Thermal Measurements in Electronics Cooling 9781003067948, 0849332796, 9780849332791

Table of contents :
Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Table of Contents......Page 6
Preface......Page 8
Chapter 1: Electronic Cooling and the Need for Experimentation......Page 16
Chapter 2: Uncertainty Analysis......Page 60
Chapter 3: Similitude in Electronic Cooling......Page 96
Chapter 4: Measuring Velocity in Electronic Systems......Page 126
Chapter 5: Temperature Measurement in Electronic Cooling......Page 182
Chapter 6: Measuring Pressure in Electronic Systems......Page 230
Chapter 7: Measuring Thermal Conductivity and Diffusivity......Page 258
Chapter 8: Heat Flux Measurements: Theory and Applications......Page 288
Chapter 9: Wind Tunnel Design......Page 336
Chapter 10: Flow Visualization Methods and their Application in Electronic Systems......Page 364
Chapter 11: Principles of Component Characterization......Page 402
Chapter 12: Acoustical Noise Measurement and Control in Electronic Systems......Page 440
Index......Page 482

Citation preview

Thermal Measurements in Electronic Cooling

edited by

Kaveh Azar

CRC Press Boca Raton London New York Washington, D.C.

Library of Congress Cataloging-in-Publication Data Thermal measurments in electronic cooling / edited by Kaveh Azar. p. cm. Includes bibliographical references and index. ISBN 0-8493-3279-6 (alk. paper) 1. Electronic apparatus and appliances— Cooling. 2. Temperature measurements. I. Azar, Kaveh. TK7870.25.T49 1997 621.3815*4— dc21

97-10722

This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the authors and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. All rights reserved. Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA The fee code for users of the Transactional Reporting Service is ISBN 0-8493-3279-6/97/$0.00+$.50. The fee is subject to change without notice. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Tradem ark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com © 1997 CRC CRC Press LLC No claim to original U.S. Government works International Standard Book Number 0-8493-3279-6 Library of Congress Card Number 97-10722 Printed in the United States of America 3 4 5 6 7 8 9 0 Printed on acid-free paper

Dedication To my parents, Toghrol and Farzaneh Azar their unconditional love and support

Contents Preface............................................................................................................................................................ vii Chapter 1

Electronic cooling and the need for experim entation.........................................1

Kaveh Azar Chapter 2

Uncertainty an aly sis.......................................................................................................45

R obert}. Moffat Chapter 3

Similitude in electronic cooling.................................................................................81

Michael T. Boyle Chapter 4

M easuring velocity in electronic system s............................................................ I l l

J. Foss, D. Williams, and C. Work Chapter 5

Temperature m easurem ent in electronic coolin g............................................. 167

James N. Sweet Chapter 6

M easuring pressure in electronic system s.......................................................... 215

George A. Pender Chapter 7 M easuring thermal conductivity and diffusivity............................................. 243 /. E. Graebner Chapter 8

Heat flux m easurem ents: theory and applications...........................................273

Ned R. Keltner Chapter 9

Wind tunnel d esig n ......................................................................................................321

Russell V Westphal Chapter 10 Flow visualization methods and their application in electronic sy ste m s......................................................................................................................... 349

Suresh V. Garimella Chapter 11

Principles of component characterization...........................................................387

John W. Sofia Chapter 12 Acoustical noise measurement and control in electronic sy ste m s.........................................................................................................................425

George C. Maling and David M. Yeager In d e x .............................................................................................................................................................467

Preface Electronic cooling problems have posed a formidable challenge to thermal engineers with respect to their solution and verification. The com plexity of the problem and the nature of the solution techniques have created a high degree of uncertainty in the results. These uncertainties and the advent of num erical simulation tools becom ing available at the PC level have also amplified the need for verification. Engineers are often times left wondering whether their answers are correct, and the immediate tendency is to verify their results by conducting an experiment. M ost engineers are either inadequately trained or not trained at all in the science of measurement. The attractiveness of numerical simulation tools with their ease of use has even pushed back the training in experim entation at the academic institutions. This lack of training and experience with measurem ent processes, accompanied with the profuse reliance of the thermal com m unity on doing experimentation, was the motivation behind putting this book together. This book attempts to cover the fundamentals of thermal m easurement while focusing on experim entation in electronics cooling. It is unique in that it addresses all facets of measurem ent in one volume. It can conceptually be divided into three sections. The first three chapters deal with the understanding of the need for experim entation and the im portant param eters that affect the process. In this section, chapter one pours the foun­ dation for what, where, and how thermal measurements are to b e considered. Chapter two deals with the im portant issue of uncertainty analysis and its role in experim ent planning. Chapter three covers the concept of similitude as applied to electronic cooling and shows how the dim ensional analysis can be used for experiment planning and elim ­ inating unnecessary measurements. The second part of the book is on fundamental measurements. These include temper­ ature, velocity, and pressure as the primary parameters, and thermal conductivity and heat flux as the secondary ones. All facets of m easuring the primary param eters are covered in chapters four, five, and six. These chapters extensively review m easurem ent techniques and sensors types at different measurement domains (components, boards, and systems). Since electronic enclosures are an aggregate of different m aterials and heat can flow in any available path, determination of thermal conductivity and heat flux becom es an im portant elem ent for engineers. These two topics are addressed in chapters seven and eight. The third part of the book offers a review of tool sets required for characterization and simulations. Oftentim es engineers need to design a wind tunnel for characterization of the test specim en or to perform flow visualization to understand the flow dynamics governing the therm al phenom enon in their systems. These topics are covered in chapters nine and ten. They offer a comprehensive review of these tools and techniques while focusing on electronic cooling applications. Likewise, many engineers are involved in com ponent characterization and acoustic noise measurement. Com ponent characteriza­ tion is an essential part of any component that will be placed on a board. The process and techniques for such delicate m easurements are reviewed in chapter eleven. The noise issue

is a major concern in any electronic system and its control and measurement require know­ how and proper instrumentation. Chapter twelve addresses this issue and provides the required inform ation for such measurements. The book is intentionally focused on the applied side of measurement. Each chapter contains how-to lists of measurement, multiple tables of the pertinent information for quick reference, and a list of providers of the thermal sensors. Although the book is put together with practitioners in mind, it covers a sufficient amount of fundamentals to make the book a useful text for academic instructions as well. In that regard, the book content clearly suggests the m ultitude of disciplines an engineer needs to be familiar with in order to successfully function in the electronics industry. Kaveh Azar, Ph.D. Editor

About the Editor Dr. Kaveh Azar has been actively involved in electronics thermal m anagem ent since 1985. He joined AT&T Bell Labs after completion of his Ph.D. at the University of Connecticut. Dr. Azar has developed a state-of-the-art thermal/fluids laboratory for sim ulation of com ponents, boards, and systems. He has been an active participant in the thermal com ­ m unity by serving as chairperson for national and international conferences, session chair at ASM E and IEEE conference, keynote speaker at a number of international conferences, and a participant in NSF workshops and other national committees. Dr. Azar has also lectured extensively at a num ber of universities as an adjunct professor and conducts short courses in analytical and experim ental methods in electronics cooling. Dr. Azar holds more than 17 national and international patents and has published more than 30 articles and 3 book chapters. In addition, he serves as the Editor-in-Chief of the Electronic Cooling M agazine.

Contributors Kaveh Azar Lucent Technologies North Andover, M assachusetts

George A. Pender Endevco Corporation San Juan Capistrano, California

Michael T. Boyle Department of Mechanical Engineering University of Maine Orono, Maine

John W. Sofia Analysis Tech (ANATECH) Wakefield, M assachusetts

J. Foss Department of Mechanical Engineering M ichigan State Univesity East Lansing, M ichigan Suresh V. Garimella Department of Mechanical Engineering University of W isconsin Milwaukee, W isconsin J. E. Graebner Bell Laboratories Lucent Technologies M urray Hill, New Jersey Ned R. Keltner Ktech Corporation Albuquerque, New Mexico George C. Maling Noise Control Foundation Poughkeepsie, New York Robert J. Moffat Department of M echanical Engineering Stanford University Stanford, California

James N. Sweet Advanced Packaging Department Sandia National Laboratories Albuquerque, New Mexico C. Wark Department of Mechanical, Materials, and Aerospace Engineering Illinois Institute of Technology Chicago, Illinois Russell V. Westphal School of Mechanical and Materials Engineering Washington State University Tri-Cities Richland, Washington D. Williams Department of Mechanical, Materials, and Aerospace Engineering Illinois Institute of Technology Chicago, Illinois David M. Yeager Motorola Acoustics Technology Lab Ft. Lauderdale, Florida

Acknowledgments While completing this book, I have had the privilege of working with some of the best experts in the field whose contributions have made this endeavor possible. I am indebted to their hard work and thank them for their patience with the multiple reviews and their dedication to seeing this book in print. Likewise, I would like to acknowledge the excellent support and cooperation of the publisher. And, last but not least, no archival literature is complete without the peer review of the material. My most sincere thanks goes to the following individuals for their invaluable input and the review of the chapters in this book. D. Quinnlan Lucent Technologies Bell Labs

F. McMaye ZealTech, Inc.

A. L. Boggess EG&G Rotron

C. J. Lasance Philips Corporation, The Netherlands

G. C. Lasuchle The Pennsylvania State University

D. Wroblewski Boston University

T. Tarter Advanced Micro Devices

A. J. Ghajar Oklahoma State University

B. Siegal Thermal Engineers Associates

C. Boit Hewlett Packard Corporation

D. Blackburn National Institute of Standards and Technology

B. Joiner Motorola Corporation

R. E. Caron Lucent Technologies Bell Labs

H. Shaukatullah IBM Corporation

R. Westphal Washington State University

W. Maltz Electronics Thermal Management

J. S. Wilson The Dynamics Consultants

R. Ayeras LSI Logic, Inc.

B. Zonit M otorola Corporation

M. Lee SUN M icrosystems, Inc.

D. Gupta Lucent Technologies Bell Labs

G. Kromann Motorola Corporation

N. Keltner Ktech Corporation

T. Tarn Kodak Corporation

T. Y. Chu Sandia National Laboratories

A. Kordyban Tellabs Operations, Inc.

S. Sathe IBM Corporation

V. P. Manno Tufts University

D. L. Smith Kodak Corporation

P. G. Simpkins Lucent Technologies Bell Labs

P. C. Lin N ational Sem iconductor Corporation

C. Rogers Tufts University

M. Zim m erman Lucent Technologies Bell Labs

R. K. M enon TSI Corporation

S. Berestecky Stratus Com puter

chapter one

Electronic cooling and the need for experimentation K aveh A za r

1.1 1.2 1.3

1.4

1.5

1.6

Introduction.......................................................................................................................................... 2 The objective of thermal m anagem ent....................................................................................3 Therm al phenom enon in electronic en closu res....................................................................4 1.3.1 C om ponent.............................................................................................................................5 1.3.2 B oard / shelf........................................................................................................................... 6 1.3.3 Fram e (enclosure).................................................................................................................7 1.3.4 Environm ent........................................... 8 1.3.5 System level approach to thermal m anagem ent......................................................8 Experim ental characterization of system, boards, and com ponents.................................8 1.4.1 System le v e l................................................... ......................................................................8 9 1.4.2 Board level............................................................. 1.4.3 Com ponent le v e l............................................... ............................................................... 11 Therm al transport model in circuit b o a rd s....................................................................... ....12 1.5.1 Fluid flow in circuit board s............................................................................................13 1.5.2 Heat transfer in circuit boards and itseffect on com ponents.............................14 1.5.3 Heat transfer in a ch an n el..............................................................................................16 1.5.4 Heat transfer from a com ponent..................................................................................17 1.5.5 Param eters to m easure.................................................................................................... 20 1.5.5.1 G eom etry.............................................................................................................. 20 1.5.5.2 Properties.............................................................................................................. 21 1.5.5.3 Tem perature.........................................................................................................23 1.5.5.4 Fluid v elo city ...................................................................................................... 25 Analysis tools and their lim itations...........................................................................................25 1.6.1 Overview of design analysis to o ls.............................................................................. 26 1.6.2 Fundam ental analysis tools........................................................................................... 27 1.6.3 Analysis proced ure........................................................................................................... 28 1.6.4 Analytical modeling: integral m ethod........................................................................29 1.6.4.1 Exam ple 1: governing equations for a single com ponent residing in a circuit board ch an n el.............................................................. 29 1.6.4.1.1 C om ponent ..............................................................................31 1.6.4.1.2 B o a rd .................................................................................................... 31 1.6.4.13 Fluid...................................................................................................... 32 1.6.4.1.4 Com ponent in terio r....................... 32 1.6.5 Com puter-based tools: num erical m eth o d ...............................................................32

0-8493-3279-6/97/$0.00+$.50 © 1997 by CRC Press LLC

7

Thermal measurements in electronics cooling

2 1.6.5.1

Example 2: air temperature distribution for a natural and forced convection component residing on a horizontal b o a rd ........................ 34 1.6.6 Experimentation: why, when, and h o w ................ .................. 36 1.6.6.1 Example 3: com ponent thermal characterization....................................37 1.6.7 How-to lists for experim entation...................................................................................38 1.6.8 Steps for successful m easurem ent................................. 38 1.7 Sum m ary.............................................................................................................................................39 1.8 Terms d efin ed ...................................................................................................................................40 N omencla ture......................................................................................................................... 40 Subscripts.................................................................. 42 References................... 42

"Experim entation is required when the problem is not phenomenologically understood."

1.1 Introduction Therm al transport in electronic systems is a prime example of a class of phenomenologically not understood problems. This difficulty can be attributed to the presence of com­ posite m aterials with different thermal conductivities, multiple heat sources with different intensities, and multi-regime fluid flows on a typical PCB. This is a unique set of problems that are typically difficult to address by classical theory. Since analytical or computational solutions may not be adequate to resolve these intricate differences, often experim entation is required and, in many cases, is the only solution approach. As we embark on experimental simulation, there are many questions that confront the experimenter. These range from the parameters that are needed to be tracked to the mea­ surement techniques and their accuracy. This is further aggravated by the typical question that one faces: "how close is the experimental simulation (and the results) to the real problem?" A bit of contemplation on this question reveals that a successful experimental study mandates understanding of the problem and all parameters contributing to it. This includes the physics that governs the problem, the capability or adequacy of sensors mea­ suring, and finally, the interpretation of data and its subsequent relation to the real problem. Experim entation is another solution technique, like analytical or com putational approaches, that strives to answer a specific question. Hence, there is a need to be focused and clear on the objective(s) as we attem pt to set up an experiment. In electronics cooling, the objective is to ensure that com ponent junction temperature meets the design specifi­ cations, and the cooling system is sufficient in providing error-free operations for the worst environment. Therefore, a successful investigation mandates the understanding of all param eters affecting junction temperature and incorporating them into the analysis. This lends itself to the discussion of thermal coupling in electronic enclosures, and how the heat generated at the component level is distributed throughout the system. To familiarize the reader with the basic characterization schemes, the ensuing discus­ sion w ill show the required experimental characterization at different levels of electronics packaging — component, board, and system. The discussion will show the process of experim entation and what is typically done if we decide to em bark on an experimental study and what the expected outcome is. Experim ental characterization requires the knowledge of w hat parameters need to be measured and what their impact is in satisfying the final objective. M easurement in

Chapter one:

Electronics cooling and the need fo r experimentation

3

electronics cooling is no exception; there is a need for scaling, planning, error analysis, and quantification of the data measured. In this chapter, parameters that should be m ea­ sured for proper characterization will be highlighted. This discussion leads into the subject of analysis tools. Their availability and domain of application will be highlighted. The chapter ends w ith a review of what this handbook covers as it applies to experim ental characterization of electronic systems. This section effectively provides a synoptical review of the remaining chapters in this book.

1.2

The objective of thermal management

The objective of thermal m anagem ent can be simply stated by the following: "The process of ensuring reliable mechanical and operational per­ formance for adverse system 's environmental conditions" This definition requires very little explanation. "Reliable m echanical" operation refers to system operation without temperature-induced mechanical failures. Mechanical failures are characterized as hard failures that require physical replacement of the failed item, e.g., component, board, fan, etc. The "reliable operation" refers to the electrical performance of the system as a function of temperature. This implies that as the temperature increases (say the system 's ambient), the system continues to perform error-free in accordance with the specifications. Based on the above definition, let's explore why tem perature and its reduction are im portant in electronics systems. Temperature-induced stresses are com m on knowledge to m ost readers. The analogy that best describes the situation is a fuse burnout case as the result of a pow er surge. The fuse elem ent cannot dissipate the excess heat brought about by the pow er surge. H ence, therm ally induced stresses cause the m echanical failure since there is no room for expansion. Therm ally induced stresses occur in elec­ tronic com ponents when they cannot be cooled adequately — resulting in their eventual failures. For instance, the m axim um stress at the flattened section of the w ire-bond is linearly proportional to tem perature (Jeannotte et al., 1989) and is described by Equation

1

( ): 1/2

vp _ ^EAcpT

2L

7tr V^ a ;

( 1)

Typical temperature-induced failures are classified as follows: • • • •

Im mediate destructive failure Increase in the rate of random failures over time (long-term reliability) Operational failure at high temperature Interm ittent operational failures at high temperature (parts of the circuit do not w ork together)

Reduction of the temperature at the device level will reduce stresses in the component internal structure. Temperature also plays a significant role in other failure mechanisms that govern the reliability of the component. This perhaps can be best depicted by looking at the activation energy and its relation to temperature as described by the Arrhenius Equation (2).

Thermal measurements in electronics cooling

4

A t = EXP

(2)

Equation (2) shows an exponential dependency of the activation energy (signifying failure rate) on temperature (Klinger et al., 1990). Assuming this equation holds for most failure models, the reader can see that reducing temperature will significantly improve the expected reliability of the component. From the performance (operational) perspective, temperature plays a pivotal role as well. Sensitivity of silicon-based devices to temperature is a known phenomenon. The switching voltage response is highly temperature dependent. Large temperature variation at the chip level will increase the range over w hich switching occurs. This can lend itself to switching errors due to noise and pow er supply fluctuations (Noble and Ellenberger, 1984). Based on this discussion, the task of thermal management is defined as designing the cooling system (natural convection to immersion cooling) such that the component junc­ tion temperature (Tj) is within the prespecified limit (from 80° to 180°C). Although there is no strong theoretical or experim ental justification for these limits, nevertheless they serve a useful task in bounding the problem. Hence, thermal management strives to ensure that any com ponent, regardless of its design, meets the temperature constraint for the worst possible ambient to which a system can be exposed.

1.3

Thermal phenomenon in electronic enclosures

The im portant role of temperature in reliability and performance of electronic systems was highlighted in the previous section. It is, therefore, the next logical step for us to focus on the parameters, processes, or sources that contribute to the magnitude of temperature. The solution approach in electronics systems starts from the environment and ends at the die part (Azar, 1989). To appreciate the impact of environm ent/system (enclosure) on thermal perform ance of components, it is necessary to review the thermal transport in an enclosure and highlight the thermal contributions to component junction temperature. The thermal transport is described by coupling between components and system parts. The term "coupling" implies interdependency. It means that the thermal performance of the com ponent is directly dependent on other components and the system. As previously discussed, the heat-transport mechanism, either by the fluid or through solid, can become complex. To gain a better understanding of thermal coupling, we must focus on each system part. We first start from the com ponent and go up to the frame and see how the heat is transported within an electronic system. This should assist us with the design process by helping to generate the necessary information or at least ask the right questions. An electronic enclosure is composed of the following: 1. 2. 3. 4. 5. 6.

Environment System Shelf (cage) Circuit board Com ponent Die parts

Figure 1 is a schematic view of the above, and Figure 2 shows the structural integration of an electronic enclosure from component to system. W hat follows is an elaboration of the above list.

Chapter one:

Electronics cooling and the need for experimentation Environment

/

Component/Die

fig u re 1

Schematic of system configuration,

Figure 2

Structural integration of an electronic enclosure.

2 . 3,2

_ . ^ l mk

Component

This section is intended to familiarize the reader with generation, spreading, and eventual departure of heat from a com ponent If provides the reader with sufficient understanding as to how the heat gets transferred from the die to the fluid which is the eventual sink for the fluid (gas or liquid) cooled system. Electronics components (modules) are made of an aggregate of materials with different physical geom etry The central core of the com ponent is the die containing resistors, capacitors, inductors, transistors, etc., typically bonded to silicon. The combination of these parts form the chip where the electrical functions are performed. The chip is mounted by an epoxy or other material onto the substrate. The chip/substrate assembly is, in some cases, molded to protect the chip from potential environmental or processing hazards. Some multi-chip modules (MCM), or single-chip modules (SCM) continue to be made without molding, but the plastic molded packaging is effectively an industry standard. The electrical signals are brought to the component via the leads and then to the chip(s) through the wire bonds or other die attach technologies. The leads are either pressfitted or soldered to the substrate. The com ponent is connected to the board through its leads either by surface-mounting, through-hale methods, or other technologies. This

Thermal measurements m elect ranks cooling

€

creates a package with potentially multiple heat sources in thermal communication with each other via the substrate and its ambient. The generated heat at the chip(s) gets transported through any available path with the bulk being transferred through the 'le a st resistant" one. The sink where the heat is eventually transferred is the cooling fluid. The paths available for heat flow are through the molding materia! and the leads. The flow of heat is impeded by each material, regardless of its thickness, as it travels from the source(s) to the sinks, The wire bond also provides another avenue for the transport of heat. This can become a major path if the cross-sectional area is proportionally large (typical wire bond diameter is 5 pm); see Figure 3, Molding

Wirabond

|

f

^

chiP

Bonding

>f

f

rj Board Figure 3

Heat transfer in an electronic component

As the heat reaches the leads, part of it is conducted to the board, and the rest is either radiated and/or convected to the ambient, Also, a similar process occurs as the heat reaches the physical boundaries of the component, The heat-transfer path through the com ponent is not usually one-dimensional, and it tends to flow in any direction that provides a path for heat transfer Combination of multiple heat sources and different possible avenues for heat flow create rather complex and nonuniform temperature fields in SCM s and MCMs,

3 , 3,2

Board/shelf

T h e shelf or card holder (cage, rack, etc.) is where the PCBs reside in the system. H ie shelf basically acts as a housing and facilitates the electrical connection of the boards through the backplane (e.g., mother board in a PC), Boards are normally inserted into the shelves through card guides. Except in some specialized cases where a latching m echanism is used to rigidly attach the board to the shelf, the boards are loosely fitted inside the shelf (e.g., a PC's m other board). In these cases, the primary holder of the circuit boards is the back-plane or the m other board. Therefore, the contact area to facilitate conduction heat transfer from the board to the shelf may be small. Heat generated at the com ponent is conducted to the board through the leads and the gap under the component. The heat is transported away from the board by all three modes of heat transfer. Because of poor mechanical contact between the board and the card guides, the conduction heat transfer is significantly less than the convection and radiation ones, respectively. This may not be the case, however, if the boards are in good thermal contact with the shelf. We can generalize, based on observation, that in most system designs, conduction coupling betw een the board anci the shelf is very weak, e.g., telecommunication rack or PC mother board. The backplane is another avenue for the heat to be transported to the ambient or to the shelf. If the thermal conductivity of the board is large, i.e., multilayered boards with several layers of copper, conduction heat transfer to the backplane can be significant

Chapter one:

Electronics cooling and the need fo r experimentation

7

provided there is adequate mechanical contact. Depending upon the magnitude of heat dissipation and the nature of contact between the board(s) and the backplane, boards can also be thermally coupled to each other via the backplane. The thermal coupling by convection and radiation heat transfer, however, tends to be significantly larger than conduction heat transfer via this path. Therefore, board/shelf com bination provides another avenue for the heat to be coupled with the rest of the system.

1.3.3

Frame (enclosure)

Frames or enclosures are boxes that house the electronics, e.g., modem, PC, test equipment, or a work station. The heat that is generated within the system norm ally finds its way out through the vent holes or by radiation heat transfer to the surroundings. Although this constitutes the bulk of heat flow, there exists significant thermal coupling between the boards/shelves and the frame. The thermal coupling for most systems, in the order of significance, is by radiation, convection, and conduction heat transfer. Since the frame is in contact with the system ambient, it can act both as a sink and a source (i.e., absorbing solar radiation) of heat for the system. In general, the heat transfer from the frame is a significant part of the thermal response of the system. Let's briefly explore the heat transfer modes that can affect heating/cooling of the frame. The magnitude of conduction heat transfer is system-design dependent. Because of contact resistance, conduction coupling tends to be small between the shelves and the frame. The other mode of heating is by convection heat transfer. Convective heating of the frame by its internal sources is very much design dependent. If the flow of the coolant (air) is in close contact with the frame, the convection heating will then be appreciably more, e.g., PC. The last mode of coupling is by radiation heat transfer that occurs between the system interior (circuit boards) and the frame. This tends to be the predominant mode of thermal coupling betw een the shelves and the frame. The radiation heat transfer tends to be even more significant if the system is cooled by natural convection. However, in m ost systems in w hich coolant flow ducting is not present (computers and telecommuni­ cation equipment) radiation and convection heat transfer are the vehicles of com m unica­ tion betw een the system interior and the frame, Figure 4.

Figure 4

Thermal coupling in electronic systems.

Thermal measurements in electronics cooling

8

1.3.4

Environment

As stated earlier, the system frame is coupled to the surrounding ambient via radiation and convection heat transfer. The system ambient can act both as a source and a sink. Convection and radiation cooling and heating is possible depending upon the nature of the system ambient, i.e., open atmosphere or climatically controlled buildings. The mag­ nitude of the heat transfer can vary significantly with the changes in the system surround­ ings. This can constitute a major portion of the total energy transport to or from the system. Thus, frame-to-am bient thermal coupling m ust be an integral part of the thermal design consideration. We can conclude that the thermal transport process in electronic systems is quite involved and can become complex. Because of many different thermal processes and strong coupling at various system levels, thermal bookkeeping is necessary for accurate analysis. In addition, it should be clear that when we characterize (experimentally or analytically) a system, we cannot only focus on a component (module) without considering the system 's environment.

2.3.5

System level approach to thermal management

We have seen how system environment can impact component thermal performance. Let's also remind ourselves that the objective of thermal design or analysis is to ensure that com ponent junction temperature meets the design specifications. It is apparent from our discussion up to now that in thermal design/characterization of any component, consid­ ering the com ponent alone is not sufficient. All param eters affecting junction temperature must be included in the process. Two procedures are recom m ended for therm al design or analysis. First, therm al design requires a system down approach. It im plies that we have to look at the system am bient and w ork our way down to the com ponent of interest. All param eters contrib­ uting to the transport of heat should be considered in the process. The second is a m ethodical approach to therm al design or analysis. In the previous section, this was referred to as "therm al bookkeeping/' W hat it im plies is that a successful analysis requires keeping track of all the param eters influencing design. Superficial or casual treatm ent of these param eters (starting from the environm ent to the com ponent) will yield less than desirable results.

1A

Experimental characterization of system, boards, and components

Ensuring operational integrity requires the knowledge of junction temperature of compo­ nents residing in a system. Junction temperature can be obtained by experimental simu­ lation (measurement) at various levels of characterization. Let's distinguish three levels of characterization, com ponent (module), board, and system, and explore what is typically done and what we should expect from these simulations.

1.4.1

System level

The objective of system level testing is to evaluate the effectiveness of the cooling system. This is to ensure that critical components receive adequate cooling such that their junction temperature m eets the design specification. The testing is typically done at two stages, evaluation and verification. At the evaluation stage (typically), a system prototype is tested for the standard parameters (pressure and velocity) affecting thermal and noise perfor­ mance. The prototype can be as elaborate as the resources permit. However, systems features such as louvers, card guides, flow guides, cable wraps, connectors, etc., affecting

Chapter one:

Electronics cooling and the need fo r experimentation

9

the flow param eters are essential to be accurately duplicated. The duplication is with respect to size and physical location. As an example, consider a forced convection air cooled system, e.g., a desktop PC. The system is composed of circuit boards with different layouts and com ponent geometry, a perforated frame, and a fluid m over (tube-axial fan). The objective is to verify the results of the analytical modeling that showed in the channel formed by the video and modem cards, the air velocity was 1.8 m/s, and subsequent component thermal analysis showed that at this velocity the video chip will function properly. The objective of the test is to determine the video chip junction temperature for two extreme cases: (a) the system has bare m inim um plug-ins; (b) all slots on the mother board are occupied. Hence, setting up a prototype that closely resembles the two conditions is required. If the prototype does not resemble the actual system, the data generated from such a characterization will lead to poor design. We should always remember that bad data are worse than no data at all The ideal situation for "evaluation" testing is to create a prototype that closely resem­ bles the system with the capability to monitor junction temperature. Although this level of characterization is resource intensive, it provides the best results and would limit any subsequent design iterations. By monitoring the junction temperature and the flow param ­ eters (velocity and pressure), the designer can quickly ascertain the accuracy of the analysis and determine the effectiveness of the cooling system. It is a rare occasion when design iterations are unnecessary. Hence, while designing the prototype, flexibility in changing configuration and placem ent of the sensors should be considered. If the prototype is designed such that modifications are made simple, exam ination of the alternatives will then become simple. Likewise, much care should be taken in placing sensors and their supporting wire or cables to eliminate major alteration of the flow structure. A sensor can easily block the flow, which reduces the flow rate in the region of interest, or trip the boundary layer, which may result in higher heat transfer coefficients in downstream components. The second stage of system testing is "verification." At this stage, the actual system is tested to ensure thermal and operational integrity. The objective is to determine whether component thermal response is within the design specifications w hen the system is exposed to different ambient temperatures. In addition to monitoring the junction tem­ perature, system electrical perform ance is also monitored. Silicon devices are temperature sensitive, and at elevated temperatures, their performance may be adversely affected, causing error in signal generation and information processing. In addition to thermalrelated issues, the system is also monitored for mechanical noise (e.g., fan) generation to ensure that the cooling system meets the audible noise as well as thermal requirements.

L4.2

Board level

Board level simulation is done to ensure the effectiveness of fluid flow distribution on the board for the purpose of com ponent cooling. The test can be done at the prototype (paper design — preferred stage) and production stages. At the prototype stage, one simulates the component and the flow obstacles (i.e., cable clips) as though the board is functional and attempts to measure the component and flow parameters. At this stage, valuable thermal inform ation is generated that can im pact board layout. At the production stage, one attempts to measure the junction temperature either in a wind tunnel or the actual system. The necessity for board level sim ulation stems from the role of component placement on flow distribution and its im pact on component thermal performance. Component placem ent affects fluid flow distribution, see Figure 5, (Azar and Russell, 1991), and can be detrimental to component thermal performance. Subsequently, board level simulation should provide sufficient data to verify that the required flow is available for component

Thermal measurements in electronks cooling

10

Figure 5

Effect of component placement on flow distribution on a PCB.

cooling, and one can reduce thermal coupling between components (conductive as well as convective) by changing board layout. Typically, at this level of simulation, flow param­ eters such as fluid temperature and velocity are measured, The data are then used for thermal analysis of the component to ensure that the junction temperature meets the required specifications. This simulation is done with a board in a wind tunnel for air-cooled applications. The distinct advantage of such simulation is that the design is at the preliminary stage, and the designer may have the luxury to alter the layout in order to attain better thermal performance. Similar to the previous case, the boundary conditions play a major role in the accuracy and repeatability of results, First, a simulated board is set up that from therm al and mechanical standpoints, closely resembles the actual board. The flow condi­ tion at the funnel inlet is set to the condition specified by the designer, For example, preliminary analysis may have shown that to cool a com ponent on this board, the air velocity at the inlet has to be 0.5 m/s with a 3CPC temperature. W hen simulating in the wind tu n n el these conditions are set at the inlet and reflect the starting point of the characterization. Of course, it should he apparent to the reader that temperature is scalable if the primary mode of heat transfer is by convection, If radiation heat transfer plays a role in the overall thermal transport, then it is recommended that the inlet conditions be set to what the analysis revealed. As a side note, the scalability for conduction and convection is because of linear dependency of heat transfer on temperature, For high-conductivity boards, the m agnitude of board level thermal coupling can amplify because of higher conduction heat transfer. For example, depending upon the complexity of the design, one may analyze the effects of board conductivity, O r one may characterize the heat transfer from the critical components by measuring the heat flux from the com ponent and its neighbors. In any such simulations, the most important point one must remember is that the test boundary condition matches the application. This includes the following: ♦ ♦ ♦ ♦

Obstructions Heat dissipation from adjacent cards Com ponent power dissipation Com ponent and board geometry

Chapter one:

Electronics cooling and the need fo r experimentation

11

The latter is of particular importance since flow distribution is directly dependent on geom etry

1 .4.3

Component level

Two levels of component simulations are typically done; "stand alone" and "in situ" The stand alone describes the component being placed on a board and its junction-to-am bient (Rja) or junction-to-case (R^c) resistances are determined. This is typically done for new components to provide thermal data to the end user. The methods associated with com­ ponent characterization are described extensively in Chapter 11. Typical outcomes of stand-alone component characterization are shown in Figure 6.

v Figure 6

Junction-to-ambient thermal resistance as function of air velocity.

In the stand-alone characterization, the com ponent is placed on a low -conductivity board and exposed to different air velocities. The com ponent itself is either equipped w ith a therm al test chip that has a tem perature-sensitive diode, or the electrical param ­ eters of the actual die are m onitored for tem perature m easurem ent. Com ponent pow er dissipation, air velocity, and tem perature are m easured for calculation of as shown by Equation (3). Rja = (Tj - Tamb )/P

(3)

where P is the component total power dissipation. The usefulness of these resistances is the subject of much debate and is not the focus of this chapter. The important point to realize is the standard industry practice and to understand its limitation and utility. However, as a side note, the author discourages the use of R^c specifically, since its m ag­ nitude is affected by all the param eters that govern the thermal transport of a component. Conversely, R^a can be made useful if utilized with caution (Azar, 1994). In situ characterization refers to the actual component residing on a PCB accompanied by other components. The objective of the characterization is to determine whether the component junction temperature will meet the design specifications once in the actual system environment (in situ). The desired component could have again a thermal test chip or an active die. Typically, experience has shown that monitoring active dies for temper­ ature-sensitive param eters is arduous. One way to overcome this difficulty is if the die

Thermal measurements in electronics cooling

12

has been provisioned with a temperature-sensitive diode. In this case, the diode can be used to measure temperature. This level of characterization can yield best results. As we look back at the three levels of evaluation, we cannot help but notice how integrated these approaches are. The only test that stands out is the "stand alone" one w hich is not part of the overall testing schem e. All other tests are heavily integrated w hich gives further credence to the notion of system level evaluation. The need to accurately replicate the system in such tests must not be overlooked. This means that the boards and com ponents should closely resemble the actual system. If the boards and com ponents need to be sim ulated, w hy not do the board level sim ulation w hile doing the system level test? The answ er is an obvious affirmative. The only time board level testing is independent of system testing is w hen issues of cost and time prevail. As you may recall, in system test, either at prototype or production stages, the entire system m ust be assem bled. If such a setup is available, it is obviously preferred since the boundary conditions are exact. If not, then it needs to be assem bled; hence, the factors of cost and time becom e a player. That is why independent board level testing, w ith correct boundary conditions, can yield accurate and quick answers and elim inate the need for expanded testing. However, it should be apparent that the foundation for success is accurate boundary conditions. Table 1 provides a synopsis of the different levels of testing for a successful thermal managem ent evaluation. Table 1 Testing level System Board

Component

1. 2. 1. 2.

