an issuing velocity U c0 on the centerline at the nozzle exit and the nozzle exit diameter D0 . When the Re is set at 2,000 (the issuing velocity U c0 = 2.55 m/s), the vortex rings are regularly formed at the frequency of 120 Hz (the non-dimensional frequency = 0.565). The frequency and r.m.s. value of the sine wave inputting a loudspeaker is set at 120 Hz and 0.2 V. In this case, the velocity of the synthetic jet at the hole exit varies from 0.5 to −0.2 m/s periodically, and the turbulent intensity to the U C0 is about 7%. Small particles for Mie scattering are introduced into the issuing air. The crosssections are visualized by using a laser sheet with the thickness of 1 mm. The two streamwise cross-sections are shown in Fig. 2. The three-dimensional imaging of the jet is obtained using a scanning laser sheet [3]. Moreover, velocity, vorticity and pressure fields are measured using a PIV system. For the PIV measurement, the nozzle is surrounded by a duct with square section. The tracer particles are mixed in both the jet fluid and the ambient fluid in the duct.

3 Experimental Results A non-dimensional coordinate system is shown in Fig. 3. The origin is the center of the nozzle exit. The r/D0 and x/D0 in Fig. 3 mean a radial and streamwise coordinates. Figure 4 shows visualized horizontal cross-sections at x/D0 = 2 for the different numbers of the synthetic jet. It is found that the top view of the jet changes by the numbers of the synthetic jets. For example, when the five synthetic jets are used, the shape becomes a pentagon, as shown in Fig. 4c. Next, we show the results of the controlled jet by six synthetic jets. Figure 5 is the flow visualizations of the streamwise cross-section on the jet centerline for an unexcited jet and an excited jet. The roll-up of the shear layer in the excited Fig. 3 Coordinate system

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Fig. 4 Flow visualizations on the horizontal plane, a 3 synthetic jets, b 4 synthetic jets, c 5 synthetic jets, d 6 synthetic jets

Fig. 5 Flow visualizations on the jet center line using a nozzle with 6 holes, a unexcited jet, b section 1 on excited jet, c section 2 on excited jet

jet approaches the nozzle exit than that in the unexcited jet, because the roll-up is enhanced by the added disturbance. The excited jet becomes narrow at section 1 and spreads at the section 2 compared with the unexcited jet. Consequently, the jet is narrow at the position of the holes for an excitation. In the cross-section 2 without the holes, the jet begins to flow into the radial outside at approximately x/D0 = 1.5. The branched flows are similar to side-jets [2, 3]. The branched flows spread further in the downstream. It is thought that the mixing of jet in the near field is enhanced by the separated flows. Figure 6 shows the variously horizontal cross-section for the excited jet. White arrows in Fig. 6 indicate the positions of the holes for the excitation. A broken circle in Fig. 6 indicates the edge of the round nozzle. A pair of vortices, such as mushroomlike flow, flows out at the positions of no holes. The generating points of the vortex

Fig. 6 Flow visualizations on variously horizontal sections for a jet excited by 6 synthetic jets

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pair are fixed by the excited holes. The vortex pairs leave to the further outside in the downstream. The six separated flows can be artificially formed at azimuthally fixed positions by six synthetic jets. Moreover, the mushroom-like flows to the inside are observed at the position of the synthetic jets at x/D0 = 2. The three-dimensional image of the excited jet is shown in Fig. 7. It is observed that the vortex ring is wavily deformed in the azimuthal direction. Measured results by a PIV are shown in Figs. 8 and 9. Figure 8 is the contours of speed, radial velocity, and vorticity on the section 2 in Fig. 2. Black arrows in Figs. 8 and 9 express velocity vectors. The separated flows are formed at about x/D0 = 1.5 in Fig. 8a, and is similar to the picture of Fig. 5c. In Fig. 8a, b, the velocity of the outflow becomes large at x/D0 = 1.5 – 2.0, so that the flows separated from the main flow are formed. It is found that the streamwise velocity in the jet column varies Fig. 7 Three dimensional imaging for a jet excited by 6 synthetic jets

Fig. 8 Measured values on the section 2 for a jet excited by 6 synthetic jets using PIV

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Fig. 9 Measured values on the horizontal cross-section at x/D0 = 2 for a jet excited by 6 synthetic jets using PIV

largely and periodically from Fig. 8a, b. The large and periodic velocity fluctuation is similar to the fluctuation in a round helium gas jet with side-jets formation [2]. The dot line in Fig. 8 is indicated at the height of the center of a vortex ring. The streamwise velocity is large at the location of the vortex ring. The outflow and inflow are observed at the top and bottom of the vortex ring. Figure 9 shows the contours of speed, vorticity, and pressure on the horizontal cross-section at x/D0 = 2.0. The pressure is estimated using the Poisson equation. The velocity is large at the parts of the outflow. The outflow is mushroom-like flow, as shown in Fig. 6. A pair of vortices is formed at the top of the outflows in Fig. 9b. The vortex pair has positive and negative vorticities. The vortex ring becomes a hexagon by six synthetic jets, as shown in Fig. 4d, and a pair of streamwise vortices is formed at between the synthetic jets. The pressure is low at the location of the vortex pair, and high pressure becomes at the position between the vortex pairs.

4 Conclusions Synthetic jets are generated at holes in the side of a round nozzle using a sound wave. Vortex ring is azimuthally and wavily deformed by the synthetic jets. The deformed shape is determined by the number of the synthetic jets. The six synthetic jets make the vortex ring a hexagon. The separated flows are formed with the deformation of the vortex ring, and are similar to side jets. The separated flows appear between the synthetic jets. The top of separated flows is a pair of vortices, and becomes low pressure.

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Reference 1. Toyoda K, Hiramoto R (2009) Manipulation of vortex rings for flow control. Fluid Dyn. Res. 41:1–21 2. Muramatsu A, Gamba M, Clemens NT (2008) Side jets generated in a round helium gas jet. In: Proceedings of 2nd international conference on jets, wakes, and separated flows (ICJWSF-2008), CD-R 3. Kawabe K, Muramatsu A (2016) Flow structure of a round jet with side-jet formation. In: Springer Proceedings in Physics, vol 185, pp 11–18. Springer, Berlin

Structure Generated Turbulence: Laminar Flow Through Metal Foam Replica Chanhee Moon

and Kyung Chun Kim

Abstract Open-cell metal foam is a promising porous media for thermo-fluid systems. Flow characteristics inside a 10 PPI (Pores per inch) metal foam with a porosity of 0.92 are analyzed with a laminar inlet flow condition. The flow inside the metal foam structure is chaotically furcated and interflowed by the interconnected pore network. Strong transverse motion is shown inside metal foam with about 23% of bulk velocity. This spanwise velocity is similar value to the result of Onstad et al. (Exp Fluids 50(6):1571–1585, 2011 [4]) who investigated flow inside metal foam using magnetic resonance velocimetry in a turbulent inlet flow condition. It is evidence that the metal foam structure has a dominant influence on transverse motion. Considerable velocity and vorticity fluctuation inside metal foam structure were found. The fluctuations are decayed at downstream. Irregular structure of metal foam generates turbulence. The results presented in this study are useful to understand turbulent characteristics of flow through metal foams. Keywords Metal foam · Structure generated turbulence · Particle image velocimetry · Refractive index matching

1 Introduction Open-cell metal foam is an irregular metallic porous media with open-cell topology. The skeletal portion of the metal foam consists of many struts and nodes. The skeletal portion, which has bone-like topology, provides desirable geometrical characteristics to thermo-fluid application such as high-porosity, large specific surface area, tortuous path, good elastic moduli, and strength. Because of applicability to the various field by these characteristics, the metal foam has been attracting attention.

C. Moon · K. C. Kim (B) Pusan National University, Busan 46241, Republic of Korea e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_43

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Various experimental and numerical approaches have been used to understand metal foam flow. Experimental flow visualization is a promising approach to understand the underlying physics of metal foam flow. Lumped-parameter study inherently neglects the localized flow characteristics. The numerical simulation requires experimental validation data although they are a powerful tool to visualize the metal foam flow. Several experimental visualization studies for upstream and downstream flows of metal foams have been performed by Hwang et al. [1], Eggenschwiler et al. [2], and Hutter et al. [3]. Onstad et al. [4] investigated characteristics of ensembleaveraged flow fields inside a 4× scale opaque metal foam replica using magnetic resonance velocimetry (MRV). A turbulent flow of bulk Reynolds number of 7900 passes through the metal foam replica that is filled in a duct. They found that the flow inside that replica has a strong transverse motion of 20–30% of the superficial velocity. MRV is the most advanced technology, which allows observing the flow inside an opaque material, but it has a drawback that cannot achieve time-resolved measurement of flow in complex and small structures like metal foam. The characteristics of flow inside metal foams are still unclear. The flow features for non-turbulent inlet conditions, temporal characteristics, and the evolution of the flow inside metal foams should be examined further. Thus, this study conducted a time-resolved PIV measurement in a 3-D printed transparent metal foam replica. The turbulent characteristics of the flow in the metal foam were analyzed under incoming laminar flow condition.

2 Experimental Setup A 10 PPI aluminum foam was prepared for the metal foam sample. An X-ray computed tomography system was used to obtain a 3-D CAD (Computer-aided design) file. Under 200 kV, 200 µA and 267 ms condition, 743 × 740 × 459 voxels were generated with a spatial resolution of 0.032 mm. The voxels were converted to a 3-D CAD file. In CAD software, a part of the metal foam replica CAD file is cropped into a perfect hexagon that has a size of 10 mm × 10 mm × 25 mm. Because of the resolution of the 3-D printer, the size of the cropped model was doubled. Therefore, the final size of the metal foam replica file is 20 mm × 20 mm × 50 mm. The metal foam replica was printed by Polyjet type 3-D printer (Objet Eden260VS, Stratasys Ltd.). Vero Clear resin and water-soluble support material (SUP707) were selected as printing materials. The refractive index of Vero Clear material is 1.515 for 532 nm. Refractive index matched (RIM) solution based on NaI was prepared. As shown in Fig. 1a, an acrylic square duct, which has size of 20 mm × 20 mm × 500 mm, was manufactured. Nondimensional sizes and distances by duct diameter (D) are indicated. That duct has one inlet and one outlet, and they are positioned above the duct to observe the flow in the spanwise plane. 3-D printed metal foam replica is placed 15 D away from the inlet. A test loop has been configured to circulate the RIM solution through the test section. As shown in Fig. 1b, it consists of a RIM solution container, a gear pump, a

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y +0.5 D (10 mm)

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flowmeter, a bubble trap, a test section, and a traverse to move the test section. The RIM solution container is partially immersed in water bath. A constant temperature hot plate with 25 °C was placed bottom of the water bath to maintain the temperature of RIM solution. The RIM solution is transported by the gear pump. Flowrate was measured by a turbine type flowmeter. One CMOS high-speed camera (1k × 1k resolution) and one continuous wave laser (532 nm, 5 W) power were used to conduct time-resolved 2-D PIV experiment. Because equivalent diameter of struts is 0.8 ± 0.06 mm, the thickness of laser sheets was set to 0.5 mm. Rhodamine B coated fluorescence polymer particle (1–20 µm) was used as tracer. Calculated bulk velocity (Ub ) from the flowrate was 0.82 m/s. Reynolds numbers based on channel hydraulic diameter and pore diameter are 511 and 100, respectively. The velocity profile at (−2.0 D, y, 0 D) shows good agreement with the laminar velocity profile from numerical solution.

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3 Results and Discussion Figure 2a shows a contour of mean velocity magnitude of u (x-direction) and v (y-direction) components on the plane at z = 0 D. Mean velocity vector field is superimposed on the contour. Fluid flows to the right side. The distance of x-direction is non-dimensionalized by the channel diameter and pore diameter, respectively. The

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former is shown on the downside of the figure and the latter is shown on the upper side of the figure. The distance of y-direction is non-dimensionalized by the channel diameter. Mean velocity is non-dimensionalized by bulk velocity. The unidirectional upstream flow of the channel is furcated into two or three by the pore network as soon as they encounter the metal foam structure. Four jets are formed at the entrance of metal foam structure (x = 0 to 0.25 D). The jets are decelerated after passing through one or two cells, but new jets are simultaneously formed through other pores. The new jet interflows into another jet. This furcating and interflowing process occurs throughout the metal foam and leads mixing of fluid inside metal foam structure. This chaotic mixing mechanism is illustrated in Fig. 2b. The arrows show the direction of flow and indicate the direction of flow is very complex. This multi-direction multi-jets generates many unstable shear layers. Considering this is just a two-dimensional plane, the number of furcating or interflowing jets could be larger than two or three. The separation area behind struts should be noted due to its influence on pressure drop. Although Fig. 2a, b do not show the out-of-plane velocity component, the flow separation behavior is similar to MRV data of Onstad et al. [4]. The size of the separation region is believed that depends on strut shape of metal foam. The shape of the metal foam strut is circular or triangular, and it depends on the porosity according to Plateau’s law. The higher porosity, the shape of strut becomes triangular from circular. The strut shape of the present metal foam is triangular. The variations in heat transfer and pressure drop due to the strut shape change of Kelvin cells were studied by Moon et al. [5], but the effects of strut shape in irregular metal foams should be investigated. When is averaged over the inside of the metal foam plane, ¯v is about 23% of Ub ; · and ¯· indicates time and spatial average, respectively. This is similar to the result of Onstad et al. [4]: 20–30%. This similar result is important because the Reynolds number of present study is much lower than that of Onstad et al. [4]. This represents that the advection flow inside the metal foam is dominantly affected by the metal foam structure itself, and is consistent well with the prediction of Onstad et al. [4] that large transverse motion may occur in laminar flow condition. Figure 2c shows the root mean squared fluctuation velocity generated inside the metal foam. Root mean squared fluctuation velocity can be defined as:

u r ms =

u 12 + u 22 + · · · + u l2 l

(1)

where u r ms is root mean squared fluctuation value of streamwise velocity, l is the number of vector frames. 10,000 frames were used to obtain u r ms . At the entrance of metal foam, u r ms /Ub is near zero, but it increases to 0.1– 0.4 inside the metal foam structure. After passing the exit of the metal foam, it approaches to zero again. Velocity fluctuation occurs at the outlet region of the pores, at the junction of the jets, and behind the struts. This represents that the fluctuation might be caused by metal foam structure. Irregular topology of metal foam generates

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,

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considerable flow instability. However, these phenomena are extremely complex, so it seems that an extensive investigation of the cause of this fluctuation should be conducted. The evolution of spanwise vorticity through metal foam structures should be investigated. Spatially averaged vorticity magnitude ( ωx 2 ) and root mean squared ωx 2 vorticity fluctuation (ωx,r ms ) of spanwise planes are shown in Fig. 3. The value increases inside the metal foam and dissipates to the original state at the down stream of the metal foam. Variation of ωx,r ms is interesting. This is also one of the evidence that the metal foam causes considerable flow disturbances even at a rela tively low Reynolds number. The ωx,r ms value increases sharply in the entrance region of metal foam. After the entrance region, the ωx,r ms value is maintained at a similar level inside metal foam structure. From x = 2.0 D, the ωx,r ms value rapidly decreases. After then, it gradually decreases in the section of x = 2.75–4 D which is downstream of the metal foam structure. The reason the ωx,r ms value rapidly decreases at x = 2.0–2.5 may be the effect of outlet flow of metal foam. On the downstream side of the metal foam, a flow separation area larger than the inside is formed, thereby lowering the static pressure. This flow separation influences the upstream flow.

4 Conclusions Fluid flow entering the metal foam structure shows turbulent features. Jet-like flows are generated by the pore network, and the flow is furcated and interflowed successively. Shear layers generated by a jet are disturbed by interflowing jets. Strong transverse velocity was generated by 23% of Ub , and this was consistent with Onstad [4]’s prediction that the strong transverse motion in a metal foam may occur even in laminar flow condition. Evolution of the spanwise vorticity in the metal foam structure was presented. Spanwise vorticity shows considerable fluctuation due to

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the complexity of flow motion in the metal foam structure. These turbulent characteristics were generated by the irregular metal foam structure: Structure generated turbulence. However, in this study, the investigation was conducted only for a single Reynolds number and single metal foam geometry. Present channel size is also not large enough to avoid wall effect. It is necessary to study the flow characteristics under the various Reynolds number and metal foam structures.

References 1. Hwang JJ et al (2001) Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams. J Heat Transfer 124(1):120–129 2. Eggenschwiler PD et al (2009) Ceramic foam substrates for automotive catalyst applications: fluid mechanic analysis. Exp Fluids 47(2):209–222 3. Hutter C et al (2011) Axial dispersion in metal foams and streamwise-periodic porous media. Chem Eng Sci 66(6):1132–1141 4. Onstad AJ et al (2011) Full-field measurements of flow through a scaled metal foam replica. Exp Fluids 50(6):1571–1585 5. Moon C et al (2018) Kelvin-cell-based metal foam heat exchanger with elliptical struts for low energy consumption. Appl Therm Eng 144(5):540–550

Dynamics of a Cambered A320 Wing by Means of SMA Morphing and Time-Resolved PIV at High Reynolds Number Mateus Carvalho, Cédric Raibaudo, Sébastien Cazin, Moïse Marchal, G. Harran, Clément Nadal, J. F. Rouchon, and M. Braza Abstract A great deal of current scientific and technological advances in aeronautics concerns innovative wing design in order to increase aerodynamic performance, it is normal to seek better efficiency and refinement for critical structures. Inspired from the nature, deformations and vibrations are applied to aircraft wings. Thanks to smart-materials that deform a structure, an electroactive morphing wing prototype at reduced scale has been realized within the Smart Morphing and Sensing project. Force measurements show that electroactive morphing increase lift up to 2% with wake thickness reduction of around 10%. High-speed time-resolved particle image velocimetry reveals important effects on flow dynamics as well as on time average. Based on these results, this paper proposes the experimental study of the influence of a Shape Memory Alloy (SMA) actuator on the dynamics of a reduced scale A320 wing by means of time-resolved PIV. The velocity fields obtained are analyzed using Proper Orthogonal Decomposition and reconstruction of the dynamic system is performed to identify coherent structures present at the flow… Keywords Aerodynamics · Turbulence · PIV · Closed-loop control · Morphing · Wind-tunnel experiments · Smart materials

1 Introduction It is well known that presently airfoil shapes are not designed to optimize the aerodynamic performance in all flight phases, but still the drag-lift ratio of an aircraft must vary depending on the flight state. Since it has been a major matter of interest M. Carvalho (B) · C. Nadal · J. F. Rouchon Laboratoire Plasma et Convection d’énergie - LAPLACE, 31000 Toulouse, France e-mail: [email protected] M. Carvalho · S. Cazin · M. Marchal · G. Harran · M. Braza Institut de Mécanique des Fluides de Toulouse - IMFT, 31000 Toulouse, France C. Raibaudo Office National d’études et de recherches aérospatiales - ONERA, 31000 Toulouse, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_44

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in aeronautical industry, recent studies [1] show that camber control of the trailing edge may be a solution to reduce aircraft operational costs. Adapting the shape of the wing during the flight can save several percent of fuel consumption for a commercial aircraft. Such concept is called morphing and it has been of extensive research for more than 40 years [1]. The concept of morphing aims to optimize drag-lift ratio by means of shape modification in order to adapt the flow in real time. The main inspiration for this project is the nature. It has been proven that some species of fish are able to manipulate surrounding turbulence to reduce muscle activity [2]. Going even further, owls have an unique mechanism to reduce noise during flight [3]. All of these aspects can and should be used to enhance the performance of aircrafts. It is not a simple task thought. Conventional electromechanical actuators are not the most suitable way to achieve shape optimization mostly because of cost, weight and complex mechanical integration [1]. These issues have motivated recent advances in the field of smart materials such as shape memory alloys (SMA) and piezoelectric macrofiber composites (MFC). Smart materials provide sufficient stiffness to withstand the aerodynamic loads, while being flexible enough to be deformed, showing the potential to be an alternative to conventional electromechanical actuators [4, 5]. Considering electroactive materials, Shape Menory Alloys (SMA) and piezoelectric materials are commonly used. SMA are characterized by thermomechanical behaviors, and most of the applications use actuation by means of Joule heating. Typical applications are shape adaptation at low deformation speed. Piezoelectric materials are activated when exposed to an electric field. Piezoelectric composites are suitable from low to very high frequencies and allow easy integration with electrodes. Electroactive morphing has been the focus of a partnership between LAPLACE and IMFT laboratories for more than 15 years in various collaborative research projects. For the Smart Morphing and Sensing (SMS) European project an electroactive reduced scale prototype has been realized. This prototype embeds both SMA and piezoelectric macro fiber composites (MFC). SMAs ensure high deformation, around 10% of the chord, for camber control while MFCs perform deformation of the trailing-edge at higher frequencies up to 400 Hz [6]. Wind tunnel experiments show that piezoelectric MFC actuation reduces the energy of the wing’s wake thanks to an interaction between the vibrating trailing-edge and the shear layer [7]. Following previous work, [7, 8], the first section of the article is dedicated to the design of the reduced scale prototype. The second section introduces the wind tunnel experimental setup, used to perform force measurements ans High Speed Time Resolved Particle Image Velocimetry (HS TR-PIV). The following sections show experimental obtained after hybrid morphing (SMA and MFC actuation) and present the perspectives for the SMS project.

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2 Prototype Description The considered prototype is an electroactive hybrid morphing wing. It embeds both camber control and Higher Frequency Vibrating Trailing Edge (HFVTE) actuators. The baseline airfoil is a wing section of an A320. The chord 700 mm and the span 590 mm. This aspect ratio affects the flow, but it does not affect the actual results, as the experiments are dedicated to the changes in the flow due to morphing compared to a non-morphing wing. Figure 1 presents the prototype and its three different sections. The actuators are sized, simulated and implemented on the last 30% of the chord, corresponding to usual flap positions. The hollow fixed leading edge contains electronics and tubing for all temperature, pressure and position transducers as well as actuator interfaces. The camber control actuator’s working principle relies on distributed structure embedded actuators: SMA wires are spread under the upper and lower aluminum skins of the wing. The actuation of the upper wires (suction side) causes bending of the trailing edge towards higher cambered shapes. Antagonistically, the actuation of SMA wires under the pressure side skin causes a decrease in camber. Figure 1b shows the SMA actuated wing section. The selected wires are made of Nickel and Titanium. Their properties are activated by a change in temperature. They are heated thanks to electric current through themselves. When warmed, the wires tend to retract by

(a) RS Prototype [9]

(b) Prototype actuated section Fig. 1 Reduced scale prototype developed by Laplace and IMFT

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Fig. 2 HFVTE actuator

a 3% strain that have been previously trained. The modification between martensite and austenite phase in the material internal structure generates a change from plastic to elastic regime, so the SMA tend to recover the initial length. The SMA actuators are designed to support the aerodynamic loads corresponding to a Reynolds number equal to 1 million, which corresponds to a flow velocity 21.5 m/s in IMFT windtunnel. They are able to generate intense stress of more than 600 MPa under these large deformation levels. These materials have been studied for decades, Lexcellent provides an accurate SMA handbook [10]. The HFVTE actuators are composed of metallic substrates sandwiched between “Macro Fiber Composite” (MFC) piezoelectric patches on both sides. MFC patches are LZT piezoelectric fibers and electrode networks encapsulated within epoxy. When supplied by a voltage, the patches stretch out and generate bending. The whole is covered by a flexible molded silicon that gives the trailing edge shape. Figure 2 illustrates the actuator topology. The active length of the HFVTE 35 mm chordwise. Push-push actuators are also seen in literature for this purpose [6]. This design allows for quasi-static tip deformation peak to peak amplitude on the order of 2 mm, while able to vibrate at amplitudes large enough up to 400 Hz. The authors invite the reader to refer to the previous publications [8, 9] for more details related to the design and the electromechanical characterization of this electroactive morphing wing.

3 Experimental Set-Up The experiments were performed in the IMFT (Institut de Mécanique des Fluides de Toulouse) wind-tunnel. The test section 592 mm width 712 mm high. The prototype is mounted at an incidence of 10°. As a result a blockage ratio of 18% is obtained, which is considered acceptable in these experiments. The turbulence intensity of the inlet section is about 0.1% of the free stream velocity. Measurements are carried out at ambient temperature (22 °C). PIV campaign was performed to investigate the influence of the SMA actuation on the flow. In other to image both the upper and the lower surfaces of the wing a 400 mm Nikon lens was chosen. Indeed, as shown in Fig. 3, the experimental set-up of this campaign, the 3 meters distance between the camera and the test section of the wind tunnel reduces the parallax effect. It was then necessary to use a flexible mask to avoid direct laser reflection on the prototype surface. Furthermore, to Particle images are recorded at a rate of 5 kHz using a digital high-speed camera Phanton V2012.

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Fig. 3 PIV equipment. Configuration used to to image both upper and lower surfaces of the wing

The laser sheet is generated by a Photonics DM60-527-DH. 0.5µm particles were employed to obtain an investigation window size of 170 per 260 mm. The commercial software DaVis10 from LaVision was used for post-processing.

4 Results The PIV campaign was performed at Reynolds number of 1 million in which corresponds to a flow velocity 21.5 m/s in the IMFT wind-tunnel. The high speed camera recorded a sequence of snapshots of the SMA actuation of the prototype. The trailing edge comes from static position, that means no actuation performed, to full cambered position in about 1.5 s. The first step for the analysis of the experimental results was to plot the streamtraces of the snapshots obtained with the PIV campaign. It is a fast and useful tool to understand the flow dynamics. In Fig. 4 one can see the snapshots corresponding to the static position and the full cambered case. As it is expected there is an increase in the recirculation zone such as in take-off and landing configurations of commercial aircrafts. A monitor point was chosen in the lower shear layer in the wake of the wing. The normalized coordinates in relation to the chord of the wing are x/c = 1.14 and y/c = −0.20. Then the power spectral density of the two velocity components were calculated. The results are shown in Fig. 5. They are consistent with numerical simulation results obtained [11] where the frequency of von Kármán instabilities were found to be 120 Hz in the lower shear layer region.

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Fig. 4 Streamtraces from PIV campaign. a No morphing, b full SMA actuation

Fig. 5 PSD of monitor point in the shear layer. a, b correspond to the position (x/c = 1.14, y/c = −0.20)

4.1 POD Analysis The Proper Orthogonal Decomposition is a mathematical method used to detect the coherent structures featured by the flow based on their wake number and frequency. It allows us to understand the flow behavior by finding the so-called POD modes that form the dynamic system. This approach is largely used in the analysis of experimental data [12, 13] and numerical simulation. The reader can find a more detailed description of the POD in [14]. In Fig. 6a we see the POD modes ranked by their energy. In the case of full camber position, higher modes have more energy than in the static case. One can see it clearly in Fig. 10 were the PSD of the temporal coefficients of the modes 3 and 5 are presented for static and cambered cases. The rise of the energy can be explained

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Fig. 6 Comparison between: a energy from POD modes and b accumulated energy

Fig. 7 a Shows the u component of the velocity corresponding to the mode 3 while, b shows the v component. c, d Show the same corresponding to the actuated case

by the increase of big coherent structures during SMA actuation. In general, we need more POD modes to describe the dynamics of the flow around the cambered wing, as it is shown in Fig. 6b. Since the recirculation zone is larger, beyond the big energetic vortices, more small structures are formed which correspond to less energetic modes (Fig. 9).

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Fig. 8 a Shows the u component of the velocity corresponding to the mode 5 while, b Shows the v component. c, d Show the same corresponding to the actuated case

Fig. 9 POD reconstruction: velocity components from mode 15

The dynamics of the flow are reined by big structures inside the recirculation zone. Figures 7 and 8 show the modes 3 and 5 respectively. In both figures we see an augmentation of the vortices after SMA actuation which is consistent with the results obtained with PSD analysis and energy rank (Figs. 9 and 10).

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Fig. 10 Comparison between PSD of modes 3 (a) and 5 (b) in static and actuated cases

4.2 Reconstruction from POD Modes Another possibility offered by the POD is the reconstruction of the dynamic system using a reduced number of modes. This approach allows us to identify the most energetic structures by suppressing small instabilities. Figure 11 presents the reconstruction of two different snapshots using 31 modes. Two solution times were chosen to capture both static (t = 1.4 s) and cambered (t = 2.36 s) configurations. The unsteady behavior of the flow in the actuated case is noticeable in both velocity components. The flow vorticity was also calculated using 5 modes to verify the increase of the turbulence in the wake of the wing (Fig. 12). Effectively, the expected result was obtained. We observe the growth of the vorticity specially inside the recirculation zone.

5 Conclusion This paper presents the experimental study of electroactive morphing using a reduced scale prototype of an A320 wing through time-resolved PIV. As it was presented in the prototype description, the wing is embedded with two types of actuators. This work focuses in the POD analysis of the flow which shows the augmentation of wake’s width caused by SMA actuation. The influence of hybrid morphing (high and low frequency actuation at the same time) will be further investigated in the following experimental campaigns. Drag and lift measurements in the wind-tunnel are foreseen such as new PIV campaigns.

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Fig. 11 Reconstruction of the flow using POD modes: a, b show the two velocity components of the static case (t = 1.4 s); c, d correspond to the full camber position (t = 2.36 s)

(a) t = 1.4 s

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Fig. 12 Vorticity of the flow calculated from reconstructed velocity fields

In the context of the SMS project, a closed-loop control system is intended. Through dynamic pressure sensors, the goal is to actuate the trailing edge at optimal frequencies to enhance aerodynamic performance. The results presented in this paper are promising in the sense that the variation in flow dynamics around the region where the pressure sensors are placed is quite perceptible.

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Acknowledgements This research is part of the EU funded project: H2020 SMS “Smart Morphing and Sensing for aeronautical configurations”, http://smartwing.org/SMS/EU.

References 1. Barbarino S, Bilgen O, Ajaj RM, Friswell MI, Inman DJ (2011) A review of morphing aircraft. J Intell Mater Syst Struct 22(9):823–877 2. Liao JC (2003) Fish exploiting vortices decrease muscle activity. Science 302(5650):1566– 1569 3. Sarradj E, Fritzsche C, Geyer T (2011) Silent owl flight: bird flyover noise measurements. AIAA J 49(4):769–779 4. Barbarino S, Saavedra Flores EI, Ajaj RM, Dayyani I, Friswell MI (2014) A review on shape memory alloys with applications to morphing aircraft. Smart Mater Struct 23(6):063001 5. Rouchon J-F, Harribey D, Deri E, Braza M (2011) Activation d’une voilure déformable par des cábles d’AMF répartis en surface, p 6 6. Scheller J, Rizzo K-J, Jodin G, Duhayon E, Rouchon J-F, Braza M (2015) A hybrid morphing NACA4412 airfoil concept. In: 2015 IEEE international conference on industrial technology (ICIT). IEEE, Seville, Mar 2015, pp 1974–1978 7. Scheller J, Chinaud M, Rouchon JF, Duhayon E, Cazin S, Marchal M, Braza M (2015) Trailingedge dynamics of a morphing NACA0012 aileron at high Reynolds number by high-speed PIV. J Fluids Struct 55:42–51 8. Jodin G, Motta V, Scheller J, Duhayon E, Döll C, Rouchon JF, Braza M (2017) Dynamics of a hybrid morphing wing with active open loop vibrating trailing edge by time-resolved PIV and force measures. J Fluids Struct 74:263–290 9. Jodin G, Scheller J, Rizzo KJ, Duhayon E, Rouchon J-F, Braza M (2015) Dimensionnement d’une maquette pour l’investigation du morphing électroactif hybride en soufflerie subsonique. In: 22e Congrès Français de Mécanique (CFM 2015). Lyon, France, Aug 2015, pp 1–13 10. Lexcellent C (2013) Shape-memory alloys handbook. Wiley, Apr 2013 11. Simiriotis N, Jodin G, Marouf A, Elyakime P, Hoarau Y, Hunt JC, Braza M, Morphing of a supercritical wing by means of trailing edge deformation and vibration at high Reynolds numbers: experimental and numerical investigation, p 41 12. Perrin R, Analyse physique et modélisation d’écoulements incompressibles instationnaires turbulents autour d’un cylindre circulaire à grand nombre de Reynolds, p 116 13. Jodin G, Hybrid electroactive morphing at real scale—application to Airbus A320 wings, p 111 14. Sieber M, Oberleithner K, Paschereit CO (2016) Spectral proper orthogonal decomposition. J Fluid Mech 792:798–828, Apr 2016. arXiv: 1508.04642

Design and Experimental Validation of A320 Large Scale Morphing Flap Based on Electro-mechanical Actuators Y. Bmegaptche Tekap, A. Giraud, A. Marouf, A. Polo Domingez, G. Harran, M. Braza, and J. F. Rouchon

Abstract This paper presents the design of an A320 larges scale and preliminary wind tunnel test carried out at Institut de Mécanique de Fluides de Toulouse within the H2020 European Research Program Smart Morphing and Sensing for Aeronautical configuration. This novel camber morphing rely on an optimized compliant internal structure, combined with a macro electromechanical actuator in order to achieve the target deflection of the trailing edge. Keywords Morphing · Electro-mechanical actuator · Wind tunnel · Trailing edge

1 Introduction The aerospace sector is supported by steady growth in air traffic. Since 1994, it has grown by almost 6% a year, so to face to environmental pressures, it is imperative to create an innovative air transport system, based on advanced technologies and demonstrators to reduce the environmental footprint of aircraft through increasing aerodynamic performance (reduced drag, increased lift), noise reduction, reduction of gaseous emissions and aircraft fuel consumption. Actually, greater part of the civil aircrafts are equipped with the conventional design of a high-lift flap in a threeelement wing configuration able to create high cambers by rigid surfaces. The control of surfaces such as the flaps and the slats, while modifying the aerodynamic profile of the wing are heavy to move by means of hydro-mechanical actuation and also Y. Bmegaptche Tekap (B) · A. Marouf · A. Polo Domingez · G. Harran · M. Braza Institut de Mécanique des Fluides de Toulouse, 31400 Toulouse, France e-mail: yannick.bmeg[email protected] Y. Bmegaptche Tekap · J. F. Rouchon LAPLACE Laboratory, 31071 Toulouse Cedex 7, France A. Giraud NOVATEM SAS, 31000 Toulouse, France A. Marouf ICUBE Strasbourg University, Strasbourg, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_45

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create a suboptimal aerodynamic performance and efficiency. According to recent advances made in the field of smart materials, essentially Shape Memory Alloys (SMA), piezoelectric actuators and Electro-mechanical Actuators (EMA), adaptive or morphing structures hold the potential to improve the aerodynamic performance during the take-off and landing (subsonic) phases of the flight. According to work doing by a multidisciplinary research team since 2009 (cf. studies of the platform www.smartwing.org in Toulouse—France, as well as by Jodin et al. [1], Chinaud et al. [2], Scheller et al. [3, 4]), The electroactive morphing hold the potential to operate at different time and length scales and the, manipulating the surrounding turbulent vortices in the shear layers and in the wake in order to increase the aerodynamic performances of the entire wing. The objective of the present work which is part of the H2020 European research project SMS—“Smart Morphing and Sensing for aeronautical configurations” N°723402, is to study the scaling up of the a reduce scale prototype previously study by our laboratory team, toward a full-scale morphing highlift flap of an Airbus A320 wing of 1 m chord. In this work, a novel actuation structure is developed for the shape control of the wing trailing edge and some preliminary aerodynamic has been done for the fixed configuration.

2 Design of Morphing Flap 2.1 Camber Control Principle, Specifications and Objectives The flap profile has been adapted from the specifications of the A320 morphing wing in the context of the SMS European project [2]. The flap chord is 1 m and is 2 m span. The morphing flap is based on articulated ribs and electromechanical actuators, which control the rotation of the elements around the hinges. The proposed concept (Fig. 2) rely on four different functions: articulated ribs define the geometry and carry the other components, hinges allow the rotation of the articulated ribs, and actuators devices transmit mechanical energy to the internal structure. The present design is able to transmit the aerodynamic forces to the structure and to render the appropriate loads after the morphing action. Additionally, mechanical stops are provided to limitate the rotations of the articulations, thus preventing overloads in the actuators. The internal structures represented by the articulated ribs consist of an engineered mechanical structure composed of ribs and spar (Fig. 1).

2.2 Actuation System Design EMAs proved their efficiency and capability to fit as actuators in aeronautical industry. They are also faster to design, produce, integrate, and provide a morphing flap for the aerodynamic tests. To articulate the flap, EMAs are used directly on the

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Fig. 1 Morphing flap target

Fig. 2 Camber morphing concept

rotation axes of each hinge. Nevertheless, considering the very high torque needed to control the camber in flight conditions, using the lever arm available above and below each hinge is an optimal solution. For each hinge, an EMA provides a linear force through the lever arm, which depends on the hinge torque (Table 1). In order to obtain a linear force, different architectures can be used. Direct linear electromagnetic actuators are not adapted to the morphing flap actuation whereas they can be used in several other applications [5]. The most suitable solution remains a rotational actuator connected to a gear and a screw-nut transmission [6], giving a linear movement from a rotational one. Gears could also be removed to have a direct driven motor [7], giving an attractive solution by removing gears and so increasing the transmission efficiency. The torque of an adapted motor torque would be too high without the reduction ratio provided by the gear, leading to a bad compactness and heating issues. The higher the motor speed, the higher its frequency and the lower the quantity of active parts (iron, copper, magnet) [8]. Finally, the most suitable solution for the morphing flap actuation is a high compact motor functioning at high speed connected to high reduction ratio gear and screw-nut transmission. The EMA is produced by NOVATEM and the morphing flap is actuated with a macro-actuator following the same specifications as the previous studies made by Jodin et al. [9] for

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Fig. 3 Morphing flap structure

the SMA actuation. An optimization algorithm have be made In order to choose the suitable position of different actuators. The macro eletromechanical actuator placed in the middle part of the flap, consists of a 6-rib structure in order to create 5-boxes where the EMAs take place, one EMA per box. Each EMA is dedicated to a specific hinge actuation (Fig. 3).

3 Preliminary Aerodynamic Results for the Fixed Configuration 3.1 Mean Pressure Measurements The mean wall pressure around the flap has been measured by pressure taps at Reynolds numbers 2.2M and 2.7M. There is a reasonable agreement between the experiments and the simulations given the fact that the simulations have been done in 2D (Fig. 4).

3.2 Unsteady Pressure Measurements The turbulent flow presents significant variations in pressure. As a consequence, it is possible to characterise the nature of the turbulence from a pressure signal that

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Fig. 4 Pressure coefficients at Re 2.2M (NSMB, Exp) and Re 2.7M (Exp)

contains the information of these fluctuations. For this purpose, a pressure sensor has been tested in the facilities of IMFT. The selected sensor was a piezoresistive pressure transducer, the model 8507C-1 by Endevco. This sensor was placed at 72% of the flap chord (x/c = 0.72), close to the trailing edge where a turbulent flow is expected. Several tests have been carried in the wind-tunnel S1 of the IMFT, always with frequencies acquisition up to 20,000 Hz, far enough from the resonance frequency of the transducer (55,000 Hz). This open return wind-tunnel has an open test section with a circular diameter of 2.40 m, with a velocity range of 1–38 m/s. Measurements are carried out at ambient temperatures (22 °C). Previous studies [1, 4, 10] has shown the importance of studying the power spectral density of the pressure to search the gains of the morphing wing. The method used to obtain the spectra is the Welch method, carried out by dividing the time signal into successive blocks, forming the periodogram for each block, and averaging. Different parameters could be changed in this method, like the number of points of each window or block, the overlap between consecutive windows, or the number of points used to calculate each periodogram. In the current spectra, Fig. 5, the tests have a duration of 10 min with a frequency acquisition of 10,000 Hz (6 Million samples) and a cut-off frequency of 3000 Hz according to the Nyquist-Shannon criterion. The configuration of interest is the Take-Off, that involves a flap deflection angle of 10° and an angle of attack (AoA) of 8° with Reynolds number of 2.2 Million. The blue spectra represents the take-off configuration at a Reynolds number of 2.2M. The orange spectra corresponds to the take-off configuration at a Reynolds of 2.7M.

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Fig. 5 a Pressure spectrum at Re 2.2M and Re 2.7M; b Pressure spectra at Re 2.2M (fVK = 17–19 Hz, f2 = 30 Hz, f3 = 110 Hz)

Both spectrum have a similar behaviour, but also present differences. The energy of the signal is higher for the case at Reynolds number of 2.7 M. The higher level of the spectrum corresponding to Reynolds number 2.7M was expected because of the turbulence level increase as Reynolds number increases. It is illustrated that both spectra display similar predominant frequency bumps. This is due to the flow instabilities being of an absolute character in the present low subsonic Reynolds number range. Among the principal instabilities, the Von Kármán mode characterises the vortex dynamics in the wake and it is measured by the present spectra. It corresponds to the frequency bump indicated in Fig. 5b. The fact that this mode appears as a bump and not as a distinct predominant peak is due to the chaotic turbulent eddies which create a smearing of the coherent alternating Von Kármán eddies. The predominant frequency at maximum amplitude in this bump is of order 17–19 Hz. This corresponds to a Strouhal number of 3.8–4.3. Furthermore, previous numerical and experimental studies [1, 4] has been proved the existence of the Von Kármán instability at low frequencies. A comparison between experimental spectra and numerical spectra has been realised. Numerical simulations were carried out with the Navier Stokes MultiBlock code, which solves the compressible form of the Navier–Stokes equations. Two-dimensional Multi-Block structured grid is built in our research team presented in Fig. 6a, c. The grid captures quite well the real physics around the wing, the flap and the wake and presented in the Fig. 6b where the Mach field contours are highlighted. The numerical signal has a duration of 2 s, obtained with a numerical sampling rate of 100,000 Hz (200,000 samples) at a Reynolds Number of 2.2M. The same incidences of the take-off configuration from the experiments has been adopted. In Fig. 5, the numerical spectrum at 72% of the flap’s chord (x/c = 0.72), with the previous experimental spectra at Reynolds number of 2.2 M. Both spectrum are obtained from pressure signals, presenting some notable similarities. The von Kármán instability bump is visible at 17–22 Hz in a close position

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Fig. 6 Multi-block structured grid for the two-element wing-flap large scale prototype

as in the experiment. It is recalled that the simulations have been carried out under a 2D approximation, whereas the physics in the experimental study are 3D. It is worth mentioning that despite these differences in the approaches, the spectra show these similarities. The slope on the right part of the numerical spectrum is quite decreased than the experimental one because of the turbulence modelling assumptions and the 2D approximation. For the same reasons, the overall level of the spectral amplitudes in the numerical results are lower than in the experiment. However, the predominant frequency peaks and bumps due to the coherent vortices clearly appear in approximately close frequency ranges as in the experiments (Fig. 7). In ongoing studies of our research team, a morphing flap is built and the take-off configuration measurements are under way involving a higher flap’s camber. The gain in the aerodynamic performances will be evaluated comparing to the present static configuration measurements. Fig. 7 Numerical and experimental pressure spectrum at Re 2.2M (fVK = 17–22 Hz, f2 = 30 Hz, f3 = 110 Hz)

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Table 1 Sums up the different torques, lever arm and corresponding forces and strokes for each hinge Hinges

Torque (N m)

Lever arm (m)

Force (kN)

Stroke (mm)

H1

446

+0.050

9.00

7.0

H2

140

+0.040

3.50

6.0

H3

88

−0.030

3.00

1.5

H4

62

−0.030

2.00

1.5

H5

28

+0.012

2.35

2.0

4 Conclusion In this paper, we presented the design of a novel morphing camber flap and some preliminary wind tunnel evaluation we made for the non-actuated configuration and validation with the numerical simulation results. The experimental results for the non-actuated configuration demonstrate very good correlation to the simulation. For the next investigations, we will focus, on evaluation of qualitative and quantitative Aerodynamic performances between the actuated configuration and nonactuated configuration according to different pressures measurement technics and flow visualisation.