Component, Board, and System Level Testing

Type

Objective

Evaluation Verification Prototype Actual

Boundary condition and system integrity Adequate flow exposure, junction temperature Rja vs. V and junction temperature

1. Stand Alone 2. In situ

Equipment System prototype, P, T, and V sensors Wind tunnel, P, T, V, and heat flux sensors Wind tunnel, current source, V , T, and heat flux sensors

P, pressure; V, velocity; T, temperature.

1.5

Thermal transport model in circuit boards

For the sake of clarity, before we em bark on the discussion of thermal transport within a board, let's define the concept of "therm al." Thermal phenomena define the procedure for removal of heat from the components. Thermal process is defined as the merger of heat transfer and fluid flow to transport the energy from a heat-dissipating component. The very nature of the thermal phenom enon is then a function of the mode of heat transfer and the fluid flow regime in a system. Thus, proper definition of thermal phenomenon requires understanding of transport m echanisms — heat transfer and fluid flow. Param eters signifying heat transfer and fluid flow are pressure, velocity, temperature, and therm odynam ic properties. Let's call the first three the primary parameters since the therm odynam ic ones are obtained from pressure and temperature. The pressure and temperature are strong functions of velocity in the problem domain, e.g., circuit board channel. Hence, to gauge the magnitude of critical parameters such as junction tempera­ ture, it is essential to acquire these parameters, either analytically or experimentally. In this section, a first-order model for fluid flow and heat transfer in channels formed by electronic circuit boards is developed. We will use these models as the means to determine which param eters require measurement.

Chapter one:

1.5.1

Electronics cooling and the need for experimentation

13

Fluid flow in circuit boards

Fluid velocity can have a major impact on the overall heat transfer. Typically, increase of velocity results in higher convective heat transfer from the heated component. In the following sections, the dominant role that the fluid velocity plays becom es more apparent as the temperature rise of the board and component is described. Here, an expression for determining air velocity in a circuit board channel based on the integral form of the m omentum equation (Murray, 1990) is presented. The focus of this section is at the circuit board and com ponent levels; however, its expansion to the system level is obvious as terms are not confined to a specific geometry. We would like to develop an expression from which air pressure drop and, subse­ quently, velocity can be obtained. Consider the local m om entum integral balance under the assumption of approximately equal inlet and outlet m omentum fluxes: Ja(AP)dAa - Aa£(KpV2/2) - JsxwdAs = m om entum flux^ - m om entum flux0Ut + buoyancy Integrating by using the first-order model yields: Ap = KpV2/2 + (l/ A

'

Pi * Mi

--------------------- ► V

Figure 1

Drag on a sphere. Fd = F1(p,ji/V,D)

Imagine a series of experiments to identify this relationship. For a given fluid (p^m), measure FD vs. V for a number of spheres each with different D values. This data could be presented as shown in Figure 1. This procedure must be repeated with different sets of density and viscosity (Px,ja2), (Pi,R3), (P2/F1)/ (P2/F2)/ *** etc* Even for this very simple problem the volume of data to be recorded is inconveniently large, especially when you consider all the different experimental facilities that m ust be used to incorporate the different fluids. Experience provides us with the tools required to make this a much less imposing task. By a number of methods we can realize that the variables of this problem may be combined into nondim ensional groups such that

F°

pV 2r-| D2

^pV D ^

= f-*-'21

1

( )

That is, only two variables are im portant to the complete description of the problem. This problem can be completely characterized by the use of a single test model (one diameter), using a single fluid (conveniently air) and by adjustment of only the free stream velocity. The identification of the minimum num ber of nondimensional parameters that are required to describe a physical problem can be accomplished in a number of ways: M ethod 1: a package designer could seek out traditional heat transfer literature to discover variables that have been used historically. M ethod 2: a very large number of experiments can be performed and the important variables identified by trial and error. Method 3: a nondim ensional presentation of the governing differential equations can be used to reveal variables. M ethod 4: a dimensional analysis, tied closely with the Buckingham Pi theorem, can be used.

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83

The author's experience shows that method 1 is usually the method of choice. Using traditional variables is sensible in that there is not a need to reinvent the dimensional analysis of previous workers. However, the engineer who inherits a coordinate system w ithout also having an understanding of the logical process used to derive the variables in that system is at a disadvantage. There is a risk that the nondimensional coordinates could be used for a design problem that is outside the useful range of the data. Careful designers often respond to this risk by avoiding dimensional analysis completely. An engineer must have a clear understanding of where nondimensional parameters come from in order to stand on firm ground and take sensible advantage of the great reduction of variables that they provide. Methods 2 and 3 are interesting and useful approaches for identifying important nondim ensional parameters. However, method 4, a dimensional analysis based upon the Buckingham Pi theorem, is the focus of the applications portion of this chapter. This method provides a fast and efficient approach for selecting a useful nondimensional coordinate system. The strategy of this chapter is to first provide an argument that dimensional analysis is grounded in logical m athem atical concepts. This discussion is based upon the power product method and follows the presentations of White (1979) and Shames (1962). Fol­ lowing the work of Hansen (1967), a matrix approach is used to determine the number of dimensionless param eters that are required to characterize a problem. The nondim en­ sional coordinates are calculated by forming dimensionless products. Finally, an efficient intuitive implem entation of the Buckingham Pi theorem is used to form dimensionless coordinates for a variety of applications. The logic of perform ing a dimensionless analysis, as described herein, is straightfor­ ward and convincing. However, in order to motivate a reader who is new to the topic, it might be wise to jum p forward in the text and examine the applications section of the chapter. The applications show clearly the savings possible by designing experiments, and num erical models, in terms of nondim ensional parameters. The motivation for spending a few hours and learning the techniques then comes easily

3.2 A Ap Cd

Nomenclature Surface area (m2) Projected area (m2) Drag coefficient (nondimensional) Constant volume specific heat

D ft

g Fd h H I Ka L M Q

( m2 \ s K

Diameter (m) Implies a functional dependence on variables included in parentheses Local acceleration of gravity Drag force

s2 Average or local film coefficient (kg/s3K) Height (m) Turbulence intensity (nondimensional) Thermal conductivity of the air (kg •m /s3K) Length (m) Mass (kg) k m2 Energy transfer rate (watts) or 6 3

Thermal measurements in electronics cooling

84 R Re

Size of vortex region (m) VDp/p — Reynolds number (nondimensional)

RjA

Thermal resistance

S t AT

Distance from leading edge of board to package (m) Represents the time dimension(s) Temperature difference between surface and ambient (K) Ambient temperature (C) Junction temperature at diode in I.C. (C) Fluid velocity (m/s) Width (m) k /(p cv) Coefficient of thermal expansion of cooling fluid (1/K) Incoming boundary layer thickness (m) The temperature dimension (K or C) Dynamic viscosity (kg/m •s)

ta

Ti V

w a

P

8

e p p

p

CO

3.3

C°s [k g m 2 J

Kinematic viscosity (m2/s) Mass density (kg/m3) Natural frequency (Hz)

Dimensions and units

The dimensions (length, time, mass, force, temperature) and units (meter, second, kilo­ gram, newton, degree kelvin) associated with physical variables make up the foundation upon w hich this chapter stands. It is essential to clearly define the dimensions for each variable that is used in a dimensional analysis. The nomenclature section provides the units for each of the variables used in this chapter. The origins of these units is clear for most parameters. However, some parameters, such as force, are w ritten in terms of dim en­ sions that surprise many engineers. A short discussion of this issue including a couple of examples is appropriate at this time. A more subtle discussion of this topic is represented by Reynolds and Perkins (1977). There is no limit on the num ber of methods a curious individual could use to define a system of units. A set of primary dimensions is chosen by the use of convenient stan­ dards. If I were a decorative tree farmer I might set the primary length dimensions by comparing the height of a tree to my own height, then name this unit as I see fit (1 Michael). In an attempt to define a standard for length that is convenient internationally, the meter is defined as the length of the path traveled by light in a vacuum during a time interval of 1/(299, 792, 458) seconds. Of course this length standard is only useful after a standard has been defined for the second. The international standard for 1 second is taken as the time required for a beam of cesium-133 atoms to resonate 9,192,631,770 cycles in a cesium resonator, Van Wylen et al. (1993). Once a set of primary dimensions is established by the use of convenient standards, secondary dimensions are obtained by algebraic definition. For example, given the alge­ braic definition of surface area as the product of the length and width of a rectangle, A = LW the secondary dimension called area is written as (length)2.

Chapter three:

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85

The SI system (Metric International System), used in this chapter, has primary dimen­ sions for length (meter), time (second), and mass (kg). The force dimension is a secondary dimension and is defined in terms of N ewton's second law. Throughout this chapter the unit of force will be expressed as K g -m

All units referenced in this chapter are for primary dimensions.

3.4

The power-product method

A method of dimensional analysis that is convincing to working engineers is called the "power-product m ethod" (White, 1979; Shames, 1962). Let us illustrate this method by application to the sphere drag problem. Functionally, the drag force on a sphere may be expressed as

2

F d = f^ p ^ Y D )

( )

Regardless of the nature of the function in Equation 2, it can be accurately represented by a polynomial approximation. Fd = (k 1pa,|j.blV c,D dl) + (k2pa2V C2D dz) + ...

(3)

where kx, k2, ... are dimensionless coefficients and al7 b x, ... a2, b2 ... are exponents required by the series. Each term in Equation 3 must have the same dimensions. Therefore, each term in the series must have the same units as FD. We can express FD and any term in the series dimensionally as "M L"

L3

t2 where

M L t

a b "M n ’ M " ’ L"

Lt

t

[L]d

= mass = length = time

Now the exponents of each of the three basic dimensions M, L, t on both sides of the equation can be equated to generate the following three equations: for

M

1= a +b

(4)

for

L

l= -3 a -b + c + d

(5)

for

t

-2 = - b - c

(6)

Since there are four exponents related by three equations, we may solve for any one of the four in terms of any other one. Solving for a, b, c in terms of d yields a = d- 1 b =2 - d c - d

Thermal measurements in electronics cooling

86

Returning to Equation 3 we temporarily restrict the discussion to the first term of the series (the extension to the remaining terms in the infinite series is evident), and replacing a, b, c in terms of d we obtain Fd = kp d~lii2^V dDd Extending this result to the other members of the series F d = k 1pdl-V 2-dlV dlDdl + k 2pd2~V2-d2Vd2D d2 + ... Grouping those terms with the same exponents together

P !d = k

pVD

+ k.

pVD

V . where pPp

and

pVD

P2 are dimensionless kl7 k2/ dl7 d2, etc. are constants. Therefore, the term (pFD)/|i2 is only a function of the Reynolds num ber (pVD)/|i pFp

/p y p N '

VAlthough the functional relationship is unknown, only two variables are required to describe this problem. Namely,

P ^ a n d ^

This is a great simplification from the five variable relationships offered by Equation 2. A calculation is perform ed at the end of this section in order to make the simplification clear. Following the discussion in W hite (1979), example 5.5, the algebraic logic leading to the above included the representation of a, b, and c in terms of d. If we instead use Equations 4, 5, and 6 to write a, c, and d in terms of b we obtain D = f ^pVD^ X5 pV 2tV D except for some constants, this is the pair of variables that is traditionally used to describe the sphere drag problem. W hat happens if we solve for a, b, and d in terms of cl We obtain:

Chapter three:

Similitude in electronics cooling

87

This is the same as the first case. If b, c, and d are w ritten in terms of a, the resulting nondimensional pair is: /pV D x pVD

7

In each of these cases the original problem in five variables has been reduced to a problem in two variables by the use of dimensional analysis, certainly a worthwhile task. This reduction of variables is accomplished by careful consideration of the fact that Equation 2 is dimensionally homogeneous. We have also generated three pairs of nondi­ mensional param eters that could be used to describe the sphere problem. We need only choose the pair that is m ost convenient for our purposes. Example: The following illustrates the advantage of using nondi­ m ensional param eters to design an experiment. Imagine that it is our task to characterize the drag force on a spherical object for a variety of diameters, for different fluids, and for a wide range of fluid velocity. First, design and perform the experiment using each of the important dimensional variables. Compare this to the exper­ iment designed by the use of nondim ensional parameters. Using dimensional variables and repeating Equation 2, F d = fi(p,tt,V,D) This equation reveals a large experimental task. In order to get started the experiment designer limits the fluid types to air and water at 1 atm and room temperature. A wide range of velocity is used and three different sphere diameters are tested. The diameters are 0.01 m, 0.03 m, and 0.05 m. Drag force data are measured and presented graphically in Figure 2 . The figure shows that drag force is strongly dependent upon fluid velocity, sphere diameter, and fluid properties. If this experiment were performed for a wide range of fluid temperature and pressure the data set would become large and the experimental facilities would be extensive. The dimensional analysis performed previously shows that the sphere drag problem can be represented as a relationship betw een two nondimensional variables. If we choose ApVD^ pV D

(7)

we can modify the left-hand side by multiplication with a few constants in order to obtain

1/2 pV

where ^ V 2

2 JtD2

= fo

pVD

(8)

been added to the denominator of the left-hand side. Although this

new function is different from that expressed in Equation 7, it is equivalent in terms of the relationship betw een the two nondim ensional parameters. In its present form the lefthand side of Equation 8 is the traditional definition of drag coefficient.

Thermal measurements in electronics cooling

88

(9)

l/2 p V 2(A p) It is convenient to use this traditional definition in order to be consistent with the drag data available in the literature. Beyond this convenience, Equation 7 could be used without any loss of utility. In fact the Cd data in the literature could be presented as written in Equation 7 without any loss of value. The experim ent designer who uses Equation 8 as a guide can work with much greater efficiency than the designer who works with a dimensional formulation of the problem. Equation 8 shows that as long as the Re range for the experiment includes the Re value of the application, the nondimensional data can be used to determine drag force. As a way of m aking this more obvious, the data of Figure 2 is plotted in the nondimensional coordinate frame provided by Figure 3. Figure 3 shows that the drag data for three different sphere diameters, two fluid types, and for a range of fluid velocity all fall upon a single curve. Restated, Figure 3 provides the function represented by Equation 8.

.01m -A ir

.03m - Air

- s - .01m-W ater

Figure 2

*

.03m - Air

.03m - Water - A - .05m - Water

Drag force vs. velocity for a sphere.

An experim ent designed to produce Figure 3 can use a single working fluid, perhaps air, yet reveal data that are useful for many fluids. Suppose Figure 3 has been obtained by the use of air in a wind tunnel. Then, a question is put to the designer. W hat is the drag force on a 0.03 m diameter sphere in a stream of water moving at 20 m/s? Calculate Re = Y P R for the application

P w ater

=

^ w a ,e r =

1 0 0 0

1 - 1 3 1

k g / m

X l O

3

- 3 k g / m

S

R e J 2 0 m / S)(.0 3 m )(l0 0 0 k g / m 3) = 5305>

Figure 5

Flow in a pipe, AP - P: - P2.

^ - = f(D/ e ,p ,ti,V ) We have six param eters that can all be expressed in terms of the three dimensions M, L, t. Therefore, if we can find three independent parameters we can reduce the problem to three nondim ensional n's. A convenient set of independent variables might be D, p, V. A designer might have these variables known and would like a correlation that would allow the AP calculation to be made in terms of these. V is the only variable with the time dimension, p is the only variable with the mass dimension. Either of these conditions establishes these three variables as independent. We can write

Thermal measurements in electronics cooling

96

TT1j = D 3lp32 r V a3 tt2 = D b^pb2V b3e ti3 =

D ClpC2V C3|x

and obtain 71.

APD LpV2

Except for a factor of 2 in the n l term, this is identical to the coordinates used traditionally for this problem.

3.9.2

Example 2: three-dimensional flow past an obstruction on aflat plateaerodynamics

An aerodynamic phenom enon that is related to the electronics cooling problem is the horseshoe vortex flow. A side view of two different horseshoe vortex flow systems is shown in Figure 6. The vortex system dramatically changes the surface heat transfer rates in its vicinity. It is im portant to know the size of this region. The author has performed measurements of the size of this region R , in both a water tunnel and a wind tunnel over a range of operating conditions for flow past a circular cylinder shape (Boyle and Langston, 1989). For this experim ent we can write R = R(V, D, 5, v) Each of the variables in this expression can be written in terms of the dimensions L and t. Therefore, we look for a maximum of two dimensionally independent variables. We choose D and v. v is the only one of the two with time for a dimension. We can write 7T-. = D aWa2R tt2 = D blvb2V k 3 = D ClvC25

to obtain

Chapter three:

Similitude in electronics cooling

97

Two Vortex Flow Pattern

L Figure 6

.

Horseshoe vortex flow systems at the base of a tall circular cylinder.

The water tunnel data m easured for this experim ent is show n in Figure 7, plotted in these coordinates (taken from Boyle and Knaub, 1988). This is certainly a concise pre­ sentation of the data as com pared to the original five coordinates. However, this is not the sim plest or best presentation of this data. Purely by a process of trial and error, and some intuition, the data are plotted in the R / 8 vs. ReD coordinate system of Figure 8 . A unique relationship

is realized in this figure. By the process of dimensional analysis, which requires only dimensional hom ogeneity in each equation, we reduced the problem from five variables to three variables. The problem is further reduced to two variables, by the nature of the fluid mechanics phenomena. By careful examination the above simplification is attribut­ able to a relationship between 5 and V. The reduction of variables that is provided by dim ensional analysis should be regarded as the m inim um reduction possible. The governing physical law s, for fluids we m ean conservation of mass and m om entum , etc., often provide further reduction. These additional reductions can be realized by a trial and error m anipulation of exper­ im ental data or by a nondim ensional organization of the governing differential equa­ tions.

Thermal measurements in electronics cooling

98

Figure 7

3.9.3

Size of the vortex system region R/D with Re and 8/D.

Example 3: a pendulum

This simple and interesting use of the m ethod of dimensional analysis is provided by Kline (1986). Although the pendulum problem is quite a bit different from the electronics cooling problem that m otivates this chapter, it is useful for an obvious example of how a nondim ensional perspective can simplify experim ent design. This problem involves the determ ination of natural frequency for the free oscillation of a pendulum , Figure 9. We can write co = f(L, M ,g) where

co L M

g

= natural frequency = length of pendulum = mass of pendulum = local acceleration of gravity

Each of these variables is written in terms of mass, length, and time. Therefore, we look for three independent variables. The obvious choice is L, m, and g because we would like co to be the dependent variable. Each of the three have dimensions that do not appear in the other two. Therefore we can construct a single n term to describe this experiment. 7i 1 = Lai NT2g a3co we obtain

Chapter three:

Similitude in electronics cooling

R /8

R e ,, Figure 8

Size of the vortex system region R /5 with Re.

Figure 9

A pendulum.

^

V2

=c

must be a constant as it is not dependent on any other tc’s.

Thermal measurements in electronics cooling

100

Therefore, the natural frequency is not a function of mass and only one experiment, to obtain the value of C, is required to describe an infinitely large family of pendulum problems.

3.9.4

Example 4: convection from a simple package mounted on a circuit board

The experim ent that is one of the prim ary topics of this book is the convection of heat from a simple package shape, or a complicated shape, mounted on a circuit board in a stream of air, Figure 4. Let us discuss the measurement of average convection heat transfer coefficient, h . We can expect the coefficient to be dependent upon the following variables: h = h(L, k, V, v, AT, p, a , H, I) The dim ensions used to describe each of these variables are mass, length, time, and temperature. Choosing L, fc, V, p as a convenient set of independent variables we scrutinize their dimensional representations as: L -L . ML k— t 0 L2 v -----t

The existence of a unique dimension in each variable makes this set independent. Therefore we write

nl = L aik a2v a3pa2h n 2 = L b'k b2vb3pb*V n 3 = -----------------AT n 4 = ---------------- a n5 = ---------------- H 7t6 = ---------------- 1 Yielding the following nondimensional groups

= *1

hL ----

7 12, =

LV

---v

*3

71, =

k

=

pAT

a — V

TC,

H =

5

—

L

n 6 = I

In order to generate a n3 term that agrees with that used traditionally, consider gAT as the independent variable rather than just a AT. We reformulate n3,

Chapter three:

Similitude in electronics cooling

101

n3 = ------------------gAT to obtain

_

_ L3PgAT 3 — V2

so that we can write the functional relationship LV hL _ f^T 'lT L t3 PgAT a H 2 ' ' T k " v v / v v L

'

( 12)

Nu = f(Re, Gr, Pr, H/L, I)

(13)

If we replace these terms by their familiar symbols,

This is not a simple functional relationship, however; it is reduced by four parameters from our original dimensional relationship. Note that if an experim ent designer is to match m odel conditions to real hardware conditions she/he must make the model geometrically similar to the real hardware (H/L must match), and all of the nondimensional parameters m ust be the same as those under w hich real hardware is operated. The model need not be the same size as the real hardware. Boyle and Asante (1990) used Equation 13 to design a large-scale electronics cooling experiment. The purpose of this work was to measure the distribution of convection heat transfer coefficient over the surface of a heated rectangular block mounted on a heated flat plate. In order to obtain a good spacial resolution over the surface area of the test model it was viewed as advantageous to have a large model. The model is approximately 10 times larger than realistic electronic package geometries. By the use of Equation 12 we can realize the test conditions that allow the use of such a large-scale model. Each of the nondim ensional 7t-groups on the right-hand side of Equation 12 must be the same for the test model and the intended electronics package application. Taking each tc individually:

The Prandtl num ber Pr = — is based upon cooling fluid properties. As both the test m odel and the application are run with atmospheric pressure, room temperature air, it is easy to m atch the test model Pr value with the application. The geometry parameter H/L is matched by adjusting the model height so that the H/L for the model equals the H/L for the real package geometry. This parameter is easily matched by the test model. At this time in the discussion it is interesting to point out that some test programs require additional geometry parameters. If the test program included rectangular shapes, instead of square, with a variety of width, w, to length L, ratios, then the list of 7c's would also include w/L. Each unique geometry variation would be represented as an additional nondimensional ratio. For this problem we are considering the adjustment of height, H, as the only variable geometry parameter. The turbulence intensity, I, is an important nondimensional parameter. Turbulence in­ tensity is used to quantify the high-frequency unsteadiness in the flow stream and for a single velocity component is defined as the RMS variation of velocity about the mean velocity, normalized to the mean velocity. Large variations in turbulence inten­ sity can have an important effect on heat transfer. For this discussion the authors

Thermal measurements in electronics cooling

102

have taken the risk of assuming that the turbulence intensity in the test system wind tunnel is similar to that provided by many real electronics cooling air streams. LV The Reynolds number, Re = — is often given the physical interpretation as the ratio of the importance of inertia effects to viscous effects on the qualities of the flow field. A large body of experim ental evidence shows the importance of Re dimin­ ishing as it increases to large values where inertia effects dominate. However, for m ost of the Re range applicable to electronics package cooling, Re is important and must be matched between the test model and the application. For the large model with Lmodel approximately 10 times larger than the real package shape we must set the wind tunnel velocity 10 times less than the real cooling velocity in order to have Re match. I% A T ^ 2 , is interpreted as the ratio of the importance of V2 buoyancy effects to viscous effects. Because of the L3 in Gr, large models are more strongly affected by buoyancy than a small model would be. In order to match the real Gr to the model Gr, the AT betw een the model surface and the cooling air stream is dropped. The effect of L3 is to cause a large Gr value in the test model. Therefore, AT must be dropped to a very low level. As AT becomes small the uncertainty in the m easurement of AT becom es large. This is the weakness in the large model. In order to m atch Gr we must sacrifice experimental resolution. By m atching all of the n's on the right-hand side of Equation 12 a nondimensional heat

The Grashof number, Gr =

transfer coefficient, called Nusselt number ^Nu = ^ j , is measured which is ap­ propriate for both the large model and the smaller application. In order to obtain the convection heat transfer coefficient, h,

air application ^application

measured ^ ^ application

j

or

Vi T

measured

'k

model

air application

^

application V

air model

/

^application

j

This is similar to the sphere drag discussion described by Figures 2 and 3.

3.9.5

Example 5: electronics cooling - overall heat transfer coefficient

An important example is that of the measurement of overall thermal resistance, from junction to ambient, for the forced convection cooling of package board geometries. 3.9.5.2

Junction tem perature

Let us imagine an experiment where a measurement of junction temperature is to be made as a function of the following variables: Tj —T j(Ta, Q, S, b, L, H, Ka, Kb, kp, pA, |iA, V, I)

Chapter three:

Similitude in electronics cooling

where

= = = = = = = = = =

Tj ta

Q s N H L kA kb kr

103

junction temperature ambient temp input pow er distance from leadidng edge of board package width package height package length thermal conductivity air thermal conductivity board thermal conductivity package

Each variable can be w ritten in terms of four dimensions M, Lf t, 0. Choose the four independent variables: L, p, Vf TA. To obtain

JL -= f Ta

Q

s b H

kA

kb

kp

11A

L2p2V 3 ' L ' L ' L ' LpV3TA ' LpV3TA ' LpV3TA ' pAL V '

This has reduced the original data set by four which is helpful; however, we still have a rather imposing set of parameters. The characterization of this problem could be simplified by use of other physical data, such as the dependence of |iAand pAon TA for air at 1 atm. For this discussion we will concentrate on the experience and traditions of the industry and introduce thermal resistance.

3 .9 .5 2

O verall resistance

Rather than including Ta, Tj, and Q as separate variables, the tradition is to combine them into a single parameter.

R

JA

=

T -T J A

Q

so that Rja = f(S, b, L, H, kA, kb, pA, |xA, V, I) Choose L, fcA, V, pA as the four independent variables to obtain

(L kAR JA) = f

S

b

H

K

K

L 'L 'L 'k / k /

Re

/ L'

(14)

For a set of experiments performed either on a single model or for models of different scale but similar shapes, S/L, b/L, and H/L are constants. Perhaps turbulence intensity is also constant, or of secondary importance. Perhaps we are not changing the board material. We obtain: (LkARJA) = f ( V k A, ReL)

(15)

This simple coordinate system would probably serve well for the presentation of a large quantity of available thermal resistance data.

Thermal measurements in electronics cooling

104

The data present by Edwards et al. (1994) is a good candidate for nondimensional interpretation. The authors provide RJA data, some from experiment and some from a num erical model, for a wide range of package types, materials, and sizes. O f particular interest to this author is the data for a 44 PLCC which was tested with four different mold compounds in order to assess the effect of kp. The 44 PLCC was modeled with three different printed circuit board materials in order to quantify the effect of kh. The intent of the authors is to show the separate effects of kp and therefore, it is not surprising that each was looked at separately and is presented in separate figures in the reference. How­ ever, from a nondim ensional perspective these separate effects can be combined to yield a m uch smaller modeling (or testing) task. At present, data from Edwards et al. (1994) for the 44 PLCC is presented graphically and is equivalent to the following two functional relations: R ja = fa(kp) at constant kb

(16)

Rja = fb(kb) at constant K

(17)

These can be logically combined as Rja/44 plcc = fc(kp/ kb)

(18)

The above statem ent implies that the convection cooling environment is constant for all cases considered. We can consider a slightly more complicated experiment than that represented by Equation 18 and test for changes in package size as well. This requires adding a dim ensional variable such as L to the independent variable list. RjA/44 PLCC = fd(kp/ kb/ L)

(19)

The addition of L is certainly not required for the dimensional analysis;however, this will allow the resulting nondim ensional coordinate frame to be similar to that discussed previously Adding L also allows the test to be conducted at various sizes if desired. Following earlier reasoning the dimensional representation of each of the variables in Equation 19 are: R

,A

ML2

L -L .

k

P or

.

ML r— b — t 30

k,

If L and kh are chosen as independent we can write n i = La'kb2R JA

n 2 = Lblk t2k p to yield

n\ ~ LkbRJA %2 = kp/kb

Chapter three:

Similitude in electronics cooling

105

or LkbRjA = f(kp/kb)

(20)

The four-dimensional problem represented by Equation 19 is converted to a two-dim en­ sional problem by Equation 20. The nondim ensional thermal resistance, LkbRJA, is only a function of the ratio of thermal conductivities. Experiments and models that are performed with a single board material, for a wide range of mold compound, will yield RJA for a wide range of board types. The presentation of Edwards et al. is extensive in that it includes many im portant design parameters. Detailed data as would be required to show that the experiments performed in order to measure the Equation 16 trend, if organized nondimensionally, could also be used to calculate the Equation 17 trend without further testing or modeling. In order to be com pletely clear, Equation 20 will be used to design an experiment where both kp and kb are important to the design of a product. The product development process requires an experiment whereby the dependence of thermal resistance, RJA, on both kp and kb is measured. Equation 19 could be used as the foundation for the design of the experiment in terms of dimensional parameters. If experiments are performed with 5 different molding m aterials and 5 different board materials, 25 unique combinations of kp and kb can be used to determine 25 values of RJA. Equation 20 can be used to design an equivalent experiment in terms of nondimensional parameters. One option would be to choose a single kb and a range of kp values (five or six molding materials). To be specific, imagine an experiment where six molding com­ pounds are tested where the kp values are:

'pl s 3K 1 2 4

6 15 22 All of the tests are perform ed w ith a package length of L = 0.01 m and a board material k s *m of k b - 1 —^— . Rja would be measured for each kp value. This data could be displayed s K in dimensional and nondim ensional coordinates. Figures 10a and 10b show plots of hypo­ thetical data in dimensional and nondim ensional systems. The data shown in Figure 10a are obtained directly from the experiment and has application limited to the range of kp tested, etc. The presentation of data in Figure 10b comes from the organization provided in Equation 20. The data shown in Figure 10b are useful for applications anywhere in the range of kp/ k b between 1 and 22. Data presented in this nondim ensional form can be used for design for any kp and kb/ as long as the ratio kp/ k b is included in the range of the kcr •JYl experiment. If a designer has an application where the board conductivity is kb = 2 —^ — ,

106

Thermal measurements in electronics cooling

the molding compound conductivity is kp = 10

kti m 3^ " /

size of the package L = 0.03 m,

and the cooling flow and the other param eters have not changed, then the RJA value for the application can be calculated as:

K (a)

kA > (b)

Figure 10

(a) RJAversus kp, dimensional; (b) Ll^R^ vs. kp = kb, nondimensional.

Chapter three:

Similitude in electronics cooling

107

k p/ k b = f = 5 From 10b at kp/ k b = 5 we obtain LkbRJA ~ 0.925 Therefore, R

= _______0.925 *

3.9.6

( ( a * * ) ^

s l 5 4 _ i!K _ )

' > * -“ 1

Example 6: forced air cooling of a board in a duct

This final example was suggested by my colleague and the editor of this book, K. Azar (personal communication, 1996). The thermal characterization of a PCB in a duct is depen­ dent on the size of the board and the size of the duct, as well as many of the variables we have already discussed. Figure 11 shows a board oriented vertically in a duct. Let us quantify the perform ance of this assembly by use of the temperature rise per unit power dissipation RJA.

Figure 11

A vertically oriented PCB in a duct.

If we consider RJA to be dependent upon R ja

=

L : , L2, pA, |iA,

k A,

Q)

We note that and L2 are used to quantify the size of the duct and board, Q is used to quantify the importance of buoyancy. Example 4 used AT and [3 to quantify buoyancy. Each of these variables can be written in terms of the four dimensions M, L, t, 0. Choose the four independent parameters:

Thermal measurements in electronics cooling

108

L 1,p /|i/k A to obtain

(21) Li/kA/RjA = f V If experiments are performed at a constant Reynolds number, then by simply adjusting the size of the duct, Lv and the power, Q, characterizations can be obtained for a wide range of board size and fluid properties. N ote that the buoyancy effect is managed by use of the variable (L1p2Q)/p3. This variable is tied more closely to electronic systems perfor­ mance than the traditional Grashof number that was presented in Example 4.

3.10 Extra variables/forgotten variables The effective design of any experim ent depends upon the ability of the designer to select important variables. This is also true for an experiment designed using nondimensional parameters. If an important variable is omitted the results of the experiment will be difficult to interpret. For example, if a package were tested at very low cooling air velocity buoyancy forces in the air would have a significant impact on heat transfer. Equation 14 does not have param eters to account for buoyancy. Equation 14 is useful for forced convection problems. If extra or unimportant variables are included in the variable list, extra (perhaps unnecessary) tests would be performed. For example, suppose the thermal conductivity of solder were included as a variable. This new variable would generate an additional nondim ensional parameter (ksoldeT/ k a) to be included in Equation 14. Extensive tests would be perform ed to determine if the k ratio is important or not. Cautious experim ent design requires including many variables in the original list so that they are not forgotten. The designer can prioritize the nondimensional list.

3.11

Summary

The method of dimensional analysis and the Buckingham Pi theorem provide an intuitive, convenient method for reducing the num ber of independent variables for most physical problems. The application to some fluids problems and to some electronics cooling prob­ lem s have been presented herein. By the realization that empirical correlations can be presented in terms of a reduced number of nondimensional parameters, experiment designers are allowed significantly increased freedom for obtaining correlations for a range of applications. Package designers can use data measured on m odels with a different physical scale, or even in a differential fluid, provided the important nondim ensional param eters in the model match those for the real hardware application.

References Boyle, M. T. and Asante, K. A., Detailed Film Coefficient Measurement on a Simple Large Scale Semiconductor Package Geometry, Proceedings of the 1990 Semiconductor Thermal and Tem­ perature Measurement Symposium, Phoenix, February. Boyle, M. T. and Knaub, C., Low Speed Wind Tunnel Testing, Proceedings of 1988 IEEE Semi­ conductor Thermal and Temperature Measurement Symposium, San Diego, February. Boyle, M. T. and Langston, L. S., Three-dimensional flow past two cylinders side by side on an endwall, ASME }. Fluids Eng., 3, Dec., 1989. Chapman, A. J., Heat Transfer, 3rd ed., Macmillan, New York, 1974.