References 1. Jodin G, Motta V, Scheller J, Duhayon E, Döll C, Rouchon JF, Braza M (2017) Dynamics of a hybrid morphing wing with active open loop vibrating trailing edge by time resolved PIV and force measures. J Fluids Struct 74:263–290 2. Smart Morphing and Sensing H2020 European Research Programme: https://smartwing.org/ SMS/EU/ 3. Scheller J, Jodin G, Rizzo KJ, Duhayon E, Rouchon JF, Triantafyllou M, Braza M (2016) A Combined Smart-Materials Approach for Next-Generation Airfoils. Solid-State Phenomena 251:106–112 4. Scheller J, Chinaud M, Rouchon JF, Duhayon E, Cazin S, Marchal M, Braza M (2015) Trailingedge dynamics of a morphing NACA0012 aileron at high Reynolds number by time-resolved PIV. J Fluids Struct 55:42–51 5. Ziegler N, Matt D, Jac J, Martire T, Enrici P (2007) High force linear actuator for an aeronautical application. Association with a fault tolerant converter. In: Electrical machines and power electronics, 2007. ACEMP’07. International Aegean Conference on, pp 76–80. IEEE (2007) 6. Rosero JA, Ortega JA, Aldabas E, Romeral LARL (2007) Moving towards a more electric aircraft. IEEE Aerosp Electron Syst Mag 22(3):3–9 7. Gerada C, Bradley KJ (2008) Integrated pm machine design for an aircraft EMA. IEEE Trans Ind Electron 55(9):3300–3306 8. Jac J, Matt D, Ziegler N, Enrici P, Martire T (2007) Electromagnetic actuator with high torque mass ratio, permanent magnet machine with synchronous and vernier double effect, application to aeronautical systems. In: International Aegean conference on electrical machines and power electronics, 2007. ACEMP’07, pp 81–86. IEEE

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9. Jodin G, Bmegaptche Tekap Y, Saucray JM, Rouchon JF, Triantafyllou M, Braza M (2018) Optimized design of real-scale A320 morphing high-lift flap with shape memory alloys and innovative skin. Smart Mater Struct /27*, N° 11 10. Chinaud M, Rouchon JF, Duhayon E, Scheller J, Cazin S, Marchal M, Braza M (2014) Trailingedge dynamics and morphing of a deformable flat plate at high Reynolds number by timeresolved PIV. J Fluids Struct 47:41–54

Manipulation of a Shock-Wave/Boundary-Layer Interaction in the Transonic Regime Around a Supercritical Morphing Wing J.-B. Tô, N. Bhardwaj, N. Simiriotis, A. Marouf, Y. Hoarau, J. C. R. Hunt, and M. Braza Abstract Wing morphing as a means to continuously modify wing geometry is employed in a numerical simulation in order to act upon aerodynamic performance in cruise flight. In this flight regime, the interaction of a shock wave and boundary layer instabilities can lead to transonic buffet, the coordinated motion of both the shock and the detached boundary layer. This flow instability induces unsteady forces on the wing which may induce dip-flutter or cause stall. Understanding where it comes from and how to act on it can be crucial for extending flight envelope or reach better fuel efficiency in the transonic regime. It has been observed that a compliant trailing edge can alter the amplitude and frequency of the buffet instability and improve aerodynamic performance by modifying the flow topology of the wake and detached boundary layer. Keywords Instability · buffet · OES · supercritical wings · compressible flow

J.-B. Tô (B) · N. Bhardwaj · N. Simiriotis · A. Marouf · M. Braza Institut de Mécanique des Fluides de Toulouse, Allée du Professeur Camille Soula, Toulouse, France e-mail: [email protected] M. Braza e-mail: [email protected] A. Marouf · Y. Hoarau Institut de Mécanique des Fluides et des Solides de Strasbourg, Strasbourg, France J. C. R. Hunt University College London, London, UK © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_46

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Nomenclature c Cp Re Ma St α fb f ac · k = u i u i /2 ε 1/4 y + = Cμ k 1/2 y/ν t Cl Cd x y

Chord Pressure coefficient Reynolds number Mach number Strouhal number Angle of incidence Buffeting frequency Morphing actuation frequency Time average Turbulence kinetic energy Rate of dissipation of turbulence energy Non-dimensional distance to the wall in the k − ε turbulence model Computation time-step Lift coefficient Drag coefficient Streamwise coordinate (in m) Vertical coordinate (in m)

1 Introduction The main purpose of this paper is to study the influence of wing morphing on the aerodynamic behaviour of a supercritical wing at high Reynolds numbers in the transonic regime—that is for Mach numbers between 0.7 and 1.2. In these flight regimes and for certain angles of attack, the acceleration of air over a wing can be such that the airflow reaches supersonic speeds over the wing even for Mach numbers lower than 1. This acceleration results in flow compression, marked by the appearance of a normal shock or a lambda shock. Due to the reverse pressure gradient caused by flow compression at the shock foot, the boundary layer is made to thicken and may separate significantly. As the turbulent boundary layer detaches, the rear flow geometry is considerably modified, with the thickening of the shear layer and wake region negatively contributing to aerodynamic performance due to an increase of pressure drag and viscous drag. The interaction of the shock and the boundary layer that detaches aft the shock may result in an oscillating motion of the entire interaction zone, causing the shock to move back and forth and the boundary layer to alternatingly thicken up and thin down. This flow instability is called transonic buffet. Over the past forty years, numerous analyses have been made to understand and predict the occurrence of buffet, with pioneering studies by Seegmiller et al. [1], McDevitt et al. [2], Levy et al. [3] or

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even Marvin et al. [4], investigating the behaviour of this instability using Schlieren imaging and early computational results. In 2012, a study by Grossi et al. [5] demonstrated how a splitter-plate placed at the aft end of a wing stifles the Von Kármán mode, and weakens the buffet instability. A feedback mechanism from the rear part of the flow—including shear layer instabilities in the detached boundary layer and the Von Kármán instability in the wake—towards the shock has thus been highlighted. The previous observations indicate that it should be possible to reduce the intensity of buffet or manipulate the unsteady aerodynamic loads thanks to morphing, i.e. the continuous transformation of the wing’s shape. The present study investigates the effects of a trailing edge monochromatic vibration on the frequency of buffet. Hybrid morphing, as a combination of a single trailing edge deflection and high-frequency vibrations, has also been studied. Finally, it is shown how aerodynamic performance can be impacted by the frequency of actuation and how drag reduction can be achieved through dynamic morphing.

2 Numerical setup The numerical domain used in this study is a two-dimensional 190,000-cell structured, C-H topology multiblock mesh (cf. Fig. 2) around an A320 airfoil of chord c = 0.15 m. This geometrical configuration comes from a collaboration between several research teams among the European project SMS—Smart Morphing and Sensing for aeronautical configurations. As such, the flow parameters and size of the wing in the numerical study have to be in accordance with those of the transonic windtunnel in the IMP-PAN Academy of Science of Gdansk, Poland. A Reynolds number of Re = 2.07 × 106 and a Mach number of Ma = 0.78 are chosen to reproduce cruise flight conditions. Two angles of attack were investigated in this paper. While most quantitative results have been generated for α = 1.8° which is the standard configuration for high altitude cruise flight, an incidence angle of α = 5° has also been studied due to the stronger SWBLI effects that appear with that angle, in order to better understand the large scale unsteadiness due to buffet. A URANS approach was chosen as an ideal trade-off between computational speed and accuracy, with a k − ε Chien model used along the Organised Eddy Simulation (OES) statistical approach as in Jin and Braza [6], Braza et al. [7], Szubert et al. [8, 9] in order to correctly represent and predict the complex dynamics of coherent structures and chaotic turbulence (Fig. 1). Thanks to the collaboration between our research group and other partners within the NSMB European Consortium, transonic computations were run using the NavierStokes Multi Block (NSMB) code (see [10]). Numerical results are found by solving the compressible Navier-Stokes equations using a finite-volume formulation. A thirdorder Roe upwind scheme has been employed for the discretization of spatial fluxes

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Fig. 1 a Transonic windtunnel test section in IMP-PAN. b The morphing wing test bed with streamlined walls above and below the wing

Fig. 2 Above: 2D structured multiblock mesh; Below: “Numerical windtunnel” 3D structured multiblock mesh

while time integration was performed through a dual-time stepping, second-order backward difference scheme as per past studies by Szubert et al. [8], Grossi et al. [5] and Tô et al. [11]. For time-accuracy, a time-step of t = 5 × 10−6 has been chosen (Fig. 2).

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3 Results 3.1 Effect of Morphing on the Force Coefficients When integrated over the surface of the wing, the unsteady loads due to the SWBLI result in a quasi-periodic signal. This is mainly due to the motion of the shock that causes the compression zone to oscillate back and forth, explaining the relatively gentle slope at x/c ≈ 0.7 in the time-averaged −C p profile of Fig. 3. Indeed, if the shock was still, the pressure distribution would be steeper in the shock area. The detached boundary layer also increases pressure aft the shock. This is due to the strong reverse pressure gradients that accompany shock-induced flow separation. It is seen, through the red curve of Fig. 5 that a slight upward deflection of the trailing edge by 2° can annihilate flow unsteadiness due to buffet, thus proving that buffet can be suppressed, although at a loss of lift. Indeed, an upward motion of the trailing edge lowers wing curvature along the suction side, thus reducing the intensity of the reverse flow and as a consequence diminishes both the thickness and extent of the detached boundary layer. Figure 4 shows an instance of strong flow separation and destabilization due to SWBLI. Additionally, the lift coefficient time series for a combined deflection and vibration at f ac = 90 Hz (blue curve of Fig. 5) shows that the average value of the lift coefficient is increased compared to that of a simple deflection of the trailing edge. This implies that adding a vibration to the trailing edge allows to modify the average values of both lift and drag by changing the flow dynamics of the turbulent viscous zones, namely the shear layer and turbulent wake. Notably, we observe that although average lift is decreased in the case of an upward deflection, average drag is decreased by a more substantial amount. Overall, timeaveraged lift to drag ratio is increased by 10.4%. It has been observed that lift to drag ratio increases in all morphing types, for both angles of attack α = 1.8° and α = 5°, even though this increase is more important for small incidences. In fact, due to the strong separation that happens for important angles of attack, small modifications of

Fig. 3 Time-averaged pressure coefficient plot for the static configuration

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Fig. 4 Density gradient iso-contours and streaklines around an airfoil at Ma = 0.78, for an angle of incidence α = 5°. The presence of the Von Kármán instability and the destabilization of the shear layer aft the shock are symptomatic of a strong SWBLI. The same behaviour can be observed, to a lesser extent, for α = 1.8° 0.58

Static configuration 2o upward deflection Upward deflection + flapping

0.56 0.54

Cl

0.52 0.5 0.48 0.46 0.44 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

t (in s) Fig. 5 Lift coefficients for α = 1.8°

the trailing edge geometry or small vibration have a lesser impact on aerodynamic performance. It has been shown by Jodin et al. [12] that hybrid morphing with highamplitude wing distortions is particularly effective for low-Mach regimes at large angles of incidence. These results are listed in Table 1.

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Table 1 Relative mean lift over drag ratio gain compared to the static case Incidence Angle of attack 1.8 Angle of attack 5 Type of actuation D D+F D D+F Cl /Cd − Cl /Cd static × 100 +10.4% +4.3% +2.5% +0.4% Cl /Cd static Note that D means “2° deflection” and “D + F” is the superposition of an immobile upward deflection and a 90 Hz flapping motion

3.2 Frequency Synchronization For the entire array of frequencies F := 100; 150; 200; 250; 300; 350; 400; 450; 500; 700; 720; 750; 800; 1000; 1500 Hz, the vibrating trailing edge appears to synchronize the SWBLI frequency as is shown in Fig. 5 and some Power Spectral Density plots below. The first peak, corresponding to the buffet mode, appears to be shifted in the frequency domain and perfectly coincides with the frequency of trailing edge actuation. As can be observed in Fig. 6, the leftmost mode represented by a wide bump corresponds to the natural buffet frequency f b = 111 Hz (for a Strouhal number St = 6.65 × 10−2 ) in the case of an immobile wing (black curve). When the trailing edge of the wing vibrates at a certain frequency f ac , the up-and-down motion of the geometry walls exerts a periodic pressure disturbance in the boundary layer which forces it to move along with the trailing edge. The separation zone is thus made to travel back and forth which causes compression waves near the separation zone— and consequently the shock—to develop an oscillatory motion that is synchronized with the vibrating trailing edge.

3.3 Time-Averaged Force Coefficients at Various Actuation Frequencies The mean values of the aerodynamic force coefficients as well as their RMS are found for frequencies f ∈ F. The actuation considered is a monochromatic flapping actuation around the static trailing edge with an angle of flapping α F = 1°. The lift coefficient is seen to increase compared to the static case for fac = 400 Hz, f ac = 450 Hz, f ac = 500 Hz and f ac = 720 Hz while drag decreases compared to the static case for all frequencies but f ac = 400 Hz, f ac = 450 Hz and f ac = 500 Hz. This shows that the only actuation frequency among those that were studied that both increases lift and decreases drag is f ac = 720 (Fig. 7). It is noticed that mean lift and drag follow the same trends. This suggests that the underlying mechanisms explaining lift and drag generation through vibrational trailing edge morphing is the same.

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Fig. 6 Power spectral density plots of the lift coefficient for f ac = 100 Hz (above) and for f ac = 400 (below). The black curves represent the PSD estimation via a Welch method applied to the lift coefficient of the unmorphed wing. The blue curves stand for morphing cases

Some frequencies stand out in terms of performance improvement. In particular, it is observed that an actuation frequency of f ac = 720 decreases drag by 1.2% and increases lift by 0.3%, cf. Fig. 8. Although lift is decreased by 1.1% and 3.8% for f ac = 300 Hz and f ac = 350 Hz respectively, drag is reduced by 3.5% for f ac = 300 Hz and by 8.9% for f ac = 350 Hz. This signifies that lift to drag ratio increases by up to 5.5% in the case of an actuation frequency of 350 Hz.

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Fig. 7 Comparison between time-averaged force coefficients for actuation frequencies f ac ≤ 450 Hz and the static case. 100 × C fi /C fi static and 100 × C fi morphing − C fi static /C fi static is the relative mean evolution (in %) of the quantity C fi . If it is positive, it means that morphing contributes to increase the average value of C fi compared to the static case and vice versa

3.4 Comparison of Mean Velocity Profiles in the Wake The wake velocity profile at x/c = 0.19 for frequencies 300, 350 and 400 Hz has been compared with the static case. The wake width is calculated from Fig. 9, and the values are listed in Table 2. It can be seen from Table 3 that the wake becomes thinner in both f ac = 300 Hz and f ac = 350 Hz, and it becomes thicker than the static case wake for an actuation frequency of 400 Hz. This coincides with observations that on average, drag decreases for both f ac = 300 Hz and 350 Hz while it increases for f ac = 400 Hz. Even more remarkably, the velocity deficit in the case of f ac = 400 Hz is more significant than that of the static case, while the velocity deficit for f ac = 350 Hz is less important. This indicates that wing morphing achieved by a vibration of the trailing edge acts on the wake dynamics by reducing or increasing total pressure deficit.

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Fig. 8 Comparison between time-averaged force coefficients for actuation frequencies f ac ≥ 500 Hz and the static case 0.04 0.03

350 Hz 300 Hz 400 Hz static

0.02 0.01 0 -0.01 180

200

220

240

Fig. 9 Time-averaged velocity profiles at x/c = 0.19 for f ac = 300 Hz, 350 Hz, 400 Hz and the static (immobile trailing edge) case

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Table 2 Wake width for different actuation frequencies, with Z = |z 1 − z 2 | 300 Hz 350 Hz 400 Hz Width of wake Z /c

3.33 × 10−2

3.22

× 10−2

3.45 × 10−2

Static 3.43 × 10−2

The coordinates z 1 and z 2 are chosen along the vertical z-axis where ||u(z)|| = 0.95U∞ Table 3 Percent change in terms of wake width compared to the static case. 300 Hz 350 Hz 400 Hz 100 × Z /Z static (in %) −2.9 Z /Z static = Z morphing − Z static /Z static

−6.1

+0.6

4 Conclusions This study presents the analysis of trailing edge morphing and its influence on the aerodynamic forces exerted on a supercritical wing in the transonic regime. Due to the presence of buffet in this range of Mach numbers which stems from a nascent SWBLI, the investigation also revolves around SWBLI manipulation through hybrid morphing. Numerical results from 2D computations show that morphing is able to considerably modify the flow dynamics around the airfoil in transonic flight, allowing to suppress force unsteadiness due to buffet with a slight upward deflection of the trailing edge, or to synchronize the instability with a vibration of the wing’s aft-end. It has also been shown that wing morphing is capable of changing the pressure distribution in the detached boundary layer and more particularly in the wake region. This contributes to either increase or decrease the width of the wake and the total pressure deficit in this viscous region of the flow, which translates in either a larger or a lower amount of pressure drag characterized by thick separation or a wide turbulent wake. Acknowledgements The authors are grateful to the LAPLACE Laboratory GREM3 research group on electrodynamics and to the National Supercomputing centers CALMIP, CINES and IDRIS for the Computer allocation, as well as the PRACE Supercomputing allocation number 2017174208. This study has been realised under the H2020 European Research programme n° 723402: SMS, “Smart Morphing and Sensing for aeronautical configurations”, http://smartwing.org/SMS/EU/.

References 1. Seegmiller HL, Marvin JG, Levy LL (1978) Steady and unsteady transonic flow. AIAA J 16:1262–1270 2. McDevitt L, Levy L Jr, Deiwert G (1976) Transonic flow about a thick circular-arc airfoil. AIAA J 14:606–613 3. Levy L Jr (1978) Experimental and computational steady and unsteady transonic flows about a thick airfoil. AIAA J 16:564–572

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4. Marvin J, Levy L Jr, Seegmiller H (1980) Turbulence modeling for unsteady transonic flows. AIAA J 18:489–496 5. Grossi F, Szubert D, Braza M, Sevrain A, Hoarau Y (2012) Numerical simulation and turbulence modelling of the transonic buffet over a supercritical airfoil at high Reynolds number. In: Proceedings of the ETMM9 9th international ERCOFTAC symposium on engineering turbulence modelling and measurements. Thessaloniki, Greece 6. Jin G, Braza M (1994) Two-equation turbulence model for unsteady separated flows around airfoils. AIAA J 32:2316–2320 7. Braza M, El Akouri R, Martinat G, Hoarau Y, Harran G, Chassaing P (2006) Turbulence modelling improvement for highly detached unsteady aerodynamic flows by statistical and hybrid approaches. In: ECCOMAS CFD 2006: European conference on computational fluid dynamics 8. Szubert D, Grossi F, Jimenez Garcia A, Hoarau Y, Hunt JCR, Braza M (2015) Shock-vortex shear-layer interaction in the transonic flow around a supercritical airfoil at high Reynolds number in buffet conditions. J Fluids Struct 55:276–302 9. Szubert D, Asproulias I, Grossi F, Duvigneau R, Hoarau Y, Braza M (2015) Numerical study of the turbulent transonic interaction and transition location effect involving optimisation around a supercritical aerofoil. Eur J Mech B Fluids 55:380–393 10. Hoarau Y, Pena D, Vos JB, Charbonier D, Gehri A, Braza M, Deloze T, Laurendeau E (2016) Recent developments of the Navier Stokes multi block (NSMB) CFD solver. In: 54th AIAA aerospace sciences meeting. AIAA SciTech Forum. American Institute of Aeronautics and Astronautics 11. Tô J-B, Simiriotis N, Marouf A, Szubert D, Asproulias I, Zilli D, Hoarau Y, Hunt JCR, Braza M (2019) Effects of vibrating and deformed trailing edge of a morphing supercritical airfoil in transonic regime by numerical simulation at high Reynolds number. J Fluids Struct 91:102595 12. Jodin G, Motta V, Scheller J, Duhayon E, Döll C, Rouchon J-F, Braza M (2017) Dynamics of a hybrid morphing wing with active open loop vibrating trailing edge by time-resolved PIV and force measures. J Fluids Struct 74:263–290

Predictive Numerical Study of Cambered Morphing A320 High-Lift Configuration Based on Electro-Mechanical Actuators A. Marouf, N. Simiriotis, Y. Bmegaptche Tekap, J.-B. Tô, M. Braza, and Y. Hoarau

Abstract The principal aim of this paper is to investigate the numerical effects of a deformable flap by means of a quasi-static cambering following an Airbus A320 designed prototype in the Smart Morphing and Sensing European project. This prototype able to camber by means of the Electro-Mechanical Actuators (EMA) to achieve high amplitude deformation up to 10 cm. This mechanism allows to improve the aerodynamic performances of high-lift system during the take-off flight stage. This study reveals the effects of cambering over the pressure field around the flap in different suggested positions. A considerable increase of the static pressure in the pressure side of the flap and a high low-pressure in its suction side is illustrated for the cambered flap compared to the reference test case, which leads to improve lift-to-drag ratio. Keywords Morphing · Camber · Airfoil · Flap · High-lift · Aerodynamic

1 Introduction During the flight the fluid flow around the wing is affected by many instabilities related to many reasons such as the airplane speed in different flight stages, as for instance the buffet phenomena that occurs during the transonic phase. This instability known as Shock Wave Boundary Layer Interaction (SWBLI), results of a non-linear interaction can may induce a considerable boundary layer detachment. In addition, the flow separation near the flap’s trailing-edge is identified according to high angles of incidence or deflections. A rigid wing or flap system is not well adapted to flow

A. Marouf (B) · Y. Hoarau University of Strasbourg, Icube, France e-mail: [email protected] A. Marouf · N. Simiriotis · Y. B. Tekap · J.-B. Tô · M. Braza Institut de Mécanique des Fluides de Toulouse, Toulouse, France © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_47

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changement in order to have improved aerodynamic performances and to handle these instabilities to avoid an exceed of fuel consumption or airplane crush. To this end, researchers interested to a partly bio-inspired morphed wings from birds toward active flow control aiming to enhance the lift, reduce the drag, suppress the separation and delay the onset of stall. It is therefore essential to understand the flow response to the dynamic actuation or wing-flap passive deformation known as camber control seeking to an optimized shape to get a desired effective performances. Woods et al. [1] constructed a Fish Bone Active Camber morphing structure concept and investigated its effects with aerodynamic measurements and compared it with flapped airfoils, their study revealed that the FishBAC airfoil generates considerably less drag and an increase of 20–25% of lift-to-drag ratio compared to flapped airfoil over a range of angles of attack. Furthermore, Jodin et al. [2] carried out forces measurements and TR-PIV on a wing prototype equipped with a coupled system of Shape Memory Alloys (SMA) and piezoelectric-actuators in the trailing-edge named hybrid morphing. Camber control at low-frequency-high-amplitude is achieved by means of the SMA. This work showed that at a specific range of cambers and trailing edge vibrations an increase of lift in the order of 27%, where only +4% are obtained by the small amplitude vibrations. The present study is performed to produce a predictive numerical solution of an Electro-Mechanical Actuator (EMA) structures for the active camber control of a Large-Scale (chord c = 2.72 m) Airbus A320 prototype in the take-off position. This concept is suggested by Bmegaptche Tekap et al. [3] in the context of the Smart Morphing and Sensing SMS European project (www.smartwing.org/SMS/EU). Experimental design of the cambered flap of chord c = 1 m as illustrated in Bmegaptche Tekap et al. [3] employs the articulated concept. An equivalent numerical model is implemented in the Navier Stokes Multi-Block (NSMB) solver and described in this study. Different shapes were tested in order to obtain a better position allowing to obtain improved performances.

2 Computational Methodology The set of the compressible Navier-Stokes (NS) equations was discretized and solved using the NSMB solver Vos et al. [4], Hoarau et al. [5]. An implicit dual time stepping was employed using the 2nd order implicit backward scheme. At each time step, iterative approach is used and defined by an external and internal loop. A 4th order central skewsymmetric scheme is selected for the space discretization. In addition, the artificial compressibility method for the preconditioning is employed to simulate conveniently the incompressible form of NS equations. A C-type mesh was generated for the Large-Scale airfoil-flap of the Airbus A320 prototype. The boundary domain is supposed as a far-field conditions of 20 chords to capture correctly the pressure field for the two-element configuration. The grid is well refined and validated adopting the right turbulence models in previous studies of Marouf et al. [6] with literature.

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Fig. 1 Quasi-static camber control of the A320 flap similar to the EMA behaviour

Fig. 2 Details of the used structured grids. a Reference case. b Cambered case

The flow around the A320 airfoil-flap is considered at 0◦ angle of attack, 10◦ angle of flap deflection and Reynolds number of 2.2 × 106 corresponding to the take-off position. Different positions of camber control were selected (see Fig. 1) with the experimental EMA movement designed in the SMS project. The structured grid is smoothly deformed while maintaining a good quality, orthogonality and skewness of the mesh cells. The reference A320 case and different cambered positions from low to high amplitude of deformation were simulated and compared. The camber distance is of 85% of the total flap’s chord and its maximum amplitude is maintained 10 cm as illustrated in Fig. 2.

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Table 1 Different camber positions selected for the computational study Camber Pref P1 P2 P3 positions

P4

Trailing-edge distance (cm)

–

3

5.7

7.8

9.2

3 Numerical Results In the following section the flow field around the reference and cambered cases is characterized. Pressure and aerodynamic forces are discussed. Converged signals are stored and the mean forces were calculated in order to analyse the camber effects over the performances of the airfoil-flap system. Different intermediate suggested positions described in Table 1 were selected to analyse the camber of the flap and its effects over the fluid flow. Table 1 illustrates 4 chosen vertical distances of the flap’s trailing-edge downward following the control low of the EMA actuators. Figure 3 corresponds to the different selected camber position compares the differential of pressure p − p0 , where p0 is the standard pressure of the air to the reference case in Fig. 3a. A gradual increase the p − p0 from the leading edge to the trailing edge in the pressure side when the flap is cambered downward. In the other hand, in the suction side a pressure decrease varies gradually from −62.25 Pa in the reference position up to −96.859 Pa in the position P4.

4 Conclusion In this paper numerical simulations were carried out for a high-lift configuration with an implemented predictive camber solution based on a new design of morphing flaps using the EMA structures. The control low of these structures is tested for different quasi-static camber positions in the downward direction in different positions. The pressure around the flap is investigated. As a result, the distribution of the difference of pressure is higher in both sides of the flap compared to the reference case. In addition, calculated mean values of lift and drag forces for different positions revealed an increase of +25% in the lift-to-drag ratio.

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(a) Pref

(b) P1

(c) P2

(d) P3

(e) P4 Fig. 3 Distribution of the of pressure field of the flap in different camber positions

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Acknowledgements The authors acknowledge the computational support and facilities of the computing centers CINES, CALMIP, HPC-Strasbourg and the PRACE allocation N 2017174208. This work was carried out under the H2020 European Research programme N 723402: “Smart Morphing and Sensing” (SMS) http://smartwing.org/SMS/EU.

References 1. Woods BKS, Bilgen O, Friswell MI (2014) Wind tunnel testing of the fish bone active camber morphing concept. J Intell Mater Syst Struct. https://doi.org/10.1177/1045389X14521700 2. Jodin G, Motta V, Scheller J, Duhayon E, Döll C, Rouchon JF, Braza M (2017) Dynamics of a hybrid morphing wing with active open loop vibrating trailing edge by time-resolved PIV and force measures. J Fluids Struct 74:263–290. ISSN 0889–9746. https://doi.org/10.1016/j. jfluidstructs.2017.06.015 3. Bmegaptche Tekap Y, Marouf A, Braza M, Giraud A, Nogarede B, Jodin G, Nadal C, Rouchon J-F (2019) A structural design of large-scale high-lift morphing compliant A320 wing based on smart materials and electromechanical structures. AIAA Aviation Forum. Dallas, Texas, 17–21 June 2019. https://doi.org/10.2514/6.2019-2908 4. Vos J, Rizzi A, Corjon A, Chaput E, Soinne E (1998) Recent advances in aerodynamics inside the NSMB (Navier Stokes Multi Block) consortium. https://doi.org/10.2514/6.1998-225 5. Hoarau Y, Pena D, Vos JB, Charbonier D, Gehri A, Braza M, Deloze T, Laurendeau E (2016) Recent developments of the Navier Stokes multi block (NSMB) CFD solver. In: 54th AIAA aerospace sciences meeting. American Institute of Aeronautics and Astronautics. https://doi. org/10.2514/6.2016-2056 6. Marouf A, Hoarau Y, Vos JB, Charbonnier D, Bmegaptche Tekap Y, Braza M (2019) Evaluation of the aerodynamic performance increase thanks to a morphing A320 wing with high-lift flap by means of CFD Hi-Fi approaches. AIAA Aviation Forum. Dallas, Texas, 17–21 June 2019. https://doi.org/10.2514/6.2019-2912

Shape Control of Flexible Structures for Morphing Applications Georgios K. Tairidis, Aliki D. Muradova, and Georgios E. Stavroulakis

Abstract In this work, shape control of flexible structures using enforced deformations as control actions is considered. The proposed scheme can be applied for morphing of truss structures, such as a radio-telescope bases, aircraft smart wings, spray booms etc. A static problem for different external loadings is considered. In order to control the shape of the structure, suitably designed deformations of selected structural members are applied. Applied deformations on selected control elements can be realized by means of several technologies: thermal stresses, piezoelectric effects, shape memory actuators etc. The shape of the structure is changed according to the environmental conditions. For instance, in order to have an optimal control of geometry of the aircraft smart wing, it should be modified in dependence of weather phenomena, air turbulence, pressure, flow velocity and others. In this paper the discrete steps of shape changing of the structure, which is under external loading and control, are shown. Keywords Morphing · Smart structures · Thermal forces · Smart wings · Trusses

1 Introduction Shape control and damage identification on smart structures including piezoelectric layers has been proposed in [1]. Namely, a beam structure which is equipped with bonded piezoelectric actuation, which provides the control forces, and genetic optimization is considered and tested. The mathematical modelling is based on the

G. K. Tairidis · A. D. Muradova · G. E. Stavroulakis (B) Technical University of Crete, GR-73100 Chania, Greece e-mail: [email protected] G. K. Tairidis e-mail: [email protected] A. D. Muradova e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_48

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shear deformation Timoshenko beam theory and Hamilton’s principle, in combination with linear piezoelectricity. Locking-free finite elements are developed, while the optimal locations of piezo-actuators and optimal voltages for shape control are obtained using genetic optimization. Static data and genetic optimization are used for the solution of the related damage identification problem. From the numerical results it is shown that only a small number of actuators can achieve shape control of the structure effectively, given that they are optimally placed, and they have optimal voltage values. The term morphing can be used to describe a wide range of elements which comply to the structural requirements of complex systems such as smart wings of aircrafts. This adaptation usually includes the change of shape in real-time, e.g., modification of wing shape during in-flight operation (see among others [2, 3]). In the book of Valasek [4], morphing of aerospace vehicles and structures is discussed in depth. Namely, the state-of-the-art, some future directions, as well as all the technical requirements of morphing aircrafts are provided. A special focus on flight control, aerodynamics, and materials, and structures of these vehicles is also given. Last, but not least, aspects as the power requirements as well as the use of smart materials, such as advanced piezo materials and smart actuators are also discussed. The optimal design of smart composites is discussed in [5]. An important aspect is that beyond classical shape and layout optimization, pointwise optimization can provide fully functional graded composites. Other smart materials such as shape memory alloys (SMA) and shape memory polymers (SMP) can be also used for this purpose. For example, in [6] the conceptual design, prototype fabrication, and evaluation of shape morphing wing using smart materials is discussed. The results indicate that antagonistic SMA-actuated flexural structures create an enabling technology which can be used for wing morphing of small aircrafts. An approach using shape memory alloys (SMAs) and macro-fiber composites (MFCs) on the trailing edge of a smart wing is presented in [7]. In the recent work of Wang et al. [8] feedback is also used for dynamic morphing of flexible wings with piezocomposite materials. In the present investigation, matrix structural analysis techniques for shape control of truss structures will be outlined. Thermal loads are used as vehicle for the introduction of static control actions, as described in [9], although piezoelectric or shape memory technologies can be used instead with small changes. The formulation covers structures and mechanisms and can be used for the study of the competitive terms of controllability and optimal stiffness, as described in the book of Connor and Laflamme [10]. Moreover, in the case of morphing smart compliant mechanisms, topology optimization can be used for the formulation of the mechanism as presented in [11]. In dynamic problems, the dynamic morphing of smart trusses and mechanisms can be achieved using soft computing such as fuzzy and neuro-fuzzy techniques. A first approach on dynamic morphing has been presented in a recent work of our team [12] regarding neuro-fuzzy control of smart truss-like radio-telescope bases. Coupling of shape control and dynamic morphing represents an area of interesting future research.

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2 Formulation of the Problem For a truss, one-dimensional bar element thermal deformation is given as {εT } = {aT }

(1)

where α is the thermal expansion coefficient and T is the thermal excitation. This deformation can be taken into account at a static finite element analysis through equivalent nodal forces of the form { fT } =

−EaT EaT

A

(2)

where E is the elasticity modulus and A is the cross-section of the bar. Therefore, at element level one has [K e ]{u} = { f M } + { f T }

(3)

where f M are the mechanical nodal forces and f T are the thermal nodal forces, while K e is the element stiffness and u the displacement vector. At structural level, after classical assembly of finite elements, one obtains K u = f + Aw

(4)

where w is the thermal vector of all thermally actuated bars, which can be used as control variables, and A is a suitable influence matrix coming from the connectivity of the finite elements. K, u and f are the global stiffness matrix, the global displacement vector and the global force vector respectively. A shape optimal control problem can be formulated as a least square minimization problem 1 min (u − u 0 )T L(u − u 0 ) + w T Qw 2

(5)

subject to the state equilibrium Eqs. (4). L and Q are weight matrices and u 0 is the desired displacement vector defining the goal of the shape control. Problem (5) is a compromise optimization, where the values of L and Q define the importance of goal satisfaction and cost of control, respectively. The combination of quadratic optimization (5) with linear static structural model (4) is simple. Nevertheless, additional requirements, either at the optimization function or at the structure, like allowable stress or buckling constraints, make the corresponding optimal design problem more complicated. The same happens in case of a mechanism, where the stiffness matrix K in (4) is singular, cf. [10]. A general genetic optimization scheme

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Fig. 1 Smart wing with truss-like inner part. Thicker lines denote the temperature actuated bars

can be used for the solution of such problems, although even local optimization techniques can be applied for specific applications. In order to give a specific numerical example, the smart wing of Fig. 1 is studied. The inner part of this wing is formulated as a 2D truss supporting structure as shown in Fig. 1. It should me noted here that the bars which are marked with thicker lines, are temperature actuated, according to the mechanism which was described above. The temperature induced bars cause changes of the form of the truss structure, and this property can in turn be used to modify the final shape of the smart wing, which is the desired outcome of morphing wings. Moreover, this procedure can be used as a prototype and it can work with other technologies such as piezoelectrics or SMAs.

3 Numerical Examples and Discussion In the present investigation, two different scenarios are discussed. For the first scenario, a high vertical force F = 1000 N is applied at the free end of the structure. Regarding the second scenario, the equivalent nodal forces of the upper actuators are considered to be high, i.e. f T 1 = f T 2 = 1000 N, while the equivalent nodal forces of the lower actuators is low, i.e. f T 3 = f T 4 = −1000 N, according to Eq. 2. The material of the truss is steel with Young’s modulus E = 200 GPa, cross section A = 0.1 m2 and thermal expansion coefficient a = 13 · 10−6 ◦ C−1 . Thus, from Eq. 2 T = 3.85 · 10−3 ◦ C. The initial and the deformed truss-like inner part of the smart wing for the first and second scenario are shown in Figs. 2 and 3 respectively.

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Fig. 2 Initial (with dashed line) and deformed (with solid line) truss for the first scenario

Fig. 3 Initial (with dashed line) and deformed (with solid line) truss for the second scenario

4 Conclusions From the numerical examples, it is shown that the thermal deformation of the bar elements of a truss, can be used as a prototype for calculating static morphing of smart wings in the sense that they can modify its shape. Of course, other technologies such as piezoelectric materials or SMAs can be used with slight modification of the proposed model. In dynamic problems, morphing can be achieved using optimal control or more general soft computing such as fuzzy and neuro-fuzzy techniques. In this case quick response cannot be realized by thermal actuation. Nevertheless, the concept of using initial prestressing or deformation for applying the control action remains valid as a suitable computational tool. In addition, usage of soft computing and artificial intelligence tools will enable easy fusion of measurements and data, in order to take into account more complicated fluid–structure interaction tasks. The

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coupling of shape control and dynamic morphing represents an area of interesting future research.

References 1. Hadjigeorgiou EP, Stavroulakis GE, Massalas CV (2006) Shape control and damage identification of beams using piezoelectric actuation and genetic optimization. Int J Eng Sci 44:409–421 2. Paradies R, Ciresa P (2009) Active wing design with integrated flight control using piezoelectric macro fiber composites. Smart Mater Struct 18:035010 3. Weisshaar TA (2013) Morphing aircraft systems: historical perspectives and future challenges. J Aircraft 50:337–353 4. Valasek J (2012) Morphing aerospace vehicles and structures. Wiley, New York 5. Tairidis GK, Foutsitzi G, Stavroulakis GE (2019) Optimal design of smart composites. In: Demetriou I, Pardalos P (eds) Approximation and optimization. Springer Optimization and its applications, vol 145. Springer, Cham 6. Sofla AYN, Meguid SA, Tan KT, Yeo WK (2010) Shape morphing of aircraft wing: status challenges. Mater Des 31:1284–1292 7. Scheller J, Jodin G, Rizzo KJ, Duhayon E, Rouchon J-F, Triantafyllou MS, Braza M (2016) A combined smart-materials approach for next-generation airfoils. Solid State Phenom 251:106– 112 8. Wang X, Zhou W, Wu Z (2018) Feedback tracking control for dynamic morphing of piezocomposite actuated flexible wings. J Sound Vib 416:17–28 9. Stavroulaki ME, Stavroulakis GE, Leftheris B (1997) Modelling prestress restoration of buildings by general purpose structural analysis and optimization software, the optimization module of MSC/NASTRAN. Comput Struct 62(1):81–92 10. Connor J, Laflamme S (2014) Structural motion engineering. Springer, Cham 11. Kaminakis NT, Stavroulakis GE (2012) Topology optimization for compliant mechanisms, using evolutionary-hybrid algorithms and application to the design of auxetic materials. Compos B Eng 43(6):2655–2668 12. Tairidis GK, Muradova AD, Stavroulakis GE (2019) Dynamic morphing of smart trusses and mechanisms using fuzzy and neuro-fuzzy techniques. Frontiers Built Environm Comput Methods Struct Eng 5:32

Continuous Adjoint for Aerodynamic-Aeroacoustic Optimization Based on the Ffowcs Williams and Hawkings Analogy M. Monfaredi, X. S. Trompoukis, K. T. Tsiakas, and K. C. Giannakoglou

Abstract This paper presents an aerodynamic/aeroacoustic shape optimization framework, running on GPUs, based on the continuous adjoint method. The noise prediction tool and its adjoint are developed by implementing the Ffowcs Williams and Hawkings (FW-H) analogy, after integrating flow time-series, computed by an unsteady Euler equations solver, along a permeable surface. The accuracy of this hybrid solver is verified by comparing its outcome with that of a CFD run, for a 2D pitching airfoil in an inviscid flow. For the same case, the aeroacoustic noise and time-averaged lift gradients computed using the adjoint solver are verified w.r.t. finite differences. Finally, the adjoint solver is used to optimize the shape of the pitching airfoil, aiming at min. noise. Keywords Aerodynamics · Aeroacoustics · Shape optimization · Continuous adjoint · FW-H analogy

1 Introduction Though adequately used in aerodynamic shape optimization, adjoint methods are relatively new in aeroacoustics. Among the few published works, a discrete adjoint to a hybrid URANS-FW-H solver, created using automatic differentiation, was developed to perform shape optimization for turbulent blunt trailing edge noise reduction [1], and far-field noise reduction for inviscid flow around a pitching airfoil [2]. In [3], the permeable FW-H formula in wave form is solved using a finite element method, leading to the necessary adjoint conditions at the interface between the Computational Fluid Dynamics (CFD) and Computational Aeroacoustics (CAA) domains. The continuous adjoint for a hybrid solver for incompressible flows using the Kirchhoff integral, for automotive applications can be found in [4]. This work, alongside M. Monfaredi (B) · X. S. Trompoukis · K. T. Tsiakas · K. C. Giannakoglou National Technical University of Athens (NTUA), School of Mechanical Engineering, Parallel CFD and Optimization Unit, Athens, Greece e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_49

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with [5], expand the above to compressible flows by alternatively using the FWH analogy. The verification of the method presented herein is restricted to the 2D unsteady inviscid flows.

2 The CFD/FW-H Solver The 2D unsteady inviscid flow equations of a compressible fluid are numerically solved in the CFD domain by the in-house GPU-enabled flow solver [6]. The Euler equations are discretized using a dual-time stepping method in which temporal derivatives are computed with second order accuracy. The spatial discretization is based on vertex-centered finite volumes, on unstructured grids. Convective fluxes are computed using the upwind Roe scheme with second order accuracy. The acoustic noise within the CAA domain is computed using the permeable version of the FW-H analogy. The pressure fluctuation in the frequency domain, at the receiver’s location xo can be written as [7]:

xo , ω) = − pˆ ( f =0

ˆ xo , xs , ω) ∂ G( ˆ xs , ω)G( ˆ xo , xs , ω)ds (1) ˆ xs , ω) ds − iω Q( Fi ( ∂ xs i f =0

where (ˆ) represents the frequency domain variable and ω the frequency. The CFD and CAA domains overlap and f is the signed distance from their interface (FW-H surface) with positive f in the CAA domain, as shown in Fig. 1a. H is the Heaviside function and G is the 2D Green function for subsonic flows. xs are the positions of the sources on the FW-H surface. Q and Fi are known as the monopole and dipole source terms respectively and are computed at the end of each time step during the flow solution. The quadrupole terms are neglected due to their small contribution. Details about the implementation of the FW-H solver can be found in [5].

3 The Continuous Adjoint Method The shape parameterization method employed utilizes Bezier polynomials, with control points denoted by bi . For aeroacoustic problems, an objective function J , can be expressed by the following integral in the frequency domain: J=

pˆ 2 ˆ 2 Re + p I m dω

(2)

ω

xo , ω) is the outcome of Eq. (1). Subscripts Re and I m refer to the real where pˆ ( and imaginary parts of complex variables. In shape optimization, adjoint methods

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compute the gradient of J w.r.t. bi . To formulate the continuous adjoint problem, an augmented objective function is defined as Faug = J + T Ω ψn Rn dΩdt, where n = 1, 4 and ψn , Rn , Ω and T are the adjoint variable fields, the residuals of the unsteady Euler equations, the CFD domain and the solution period, respectively. By differentiating Faug w.r.t. bi and setting the multipliers of the derivatives of the flow variables within the field integrals equal to zero, the unsteady adjoint equations are obtained: −

∂ψn ∂ψm − Anmk + S F W −H m δ( f ) = 0 ∂t ∂ xk

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δ f nk , with Um and f nk being the conservative flow variables and inviswhere Anmk = δU m cid fluxes, respectively. δ is the Dirac delta function and S F W −H m includes contributions from the FW-H analogy into the adjoint equations. This source term is added only along the FW-H surface. For the mathematical derivation of this term one should refer to [5]. The expression that, finally, gives the J sensitivities is:

δxe ∂Un ∂ δxk ∂ f nk ∂ dΩdt − dΩdt ψn ψn ∂ xk ∂t δbi ∂ xe ∂ xk δbi T Ω TΩ δn k − ψn f nk dsdt δbi

δJ =− δbi

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T Sw

where n k is the normal vector to the solid wall Sw . The workflow of an optimization loop is as follows: an unsteady flow solution is performed followed by the computation of the pressure fluctuations at the receiver’s location using Eq. (1). Then, the adjoint solver computes S F W −H m and solves Eq. (3) by integrating it backwards in time. Upon completion of the adjoint solution, design sensitivities are computed using Eq. (4) and these are used to update bi by means of a descent algorithm.