Chapter three:

Similitude in electronics cooling

109

Edwards, D., Hwang, M., and Stearns, B., Thermal Enhancement of IC Packages, Proceedings of 1994 IEEE Semiconductor Thermal Measurement and Management Symposium, San Jose, Feb­ ruary Hansen, A. G., Fluid Mechanics, John Wiley & Sons, New York, 1967. Kline, S. J., Similitude and Approximation Theory, Springer-Verlag, Berlin, 1986. Li, W. H. and Lam, S. H., Principles o f Fluid Mechanics, Addison-Wesley, Reading, MA, 1964. Reynolds, W. C. and Perkins, H. C., Engineering Thermodynamics, 2nd ed., McGraw-Hill, New York, 1977. Shames, I. H., Mechanics o f Fluids, McGraw-Hill, New York, 1962. Van Wylen, G. J., Sonntag, R. E., and Borgnakke, C., Fundamentals o f Classical Thermodynamics, 4th ed., John Wiley & Sons, New York, 1993. White, F. M., Fluid Mechanics, McGraw-Hill, New York, 1979.

chapter four

Measuring velocity in electronic systems J. Foss, D. Williams, and C. Wark Pressure-based probes and hot wire anemometers, J. Foss 4.1 Introduction........................................................................................................ 4.2 Specific fluid m echanics term s.................................................................... 4.3 Measurement of velocity............................................................................... 4.4 Displacement/tim e m ethods....................................................................... 4.5 Pressure-based velocity measurement tech niq u es.............................. 4.5.1 M ulti-hole p robes............................................................................. 4.6 Plenum-static m easurem ents....................................................................... 4.7 Thermal anem om etry..................................................................................... 4.7.1 Basic principles of operation........................................................ 4.7.1.1 Electrical............................................................................. 4.7.1.2 Convective heat tran sfer............................................. 4.7.1.3 The response eq u a tio n ................................................ 4.7.2 Types of anem om eters.................................................................... 4.7.3 C alibration.......................................................................................... 4.7.3.1 A jet-flow calibration d e v ice..................................... 4.8 Practical considerations for velocity m easurem ents........................... 4.9 Sampling theorem s......................................................................................... 4.10 How-to list of measurement with H W A ................................................. 4.11 Equipment required........................................................................................ 4.12 N om enclature.................................................................................................... Laser doppler velocimetry, D. Williams 4.13 Introduction........................................................................................................ 4.14 Basic principles................................................................................................. 4.15 Pros and cons of L D V .................................................................................... 4.16 Basic operational p rin cip le........................................................................... 4.17 Process of m easurem ent................................................................................ 4.17.1 Flow seed in g ...................................................................................... 4.17.2 Optical com ponents........................................................................ 4.17.3 Transmitting o p tics......................................................................... 4.17.4 Receiving optics................................................................................ 4.17.5 The burst sign al................................................................................ 4.17.6 Signal processing.............................................................................. 4.17.7 Reverse flow m easurem ents......................................................... 0-8493-3279-6/97/$0.00+$.50 © 1997 by CRC Press LLC

.112 .113 .115 .115 .116

.120 .120 .122 .122 .122 .125 .125 .126 .127 ,127 .132 .132 .138 .139 .139 .140 .140 .141 .141 .142 .142 .143 .143 .145 .146 .146 .148

111

112

Thermal measurements in electronics cooling

4.17.8 Frequency d ow nshifting...........................................................................................148 4.17.9 Data analysis................................................................................................................. 148 4.17.10 LDV calibration ............................................................................................................149 4.18 How-to list for m easurem ent................................................................................................. 150 4.19 Error estimation in L D V .......................................................................................................... 150 4.20 Com parison of LDV with hot-wire anemometry and particle image velocim etry........................................................................................................................151 4.21 Equipment required for LDV m easurem ents................................................................... 151 4.22 Sum m ary ..........................................................................................................................151 4.23 Terms d efin ed .............................................................................................................................. 152 4.24 N om enclature................................................................................................................................153 Particle image velocimetry, C. Wark 4.25 B ackgrou n d ...................................................................................................................................153 4.26 Data acquisition.................................................................... 155 4.26.1 Seeding considerations.............................................................................................. 155 4.26.2 Illum ination....................................................................................................................155 4.26.3 Image recording............................................................................................................156 4.27 PIV image analysis......................................................................................................................157 4.27.1 A uto-correlation...........................................................................................................158 4.27.2 Cross-correlation...........................................................................................................159 159 4.28 How-to list for m easurem ent........................................................................ 4.29 Sam ple PIV results...................................................................... 160 4.30 Equipm ent required for PIV m easurem ents......................................................................161 4.31 Terms d efin ed .....................................................................................................................161 4.32 N om enclature................................................................................................................................162 Appendix: velocity meter vendors..................................................................................................... 162 References....................................................................................................................................................163

Part 1: Pressure-based probes and hot-wire anemometers J. Foss

4.1 Introduction Free and forced convection heat transfer from components, boards, and systems occur when they are exposed to a gas or liquid. Regardless of the type of cooling fluid, knowledge of the fluid velocity is required for characterization and design of electronic systems. This is independent of the cooling system type w hich could be either closed (cold plate) or open (conventional air cooled system). Hence, to obtain the fluid velocity, one must either measure or compute its value for the design of the given system. The fluid flow types encountered in electronic enclosures are, in general, among the most complex observed in fluid m echanics applications. This assertion is given substance by reference to Figure 1 which depicts a typical configuration of components mounted on a circuit board. The flow is made visible by use of ink injection into water (Azar, 1993). The indicated flow could be "induced" by a fan or natural convection, lending itself to the presence of multiple flow regimes (laminar, turbulent, periodic, etc.) in the domain of interest. In such a board level configuration, the designer needs to know the local fluid velocity in the neighborhood of an electronic component to determine the adequacy of the cooling system.

Chapter fou r:

Measuring velocity in electronic systems

113

Figure 1 Fluid flow over a typical printed circuit board Nnte water flow visualization using ink as the coloring agent is shown. The design should be based upon two aspects of the velocity field. These are the spatially averaged velocities at the inlet of the circuit board channel and the local velocity distribution in the neighborhood of an electronic component. The latter is characterized by an approach velocity, V0. Note that the inlet ""average velocity"" is equivalently described as the entering flow rate (q) divided by the inlet area. These two aspects are required for a number of applications as enumerated below. • Component characterization — where component thermal resistance (junction to ambient or case) is expressed as a function of 14 • Fan sizing — where system pressure drop is expressed as a function of volumetric flow rate ty) • Noise m anagem ent — where the noise emitted from the system is proportional to the fluid mover, and its characterization is required in order to ensure noise mini­ mization does not adversely impact thermal performance This chapter deals with the process and steps required to measure velocity at different locations of electronic system s and reviews sensors suitable for these types of measure­ ments,

42

Specific fluid mechanics terms • Velocity, in solid mechanics, is a well-defined quantity. For Xfl as the position vector of the center of gravity of body "B," the velocity of "B " is:

( 1)

Thermal measurements in electronics cooling

114

Specifically, if the N molecules in a given spatial domain (centered at (xlf yv zf) and of size S3 exhibit a net translation (85) in a small increment of time (8 1) then the fluid velocity V (xv yv z1}

V (x1/yi, Zl) = ^

•

• • • •

•

•

•

•

•

•

(2)

The im portant distinction, with respect to that of solid mechanics, is that there is not a physical entity to which this velocity can be ascribed in a fluid mechanics description. Lagrangian — A fluid dynamic particle is identified and the property of interest: velocity, pressure, temperature, etc., of that particle is described as a function of time. Eulerian — All properties (V, p, T, etc.) are assigned at points in space (*, yf z) and as function of time (f). Transient — A "global" and tim e-dependent change in the flow field. Separation — A flow pattern that is not streamlined, i.e., it does not follow the geometrical contours of a physical surface. Streamline — At any instant, an infinity of lines can be traced through the flow that are everywhere tangent to V . (Clearly this requires a knowledge of V at all points in space at that given instant. Hence, this is an Eulerian feature of a flow field.) Pathline — The path taken by a discrete particle over a given time period. That is, a "tim e exposure," as provided, for example, by a patch of smoke or dye or aerosol particles, would be needed to record a pathline photographically. (This is a Lagrangian feature of the flow field.) Streakline — An instantaneous representation of the particle locations that passed a given location. A snapshot of the dye or smoke streaks from a "p oin t" source would be common examples. (This is an Eulerian description of the flow field.) Steady — A steady-state condition exists if the rate of change of velocity with respect to time is zero at the point of interest. The term "steady flow," applies to all points in the flow field. Viscous flow — The type of flow where fluid viscosity plays a role in formation of the flow structure. The partial balance of the effects: (1) acceleration, (2) pressure gradient, (3) body force, must also include viscous effects in order to characterize the resultant velocity field. Inviscid flow — The type of flow where the effect of fluid viscosity is negligible. Or, the balance of effects (1), (2), and (3) above is sufficient to characterize the velocity field. Incompressible — The density (mass/unit volume) of a fluid dynamic particle re­ mains constant (D p/D t = 0) as the particle traverses the flow field. (This definition can be evaluated in terms of a Lagrangian description: D p/D t or its Eulerian counterpart: 9p/9t + V .Vp - 0 .

It is noted that some words in com m on usage: "lam inar, turbulent, vortex, eddy," defy precise verbal definitions. This is true for "lam inar-turbulent" because the instantaneous m otion for both is described by exactly the sam e governing equations. Regarding the terms: "v o rtex " or "ed d y ", the literature does not provide unam biguous definitions for these words. It is best to recognize that these four words do not perm it the user nor the listener/reader to com m unicate or infer anything of precision about the flow by their use.

Chapter fou r:

4.3

M easuring velocity in electronic systems

115

Measurement of velocity

Five principle m easurements are considered for velocity. Ordered in the degree of com ­ plexity, these are • • • • •

Particle tracing Pressure probe sensors Hot-wire anemometers Laser doppler velocim etry Particle image velocimetry

The following table provides a general description of each technique. Table 1

General Description of Different Velocity Measuring Techniques

Method

Mechanism

Remarks

Displacement/ time — particle tracing

Visualizing the flow and measuring the time traveled in a given distance Inference of velocity using the terms of the Bernoulli equation (see Equation (5))

Applicable to low speed flows, i.e., natural convection, with minimal mixing Useful for flow speeds above 2 m /s, the probes are intrusive which may alter the flow structure Suitable for all ranges of flow; requires careful calibration for low velocities; sensitive to changes in the temperature of the flowing gas Suitable for all ranges of flow; requires seeding of the flow and a view window; obstructions, such as components, may make measurement difficult Similar requirements as above; however, data processing is labor- and time-intensive

Pressure probes

Hot-wire anemometers

Heat transfer from a hot wire is correlated to velocity

Laser Doppler velocimetry (LDV)

Use of light scattering (small particles and interpretation of a "beat frequency" from two incident laser beams to infer the fluid velocity Inference of velocity from particle images at t and 5f (see Equation

Particle image velocimetry (PIV)

(2))

The details of each m easurement technique will be further highlighted in the following sections. Sections 4.13 to 4.32 contain full descriptions of the LDV and PIV methods.

4.4

Displacement/time methods

Approximate values for the velocity in a flow field can be usefully extracted by the application of Equation (2). Namely, if an identifiable element in the flow can be visualized: a dye or ink patch in water, smoke, oil, or dust in air, and if the observer can record two positions ( x e) at known times, then the displacement of the marker (8 x ) for the elapsed time (5 1) gives - = [x«(t + 5 t ) - x ,( t ) ] 8t

(3)

Thermal measurements in electronics cooling

116

The crudeness of this method can be appreciated in that "velocity is a point function" (i.e., a blob of ink does not show a point-wise velocity), the marker w hich can be seen is not the fluid (whose velocity is sought), and imprecision in the spatial locations and possibly the times can be anticipated. Image acquisition techniques employed with this method can include (1) photographic — m otor drive camera or a motion pictures camera; (2) video recording; or (3) or simply visual sighting. The known framing rate of (1) and (2) provides 8 1; (3) would require an independent time record (e.g., a stopwatch). This m ethod is most effective for slow flows such as the ones observed in natural or mixed convection cooling of electronic systems. With high speed flows (because of the level of mixing) it may be difficult to track a marked entity in the flow. A further cautionary point is that the visualization agent should not alter the flow configuration.

4.5

Pressure-based velocity measurement techniques

This method takes advantage of the Bernoulli equation (whose derivation appears in many fluid m echanics texts: W hite, 1994, or Potter and Foss, 1975) which simply relates a pressure difference to velocity. This is defined by the following, which is the appropriate form of the equation for this discussion:

v2

P + P ^ = Pt

(4)

The reader m ust note that the use of the Bernoulli equation is restricted to those cases when the flow can be considered to be inviscid (i.e., negligible effect of viscosity), steady and incompressible (D p/D t = 0). Also note that Equation (4) is void of body forces since, for a "subm erged" flow along a streamline, the body forces do not play a role in the flows of interest. The symbol pTis termed a "total pressure" and pV2/ ! is often termed "dynam ic pressure." As a side note, and for reasons made clear in Potter and Foss (1975), neither term is a true pressure. Simply stated, pT and pV2/2 depend upon the coordinate system in which the measurement of ( V ) is to be made. Since pressure is a scalar and a scalar is independent from the definition of a coordinate system, pTand pV212 cannot be pressures. One of the m ost common probes used for pressure-based velocity m easurements is a Pitot-static or a Prandtl probe, see Figure 2. If the above constraints on Equation (4) are valid from the indicated point in front of the nose* to the nose itself, then the velocity at the upstream point may be inferred using

(5a)

If the side tap orifices of the probe experience the same pressure as that at the upstream point (*), then the connections shown permit V to be evaluated from the pressure differ­ ence. By implication, this states that the presence of the probe cannot cause the flow to accelerate from (*) to the plane containing the side taps. An acceleration would occur if the probe were placed in a confining flow passage such that the frontal area of the probe was not negligible with respect to the area of the passage. A simple Pitot probe can also be fashioned to determine the velocity in the streamwise direction; see, e.g., Figure 3a. The required pressure for (4) can be obtained as shown in the figure if the pressure is constant between the wall tap and the Pitot tube opening.* The validity of the assumed constancy of the static pressure between the surface and the * The pressure measuring equipment for the configuration is shown in Figure 3b.

Chapter fou r:

M easuring velocity in electronic systems

117

& £5 £ d * is the resistance at the reference temperature T0 and oc is the temperature coefficient of resistance. Hence, a non-zero a will cause the temperature — and the resistance — of the sensor to increase if L > Cl

Chapter fou r:

Figure 8

M easuring velocity in electronic systems

125

A basic thermal anemometry circuit.

4.7.1.2

C onvective heat transfer

In thermal equilibrium, the dissipated power (IS2RS) balances the convective heat transfer (qh). The latter can be described as

qh = A '(T ,-T g) + B'(Ts - T g)V*

(12)

where A' and B' are dimensional constants for a fixed value of the gas temperature, Tg. The techniques by which these (A', B', and n) and the other coefficients in this section can be evaluated are described below. The circuitry described above is to maintain the sensor at a given temperature (Ts). However, the gas temperature (Tg) may be time dependent if the flow is not isothermal. This condition, which can be expected if the measurements are made w ith powered elements in the electronics package, is considered in a later section. The original "K ing's law " (see King, 1914) identified the exponent "n " as 0.5. A more recent study by Collis and W illiams (1959), of heat transfer from cylinders that are typical of hot-wire probes (i.e., length/diam eter of the wire >200), proposed that an appropriate "n " value is 0.45. As noted below, it is feasible to permit "n " to be established by a direct calibration and it is recommended that it be gained from such a calibration. For com pleteness, it is also noted that the A' and B' values are functions of temperature given their dependence on various thermodynamic properties. This dependence (for air) may be adequately described (see Collis and Williams, 1959) in terms of the mean film temperature [Tm = (Ts + Tg)/2 ] and Tg as A' = A " (T JT g)™ and B' = B"(Tm/T/ - 17

(13)

Note that the "film tem perature" is a convenient w ay to characterize the "average" tem perature in the boundary layer that form s on the wire of the HWA. It is evident from this w eak tem perature dependence that, if the calibration is executed at the nom inal tem perature of the m easurem ents, then the tem perature difference, as expressed in Equation (12), w ill suffice to characterize the effects of variable Ts for m ost electronics cooling applications.

4.7.1.3

The response equation

Combining the electrical power dissipation (I£RS ~ Eq) and Equation (12) provides the voltage/velocity transfer function. This can be written as

Thermal measurements in electronics cooling

126

(14)

E20 = A + BVn for isothermal flow (i.e., constant (Ts - Tg) operation). Alternatively, the expression is 0.17

(15a)

for Ts ~ Rs = constant and moderately variable temperatures (Tg) of the subject gas flow. 4 .7 .2

Types of anemometers

Anem om eters are classified in two categories, hand-held and research quality. These units have the following characteristics. Hand-held units — sometimes referred to as flow speed indicators — are relatively low cost (approximately $1,000) units that may be purchased and used without additional equipment. (Note, however, that maintaining the anemometer at calibration is strongly recommended). The circuitry for this device is basically that shown in Figure 8 but the amplifier gain (and hence the frequency response) is somewhat less than the researchquality one. The sensor element for such devices is quite robust albeit it can be damaged by im proper use. This robustness is compatible with the use of the device as a source of the time averaged velocity. Namely, the natural response time is relatively large for such sensors and the amplifier is selected for its modest cost at the sacrifice of noise level and frequency response. (Note that electronic noise is self-canceling in the averaging process to obtain the m ean velocity.) Hence, if relative magnitudes or the gross features of the velocity field were desired then the flow speed indicators of this section are appropriate diagnostic tools. The research quality unit utilizes a fragile wire or film whose thickness typically does not exceed 5 |im. The small size of the sensing element allows for a much faster response. The more slender probe bodies that are typically used for these anemometers result in a smaller intrusion into the flow field. The typical application of the research quality ane­ mom eter can be categorized by the following. 1. Velocity components 2. Time series data leading to a. Spectral information b. Mean, fluctuating intensity and higher moments of the distribution The small diameter sensor of the research anemometer makes it vulnerable to damage by inadvertent contact between the probe stem and a solid surface (shock-vibration as a source of probe damage). Consequently, this type of anemometer requires a traversing unit and a sensor support for flow measurements. Because a heated sensor is much more fragile than one at ambient temperature, it is advisable to switch the unit to " standby" before it is moved if the danger of inadvertent contact exists. If one desires to determine the flow m agnitude and direction in the vicinity of the com ponent, then a research quality anemometer and a probe traversing unit will be required.* However, if one is interested in a "representative velocity" at the inlet of the channel formed by two printed circuit boards (PCBs), the hand-held anemometer can be

* Various techniques exist for processing hot-wire signals in order to evaluate the velocity components. An effective and simple method is available from Bradshaw (1971). Other methods are described by Brunn (1995).

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M easuring velocity in electronic systems

127

used for such a measurement. (Note that a traverse over this inlet plane would be required in order to define a spatially averaged velocity)

C a lib ra tio n

4 .7 .3

Thermal anemometers provide an indirect (i.e., heat transfer based) measurement of the velocity; hence, it is im portant that their voltage-velocity transfer function be calibrated using an independent standard. That is, all thermal anemometers should be regularly calibrated. Fortunately, the Bernoulli equation provides a relatively simple and accurate method for such a calibration. Unfortunately, the very low speeds relevant to electronics cooling applications can make it difficult to utilize the Bernoulli equation directly in the velocity range of a given application. This concern is addressed in detail in the following.

4.7.3.1 A jet-flow calibration device A preliminary note of caution is appropriate for this section: A probe should always be calibrated in the orientation to the flow in which it is to be used. Specifically, if the probe will be inserted such that the stem is perpendicular to the flow, then in Figures 9 and 10, its axis should be perpendicular to the flow direction. Conversely, if the more favorable situation of its probe shaft alignment with the flow is possible, then its axis should be parallel with the flow direction for both the calibration and measurement as shown in Figures 9 and 10.

FROM FAN

Figure 9

A calibration nozzle for thermal anemometry sensors (pressure side).

Free jets are commonly used to provide a calibration air stream. The advantage of such a flow is that the jet will exhaust to the local ambient pressure and the upstream plenum pressure can be easily measured. Figure 9 shows a generic representation of such a device. Consider that H represents the diameter of a cylindrical plenum and that W represents the similar dim ension of the jet exit. Using one-dimensional flow considerations,

Thermal measurements in electronics cooling

128

atm

Figure 10

A calibration nozzle for thermal anemometry sensors (suction side). A_,___ plenum



O’

(15b)

where the < > symbol represents a spatial average. Using Equation (15), it is apparent that a condition for which < A plenum > ^ 1QQ < A jet >

will suffice to neglect V^k„um in the following equation: Vplenum 2 P plenum + P

V jet 2

.

= Pjet + P

~ijT

(16a)

H ence, for sufficiently large (H/W), this becomes (for pie, = patm)

yi P plenum

P atm

(16b)

If H = 10 W and if the calibration jet is axisymmetric, then V^lenum = (Vjet/ 10,000) and the desired inequ ality is obviously satisfied. If the contraction w ere planar, then Vpienum = (Vfet/100), which is a typically '"acceptable" value for the accuracy of the cali­ bration required in electronic cooling studies. The nozzle shape of Figure 9 is, in general, quite "forgiving." For example, a flexible ruler can be used to define the shape for a planar contraction: hold the two ends in a

Chapter fou r:

M easuring velocity in electronic systems

129

parallel but displaced fashion and mark the trajectory of the ruler. If this method is used, it is important to avoid too steep a curvature on the upwind end. As a "rule of thum b," the length of the contraction should be at least 1.25 times the inlet width. More precise contractions can be obtained from Morel (1975, 1977). The configuration of Figure 9 implies that the calibration unit is operating "on the pressure side" of the air flow device (typically a centrifugal fan). If the pressure side is used, it is important to ensure that the "jetting flow " from the outlet of the prime mover (typically a centrifugal fan) is destroyed and that the flow "uniform ly" fills the plenum. This is not a simple matter! A technical report, Foss (1995), provides detailed instructions regarding a geometric configuration that w ill provide a nominally uniform flow following a sudden expansion. Note that a schematic representation of this device is included in Figure 11. An alternative configuration, that has the distinct advantage of providing a viable technique for quite low speed flows, is shown in Figure 12. This planar configuration is termed a slit-jet; it is relatively simple to configure as a suction tunnel: the outward faces of the planar slit-jet nozzles should simply extend some 10W to each side of the opening, albeit the receiver can be much smaller (±3W would be quite satisfactory). If a "pressure side" configuration is used, it is important to provide an adequately large upwind plenum. As shown by Ali (1991), a plenum width characterized by H/W > 1 3 provides a quite satisfactory approximation to an infinite plenum. The importance of a uniform approach flow is, of course, also present in this slit-jet flow field. Experimental data from Ali (1991) show that the inviscid relationship for

prou0 vides an excellent fit for even low Reynolds number flows (Rew = 500). Hence, the values in Table 3 can be used with confidence for Reynolds numbers of this magnitude and larger. As an example, consider a suction side slit-jet calibration tunnel that meets the geo­ metric conditions noted above and that incorporates a slit width of 3 cm. A wall tap at x/zv = 1.5 and y = 0 can be used with the atmospheric pressure to determine as given by Equation (16b). If a m oderately precise pressure transducer is available — to provide a reliable (±5%) pressure reading at the level h = 0.01 in. H20 — then (for STP air):

Vjel= U o = (20.3) lh^@ 2 ^

If a calibration velocity of 0.3 m/s were desired, then the probe should be located with its sensor at x/zv = -1 .2 5 with (ppJenum - p(atm)) = 0.01 in. H20 . The analytical expression (14) for the voltage - velocity transfer function can, in general, be utilized to about 0.2 mps; see Haw and Foss (1990). Hence, an "optim al" pressure transducer would, for the slit-jet calibrator, provide a viable measure of U0 = 1.33 m/s. The corresponding pressure drop will be 4 x 10-3 in. H20 . This accuracy is available if a high end pressure transducer (e.g., M KS Baratron) were used with the slit-jet calibration device. In contrast, note that the direct measurement of 0.2 mps would require a pressure drop of 10^ in. H 20 . A pressure drop of this magnitude could not be measured with acceptable precision by any transducer! An alternative method of low speed calibration, that does not require the use of an accurate pressure transducer, has been described in detail by Haw and Foss (1990) and Azar and Russell (1991). The probe to be calibrated is attached to a pivoted arm and allowed to "fa ll" under the action of gravity. An accurate m easurement of 0(f) (where 0 is the angle formed by the probe tip with respect to a reference line) provides the infor­ mation to record the velocity experience by the probe tip as

Thermal measurements in electronics cooling

130

w

TRAVERSE THE T H IS

H O T -W IR E

PLEN U M F A C IL IT Y

IN

PROBE

ORDER

FOR

THE

TO LOW

IN T O U T IL IZ E SPEED

C A L IB R A T IO N

Figure 11 A controlled sudden expansion (schematic representation) and a slit-jet geometry for very low speed calibrations of thermal anemometry probes.

uQ(f) = R (dd/df) Clearly, the frequency response of the probe and the recording equipment must be suffi­ cient to faithfully record this transient event. This technique, once developed, provides an efficient and effective means of calibrating such probes given an adequately distur­ bance-free environment through w hich the probe falls.

Chapter fou r:

M easuring velocity in electronic systems

131

Ppl t

p.,

Uo

c) SCHEMATIC OF THE FLOW

•

UQ

b) TOP VIEW

d) VELOCITY DISTRIBUTION CORRESPONDING TO (c)

Figure 12 Detailed view of a slit-jet geometry for very low speed calibrations of thermal anemometry probes. Table 3 Centerline Velocity Values Computed Using Inviscid Flow Theory Regular increments in x /w x /W u(x)/U 0 2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

1.000 1.000 1.000 1.000 1.000 1.000 0.999 0.999 0.999 0.997 0.996 0.993 0.988 0.980 0.968 0.948 0.918 0.872 0.811 0.734 0.648

Regular increments in x /w x /W u(x)/U 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -0.1 -1.1 -1.2 -1.3 -1.4 -1.5 -1.6 -1.7 -1.8 -1.9 -2.0

0.562 0.482 0.414 0.358 0.313 0.276 0.246 0.221 0.201 0.184 0.167 0.157 0.146 0.137 0.129 0.122 0.115 0.109 0.104 0.100

132

Thermal measurements in electronics cooling

4.8

Practical considerations for velocity measurements

Two issues are addressed in this section: (1) the effect of an invasive probe on a flow field, and (2) sampling strategies for adequate evaluations of the flow field statistical quantities. The relatively small passages of electronics circuit boards make the possibility of "probe interference effects" a strong concern in studies of such flow fields. The investigator must be aware of two different issues in this regard: 1. The presence of the probe body may alter the flow at the region of interest such that the probe's response gives a misleading indication of the velocity in the "u n ­ disturbed" environment. Note that, at best, approximations to the desired informa­ tion will be available in such a situation. 2. The presence of the probe may alter the volum e flow (q) in a given passage with­ out altering the relative velocity ( V /) at the measurement location. Hence, if an independent m easurement of the channel average velocity can be obtained, the velocity at the probe tip: V , can be made nondim ensional with the average velocity . If turbulence effects dominate the flow field (as could be expected for the bluff geometry of flow past components), then V / should be a weak function of the Reynolds number:

v where it is a length scale for the flow of interest. One such length can be the spacing betw een the component top surface and the adjacent PCB. This situation is represented schematically in Figure 13. The static tap and Pitot tube at the forward edge of the circuit board permit a reference velocity Vrej to be defined. It is reasonable to assume that the Pitot tube presents such a small obstruction that its influence on the average velocity in the space betw een the two cards is quite small. The larger, horizontally mounted hot-wire probe can, however, be expected to alter the relative flow rate through — and above/below — the space betw een the two cards. Once installed, this probe will decrease the average velocity but its long and narrow prongs will not disturb the local flow behavior at its measurement location. Hence, the indicated hot-wire probe's response can be used to record V i Vny and to infer V in the absence of the probe, as

w /o probe

4.9

n

) o probe

Sampling theorems

Turbulence is the typical flow condition to be encountered in electronic cooling applica­ tions. Exceptions can be expected in some of the thin laminar boundary layers on com­ ponents or heat exchange elements. However, the data acquisition protocols should address turbulent flow issues on a scale characteristic of the "larger" devices. It can be expected that the primary descriptions of a cooling flow will be based upon the first (the mean value) and the second (the mean square fluctuation value) moments of the "distribution" of values. The concept of a "distribution" is best communicated using an example. Figure 14 shows the population of velocity values that were obtained in the turbulent boundary layer that was used to create the u(t) time series in Figure 15. Note that they have been sorted into bins that extend from the minimum to the maximum of

Figure 13

A hot-wire probe measurement within a circuit pack.

Chapter four: Oj Oj

Measuring velocity in electronic systems

Thermal measurements in electronics cooling

134

time (sec) Figure 14

Demonstration time series of velocity (from a turbulent boundary layer).

Figure 15 Histogram of the complete data record (10 s) from which the sample shown in Figure 14 was extracted.

the observations. The relative "sm oothness" of the distribution reflects its relatively large size; that is, there are 300,000 individual samples in this distribution in contrast to the 1000 samples shown in Figure 15. The following formal definitions are appropriate for this discussion. Let u(tt) be the x-com ponent velocity at the sample time t{ and let N represent the total number of samples. The mean value of u (i.e., u ) can be computed by

u=

1 N

u (t; ) for N —»

(

1

i=l

The m ean square value ( u ')2 of the fluctuation (i.e.,

= (u(tt) - u )) is

7

)

Chapter fou r:

M easuring velocity in electronic systems

135

(18a) i=l The square root of this quantity is referred to as the rms value.

U -

U

12

1/2

(18b)

The abbreviation rms represents the operations of (18b), namely, the square root of the mean square of u(t). The dimensions of u, u , and u are length/time. Typical units are meters per second (m/s), and feet per second (ft/s) or feet per minute (ft/min). Note that N -> simply indicates that if the number of samples (N) is sufficiently large, then adding more will not change the statistical value. These two quantities, for the population shown in Figure 14, are u = 2.92 m/s and u = 0.372 m/s. A most useful theorem relates to the number of independent samples (Nj) required to establish the mean value to within a stated uncertainty. This quantity (Nj) can be characterized as follows. Consider that a physical process (such as the shearing flow in the boundary layer) leads to a Gaussian distribution (as approximated by the measured distribution of Figure 14). The average value for an infinite sample ( u J will be expected to differ from the average value of a finite sample ( u ) by the magnitude: lu - u ^ u ^ N j/ N j

(19)

where Nj represents the number of independent samples. Consider that u j u ^ were equal to 0.2. The entries in the following table then show the required num ber of independent samples for a given agreement between the popu­ lation m ean ( u ) and the mean value of the infinite population. Table 4 Demonstration Data — Relationship of Sample Size to Convergence Effects in Measurements lM

1%

3%

10%

400

49

4

lix NI =

Note: u©o /iu oo - 0.2.

The important, and the somewhat nonintuitive issue, is that of independent samples. Its basis can be described in terms of the time series data (Figure 15) that were used to create the population shown in Figure 14. Recall that Figure 15 shows the first 1000 points of a 300,000 point sample. The sample rate was 30,000 samples per second. This high rate permitted other inform ation — than that discussed here — to be extracted. In order to show the concept of independent samples, consider the "experim ent" in which the time series is "flagged" for those instants for which

u - 0.01 < u(tj) < u + 0.01 mps

Thermal measurements in electronics cooling

136

and then a new population of values is formed by delaying an integer number of time steps from the flagged value. As an example, if u(tt) satisfies the above criterion for t} = 0.0075 s and if the integer number were 100, then for the 30 kHz sample rate shown in Figure 15, an elapsed time of

100

1 30,000

= 0.0033... s

would be sustained from the flagged to the sampled value. The sampled value in this case is nom inally 3.08 mps. A distribution of these conditionally sampled values can then be created and statistical measures evaluated from it. It is apparent that a "short delay" will cause the resulting values to be close to u ; that is, the newly created population will be more narrow than the original one. Conversely, as the elapsed time becom es larger, the delayed sample becom es more independent for the flagged condition and the distribution becom es wider. This can be quantitatively represented by plotting the standard deviation ^ ju'2 - uj of the delayed distribution as a function of the number of delay steps; see Figure 16.

Figure 16

Evaluation of the elapsed time to recover independent samples from the data record characterized by Figures 14 and 15. This figure shows that nom inally 500 steps are required to have the conditional and the unconditional populations exhibit the same standard deviation. Hence, in this example, independent samples are formed each 500 steps or

500 = 0.0167 s = 8t, 30,000 1 This dimensional time does not have apparent relevance in the physical problem; however, its nondim ensional expression does! Namely, for the 49 mm high boundary layer (8) of this example and for the free stream ( U J velocity of 4.5 m/s, one can indicate that a characteristic length (8) is convected past a stationary observer at the rate

Chapter fou r:

M easuring velocity in electronic systems

characteristic time =

U.