4 Verification of the Hybrid CFD/FW-H Solver In order to verify the accuracy of the noise prediction method, results of the FW-H integral are compared to a well-known analytical solution of the sound field generated by a monopole source in a uniform flow. For the sake of shortness details are not included in this paper (see [1, 5]). Comparison of directivity plots in Fig. 1b, shows that the results of the FW-H integral exactly match the analytical solution. Next, the results of the CFD/FW-H are compared with the outcome of a pure unsteady CFD simulation. A NACA12 isolated airfoil is pitching about the quarter-chord point, in an inviscid flow with a 1 deg amplitude and period equal to 0.114 s with 40 time steps per period. The free-stream Mach number is M∞ = 0.4. A 2D unstructured grid which extends 50 chords (chord length, C = 1 m) away from the airfoil is used,

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Fig. 1 a Sketch of the computational domain. b Monopole source in uniform flow with M = 0.6. Comparison of the directivity plots at R = 500 m. c Directivity plot ( pr ms ) around the pitching airfoil at radius R = 20C

with 51,000 nodes overall, among which 402 nodes on the airfoil contour and 151 nodes on the still FW-H surface at R = 4C from the airfoil mid-chord (0.5C, 0). The directivity pattern at R = 20C is plotted in Fig. 1c and shows a very good agreement between results of the unsteady CFD-based computation and the application of the FW-H integral on the flow time-series computed along the FW-H surface (hybrid solver).

5 Optimization Results Before proceeding to the aeroacoustic optimization, the gradients of the timeaveraged lift and noise (Eq. 2) computed by the adjoint method are verified w.r.t. finite differences (FD). The case and the grid is the same as the previous section, the only difference being that the Mach number and the amplitude of pitching are now equal to 0.6 and 2.4 deg, respectively. The airfoil pressure and suction sides are parameterized using two Bezier curves, with 8 control points which are free to move in the y direction. Since the first and last control points are fixed, this case has 12 design variables. Figure 2a, b show a good agreement with FD results for both of the time-averaged lift coefficient and noise, respectively. Next, the optimization framework is used for aeroacoustic noise reduction. The receiver is located at xo = (0, −20c). Three different sub-cases are considered. In Case 1, the whole airfoil shape can change during the optimization, while in Case 2 only the suction side can change. In Case 3, the shape of the trailing edge is fixed. As illustrated in Fig. 2c, after 4 design cycles, the noise objective function, Eq. (2), is reduced by about 20%, 8% and 2%, in Cases 1, 2 and 3, respectively. In all cases, this results to a lower amplitude in pressure fluctuation in Fig. 2d. Comparison of the sound directivity of the baseline and optimized airfoil of Case1 in Fig. 2e shows an omni-directional sound reduction. Figure 2f compares the baseline airfoil with the optimized shapes. It can be seen that the shapes optimized for noise are slightly thinner close to the leading edge and much thicker at the trailing edge (apart from

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Fig. 2 a Time-averaged lift sensitivities using the adjoint method and FD. b Noise (Eq. 2) sensitivities using the adjoint method and FD. c Value of objective function. d Time history of pressure fluctuation within a period. e Comparison of the directivity plot between the baseline and optimized airfoils after 4 design cycles. f Shape of the baseline and optimized airfoils after 4 design cycles

Case 3 in which the trailing edge is fixed). The effect of the trailing edge as a main mechanism in noise generation can be seen by comparing Cases 2 and 3; keeping the trailing edge fixed during the optimization in Case 3 resulted in a lower drop in the noise objective value, even though a greater part of the airfoil is allowed to change. Regarding lift, the baseline airfoil has a zero lift coefficient due to its symmetrical shape and the pitching around the horizontal axis. The lift coefficient for the noise optimized shape in Case 1 becomes −0.89 × 10−3 . Freezing the shape of the pressure side in Case 2 and of the trailing edge in Case 3, increases the lift coefficient to 0.4345×10−2 and 0.415×10−3 , respectively.

6 Conclusions The in-house flow/adjoint solver is extended to include an aeroacoustic noise prediction tool and its adjoint. Adjoint sensitivities are verified w.r.t. the FD for time averaged lift and noise. Aeroacoustic shape optimization is performed and results show that the objective function value is significantly improved; however, this considerably affect the aerodynamic performance. This highlights the importance of coupled aeroacoustic and aerodynamic optimization. Results of the aeroacoustic optimization in Case 3 showed the importance of the trailing edge shape in airfoil self noise generation.

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Acknowledgements This project has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 722401.

References 1. Rumpfkeil M et al (2010) A hybrid algorithm for far-field noise minimization. Comput Fluids 39(9):1516–1528. https://doi.org/10.1016/j.compfluid.2010.05.006 2. Zhou B et al (2015) A discrete adjoint framework for unsteady aerodynamic and aeroacoustic optimization. AIAA paper 3355. https://doi.org/10.2514/6.2015-3355 3. Economon T et al (2012) A coupled-adjoint method for aerodynamic and aeroacoustic optimization. AIAA paper 5598. https://doi.org/10.2514/6.2012-5598 4. Kapellos C et al (2019) The unsteady continuous adjoint method for minimizing flow-induced sound radiation. J Comput Phys 392:368–384. https://doi.org/10.1016/j.jcp.2019.04.056 5. Monfaredi M et al (2019) An unsteady aerodynamic/aeroacoustic optimization framework using continuous adjoint. In: Eurogen conference 2019, Guimarães, Portugal. https://doi.org/10.1007/ 978-3-030-57422-2_10 6. Kampolis I et al (2010) CFD-based analysis and two-level aerodynamic optimization on graphics processing units. Comput Methods Appl Mech Eng 199(9–12):712–722. https://doi.org/10. 1016/j.cma.2009.11.001 7. Lockard D (2000) An efficient, two-dimensional implementation of the Ffowcs Williams and Hawkings equation. J Sound Vib 229(4):897–911. https://doi.org/10.1006/jsvi.1999.2522

On Boundary Conditions for Compressible Flow Simulations Javier Sierra, Vincenzo Citro, and David Fabre

Abstract Global linear stability analysis of open flows in truncated domains suffers from imperfect boundary conditions, leading to either spurious wave reflections (in compressible cases) or to non-local feedback due to the elliptic nature of the pressure equation (in incompressible cases). A novel approach is introduced to solve such an issue. The technique is based on the analytical continuation of the spatial coordinate system in such a way that undesired waves, e.g. reflected acoustic waves, do not affect the spatial region of interest. Such a method is named Complex Mapping (CM) technique and it can be understood as a particular case of a more general family of non-reflecting boundary conditions, Perfectly Matching Layer (PML). Nonetheless, the straightforward application of the latter increases the number of degrees of freedom. A similar situation is observed with the application of sponge or buffer regions, which require a large damping region of the order of several wavelengths of the wave to damp, e.g. forward acoustic wave. We demonstrate the application of simple complex mappings in the hole-tone configuration, namely a jet passing through two successive circular holes. In this configuration the use of complex mapping is particularly efficient with respect to sponge techniques, because the low Mach numbers involved in the computations imply large sponge regions. Keywords Compressible flows · Non-reflecting boundary conditions · Acoustics

1 Introduction Simulations of real flow configurations generally require Artificial Boundary Conditions (ABC) to allow acoustic (resp. vortical) structures to freely escape from the domain and avoid wave reflections. The most common ABC chosen for stability J. Sierra (B) · D. Fabre IMFT, UPS, Allée du Professeur Camille Soula, 31400 Toulouse, France e-mail: [email protected] URL: https://stabfem.gitlab.io/StabFem/ V. Citro DIIN, University of Salerno, 84084 Fisciano, Italy © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_50

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studies in frequency domain (resp. time domain) of compressible flows are sponge regions which are chosen due its simplicity and are set to produce sufficient decay of waves in the vicinity of boundaries of the domain. However, it generally leads to extremely large discretizations of the physical domain, where a large number of elements are located outside the region of interest. Further cases of application and motivating examples may be found in [1]. The purpose of this work is to demonstrate the applicability of CM technique to the linear stability analysis of compressible flows. In particular, we aim to show the effectiveness of the proposed method as non-reflective condition for acoustic (resp. vortical) perturbations. We will demonstrate the efficiency of the technique for the hole-tone configuration, namely the flow through two successive circular holes (we refer to [1] for further details).

2 Complex Mapping Governing Equations The fluid motion is described by the compressible Navier + N S(q) = 0, in the non-conservative form √ of the flow - Stokes equations, B ∂q ∂t field q = [ρ, u, T, p]. M = U∞ /c∞ denotes Mach number (with c∞ = γ r T∞ the velocity of sound), Re = ρ∞ U∞ L/μ is the Reynolds number, and Pr = μ/(ρκ) the Prandtl number. The flow instability is investigated here by using the classical tools of the linear theory and normal mode analysis. The linearised Navier-Stokes equations (LNSE) may 1 + LN S q0 (q1 ) = 0. be written in operator form as follows (see [2] for details) B ∂q ∂t −iωt , we are left with a generIntroducing then the normal mode ansatz q1 = qˆ1 e alised eigenvalue problem Miω qˆ 1 = iωBqˆ 1 + LN S q0 (qˆ 1 ). Here ω = ωr + iωi is the complex eigenvalue, containing the growth rate ωi and the oscillation rate ωr , and qˆ 1 is the corresponding eigenvector. Definition As explained in the introduction, truncating the domain x = [0, ∞] to a finite domain X = [0, X max ] leads to problems associated to the fact that the linearized Navier-Stokes equations admit both unwanted oscillating solutions (the reflected waves) and exponentially growing physical solutions (the vortical waves associated to shear instabilities) in the vicinity of the outlet plane (X = X max ). The idea is to consider an analytical continuation of the LNSE in a direction of the complex X -plane in which all the physical solutions (outgoing acoustic wave and vortical wave) are evanescent while the unwanted reflected wave is exponentially growing, and thus easily controlled. We will thus define a mapping from the numerical coordinate X ∈ [0, X max ] (necessarily real) to the physical coordinate x = Gx (X ) (considered as complex) as follows: Gx : R → C such that X → Gx (X ) = X + i X γc g(X )

(1)

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Here g(X ) is a smooth function which verifies g(X ) = 0 (hence x = X ) for X < X 0 and g(X ) ≈ 1 (hence x ≈ X + iγc X ) for X (X 0 + L c). In our studies 2 0 we consider a regularisation of the step distribution g(X ) = tanh X −X Thus Lc X 0 is the location before which the coordinate is not changed by the mapping, L c is a “transition length” along which the CM is progressively applied, and γc prescribes the direction of the x path in the complex plane. When considering PDE systems such as the LNSE, the effect of the CM method is thus to modify the spatial derivatives as follows ∂ ∂ ≡ Hx with Hx (X ) = ∂x ∂X

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In practice, it is thus very easy to implement the present method in any existing code, by simply modifying the X-derivatives according to this ansatz. The resulting form of the Linearized Navier-Stokes equations using this transformation (in the incompressible case) can be found in Ref. [3].

2.1 Plane-Wave Solutions To explain the effect of the CM method, let us suppose the independency of the flow field on x in the vicinity of the outlet plane. Let us consider a flow which is characterised by a mean velocity U∞ and a finite velocity variation amplitude U . In the case of a jet flow in a quiescent open domain U∞ ≈ 0 and U ≈ U∞ . Under those hypotheses, the solution of the eigenvalue problem can be expected as a superposition of plane-wave solutions, namely q1 (x, y)e−iωt = k qˆ 1 (y)k,ω ei(kx−ωt) . Two kinds of solutions can be expected, the first kind corresponds to acoustic waves. Restricting to longitudinal waves (independent of the y-direction), two solutions are defined as ω − ± = ±c0 + U∞ . If the mean flow is subsonic, U∞ − c0 < 0 then the solution k ac is kac the upstream-propagating wave which has to be cancelled by the boundary condition. The second kind corresponds to vortical waves. The corresponding values for k can be obtained from the local stability analysis of the considered shear flow using U . Both solutions are physically relevant but incompressible theory, k +ω = 1±i 2 H,u|s

the solution k + H,u is exponentially growing as x → ∞ and must not be affected by the boundary condition. The effect of CM on these waves is schematised in Fig. 1.

3 Application Case: Hole-Tone Configuration We illustrate the efficiency of the method for a hole-tone configuration, namely the flow through two successive circular holes. Attempts to characterise the instability mechanism were previously made using incompressible and compressible LNSE [4],

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Fig. 1 Sketch of the propagation of hydrodynamic and acoustic waves, where for the sake of illustration L C M (length of CM region) and L c (adaptation length) are depicted intentionally large with respect to the physical domain. In ordinate the amplitude of a plane-wave, ||eikx qˆ k,ω ||1 , is + represented. a without CM: waves k + H,u and kac are present at the outlet, thus leading to reflected + + waves (only the reflections caused by wave k H,u are represented). b with CM: Waves k + H,u and kac are damped when reaching the boundary, so no reflection is generated Table 1 Mesh definition and performances. [X min , X max , Rmax ] denotes the size of the computational domain, X 0 the location above which the CM is applied (in both (r, x) directions) and Nv the number of mesh vertices where the boundary conditions are effectively applied Mesh Methodology Nv [X min , X max , X 0 γc ω Time (s) Rmax ] M1

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and allowed to identify the difficulties associated to boundary conditions. We show that the CM technique applied to this case allows efficient calculation at a much lower cost compared to the use of sponge layers. The flow is assumed axisymmetric. Base flow is computed with rigid adiabatic wall boundary condition on walls wall , symmetry boundary condition at axis , zero-stress at outlet and a constant velocity profile u0 = ( SQin , 0)T at the inlet inlet , where Q is the volume flow rate. The complex mapping technique is used for the axial variable x in both upstream (x < −X 0 ), downstream (x > X 0 ) and radial (r > X 0 ) directions, with parameters reported in Table 1. The perturbation qˆ 1 satisfies homogeneous boundary conditions. The procedure to compute the base flow and generate an adapted mesh is as described in [5] (Fig. 2).

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(b) Mode 4 at Re = 1600 at M∞ = 0.05

Fig. 2 Imaginary pressure component pi of two global modes. a The second mode and b the fourth mode. Radiating acoustic field is displayed in the main figure whereas the zoomed region reports the spatially localized hydrodynamic mode

4 Conclusion A novel non-reflecting boundary condition for global stability analysis has been introduced. Complex mapping is a non-reflecting boundary treatment that preserves the number of d.o.f. and it is easy to implement in any numerical code that accepts complex arithmetic. CM overcomes the increase of the number of degrees of freedom imposed by sponge or Perfectly Matched Layer methods, with similar numerical precision as it has been demonstrated in the hole-tone configuration. In such a case, the number of mesh vertices was reduced by about 50 times compared to a sponge method, demonstrating the usefulness of the methodology. This method is potentially applicable to a large range of compressible [6] and incompressible flows, like [7] and also suited to the computation of adjoint, structural sensitivity [8] and adjoint-based control methods.

References 1. Sierra J, Fabre D, Citro V (2020) Efficient stability analysis of fluid flows using complex mapping techniques. Comput Phys Commun 251:107100 2. Fani A, Citro V, Giannetti F, Auteri F (2018) Computation of the bluff-body sound generation by a self-consistent mean flow formulation. Phys Fluids 30:036102 3. Fabre D, Longobardi R, Bonnefis P, Luchini P (2019) The acoustic impedance of a laminar viscous jet through a thin circular aperture. J Fluid Mech 864:5–44 4. Longobardi R, Fabre D, Bonnefis P, Citro V, Giannetti F, Luchini P (2018) Studying sound production in the hole-tone configuration using compressible and incompressible global stability analysis. In: IUTAM symposium on critical flow dynamics. Santorini, Greece, 18–22 June 2018 5. Fabre D, Citro V, Sabino DF, Bonnefis P, Sierra J, Giannetti F, Pigou M (2019) A practical review to linear and nonlinear approaches to flow instabilities. Appl Mech Rev 70(6):060802

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6. Citro V, Giannetti F, Sierra J (2020) Optimal explicit Runge-Kutta methods for compressible Navier-Stokes equations. Appl Numer Math 152:511–526 7. Giannetti F, Camarri S, Citro V (2019) Sensitivity analysis and passive control of the secondary instability in the wake of a cylinder. J Fluid Mech 864:45–72 8. Citro V, Giannetti F, Pralits J (2015) Three-dimensional stability, receptivity and sensitivity of non-Newtonian flows inside open cavities. Fluid Dyn Res 47:1–14

Large-Eddy Simulation on Jet Mixing Enhancement Using Unsteady Minijets Yanyan Feng, Dewei Fan, Bernd R. Noack, Hong Hu, and Yu Zhou

Abstract Minijet is one of the most promising active methods for the enhancement of jet mixing. The injection of minijets into a turbulent jet before the jet exit may have multiple impacts on the jet mixing structure. This work aims to understand the jet flow structure controlled by multiple unsteady minijets, especially the effect of the minijet phases on the jet mixing enhancement. Large eddy simulation was conducted for a round, turbulent jet, disturbed with six unsteady minijets, with a view to reveal the flow structures for various control modes and enhance the jet mixing. The Reynolds number is 8000 based on the jet exit diameter and jet centerline velocity at the jet exit. A space/time-dependent boundary condition at jet exit is deployed to generate a statistically stable turbulent jet flow field within an acceptable short computational time. Keywords Large-Eddy simulation · Jet mixing enhancement · Unsteady minijet

1 Introduction Among the methods for enhancing jet mixing, active control with steady or unsteady minijets is actively investigated. With two steady and unsteady minijets, Zhou et al. [7] and Yang et al. [6] experimentally improved the mixing performance of a turbulent jet, respectively. Hilgers and and Boersma [3] reported their direct numerical simulation (DNS) study to optimize a combination of axisymmetric and helical actuation, while Koumoutsakos et al. [4] employed a flapping mode, and Trushar et al. [5]

Y. Feng (B) · D. Fan · B. R. Noack · H. Hu · Y. Zhou Harbin Institute of Technology, Shenzhen 518055, China e-mail: [email protected] B. R. Noack LIMSI, CNRS, Université Paris-Saclay, Bât 507, rue du Belvédère, Campus Universitaire, 91405 Orsay, France Technische Universität Berlin, 10623 Berlin, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_51

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presented a helical structure by vortical structure evolution. The Reynolds numbers in the above DNS studies were relatively low (500–1500). Fan et al. [2] developed an artificial intelligence (AI) control system to enhance the mixing of a round turbulent jet by deploying six unsteady minijets as actuators. Here, AI control finds successively four increasingly better control laws: an axisymmetric, helical, flapping, and a novel combined mode. Based on their investigation, largeeddy simulations (LES) are conducted to understand the details of the evolution of the flow fields for the natural jet and the four controlled jet.

2 Numerical Method Figure 1 shows a schematic of the minijet-controlled jet mixing model and the computational grid. As shown in Fig. 1a, the jet inflow domain includes a contraction section followed a contour specified by the equation R = 57 − 47 sin1.5 (90 − 9x/8) mm and a 47-mm-long smooth nozzle of diameter D = 20 mm, as used by Fan et al. [2]. The jet outflow domain is cylindrical and extends to 15D downstream and 10D radially, with a grid of 100 × 75 × 138 points in the streamwise, radial, and azimuthal direction, respectively. Six unsteady radial minijets are equidistantly placed 0.85D (Fig. 1b) 15D

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upstream and issue from orifices with a diameter d = D/20 (Fig. 1c). Velocity inlet condition is used for the mainjet and minijet inlets. The jet nozzle and the surface just out of the jet exit are set as no-slip wall condition. Other surfaces are outlet condition. The unsteady three-dimensional incompressible Navier–Stokes equations are solved using the OpenFOAM (Open Source Field Operation and Manipulation) platfoam. Finite volume discretization scheme for the first time derivative terms is backward, and for the gradient terms is Gauss linear. The discretized equations are solved by PISO (Pressure-Implicit with Splitting Operators) algorithm. The subgrid stress is modeled by dynamicKEqn (dynamic one equation eddy-viscosity subgrid scale model). Due to the fine meshes in the jet nozzle boundary layer, the computational time step for the controlled jet is on the order of 10−8 –10−7 s and thus excessively long simulation time. Since the controlled jet has a strong periodicity, we apply a space/timedependent boundary condition at the jet exit to speed up the jet mixing computations. After conducting a simulation on the full-domain for several actuation periods, the velocity and pressure information at the jet exit is extracted and interpolated to the inlet of a new domain with only the downstream. The simulation of the jet is continued until a statistically stable jet flow field is obtained. Without simulating the meshes of the nozzle boundary layer, the time step amplifies to the order 10−5 s and thus almost 99% original computation time is saved.

3 Results and Discussion The minijet excitation frequency f e and mass flow rate C m (ratio of mass flow of single minijet to mainjet) are fixed as 67.5 Hz and 0.4%, respectively. The corresponding Strouhal number St (f e D/U e , where U e is the jet centerline velocity at jet exit) is 0.225. The natural jet flow is simulated first to validate the accuracy of the numerical method. Then the minijets are injected before the jet exit inlet to form different control laws. Square wave signals are deployed for the on and off status of the six minijets. The mainjet parameters and the periodic-actuation phases of each minijet for the four considered control laws are set to be the same as in experiments of Fan et al. [2]. Figure 2 shows the mean streamwise velocity U * and the root-mean-square (RMS) values of streamwise velocity Ur∗ms , both normalized by U e , for the natural jet (without controlling) and four controlled jets. From the comparison of the LES results and experimental results [1], the magnitude and variation of flow velocity decay and velocity fluctuation on the jet centerline obtained from LES have a good agreement with experimental data. The calculated Ur∗ms is more significant than the experimental one from x/D = 5 to 8, while the difference is acceptable. The results provide a validation that the LES platform can accurately reflect the jet flow characteristics. The jet velocity decay in Fig. 2a shows that all the controlled jets reduce the centerline velocity drastically for almost all the streamwise locations. Moreover,

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the centerline velocity decays rapidly (around 0.6 of the natural jet at x = 5D) from the jet exit for the axisymmetric and flapping control modes and from x = 3D (around 0.8 of the natural jet at x = 5D) for the helical and combined control modes. The axisymmetric and flapping control modes have a duty cycle of 13.3%, the helical control mode of 40%, and the combined control mode of 20–63.4% for various minijet. At the same minijet flow rate (C m = 0.4%), the minijets in the helical and combined control modes have a much smaller velocity, which may not be sufficient for penetrating the mainjet core and stimulating it effectively. From Fig. 2b, it can be seen that with minijets injection, the velocity fluctuation is higher than the natural jet at the area near the jet exit of x/D < 2, which can attribute to the velocity decay on the jet centerline. From x/D = 5 to the end of the computational domain, the velocity fluctuation of controlled jet flow returns to the same magnitude and is slightly lower than that of natural jet flow. At the same time, it can be noted that the velocity fluctuation of the combined mode is relatively minimal, corresponding to small minijet velocity and weak jet mixing effect. For the natural jet and four controlled jets, Fig. 3 provides instantaneous isosurfaces of the radial velocities V and W (red color denotes U e /6, and blue color denotes −U e /6). It shows that for the natural jet, the lateral spread appears late in streamwise direction only after x/D = 3. With minijets actuation, the jet has more significant radial motion near the jet exit and the flow goes turbulent earlier. For flapping control mode, the jet flow shows a much stronger spreading on the x–z plane than other control modes. However, the jet flow gathers in the area near the jet centerline and the spreading is less pronounced on the x–y plane. A similar obvious lateral spreading can be found for the axisymmetric actuation. While for the helical and combined mode, the isosurfaces of V and W are relatively confined. Besides, Fig. 3 indicates that the effect of the minijet control disappears beyond 8D, which mesns that the control is only effective in the near field of jet. Zhou et al. [7] also found that the effect of the minijets on jet mixing is limited to the near field of the main jet and the perturbed jet recovers almost completely its natural decay rate after x/d = 5.

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4 Conclusion The effect of four AI control modes (axisymmetric, helical, flapping, and combined) of a turbulent jet mixing is studied using LES. A space/time-dependent boundary condition is used at the nozzle exit to avoid computing the domain upstream and thus to save the computational time. This domain reduction has reduced CPU time on a 32-processor cluster node by almost two orders of magnitude to 100 h for each simulation. Results show that for the axisymmetric and flapping control modes, the jet centerline velocity decays rapidly from the jet exit and obvious lateral spreading appears compared with the natural jet. For the helical and combined control modes, the jet velocity at x = 5D is about 0.8 of the natural jet velocity and the radial mixing is less distinct. The reason is quite likely the small minijet-actuation velocity at these two control modes. Acknowledgements This work is supported by the China Postdoctoral Science Foundation (Grant No. 2019M651285).

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References 1. Fan DW, Wu Z, Yang H, Li JD, Zhou Y (2017) Modified extremum-seeking closed-loop system for jet mixing enhancement. AIAA J 55(11):3891–3902 2. Fan DW, Zhou Y, Noack BR (2018) Artificial intelligence control of a turbulent jet. In: 21st Australasian fluid mechanics conference. Adelaide, Australia, pp 1–4 3. Hilgers A, Boersma BJ (2001) Optimization of turbulent jet mixing. Fluid Dyn Res 29:345–368 4. Koumoutsakos P, Freund J, Parekh D (2001) Evolution strategies for automatic optimization of jet mixing. AIAA J 39(5):967–969 5. Trushar BG, Arun KS, Muralidhar K (2011) Direct numerical simulation of naturally evolving free circular jet. J Fluids Eng Trans ASME 133, 111203 6. Yang H, Zhou Y (2016) Axisymmetric jet manipulated using two unsteady minijets. J Fluid Mech 808:362–396 7. Zhou Y, Du C, Mi J, Wang XW (2012) Turbulent round jet control using two steady minijets. AIAA J 50:736–740

Mixing Characteristics of a Flapping Jet of Self-Excitation Due to a Flexible Film M. Wu, M. Xu, and J. Mi

Abstract This study investigates a new type of turbulent flapping jets ‘self-excited’ through a thin FEP film fixed the jet nozzle exit by measuring their mixing characteristics. The study is conducted with varying film length (L) from L/D = 0.75 to 2.0 at the Reynolds number of Re = 30,000, where Re ≡ U o D/ν with U o & D and ν being the jet-exit velocity & diameter and fluid viscosity. Hot-wire anemometer and flow visualization are used to measure the flapping jets and also a free circular jet. Results show that the flapping jet decays and spreads far more rapidly than the free jet. As L/D grows from 0.75 to 2.0, the decay and spread rates increase first and then decrease with their maxima at L/D ≈ 1.25. In other words, an optimal film length is found for the strongest flapping, which is L ≈ 1.25D for the present FEP film. Moreover, the flapping jet generally has a stronger or better mixing at both large and small scales than the non-flapping free jet. This results in the approximate Gaussian PDF of the fluctuating velocity at x/D = 22.5 for all the flapping jets but not for the free jet. Keywords Flapping jet · Self-excited oscillation · Flexible film

1 Introduction The control of jet mixing has long been an interesting research topic for the community of fluid mechanics. A popular approach for the jet control is to use active excitation, such as acoustic excitation [1] and mechanical excitation involving moving parts [2, 3]. These active excitation techniques were proved quite effective in laboratory studies but less feasible and ineffective in practical applications due to their weight,

M. Wu · J. Mi (B) College of Engineering, Peking University, Beijing 100871, China e-mail: [email protected] M. Xu · J. Mi College of Marine Engineering, Dalian Maritime University, Dalian 116026, China © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_52

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power and maintenance requirements. For practical applications, the excitation technique should be simple and effective with no moving components. In this context, several types of practical self-exciting nozzle were developed for the enhancement of jet mixing, such as the flip-flop jet [4, 5], precessing jet [6], oscillating jet [7, 8] and the “whistler” nozzles [9]. Those mechanical devices naturally excite the jet itself into time-dependent self-oscillation. It has been recognized that such a dynamic self-excited oscillation significantly increases the large-scale mixing of the jet and so benefits for some practical processes. The self-exciting nozzles have found various industrial applications [10]. Also, several fundamental studies have been performed for the self-excited jet oscillation [11, 12]. However, the above passive self-exciting nozzles commonly cause a significant loss of pressure (energy) during their operation. This pressure loss is local and mainly due to sudden expansion and/or contraction that the fluid flows through. To avoid this loss, Xu et al. [13] have developed a new type of flapping jets that are self-excited by the flutter of a flexible film fixed axially at a round nozzle exit. The related nozzle has very low pressure loss due to the flapping motion because no sudden expansion and contraction exist. As a continuation of [13], the present work is designated to investigate by experiment the mixing characteristics of this type of flapping jets under varying the film length versus a free circular jet. To examine the jet mixing and decay features, not only the flow visualization was taken but also the mean and RMS (root-mean-squared) velocities along jet centerline were measured using hot-wire anemometry.

2 Experimental Description Figure 1 shows the experimental setup. Here below, only a brief description for present experiments is provided (see [13] for more details). The flapping jet was generated with a rectangular film placed at a round nozzle exit of diameter D = 40 mm. The film is made of FEP with the 50 µm thickness. Six lengths of the film are selected for the study: i.e., L/D = 0.5, 0.75, 1.0, 1.25, 1.5 and 2.0. Instantaneous flow images of a smoked jet were taken by a Canon camera (EOS 5D Mark iii) equipped with the focal length 24 ~ 105 mm. The smoking was realized through a fog machine whose spray volume is 11.8 m3/s with a nozzle diameter of 1.0 mm. The evergreen light source is class IV laser product for applications (532 nm wavelength, < 10 W peak power). The track of the laser volume was parallel to the xy plane with the illuminated region extending for about 1000 mm along the x direction and for about 500 mm along the y direction. Here, x is the downstream distance measured from the nozzle exit and y is the lateral distance from the centreline. Of note, the film flaps predominantly in the y direction. The centreline mean and RMS velocities were measured by a single hot-wire (tungsten) probe operating with an in-house constant temperature circuit at the overheat ratio of 1.5. The hot-wire sensor, aligned perpendicular to the x-axis, is 5 m

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Fig. 1 Experimental facilities and schematic of a smooth contraction nozzle with a flapping jet, together with the coordinate system

in diameter (d w ) and approximately 1.0 mm in length (lw ) so that lw /d w 200, which enables the central portion of the wire to have a uniform temperature distribution. For the experimental conditions, the frequency response of the hot wire and anemometer, determined by the square-wave technique, is about 100 kHz, so that the temporal response of the wire is approximately 10−5 s.

3 Results and Discussion Figure 2 shows the images of the smoked free jet and flapping jets taken for L = 0.75D ~ 2.0D at Re = 30,000. Two observations can be made straightforwardly: (1) the flapping jets spread much more widely in the xy plane than does the nonflapping free jet, see Fig. 2a; (2) the flapping jets exhibit a far less spreading rate in the xz plane than in the xy plane, despite being larger than that for the free jet. These qualitative observations suggest undoubtedly that the flapping jet has substantially stronger mixing than does the free jet. The above suggestion may be verified by comparing the centerline mean velocity and turbulence intensity distributions, and various typical turbulence scales of different jets. Figure 3a shows the centreline velocity decay rate measured by the ratio R = U o /U c where U c and U o are the local centerline mean velocity and its exit value, respectively, for various film lengths at Re = 30,000. For reference, the present free-jet result and that of Mi and Nathan [14] obtained at Re = 15,000 are also provided. Notably, a good agreement between the two is demonstrated and so credits the present hot-wire measurements. Indeed, as expected, the flapping jet

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Fig. 2 Images of the smoked jets, in a the xy plane and b the xz plane, from the nozzle with L = 0.75D ~ 2.0D versus the free jet at Re = 30,000 0.5

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decays generally at a much higher rate than does the free jet. This is consistent with the spreading width of the flapping jet being far greater than that of the free jet seen in Fig. 2. Moreover, Fig. 3a illustrates that, for different L, the flapping-jet decay rate first rises and then drops from L/D = 1.25 as L is increased. To characterize the turbulent mixing, Fig. 3b shows the relative turbulence intensity u’ c ≡ < u2 c > 1/2 /U c along the jet centreline at Re = 30,000 for different lengths of the film. At x/D < 8, the present intensity is lower than that of [14] while the difference become negligible at x/D ≥ 8. Compared with the free jet, the flapping jet exhibits a much stronger fluctuation and consequently a far higher value of u’ c due to the large-scale flapping motion. In particular, as the flow proceeds downstream, the turbulent intensity initially grows and then turns to decrease around x/D = 5, gradually narrowing the gap from that for the free jet. Overall, u’ c is substantially greater in the flapping jet than in the free jet. Note that the turbulence intensity represents the degree at which the turbulent mixing occurs at the large scales of turbulent fluctuation. So, Fig. 3b suggests that the flapping jet generally has a much greater large-scale mixing than the non-flapping jet even at x/D > 10. It is interesting to note that, at x/D > 12, either u’ c or R becomes approximately equal and considerably smaller for the shortest and longest films (i.e., L/D = 0.75 and 2.0) than the other cases of the flapping jet. This might result from less coherent motion of flapping for these two cases. Overall, the fluttering film, particularly at L ≈ 1.25D, plays a significant role in enhancing the large-scale mixing of fluid in the jet flow. It appears that there is an optimal film length for the strongest flapping, which is L ≈ 1.25D for the present case. In addition, the PDF of u obtained at x/D = 22.5 is found approximately Gaussian for all the flapping jets but not for the free jet (not presented here). This suggest a more thoroughly mixing of the flapping jet than the free jet in the middle region since the better fine-scale mixing corresponds to a closely Gaussian distribution.

4 Conclusion The present study has extended our recent work [13] that disclosed a new type of selfexcited flapping jets due to a flexible film fixed axially at a nozzle exit. We presently investigated the mixing characteristics of the flapping and non-flapping free jets. For the flapping jet, as L/D grows from 0.75 to 2.0, the decay and spread rates increase first and then decrease with their maxima at L/D ≈ 1.25. Significantly, the flapping jet decays and spreads far more rapidly and exhibits considerably stronger turbulence intensity than does the free jet. This suggests that the fluttering film can enhance the large-scale mixing of fluid in the jet flow. Also, the present flapping jet appears to improve the small-scale mixing too, although Mi & Nathan [15] found that the flapping jet from the fluidic nozzle results in poor fine-scale mixing. The PDF of u seems to support the improvement since it is nearly Gaussian at x/D = 22.5 for the flapping jets.

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References 1. 2. 3. 4. 5.

6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

Crow SC, Champagne FH (1971) Orderly structure in jet turbulence. J Fluid Mech 48:547–591 Simmons JM, Lai JCS (1981) Jet excitation by an oscillating vane. AIAA J 19:673–676 Davis MR (1982) Variable control of jet decay. AIAA J 20:606–609 Viets H (1975) Flip-flop jet nozzle. AIAA J 13:1375–1379 Mi J, Nathan GJ (2001) Scalar mixing characteristics of a self-excited flip-flop jet nozzle. In: Proceedings on 14th Australasian Fluid Mechanics Conference, Adelaide University, Adelaide, Australia, pp 817-820, 10–14 Dec 2001 Nathan GJ, Luxton RE (1991) The entrainment and combustion characterisics and an axisymmetric, self exciting, enhanced mixing nozzle. ASME/JSME Therm Eng Proc 5:145–151 Mi J, Nathan GJ, Luxton RE (2004) Oscillating jets, PCT/AU98/00959, US Patent No. 6685102 (2004.2), European Pat. No. 1032789 (2004.9) Nathan GJ, Mi J, Alwahabi ZT, Newbold GJR, Nobe DS (2006) Impacts of a jet’s exit flow pattern on mixing and combustion performance. Prog Energy Combust Sci 32:496–538 Hill WG, Greene PR (1977) Increased turbulent jet mixing rates obtained by self-excited acoustic oscillations. ASME J Fluids Eng 99:520–525 Manias CG, Nathan GJ (1993) The precessing jet gas burner—a low NOx burner providing process efficiency and product quality improvements, World Cement (March), pp 4–11 Raman G, Cornelius D (1995) Jet mixing control using excitation from miniature oscillating jets. AIAA J 33:365–368 Xu M, Mi J, Li P (2012) Large eddy simulations of an initially-confined triangular oscillating jet. FLOW Turbul Combust 88:367–386 Xu M, Wu M, Mi J (2019) A new type of self-excited flapping jets due to a flexible film at the nozzle exit. Exp Thermal Fluid Sci 106:226–233 Mi J, Nathan GJ (2010) Statistical properties of turbulent free jets issuing from nine differentlyshaped nozzles. Flow Turbul Combust 84:583–606 Mi J, Nathan GJ, Luxton RE (2001) Mixing characteristics of a flapping jet from a self-exciting nozzle. Flow Turbul Combust 67:1–23

Flow-Induced Vibration Characteristics of a Fix-Supported Elastic Wing S. Peng, S. L. Tang, Md. Mahbub Alam, and Yu Zhou

Abstract The aerodynamics and responses of an elastic high-aspect-ratio (AR = 9) NACA0012 airfoil with two-end-fixed supports were experimentally investigated. The chord-based Reynolds number is 1.5 × 105 and the angle of attack (α) of the wing varies from 0° to 90°. The lift, drag coefficients (C l and C d ), deformation (A* , where the asterisk denotes normalization by the chord) of the wing, as well as the velocity fluctuation (u) in the wake were measured simultaneously. Based on the behaviors of C l , C d and A* , and their spectral coherences with u, four regimes are identified, i.e. α = 0º − 4º, 6º − 8º, 10º − 50º and 60º − 90º, respectively. In the regime of α = 0º − 4º, the wing keeps stable, while the dramatic structural vibration emerges for α in the range of 6º − 8º because of the occurrence of the flutter. As α is increased to stall angle (α = 10º), a rapid drop is observed in the RMS value of lift, drag and displacement. Beyond the stall angle, the fluctuation of lift and drag forces increases slowly with α in the range of 14º < α < 50º while the vibration of the displacement hardly changes. In this range, one pronounced peak corresponding to the vortex shedding occurs in their spectral coherences. As α overs 60º, the fluctuations in lift, drag and structural response are impaired, becoming negligibly small. The peak associated with vortex shedding in the spectral coherences is not distinct. Keywords High-aspect-ratio wing · Flexible structure · Fluid–structure interaction

1 Introduction High aspect ratio wing (HARW) has been increasingly prevailing in aircraft designing such as the unmanned aerial vehicles and high-altitude long endurance aircraft because of its high performance and efficiency [1, 2]. In contrast to low aspect ratio wing which is relatively “rigid” when interacting with the oncoming flow, HARW can easily occur large 3D deformation (bending, torsion) and vibration, which makes S. Peng · S. L. Tang (B) · Md. M. Alam · Y. Zhou Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, P. R. China e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_53

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flow around the wing much more complex and has significant effect on the aerodynamic characteristics. Past research of this kind of problems has largely focused on aerodynamic response characteristics of the HARW, not on the flow structures. For example, Tang and Dowell [3] conducted an experimental and theoretical study of a HARW and found that the geometric structural nonlinearity effects depend on the ratio of the flap bending stiffness to chordwise bending stiffness. In particular, a hysteresis phenomenon caused by the stall aerodynamic nonlinearity was observed from their theoretical analysis and experimental measurement. Tang et al. [4] further examined the gust response of a HARW theoretically and experimentally. Their results show that the gust response depends significantly on the gust center position along the span,the structural response was increased as the gust center position moves toward the wing tip. However, the correspondence between flow structure and response is not well understood, albeit crucial for the understanding of the fluid– structure interactions. This work aims to study the flow-induced vibration response and flow structures of a fix-supported elastic wing, with a view to understanding the mechanisms of highly non-linear fluid–structure interactions.

2 Experiment Details The experiments were conducted in a closed-circuit wind tunnel with a test section of 5.6 m × 0.8 m × 1.0 m. An elastic NACA0012 wing with an aspect ratio l / c = 9 (chord c = 78 mm) was tested (Fig. 1a). The wing was composed of a steel square-section beam, 23 airfoil sections made of aluminum alloy and 22 fractions of NACA0012 airfoil shells made of ABS resin. As shown in Fig. 1b, the steel beam is inserted through the center of the airfoil sections, acting as the elastic axis and its effective section size is 0.008 m × 0.0014 m. There is a lead bar of 2 mm in diameter embedded in each airfoil section, 0.25c away from the geometric center. Each space between two airfoil sections is covered with the airfoil shells as shown in Fig. 1c, which provides the geometric profile of the wing. The mass ratio m* (= m / (ρπc2 l/4)) was 87, where m was the total vibrating mass, and ρ was the air density. The natural frequency f n of the wing system was around 6.6 Hz and exhibited no obvious dependence on the root angle of attack α. The damping ratio ζ was estimated to be about 0.029. During the experiment, the free-stream velocity U ∞ is 28 m/s, corresponding to reduced velocity U r = 54 and Re = 1.5 × 105 . The longitudinal turbulence intensity was less than 0.3%. The force acting on the wing was measured through a load cell which was placed outside the wind tunnel (see Fig. 1a). Since the loads acting on the wing can be considered to be evenly distributed, the supporting forces on both sides are considered to be equal, and the total lift was calculated as F y = 2 × F yl (F yl is the lift force measured by the load cell) and normalized as lift coefficient Cl = Fy / (0.5ρU2∞ lc). The drag force is processed in a similar way. A movable single hotwire probe was used to measure the velocity fluctuation in the wake (Fig. 1a). The strain ε on the surface of the beam at three positions (1/4, 2/4 and 3/4 of span) were measured using the fiber-optic Bragg grating (FBG) sensors

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Fig. 1 a Experimental arrangement; b details of airfoil cross section; c details of airfoil shell and FBG sensor arrangement

(Fig. 1 c), which allows for the estimation the displacement (A) of the wing through the following relations sinh λn l + sin λn l A= cosh λn z − cos λn z + − (sinh λn z − sin λn z) (1) cosh λn l − cos λn l n=1

n=N

A¨ = ε j /(h/2), j = 1, 2, 3

(2)

where N = 3, λn = (n + 21 )π/l, and h is the thickness of the beam.

3 Results and Discussion −

−

Figure 2 shows the dependences of the time-averaged lift force (Cl ), drag force (Cd ), −

and displacement ( A∗ ) as well as the corresponding RMS values of fluctuating lift (Cl ), drag (Cd ) and displacement ( A∗ ) on the angle of attack α. In terms of the dependence of aerodynamic forces and structural response on α, four α regimes can be identified, namely 0–4°, 6–8°, 10–50° and 60–90° respectively. For α in the −

−

−

range of 0–4°, both Cl and A∗ increases monotonically with increasing α while Cd decreases slightly. Cl , Cd and A∗ in this regime are negligibly small. In contrast, for

−

α = 6–8°, Cl , Cd and A∗ all increase dramatically due to the onset of flutter and Cl ,

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Fig. 2 Dependence on α of Cl , Cd , A∗ , Cl Cd and A*’ , normalized by U ∞ and/or c −

−

Cd and A∗ reach their local maximum. As for the third regime (α = 10° − 50°), the −

stall occurs at about α = 10°, which is characterized by a rapid drop inCl . At the same time,Cl , Cd and A∗ also show a sharp decrease. Beyond the stall α, the time-average −

−

forces (Cl andCd ) and the corresponding RMS values (Cl and Cd ) increase with α. −

Within this regime, A∗ rises with the increasing α and tends to stabilize as α is over 40° while the RMS value of A∗ changes little in this α regime. As α is increased beyond 60°,Cl , Cd and A drop first and then become negligible. The spectral coherences Coh(A∗ , u), Coh(Cl , u) and Coh(Cd , u) that provide a measure of the degree of correlation between aerodynamic response or forces ( A∗ , Cl and Cd ) and velocity fluctuation (u) at four typical α which represents the four regimes are shown in Fig. 3. At α = 0º (Fig. 3a), there seems no obvious peak, implying a weak correlation between vortex shedding and structural response. At α = 8°, corresponding to flutter (Fig. 3b), spectral coherences all reach about 1 at f r * (= fc/U ∞ ) = 0.092, suggesting a strong correlation between the flow and aerodynamic response or forces. Figure 3b displays some other spikes at the harmonics of the oscillation frequency. In contrast, the spectral coherences at α = 14° (Fig. 3c) show an evident peak at f r * = 0.604, and a broad-band peak at around 0.05. The higher frequency peak (f r * = 0.604) indicates a coherence between the response and vortex shedding while the mechanism of the

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Fig. 3 Spectral coherence between aerodynamic response or forces (A* , C l , C d ) and velocity fluctuation (u) at a α = 0º b α = 8º c α = 14º d α = 60º. f r * = fc/U ∞ For α = 0º − 14º, u was measured at x * = 2.5, y* = − 1.0. For α = 14º − 30º, u was measured at x * = 2.5, y* = − 1.5. For α = 40º − 90º, u was measured at x * = 3, y* = − 1.5

broad-band peak is not clear yet. As α is further increased to 60° (Fig. 3d), the higher frequency peak gets further weak and even disappears. The cross communication between the flow and responses is thus impaired as α increases.