(4.5)

137

= \ q9 x 10 2s

Hence, independent samples can be recorded each St,

_ 0.0167 _ 1 5 3

8/U j oo

0.0109

characteristic times. Since there were 300,000 samples at the rate of 30,000 samples per second, the measurem ent time was 10 s. Given that one must wait 8 tj = 0.0167 s between samples in order for them to be independent, the number (Nj) of independent samples can be computed as:

Nt = 10 s/0.0167 = 599 samples for this example. If it is assumed that the rms value of the population is nominally equal to the true rms value, then the confidence level of the inferred mean value is u -u

VN u

N

0.372 V599 ~ 2.92

599

= 0.0052 = 0.52% The important issues are: 1. The N{ independent samples (599 in the above example) and not the total number of samples (N = 300,000) are of use in defining the moments of the distribution. Also, the degree of convergence to a statistically stable value depends upon Nj and not (8f) nor the total num ber of samples (N). 2. It is usually not possible to state, a priori, the magnitude of the sample rate 8 f that will provide independent samples; however, it is true that 8 f will be accurately represented as some multiple of a characteristic length divided by a characteristic (convection) velocity. This was represented as (8 / UJ) for the boundary layer prob­ lem and, with experience, the appropriate scales can be similarly chosen for other problems of interest. Item (2) can be interpreted for electronic cooling applications as requiring the "passage of N body lengths" to ensure proper convergence of the measurement. Specifically, if an element were of dimension b (in the flow direction) and if a flow speed of U characterized the velocity of approach, then it can be asserted that one body length (b) of fluid passes a fixed location (e.g., leading edge of the obstruction) in an elapsed time of

^passage

bI'd

Thermal measurements in electronics cooling

138

Hence, if a nominal convergence of 3% were required for the mean values where u/ u ~ 0.25, then

0.03 = ^ - ( 0 . 2 5 ) i ^ U. Nj and N j = 70 or the measurem ent duration should be

8T = 70k — U where k represents the num ber of convected body lengths to achieve independent samples. Typical k values can be selected to be of order 1, namely, 1, 2, perhaps 3 body lengths would be required between samples. It is invariably true that the sample rate can be relatively slow and still be fast enough to ensure that the statistics, defined using the sample population, will converge to the population m ean value "as soon as possible." For example, if the component has a dimen­ sion of 1 cm with a flow speed of magnitude 50 cm/s and if five samples per body length are obtained, then a sample rate of 1 cm 8t _ 1 - 0.004 s sample 5 50 cm/s or, defining the sample frequency as the reciprocal quantity,

f s a m p l e = 250 Hz is suggested. Note that increasing the sample frequency will not cause faster convergence if independent samples occur each 0.2 (or greater) body lengths. It is im portant to realize that this discussion does not address the issue of the response time of the instrument. Such effects can bias the inferred mean value and underestimate the true rms value. These issues are to be considered for the separate probes by the investigator.

4.10 How-to list of measurement with HWA As was made clear in this chapter, measuring velocity with hot wire probes is perhaps the most desired method when compared with the pressure probes. Hence, the steps enumerated below reflect measuring the velocity magnitude with a hot-wire anemometer. However, if the flow velocity is sufficiently high to yield accurately m easurable pressures, the procedure also applies to pressure probes. In either case, but especially for the hot­ wire m easurements, the user is strongly encouraged to make use of digital acquisition methods. A PC-based system can be readily configured for this purpose. The speed, accuracy, and capability of such a system will significantly enhance the u ser's capability to decipher E(t) and improve the data interpretation process.

Chapter fou r:

M easuring velocity in electronic systems

139

• Ensure sensor and its support (either research quality or hand-held) dimensions are significantly smaller than the area of measurement* This implies that the sensor does not alter the flow field by causing redistribution of flow in the PCB channel. For example, the probe diameter should be less than 20% of the PCB-channel's hydraulic diameter. Corrections can be made; see Section 4.8. • Calibrate sensors and ensure that the calibration is repeatable. • Determine the sampling rate and duration which matches the flow dynamics and the desired accuracy • If the flow is nonisothermal (a typical situation for most electronics cooling appli­ cations) fluid temperature, at the location where the sensor is placed, must also be measured and used to correct the inferred velocity. • Place sensor in the flow field and allow time for the flow to reestablish itself before commencing measurement. • Record sensor output and ensure that the result is not dependent upon the length of the sample time period. Specifically, using the digitally recorded values, compute the m ean and rms values for the full record length and then determine u (p)/ u (p = 100) and u (p )/u (p = 100) where p is the percentage of the record length used in the computation. A plot of these ratios as a function of p for 50 < p < 100 will indicate if the data are converged. If the objective is to measure the flow distribution (obtaining velocity profiles) around or on top of component, one should use a research quality hot wire probe that is supported with a traversing unit. In this case, the desired region of interest needs to be probed incre­ mentally. At each traversing station, the velocity needs to be measured using the procedure described above. The number of increments (traversing stations) is problem specific.

4.11 • • • •

Equipment required Calibrated probe Sensor support (either traversing or stationary) Data acquisition Computer

Note that because of the dynamic situation associated with velocity measurements, spe­ cifically with respect to electronic enclosures, a large quantity of data can and should be generated. Hence, a data acquisition system and a computer are considered to be essential meaningful velocity measurement.

4.12 Nomenclature A, B , n b cd D( )/D t

Eb kp/ kn Kp/ Kh m N,NI P

Calibration coefficients for a hot-wire anemometer; see Equation (14) (also, see (12) and (13) for variable Tg conditions) Barometric pressure; or a body dimension Discharge coefficient (see Equations (8) and (9)) A Lagrangian (or material) derivative of ( ) Bridge voltage Coefficient for the evaluation of velocity: non-standard T, b ; see (6a, 7a) Coefficient for the evaluation of velocity: standard T, b; see (6b, 7b) Mass flow rate (Equation (9)) Number of samples, num ber of independent samples Pressure

Thermal measurements in electronics cooling

140

q

To

u0

Vi

v,v 8 6( ) P 0

0 o 0 .

Volume flow rate (Equation (8)) Rate of heat transfer (energy/time) Electrical resistance for the ( ) condition as: "s"-sensor, "(/'-control, "(/'-refer­ ence Absolute temperature for the ( ) condition as: "g"-gas, "m"-mid-value [(Ts + Tg) / 2], "s"-sensor The approach velocity (or free stream velocity) for a given component Spatial average of the velocity magnitude over a cross-sectional area normal to the flow The velocity at a point on a streamline that has experienced negligible shear stress betw een the upstream plenum (p = pT) and the local point; see (8) and (9). Velocity vector, the scalar magnitude of V Size of a fluid dynamic particle, or size of a boundary layer A n increment of ( ) Density Angle in the swinging arm calibrator; see (16) Instantaneous value of a parameter Averaged value of a parameter A property, ( ) , of an infinitely large population of measured values

Part 2: Laser doppler velocimetry D. Williams

4.13 Introduction The cooling air flow around electronic com ponents is characterized by complex flow patterns and large temperature variations. As illustrated in the flow field of the exemplar problem and the sketch in Figure 1, such flows consist of separated regions, reattachment zones, saddle points, strong vortices, large scale and large amplitude turbulent fluctua­ tions. These flow patterns create a challenging environment for the engineer to obtain accurate m easurements of the flow velocity. The laser Doppler velocimeter (LDV) is an optical flow measurement technique that can be useful in resolving complex flow phe­ nomena. The LDV technique becam e a popular laboratory tool for measuring fluid veloc­ ities after its introduction by Yeh and Cummins (1964). It matured rapidly in the following decade, becom ing a method capable of nonintrusive, multicom ponent measurements in both forward and reversed flow situations. A comprehensive introduction to the field can be found in the text by Drain (1980).

4.14 Basic principles The LDV technique measures the speed of micron-sized particles that are convected by the flow through a pair of focused laser beams. The particles may be naturally present in the flow or artificially added, which is referred to as seeding the flow. It is assumed the particles are moving with the flow. In the m ost common LDV configuration (the dual beam m ethod), a laser beam is split into two beam s then recombined at a point in the flow where the m easurement is to be made. The intersection of the two beam s forms a m easurem ent volum e of light and dark interference fringes with a known spacing. As the light scattering particles pass through the measurement volume they scatter light at a frequency proportional to their speed and inversely proportional to the fringe spacing.

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141

The light scattered by the particles is collected by a lens and focused onto a photodetector. Signal processing electronics measure the oscillation frequency of the scattered light signal and convert it into usable form, such as a digital word or analog voltage. With care, one can obtain velocity signals w ith temporal and spatial resolution sufficient for computing turbulence statistics, correlations, and spectra, etc.

4.15 Pros and cons of LDV Some of the major advantages and disadvantages of the LDV compared to the hot-wire technique are listed below. Table 5

Advantages and Disadvantages of Hot-Wire and Laser Doppler Anemometers Hot-Wire Anemometer

Laser Doppler Velocimeter

Advantages Less expensive than LDV systems (thousands of dollars) Easy to use, no seeding required Capable of measuring low velocity fluctuation levels (less than 1% of flow speed) Very good spatial resolution High frequency response Wide range of velocity measurement Disadvantages Near-wall measurements difficult Inaccurate in reversed flows Very sensitive to flow temperature changes and thermal drift Nonlinear calibration of voltage to velocity Difficult to measure multiple velocity components Measures the total velocity component perpendicular to the wire

Measures true velocity components perpendicular to fringe plane Capable of simultaneous measurements of three velocity components Nonintrusive measurement with laser light

Linear calibration Insensitive to flow temperature changes Capable of measurements in reversed flow Loss of signal near surfaces due to "flare" Seeding material required Substantially more expensive than hot-wire anemometer Difficult to measure velocity fluctuation levels below 1% of speed. Obtaining optical access of laser beams to the desired measurement point can be difficult More expensive than hot-wire technique (tens of thousands of dollars)

4.16 Basic operational principle The basic m easurement in the flow field is obtained by particles crossing the measurement volume. The measurement volume is formed by the interference between coherent light waves in the intersection region of two laser beam s as shown in Figure 17. This interference pattern is commonly referred to as "fringes." The calibration of the LDV amounts to determining the fringe spacing, df, which is given by df = A,/(2sin(0 /2))

(20)

where 0 is the beam intersection angle, and X is the wavelength of laser light. W hen a micron-sized light scattering particle (seeding particle) is convected through the measure­ m ent volume, it scatters light from each of the fringes. A photodetector converts the

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Figure 17 Contours of light intensity showing the instantaneous interference pattern obtained by the intersection of two coherent laser beams. Fringes are produced in the region of overlap.

scattered light signal into a fluctuating voltage signal, which oscillates at the "D oppler" frequency* fD = u/df

(21)

where u is the velocity component of the particle perpendicular to the fringe plane. It is apparent that the frequency is linearly related to the velocity, which is one of the major advantages of the LDV technique. It can also be seen from Figure 17 that only the velocity com ponent perpendicular to the bisector and in the plane of the beam s can be detected. If the light scattering particle moves parallel to the fringes, the scattered light intensity w ill not change and a fluctuating light signal will not be produced (fD = 0).

4.17

Process of measurement

4.17.1

Flow seeding

Often micron-sized seeding particles are added to the flow in order to scatter light from the fringes and provide an increased signal data rate. The best choice of seeding material to be used is dependent on the fluid and the flow speed. The particles should have a specific gravity close to 1 in water, and be small enough to accurately follow the changes in flow speed as it varies over space and time. On the other hand, the particles should be large enough and have a refractive index different from the fluid for good light scattering characteristics. A num ber of in-depth studies on the characteristics of seeding particles have been conducted. The work by Adrian (1984) and Adrian and Yao (1985) on particle scattering characteristics applies to both LDV and particle image velocimetry. As a starting point one generally uses seeding particles with diameters that are comparable to the fringe spacing to obtain a high signal-to-noise ratio. W hen working in water, it is recommended that the water be filtered to a nominal level of 1 to 2 pm before adding seeding particles.** Particles smaller than 1 pm often contribute more noise to the photodetector signal than actual Doppler signal, so they should be removed. Polystyrene latex spheres, aluminum oxide, and silicon carbide make excellent seeding particles, although the high specific gravity of the latter two limit their use to flow speeds 1 m/s and higher. Particle diameters ranging from 2 to 5 \im will meet * The Doppler effect refers to a change in frequency that occurs when there is relative motion between the source (particle) and the observer. The change in pitch of a passing fire truck's siren is an example of the Doppler effect. ** As a general rule, if the laser beam has a "milky" appearance or halo surrounding it, then the water should be cleaned. Clean water with proper seeding gives the laser beam a "grainy" appearance from the seeding particles.

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the criteria of strong light scattering and an ability to accurately follow the flow. Only small amounts of seeding should be added to the water, then thoroughly mixed to get the desired data rate (velocity measurements per second) from the LDV system. Eventually a maximum will be reached, then as more seeding is added the data rate will begin to fall off. In practice, finding the optimum seeding density tends to be a trial and error proce­ dure. Providing the proper level of seeding in air flows usually requires an atomizer or aerosol generator. Best results are obtained when the particles are uniform in diameter. Commercially available particle generators are recommended, because they usually offer better control over particle size than can be obtained with "hom em ade" equipment. Mixtures of water with glycerin, dioctyl phthalate (DOP), olive oil, salt, sugar, etc. have been used. Particle diameters ranging from 0.8 to 5 pm can be produced. Our experience with atomizers has indicated the device must be cleaned frequently to produce high quality particles. W hen working with high temperature flows in air, the seeding particles may evaporate too quickly to reach the measurem ent volume. In this case, a fluidized bed-type aerosol generator can be used to disperse dust particles from aluminum oxide or silicon carbide powders.

4172

Optical components

Adrian (1983) describes three fundam entally different types of LDV optical systems in his review of the LDV technique. These are the "reference beam ," the "dual scatter," and the "dual beam ." The reference beam and dual scatter systems require only a single beam for illumination of the seeding particles in the measurement region. The dual beam method uses two intersecting laser beam s for particle illumination as sketched in Figure 17. Because it offers better signal-to-noise ratio the dual beam system is the most common, and discussion will be limited to this type of optical arrangement. The basic components of a dual beam system are shown in Figure 18 for the forward scatter mode of operation. W hen feasible, this configuration offers significant advantages in terms of signal-to-noise ratio over other LDV systems. The optical system can be divided into the laser and transmitting optics, and the receiving optics and photodetector. The purpose of the transm itting optics is to provide a focused measurement volume. The receiving optics are designed to collect the light scattered from the seeding particles in the flow. In this figure they are placed along the optical axis in the forward scatter mode. The dual beam configuration has the advantage that receiving optics may be placed in off-axis locations, or combined with the transmitting optics to form the so-called backscatter configuration.

4173

Transmitting optics

The most commonly used lasers are helium neon (^ = 632.8 nm) and argon ion (^ = 488.0 nm and 514.5 nm) where X = wavelength. Typical laser power levels range from 5 mW to 5 W. The investigator should be aware that lower power helium neon lasers are usually limited to forward scatter applications, and the more powerful argon ion lasers may require three-phase current and water cooling. The beam splitter divides the initial laser beam into two beams of equal intensity. In m ost LDV systems the beam s are parallel to the optical axis entering the focusing lens. Beam steering optics, such as adjustable prisms or mirrors are included in well-designed LDV systems to allow the two laser beam s to be precisely aligned with the optical axis. The beam intersection should occur at the focal point of the focusing lens. The distance

144

Figure 18

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Basic optical components of a dual beam-forward scatter LDV system.

betw een beam s at the front of the focusing lens and the focal length of the lens define the beam intersection angle, 0 . The highest quality focusing lens will only focus the laser beam s to the so-called "G aussian lim ited" spot size. To determine the actual spot size and the size of the m ea­ surement volum e it is necessary to use Gaussian beam theory. The light leaving the laser is not perfectly parallel, but converges to a minimum diameter called the beam waist near the exit of the laser before diverging very gradually. Assuming the beam leaving the laser has a beam waist w ith diameter d : and the focusing lens is placed a distance La from the waist, then the beam will be focused to a spot size d2 at a distance L2 from the lens as shown in Figure 19. For the optical geometry shown the important equations that determine the distance to the focal point, L2, and the actual spot size, d2, are given by

L2 = f + (Li - f ) / [ ( V f - l)^ + ( b . / i m

(22)

and l/ (d 2)2 = l / i ^ m

- V f )2 + (bi/2)2

(23)

where b a = n dx/2X is the confocal parameter, and f is the focal length of the lens. W hen the lens is placed such that La = f, then the following approximations are obtained: L2 - f

(24)

d2 - (4Xf/rcd,)

(25)

and

If the spot size, d2, needs to be reduced, then it is clear from these equations that the focal length of the lens m ust be decreased or the beam entering the lens must be expanded. Using a beam expander prior to the focusing lens will reduce the size of the measurement volume by the expansion ratio factor and increase the intensity of the fringes by the square of the expansion ratio.

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Once the spot diameter is known, then the dimensions of the measurement volume can be approximated. The minimum diameter is d2/cos(0/2) and the length is d2/sin(0/2). Small beam intersection angles lead to relatively long measurement volumes. The spatial resolution of the oblong m easurement volume is typically around 0.2 mm diameter and about 3 to 4 mm in length. W hile this is not quite as small as the typical hot-wire anemometer, it is more than adequate for many applications.

4 .1 7 .4

R e c e iv in g o p tics

The image of the measurement volum e is focused by the collecting lens on the face of the pinhole section. The pinhole is carefully adjusted to allow only the light from the seeding particles to reach the photodetector. Accurate positioning of the pinhole is important to reduce contam ination by stray light and to improve the signal-to-noise ratio. It is not necessary for the receiving optics to be placed in-line (coaxial) with the transmitting optics. In fact, it is possible to improve signal-to-noise ratio and spatial resolution by placing the receiving optics off-axis. The effects of flare and other background light can be reduced by using the off-axis approach, but the disadvantage is the additional complication in traversing the system and alignment of the optics. W hen the measurement volum e is moved to a different spatial location, the receiving optics will also need to be moved and readjusted. It is not uncom m on to find the LDV system fixed in the laboratory, and the experimental apparatus traversed relative to the measurement volume in order to make measurements at different spatial locations. In the backscatter configuration the focusing lens also acts as the collecting lens for the receiving optics. The illuminating laser beams and receiving optics are co-axial, which reduces the number of components, and makes it possible to measure from one side of the experiment. It is not necessary for the test section to be transparent on two sides, and traversing the entire system is easier since one need not realign the receiving optics when the measurement volume is traversed. The disadvantage of this approach is reduction in scattered light intensity from the seeding particles. Higher power lasers, such as argon ion lasers, are usually required for backscatter operation compared to forward scatter systems. Since 1986 LDV systems using fiber optic components have been commercially avail­ able. These systems offer a high degree of flexibility in probe positioning, w hich is well suited for measuring flow speeds between electronic components shown in the exemplar problem of Figure 1. With the conventional LDV fixed-optical systems the investigator may have difficulty measuring close to the surface, if the beam s are blocked by components on the board. This problem may be avoided or reduced with the fiber optic LDV. The fiber optic LDV configuration is a subset of the backscatter dual beam design. The transmitting and receiving optics are combined into a compact probe head. The probe head is connected by long fibers to the transmitting section that contains the laser, Bragg cell, color separator, and fiber alignment devices. Both low power He-Ne and higher power argon lasers can be used with these systems.

d1

Lens

Figure 19

Sketch of the geometry of a focused laser beam.

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4,17.5

The burst signal

The intensity of the laser light across the beam cross section has a Gaussian intensity distribution, w hich is referred to as the TEM 00 model.* Consequently, the intensity of the fringes also varies across the m easurement volume, i.e., fringes in the middle region will be brighter than those at the edges. W hen a particle passes through the m easurement volum e there will be an amplitude m odulation of the Doppler signal. The overall signal pattern shown in Figure 20 is referred to as a Doppler burst. The low-frequency modulation is referred to as the pedestal signal, and is shown by the dotted line in Figure 20a. Normally, the pedestal signal is at a much lower frequency than the Doppler signal, and can be removed with a high pass filter during signal processing. The objective of the signal processing equipment is to extract the velocity information (Doppler frequency) from the burst signal.

Figure 20 Idealized burst signal, (a) The overall burst signal, with dotted line indicating the pedestal signal, (b) Doppler frequency signal after high pass filtering.

Each particle w ill produce a burst signal. If multiple particles exist in the measurement volum e simultaneously, then overlapping of the bursts w ill occur. Adrian (1983) refers to this as the burst density, and shows that it is related to the average num ber of particles in the measurem ent volume at any instant. The choice of the signal processing electronics is strongly affected by the value of the burst density.

4 1 7 .6

Signal processing

The m ain objective of signal processing is to measure the Doppler frequency from the burst signal obtained by the photodetector. There are four different schemes commercially available for signal processing: 1. Frequency tracker * The actual intensity distribution of the laser beam can be checked by placing a microscope objective lens in the beam. By projecting the beam onto a piece of paper placed about a meter away, it is easy to see if the laser has a Gaussian distribution or not. If the beam is distorted, then it should be "cleaned up" with a spatial filter. The same technique can be used to visualize the fringes in the measurement volume when frequency shifting is not used. This if often useful when setting up an LDV system for the first time to check if the beams are actually intersecting and producing an interference pattern.

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2 . Counter processor 3. Correlation analyzer 4. Spectrum analyzer The selection of a particular type of processor depends on the quality of the signal, the seeding particle density, the accuracy required, and the investigator's budget. Brief descriptions of these techniques are given below. 1. The frequency tracker approach is the least expensive. Trackers work best when the seeding concentration is sufficiently high that the burst signal is nearly contin­ uous. The tracker processor uses a phase-locked loop to lock-on to the Doppler burst frequency A com parison of the phase between an internal voltage-controlled oscillator (VCO) and the burst signal is made by the tracker. W hen there is a change in flow speed then a phase difference between the two signals occurs, and the control voltage to the VCO is adjusted to re-establish the phase lock. The control voltage then provides an analog output voltage proportional to the burst frequency The tracker may lose its lock if the burst signal amplitudes drop or the burst density is too low. This is referred to as signal dropout. Normally, the tracker is designed to hold the last recorded velocity value until a new lock is established. Orloff (1978) found that high particle densities result in overlapping particle signals on the photodetector. These generate random phase shifts in the net optical signal that the tracker processes as velocity fluctuations. Consequently, trackers have a limited measurement range in unsteady flows, and are nearly obsolete. For additional information on tracker performance, refer to Fridman et al. (1975). 2 . Counter-type processors are the most common signal processors used in LDV systems. They measure the time required, tm, for a seeding particle to cross a predetermined num ber of fringes, Ncycles. The burst frequency is obtained by divid­ ing Ncycles/tm. In contrast to trackers, the counter processors perform best with low burst density signals, produced by individual particles. If the seeding concentration is high enough that multiple particles are present in the measurement volume, then the counter will reject the measurement and the average data rate will begin to drop. The standard counter configuration uses two timers to measure the time it takes a particle to cross Ncycles (typically eight fringes). The zero crossings of the burst signal are determined, and the two timers are started. One timer measures the time for five fringes to be crossed, while the other timer measures the time for eight fringes to be crossed. At the end of eight cycles, the ratio of the two times is computed. If the ratio is within 5/8 ± error, where the error is a preset value (1.5% in commercial systems), then the measurement is considered to be valid. The Doppler frequency output of the counter is expressed in digital form usually as a 12-bit digital word. Data rates up to 10 MHz are possible in principle, depending on flow parameters. 3. In a digital correlation analyzer signal processor, the burst frequency is obtained by com puting the correlation coefficient betw een the burst signal and a time de­ layed version of the signal. The phase difference betw een the two signals, divided by the time delay which m aximizes the correlation coefficient determines the fre­ quency. Commercially available correlators specifically designed for LDV applica­ tions can operate at data rates up to 100,000 samples per second. 4. Digital spectrum analyzers (or burst processors) are perhaps the most robust signal processors in their ability to extract the burst frequency from noisy signals. How­ ever, they are also the most expensive. The Fourier transform of the burst signal is obtained digitally by a hard-wired fast Fourier transform (FFT) processor. The modulus of the complex FFT is obtained, and its peak corresponds to the burst

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frequency. Recent progress in this area has led to equipm ent that can operate at 600,000 samples per second with 14-bit resolution.

4.27.7

Reverse flow measurements

With stationary fringes a particle that is not m oving across the fringes cannot produce a D oppler signal. W hen a seeding particle m oves at constant speed in either the positive or negative x-direction (across the fringes), the same Doppler frequency w ill be pro­ duced. Therefore, a stationary fringe m easurem ent volum e cannot distinguish the dif­ ference betw een forw ard and reversed flow directions. This phenom enon is know n as "directional am biguity." The solution to this problem is to introduce a frequency shift with an acousto-optic m odulator (AOM or Bragg cell) to one of the crossing laser beam s. A single laser beam entering the AOM at a specific angle will be diffracted into a fundam ental frequency fc and its sidebands, fc ± Af ± 2Af ± ..., where Af is the acoustic w ave frequency. A frequency shift Bragg cell w ith Af = 40 MHz is com m only used in com m ercial equipm ent. W hen the shifted beam interferes with the unshifted beam, then the fringe pattern in the m easurement volume will move in either the positive or negative x-direction. The direction of fringe motion depends on which diffracted beam from the AOM was chosen. If a particle is positioned inside the measurement volume, the "m oving" fringes will produce a scattered light signal at 40 MHz. W hen the particle moves against the fringe direction the scattered light frequency will be increased to 40 Mhz + fD. Likewise the frequency will be reduced to 40 MHz - fD when the particle moves in the same direction as the fringe motion. In this way, the directional ambiguity problem is resolved, given that fD < 40 Mhz.

4.17.8

Frequency downshifting

In m ost applications the 40 MHz frequency shift is too large for the signal processing electronics to provide resolution of the Doppler signal. For example, consider the m ea­ surement of convective flows over electronic components, where flow speeds on the order of 1 m/s or less are anticipated. With a fringe spacing in the measurement volume of 5 pm (5 x 10-6 m), the Doppler frequency will be 200 kHz or less. Since the Doppler signal is an order of magnitude smaller than the frequency shift signal, it will be difficult to resolve during signal processing. Therefore, an electronic frequency mixer unit should be added to "dow nshift" the 40 MHz shift to a lower value. Commercial frequency mixers downshift the signal to the range of 2 kHz to 10 MHz. The desired shift is based on the flow velocity range of interest. One m ust be careful to use a frequency shift that is larger than the maxim um reversed flow Doppler frequency, but small enough to preserve the velocity resolution. According to W hiffen (1975) a good starting point is to use a frequency shift that is twice the frequency corresponding to the maximum negative velocity. A closer look at the problem of velocity resolution and a sample calculation are given in the next section.

4.17.9

Data analysis

W hen the velocities being measured are steady, i.e., the turbulent fluctuation levels are small (much less than 1%) compared to the m ean flow speed, then calculation of the mean flow speed is easily obtained by averaging the readings. The burst frequency from the counter is read, then the frequency shift value is subtracted to obtain the Doppler fre­ quency of the seeding particle. The calibration is then applied to obtain the speed, u = fD*df.

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Since the measured burst frequency contains both the Doppler frequency and the frequency shift in a 12-bit digital word as output from the processor, one must be careful about frequency shifting in order not to sacrifice velocity resolution by using a frequency shift that is larger than necessary The 12-bit digital word from the counter contains 8 bits for the mantissa and 4 bits for the exponent, such that fD = mantissa x 2exPonent. We can exam ine the effect of frequency shifting on the velocity resolution by way of exam ple. Assum e the frequency shift was set equal to the m axim um Doppler fre­ quency expected, say 200 kHz each. Then the total burst frequency m easured by the counter w ill be 400 kHz. The m axim um value of the 8-bit m antissa is 255, so the exponent m ust be set at 11 (2n = 2048) to achieve m axim um velocity resolution. Therefore, the 400 kHz burst signal is actually represented as 195 x 2n = 399,360 Hz on the output of the counter. From this one subtracts the frequency shift value of 200 kHz to obtain a m easured Doppler frequency of 199,360 Hz. Compared to the true value of 200 kHz we see that the error in conversion is 0.32%. This example illustrates how the velocity resolution is dependent on the exponent 2n. In effect, the exponent determ ines the frequency resolution. In this exam ple a 1-bit change in the m antissa is equivalent to the m inim um detectable change in frequency of 2048 Hz. For a 200 kHz Doppler signal, then the frequency resolution is 1.02%. Furthermore, this shows that it is pointless to attem pt to m easure velocity fluctuations less than 1% w ith these flow param eters. If a larger frequency shift had been used for the same flow field, say 400 kHz, then the exponent would have to be increased to accom m odate the new burst frequency of 600 kHz. The new exponent becom es 12 (212 = 4096), and the digital word output w ill be 146 x 2 12. The velocity resolution is 4096 Hz or 2.05% of the true burst frequency. Hence, increasing the frequency shift increases the m inim um resolvable velocity. The experi­ m enter m ust be careful not to choose a frequency shift that is any larger than necessary to avoid directional ambiguity. W hen in doubt about the accuracy, the m easurem ent should be repeated using a different frequency shift value. A different type of error can occur when velocity fluctuations are present. In the situation where there are large amplitude velocity fluctuations in the flow field, the calculation of all statistical properties may be biased if one uses a simple averaging technique. The heart of the biasing problem is that in a specific time interval more particles cross the measurement volume during the high-speed phase of the fluctuation than during the low-speed phase. Then a simple average of the velocity m easurements to obtain the m ean speed, U = 1/n Zu* will overestimate the true mean, i.e. a bias error occurs. This error is peculiar to the LDV technique, w hich measures individual particle speeds, and will not occur with the hot-wire anemometer. The effects of biasing are well known, and have been thoroughly studied by a number of researchers. A com parison betw een a number of different techniques was made by Gould and Loseke (1993). M cLaughlin and Tiederman (1973) were the first to identify the problem and propose a correction. In their approach the mean velocity is computed by averaging the reciprocals of the velocity, i.e., U = 1/n £[1/(1/^)]. Adrian (1983) gives an excellent summary and relates it to the turbulent flow scales. A number of articles related to LDV signal processing and the appropriate corrections can be found in the Proceedings of the Dynamic Flow Conference (Hansen, B. W., ed., 1978). Articles by George, Lading, Coghe and Ghezzi, and M ayo deal specifically with the corrections necessary toobtain unbiased estimates of the flow statistics from LDV signals.

4,17.10 LD V calibration Calibration of the LDV amounts to determining the fringe spacing, which is done by measuring the beam intersection angle, 0. To obtain 0, the spacing, D, between laser beams

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at known distance, L, from the intersection point is measured, and the trigonometric formula 0/2 = tan_l(D /2L) is used. If the entering beams are parallel and D is measured at the focusing lens, then L is the focal length of the lens. If space permits, a more direct approach is to use an "optical protractor." A mirror can be m ounted on a rotating mount with a vernier to measure the angle. The angle is measured by placing the mirror at the point of intersection, and rotating it so that each beam is reflected back on itself.

4.18 How-to list for measurement The following list summarizes the basic steps required to measure the flow around the electronic com ponents illustrated in the exemplar problem. In practice the procedure is iterative, i.e., m easurements must be repeated and the frequency shifting, seeding, biasing corrections are "fine tuned" as one obtains velocity information about the flow. 1. Determine the proper type and am ount of seeding to optimize the data rate from the signal processor 2. Calibrate the system by measuring the beam intersection angle and computing the fringe spacing, df 3. Set the frequency shift, fs 4. M easure the burst frequency, fb 5. Compute the Doppler frequency by subtracting the frequency shift value, fD= fb - fs 6. Compute the velocity value, u = df * fD 7. Apply any necessary corrections to remove biasing effects

4.19 Error estimation in LDV The basic error estimate of the LDV velocity m easurements can be obtained from the uncertainties in the frequency measurement and the fringe spacing. This is known as the external error. The normalized error in velocity is eu = eu/u, where eu is the absolute error in the velocity, u. Similarly, for the Doppler frequency, ef = ef/fDis the normalized frequency error and the error in the distance between fringes is ed = ed/df. Since u = fD*df, the error in velocity will be given by £u= ef + ed

(26)

As discussed earlier in Section 4.17.9, the uncertainty in the frequency m easurement depends strongly on the frequency shift value used. If we assume a typical value of ef = 0.01 and ed - 0.01, then from Equation (26) we obtain the normalized velocity error to be eu = 0.014. The researcher can also estim ate the error using internal error analysis. In this approach, the velocity m easurements are repeated several times at a point in the flow where the velocity fluctuations are lower than 1%. Typically, such regions can be found in the freestream region, away from sidewalls, entrances, or com ers. For example, in the freestream of a good wind tunnel the velocity fluctuations will be on the order of 0 .1% of the velocity. The standard deviation of the set of measurements is then computed to obtain the internal error estimate. This approach gives a direct estimate of the uncertainty in the velocity m easurem ent caused by the overall inaccuracy of the LDV system. The internal and external error estimates should be within the same order of magnitude.

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4.20 Comparison of LDV with hot-wire anemometry and particle image velocimetry The LDV and HWA are point-wise measurement techniques, whereas particle image velocim etry (PIV) measures velocity over a plane. The LDV and hot-wire methods allow one to make time-resolved m easurements of the velocity, in contrast to the PIV technique which provides "snapshots" of the flow field. In very low-speed flows the PIV technique is capable of time-resolved m easurements as described in the following section. If interest is prim arily in spatial distributions of velocity, then PIV may be chosen over the pointwise measurem ent techniques. Normally, researchers begin by investigating the timeaveraged quantities, such as the mean velocity, root mean square velocity, etc. at a few locations in the flow. In this case the choice would be either LDV or HWA. While HWA systems are less expensive (thousands of dollars) than laser anemometers (tens of thousands of dollars), they produce false readings in regions of reversed flow, and temperature variations around electronic components may significantly affect the calibra­ tion. If one is measuring in regions of strong velocity fluctuation levels, then the LDV is able to resolve two components of velocity more accurately than the hot-wire technique.

4.21

Equipment required for LDV measurements

The essential components for the most basic laser anemometer system can be summarized as 1. 2. 3. 4. 5.

Laser Optics Signal processor Frequency shifter Particles or particle generator

It is possible to design and construct specialized LDV systems. The reader is referred to Durst et al. (1976) for details on selecting the required components. However, to obtain the best signal-to-noise ratio, accuracy, and data rate, the components should be carefully matched to each other. For example, the optic components are sensitive to the wavelength of laser light used. Consult the vendor section of the chapter for the list of vendors of research quality LDV equipment.

4.22

Summary

Referring again to the exemplar flow in Figure 1, where the electronics are cooled by placing the fan downstream of the circuit board, we can outline a typical approach to using the LDV to measure the flow. Assum ing the experim ent is to be conducted in air, the first consideration is to gain optical access to the area of measurement. This can be done using clear plastic sidewalls surrounding the board to be studied. Neighboring circuit boards could also be replaced by clear plastic panels. A fiber optic LDV will make mea­ surements between the various components easier to obtain than the conventional LDV with fixed optics. Either system will require a traversing system to allow accurate posi­ tioning of the probe volume. The next concern of the investigator is to achieve high quality seeding of the flow. One of the commercial atomizers could be used with a glycerin/water mixture (30:70) to produce a mist of particles outside of the entrance to the circuit board. The seeding particles

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will be ingested by the flow entering the passage betw een neighboring boards. The flow near the entrance to the board is expected to be reasonably free from disturbances, and should be used for the initial measurements. The investigator should fine-tune the atom ­ izer and the LDV parameters (optic alignment and frequency shifting) on the initial lam inar flow before attempting measurements in turbulent areas or regions of reversed flow. The highest possible data rate will be probably be achieved at the laminar entrance flow. The first flow field survey would be attempted by traversing the LDV measurement volum e in small incremental steps throughout the regions of interest. Care must be taken to w atch for reversed flow regions, and to adjust the frequency shift values as the flow conditions change. Repeating flow measurements with slightly different frequency shift values is a good way to verify if a reversed flow region has been entered. In regions with large velocity fluctuations, the velocity bias corrections may be applied.

4.23

Terms defined

Acousto optic modulator (or Bragg cell)

Back scatter

Beam waist Burst signal External error Flare Forward flow Forward scatter Interference fringes

Internal error Measurem ent volum e (or probe volume)

Optical axis Pedestal signal

Photodetector Reattachm ent region

An optical transducer that uses sound waves to diffract light waves and shift the frequency of the light (up or down) by the sound fre­ quency. Light scattered in the opposite direction to the optical axis, i.e. toward the transmitting optics. A region in a laser beam where the diameter is minimum and nearly constant. Scattered light signal produced when a par­ ticle passes through a fringe volume. Measurement error estimates based on com ­ ponent uncertainties. Diffusely scattered light from a surface. Flow in the same direction as the freestream or external flow. Light scattered in the direction of the optical axis. Bands of light and dark regions produced at the intersection volume of two coherent light beams. M ea su re m en t erro r e s tim a te b a se d on repeated measurements of a fixed quantity. Region of the laser beam where the seeding particles can be observed by the receiving optics. Centerline through the transmitting optics forming the measurement volume. Low frequency component of the burst signal due to the Gaussian intensity profile of the intersecting laser beams. Light-sensitive detector such as a photodiode or photomultiplier tube. Area where a fluid layer impinges on a sur­ face.

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Reverse flow.

153

F lo w in th e o p p o site d ire c tio n to the freestream or external flow. N umber of seeding particles per volume. M icron-sized particle used to follow the flow and scatter light to produce a signal for the LDV. A region where the fluid layer near a surface leaves the boundary and is accompanied by a region of reversed flow. Electronic device for converting the Doppler signal to a velocity measurement. Laser cavity oscillations occur purely by lon­ gitudinal modes w hich produces a nearly Gaussian intensity profile.

Seeding density Seeding particle

Separated region

Signal processor TEMoo mode

4.24 Nomenclature Fringe spacing = X/(2 sin0 /2) Doppler frequency - u/df/ or Ncyles/tm N,cycles Number of fringes crossed by a particle and used by a counter signal processor to determine the Doppler frequency u Instantaneous flow speed = fD * df Averaged flow speed U X Wavelength of laser light Included angle of laser beams intersecting to form the probe volume 0 Time for a seeding particle to cross a predetermined num ber of fringes Absolute error in velocity, frequency, and fringe spacing c f/ c d ef , ed Relative error in velocity, frequency, and fringe spacing d,

Part 3: Particle image velocimetry C. Wark

4.25 Background Particle image velocim etry (PIV) is a relatively new technique to measure the velocity at multiple points sim ultaneously in a flow field. The basic premise of PIV is to measure the velocity of "m arkers or seeding particles" in the flow over a two-dimensional grid. In this sense PIV provides a Lagrangian description of the velocity, since the evaluation of the velocity vector is performed by following the seeding particles. Specifically, the velocity is determined using the basic definition

V

}

At -> 0

At

V

where A s is the displacem ent vector of the seeding particle(s) during the elapsed time At. Figure 21 is a schematic of a typical experimental setup for acquiring PIV velocity data with the direction of the bulk flow as indicated on the figure. Seeding particles are introduced into the flow upstream of the measurement region and are illuminated using a pulsed light sheet of thickness Az0. The light sheet is pulsed with a frequency of 1/At

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X

Photographic plate

FLOW

Light sheet of thickness Azq

Figure 21

Schematic of particle image velocimetry setup. (From Ullrich, S. A., M.S. Thesis, Illinois Institute of Technology, Chicago, 1993. With permission.) and the duration of each pulse m ust be sufficiently short to essentially " freeze" the image of the particle(s) on the recording media. The scattered light from the particles is captured on optical recording media such as photographic film or a CCD array. The time between the two pulsed light sources is usually known to within nanoseconds and the displacement vector, A s , is resolved in one of several ways to determine V . The determination of A s is prim arily based upon the particle seeding density: it is this feature that separates the various categories in pulsed light velocimetry. PIV is one category of a larger class of pulsed light velocimetry (PLV) techniques. The advantage of PLV over more conventional velocim etry techniques is that PLV can provide the investigator with the velocity at numerous points in space simultaneously: depending upon the size of the PLV realization, the velocity field could contain a few hundred up to several thousand independent velocity vectors. PIV has been used successfully to acquire the spatial dependence of the velocity vector, V ( x ), in both high (Molezzi and Dutton, 1993) and low speed (Rockwell, 1992) flows. However, the main disadvantage of PLV techniques is the limited ability to acquire tem poral information, V (t). To resolve V (t), the particle(s) image at several consecutive time increm ents is required. For example, typical video framing rates are on the order of 30 frames per second. At this rate the particle(s) would travel a distance betw een successive fram es equal to U c times At, where U c is a convection velocity and At would be 1/30 s. For all but very low values for Uc, this distance would be considered too large to accurately resolve V ( t). Nevertheless, since the flow speeds encountered in the field of electronic cooling are typically very small, the temporal resolution limitation of PLV may not be a factor for many electronic cooling applications. This will be discussed further in the forthcom ing section. At low particle seeding densities, particle tracking velocimetry is employed and as the name implies, individual particles are identified and tracked to determine A s . This would not be the recommended category of PLV techniques to use in electronic cooling applications, since these flows are highly mixed with relatively large velocity gradients

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occurring within the region of interest. At high particle seeding densities, the scattered light from neighboring particles causes an interference pattern known as speckle and laser speckle velocim etry techniques are employed to determine A s (see Simpkins and Dudderar, 1978 and Meynart, 1983). The intermediate particle concentration range, where individual particles can be identified, is known as particle image velocim etry Because tracking each particle in PIV is too time consuming, a different technique for determining the displacement vector is used. The PIV technique uses an average displacement vector of all particles within an arbitrarily chosen spatial domain. This will be discussed in greater detail later. The vast m ajority of PIV investigations have been conducted using a single recording camera focused on a relatively thin light sheet on the order of 1 mm. The particle images recorded in this fashion w ill provide two components of the velocity in a two-dimensional plane in the flow: this is com m only referred to as planar PIV Alternatively, stereo PIV utilizes two recording cameras focused on a thin light sheet, w hich will provide all three components of the velocity in a two-dimensional plane (Prasad and Adrian, 1993). How­ ever, since the two recording cameras for stereo PIV need to be precisely aligned this technique is considered to be too complex for electronic cooling applications; consequently, planar PIV is the recommended choice for electronic cooling investigations.

4.26 Data acquisition 4.26.1

Seeding considerations

Two m ain and conflicting issues are raised when seeding the region of interest in the flowfield with small diameter particles: (1) the particles must be sufficiently small, such that they "follow the flow," and (2) the light scattered by the particles must be adequate to be captured by the optical recording media. The former concern favors small particles, whereas the latter favors larger particles. W hen using water as the working medium, hollow spheres such as com m ercially available polystyrene particles of -1 0 to 30 |im in diameter with a specific gravity near 1 are com monly used. If air is the working fluid, atomized oil or an atomized 10% polyethylene glycol, 90% water mixture are effective. The mean particle diameter using commercially available atomizers is typically in the range of 1 to 5 |im. 4 .2 6 .2

Illu m in a tio n

The amount of light scattered by the particles must be sufficient to register on the recording medium; therefore, high-energy lasers are required due to the scattering characteristics of the seeding particles com m only used in PIV The incident light on the particles must be short in duration so that the particle images are essentially "frozen" on the recording media. For this purpose, pulsed light sources such as Nd:Yag lasers are typically used. These units can provide -1 0 0 to 300 m j per pulse at a 10 to 50 Hz repetition rate with pulse durations on the order of 1 to 10 nsec. The 10 to 50 Hz repetition rate of Nd:Yag lasers yields At values which are typically too large (with regard to the basic definition of velocity given above) for m ost applications. Therefore, a pair of lasers is com m only used to provide the two successive light pulses (Eggels et al., 1993; Molezzi and Dutton, 1993). The light beam from the pulsed lasers is formed into a light sheet and focused at the region of interest in the flow field. Consider a pulsed laser with a 50 Hz repetition rate: the time between successive pulses would be 20 msec. In a flow where the mean velocity is say 1 m/s, a particle would travel approx­ imately 2 cm between light pulses. For m ost cases, this distance is far too large to consider

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the resultant velocity vector a point measurement. Alternatively if one is using two lasers, the pulse trains from the two lasers could be offset by 0.3 msec, thereby allowing the particle to travel approximately 0.3 mm between two successive light pulses. However, for low-speed flows, such as those occurring in electronic cooling applications, a single laser with a 50 Hz repetition rate may be used. If the m ean velocity is 2 cm/s, a particle would only travel approximately 0.4 mm betw een light pulses. Another possibility for these relatively low-speed flows is the beam from a continuous wave laser such as an argon-ion laser can be scanned through the flow field with a rotating mirror or galvanometer-type scanner. The shutter speed on the camera is controlled such that multiple exposures of the particle image, corresponding to successive scans of the laser, are captured on the recording medium (Rockwell, 1992; Towfighi and Rockwell, 1994; Lin and Rockwell, 1994).

4.26.3

Image recording

The light scattered by the seeding particles is captured on either photographic film or CCD array. The form er is referred to as photographic PIV (PPIV) and the latter is digital PIV (DPIV). The advantage of PPIV as compared with DPIV is that the resolution of PPIV is an order of magnitude greater than DPIV (see Adrian, 1991). Specifically, a 4 by 5 in. (100 by 125 mm) photographic film recorded w ith a magnification of 1:1 can provide 12,500 independent velocity vectors each with a spatial resolution of 1 by 1 mm over a 100 by 125 mm region in the flow. Alternatively, CCD sensors of 512 by 512 will provide less than 100 velocity vectors with a 1 by 1 mm spatial resolution and the field of view will be limited to ~ 5 by 5 mm. If one is willing to tolerate a larger measurement volume, the field of view can be increased accordingly. A significant advantage of DPIV over PPIV is the ease of use. With DPIV, the particle im ages are digitized and sent to the com puter during acquisition and are subsequently processed (W illert and Gharib, 1991). W ith PPIV, the photographic film is first developed and then a tedious process known as "interrogation" is required to digitize the negative. The interrogation procedure involves illum inating small regions of the photograph, capturing the im age onto a CCD array, and sending the digitized im age to the com puter for further processing (M einhart et al., 1993). Scanning the photographic plate could be an option. However, to achieve sim ilar resolution as that resulting from the process described above, that is, from PIV with a 1 by 1 mm interrogation region digitized into 64 by 64 intensity values, the scanner resolution required would be 1600 (25 x 64) dots/inch (DPI). PPIV is generally the preferred mode of PIV w hen attempting to resolve the smallest scale flow structures such as those inherent in turbulent flows. However, in most flow situations, including electronic cooling applications, the spatial resolution limitation of DPIV is not a serious factor and the ease of use makes DPIV the "tool of choice." Two successive images are required to determine the displacement vector of the marker, A s . The images are commonly recorded in single-frame, double-exposure mode w hen using PPIV or alternately in double-frame, single-exposure mode for DPIV. For the former, the shutter on the lens remains open for both laser pulses, thereby, superposing the particles image at x and at x + A s on a single photographic plate. For DPIV, the par­ ticles image at x and at x + A s are recorded on two separate frames of the CCD array. The double-fram e, single-exposure mode is not desirable for PPIV because of the inability to precisely align the two separate photographic plates in the film cartridge. W hen using DPIV, an important consideration is the framing rate of the camera. If one is using a single CCD array to acquire both images of the particles at t and t + At, then the m inim um At would be directly dependent upon the maximum framing rate of the camera. To utilize DPIV in higher-speed flows, a two-camera system could be used to

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achieve the desired At. The choice of At is dependent upon the magnitude of the average velocity and the desired spatial resolution and is discussed below in 4.27/1.

4.27 PIV image analysis The analysis of PIV images begins with subdividing the entire PIV image into small 'interrogation"' regions. As mentioned above, for PPIV the photographic plate must be developed and then digitized, whereas for DPIV the particle images are essentially digi­ tized during the acquisition stage. Figure 22 is an example of a single-frame, double­ exposed image taken in a 8 by 8 mm region of a turbulent boundary layer* A typical interrogation volum e would be a 64 by 64 pixel region of the image as shown by the enclosed area of the figure: this region is shown enlarged in the lower left-hand com er of the figure. As can be seen, each interrogation region contains several particle images. It has been shown by Adrian (1991) that the As determined, using the analysis techniques described below, represents an average displacement vector of all particles within the interrogation region. This is analogous to the spatial averaging effect over the m easure­ ment volume inherent to thermal anemometry and LDV techniques.

Single-frame, double-exposed image taken in a turbulent boundary layer with a single interrogation region highlighted and resultant two-dimensional auto-correlation field.

Figure 22

* From Ph.D. dissertation work by W deOjeda at HI (in progress).

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The accuracy of the velocity vector is dependent upon the accuracy with which A s and At can be determined. Typically At is known to within 0.1%; hence, the accuracy of V is mainly dependent upon the evaluation of A s . There are basically two methods in use to determine As : the auto-correlation and cross-correlation methods.

4.27.1

Au to-correla Hon

Consider the auto-correlation method. The interrogation region is subdivided into a N by N array of intensity values, 1 ( x ). 1 ( x ) is then sent to the host computer so that the discretely determined autocorrelation function R( s ) may be computed on the N by N array of intensity values as follows:

R{s) = j I(x )l(x + s)dx

(28)

The spatial autocorrelation is a function of the spatial offset ( s ) and provides quantitative inform ation about how well 1( x ) correlates with neighboring values of 1( x + s ) for all values of s . Since 1( x ) nom inally contains two images of each particle, within the given interrogation spot, w hich are separated by the displacement vector, As , one would expect a relatively large correlation coefficient at s = A s . As Adrian (1988) suggests, R( s ) includes contributions from the following:

R{s) = Rc{s) + R f {s ) + R d+{s ) + R d_(s ) + Rp{s)

(29)

where Rc( s ) is the convolution of the mean interrogation spot intensity, RF( s ) is a fluc­ tuation noise com ponent due to random pairing between particle images, RD+( s ) and Rd_( s ) are the positive and negative displacement peaks, respectively, due to the corre­ lation of particle pairs, and Rp( s ) is the self-correlation peak. Since the auto correlation is a symmetric function, the peaks, RD+( s ) and RD_( s ), are equal in magnitude and occur symmetrically about the origin. The self-correlation peak, Rp( s ), is centered at the origin and has a value of one at the origin ( s = 0) since every pixel is perfectly correlated w ith itself. An example of R( s ) for the 64 by 64 pixel inter­ rogation region highlighted in Figure 22 is given in the lower right-hand com er of the figure. The center self-correlation peak is obvious and the positive and negative displace­ m ent peaks are well above the background noise peaks. The vector from the origin to the centroid of RD+( s ) (or RD_( s )) is taken to be the displacement vector (A s ) used in determining V . Since the auto correlation coefficient is symmetric, the choice of RD+( s ) or RD_( s ) is based either on some a priori knowledge of the flow or an imposed image shift. If no regions of reversed flow exist within the entire imaged region, then the choice of RD+( s ) is valid. However, when flow fields with reversed flow regions are investigated, an imposed shift of the particles image at x + A x greater than IA x I is required to allow the investigator to measure reversed flow. The magnitude of the image shift is subsequently subtracted from the A s determined from RD+( s ) to yield the velocity vector. Birefringent crystals and rotating mirrors are two of the image-shifting techniques developed (Landreth and Adrian, 1988; Adrian, 1986) for this purpose. The im portance of m aximizing the displacement peak RD+( s ) (and RD_( s )) while m inim izing the noise peaks, RF( s ), is param ount to increasing the accuracy of the velocity vector. A sim ulation study by Keane and Adrian (1990) showed that optimal results are achieved if the time betw een the successive images, At, is chosen such that the particles

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will displace approximately 1/4 to 1/3 of the interrogation region from time t to t + At. If At is too small the displacem ent peaks will not be distinct from the self-correlation peak and if At is too large, a significant fraction of the particles within the interrogation region at time t will have traveled out of the region at time t + At. This will result in a decrease in the magnitude of the displacement peak. In addition, the size of the interrogation region is chosen based upon the desired spatial resolution, particle seeding density, and the magnitude of the velocity gradient within the interrogation region. The study by Keane and Adrian (1990) concluded that the interrogation region should contain between 10 and 20 particle pairs, and the variation of the velocity of the individual particles within a given interrogation region should not differ by more than 20%. Recall that the interrogation region is a small fraction (on the order of 1 by 1 mm) of the entire region of interest and hence, the variations of the m ean velocity within the entire region of interest can deviate by more than 20%. However, if the m ag­ nitude of the velocity gradient w ithin the relatively small interrogation region is too large, then the displacement peaks will be broadened and the magnitude of the peak will be decreased.

4.27.2

Cross-correlation

The cross-correlation technique is a method to improve the accuracy of the velocity vector. This technique reduces the self-correlation peak and increases the magnitude of the dis­ placem ent peak. The cross-correlation function, C( s ), is determined by

C(s) =

J

/,(x) I2(x )d x

(30)

where I f x ) and I2( x ) are two image fields within the larger PIV realization. With a priori knowledge of the flow, such as a m ean flow speed or imposed image shift, I2( x ) would be chosen with a corresponding spatial offset from I f x ). This would increase the chances that a particle's image at t in image field I f x ) would be located at t + At in image field I f x ) . For more details on the cross-correlation and auto-correlation methods, the reader is referred to Adrian (1991), Keane and Adrian (1990), and M einhart (1994).

4.28

How-to list for measurement

The application of PIV to electronic component cooling problems will be discussed in this section w ith respect to the exemplar problem shown in Figure 1. For this discussion the coordinate system is defined to be: x in the streamwise direction, z perpendicular to x and in the plane of the figure, and y in the direction perpendicular to the plane of the figure. The components of the velocity in the x, y, and z directions will be referred to as u, v, and w, respectively. W hen setting up the experiment one must keep in mind that optical access is required to place the light sheet in the appropriate plane and for recording the particle(s) images on the recording media. Test section walls fabricated from glass have worked well; however, Plexiglas is not recommended if one is using high-powered lasers. To investigate the x-z plane, the light sheet could be brought into the test area, parallel with the circuit boards, at the y location of interest, by entering and exiting through the glass sidewalls. The recording optics could be placed either above or below the printed circuit boards to record the particle displacements in the x-z plane. The location of the recording plane with respect to the field of view will depend upon the focal length of the recording optics and upon the desired magnification.

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The magnification, M, is defined in the conventional manner as M = —■ —(see Figure o

21). The dimensions of the interrogation region on the film are related to the flow field dimensions by the magnification. Namely, the interrogation region dimensions on the film are equal to the effective interrogation region (spatial resolution in the flow field) multiplied by the magnification. The calibration of the PIV system amounts to determining the magnification of the recording system. This is easily accomplished by recording the image of a precision ruler placed in the plane of the pulsed light sheet. With the magnification and interrogation region size determined, the required time betw een the two laser pulses can be calculated. Using the average velocity as a convection velocity, At is selected such that the particles will travel approximately 1/4 to 1/3 the length of the interrogation region on the CCD array (or film). In general region 0.3 - M - size of effective interrogation region tJB 0.3 *size of CCD interrogation _ = _

The next consideration is the seeding particles. For air flow, atomized olive oil or a 10%-90% polyethylene-glycol-water mixture has been shown to work well. Commercial atomizers such as the TSI atomizer provides particles with approximately a 1 jam mean diameter. For water flows, neutrally buoyant polystyrene particles with a mean diameter of approxim ately 10 jam have been used successfully. The seeding density is determined by the desired spatial resolution of the velocity measurement. That is, the size of the interrogation region on the CCD array (or film) should contain 10 to 20 pairs of particles. Finally, since electronic component cooling flows often have regions of flow reversal, a means to shift the image of the particles at t + At is required to resolve the correct direction of the particle's displacement. As discussed above, this is a necessity based on the sym m etry property of the FFT. The magnitude of the image shift is related to the m axim um magnitude of flow reversal. For example, if urev is the maximum negative velocity in the region of interest, the required magnitude of the image shift on the recording media would be M* I urev I *At. Once the particle images are recorded they are digitized and sent to a host computer and subdivided into interrogation regions. Two-dimensional FFTs are performed on each interrogation region to compute either the auto-correlation or the cross-correlation of the image field. The resultant two-dim ensional correlation is searched for the displacement peak and the distance from the origin is divided by the magnification, M, to yield the average displacem ent vector, A s, of the particles contained within the flow field interro­ gation region. A similar procedure would be followed if one were to investigate the x-y plane. The light sheet could be brought in through the top or bottom of the test section at the desired z position, with the recording optics focused on the flow field through the sidewalls of the test section.

4.29

Sample PIV results

Figure 23 represents the mean-removed velocity field in turbulent flow over a flat plate. Two com ponents of the velocity vectors were determined using the single-frame, double­ pulse mode of PIV in a two-dimensional plane. Two Nd:Yag lasers were used to provide the two light pulses and a time delay of 50 jasec betw een the two pulses was chosen based upon the mean flow speed and an interrogation size of 1 by 1 mm. Each interrogation region was digitized and a 128 by 128 two-dimensional auto-correlation was performed

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xfrm) Sample PIV results from a turbulent Mow illustrating the capabilities of PIV in resolving instantaneous spatial structures, Figure 23

on the digitized image, The advantage of PIV over conventional velocimetry techniques is clearly illustrated by the results in Figure 23; namely; the instantaneous spatial features of the flow would not be available using a single-point, time-resolved, measurement technique,

4.30 Equipment required for PIV measurements The essential com ponents for the most basic PIV system can he summarized as T 2, 3* 4, 5,

Laser Optics Particles or particle (seeding) generator Recording camera: CCD array or photographic camera Computer for acquisition and processing of PIV images

It is possible to design and construct a PIV system. However, TSI and Dantec manu­ facture a “'turn key"' system which includes the hardware and software necessary for acquisition and processing of PIV realizations. The address for both companies can be found in the Appendix.

4.31

Terms defined

Dou b 1e- fra me, si n g le-e x pos ure D P iv FFT Interrogation spot (or region)

Laser repetition rate

Particle images at t and t 4 At recorded on two separate frames of ihe recording medium. Digital particle im age velocim etry; particle im ages recorded digitally using a CCD array Fast Fourier transform A "sm all" region of the photograph (which includes approximately 10 to 20 particle images) over which an average velocity vector is determined Lime between successive pulses lor pulsed lasers

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Thermal measurements in electronics cooling

Magnification (M) Planar PIV PPIV Recording medium Seeding particle Single fram e, double-exposure Stereo PIV

The magnification of the PIV acquisition system, M = di/d0 Images of particles in a two-dimensional plane recorded by a single camera P h o to grap h ic p article im age v elo cim etry: p article images recorded on photographic film CCD camera or photographic film M icron-sized particle used to follow the flow and scatter light Particle images superposed at both t and t + At on a single frame of the recording m edium Images of particles in a two-dimensional plane recorded by two (stereo) cameras

4.32 Nomenclature di dG

Distance from lens plane to image plane (recording plane) Distance from lens plane to object plane (flow field plane)

I (x) R( s ) s A s ( x ,t)

Intensity of the recorded particle images w hich is a function of space Auto-correlation coefficient Spatial offset between two points Displacem ent vector of seeding particles which in general is a function of both space and time Elapsed time betw een light pulses Thickness of pulsed light sheet M aximum negative velocity in region of interest Convection velocity of particles

At Az0 urev Uc V ( x ,t)

Velocity of seeding particles w hich in general is a function of both space and time

Appendix: Velocity meter vendors Measurem ent Solutions Inc. 36 Jaconnet St. Newton, MA 02161 (617)-320-0909 TSI Incorporated 500 Cardigan Road P.O. Box 43394 St. Paul, MN 55164 (612)-490-2811 DANTEC Measurem ent Technology Inc. 777 Corporate Dr. M ahwah, NJ 07430 (201)-512-0037

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References Adrian, R. J., Statistiscal properties of particle image velocimetry measurements in turbulent flow, in Laser Anemometry in Fluid Mechanics, III, LADOAN, Instituto Superior Tecnico, Lisbon, Por­ tugal, 1988, 115-129. Adrian, R. J., Image shifting technique to resolve directional ambiguity in double-pulsed velocimetry, AppL Opt, 25(21), 3855-3858, 1986. Adrian, R. J., Particle-imaging techniques for experimental fluid mechanics. Annu. Rev. Fluid Mech.f 23, 261-304, 1991. Adrian, R. J. and Yao, C.-S., Pulsed laser technique application to liquid and gaseous flows and the scanning power of seed materials, AppL Optics, 24, 44-52, 1985. Adrian, R. J., Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry vs. particle image velocimetry, AppL Optics, 23,1690-1691,1984. Adrian, R. J., Laser velocimetry, in Fluid Mechanics Measurements, Goldstein, R. J., Ed., Hemisphere Publishing, Washington, D.C., 1983, 155-244. Ali, S. K., Instability Phenomena in a Two-Dimensional Slit-Jet Flow Field, PhD Thesis, Michigan State University, 1991. Azar, K., Thermal design considerations for multichip module applications, in Multichip Module Technologies and Alternatives: The Basics, Doane, D. A. and Frazon, P. D., Eds., Van Nostrand Reinhold, New York, 1993, 569-613. Azar, K. and Russell, T. E., Design of a technique for calibration of hot wire anemometers for velocity measurement in natural and mixed convection flow regimes, ASME 3rd Triannual International Conference on Fluid Control, Measurement and Visualization, San Francisco, CA, 1991a. Azar, K. and Russell, E. T., Effect of component layout and geometry on the flow distribution in electronic circuit packs, ASME }. Electron. Packaging, 113, 50-57, 1991. Blackwelder, R. F., Hot-wire and hot-film anemometers, Methods Exp. Phys. Fluid Dynamics, 18, 259-314, 1981. Blevins, R. D., Applied Fluid Dynamics Handbook, Van Nostrand Reinhold, New York, 1984. Bradshaw, P., An Introduction to Turbulence and Measurement, Pergammon Press, 1971. Bremhorst, K., Effect of Fluid Temperature on Hot-Wire Anemometers and an Improved Method of Temperature Compensation without Use of Small Signal Sensitivities, /. Phys. E: Sci. Instrum., 44-49, 1985. Brunn, H. H., Hot-Wire Anemometry, Oxford University Press, 1995. Chevray, R. and Runi, N. K., Simultaneous Measurements of Temperature and Velocity in Heated Flow, Rev. Sci. Instrum., 43, 1417-1421, 1972. Collis, D. C. and Williams, M. J.,/. Fluid Mech.f 6, 357, 1959. Comte-Bellot, G., Hot-wire anemometry, Annu. Rev. Fluid Mechanics, 209-231, 1976. Davis, D. G. and Gessner, F. B., An improved single rotatable hot-wire probe for Reynolds stress measurements, in Fluid Measurements and Instruments, Morrow, T. R., Morrison, G. L., and Gore, R. A., Eds., FED Vol. 183, American Society of Mechanical Engineers, New York, 1994, 53-58. DeGrande, G. and Kool, P. J., Improved experimental method to determine the complete Reynolds stress tensor and a single rotating slanting hot-wire,/. Phys. E, 14, 196-201, 1987. Drain, L. E., The Laser Doppler Technique, John Wiley & Sons, New York, 1980. Drubka, R. E., Tan-atichat, J., and Nagib, H. M., Analysis of Temperature Compensating Circuits for Hot-Wires and Hot-Films, DISA Inf., 22: 5-14, 1977. Durst, F., Melling, A., and Whitelaw, J. H., Principles and Practice of Laser Doppler Anemometry, Academic Press, New York, 1976. Eggels, J. G. M., Westerweel, J., Nieuwstadt, F. T. M., and Adrian, R. J., Comparison of vortical flow structures in DNS and PIV studies of turbulent pipe flow, in Near Wall Turbulent Flows, Elsevier, Amsterdam, 1993, 413-422. Falco, R. E. and Chu, C. C., Measurements of two-dimensional fluid dynamic quantities using a photochromic grid tracing technique, Proc. SPIE, 814: 706-710, 1987. Falco, R. E. and Nocera, D. G., Quantitative multipoint measurement and visualization of dense liquid solid flows using laser induced photochemical anemometry, (LIPA), in Particulate TwoPhase Flow, Rocco, M. C., Ed., Butterworth-Heinemann, London, 1992, 59-126.

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Foss, J. F., A Controlled Sudden Expansion, TSFL Report No. R-041, 1995. Foss, J. F., Vorticity, circulation and vortices, ASME FED 238: 83-96, 1996. Foss, J. F., Klewicki, C. L., and Disimilie, R J., Transverse Vorticity Measurement Using an Array of Four Hot-Wire Probes, NASA CR 178098, 1986. Foss, J. F., Wallace, J. M., and Wark, C. E., Vorticity measurement, in Handbook of Fluid Dynamics and Fluid Machinery, Schetz, J., Ed., John Wiley & Sons, New York, 1995. Fridman, J. D., Young, R. M., Seavey, R. E., and Orloff, K. L., Modular high accuracy tracker for dual channel laser Doppler velocimeter, Proceedings of the Minnesota Symposium on Laser Anemometry, 1975, 485-503. Gendrich, C. P., Koochesfahani, M. M., and Nocera, D. G., Analysis of molecular tagging velocimetry (TV) images for obtaining simultaneous multi-point velocity vectors, Bull Am. Phys. Soc.f 39(9), 1980, 1994. Gould, R. D. and Loseke, K. W., A comparison of four velocity bias correction techniques in laser Doppler velocimetry, J. Fluids Eng., 115, 508-514, 1993. Haw, R. C. and Foss, J. F., A facility for low speed calibrations, mThe Heuristics of Thermal Anemometry, Stock, D. E., Sherif, S. A., and Smits, A., Eds., ASME FED, 97: 29-34, 1990. Honkan, A. and Andreopoulos, J., Direct calibration mapping and data analysis, in Triple Wire Anemometry; Thermal Anemomety, Stock, D. E., Sharif, S. A., Smits, A. J., and Davidson, J., FED Vol 167, ASME, New York, 1993, 67-78. Keane, R. and Adrian, R. J., Optimization of particle image velocimeters. Double pulsed systems, Meas. Sci. Technol, 1, 1202-1215, 1990. King, L. V., Philos. Trans. R. Soc. London Ser. A., 214, 373^ 32, 1914. Koochesfahani, M. M., Gendrich, C. P., and Nocera, D. G., A new technique for studying the Lagrangian evolution of mixing interfaces in water flows, Bull. Am. Phys. Soc., 38(12), 2287,1993. Kovasznay, L. S. G., Favre, A., Buchave, P., and Fulachier, L., in Proceedings of the Dynamic Flow Conference 1978: on Dynamic Measurements in Unsteady Flows, Hansen, B. W., Ed., Marseille France and Johns Hopkins Univ. Baltimore, MD, 1978. Landreth, C. C. and Adrian, R. J., Electrooptical image shifting for particle image velocimetry,Appl. Opt., 27(20), 4216-4220, 1988. Larouse, A., Martinuzzi, R., and Tropia, C., Flow around surface-mounted, three-dimensional ob­ stacles, 8th International Symposium on Turbulent Shear Flows, Munich, FRG, September 9-11, 1991, Springer-Verlag, New York, 1993. Lekakis, I. C., Adrian, R. J., and Jones, R. G., Measurement of velocity vectors with orthogonal and non-orthogonal triple-sensor probes, Exp. Fluids, 7, 228-240, 1989. Lin, J. C. and Rockwell, D., Cinematographic system for high-image density particle image veloci­ metry, Exp. Fluids, 17, 110-114, 1994. Martinuzzi, R., Experimentelle Untersuchung der Umstromung Wangebundener, rechteckiger primatischer Hindermisse, Doktor, Thesis, Univ. of Erlangen-Niimburg, 1992. Martinuzzi, R. and Tropea, C., The flow around surface-mounted, prismatic obstacles placed in a fully developed channel flow, ASME J. Fluid, Eng., 115, 85-92, 1993. McLaughlin, D. K. and Tiederman, W. G., Biasing correcting for individual realization of laser anemometer measurements in turbulent flows, Phys. Fluids, 16, 2082-2088, 1973. Meinhart, C. D., Investigation of Turbulent Boundary Layer Structure Using Particle-Image Veloci­ metry, Ph.D. thesis, Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, 1994. Meinhart, C. D., Prasad, A. K., and Adrian, R. J., Parallel digital processor system for particle image velocimetry, Measurement Sci. Technol, 4, 619-626, 1983. Meynart, R., Speckle velocimetry study of vortex pairing in a low-Re unexcited jet,Phys. Fluids, 26, 2074-2079, 1983. Miles, R. B., Connors, J. J., Markovitz, E. C., Howard, P. J., and Roth, G. J., Instantaneous profiles and turbulence statistics of supersonic free shear layers by Raman excitation plus laser-induced electronic fluorescence (RELIEF) velocity tagging of oxygen, Exp. Fluids, 8, 17-24, 1989. Molezzi, M. J. and Dutton, J. C., Application of particle image velocimetry in high-speed separated flows, AIAA Journal, 31(3), 438^ 46, 1993. Morel, T., Design of two-dimensional wind tunnel contractions,/. Fluids Eng., 371-378, 1977.