4 Conclusions An investigation has been experimentally carried out on the flow-structure interaction of a NACA0012 flexible wing with two-end-fixed supports at chord based Re = 1.5 × 105 in the range of α = 0° ~ 90°. According to the dependence of C l , C d , A* and the spectral coherences (coh(C l , u), coh(C d , u), and coh(A* , u)) on α, four α regimes are proposed, i.e. 0° − 4°, 6° − 8°, 10° − 50° and 60° − 90°. At α = 0° − 4°, the vibration of wing is negligible. The mean and RMS of C l , C d and A* are small and the spectral coherences exhibits no evident peak. At α = 6° − 8°, the flutter takes place, resulting in a sharp increment of theCl , Cd and A∗ and the prominent peaks in coh(C l , u), coh(C d , u), and coh(A* , u). However, a rapid drop is observed in the aerodynamic forces and structural response once α is increased to the stall angle of attack of about 10°. In the range of α = 14° − 50°, the forces and response rise with α. One pronounced peak corresponding to the interaction between the structure

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response and vortex shedding is observed in the spectral coherences. As α > 60°, the vibration of the wing and the fluctuation of aerodynamic forces are impaired and the peak in the spectral coherences associated with vortex shedding is eliminated.

References 1. Afonso F, Vale J, Oliveira É, et al (2017) A review on non-linear aeroelasticity of high aspect-ratio wings. Progress Aerospace Sci 89:40–57 2. Sarkar S, Bijl H (2008) Nonlinear aeroelastic behavior of an oscillating airfoil during stallinduced vibration. J Fluids Struct 24(6):757–777 3. Tang D, Dowell EH (2001) Experimental and theoretical study on aeroelastic response of highaspect-ratio wings. AIAA J 39(8):1430–1441 4. Tang D, Grasch A, Dowell EH (2010) Gust response for flexibly suspended high-aspect ratio wings. AIAA J 48(10):2430–2444

On the Transient Effects Induced by Jet Actuation Over an Airfoil Armando Carusone , Christophe Sicot, Jean-Paul Bonnet, and Jacques Borée

Abstract Flow control experiments using pulsed vortex generator jets (PVGJs) are carried out to improve the performance and maneuverability of a NACA 0015 airfoil. The analysis, which is mainly provided for fully separated flow fields in the literature, is extended both to partially separated and attached flows over the airfoil. Actuation is implemented through a spanwise array of 44 PVGJs embedded on the suction side of the airfoil at 30% of the chord, measured from the leading edge. A special focus is given to the transient dynamics induced by a single-pulse actuation. It induces an initial small negative lift peak followed by a higher positive peak, within a brief period. This pattern is found out both for partially separated and attached flow fields. The investigation of the characteristic time-scales of the lift evolution provides insights on the development of smart open/closed-loop control strategies. Keywords Airfoil loads control · Transient dynamics · Fluidic actuation

1 Introduction Aircraft conception may rely on active flow control techniques, as pulsed-jet actuation, to obtain performance improvement within the flight envelope (e.g. during take-off, landing, gusts, etc.). Amitay [1], and Woo [5], evidenced that pulsed actuation over fully separated airfoils results in a great, transitory, loads variation. In the present study, the analysis is extended to the cases of attached and slightly separated flow fields with a special focus on the dynamics and characteristic time-scales of the phenomenon.

A. Carusone (B) · C. Sicot · J.-P. Bonnet · J. Borée Fluids, Thermal and Combustion Sciences Department, Institut PPRIME, UPR CNRS 3346, Université de Poitiers, ENSMA, Téléport 2, 1 Avenue Clément Ader, 86360 Futuroscope-Chasseneuil, France e-mail: [email protected]; [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_54

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2 Experimental Details The experiments are carried out in the S620 closed-loop wind tunnel of ISAEENSMA with a test section of 2.4 × 2.6 m2 and a turbulence intensity less than 0.5% at 40 m s−1 . The wing model is based on a NACA 0015 airfoil with a chord length (c) of 0.35 m, mounted between two side walls spaced 1.30 m apart (Fig. 1). The free-stream velocity (V∞ ) is set at 20 m s−1 , corresponding to a chord-based Reynolds number (Rec ) of 4.6 × 105 . Transition is triggered using a 100 µm carborundum grit near the leading edge. Actuation is performed via a spanwise array of 44 pulsed vortex generators jets (PVGJs) ejected from 1 mm diameter orifices and spaced 15.5 mm apart so that they occupy the central half spanwise portion of the airfoil. The orifices are embedded on the suction side of the airfoil at 30% of the chord, measured from the leading edge. The PVGJs have a pitch angle of 30◦ and a yaw angle of 60◦ (Fig. 1), deduced from [4]. The pulsed blowing is triggered through four Matrix 820 solenoidal valves. The jet momentum coefficient (Cμ ) is 0.0125 (Eq. 1) where V jet (φ) is the phase-averaged jet exit velocity (obtained through hotwire measurements), A jet is the area covered by all the 44 orifices, Sr e f is the wing surface containing the PVGJs array, τ is the actuation period, ρ j and ρ∞ are the jet and free-stream fluid densities, respectively. The time (t) and actuation frequency ( f a ) are normalized by c and V∞ resulting in the dimensionless time T + = t V∞ /c and frequency F + = f a c/V∞ . Static pressure is measured using an electronic pressure scanner system of 200 Hz bandwidth connected to 60 pressure taps around the airfoil. The aerodynamic forces and moments are assessed through the integration of the pressure distribution, but only the lift coefficient is presented here. The flow field over the airfoil is explored using 2D-2C particle image velocimetry (PIV) measurements with a field of view (FOV) of 0.7 × 0.35 m2 (Fig. 1). Oil flow visualizations are used to detect the mean separation length (L s ). Separation begins at an angle of attack (AoA or α) of 9◦ and spreads up to 60% of the chord at 16◦ . τ 2 1 ρ j A j 0 V jet (φ)dt Cμ = 1 τ ρ V2 S 2 ∞ ∞ ref

(1)

3 Results and Discussion 3.1 Time-Averaged Control Effects The time-averaged actuation effects on the lift coefficient (Cl ) are presented in Fig. 2, both for baseline and controlled cases. Steady blowing results in a Cl increase of 9% at 5◦ and 30% at 14◦ , compared to the baseline value. A lift-to-drag ratio enhancement of about 19% at 5◦ and 24% at 14◦ is, also, obtained. The control leads to flow attachment

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Fig. 1 Sketch of the wing model installation. The red arrow represents the PVGJs direction. The green rectangle depicts the PIV FOV

Fig. 2 Time-averaged lift coefficient (Cl ) vs the angle of attack (α) both for baseline and controlled cases

at high AoA, postponing the stall angle, as discussed by [3]. The moment, relative to the quarter chord, increases in the counter-clockwise sense. Periodic actuation (with a duty cycle of 50%) equals the effects of steady blowing when F + 1 (see [2] for further discussion on the role of actuation frequency).

3.2 Transient Effects The transient dynamics induced by a single-pulse actuation of duration 8 ms (i.e. ΔT + = 0.46), with a peak velocity of 5 × V∞ is investigated. The phase-averaged temporal variation of the lift coefficient (ΔCl ) following the actuation onset is presented in Fig. 3, as a percentage of the baseline value (Cl0 ). A similar lift pattern is observed both for completely attached (5◦ , L s = 0) and partially separated flow fields

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Fig. 3 Phase-averaged temporal variation of the lift coefficient (ΔCl ) induced by single-pulse actuation for several AoA. Cl0 is the baseline value. The actuation signal is in violet

(from 12◦ to 16◦ ). A negative peak at T + = 1 (e.g. decrease of 5.3% of lift at 14◦ ) is followed by a positive peak at T + = 1.9 (e.g. increase of 16.3% of lift at 14◦ ). After T + = 1.9, the actuation effects slowly vanish and the lift coefficient returns to the baseline value. The slope of the lift curve between T + = 1 and 1.9 in the completely attached case is remarkably lower than in the partially separated cases, suggesting the dependence of the dynamical behavior of the system from the baseline flow configuration. A similar lift evolution is found out for pulse duration even smaller or bigger than ΔT + = 0.46 (not shown here), so the transient dynamical behavior is not affected by the perturbation intensity. From Fig. 3 one notices that the time required to attain the maximum lift increases with L s . On the contrary, when the flow is partially separated over the airfoil the minimum lift is attained at T + ≈ 1 whatever the separation length. The transient flow dynamics induced by single-pulse actuation is investigated using phase-locked pressure and PIV measurements, using the actuation electric trigger for conditional sampling. The phase-averaged variation of the pressure coefficient (ΔC p ) relative to the baseline value (C p0 ) is presented at T + = 1 and T + = 1.9 in Fig. 4 for an AoA of 14◦ (i.e. L s = 0.4), as an example of partially separated configurations. The corresponding phase-averaged distribution of the horizontal velocity (Vx ) is shown for the baseline case in Fig. 5a and following the actuation onset in Fig. 5b–f. In the baseline configuration, a stagnation point S0 marks the beginning of the separated region. The perturbation induced by singlepulse blowing interacts with the separated shear layer at T + = 0.75 leading to the formation of another stagnation point S1 upstream of the recirculation region, while S0 moves away from the airfoil (Fig. 5b). The recirculation region is, then, advected downstream through a spanwise, clockwise, vortex that enhances the free stream entrainment toward the airfoil, promoting the flow attachment upstream of S1 (Fig. 5c–d). The minimum lift is obtained at T + = 1 (Fig. 5c), when S1 is responsible for a local compression zone on the airfoil suction surface between x/c = 0.5 and 0.9 (Fig. 4a). The recirculation region is evacuated from the airfoil at T + ≈ 1.4 and the

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Fig. 4 Phase-averaged variation of the pressure coefficient (ΔC p ) around the airfoil at (a) T + = 1 and (b) T + = 1.9. C p0 is the baseline value. α = 14◦

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flow attaches (Fig. 5e). The ensuing downward tilting of the streamlines in the near wake (as a fluidic flap effect) slowly affects the pressure field around the airfoil. Paradoxically, while the lift is increasing, as a consequence of the pressure redistribution induced by the attachment, the flow begins to re-separate. The maximum lift peak is attained at T + = 1.9, due to a depression on the suction surface and a compression on the pressure surface (Fig. 4b), while a small recirculation zone is found near the trailing edge (Fig. 5f).

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4 Conclusion and Perspectives Single-pulse actuation on a NACA 0015 airfoil results in a great lift variation, within a small period. A similar lift pattern is observed both for partially separated and attached flow fields. In the case of partially separated airfoils, the actuation leads to the evacuation of the separated shear layer through a spanwise clockwise vortex, while the upstream flow gradually attaches. A local compression zone on the airfoil suction surface, induced by a stagnation point upstream of the evacuating recirculation zone, is responsible for an initial negative lift peak. It is followed by a positive lift peak, attained when the flow has already begun to re-separate. The transient dynamics and the time-scales of the phenomenon are investigated in order to implement, in future studies, smart open/closed-loop control strategies leading to aircraft performance improvement and/or energy-saving. Acknowledgements This work is supported by Direction Générale de l’Armement (DGA) and the CPER FEDER project of Région Nouvelle Aquitaine. The authors would like to thank Jean-Marc Breux, François Paille, Patrick Braud, Romain Bellanger, Bastien Robert and Mathieu Rossard for their valuable technical support during the experiments.

References 1. Amitay M, Glezer A (2006) Aerodynamic flow control using synthetic jet actuators. In: Koumoutsakos P, Mezic I (eds) Control of fluid flow, vol 330. Lecture notes in control and information sciences. Springer, Berlin, pp 45–73. https://doi.org/10.1007/978-3-540-360858_2 2. Greenblatt D, Wygnanski IJ (2000) The control of flow separation by periodic excitation. Prog Aerosp Sci 36(7):487–545. https://doi.org/10.1016/S0376-0421(00)00008-7 3. Seifert A, Darabi A, Wygnanski IJ (1996) Delay of airfoil stall by periodic excitation. J Aircr 33(4):691–698. https://doi.org/10.2514/3.47003 4. Siauw WL, Bonnet JP (2017) Transient phenomena in separation control over a NACA 0015 airfoil. Int J Heat Fluid Flow 67:23–29. https://doi.org/10.1016/j.ijheatfluidflow.2017.03.008 5. Woo GTK, Glezer A (2013) Controlled transitory stall on a pitching airfoil using pulsed actuation. Exp Fluids 54(6):1507.1–1507.15. https://doi.org/10.1007/s00348-013-1507-5

Artificial Intelligence Control of a Turbulent Jet Dewei Fan, Yu Zhou, and Bernd R. Noack

Abstract An artificial intelligence (AI) control system is developed to manipulate a turbulent jet targeting maximal mixing. The control system consists of sensors (two hot-wires), genetic programming for evolving the control law and actuators (6 unsteady radial minijets). The mixing performance is quantified by the jet centerline mean velocity. AI control discovers a hitherto unexplored combination of asymmetric flapping and helical forcing. Such a combination of several actuation mechanisms, if not creating new ones, constitutes a large challenge for conventional methods of parametric optimization. AI control vastly outperforms the optimized periodic axisymmetric, helical or flapping forcing produced from conventional open- or closed-loop control. Intriguingly, the learning process of AI control discovers all these forcings in the order of increased performance. Our study is the first AI control experiment which discovers a non-trivial spatially distributed actuation optimizing a turbulent flow. The results show the great potential of AI in conquering the vast opportunity space of control laws for many actuators, many sensors and broadband turbulence. Keywords Artificial intelligence · Jets · Flow control

D. Fan · Y. Zhou (B) · B. R. Noack (B) Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Harbin, People’s Republic of China e-mail: [email protected] B. R. Noack e-mail: [email protected] B. R. Noack LIMSI, CNRS, Université Paris-Saclay, Bât 507, rue du Belvédère, Campus Universitaire, 91405 Orsay, France Institut Für Strömungsmechanik Und Technische Akustik (ISTA), Technische Universität Berlin, Müller-Breslau-Straße 8, 10623 Berlin, Germany © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_55

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1 Introduction Our experimental study builds on the pioneering numerical jet mixing studies [1, 2]. The former deployed an evolutionary strategy to optimize a combination of axisymmetric and helical forcing characterized by four parameters, while the latter optimized a flapping mode [3]. The present optimization method, based on linear genetic programming (LGP), may work on a much larger search space of spatio-temporal forcing including all known three-dimensional actuations, multi-frequency forcing and sensor feedback. In general, active control of jets is divided into open-loop and closed-loop control. Note that closed-loop control shows the potential to significantly reduce power requirements in comparison to open-loop control strategies, since the random aspect of these structures reduces the effectiveness of an open-loop configuration [4]. Most literature on closed-loop turbulent flow control falls in two categories, i.e. modelbased and model free tuning of the control laws. For model-based control, the discretised Navier–Stokes equations and linear stochastic estimation are used to resolve all flow physics and nonlinearities [5]. In the previous work [6], reduced-order models were applied to a few non-normal global eigenmodes of the linearized Navier- Stokes equations as a basis for Galerkin projection. Yet, these approaches have limited applicability to unstable advection dominated flows [7]. The control logic based on models is the most accurate. However, the accurate control consumes too much time. Therefore, model-free control is most widely applied in the turbulent flow control. The adaptive control PID was used to suppress cylinder vibration [8]. Extremum seeking control (ESC) was used for separation control on a high lift configuration [9]. Yet, in all reported cases the resulting control law was simple, e.g. based on a single actuator characterizable by one or two parameters. The optimization of such control laws is achievable with conventional techniques [10]. The nonlinear control optimization involving many independent actuators can be unimaginably complex. Take the manipulation of a turbulent jet based on unsteady radial minijets for example. One single periodically operated minijet of a given exit diameter may be associated with three control parameters, namely, the actuation frequency f a , mass flow rate mmini and duty cycle α [11]; however, multiple, say six, equally separated independent minijets introduce the complexity of distributed actuation or additional dimensions. The minijets can be active or off and six minijets may occur alternately from one configuration to the other. As a result, the complexity of the problem grows tremendously. The optimization of nonlinear control laws for such high dimension problems is largely terra incognita, which is extremely too time consuming, if not impossible, for conventional techniques. This is a great challenge for turbulence control. Then could artificial intelligence method conquer the vast opportunity space of control laws and, in doing so, generate an outcome or alter the turbulence to a desired state that has been so far prohibitive from conventional methods? This work aims to answer the above question. An AI control system is developed to manipulate a turbulent jet, one of the few best investigated and highly complicated

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classical flows, for maximized mixing. Six unsteady minijets are deployed as actuators. Following [12], genetic programming is chosen as a very powerful regression solver for the control law.

2 Experimental Details A turbulent round jet facility, including an air supply system, main round jet and minijet actuators is applied. Figure 1a shows the schematics of the main jet facility. The details are described by Fan et al. (2017). The Reynolds number ReD = U j D/ν of the main jet is fixed at 8000, where U j is the jet centerline time-averaged velocity measured at the nozzle exit, ν is the kinematic viscosity of air and D = 20 mm is the diameter of the nozzle. The centre of the jet exit is set as the origin of a Cartesian coordinate system, where the x-axis is aligned with the streamwise direction and the y-axis contains minijets No. 1 and No. 4 (Fig. 1c). The actuation is performed with 6 independent minijets upstream of the nozzle exit. The minijets are connected to six different channels each of which consists of a mass flow meter and flow-limiting valve. The mass flow rate is controlled by the flow-limiting valve and measured by the mass flow meter. The six minijets have orifice diameter of 1 mm are equidistantly placed at x i = −0.85 D, yi = (D/2) cosθ i , zi = (D/2) sinθ i , where θ i = (i−1)2π/6, i = 1, …,6. The locations of the actuators

Fig. 1 Sketch of the experimental setup: a main jet facility; b minijet assembly; c minijet arrangement

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are shown in the Fig. 1b. The minijets are operated by electromagnetic valves in an ON/OFF mode. The valves limit the frequency of the minijet to 500 Hz, more than three times the characteristic shedding frequency of the unforced jet f 0 = 135 Hz and more than seven times the actuation frequency of this study f a = 67 Hz. The jet exit velocity at (x/D, y/D, z/D) = (0, −1/4, 0) is measured with a tungsten wire of 5 μm in diameter. This hot-wire is operated on a constant temperature circuit (Dantec Streamline) at an overheat ratio of 0.6. The centreline jet velocity at x/D = 5 is monitored with a second hot-wire. U j and U 5D denotes the averaged velocities at nozzle exit and after the potential core, respectively. Note that hot-wire is in the plug flow nozzle exit region but slightly of center to allow simultaneous measurements of both quantities in the experiment. The hot-wires are calibrated at the jet exit using a Pitot tube connected to a micromanometer (Furness Controls FCO510). The experimental uncertainty of the hot-wire measurement is estimated to be less than 2%. A planar high-speed PIV system, including a high speed camera (Dantec Speed Sence90C10, 2056 × 2056 pixels resolution) and pulsed laser source (Litron LDY304- PIV, Nd:YLF, 120 mJ/pulse) is deployed for flow visualization in the x−z, x−y and y−z planes. An oil droplet generator (TSI MCM-30) is used to generate a fog for seeding the flow. The seeding particles are supplied into the mixing chamber (Fig. 1a) to mix with air. Flow illumination is provided by a laser sheet of 1 mm in thickness generated by the pulsed laser via a cylindrical lens. Particle images are captured at a sampling rate of 405 Hz, corresponding to 3 f 0 and 6 f a .

3 Artificial Intelligence Control 3.1 Control Problem and Benchmark Actuations The AI control system is sketched in Fig. 2. Generally, a control system (solid line inside) facilitates a control goal for a plant (yellow) by control hardware and a control logic/controller (red). The control hardware includes sensors (green) and actuators (blue), discussed above, which monitor the plant output (velocity signals) and execute instructions from the controller, respectively. The open-loop arrangement is shown −

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in Fig. 1d for computing the cost value J = U 5D /U j . The minimized J corresponds to the maximized decay rate K = 1-J of jet centreline mean velocity, which is an indicator of the mixing efficacy of the jet [13]. The ith minijet blows if the actuation command bi command is positive and is closed otherwise. The sixdimensional vector b = [b1 , …, b6 ]† comprises all actuation commands. The actuation may depend on the harmonic functions hi = cos (ωt − φ i ), φ i = 2πi/6. We use six linearly dependent signals instead of two linearly independent ones to simplify the expressions for helical forcing. The angular frequencyω corresponds to 67 Hz or approximately half the characteristic unforced shedding frequency. This value has been optimized for flapping forcing with a single minijet

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Fig. 2 Principle sketch of the artificial intelligence control system

under the same conditions [14] and predicted by a global stability analysis [15]. The six-dimensional vector h = [h1 , …,h6 ]† includes all these harmonic functions. In this notation, axisymmetric bi = h 1 − ca , i = 1, . . . , 6;

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Here, the constants ca , ch , cf define the duty cycles and have been optimized with respect to the cost. The costs J a , J h , J f of the optimized axisymmetric, helical and flapping forcing constitute the benchmarks for AI control.

3.2 Control Optimization Using Linear Genetic Programming Further AI-based jet mixing optimization is based on a general ansatz for periodic open-loop forcing—including the above mentioned forcing: b = K (h)

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Note that the nonlinear function K can create arbitrary higher harmonics, like the 10th harmonics via h1 10 − 1/2 as well as arbitrary phase relationships. The control law (4) is optimized with respect to the cost J using the powerful linear genetic programming (LGP) as a regression solver. We take the same parameters for control law representation and for the genetic operations as Li et al. (2017) for drag reduction of the Ahmed body. The first generation of LGP, n = 1, contains N i = 100 random control laws K i 1 (h), i = 1, …, N i , also called individuals. Each individual is tested for 5 s in the experiment to yield the measured cost J i 1 . Subsequent generations are generated from the previous ones with genetic operations (elitism, crossover, mutation and replication) and tested analogously. After the in situ performance measurements, the individuals are re-numbered in order of performance, J 1 n ≤ J 2 n ≤ … ≤ J Ni n , where the superscript ‘n’ represents the generation number. As plant-specific rule, we discard and replace any individual for testing if one actuator is not active or constant blowing.