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Morel, T., Comprehensive design of axisymmetric wind tunnel contractions,/. Fluids Eng., 225-233, 1975. Orloff, K. L., Laser Doppler anemometry diagnostics in unsteady flows in Proceedings of the Dynamic Flow Conference 1978: on Dynamic Measurements in Unsteady Flows, Hansen, B. W., Ed., Marseille France and Johns Hopkins University, Baltimore, MD, 1978. Panton, R. L., Incompressible Flow, John Wiley & Sons, New York, 1984. Papoulos, Probability Random Variables and Stochastic Processes, McGraw-Hill, New York, 1965. Pessoni, D. H. and Chao, B. T., A simple technique for turbulence measurements in nonisothermal air flows, Proc. 5th Int. Heat Transf. Conf. Tokyo (ISME), 5, 278-82, 1974. Potter, M. C. and Foss, J. F., Fluid Mechanics, Ronald Press (now published by the Great Lakes Press Co., Okemos, MI 48864), 1975. Prasad, A. K. and Adrian, R. J., Stereoscopic particle image velocimetry applied to liquid flows,Exp. Fluids, 15, 49-60,1993. Prasad, A. K., Adrian, R. J., Landreth, C. C., and Offutt, P. W., Effect of resolution on the speed and accuracy of particle image velocimetry interrogation, Exp. Fluids, 13, 105-116, 1992. Rockwell, D., Quantitative visualization of Bluff-body wakes via particle image velocimetry, inBluffBody Wakes, Dynamics and Instabilities, Springer-Verlag, New York, 1992, 263-270. Simpkins, P. G. and Dudderar, T. D., Laser speckle measurement of transient Benard convection, }. Fluid Mech., 665-671, 1978. Stewart, R. W., 21626 Turbulence, Film Produced by NCFMF/EDC, Encyclopaedia Britannica Cor­ poration, Chicago, IL. Towfighi, J. and Rockwell, D., Flow structure from an oscillating nonuniform cylinder: generation of patterned vorticity concentrations, Phys. Fluids, 6(3), 531-536, 1994. Ullrich, S. A., Development of a Particle Image Velocimetry Interrogation Systems, M.S. thesis, Department of Mechanical and Aerospace Engineering, Illinois Institute of Technology, Chicago, 1993. Urushihara, T., Meinhart, C. D., and Adrian, R. J., Investigation of the logarithmic layer in pipe flow using particle image velocimetry, Near Wall Turbulent Flows, Elsevier, Amsterdam, 1993,443^46. Whiffen, M. C , Polar response of an LV measurement volume, in Minnesota Symp. on Laser Anemometry Proc., Eckert, E. R. G., Ed., University of Minnesota, Department of conferences, Minneapolis, 1975, 592-592. White, F. M., Fluid Mechanics, 3rd ed., McGraw-Hill, New York, 1994. Willert, C. E. and Gharib, M., Digital particle image velocimetry, Exp. Fluids, 10, 181-193, 1991. Yeh, Y. and Cummins, H. Z., Localized fluid flow measurements with a He-Ne laser spectrometer, AppL Phys. Lett., 4, 176-178, 1964.

chapter five

Temperature measurement in electronic cooling James N. Sweet 5.1 5.2

5.3

In troduc tion.....................................................................................................................................168 Temperature and heat transfer................................................................................................. 169 5.2.1 General con cep ts..............................................................................................................169 5.2.2 Therm odynam ic definition of tem perature.............................................................169 5.2.3 H eat transfer considerations....................................................................................... 171 5.2.4 General temperature m easurement p ro b lem ........................................................ 173 5.2.5 Temperature transd ucers..............................................................................................175 Specific temperature sensors and measurement tech niq u es....................................176 5.3.1 Resistance therm om eters..............................................................................................176 5.3.1.1 General description........................................................................................ 176 5.3.1.2 General use considerations..........................................................................178 5.3.1.3 Exam ple of u s e ................................................................................................178 5.3.1.4 C alibration.........................................................................................................181 5.3.1.5 How to use a resistance therm om eter.....................................................181 5.3.2 T herm ocouples.................................................................................................................181 5.3.2.1 General description........................................................................................ 181 5.3.2.2 Types of therm ocouples............................................................................... 184 5.3.2.3 Calibration and error an aly sis...................................................................184 5.3.2.4 How to use therm ocouples.........................................................................186 5.3.3 Sem iconductor d evices.................................................................................................. 187 5.3.3.1 General description........................................................................................ 187 5.3.3.2 Exam ples of use and calibration................................................................188 5.3.3.3 Therm al resistance m easurem ent..............................................................190 5.3.3.4 Sem iconductor device u sag e.......................................................................191 5.3.4 Radiation therm om etry................................................................................................. 191 5.3.4.1 General description........................................................................................ 191 5.3.4.2 Infrared temperature m easurem ent......................................................... 191 5.3.4.2.1 Backgrou nd ....................................................................................191 5.3.4.2.2 Types of infrared systems and detectors...............................193 5.3.4.2.3 Measurem ent sy stem s................................................................195 5.3.4.2.4 C alibration...................................................................................... 196 5.3.4.2.5 Commercial infrared imaging system s................................. 197

0-8493-3279-6/97/$0.00+$.50 © 1997 by CRC Press LLC

167

Thermal measurements in electronics cooling

168 5 .3 .4 3

Optical probe system s.................................................................................... 197 5.3.4.3.1 B ackgrou nd .....................................................................................197 5.3.43.2 Probe typ es......................................................................................199 5.3.43.3 C alibration....................................................................................... 199 5 3 .4 3 .4 Optical probe u sag e..................................................................... 199 5.3.5 Bulk effect d ev ices........................................................................................................... 199 5.3.5.1 Liquid cry sta ls.................................................................................. 199 5.3.5.1.1 General considerations................................................................199 5.3.5.1.2 Liquid crystal usage..................................................................... 201 5 3 .5 .2 Thermochromic m aterials............................................................................. 201 5.4 Specific measurem ent problem s.............................................................................................. 201 5.4.1 Device tem perature ....................................................................................................202 5.4.2 Board or substrate tem perature....................................................... 202 204 5.4.3 Fluid tem peratu re.................................. 5.4.4 Transient vs. steady-state m easurem ents................................................ 205 5 .4.4.1 Situations in which the same solid-state junction device is used for heat input and therm om etry................................... 205 5.4.4.2 Situations in which it is desirable to learn something about the location of various components of the thermal resistance.............................................................................................206 5 .4 .4 3 Transient applications.................................................................................... 208 5.5 Sum m ary.................. 208 5.6 For further stu d y ............................................................................................................................208 5.7 Defining term s................................................................................................................................ 210 References................................................................................................................................................... 212

5.1 Introduction Temperature measurement plays an im portant role in determining and measuring the heat transfer characteristics of an electronic system. The basic problem or situation we are trying to understand is how large a temperature excursion will be produced for a given power input from the integrated circuits (ICs) or other active devices in the electronic system. In general, the input power to the system can be measured very accurately. However, measurem ent of temperatures in the devices or other parts of the system depends on both the nature of the therm om eter or thermal sensor as well as the specific conditions under which the m easurement is to be made. This temperature measurement problem is the subject of this chapter. We have an intuitive idea of w hat the concept of tem perature is and of how it is m easured. From childhood we have observed therm om eters and felt w hat it is like to be hot or cold. However, in experim entally studying heat transfer in com plex system s, it is useful to have a solid foundation in the more quantitative concepts of tem perature and to know how it can be m easured using various types of therm om eters or, more generally, tem perature sensitive devices. Electronic devices or system s involve m any com plex m aterials such as glass-epoxy printed circuit boards, m oving air, pumped fluids, and integrated circuits with localized heat sources. The m easurem ent of tem per­ ature in each of the above m aterials involves use of special therm om eters or therm al transducers and special techniques. The major goal of this chapter is to acquaint the reader with the different m ethods com m only used to measure temperature in electronics systems. In Section 5.2 general concepts of heat transfer and the temperature measurement problem are discussed. The

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major content of this chapter is contained in Section 5.3 where specific types of temperature sensors are reviewed. For each sensor, the initial general discussion covers the theory of operation of the specific sensor. Following this general description, we present one or more examples of the use of the sensor in actual measurements. Readers who are most interested in practical how to information about use of a sensor are urged to go to the end of the relevant sensor section where a discussion of how to use the sensor is given in tabular form. In Section 5.4, specific measurement problems in electronic cooling are discussed. Many of these problems are discussed in more detail elsewhere in this volume. Finally, in the summary, Section 5.5, some specific recommendations are given for specific techniques or sensors which can be used for various temperature measurement problems. This treatment is not meant to be exhaustive and it does not cover every known or reported temperature m easurement technique. Rather, I discuss the m ost used methods and give some illustrative examples. For further details on these methods, as well as methods not discussed, the reader is urged to consult the references and Section 5.6.

5.2

Temperature and heat transfer

5.2.1

General concepts

The concepts of temperature and heat transfer are intimately linked, as the reader undoubt­ edly knows from personal experience. If heat is transferred to a body, the temperature increases. The rate of increase is dependent on the heat or power input, the resistance to heat flow between the body and the source, and the size and heat capacity of the source and body. In this section, we discuss the general concepts of temperature and heat transfer which are useful for or needed to understanding the detailed discussions of the different measurement techniques.

5.2.2

Thermodynamic definition of temperature

In most introductions to the concept of temperature, a model system is examined which is considered to be isolated from its surroundings. By isolated, we mean that the system under study cannot exchange energy with its surroundings. Although there is no way to actually m ake such a system, it is possible to experimentally approximate one. For exam­ ple, a container of gas which is enclosed in a box with mirrored walls and surrounded by a good insulating material would be such a m odel system. Temperature is then defined as a property or param eter of this system such that (Reif, 1965, pp. 103-106): 1. If two systems separately in equilibrium are characterized by the same value of the parameter, then the systems will remain in equilibrium with the same value of the parameter when they are brought into thermal contact. 2. If the two system s are characterized by different values of the parameter, then they will not rem ain in equilibrium when brought into therm al contact with each other. The above definition of the temperature motivates the idea of the temperature being a parameter which is proportional to something like the average energy per particle or per constituent of the system. If two systems of identical particles, such as two boxes of N 2 gas, have the same temperature, T, then it appears reasonable that the average energy per molecule in the two systems would be the same. It can be shown from the kinetic theory of gases that the atoms in a monatomic gas such as Ar have an average energy per molecule, e, given by (Reif, 1965, pp. 239-242):

Thermal measurements in electronics cooling

170

e = ? k nT

(1)

In Equation (1), T is the absolute temperature in degrees Kelvin (K) and kB is the Boltzm ann constant, kB = 1 3 8 x 10“23 J/K. At room temperature, T = 295 K, kBT ~ 0.025 electron volts (eV) = 4 x 10-21 J. All systems are composed of some sort of particles (atoms, electrons, photons), and these particles have a distribution function in energy which depends on the absolute temperature. For example, in the case of the monatomic gas, the num ber of atoms per unit volume, dN, with energies in the range E to E + dE is given by the M axwell-Boltzm ann distribution function (Sears, 1965, pp. 239-241).

d N (E ,T ):

2 N_o (k BT)"3/2E V2 exp(-E/kBT)dE . VJt

(2)

In Equation (2), N 0 is the total num ber of atoms per unit volume. Equation (2) illus­ trates the general principle that the particle energy distribution function includes the absolute temperature as a parameter. The function dN(E,T)/dE from Equation (2) is shown graphically in Figure 1. It may be shown from Equation (2) that the energy corresponding to the peak in the distribution, E , is kBT/2 while the average energy is, from Equation (1), Eavg = 3kB/2. Figure 1 illustrates the concept that in an equilibrium situation, all possible energies are present. The distribution function has a long tail of high-energy particles w hich have energies considerably in excess of the average energy.

E^D Figure 1 Maxwell Boltzmann energy distribution function characterizing the distribution of en­ ergies in a gas of single atoms like Ar. The average energy characterizing this distribution function is given by Equation (1).

Although temperature as defined above applies to isolated systems, it can also be applied to system s w hich are not isolated. In this situation, if we examine a sufficiently small part of the system, that part will have an essentially uniform temperature and will have all the properties of an isolated system. In general, for nonequilibrium systems in w hich heat is flowing in and out and the temperature is changing with time, the energy distribution function depends on both position and time. However, for sufficiently small

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171

volum e elements AV, and time intervals At, the distribution function may be considered as essentially constant. It is given by a function such as that in Equation (2), where the temperature is now considered to he a function of position and time, T -> T( f ,t), with the position vector r characterizing the location of the centerpoint of the volume elem ent AV. In this w ay the concept of the temperature of an isolated system in thermal equilibrium can be taken over to system s which are not isolated nor in thermal equilibrium. For the remainder of this chapter, we shall consider the temperature to he a well-defined system property which may be a function of time and vary from point to point in the system. In the m easurement process, it is important to have some knowledge of this variation so that the transducer and measurem ent system time response characteristics may be chosen appropriately

5 .2 3

Heat transfer considerations

As stated above, the concept of temperature measurement is intimately linked with the fundamentals of heat transfer. If we have two isolated bodies or systems, one at temper­ ature T :, and one at temperature T , and they are brought into some sort of thermal contact, heat q will flow from the hotter body to the colder body until they reach thermal equilib­ rium at some intermediate temperature, T f. Such a system is illustrated schematically in Figure 2. Depending on the nature of the systems and the material in the intervening space between the systems, heat will flow by one or more of the conventional mechanisms: conduction. am vecfion t or radial ion.

•

fa)

*

T( (b) T2-*T , ~AT* —Tr Ti-VT^+AT, = Figure 2 (a) Two isolated systems, each in thermal equilibrium, one characterized by a temper­ ature Tf and the other by T > Tv (b) The two systems after a thermal link is established which allows heat transfer. Heat flows from the hot to the cold system through the link until equilibrium: is again reestablished. The hotter body decreases in temperature by AT* while the colder body increases by ATXand both bodies arrive al the same final temperature Tr

Conduction is a mechanism by which energy is transferred through direct contact of some type. For example, if the two systems were blocks of solid material such as silicon and were placed in contact, then the vibrating molecules at the contact surface in the hot body would lose some of their energy to molecules in the cold body, resulting in an energy flow from hot to cold. If the bodies were separated but connected by a gaseous material such as air, conduction from the hot body would heat the nearby air which in turn could flow over the cold body and heat it. This is an example of convective heat transfer. Finally, even if the two bodies were in a vacuum, the two bodies would exchange energy through thermal radiation. Since the energy radiated per unit time from the hot body would be greater than that radiated from the cold body; the cold body would warm while the hot body cooled. This Is an example of radiative heat transfer. All of these mechanisms play a role in various types of thermometry used in electronic cooling experiments.

172

Thermal measurements in electronics cooling

Therm ometry and heat transfer are intimately related because the mechanics of energy transport from the sample to the therm om eter or temperature sensing device determine both how rapidly the thermometer com es into equilibrium with the sample and how large a temperature drop may exist betw een the temperature at the sensitive element of the therm om eter and that at the sample position whose temperature is being measured. Thus, in order to understand the functioning of a temperature sensing device, it is necessary to understand how heat is transported to the sensor. For temperatures T1 and T2 which are not too different, the heat transfer in a wide variety of situations can be characterized by N ew ton's law of cooling (Eckert and Drake, 1972, pp. 27-29). q = h(T2 - T 1)

(3)

In Equation (3), q is the heat transferred per unit time and unit area with units of pow er per unit area (W/m2), while h is called the heat transfer coefficient with units W /m 2*K. Much w ork in heat transfer has been devoted to the subject of finding expressions for h as a function of the variables in the problem. In general, h is temperature dependent and depends on the nature of m aterials and joints between the bodies. If the temperatures are changing w ith time, Equation (3) still applies but q, Tl7 and T2 will all be functions of time. In certain cases, h may be derived from theoretical considerations but in many complex situations, h is found experimentally. A thorough discussion of the subject of heat transfer coefficients as they relate to electronic cooling may be found in a recent series of books on the subject (Bar-Cohen and Kraus, 1988; 1990; 1993).

Figure 3 Heat transfer by conduction along a bar with length I and cross-sectional area A. The heat flux q (W /m 2) is uniform in the bar and directed along the axis. The thermal resistance of the bar is given by R = 1 / Ak.

One situation w hich occurs frequently is that of axial conduction through a uniform material or bar of length i and cross sectional area A = wt, where w = bar width and t = bar thickness, as illustrated in Figure 3. In this case, if T2 and are the temperatures of the ends of the bar, then h is given by the formula in Equation (4): h = k/€

(4)

where k is the thermal conductivity of bar material. The total heat flow in the bar in W is given by P = qA, or P = hAAT

Chapter five:

Temperature measurement in electronics cooling

173

where AT - T 2 - T v The quantity kA/C has units of W/°C and is called the

thermo!

conductance. In most situations in electronic cooling, the power P is known and the quantity desired is AT In this case, Equation (5) is written with P as the independent variable, AT =* ( ( /AR)P, where the quantity ( / Ak is called the thermal resistance in CC/W. This thermal resistance is analogous to electrical resistance, with temperature rise being equivalent to voltage and heat flow rate or power being analogous to current. The analogous relations between electrical and heat current flow are shown in Table 1. This table shows, for example, that electrical current, I, is equivalent to thermal powder, P, and electrical voltage, V, is equivalent to temperature, T Table 1 Analogies Between Steady-State Heat Flow and Electrical Current Transport

Parameter

Electric current flow

Current Current density-current/unit area Potential or temperature Conductance or conductivity Resistance - R ' Current-potential (Temp) relation

52A

Heat flow

1 (A) j (A /m 3)

PiVV) q (W/m*)

V (V)

T fC ) or (K) k (W /nvK) R - f/(A k ) f C /W ) AT - PR (CC)

a (Mho or £T) R = f /(A a) [Q) AV ~ IR (V)

General temperature measurement problem

A model representing, in an approximate way, the general temperature measurement problem is illustrated schem atically in Figure 4, 'The model temperature sensing system shown in Figure 4 is not inclusive of every possible temperature measurement process hut it does typify many of the processes found in electronics cooling measurements, We shall refer to this figure and the quantities in it as we discuss the different techniques. The sam ple or system S under study has a temperature which depends on the position in the sample F „ and the time t, denoted by T( f s,t)> In an experimental electronics cooling measurement, the "system " under study may be a component such as an integrated circuit, a subassembly such as a printed circuit board with heat producing ICs, or a full assembly such as a chassis with circuit hoards, fans, etc, The "sample"" represents that part of the system for which the temperature is being measured. It may be, for example, an IC heat source, a part of a circuit board, or the air at some position in the chassis. Tf

Sensor

■FWii System*

RTfet))

Sample - S

Sensor body Amplifier Probe or & transducer Readout

Figure 4 Diagram of the general temperature measurement process. It is desired to measure the sample temperature at the point r .v The sensor system is the portion in the dashed outline. The transducer is in thermal contact with the system under study at the point f ,> The transducer output is some quantity f{T) whose value depends on the transducer temperature, TD> In electronics cooling problems, the quantity of interest is usually the temperature rise with respect to some system ambient temperature, T,. This temperature increase in the

Thermal measurements in electronics cooling

174

sample or system above Ta is caused by the production of power P0 somewhere in the system. Hence the temperature rise in the sample is proportional to P0/and so we can write: T(rs , t)

Po0 r(rs , t) + Ta

(6)

where the quantity 0r represents the temperature rise produced by a unit power (P0 = 1 W) input into the sample. 0r is usually called the thermal resistance of the system because it represents the temperature rise above ambient per unit power input. We wish to measure the temperature of this sample at some p o in t say rsl with a thermal sensor system and probe of some sort. Because of probe positioning errors and possibly the finite size of the probe, the temperature actually being sampled is at some other nearby point rs2 or is the average over some region of the sample and the nearby surroundings. This introduces a measurement error given by AT = T( rs2 ,t) - ( rsl,t). In addition, there may be an intrinsic thermal resistance between the probe and the desired sample point, rsl. In both cases, the temperature difference or error is proportional to the source power, so it may be associated with a thermal resistance, R 12, as shown in Figure 4. This type of error typically occurs in the m easurem ent of a package surface tem perature in a flowing airstream . If a therm ocouple bead is attached to the package with epoxy, it will actually m easure a tem perature in the epoxy w hich is interm ediate betw een the true package surface tem perature and the air tem perature adjacent to the package surface. The surface tem perature m easurem ent error could be m inim ized by drilling a small hole in the package and epoxying the bead in the hole and through use of therm ally conducting epoxies. The sensor itself may be a complex system, but in many cases it can be represented by the com ponents shown in the dashed boundary of Figure 4. A thermal resistance of magnitude Rc connects the probe to the sensor or detector body w hich has a mass m, specific heat Cp, and a very large thermal conductivity kD —> . This is an assumption associated with an "id eal" sensor which may not be satisfied in an actual situation. The sample is assumed to be tied to the ambient environment through a thermal resistance, RgA, while the sensor body is thermally connected to the ambient environment through a thermal resistance, RDA. In actual cases, these are distributed resistances but for purposes of gaining an understanding of temperature probe systems it is reasonable to consider them as single discrete thermal resistors. Heat that flows from the sample through the sensor to ambient via RDA can produce an error in the temperature measurement by reducing the sample temperature at the probe location below the value it would have if the probe were absent. In steady state, dT(rsl,t)/dt = 0, the sensor will come to the constant temperature:

(7)

c

■DA

Equation 7 illustrates the important points that, to minimize the difference between Td and T( rs2), we want the probe-sensor body resistance, Rc, to be as small as possible and the sensor body to ambient resistance, RDA, to be as large as possible. In a transient situation, either the sample power may be varying or the connection between the probe and the sample is suddenly established at t = 0 and a finite time is required to heat the sensor mass to the steady-state temperature. In this second case, an am ount of heat dQ(t) flows into the sensor body during the time dt and, assuming RDA —» oo, this is related to the sensor temperature rise by

Chapter five:

Temperature measurement in electronics cooling dQ(t) = mCpdTD(t)

175 (8)

The heat flux or power dQ(t)/ dt which flows through the resistor R,, is related to the temperature difference ST(t) = TD(t) - T( rs2 ,t) by the relation dQ(t)/dt = - 8T/RC

(9)

With the infinite thermal conductivity assumption for the detector the temperature remains uniform throughout its bod y Substituting mCpdTD For dQ yields the following differential equation for 8T: d £Q __«! p dt Rc

v '

The solution to Equation (10) is given by the relation:

8T(t) = 8T(0) e '^ mCpRc^

(11)

Equation (11) shows that the sensor responds to a step change in temperature with the characteristic time constant t d = mCpRc. In order to minimize t D, it is desirable to minimize the sensor mass and the sensor thermal resistance between the probe and the sensor bod y From Equation (11) it may be seen that ST(t) ~ 0 when t > 5 td, a commonly used condition for steady state. Finally, the signal from the sensor body or transducer is amplified and an output signal, P = f[T( rg2 ,t)] is displayed, where f represents the functional dependence between the displayed parameter p, such as a current or a voltage, and the probe or transducer temperature, T. Ideally P is directly proportional to the probe temperature, P = f[T( rg2 ,t)] = cT( rg2 ,t), where c is a constant. In actuality, there may be sources of error intrinsic to either the technique or the geometry w hich introduce additional sources of error that destroy this proportionality. In other cases, such as infrared temperature sensing, the sensor is intrinsically nonlinear. In such a case, the functional relation must be inverted by the readout or processing unit to find T = fl^P)- The determination of the function f (or possibly its inverse) is performed by sensor calibration. We shall discuss the calibration procedure for each of the sensors individually, but, in general, it is usually done by m easuring the temperature of a suitable sample with both the sensor under test and a previously calibrated sensor which determines the sample temperature.

5.2.5

Temperature transducers

As discussed above, the m easurement of temperature is accomplished by determining the value of some parameter or variable of the transducer which is sensitive to the tem pera­ ture. The transducer in Figure 4 is a physical part with some quantity or variable P whose value depends on the transducer temperature, P = f(T). In m ost situations, P is an easily measured electrical parameter such as a current or a voltage. In some cases, P may be a nonelectrical parameter. Liquid crystals measure temperature through color changes, and in this case P would represent the liquid crystal color. The general temperature measurem ent problem may then be stated as: 1. Calibrate the sensor at a series of known temperatures to determine the function f. This is accomplished by holding the transducer at a series of known temperatures:

Thermal measurements in electronics cooling

176

Tv T2, T

n and measuring the param eter P at the hold temperatures to determine p. = f(T\). From these data, a curve fit is made to determine the calibration function. 2 . Measure the parameter P in the experiment. 3. Find the temperature from the inverse function, f-1; T = h^P) A sum m ary of the relevant characteristics and param eters of the transducers or sensors com m only used in electronic cooling experim ents and discussed in this chapter is given in Table 2 . The detailed features of the transducers are discussed in the next section. Table 2 Transducer or probe

Characteristics of Transducers Described in this Chapter

Temperature sensitive parameter

Contact method

Remarks

Resistor

Electrical resistance or voltage at constant current

Direct contact

Usually calibrated against a ther­ mocouple. However Pt RTDs are one of the most accurate temperature sensors available.

Thermocouple

Open circuit voltage

Direct contact

Useful as a "point"sensor.

Diode or transistor

Voltage, usually with constant forward bias current Detector voltage

Direct contact

Usually employed to measure an active device or IC temperature.

Line-of-site or optical contact

Can yield either a point temp­ erature or a thermal map or image. Not strictly quantitative unless sample emittance is known at the image points.

Fluorescent detector

Detector voltage

Direct contact (proximity)

Approximate point detector, contact resistance a problem.

Liquid crystal

Color

Direct contact

Yields a temperature map, semiquantitative unless a detailed calibration is performed to quantify color vs. temperature relation.

Infrared or radiation

5.3

Specific temperature sensors and measurement techniques

5.3.1

Resistance thermometers

5 3 .1 .1 G eneral description The resistance thermometer (resistance tem perature detector or RTD) is essentially a twoterm inal electrical device w ith the property that its electrical resistance is a function of tem perature. U sually the RTD is configured as a four-term inal device, w ith separate high and low leads for both a current source and voltmeter. This is called a Kelvin configuration and it rem oves the errors caused by lead resistance being included in the resistance m easurem ent. The probe or transducer is the resistor structure and the sensor body includes the resistor plus the leadwires. The subject of resistance therm om etry is discussed in detail by Quinn (1983, chap. 5). Flere we shall concentrate on those aspects of the subject w hich are of m ost interest for electronics cooling experim ents. Electrical

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resistors are com pletely analogous to therm al resistors, of the type illustrated in Figure 3, as show n in Table 1. For a resistor of length € and cross-sectional area A com posed of a m aterial w ith an electrical resistivity p = c r1, the resistance is given by R = p€/A

(12)

The resistivity is an intrinsic property of the resistor material and is independent of the resistor size and shape. As the temperature of the resistor increases, all of the quantities on the right side of Equation (12) vary Both € and A increase as a result of thermal expansion, while the variation of p depends on the nature of the resistor material. For metal and metal alloy resistors, R increases with T, while for lightly doped or intrinsic semiconductor resistors, R decreases with increasing T. In either case, almost all of the variation of R with T is accounted for by resistivity variation with temperature and not changes in the resistor dimensions, A and €. In any case, the function R(T) is always determined by calibration against a known temperature sensor, so the source of the vari­ ation in R is not important. Resistance thermometers are of special interest for electronics applications because they can be fabricated directly on a hybrid or multichip module (MCM) substrate or on an IC chip. This method of fabrication ensures that the sensor is in intimate thermal contact w ith the object whose temperature is being determined, thereby minimizing R 12 in Figure 4. The m ajor drawback is that the resistor material is usually subject to process variability w hich affects the resistivity function, p(T), and hence the resistors on different substrates or die may have to be individually calibrated to achieve the desired accuracy. The resistance of most metals increases reasonably linearly with temperature in the range — 100 to 800°C. The general dependence of R on T can be written as a power series T, with terms to second order usually being sufficient to describe the R(T) function about some reference temperature, T0: R(T) = Roll + Cl(T - T0) + c2(T - T0f + ...]

(13)

In Equation (13) R0 is the resistance at the reference temperature T0, while Ci and c2 are constants which must be determined by calibration. Higher-order terms are not needed to describe R(T) in the temperature range of interest in common electronics cooling prob­ lems. In most commercial resistance thermometry, T0 = 0°C because an accurate ice-point reference at that temperature is easy to establish. For laboratory calibration of substrate or IC thermometers, it is usually convenient to establish T0 as room temperature, T0 ~ 24°C. Industrial resistance thermometers, commonly known as resistance temperature detec­ tors (RTDs), are frequently made of Pt because this element is chemically inert and hence the resistivity function, p(T), is highly reproducible from supplier to supplier. In addition, the R(T) function is highly linear over a wide temperature range. A typical platinum resis­ tance thermometer has parameters (Bentley, 1988), Rq = 100 ft, R(100°C) = 138.5 Q with c, = 3.91 x 10“3°C_1, and c2 = -5.85 x 10_7oC 2. The change in resistance between the ice point and steam point, R(100)-R(0) = 38.5 ft and the maximum nonlinearity is 0.76%. The above information is sufficient for the user to employ a platinum RTD without performing further calibration. All that is required is the Rq value for the specific RTD being used. In contrast to the platinum RTD, most thin film or electroplated resistors used in electronics fabrication are made of materials such as Al, Cu, W, and polycrystalline Si. The resistivity of these materials depends on such variables as the grain size, impurity content, and the amount of oxidation which may occur. As a result, the thermometers need to be calibrated over the range of interest to the experimenter. In addition, the resistor material may not be fully annealed or stabilized during the device fabrication process. As a result, the calibration function, R(T), may shift during extended use at high temperatures. The

Thermal measurements in electronics cooling

178

accuracy with which the calibration needs to be performed depends on the specific nature of the experiment. Resistance therm om eters made from lightly doped sem iconductor m aterials are known as thermistors. The resistance of these materials decreases with temperature, and over a limited range of temperature varies as /

\ (14)

In Equation (14) T0 is the reference temperature in K and q is a constant. 5 . 3 . 1.2

General use considerations

Resistance thermometers are available in many forms such as beads, rods, or disks. The selection of a suitable geometry depends on the nature of the measurement problem. There are three im portant considerations for resistance thermometry which affect the selection of a suitable RTD: 1. The resistor must be in intimate thermal contact with the part under study. For the highest accuracy, a solder attachment is desirable. Thermally conducting epoxies are frequently used, but may produce additional thermal resistance, R12 in Figure 4. 2. For accurate temperature m easurement, the whole resistor must be at the same temperature. Thus, it is necessary that the temperature not vary appreciably over the m aximum resistor dimension. If the resistor is located in a region of high thermal gradient such as a boundary layer or near a material interface or localized heat source, it will measure some average temperature and not a point temperature. 3. The power dissipated in the resistor should be limited to ensure that the resistor self-heating does not affect the measurement. In most commercial ohmmeters, current levels ~ 100 \iA or less are used, resulting in a power dissipation i2R - 10 p,W in a 1 kQ resistor. This pow er level will usually not produce measurable distortions of the temperature field under study. 5 .3 .1 .3

Exam ple o f use

As an exam ple of practical resistance thermometry and the associated calibration, we consider the Sandia Laboratories ATC02.5 Assembly Test Chip shown in Figure 5. This chip has six resistive heaters and three polysilicon resistance thermometers. In addition it has 12 alum inum metal resistive triple track structures which are normally used for corrosion studies but w hich may also be employed for resistance thermometry. The poly­ silicon resistors have a Kelvin or four terminal connection to ensure that all of the voltage drop being measured occurs in the resistor structure and not in the wirebonds or external leads. The chip may be biased with a current source and the voltage measured with a digital voltm eter or a commercial four-terminal ohmmeter may be used. The calibration was performed with a packaged chip placed in a convection oven whose temperature was measured by a type K thermocouple (see below on thermocou­ ples). The thermocouple, which was calibrated against a primary standard, was placed in contact with the part being calibrated and the resistance was then measured at 25°C intervals in the temperature region of interest, usually 25 to 150°C or so. The attainment of therm al equilibrium at a setpoint is observed by measuring the resistance vs. time and noting w hen a constant level has been attained. Typical data from the polysilicon resistor calibration are shown in Figure 6 for one resistor on each of eight parts. Figure 6(a) shows that there is a fairly large spread in the 25°C resistances, Rq = R(25°C). However, the critical parameter is the slope of the R(T)

ATC02.5

.XU ::j |

Figure 5 Sand la ATC025 Assembly Test Chip used for measuring the thermal resistance of electronic assemblies- The chip has six polysilicon resistive heaters which cover most of the die surface. Then? are three poly silicon resistance thermometers along one of the chip diagonals and 12 aluminum triple track structures which can also be used for thermometry

Al triple track corrosion test structure

Polysilicon resistance thermometer

Polysilicon heater

j-a

Thermal measurements in electronics cooling

180

T(°C)

(a)

(b) Figure 6 (a) Resistance calibration data from eight ATC02.5 die. The temperature was measured with a calibrated type K thermocouple, (b) The same data plotted as relative resistance changes, (R(T) - R(25°C))/R(25°C) to show how accurately the temperature can be determined from a measurement of that quantity.

curves, and it is evident that all the samples have nearly identical slopes or q values from Equation (13). In the case of these data, a first-order or linear fit is sufficiently accurate and nothing is gained by adding a quadratic term. If the temperature spread had been wider, it might have been necessary to use a higher-order term. The data are replotted in Figure 6(b) in the form AR/Rg = [R(T) - Ro]/Ro vs. T to emphasize the slope uniformity. The vertical dashed lines show the spread in derived temperature values for a AR/Rq = 0.065, corresponding approximately to AT = 95°C. The spread on either side of the average value temperature rise, Atavg ~ 95°C is about 3°C, corresponding roughly to 2o/ATavg = 0.03, where a is the standard deviation of the predicted temperatures for a fixed AR/Rg. The actual experimental value of 2a/ATavg for 25 die was 0.041. This spread is fairly typical for resistance thermometry using integrated circuit resistive structures. A universal cali­ bration curve for a resistive device can be used to predict the temperature rise to within about 4% of the actual rise which would have been measured if the specific device calibration curve had been used. The Al resistors on the ATC02.5 chip showed a similar spread but have a higher temperature coefficient or q value. For the poly silicon resistors, AR/(RqAT) had a value ~ 7 x 10^°C_1, while for the Al resistors, AR/(RqAT) ~ 3.5 x 10“3oC_1. However, the Al can

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181

anneal and change calibration after prolonged exposure to temperatures of 125°C or higher, so the polysilicon resistive thermometers are preferred for thermom etry when prolonged high temperatures are used.

5.3.1.4

Calibration

Resistance thermometers are calibrated by a procedure such as the one discussed in the previous section. The resistance as a function of temperature, R(T), is determined by m easuring R with the RTD under test, while measuring T with a calibration standard. This standard is usually a therm ocouple, which itself may have been calibrated against a primary standard, such as the one discussed above. Although the calibration above was performed in air in an oven, usually more con­ sistent results are obtained if the calibration is performed in a well-stirred fluid. If a fluid of relatively high thermal conductivity is used, such as a heat transfer oil, and the RTD under test is placed close to the calibration thermocouple, then the temperature difference between the RTD and the standard will be minimized. In our experience, using one calibration thermocouple as the standard and a second calibration thermocouple as the sensor to be calibrated, fluid temperature differences between standard and sample (cor­ responding to the AT produced by R12 in Figure 4) are < 0.1°C. Care must be taken to ensure that the fluid comes to equilibrium at the test temperature before the calibration measurements are made.

5.3.1.5

H ow to use a resistance therm om eter

Resistance thermometers are available commercially in many forms: wire wound, film, etc. Commercial RTDs tend to be large by microelectronic standards and are not used too frequently for electronics cooling studies. Integral RTDs, such as the one described above on the ATC02.5 chip, are frequently used to measure the temperature of printed circuit boards, multichip module or hybrid circuit substrates, and integrated circuits. The following list gives a step-by-step method for using an RTD: Description

Process

No.

Attachment

2.

Instruments

Measurement

5 .3 .2

A non-integral RTD used to measure a surface temperature must be carefully bonded to the surface using either thermally conductive epoxy or a solder bond. If a commercial system is not used, it is important to minimize leadwire errors. A four-terminal ohmmeter circuit is suggested in which separate current and voltage leads are used. The measurement current, iM, should be selected so that the power dissipated in the resistor, PD= iM2R, is negligible, where R is the RTD resistance. A voltmeter with enough digits of accuracy needs to be selected such that the resistor voltage, V = ^R, can be resolved with sufficient accuracy. Measurement instruments and the current source should have a single point ground. Because of high thermal capacitance, commercial RTDs are best for steady-state measurements. The achievement of steady state should be monitored by observing no change in RTD resistance (or voltage) as a function of time within some error band.

T h erm o co u p les 5 .3 2 .1

G eneral description

Unlike resistance thermometers which are bulk effect devices, thermocouples are essentially point devices which measure the temperature in a very localized region. Thermocouples are widely used for temperature measurem ent and there are many books and articles on

Thermal measurements in electronics cooling

182

the subject of thermocouple thermometry. General overviews are given by Quinn (1983, pp. 241-283) and by Michalski et al. (1991, chap. 4). A simplified discussion with many practical hints for the experimenter has been presented by the Hewlett Packard Company (1983). A more detailed but still practical description of thermocouples is given by the ASTM (1993). Therm ocouples are devices m ade w ith two different types of m etals or metal alloys as shown in Figure 7. This shows a com m on configuration in w hich wires of two different m aterials, A and B, are joined and then each of these wires is connected to a third type of wire C. Both the AC and the AB junctions are m aintained at a reference temperature T0. A lthough these junctions are shown separated in space to illustrate the principle of operation, they are actually placed closely together to ensure that they are at a com m on tem perature. From the reference junctions, the m aterial C extender wires are run to an external detector, usually a digital voltmeter. The voltm eter m easures a voltage, VAB, w hich is a function of the tem perature difference, AT = T - T0. All wires must be electrically separated or insulated to ensure that they do not accidentally short against an adjacent wire or conducting m aterial in the sample at a different potential. As norm ally used, the only current flowing in the therm ocouple circuit is the small volt­ m eter source current.

Detector

Figure 7 Electrical potentials along the wires of a thermocouple made up of thermoelements A and B having a hot junction in a region of uniform temperature T and connected to a pair of identical conductors C at cold junctions at the temperature T0. The C conductors are in turn connected to a detector in a region of uniform temperature Tv The measured quantity, VA - VB does not depend on Vc, assuming that the AC and BC junctions are both at the same temperature, T0.

Each of the wires A and B in the thermal gradient characterized by AT = T - T0 develops a potential difference, VA and V B, respectively, along its length. This voltage is known as the Seebeck voltage, after its discoverer T. J. Seebeck. The rate of change of the potential difference with respect to temperature is called the Seebeck coefficient. For the two legs of the therm ocouple, the Seebeck coefficients are given by

M

a .( T ) = M

, 15)

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Temperature measurement in electronics cooling

183

The Seebeck coefficient a depends only on the material, the material state, and the temperature. Physically, the voltage develops because the energy distribution functions characterizing the particles in the wires vary as a function of temperature and hence position. For example, consider a metal thermocouple wire where electrical current is carried by electrons. The electrons at the hot end of the wire have a higher average energy and velocity than those at the cold end. Subsequently, there is net diffusion of electrons from the hot to the cold end. However, this results in a small net negative charge devel­ oping at the cold end and positive charge developing at the hot end and these charges establish an electric field which produces the Seebeck voltage. This voltage results in a resistive current flow which is equal and opposite to the diffusion current, with the result that the net current is zero with the wire open circuited. Since a positive test charge placed in the wire would experience a force pushing it to the negative cold end, the electric field points from hot to cold, and voltage drop AV = V(T) - V(T0) is positive. A net Seebeck voltage, VAb(T0 —> T), develops because the Seebeck coefficients for the individual legs are unequal. Based on Equations (15), this voltage is given by the relation: T

(16)

The voltage VAB(T0 —>T ) is not, in theory, affected by the extension wires and associated junctions because the voltage drops are equal in each C wire and hence they cancel in the voltage difference measurement, as shown in Figure 7. Equation (16) is the fundamental relation governing thermocouple thermometry and it expresses the notion that the thermal voltage depends only on the nature of the materials and the net or total temperature difference betw een the reference and sample junctions. It can be seen from Equation (16) that the exact nature of the variation of T along the thermocouple legs does not matter; only the temperatures of the sample and reference junctions , T and T0, respectively. The expression for VAB in Equation (16) also shows that this voltage does not depend on any intrinsic property of the AB junction itself, only on the nature of the wires. For various types of thermocouple wire the a(T) functions are well known and characterized. However, any nonhomogeneity in the wire can produce variations in this function which affect the accuracy of the thermocouple. It is perhaps more illum inating to write Equation (16) in terms of the position, x, along the thermoelements. With reference to Figure 7, the temperature variation along the thermocouple wire, T'(x), has the property that T'(x0) = T0 and T'(0) = T. Using the differential relation, dT' = (dT'/dx)dx, the integral in Equation (16) can be written as o

Vab(T0 ^ T ) =

J

[a A( T '( x ) ) - a B( T '( x ) ) ] ^ d x

(17)

Equation (17) shows that the main contributions to the integral defining VAB come from regions in which the temperature gradient has a large magnitude. If a nonhom oge­ neity in one of the thermocouple wires exists in such a region, there is the potential for error produced by a shift in the a(T) functions from that assumed or existing at the time of calibration. This result shows why it is very important not to bend or twist thermocouple wire, especially in regions of high thermal gradient. Although the therm ocouple arrangement shown in Figure 7 is the most commonly used one, it is not the arrangem ent which is usually shown in textbooks. In Figure 8 (a) the more common configuration is illustrated. One leg of the thermocouple goes to an

Thermal measurements in electronics cooling

..... : *

tso^herm&l -

Isoihermas... ? atoci $

«

A

U i — s !A

JL i

j BA H

LH j

V V\ Isomermai— * Block

T, Vollmeler

— 'C3|j S! ^ ^ j '

V Volfmelw

(a)

IT

>

A

(b)

Figure 8 (a) Thermocouple circuit with a sample at temperature T and reference junction at % with extender wires connected to a break in the material A wire. Extender wires C connect the circuit to the voltmeter (h) The reference and isothermal blocks are joined together on a block at temperature T0. (c) The material A leg between the two lower junctions at T0 is removed, producing a circuit equivalent to that in Figure 7,

iso th e r m a l b lo c k , w h ile th e se c o n d leg g o e s to th e referen ce ju n c tio n held at s o m e te m ­ p e ra tu r e T a, p e r h a p s b y an ic e b ath. T h e iso th e rm a l b lo ck m a y b e at a n y tem p er a tu re a s lo n g a s th e tw o ju n c tio n s o n th e b lo c k a re tru ly a t th e sa m e tem p era tu re, In F ig u re 8(b) th e iso th e rm a l a n d referen ce tem p er a tu re b lo c k s are c o m b in e d in a b lo ck h e ld at T0. F rom E q u a tio n (16), w e ca n s e e th a t th ere is n o c o n tr ib u tio n to th e v o lta g e fro m th e m eta l A le g b e tw e e n th e tw o lo w e r iso th e rm a l b lo c k ju n c tio n s b e c a u se th e y are at th e sa m e tem p er a ­ ture, T h u s, th e se tw o ju n c tio n s m a y b e c o m b in e d in to a s in g le ju n ctio n , as s h o w n in F ig u re 8(c), T h e circu it in F ig u re 8 (c) is th e sa m e a s th at shown in F ig u re 7, th ereb y v e r ify in g th e fu n c tio n a l e q u iv a le n c e o f th e tw o th e r m o c o u p le circu it d e sc r ip tio n s, 5 .3 .2 .2

Types o f th erm ocou p le

T h e s e v e n in te r n a tio n a lly a d o p te d th e r m o c o u p le s, the so -c a lle d '"standardized th e r m o ­ co u p le s" a re d e sc r ib e d in T ab le 3 (Q u in n , 1983, p p , 249-251), T h e S e e b e c k c o e ffic ie n t or a A - a B v a lu e s in T ab le 3 are th o se ty p ic a l o f th e tem p er a tu re ra n g e - 0 to 20O °€ in w h ic h w e h a v e o u r p r im a r y in terest. A ctu a lly th e a A - a B fu n c tio n is tem p er a tu re d e p e n d e n t, a s s u g g e s te d in E q u a tio n , (15), D e ta ile d ta b les for VAB(T) v s, T a n d p o ly n o m ia l cu rv e fit co e ffic ie n ts for fin d in g T as a p o w e r se r ie s in V are g iv e n in th e A m er ica n S o c ie ty o f M ech a n ica l E n g in e ers (A S M E ) th e r m o c o u p le m a n u a l (A S T M , 1993, p p , 189-213), T h e se ta b les are u s u a lly im p le m e n te d a u to m a tic a lly in co m m e rcia l th e r m o ­ c o u p le e q u ip m e n t w h ic h rea d s out d ir e c tly in tem p er a tu re u n its. T h e n o r m a l error lim its are from H e w le tt P ack ard (1983) a n d in d ic a te, in a n a p p r o x ­ im a te w a y , h o w far a th e r m o c o u p le tem p er a tu re, as d e te r m in e d from the fa b les or fro m a u to m a tic e q u ip m e n t, m a y v a ry from th e a ctu a l tem p er a tu re in th e r a n g e 0 to 2O0°C. 5 .3 .2 .3 Calibration and error analysis A n e s tim a te of th e n o r m a l error lim it or a c c u r a c y w ith c o m m e r c ia l m e a su r e m e n t s y s te m s is g iv e n

of in

u n c a lib r a te d th e r m o c o u p le s u s e d T ab le 3, E rrors in th e r m o c o u p le

Chapter five:

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185

Table 3 Letter Designations and Compositions for Standardized Thermocouples (the thermocouple arm producing the more positive voltage is designated by P, the other arm by N)

Type designation

Material A (P)

Material B (N)

a A- a B (|iV/°C)

Normal error limit ±°C

B

Platinum-30% rhodium

Platinum-6% rhodium

1

0.0

E

Nickelchromium alloy Iron

A coppernickel alloy

62

1.7

Another coppernickel alloy

51

2.2

K

NickelNickelaluminum chromium alloy (Alumel3) alloy (Chromel3)

40

2.2

R

Platinum-13% rhodium Platinum-10% rhodium Copper

Platinum

7

5.0

Platinum

7

5.0

40

1.0

J

S T

Copper-nickel alloy (constantan)

Remarks Not useful below 50°C, best for very high temperature measurements Well suited for low temperature measurements Iron P leg subject to variations in a from impurities, generally used at high temperatures Very popular for electronics cooling experiments; can be used in oxidizing environments Very stable

Well suited for electronics cooling measurements if high Cu thermal conductivity not a problem; Seebeck coefficient relatively constant over wide temperature range

a The terms "Chromel" and "Alumel" are in common usage but are trademarks used by the Hoskins Corp. Similar wire is available from other manufacturers under other tradenames.

m easurem ents can arise from a variety of sources, as suggested by the discussion in Section 5.3.2.1 above. The follow ing table gives a list of the m ost comm on potential sources of error in therm ocouple tem perature m easurem ents. In practical thermocouple thermometry, as commonly employed in electronics cooling studies, the achievable accuracy depends on how much effort is spent on solving or addressing the potential problems in Table 4. Typically, commercial equipment m anufac­ turers will quote two num bers, resolution and accuracy (OMEGA Engineering, 1991). Res­ olution specifies how small a temperature difference may be resolved by the equipment. For typical hand-held and benchtop meters the resolution will be about 0.1 °C or so, a value almost always adequate for electronics cooling experiments. The accuracy specifies how accurately the absolute temperature can be determined by a given piece of equipment, assuming that the wire associated error is within some given specification and that all required isothermal regions are truly isothermal. The accuracy is prim arily dependent on the reference temperature system and associated circuitry for a given instrument. There may also be a dependence on the percent of full-scale deflection.

Thermal measurements in electronics cooling

186

Table 4

Potential Sources of Error in Thermocouple Temperature Measurement

Error source Thermocouple wire Seebeck coefficient deviation from the standard value

Reference junction temperature not at correct value

Connection voltage errors Extender wire voltage shifts

Causes

Solution or mitigation

1. Calibration of wire from a spool. 2. Care in using thermocouple wire only in the environment suggested for the given wire type. 3. Avoid kinking or cold working wire. 1. Error in reference temperature 1. Use external ice bath reference. determination or compensation 2. Use commercial cold junction compensators or electronic ice in commercial equipment. point references. 3. Measure reference temperature with a calibrated temperature sensor. 1. Connector blocks (Figure 8) not 1. Insure that all connection a true isothermal region. regions in the thermocouple circuit are truly isothermal. 1. Extender wire Seebeck 1. Use extender wires from same spool. coefficients not matched. 2. Damaged regions in extender 2. Take same care with extender wire in high thermal gradients. wire as with thermocouples.

1. Wire manufacturing random variations. 2. Variations produced by oxidation or other chemical changes.

The typical accuracy associated with hand-held readout units is ~1°C ± 0.5% of the temperature corresponding to full-scale deflection, corresponding to an absolute accuracy of about ±1.5 to 2°C. Benchtop units have somewhat better reference junction com pensa­ tion circuitry and have specified accuracy better than ±1°C for type J, K, and T therm o­ couples which are commonly used for electronics cooling experiments. To achieve the highest accuracy, a therm ocouple and its associated meter or instru­ mentation unit is calibrated against a standard, as discussed in the previous section for resistance thermometer calibration. In our laboratory, we use a type K thermocouple as a secondary standard. The type K has been calibrated against a type R primary standard thermocouple. Again, the best method for calibration is to immerse both the calibration and test thermocouples in a well-stirred fluid whose temperature is then varied over the desired range. A frequently used laboratory calibration method for new wire is to calibrate the therm ocouple in an ice bath and a bath of boiling water. For the ice-point measurement, finely cracked ice is used w ith just enough water to fill the interstitial space. The ice water mixture can be put in a dewar vessel to minimize melting effects. If the thermocouple is not in a closed hermetic tube, it can be placed in a tube filled with a good thermal conducting liquid such as a silicone oil (Baker et al., 1975, pp. 59-61). A water boiling point measurement is less precise but still very useful for an approximate calibration. The temperature m ust be corrected for the ambient pressure at the local elevation (Lide, 1994, p. 6-17).

5.3.2A

Hon? to use therm ocouples

In most experiments performed in our laboratory, we use type K thermocouples and com­ mercial measurement/readout equipment. For typical commercial type K wires in the range 0.001 to 0.005 in. diameter, we find that the indicated measured temperature is within about ±1.5°C of the actual temperature, as measured with a calibrated thermocouple. Care must

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be taken not to bend or damage the thermocouple wires, especially in the smaller diameter sizes, as this may seriously affect the calibration, as discussed above. Some investigators use type T thermocouples for electronics cooling experiments. These work well and are felt to be somewhat more accurate than type K, as shown in Table 3. The principal disadvantage of the type T thermocouple is the high thermal conductivity of the elements which can produce possible heat loss problems. This is usually not a serious issue if small diameter wires (-0.003 in.) are used. Various methods of welding thermocouple wire and insulating the wires are described in Eckert and Goldstein, 1976. If possible, it is desirable to imbed the thermocouple test junction or tip in the sample for solid measurements. As was mentioned in the discussion following Equation (15), damage to thermocouple wire can produce a shift in the Seebeck coefficient w hich w ill lead to an error if the damage location has a large thermal gradient. Since damage is likely to occur near the thermocouple tip, particularly if it is unsheathed, it is good practice to try to keep the wire near the tip in a relatively isothermal region. For example, in a solid surface temperature measurement where the solid is cooled by a moving fluid, it is considered good practice to bring the wire out along the solid surface for some length before it goes into the fluid through a high thermal gradient region. In addition, to avoid cold work damage, it is desirable to make all changes of wire direction gradual to avoid sharp bends. For fluid m easurements, the thermocouple is immersed directly in the fluid at the measurement point. For air temperature m easurements, it is usually desirable to eliminate radiation effects by shielding the bead and wires if there are nearby hot sources. It is also desirable, if possible to place the thermocouple in a region of low or zero air flow to minimize errors caused by convective effects. Many practical hints on solving various measurem ent problems are given in Quinn (1983), Hewlett Packard (1983), and Michalski et al. (1991). Further discussion of the fluid temperature measurement problem is given in Section 5.4.3 below. The table on the following page gives the general procedure for using a thermocouple for temperature measurem ent in electronics cooling studies. 5 .3 .3

S e m ic o n d u c to r d ev ices

5.3.3.2 G eneral description Semiconductor devices, both junction and channel, can be used as thermometers because they have temperature sensitive electrical properties. Examples of such properties are the threshold voltage of a metal oxide semiconductor (MOS) transistor and the forward bias voltage at constant current of a p-n junction diode. The physical m echanism underlying device thermometry is the dependence of the given device property on the thermally excited carrier concentration which is found from the carrier energy distribution function. In all cases, the param eter temperature dependence, P(T), must be derived through cali­ bration experiments in w hich P(T) is determined at a number of known temperatures The details of device thermometry are given in another chapter in this book. Here, we present some sample calibration data for a p-n junction diode device to illustrate the general nature of the technique. Space limitations do not permit a detailed discussion of the device physics underlying the theory of operation of device thermometry. However, there are many excellent and detailed references on the subject. One of the most useful with practical guidelines has been presented by Oettinger and Blackburn (1990). Verster discusses the use of bipolar transistors as temperature sensors (1972, pp. 1125-1134). Almost all of his discussion is applicable to junction diode thermometers.

Thermal measurements in electronics cooling

188

Thermocouple Measurement Procedure No.

Process Attachment

Instruments

Thermocouple type and wire size selection

Wiring connection and care

Measurement

Calibration verification

Description For a surface, or solid measurement, the thermocouple sensor element needs to be carefully bonded to the sample. Thermally conducting epoxies such as those used for die attachment work well. In regions where the thermal gradient is small, super glue is a fast and reliable bond material. Thermal grease can be used for a quick temporary connection of the tip, with the sheath held down with epoxy or superglue. For a fluid element, the sensor should be in a well stirred area. Wire near the tip should be kept in a relatively isothermal region, if possible. In most electronic cooling studies, commercial measurement systems are used which include an internal reference junction. All manufacturer instructions should be carefully followed. If very high accuracy is required, the instrument and wire should be calibrated against a standard instrument and wire. The thermocouple type should be selected such that the thermocouple is working well within its normal operating range and within its environmental limits. In most cases, type K thermocouples should be used. The thermocouple wire diameter should be as large as possible consistent with the required junction size and the need to avoid thermal shunting in Figure 4). Most thermocouple measurement errors are caused by problems in connecting or using the wiring, thermocouple wires should not be bent or crimped in any way. These effects can cause calibration shifts. All terminal connections need to be tight and soldered connections need to be verified for integrity. Thermocouple wire insulation should be checked for integrity, as shorts away from the test junction will produce errors. Prolonged exposure to high temperatures can damage thermocouple wire insulation. All connection regions should be as isothermal as possible. In a high electrical noise environment, a shielded cable should be used around the thermocouple wire. The shield should be connected to the ground on the digital voltmeter or commercial thermocouple monitor. Since thermocouple wire is easily damaged, with a consequent calibration shift, all thermocouple wire calibrations should be checked at regular intervals by measuring a fluid at a known temperature.

As in the case of the RTD, it is desirable to use a four-terminal or Kelvin measurement geometry, with separate leads for current bias and voltage measurement. If this is not done, the circuit acts like a resistance therm ometer or RTD in series with a diode. Depend­ ing on the lead resistance in the circuit, the effect of tem perature-induced variations in this resistance component may be larger than the effective change in diode resistance. Since portions of the leads may be at temperatures significantly different than that of the diode, an error can be introduced in a two-terminal m easurement configuration. 5 .3 .3 .2 Exam ples o f use and calibration In Figure 9 we show calibration data for seven diodes on a Sandia Laboratories ATC04 Assem bly Test Chip (Sweet et al., 1994). This chip contains an array of 25 piezoresistive

Chapter five:

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189

0.9

0.8

>

CD

0.6

0.5

-50

0

50

100

150

T(°C) Figure 9 Forward bias diode voltage, VBE vs. T, for seven diodes on an ATC04 Assembly Test Chip. There are 25 piezoresistive addressable cells on the chip, each of which has a centrally located diode for thermometry. The chip also contains four resistive heaters to enable thermal resistance testing.

stress sensing cells, each of w hich contains a centrally located diode for thermometry. The diodes were biased at 100 |nA forward bias using a precision current source and the diode or base-emitter voltage, V BE, was used as the temperature sensitive parameter. The term VBE originates from the base-em itter voltage rise in a bipolar transistor. If the collector-base junction is open circuited, then the base-em itter circuit acts as a simple junction diode. Even if the collector is not open, the base-em itter voltage at constant emitter current still acts as a temperature sensitive parameter. On the scale on which these calibration data are plotted, the calibration curves lie on top of each other. For the full scale AT ~ 200°C, the standard deviation of the least squares curve fit to the data from all 25 chip diodes is about 0.25°C. If different chips from the same wafer are calibrated, the standard deviation increases to about 1°C, or about 0.5%. If chips from different wafers from the same wafer lot are examined, the standard deviation increases to about 1%. These data show that device thermometry can be very precise and that the accuracy is probably limited by the accuracy associated with the calibration thermocouple and readout devices such as the digital voltmeter used to measure the diode voltage. Another detailed description of diode therm om etry is given in a description on the use of test chips in m easuring the tem perature distribution in a three-dim ensional m ultichip m odule (MCM) (Sweet et al., 1993). In this work, about a 5% spread was seen in the diode calibration functions for 48 diodes on a Sandia ATC03 die. The high spread occurred because two-term inal m easurem ents were utilized on this chip. This illustrates the im portant point that the precision of a sem iconductor device can be very dependent on both the circuit design on-chip as w ell as the outside m easurem ent circuitry and instrum entation. Calibrations can also be performed in a fluid bath. Over a limited range of temperature, the T(Vbe) function can be written as,

(18)

Thermal measurements in electronics cooling

190

In Equation (18), T0 is a reference temperature, usually near room temperature. One report of a round robin calibration study involving both fluid and air bath calibrations for diodes reported good agreement in the slope, 3T/3VBE, of the T(VBE) function but measurable variance in the constant term or intercept, T0 (O Mathuna et al., 1993). The details of the calibrations are given by O M athuna and coworkers (1993) and they conclude that diode therm om etry is more accurate in m easuring temperature differ­ ences than in m easuring absolute tem perature. For the m ost accurate thermal resistance m easurem ent, the chip with the therm al diodes is first m easured at the am bient tem­ perature, Ta. The chip is then pow ered and allowed to come to equilibrium and VBE is again m easured to find the AVBE produced by the tem perature rise AT = T - Ta. The junction to ambient thermal resistance ,0ja, is then calculated from the form ula

AYBE 6 ia=-

3T

av,BE J

(19)

where P = chip power. It should be pointed out that the term junction applies to the p-n junction of the thermal test diode or transistor and not the junction of other powerproducing active devices on the die. 5 .3 .3 .3 Therm al resistance m easurem ent In the determ ination of a powered device temperature and subsequent use of Equation (19) to derive the junction to ambient thermal resistance, 0ja, several considerations need to be noted: 1. Some types of devices may exhibit calibration shifts (aging effects) after prolonged high temperature operation. It is im portant to verify the device calibration period­ ically. 2 . The errors associated with a device measurement of a temperature difference de­ pend on both the accuracy of the calibration and the potential shift in calibration after high temperature operation. In a calibration of a diode in an oven using a type K thermocouple for temperature measurement, the quantity 3T/3VBE can be determ ined to an accuracy «2% over a temperature range T = 20 150°C. This accuracy is determined by both the type K calibration accuracy and the possible difference between the thermocouple and device temperatures in the oven. The error is also dependent on whether a two-terminal or a four-terminal (Kelvin) wiring configuration is used. 3. As was noted in Section 5.3.1, it is possible to use a resistance thermometer on the chip to measure the die temperature. The attainable accuracy is somewhat lower that that for device therm om etry but is usually adequate for thermal resistance determination. 4. In the measurem ent of therm al resistance, the device power P is derived from the measured pow er supply current and voltage. It is important to ensure that this measured power is all dissipated in the device and not in leadwires or board circuitry.

Chapter five:

Temperature measurement in electronics cooling

5.3.3.4 No.

Sem iconductor device usage Process

1

Attachment

2

Wiring

3

Instrumentation

4

Validation

5.3.4

191

Description In most cases, device thermometers are integral with the device whose temperature is being measured, so no attachment is nec­ essary. If a discrete device is used for thermometry, attachment considerations are the same as those for RTDs and thermocouples. It is highly desirable to make a four-terminal connection with two terminals for bias current and two for voltage measurement since device connections frequently have high series resistance. For devices on ICs, proper grounding is important and manufacturer's specifications should be followed. An accurate current source is used to bias the junction or device under test. Care should be taken to ensure that the measurement current is the same as that used in the device calibration, as the device voltage is a strong function of current as well as temperature. A digital voltmeter with a sufficient number of digits of accuracy should be used to obtain the required temperature resolution. If possible, the device calibration should be checked against a standard thermocouple. Some semiconductor devices are very prone to calibration deviations resulting from process variations in their fabrication.

Radiation thermometry 5.3.4.1

General description

Radiation thermometry involves the use of electromagnetic radiation to determine the tem­ perature of a body or test volume. In one case, called infrared radiometry, the intrinsic infrared radiation emitted by an object is observed with a suitable detecting or sensing system and the measured radiation intensity as a function of wavelength is used to infer the temperature of the emitting body. This method is equivalent to observing the color of a hot body, such as a piece of steel in a blacksmith's fire, with the eye and then inferring the body temperature from that color. In the second case, optical energy from an external source is used as a sensing probe to detect some temperature-induced change in an optical property such as reflectance or fluorescence intensity. We first turn to the more common field of infrared (IR) radiometry and then discuss one type of external source optical thermometer.

5 .3 .4 2

Infrared tem perature m easurem ent

5.3.42.1 Background. As mentioned above, a very hot object (>500°C), such as the sim, can be observed by the visible light or radiation it emits. As the object grows colder, it ceases to emit visible radiation but continues emission at longer or infrared wavelengths. The observation of this radiation with suitable infrared optical systems can be used to find the temperature of the emitting body. This method of temperature measurement is called pyrometry. In a literal translation from the ancient Greek roots of the word, pyrometers are fire measurers. I shall review the theory of thermal radiation in enough detail to enable the reader to understand the fundamental principles of operation of different types of infrared instruments used to measure temperature in electronic cooling experiments.

192

Thermal measurements in electronics cooling

Any body or object consists not only of atoms, molecules, and electrons but also a collection or gas of optical quanta called photons. In addition, a radiation or photon field may exist within a suitable enclosure which otherwise contains only a vacuum. The average energy or frequency of the photons is directly proportional to the temperature, in analogy with Equation (1). If there are also material bodies within the enclosure, then, by exchange of radiation energy (photons) the temperature of the bodies and the radiation will becom e the same. If a body is initially hotter than its surroundings, it will radiate more energy to the surroundings than it receives, and this net energy loss will be reflected as a temperature decrease in the body. The fundamental principle of pyrometry is the detection of the radiation emitted by the test sample and the use of that measurement to infer the temperature of the sample. Each type of particle in the system has an energy and the group of such particles has an energy distribution function, such as that in Equation (2) which describes atoms in a monatom ic gas. Similarly, the gas of photons in the body is characterized by a distribution function called the Planck distribution after its discoverer. This distribution may be used to find the radiated intensity from a body at a given temperature (Reif, 1965, pp. 373-388). W hen written in terms of the wavelength A, of the emitted radiation, the intensity, pe(A,,T), in units of power per unit area and per unit wavelength is given by:

«

Q(A/1j

4jc2c2te(*.,T) /_ x \

^ f

exp V

' IctlK

'

I m -t J

(20)

-1 /

In Equation (20), c = speed of light, 3 x 108 m/s, ||= Planck's reduced constant, 1.054 x 10-34 J s, and e(A,,T) is a temperature- and wavelength-dependent function characteristic of the material, called the emittance. Usually pe(A,,T) is expressed in units of watts power per m2 area per pm wavelength, W /m 2*pm. The total power in W emitted by an element of area dA of the body in a wavelength interval between X and X + dA, is then: dP(W) = pe(A,,T)dAdA,

(21)

The emittance has the property that 0 < e(A,,T) < 1 and it characterizes how efficiently a body transfers energy by radiation. In most cases of interest in electronics cooling, e may be considered a constant for a given m aterial and surface finish over the temperature and wavelength range of interest. A material w ith a high e emits efficiently and appears like a black body. A black body is a hypothetical material which is a perfect emitter with e = 1. Materials like flat black paint or smooth w ater have e > 0.95, while at the other end of the material spectrum some polished metals have e < 0.05. Artificial black bodies are frequently used for calibration purposes. These are cavities with an aperture such that any radiation entering the aperture is effectively trapped in the cavity and not reflected or emitted back toward the source. Several examples of cavity black bodies are given by Quinn (1983, pp. 316-320). A cavity black body can have an emittance e 5; 0.99. Quinn shows one cavity black body with e S: 0.9999. As stated above, the net amount of radiation emitted within a small wavelength interval dA, centered about A, is dPe = pe(A,,T)dA,. The total power emitted per unit source area is then given by the integral of Equation (21) over all wavelengths. If we assume that the emittance is only a function of temperature, e(A,,T) —> e(T), than the integral may be perform ed with the result:

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Temperature measurement in electronics cooling

193

Pe( T ) = f Pe(*,T)dX

{

(22)

= e(T )aT 4 Equation (22) represents the famous T4 law for radiated energy and illustrates why the radiated energy intensity increases very rapidly with temperature. The quantity a in Equation (22) is called the Stefan-Boltzm ann constant and has the value, a = 5.669 x lO^8 W /m2 K4. From an atomic point of view, it can be seen that good absorbers of radiation are also good emitters. If radiation of a certain wavelength produces an atomic transition in a material, then the radiation will be efficiently absorbed. Similarly, if thermal energy agi­ tation results in atomic excitation, then the atoms will emit radiation at the same wave­ length. It can, in fact, be shown that the wavelength dependent absorptance a(^) and emittance e(^) of a material are equal, a(^) = e(^), (Eckert and Drake, 1972). The absorp­ tance, a(^), is defined as the fraction of the incident radiation in a wavelength interval d k about X which is absorbed by the sample. In addition, at some wavelengths, a material may transmit radiant energy instead of absorbing or reflecting it. Si is an example of a material w hich reflects or absorbs in the visible but transmits in the infrared.

AOim) Figure 10 Radiation intensity spectrum for a black body at several temperatures between 25 and 200°C. The peak in the spectrum moves to shorter wavelengths as the temperature increases in accordance with Wien's displacement law, Equation (18). The dashed line shows the trajectory of the peak as the temperature decreases.

A graph of pe(^,T)/e(X,T) for several temperatures in the range 25 to 200°C is shown in Figure 10. From this figure it may be seen that the peak in the radiation intensity function moves to shorter wavelengths as the temperature increases. In fact, the product of the w avelength corresponding to the peak, ^max, and the absolute temperature is constant and given by W ien's displacem ent law (Reif, 1965). * max (pm)T(K) = 2896 pm K

(23)

53.4.2.2 Types o f infrared systems and detectors. There are many types of infrared detectors and im aging systems for measuring the temperature of remote objects. A detailed discussion of these is given by Michalski et al. (1991, pp. 152-221). Total radiation detectors

Thermal measurements in electronics cooling

194

such as thermopiles and bolom eters function by absorbing infrared radiation over a broad spectrum with consequent heating of the sensor. This heating produces a temperature increase in the sensor which is measured and used to infer the source or sample radiance. In the infrared imaging systems used to study electronics cooling, photoelectric detectors are commonly employed. In the photoelectric detector, the incident radiation does not directly change the temperature of the detector. Instead, the incident photons generate charge carriers in the detector when they are absorbed and the resulting photocurrent is detected by suitable electronics. There are two commonly used detector materials, indium antim onide (InSb) and mercury cadm ium telluride (HgCdTe). These are narrow band gap sem iconductor materials and they have wavelength- and doping-dependent absorptance characteristics. InSb absorbs in the range AX ~ 2 to 7 pm while HgCdTe absorbs at longer w avelengths, AX ~ 5 to 12 pm. The detector signal, V(T), is given by a relation of the form:

(24) o where D(X) is the spectral response function characterizing the detector and filters if any, c0 is a constant characteristic of the detector, and pe is the radiation intensity function from Equation (20). V(T) could be a voltage or a current, depending on the exact nature of the detector and detection circuitry. The detector response function, D(>,), depends on both the detector type and the nature of the noise developed in the optical system, detector, and electronics. In addition, a detecting system is usually modulated at a frequency f to minimize electrical noise. Detec­ tors are classified by the lowest infrared power which they can resolve, called the noise equivalent power or NEP. This is an amount of power which would produce a detector current equal to the intrinsic detector noise generated current. The detectivity, D, of a detector is defined as the inverse of the NEP, D = 1/NEP. The higher the D, the more sensitive the detector. It can be shown that the detectivity is inversely proportional to the square root of the detector area, A d, and the detector system frequency bandwidth Af centered about the detector frequency (Dereniak and Crowe, 1984, pp. 32-58): D oc (AdAf)_1/2

(25)

In order to compare detector systems with different areas and different bandwidths, a quantity D * is defined such that D* = D V'A dAf

(26)

In general D* is a function of the wavelength X and the center detection modulation frequency f, D* = D*(>,,f). Typical D* functions for the two common types of detectors used in im aging systems are shown in Figure 11 (Barnes Engineering, 1983). In both cases the detectors are cooled to liquid nitrogen temperatures, 77 K, to minimize detector generated noise, resulting in a higher D*. It can be seen that the HgCdTe detector responds at longer wavelengths than the InSb detector although the latter has a higher D* within its useful bandwidth. From the radiation intensity curves in Figure 10 it can be seen that good resolution of temperatures in the 25 to 100°C range requires a detector with a spectral response at wavelengths >5 pm and hence the HgCdTe detector is the most suitable for temperature sensing in this range.