4 Results and Discussions Figure 3 displays 3000 evaluated cost functions under AI control. The unforced

Fig. 3 Learning curve (3000 individuals) of AI control for (u) unforced jet, (a) axisymmetric, (h) helical, (f ) flapping and (c) combined forcings. J u , J a , J h and J f are costs corresponding to the benchmarks of unforced, open-loop axisymmetric, helical and flapping forcings, respectively

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benchmark cost J u is marked by an solid square at generation 0 and continued as horizontal solid line. The corresponding flow visualization in subfigure (u) shows the dye from the nozzle exit in the x − y plane. The displaced vortex rings shed with frequency f 0 = 135 Hz. The following open squares at generation n = 1, …, 30 mark the first and best individual of each generation with N i = 100 individuals. The remaining costs of each generation are displayed by the monotonously increasing curve. Every curve has a unique color. The best individual of the first generation has an axisymmetric control law b1 = b2 = b3 = b4 = b5 = b6 = − 0.832 + sin (ωt + 4/6π). This law is equivalent to (1) modulo a time shift. The performance J 1 1 = 0.626 is slightly better than the optimized axisymmetric performance (1). The reason may be attributed to the converged long-term velocity measurement J a as compared to the short and less accurate measurement of AI control. From several similar or equivalent control laws, only the best value is monitored. It should be noted that learning of AI control only requires an approximately accurate relative ordering of the individuals. An accurate long-term evaluation of the cost is only performed in the last generation n = 30. Subfigure (a) shows the corresponding flow visualization and the dashed horizontal line represents J a . In the second generation, AI control discovers the better performing helical forcing bSequential photographs of the cross-sectional flow = sin(ωt + 4/6π) – 0.145, b2 = − 0.347sinωt, b3 = ((sin(ωt + 8/6π) + (sin(ωt + 8/6π)2 + sin(ωt + 2/6π)2 ))sin(ωt + 8/6 π), b4 = 2sin(ωt + 10/6π)((sin(ωt)2 − sin(ωt + 2/6π)(sin(ωt)2 − sin(ωt + 2/6π)), b5 = 1/(−0.313 + sinωt) + sinωt), b6 = − 0.354sin(ωt + 8/6π). This forcing is not of the form (2), but it clearly shows a uniformly traveling wave in azimuthal direction. The corresponding flow visualization (3 h) shows a more regular pattern and the cost J h is marked by a dot horizontal line. In the fifth generation, AI control learns flapping forcing b1 = b2 = b3 = − 0.811 + sin(ωt + 2/6π), b4 = b5 = b6 = − 0.782 − sin(ωt + 2/6π). Similiar to the Eq. (3), this forcing is asymmetric. An optimized asymmetry yields a reproducibly better mixing. Subfigure (f ) shows a strong mixing in the flapping plane (Fig. 3f 1) and a less pronounced mixing in the orthogonal plane (3f 2) which is symmetric with respect to the two synchronous actuator groups. The cost J f is marked by a dashed dot horizontal line. In the eleventh generation, AI control discovers a novel combination of asymmetric flapping forcing and helical forcing, significantly outperforming the flapping forcing of generation n = 5 and yielding a decrease of the centerline velocity by more than a factor 3. The corresponding flow visualization (3c) indicates the flapping mechanism (compare with (3f 1)). The helical component will be shown in a later analysis. After this generation, cost and actuation mechanism hardly change in subsequent generations, indicating the convergence of the AI learning process. This actuation mechanism is reproducible, i.e. the combined flapping and helical forcing and very similar cost has been observed in all experiments with different initializations of the first generation. The learning process may not display all of the three symmetric forcings as the best individuals. The flow response to the four different forcings of AI control is depicted in a near-field cross-plane in Fig. 4. The first row shows the axisymmetric forcing at

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Fig. 4 Sequential photographs of the cross-sectional flow structure captured at x/D = 0.25. From top to bottom: six instants at t i = iT /6 (i = 1, 2 …, 6) in one actuation period T (= 1/f a )

6 consecutive times representing one actuation period. Subfigure (a2) displays the footprint of a vortex ring which disintegrates later in six mushroom-like structures (Fig. 4a5, a6). In the second row, helical forcing is clearly evidenced by the clockwise rotating satellite region (Fig. 4h1-h6). The third row illustrates flapping flows with patches of dye in the flapping plane (4f 3, 4f 6) and mushroom-structures at other instances. The bottom row shows the best AI control, combination of asymmetric flapping and helical forcing. The footprints of helical can be seen by the clockwise ring structures (Fig. 4c1-c6).

5 Conclusions An AI control system has been developed which learns automatically how to optimize a spatially distributed actuation and thus a turbulent jet for the targeted cost. Like virtually all control strategies of nonlinear dynamics, AI control solutions do not come with a proof of global optimality. Yet, the results for jet mixing optimization demonstrate a number of highly desirable features. First, AI control has unveiled a few typical control laws or forcings, i.e., axisymmetric, helical and flapping, in its learning process and eventually converged to a sophisticated spatio-temporal actuation which is the combination of the individual forcings. This combination has

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produced a fascinating turbulent flow structure characterized by rotating and flapping jet column, along with the generation of mushroom like structures, all acting to enhance jet mixing and thus vastly outperforming several known optimal benchmark actuations. Note that the learning time of 3000 individuals or 6 h wind-tunnel testing is remarkably short for such a complicated solution. Second, unlike other simple conventional open or closed loop control methods, AI control could find optimal control laws without any model or assumptions about the actuation mechanisms. Third, the cost J corresponding to AI-learned combination is reproducible with other initial generations. The control laws may analytically differ but produce almost identical actuation commands. Fourth, the parameters of the underlying genetic programming were already proven useful in many other experiments. No sensitive dependence on the parameters has been observed so far and AI control can be expected to yield near-optimal results in its first application to a new plant. Finally, the search space for a control law is extremely large and of very high complexity/dimensions, including multiple frequencies, minijet configurations, temporal and spatial phase differences between the configurations, and duty cycles of minijets, along with sensor feedback. Acknowledgements YZ wishes to acknowledge support given to him from NSFC through grants 11632006, 91752109 and U1613226. This work is supported by the French National Research Agency (ANR) via the grants ANR-11-IDEX-0003-02 (iCODE), ’ACTIV ROAD’ and ’FlowCon’, and by the OpenLab Fluidics consortium ([email protected]) of PSA Peugeot-Citron and Institute Pprime.

References 1. Hilgers A, Boersma B-J (2001) Optimization of turbulent jet mixing. Fluid Dyn Res 29:345–368 2. Koumoutsakos P, Freund J, Parekh D (2001) Evolution strategies for automatic optimization of jet mixing. AIAA J 39:967–969 3. Rechenberg I (1973) Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart 4. Moin P, Bewley T (1994) Feedback control of turbulence. Annu Rev Fluid Mech 47 5. Sipp D, Marquet O, Meliga P, Barbagallo A (2010) Dynamics and control of global instabilities in open-flows: A linearized approach. Appl Mech Rev 63:030801 6. Akervik E, Hoepffner J, Ehrenstein U, Henningson D-S (2007) Optimal growth, model reduction and control in a separated boundary-layer flow using global eigenmodes. J Fluid Mech 579:305–314 7. Onofrio S, Shervin B, Luca B, Henningson D-S (2011) Feedback control of three-dimensional optimal disturbances using reduced-order models. J Fluid Mech 677:63–102 8. Zhang M-M, Cheng L, Zhou Y (2004) Closed-loop controlled vortex shedding and vibration of a flexibly supported square cylinder under different schemes. Phys Fluids 16:1439–1448 9. Becker R, King R, Petz R, Nitsche W (2007) Adaptive closed-loop separation control on a high-lift configuration using extremum seeking. AIAA J 45:1382–1392 10. Wu Z, Wong C-W, Zhou Y (2018) Dual-input/single-output extremum-seeking system for jet control. AIAA J 56:1463–1471 11. Perumal A-K, Zhou Y (2018) Parametric study and scaling of jet manipulation using an unsteady minijet. J Fluid Mech 848:592–630

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12. Duriez T, Brunton SL, Noack BR (2016) Machine learning control—taming nonlinear dynamics and turbulence. Fluid Mech Appl Springer-Verlag, vol 116 13. Yang H, Zhou Y (2016) Axisymmetric jet manipulated using two unsteady minijets. J Fluid Mech 808:362–396 14. Wu Z, Fan D, Zhou Y, Li R, Noack B-R (2018) Jet mixing optimization using machine learning control. Exp Fluids 59:131 15. Garnaud X, Lesshafft L, Schmid P-J, Huerre P (2013) The preferred mode of incompressible jets: linear frequency response analysis. J Fluid Mech 716:189–202

Turbulent Friction Drag Reduction: From Feedback to Predetermined, and Feedback Again Koji Fukagata

Abstract We overview the recent attempts for turbulent friction drag reduction and related studies, by focusing on those conducted in our research group. While the earlier studies for friction drag reduction mainly targeted at suppression of quasistreamwise vortices using feedback control, predetermined control methods using streamwise traveling waves or a uniform blowing have also been extensively investigated in the last decade. For both the streamwise traveling wave of wall deformation and the uniform blowing, their drag reduction capabilities have been confirmed well by direct numerical simulation at relatively low Reynolds numbers. Prediction of their drag reduction capabilities at higher Reynolds numbers and attempts for experimental confirmation are also intensively ongoing toward their practical implementation. We also introduce our practice on the application of resolvent analysis for designing a more effective feedback control law. In addition, we briefly introduce some recent attempts on the applications of machine learning to turbulent flows, which may be utilized for a better design of flow control in future. Keywords Turbulent flow · Flow control · Drag reduction

1 Introduction During the past three decades, novel turbulent friction drag reduction techniques have been intensively investigated based on the physical understanding of turbulence or through a combination with modern control theory [1–3]. Since the higher friction drag in turbulent flow is caused by the quasi-streamwise vortices (QSVs), the early attempts have mainly devoted to suppress these QSVs using feedback control. The pioneering work of such attempts to suppress QSVs is the opposition control proposed by Choi et al. [4]. In the opposition control, distributed blowing and suction is applied on the wall so as to oppose the wall-normal velocity sensed above the wall, and about 20% friction drag reduction was attained in direct numerical simulation K. Fukagata (B) Keio University, Yokohama 223-8522, Japan e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021 M. Braza et al. (eds.), Fluid-Structure-Sound Interactions and Control, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-33-4960-5_56

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(DNS) of turbulent channel flow at a relatively low Reynolds number. Since the sensing of wall-normal velocity above the wall cannot be implemented in practice, a number of studies have been made to attain the similar control effect by sensing the physical quantities measurable on the wall only. For instance, Lee et al. [5] applied a suboptimal control to a turbulent channel flow and attained about 20% drag reduction by using the wall pressure or the spanwise wall shear as the sensor signal; but at the same time they reported failure to gain a drag reduction effect using the streamwise wall shear signal. For practical applications, the streamwise wall shear is the quantity considered easiest to measure, as was actually used in a wind-tunnel experiment [3]. Although some other attempts have been made to reduce the drag using the streamwise wall shear signal only, the maximum drag reduction rate attainable by using the streamwise wall shear signal only stayed around 10% [3, 6]. During the studies on feedback control above, the mathematical relationship between the friction drag and the Reynolds shear stress (RSS) profile has been clarified, called the FIK identity [7], which states that the increment in the friction drag in wall turbulence is expressed by a weighted integration of RSS profile. According to the FIK identity, turbulent friction drag can be reduced by reducing RSS near the wall, without explicitly targeting at the suppression of QSVs. Based on this implication, predetermined control techniques, which do not require sensing the detailed flow information, have been investigated by several research groups to reduce turbulent friction drag. In the present paper, we first briefly overview some of such predetermined control techniques for turbulent friction drag reduction (mainly the studies made in the author’s group). Subsequently, we introduce our recent attempts to reconsider feedback control. Finally, we introduce some of our recent attempts on applications of machine learning to turbulence toward better turbulence control.

2 Predetermined Control 2.1 Streamwise Traveling Wave As mentioned in the introduction, turbulent friction drag can be reduced by reducing RSS near the wall. To reduce it, Min et al. [8] proposed a streamwise traveling wave of blowing and suction. Through the linear analysis and DNS, they found that upstream-going streamwise traveling waves of blowing and suction create negative RSS near the wall and result in sublaminar drag, although this sublaminar drag is not the ultimate goal in terms of net energy saving [9, 10]. A similar sublaminar drag was also observed in the case of feedback control designed to make a negative RSS [11]. Another linear analysis [12] revealed that the negative RSS with the upstream traveling wave is attributed to a phase difference between the wall-normal velocity due to blowing and suction and the induced streamwise velocity fluctuations though

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viscosity and that the thickness of such a layer can be scaled similarly to the Stokes second problem. The streamwise traveling wave-like blowing/suction velocity distribution can also be created by a motion of streamwise traveling wave-like wall deformation. Hœpffner and Fukagata [13] compared the streamwise traveling wave-like blowing/suction and deformation in the absence of mean pressure gradient, and found that the directions of pumping effect are opposite in these two cases. With blowing/suction the pumping takes place in the direction opposite to the wave, while with deformation it is in the direction same as the wave. This also explains why the drag was reduced by an upstream traveling wave of blowing/suction [8], which pumps the flow downstream to substitute the external mean pressure gradient. On the other hand, Lee et al. [14] performed a stability analysis of the streamwise traveling wave-like blowing/suction and found that downstream waves tend to stabilize the flow. Summing up the information above, in the case of traveling wave-like wall deformation, drag reduction is expected to be attained with downstream traveling waves in terms of both pumping effect and stabilization effect. Nakanishi et al. [15] confirmed this by DNS of turbulent channel flow at a low Reynolds number. In their DNS, the flow rate was kept constant at the bulk Reynolds number of Reb = 2U b / δ ν = 5600 (where U b , δ, and ν denote the bulk-mean velocity, the channel half-width, and the kinematic viscosity, respectively), which corresponds to the friction Reynolds number of Reτ = uτ δ/ν = 180 (where uτ is the friction velocity) in the uncontrolled case. Through a parametric study varying the phasespeed, the deformation amplitude, and the wavenumber of the traveling wave, they observed that the flow was completely relaminarized in some cases, as shown in Fig. 1, which corresponds to about 70% drag reduction and 65% net power saving. Relaminarization has also been observed in the case of streamwise traveling wave-like blowing/suction, also by downstream waves [16]. Investigation on the streamwise traveling wave-like wall deformation toward its practical implementation is still ongoing. Suzuki et al. [17] installed a rubber sheet driven by a piezoelectric actuator in a channel and experimentally studied the drag reduction effect by the streamwise traveling wave-like wall deformation. Although

Fig. 1 Vortical structure in turbulent channel flows under a constant flow rate at Reb = 5600: a uncontrolled flow; b flow controlled using streamwise traveling wave-like wall deformation [15]. Visualization was made by K. Uchino (Keio University)

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Fig. 2 Turbulent channel flow controlled by streamwise traveling wave-like wall deformation under constant pressure gradients at different friction Reynolds numbers [18]: a mean velocity profiles obtained in DNS; b preliminary prediction of drag reduction rate RD at higher Reynolds numbers

there are some differences in the control parameters from those in the simulations, they clearly observed a substantial amount of drag reduction. Nabae et al. [18] attempted to predict the drag reduction effect at practically high Reynolds numbers based on the scaling found in the DNS performed at low Reynolds number ranges (Fig. 2). According to their prediction, about 25% drag reduction by the streamwise traveling wave-like wall deformation can be expected even at practically high Reynolds numbers of Reτ = 105 , although this prediction should be validated in future, preferably by experiments.

2.2 Uniform Blowing A small amount of uniform blowing (UB) from the wall surface is one of the classical predetermined control techniques, which had already been intensively investigated more than 50 years ago experimentally and theoretically [19]. Its detailed effects on turbulent statistics were investigated by means of DNS for a channel flow [20] and a spatially developing zero-pressure-gradient boundary layer [21] as shown in Fig. 3. In both cases, when UB velocity is on the order of 0.1%-1% of the freestream velocity, the mean velocity profile is displaced away from the wall, while the turbulence intensity is enhanced. Since the former effect exceeds the latter, the drag is reduced as a whole, as quantitatively confirmed using the FIK identity [7, 21]. For instance, in the case where UB at 1% free-stream velocity is applied to a spatially developing turbulent boundary layer at the Reynolds number of Reθ = 430 (where θ is the momentum thickness), about 70% drag reduction has been confirmed in DNS [21]. The above drag reduction effect of UB is essentially the same for higher Reynolds numbers [22, 23], for the case where the blowing is made with discrete slots [24], at

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Fig. 3 Uniform blowing applied to a zero-pressure-gradient turbulent boundary layer by Kametani and Fukagata [21]: (left) vortical structure; (right) decomposition of different contributions to drag using the FIK identity. Reprinted with permission from Cambridge University Press

higher Mach numbers [25], and even on transitionally rough surfaces [26]. However, all these studies are numerical and have been performed for zero-pressure-gradient turbulent boundary layers or channel flows. For examination toward practical applications, such as for airfoils, it is necessary to investigate the effect of UB in more practical configurations. Recently, Eto et al. [27] have conducted a wind-tunnel experiment to reduce turbulent friction drag on a Clark-Y airfoil using UB. The Reynolds number based on the chord length c of the airfoil model was Rec = 1.5 × 106 . The air for UB was supplied by an external compressor to attain the UB velocity of 0.14% of the freestream velocity. Through the hot-wire measurement of velocity profiles in the boundary layer and a viscous scaling of the velocity profiles taking into the pressure gradient, they quantitatively confirmed 20–40% drag reduction in the area where UB was applied. As a continuation of the work above, Hirokawa et al. [28] consider taking the air passively from the front region of the Clark-Y airfoil (Fig. 4) and confirm 4–23% drag reduction in a wind-tunnel experiment. In addition, numerical simulations for this configuration are performed by different research groups to seek the optimum intake and UB locations [29, 30].

3 Feedback Control Again Despite the promising results of the predetermined control above, feedback control is still attractive because of its potential. Recently, we have revisited the suboptimal control proposed by Lee et al. [5] using the resolvent analysis proposed by McKeon and Sharma [31] to seek for a possible modification of suboptimal control law so that a substantial drag reduction effect is attained by using the streamwise wall shear

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Fig. 4 The Clark-Y airfoil model for wind-tunnel experiment of passive UB, developed by Hirokawa et al. [28]. The air is taken from the front and uniformly blown from the down-stream part of the upper surface. In-between the intake and the blowing surface, an electro-magnetic valve and a flow meter are installed to switch on and off the blowing and to meas-ure the flow rate. Picture is taken from the JSME-FED Newsletter. http://www.jsme-fed.org/newsletters-e/2019_3/no4.html

information only. Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes identified via a gain-based decomposition of the Navier–Stokes equations, and it enables targeted analyses of the effects of suboptimal control on high-gain modes. Nakashima et al. [32] compared two suboptimal control laws generating blowing and suction at the wall proportional to the fluctuating streamwise (Case ST) or spanwise (Case SP) wall shear stress. It was shown that both Case ST and SP can suppress resolvent modes resembling the near-wall cycle. However, for Case ST, the analysis revealed that control leads to substantial amplification of flow structures that are long in the spanwise direction. Following the work above, Kawagoe et al. [33] proposed modified versions of Case ST so as to eliminate the detrimental effect indicated by a blue region and enhance the favorable effect indicated by red in Fig. 5a. First, resolvent analysis is used to design and provide a preliminary assessment of modified control laws that rely on sensing the streamwise wall shear stress, as shown in Fig. 5b. Then, control performance was assessed by means of DNS and about 10% drag reduction was confirmed. Not only the drag reduction rate, the characteristic vortical structure under the modified control was also well predicted by the resolvent analysis, as shown in Fig. 6. Although the attained drag reduction rate is unfortunately not higher than that in the previous work using the streamwise wall shear only [6], the present study is considered to have opened a possibility to use the resolvent analysis not only for assessing the existing control laws [32, 34] but also for designing new control laws [33, 35].

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Fig. 5 Resolvent-based predictions for singular-value suppressions Rσ for different streamwise and spanwise wavelengths (λx + , λz + ) by Kawagoe et al. [33]: a the original suboptimal control law sensing the streamwise wall shear stress; b modified control law. Reprinted with permission from Cambridge University Press

Fig. 6 Characteristic vortical structure under modified control [33]: a conditional sampling of DNS result; b resolvent analysis. Reprinted with permission from Cambridge University Press

4 Toward the Future Owing to the third boom on artificial intelligence, machine learning has recently gathered increasing attention everywhere. Application of machine learning to flow control problems, however, has a relatively long history. For instance, Lee et al. [36] devised a single-layer perceptron to learn the control input of opposition control [4]. Milano and Koumoutsakos [37] had already attempted “deep learning” about 20 years ago using a multilayer perceptron with 26,000 inputs to estimate the flow field above the wall from the information on the wall. In recent few years, again, the number of studies concerning the application of machine learning to fluid mechanics has increased due to the boom mentioned above, as reviewed by Brunton et al. [38]. One thing we can expect for the machine learning for flow control problems is a possibility to construct a nonlinear feature extraction method, which can extract

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Fig. 7 Machine learning of turbulent channel flow [40]: a training process b machine-learned turbulent inflow generator Taken from: K. Fukami, Y. Nabae, K. Kawai, and K. Fukagata, Phys. Rev. Fluids 4, 064603 (2019). Copyright © 2019 by the American Physical Society. Reprinted with permission

important nonlinear dynamics that cannot be extracted by the well-established linear methods such as the proper orthogonal decomposition (POD) and the dynamic mode decomposition. Once such a nonlinear feature extraction method is developed, it can be used as a nonlinear reduced order model to design an effective control law. Such attempts are also made in our research group. For instance, Fukami et al. [39, 40] applied a convolutional neural network (CNN) to perform a super-resolution reconstruction of a turbulent flow field and to develop a machine-learned inflow generator (Fig. 7). Also, although not for turbulent flows but for an unsteady laminar flow around a circular cylinder, Hasegawa et al. [41] showed that the network based on CNN and long short term memory (LSTM) trained for several Reynolds numbers can predict flows at different Reynolds number at reasonable accuracy, and Murata et al. [42] demonstrated that a single reduced-order nonlinear mode obtained using CNN contains multiple POD modes in a physically interpretable manner. Although these attempts are still in their early stage, we hope that these techniques can be used in near future to design more effective control laws. Acknowledgements The author thanks the former and current students at Keio University and all the collaborators involved in the studies introduced here. These studies were supported through JSPS KAKENHI grant numbers 25420129, JP16K06900 and JP18H03758 by the Japan Society for the Promotion of Science (JSPS).

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