Chapter five:

Temperature measurement in electronics cooling

tm

-5 0 X 8 8

2

3

4

5 6 7 8 910

20

30

1 (urn)

Normalize detectivity D* functions for InSb and HgCdTe defector systems cooled to 77 K. The 50CC black body spectrum curve from Figure 10 (dashed line) is superimposed to show that it has substantial overlap with the HgCdTe D* function. Hie units for this curve are arbitrary,

Figure 11

5 3 . 4 2 3 M easurement systems, A block diagram of an infrared measurement sys­ tem is shown in Figure 12(a), Radiant energy from the sample is focused by an infrared (IR) lens, such as Si, onto a photoconductor. The rotating disk with the aperture chops or modulates the incoming IR signal and converts it into a square wave at the chopping frequency; The signal from the photoconductor is amplified and then detected in the synchronous detector. The synchronous detection at the modulation or chopping fre­ quency facilitates reduction of noise by eliminating signals which are not in phase with the rotating disk and at or near the same frequency. In a scanning or imaging system, the sample point is swept using rotating or vibrating IR prisms or mirrors, as indicated schematically in Figure 12(b). Rotating Disk

(a) Block diagram of a modulated photoelectric IR detection system, In this system, the rotating disk motor sets the modulation frequency f and converts the incoming IR signal to a square wave. The photoconductor signal is amplified and detected synchronously with a reference signal from the motor driver, (b) Scanning IR system for imaging. The two rotating prisms image a variable source point on the defector. Figure 12

196

Thermal measurements in electronics cooling

The infrared energy arriving at the detector arises from both the direct sample emission and also from background radiation that is reflected from the sample into the detector. If we assume for simplicity that the source emittance is independent of temperature and wavelength, then the signal or radiance reaching the detector, pdet, is given by: Pdet(VT) = epBB(V r) + (1 - £)pBB(X,To)

(27)

where pBB is the black body intensity, Equation (20) with e = 1. The first term in Equation (27) represents the direct thermal radiation from the source, while the second term is the radiation reflected by the sample from a background black body source at temperature T0. The factor of (1 - e) in the second term of Equation (27) arises because a fraction 1 - a of the incident background radiation is reflected by the sample into the detector, where a = sample absorptance defined above, and the absorptance is assumed equal to the em it­ tance, a = e. W hen the relation in Equation (27) is substituted for pe(A,,T) in Equation (24), we arrive at the fundamental relation governing infrared imaging thermography: V s(es,Ts,T0) = esV(Ts) + (1 - es)V(T0)

(28)

In Equation (28), Vs is the measured detector signal when the sample with emittance es and at temperature Ts is imaged in the presence of background radiation coming from sources at temperature T0 and V(T) is ^iven by Equation (24). The V(T) function can be evaluated num erically using detector D (A,) curves, such as those in Figure 11, in Equation (24). In practice, V(T) is determined by manufacturer calibration and built into the supplied data reduction software, so that the operator need only enter es and T0 to obtain the sample temperature, Ts. The data reduction software solves Equation (28) for V(TS) and then inverts the function to find Ts.

5.3A.2A Calibration. The fundamental problem in making quantitative tempera­ ture m easurements is to account for the unknown sample emittance es in Equation (28). For a sample consisting of a uniform or hom ogeneous material, such as a large painted or coated surface which fills the detector field of view, the emittance may be determined through a manual calibration procedure. In this procedure the sample is brought to a uniform temperature which is measured with another sensor, typically a thermocouple. The emittance is then adjusted until the IR instrument temperature equals the thermocou­ ple temperature. M ost commercial IR systems can accept an emittance input setting for subsequent direct display of temperature. In laboratory calibrations, artificial or cavity black body sources are used for calibra­ tion. The cavity is heated and its temperature determined by a primary sensor such as a therm ocouple or RTD. The infrared system is focused on an aperture in the cavity which, as stated above, can have an effective emittance e > 0.99. Details of this type of calibration are given by Quinn (1983). In commercial im aging or scanning systems with nonhomogeneous samples, a com­ monly used method of determining the emittance of the materials in the sample surface experim entally is to measure the sample radiance of each sample image point or pixel at two known temperatures. This is achieved by heating the sample on a temperaturecontrolled stage whose temperature is determined by thermocouple measurement. The m anufacturer's assum ption is that all points on the sample surface will be at the tem per­ ature determined by the thermocouple. In practice, it is useful to verify this, if possible, by m aking some surface temperature m easurements with another type of probe. Equation (28) may then be used to derive the emittance for each sample point. If V : and V2 are the measured signals received from an imaged sample point when the tem­ peratures are Tl and T2, respectively, then the sample point emittance is given by:

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197

^ v r i - v k )

(29)

where V(T) is, again, the function defined by Equation (24).

53.4.2.5 Commercial infrared imaging systems. A listing of some commercial scan­ ning or im aging infrared systems which have been used in electronic cooling studies is shown in Table 5. Table 5 Thermography Imaging Equipment for Electronics Applications

Company/models AGEMA IR Thermovision 782LWB Barnes Engineering Computherm RM-2A Microscope Inframetrics Model 600 Mikron Instrument Thermo Tracer 6T61 UTI CCT-9000 Flir Model 812

Detector (std/opt)

Max. IR spectral range in pm (std/opt)

Temperature range (low/high °C)

Temperature resolution (°C/@°C)

Spatial3 resolution

InSb/ HgCdTe

2-5.6/8-12

-20/1600

0.1/30

15 pm

InSb InSb

1.5-5.5 1.5-5.5

amb/ 600 amb/500

0.1/75 0.1/75

15 pmb 8 pm

HgCdTe HgCdTe/ InSb

3-12 8-13/1.5-5.5

-20/1500 -50/2000

0.1/30 0.1/70

30 pm 100 pm

HgCdTe HgCdTe

8-14 8-12

-50/350 -20/500

0.1/75 0.06/30

600 e/1 1.5 mrad

Notes: std = standard; opt = optional; amb = ambient; e/1 = elements per line. a Spatial resolution using microscope objective. b Their latest system quotes 4 pm spatial resolution.

In almost all cases, the investigator will be using a commercial IR system for temper­ ature measurement and will have detailed operating instructions available. Most of the important considerations and warnings will be in these instructions. The list on the next page outlines the general process to be followed.

5 .3 .4 3

O ptical probe system s

5.3.4.3.1 Background. Infrared systems detect the intrinsic thermal radiation given off by the test body or sample. In contrast, optical probe systems illuminate the test body with source radiation and detect either reflected radiation or stimulated radiation such as fluorescence. A variation of the sample temperature produces some change in an optical property such as the reflectance or the fluorescence decay rate. Through m easurement of the tem perature-sensitive optical property, the temperature is then inferred from the measured property value. An example of a surface probe w hich is widely used in the industry is the fiberoptic probe or therm om eter manufactured by the Luxtron Corp., Mountain View, CA. (Sun et al., 1985). In this probe, the fluorescence decay time of a temperature sensitive phosphor is measured. This decay time is a sensitive and reproducible function of the phosphor

Thenmtl measurements in electronics cooling

Infrared Measurement System Usage No.

Process

Description

Sample preparation

Since IR temperature measurement Is non-contacting, there are no sample connection requirements. For highest accuracy, it is desirable to coat the sample with a high emittance flat black paint This is necessary for semitransparent samples such as Si. However, in many cases this coating is impossible. Calibration of an IE system consists of determining an effective emittance such that the indicated IR temperature is the same as a contact sensor measured temperature. Calibration is discussed above. As discussed above, the IR indicated temperature is affected by background radiance that enters the optical system from the environment. If possible J t is desirable to shield the optics from nearby hot sources which are not part of the electronics system under test. It Is also necessary to prevent IE energy emitted by the heat source on the sample under test from being reflected back into the lens from nearby surfaces.

Calibration

Experimental setup

temperature. In the Luxtron probe, the phosphor-sensitive material is manganese-acti­ vated magnesium fluorogermonate. The phosphor is placed at the end of a fiberoptic cable, as shown in. Figure 13, The phosphor is excited in the wavelength interval -3 5 0 to 550 pm by a blue-violet pulse of light from a filtered xenon flash lamp, It then fluoresces in a wavelength interval ~ 600 to 800 pm with a temperature-dependent decay time varying from - 3 msec at 0°C to -1 msec at 300GC The time constant of the decay is measured and compared to values in a lookup table to find the temperature. Surface probes have a thin layer of the phosphor on the outside which is bonded with a soft elastomer which can deform to bring the probe tip into good contact with the sample. The probe is not highly conducting and hence does not modify the existing temperature field much. However, thermal contact resistance between the probe tip and sample produces a negative temper­ ature error, typically -2 % to 5%, depending on the nature of the sample surface.

Incident X# light pulse

Exciting light puls® Ruore&cerrt

Jacket

Optical fiber com

Thin phosphor elastomer , Surface to be measured

\

\

' Clear silicone elastomer

Figure 13 Luxtron surface probe detector, A thin elastomer containing the phosphor is applied to the tip of the probe, The Inset figure shows the optical Intensity at the phosphor, After the large exciting pulse transient ends, the fluorescent signal decay time is measured to determine the phos­ phor temperature,

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5 3 .4 3 .2 Probe types. A wide variety of probes is available for commercial systems (Luxtron Corp.). Surface probes typically work in the -5 0 to 200°C range and have a sensing spot size of 0.010 to 0.050 in. However, probes are available with tip sizes down to 0.001 in. In one experiment with a 0.050 in. probe, we compared probe temperature results with temperatures measured over a test die surface with diode thermometers (Sweet et al., 1993). For a chip surface temperature distribution which did not have sharp thermal gradients we found good agreement betw een the shape of the thermal profiles as measured by the two techniques. However, the probe temperatures were typically 2 to 3°C below the diode temperatures in the range - 60 to 90°C. For improved accuracy, the sample can be coated directly with a solution consisting of the phosphor material in pow der form and a suitable binder, typically a silicone material. Different binders are used for different temperature ranges. The powder is mixed with the binder liquid and applied to the sample. W hen dried, the pow der binder coating serves as the sensor and a remote sensing probe consisting of a fiber with a polished end is used to illuminate the coating and observe the fluorescence signal. 53.4.3.3 Calibration. As with other temperature sensors, calibration is performed by comparing the temperature obtained by probe with that obtained by another technique. We have discussed the com parison of probe and diode temperatures for IC device tem­ peratures. The readings obtained with the fiberoptic probe depend on the nature of the probe contact to the sample, the nature of the sample surface, and any errors which may be present in the m anufacturer's supplied calibration data which are used to convert fluorescence decay data to temperature. Thus it is difficult to specify a user calibration procedure which will work in all cases. For m easurements on a surface such as a printed circuit board, the following procedure is suggested: 1. Select a small piece of board, about 1 in. square, and mount a calibration thermo­ couple in a small drilled hole with conducting epoxy. 2. Heat the board on a hotplate at about 5°C intervals, over the temperature range of interest, using the thermocouple to monitor the attainment of thermal equilibrium. 3. Make ten successive probe temperature measurements of the board surface tem­ perature at a point near but not on the thermocouple. Use the average probe temperature as the measured temperature. If the probe needs to be hand held for the actual m easurement, do a hand-held calibration and check for systematic con­ tact errors by using different operators. 4. Determine the calibration function by fitting the thermocouple temperature vs. probe temperature function to a linear or quadratic function.

5.3.43.4 Optical probe usage. Commercial systems provide detailed instructions on probe system usage and operation of the electronic detector system. The general procedure given on the next page should be followed in the measurement process.

5.3.5

Bulk effect devices

There are a num ber of devices available which can qualitatively or semiquantitatively indicate temperature through a change in optical reflectance and hence color.

5 3 .5 .1

Liquid crystals

5.3.5.1.1 General considerations. Certain liquid crystals have a tem perature-depen­ dent reflectance in the visible w avelength range. Liquid crystals are long-chain m olecules with periodicity in one direction w hen bundled together but w ith w orm like nonperi­ odicity in the other two directions. The alignm ent is therm ally sensitive and the color

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200

Optical Probe Usage No.

Process Probe care

Probe positioning

Optical shielding Calibration

Description Probe life is highly dependent on the application. The probe and fiber should be handled with care and not bent or damaged. If any doubt exists about probe condition, the probe should be replaced. If possible, a probe holder and micromanipulator should be used to position the probe over the desired measurement location and to lower the probe into contact with the sample. In situations where a manipulator will not fit, hand positioning will be required. Great care should be exercised. It is desirable to shield the sample from stray light sources which could produce reflections back into the fiberoptic detector. A low ambient light level is suggested. Commercial probes have a calibration procedure so that indicated temperature may be set to that obtained by another thermometer such as a thermocouple. This procedure should be carefully followed.

changes are related to interference associated w ith the crystal spacing. They are applied by spreading a 1 to 20 pm thick coating onto the sample. Suitably chosen mixtures of cholesteryl ester or carboxylic acids, depending on the tem perature range, are used for the production of the liquid crystals. Since the crystal can be affected by radiation reflected from the sam ple surface, it is desirable to coat the sam ple with a black m atte varnish before applying the liquid crystal film. These m aterials are useful for obtaining inform ation on the form of the tem perature variation as a function of position in cases where the surface cannot be observed w ith an infrared im aging system. Liquid crystals are usable only under a restricted temperature range. Within the useful range of a given film, the color w ill change as a function of temperature. The major experim ental challenge is that of calibrating the liquid crystal color so that a quantitative m easurem ent of temperature can be made. An excellent discussion on the use of liquid crystals for determ ining the tem perature distribution of an electronic system has been given by Azar et al, (1991). In the experi­ ment reported by these authors, a thin film resistor was coated w ith a thin layer of black paint followed by the liquid crystal w hich had a tem perature-dependent reflectivity in the tem perature range 40 to 50°C. The liquid crystal was calibrated by m ounting a test specim en on an isotherm al plate w hose tem perature was determ ined with type J ther­ m ocouples. The liquid crystal filled the field of view of a recording video cam era and im ages obtained at 0.5°C intervals were characterized by their red, green, and blue content. In this way, the liquid crystal color was quantitatively linked to the sample tem perature. In the m easurem ent of the resistor tem perature, the sam ple was heated until its surface tem perature was in the range of the liquid crystal being used. The color im age was then recorded and each pixel in the im age was converted to an equivalent tem perature using the calibration inform ation. The accuracy claimed was ±0.5°C. In another reported experim ent w ith liquid crystals, N ishiguchi et al. (1991) com ­ pared the liquid crystal-determ ined tem perature with that m easured by a surface diode on a GaAs IC surface. These authors used a technique in w hich the film transition from liquid crystal to liquid was observed in a polarizing m icroscope. The reported precision of the m easurem ent, as determ ined by com parison with the diode tem perature was ±2°C. It appears that reasonably accurate m easurements can be made with liquid crystals at the expense of some m easurement com plexity if quantitative information is desired. However, if only a qualitative determ ination of a surface temperature distribution over a restricted temperature range is desired, the liquid crystal technique is very useful.

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53.5.1,2 No.

201

Liquid crystal usage.

Process

1

Sample preparation

2

Coating

3

Optics

Description To prevent spurious reflections from the sample, it is desirable to coat it with a flat black paint. The surface treatment should be the same as that used in the liquid crystal calibration. It is desirable to test the calibration and treated test surfaces simultaneously. A uniform coating thickness is essential for obtaining an accurate result. The sample and calibration films need to have the same thickness and should, if possible, be applied at the same time. If an imaging system is used, the optical setup for calibration and test should be identical (source to sample distance and sample to observing lens distance).

5 3 .5 .2

Therm ochrom ic m aterials A variety of thermochromic paints is available for temperature indication and rough tem­ perature measurement. These paints change color as a function of temperature in either a continuous or a discontinuous way. Reversible paints regain their original color after cooling, while irreversible paints undergo a permanent color change. The color may also be a function of the heating rate. These paints may be useful for determining whether a part ever experienced a high temperature excursion. As an example, the No. 69 paint manufactured by Synthetic and Industrial Finishes Ltd. has the following color transition temperatures (Michalski et al., 1991, pp. 37-39): Transition temp. (°C) Original color 150 240 310

Color Light tan Bronze green Deep purple brown Pale indian red

A new product for the electronics industry is the thermo-chromic board.* These are PC boards which are coated with a thermal ink which registers different colors with temperature changes. A temperature resolution of 1°C is claimed.

5.4

Specific measurement problems

There are many specific problems which the reader might encounter in the course of making temperature m easurements in electronics cooling heat transfer experiments, and it is impossible in a limited space to discuss them all. In the following sections, I shall discuss several problems which are common to m ost studies. The goal of almost all experiments is to determine the temperature rise of an active device above the ambient temperature as a function of various parameters in the problem such as the packaging architecture, air flow rate, etc. The result is the determination of a thermal resistance 0jx:

* Manufactured by VERO Electronics, Hamden, CT.

Thermal measurements in electronics cooling

202

where Tj is the junction or active device temperature, Tx is the ambient or reference temperature, and P is the device or circuit power. 0jx has units of °C/W and gives the increase in device temperature above ambient per unit power input. In many cases, 0jXis broken up into components which can be individually measured. For example, in an aircooled system, we might define a junction to case thermal resistance, 0jC, and a case to board resistance, 0cb, and a board to ambient resistance, 0ba. The junction to ambient thermal resistance 0ja is then the sum of these individual components. Determination of these various components involves measuring the junction (device), case, board, and ambient air temperatures. Each of these m easurements involves special problems. We now turn to a brief discussion of some of the more common measurement problems.

5.4.2

Device temperature

We have previously discussed the measurement of device temperature with temperature sensitive diodes or transistors. Many experimenters utilize thermal test chips which have resistive heaters to power the chip and one or more diodes or resistors for temperature measurement. The general subject is discussed extensively by Oettinger and Blackburn (1990) and by Oettinger (1984) and many examples have been given in the Proceedings of the IEEE Semiconductor Thermal M easurement and M anagement Symposium (SEMI­ TH ERM 5*'). If test chips are not available, it is sometimes possible to do thermometry with active ICs. All MOS and CMOS ICs utilize protection diodes on logic input bond pads to prevent overvoltages from destroying the MOS transistors. Although these diodes are reverse biased in normal operation, they can sometimes be forward biased for both pow ering the chip and temperature measurement. The major potential problem in the determination of Tj is the variation of die surface temperature with position which results from the nonuniform heat flux caused by the discrete nature of the heaters or other pow er producing circuitry. This issue is discussed by Oettinger (1984, p. 32), who advocates the use of computer programs to calculate the chip surface temperature distribution, Ts(x,y), for the known chip heater configuration. The measured Tj at the diode location can then be fitted to the calculated temperature, Ts(xd,yd), where xd and yd are the diode coordinates. The Ts function can then be used to find or predict either the chip average or peak temperatures. At Sandia we utilize this technique together with the commercial TAMs program (Ellison, 1984) to find the Ts(x,y) function for our Assembly Test Chips w hich have several rectangular resistive heaters. The relative variation in the Ts(x,y) function can also be checked approximately with either a fiberoptic probe sensor or an IR imaging system with high spatial resolution if an open die package is available. We use this method with chips mounted in unlidded ceramic leadless chip carriers which are mounted on a heat sink to produce an approximately isotherm al condition on the package back surface. This method also provides a measure of the difference between temperatures determined by the probe and the chip temperature sensor.

5.4.2

Board or substrate temperature

The m easurem ent of a printed circuit board or multichip module substrate temperature depends to a great extent on the com ponent thermal environment. There are four funda­ mental problems or causes of measurement difficulty or error in board temperature m ea­ surement:

* SEMI-THERM is a trademark of CS Communications. Proceedings for 1984-1986 are available from CS Communications, P.O. Box 23899, Tempe, AZ 85282. Proceedings for later years are available from the IEEE: IEEE Service Center, 445 Hoes Lane, Piscataway, NJ 08854.

Chapter five:

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203

L The presence of large thermal gradients at the measurement point may decrease the accuracy of the measurement as a result of either sensor positioning errors or from distortions of the temperature field. 2. Errors or uncertainty in knowing exactly what point or location in the sensor determ ines the measured sensor temperature. 3. Distortions of the temperature field produced by heat flow from the hoard or substrate into the sensor or probe. 4. Thermal contact resistance betw een the sensor and the sam ple point. The first two types of error are essentially similar in nature and are frequently com­ bined. Michalski et al. (1991, chap. 10) give a detailed discussion of the types 2, 3, and 4 errors for a surface temperature m easurement above an air-cooled isothermal surface. Their discussion applies to contact sensors such as thermocouples, resistance thermome­ ters, optical probes, etc. which contact the sam ple and may extract heat from i t Figure 14 show s the situation analyzed by Michalski et al. (1991). A solid surface is cooled by a gas and in a restricted region all heat flow is normal to the surface with the result that the isotherms in the solid and gas regions are parallel to the surface. When a probe such as a thermocouple is brought into contact with the surface some of the heat flows into the probe, distorting the isotherms as shown. This distortion or type 3 error results in a lowering of the actual surface temperature with a resultant negative temper­ ature error. The error can be minimized by increasing the thermal resistance in the probe and its connection to the outside world. As was previously discussed, it is good practice to bring the thermocouple wire out parallel to the surface for some distance to avoid sharp gradients near the probe tip region. To minimize the type 3 error, it is desirable to have a significant length of wire before the wire goes through a region where convective cooling will remove heat from it. Another source of error or type 4 error is the thermal contact resistance between the probe and the surface. The magnitude of this resistance depends on the nature of the probe-surface contact. A soldered connection may have a very low resistance, while a pressure contact will have a much higher resistance. In any case, thermal contact resistance results in a lowering of the indicated temperature relative to the actual temperature. Solid body

Solid body Gas

Gas

I isotherms

Qhg temp, profile

\ T

(a)

z

Surface temperature measurement using a contact probe, (a) Undistorted temperature field with all heat transfer from surface to liquid or gas in a normal direction; (h) distortion of the thermal field produced by the probe.

Figure 14

Thermal measurements in electronics cooling

204

The sensitive point in the probe, such as a thermocouple bead, may be located at some depth from the probe surface, with the result that the temperature drop between the surface and the probe location produces a decrease in measured temperature, much as contact resistance does. Thus it can be seen that all error sources produce a lowering of the measured temperature relative to the actual undisturbed temperature. In m aking a decision on a temperature measurement technique for surface measure­ ments it is useful to analyze the problem in sufficient detail so that the errors can be estimated. I have found the following steps useful in m aking technique decisions: 1. Make a heat transfer analysis in sufficient detail to enable the prediction of the isotherm pattern on the board or surface to be measured. 2. Decide w hat tem perature accuracy, 8T, w ill be required in the specific m easure­ m ent. This is usually determ ined by how accurately the therm al resistance in question needs to be determ ined. For exam ple, if a package case tem perature is to be m easured for a junction to case therm al resistance, but the therm al resistance of the system is dom inated by the case to board resistance through the package pins, then it may not be w orthw hile to measure the case tem perature to very high accuracy. On the other hand, it is necessary to determ ine the device or junction tem perature to at least the accuracy w ith w hich the therm al resistance needs to be found. 3. From the calculated isotherm pattern in the board, determine the size of the trans­ ducer (sensor) which will be required to resolve the temperature adequately. a. If the isotherm pattern is like that in Figure 14 with isotherms parallel to the surface, the least perturbation of the temperature field will occur if the thermo­ couple contact area is large and the thermocouple is thin. Film thermocouples are ideal for such an application. b. If the isotherms are close together, a small localized sensor will be required, with a lateral dimension which is small relative to the distance Ax over which the temperature changes by the required accuracy, 8T. 4. From the estimated thermal gradient normal to the surface and the surface heat flux, determine how well the sensor needs to be coupled to the surface and what type of joining technique is required. a. If there is a high magnitude gradient, such as might be encountered in a MCM w hich is mounted directly on a fluid cooled block, then it might be worth the effort to embed the thermocouple bead in a groove or hole in the substrate to obtain reliable surface or near-surface temperature measurements. b. If the gradient is relatively small, such as that outside a printed circuit board with low air flow, then epoxy connection of a film thermocouple might be perfectly adequate for obtaining the required temperature data.

5.4.3

Fluid temperature

Fluid temperature m easurement problems present some of the easiest and most difficult problems to the experimenter. A relatively thorough discussion of the subject is presented by M ichalski et al. (1991, chap. 12). A brief but interesting discussion of measuring air temperature in electronic enclosures is given by Moffatt (1992). In the case of still liquids, such as water or a heat transfer oil, the sensor is well coupled thermally to the bath and there is little or no error in the measurement. In this situation, the temperature is usually measured with sheathed thermocouples or resistance thermometers placed in the fluid. It is important to keep the fluid well mixed to prevent gradients from influencing the measurement. It is a good idea to use multiple sensors in order to ensure that the fluid temperature is in fact uniform.

Chapter five:

Temperature measurement in electronics cooling

205

In the case of moving gases with high gradients and nearby radiating surfaces at temperatures far removed from the gas temperature, the measurement may be very difficult and require some elaborate construction to obtain the required accuracy. One of the m ost common m easurements in electronics cooling studies is that of determining the air temperature in an enclosure. The flow in an electronics enclosure tends to be highly stratified and it is difficult to find a representative location to measure a meaningful temperature. Frequently, it is necessary to use multiple probes to characterize the air temperature completely. An array of thermocouples across a flow channel is a conventional arrangem ent for characterizing a flow inlet temperature. A n im m ersion sensor such as a thermocouple is subject to three kinds of environmental errors: conduction, radiation, and velocity errors. Conduction errors arise because the thermocouple wire has a high thermal conductivity relative to that of air and hence the wire conducts heat from the air to the wall in which the wire enters the flow. Hence a low conductivity thermocouple wire such as type K is desirable for this type of measurement. The longer the wire length in the flow the greater will be the thermal resistance between the junction and the wall according to the expression for thermal resistance in Table 1. It is generally suggested that a minimum of about 20 wire diameters be extended into the flow in order to minimize conduction error. Radiation error occurs from the transport of radiation from nearby hot surfaces to the thermocouple junction region. Analysis shows that the error will be inversely proportional to the heat transfer coefficient between the probe and the moving air. Hence the error will be the largest for still air measurements. Estimates show that the largest magnitude error possible will be about 1°C for every 10°C that neighboring components are hotter than the indicated air temperature for a situation where the airflow rate is 0.1 m/s (Moffat, 1992). Velocity errors occur because flowing gas molecules which strike the thermocouple junction region transfer energy to it. This energy transfer is distinct from that associated with random collisions produced by thermal motion. This error typically increases as the square of the flow velocity but is usually not significant at velocities ^ 20 m/s.

5A A

T ran sien t v s . ste a d y -s ta te m ea su rem en ts

In most electronics cooling measurements, the system is allowed to reach steady state, a situation in which the system temperatures are constant in time. In cases where conduction heat transfer is the primary cooling mechanism steady state is usually achieved very rapidly, typically on the order of a few seconds or less. On the other hand, in cases where convective air cooling is the primary heat exchange process, it may take hours to reach steady state. In any case, when steady state is achieved, measurements are made with conventional recording and monitoring equipment. There are, however, situations in w hich it is desirable to make transient measurements. In such cases, the time response characteristics of the sensor and associated electronics must be suitable for resolving the time varying temperature. In m ost cases of interest in electronics cooling, the smallest typical time variation w hich needs to be resolved is x s 0.1 msec. Temperature sensor sampling at a rate f = 1/x ^ 10 kHz can easily be done with thermocouple, resistance, or diode transducers and appropriate m easurement circuitry (National Instruments, 1995). During the transient, the transducer output is sampled and the data are stored for display and post-processing purposes. Several situations where transient measurements may be preferred over steady-state m easurements are listed below.

5 AAA

Situations in w hich the sam e solid state junction device is used fo r heat input and therm om etry

A com m on situation is one in which a transistor or diode is used for both heating and temperature sensing. A detailed explanation of such a measurement is given by Oettinger

Thermal measurements in electronics cooling

206

and Blackburn (1990). As an example, we consider the case where the source is a bipolar transistor. In the heating mode the base-em itter junction is driven by a large forward bias heating current Ih and steady state is observed when the base-em itter voltage V BE is a constant. The power input is given by P - IhV BE. The current is then switched to a small constant measurement current Im at a time t = t0 and the transistor is then used for thermometry. After a short transient, typically < 50 psec (0.05 msec), V BE settles from its heating value to its equilibrium transient value. The temperature decay is then observed through the m easurement of V BE(t). By backward extrapolation of V BE(t) to the turnoff time, t = t0, the temperature at the start of the transient is determined. This measurement is illustrated in Figure 15.

t(ps) 160

510 20 40

80

160

320

150 140 O o

130

P

120 110 100 90

flfl

0

2

4

6

8

10 12

14 16 18 20

t1/2(ps)1/2 Figure 15 Transient temperature measurement after step change heating. After a short transient, the temperature varies as (t - t^)1/2. Extrapolating this region to t = ^ yields the estimated temperature prior to the switching transient, = 0 in this figure.

Oettinger and Blackburn (1990) indicate that this extrapolation can be made using a

f i t - tf) time dependence to find the temperature T0 at the start of the transient:

T(t) = T0 - K V' t - t 0

(31)

In Equation (31), K is a constant. This relation comes from one-dimensional heat conduc­ tion theory. Eckert and Drake (1972, pp. 168-169) show that when a semi-infinite solid is suddenly exposed to a constant heat flux at its boundary, the temperature of that boundary increases as f t for all times. It is reasonable to assume that if that heat flux was switched off at t = t0, the temperature will decay as predicted by Equation (31), at least for times near t0. The technique is useful for finding the thermal resistance of devices such as power transistors or solar cells.

5A A .2

Situations in which it is desirable to learn som ething about the location o f various com ponents o f the therm al resistance

By their nature, steady-state therm al resistance m easurem ents only yield inform ation about the net resistance betw een the heat source and the reference m easurem ent point. H ow ever, it is frequently useful to determ ine w hat m aterials or interfaces in an assem bly are contributing the m ost to this resistance. For exam ple, in a typical IC

Chapter five:

Temperature measurement in electronics cooling

207

package resistance contributions arise from the die, the die-attach layer, the leadfram e or heat spreader, and the connection betw een package and board. In order to evaluate this type of structure a technique called the transient therm al test or heating curve m ethod is frequently used (Siegal, 1986). In this technique, a constant value heat flux or heating pulse is supplied for a tim e interval tH. At the end of the heating interval, the pulse pow er supply is turned off and the temperature of the heat source, Ts, is m easured, possibly as described in the previous section. In addition, the reference tem perature may need to be m easured sim ultaneously w ith the source tem perature if the reference is time varying also. Typically, tH is varied from several m illiseconds to a time at w hich Ts reaches steady state. A n excellent description of the technique and the analysis of transient data to extract useful param eters has been given by Sofia (1995). He fits the experim ental heating curve data to a heat conduction equation solution in w hich the various regions in the device or system under test are represented by lumped therm al resistances and capacitances. In order to illustrate the technique described by Sofia, I consider a m odel experim ent consisting of a m easurem ent of the therm al resistance of an IC m ounted on a substrate w hich is attached to a printed circuit board w ith soldered leads. The m odel system is show n in Figure 16(a) and consists of a die attached to a substrate w ith an epoxy die attach. The substrate, in turn, is m ounted to a circuit board through soldered legs. The heating curve function Ts(tH) is shown in Figure 16(b), where the quantity measured is 9jb = (Tj - Tb)/P, where P = heating power. The board tem perature, Tb, is measured w ith a therm ocouple and the junction tem perature, T]f w ith a diode or resistor on the IC. The first region of the heating curve, corresponding to 0 < tH ^ 0.01 s, represents the time in w hich the heat pulse propagates through the Si die toward the die attach layer. The tem perature increase is initially small because the high therm al conductivity of the die facilitates efficient heat spreading. The first steep region at t ~ 0.02 s corresponds to the therm al pulse encountering the high resistance die attach region. Heat then spreads through the substrate w hich has a high therm al capacitance and conductivity, w ith the consequence that the heating curve is relatively flat in the region, 0.02 s 5 tH 5 0.1 s. W hen the therm al pulse reaches the high thermal resistance leads at tH ~ 0.2 s, there is another steep region in the heating curve. Finally, for t S: 1 s, the system reaches steady state w ith no further change in Tj - Tb. The steady-state therm al resistance, 0jb(ss), is the quantity that would be m easured in a steady-state thermal resistance experiment. A lumped thermal circuit model for the system in Figure 16(a) is shown in Figure 16(c). The top node represents the chip heat sources and the quantities Rj and Q represent the thermal resistance and capacitance of the first region, corresponding in an approximate way to the die and die attach. M ost of Ra is associated with the die attach layer. For a hom ogeneous material, the thermal capacitance is given by mCp, where m is the mass and Cp the specific heat, as discussed in the derivation preceding Equation (7). The second node in Figure 16(c) with its associated capacitance C2 correspond roughly to the substrate, while the second resistor R2 represents spreading in the substrate and the resistance of the package leads. Rather than use R and C as parameters, Sofia uses R and the time constant t = RC as the independent param eters which are determined by fitting experi­ mental heating curve data to the predicted model results. In most cases discussed in the literature, the reference temperature is the air ambient temperature and not the board temperature. In that situation, there is a long final time constant for the board to come into equilibrium with the air, typically S 1 0 0 0 s. Sofia (1995) shows how data from this type of experiment can be fitted to a model such as that in Figure 16(c) to extract thermal resistance components and the time constants associated w ith these resistances. He also gives many examples of experimental data obtained with the technique.

2 is

Thermal measurements in electronics cooling

' Die attach

\ -Legs

'

Subs •

Board leads

v 'Board

(a) Chip |unotion, I 3

10"

10’

10*

10’

1Q»

heating time t* f$)

(b)

1 H

x

i

Board iy

(c) Transient thermal test method heating curve, (a) Model system with a heat producing die mounted on a substrate with an epoxy die-attach. The substrate is then mounted on a board and the board temperature is measured with a thermocouple, (b) Heating curve for the model experiment. The two steep regions on the curve correspond to high thermal resistance regions in the sample, (c) Lumped thermal circuit model for the system. The top node corresponds to the chip junction and die, while the second node corresponds roughly to the substrate. Figure 16

5 ,4 ,4 ,3 T ransient a p p lica tio n s In some electronics applications, high heat transients are encountered and it is necessary to measure the source temperature during the transient. Similar techniques to those dis­ cussed above can be used.

5.5

Summary

A variety of techniques for measurement of temperature in electronics cooling studies has been reviewed and some examples have been presented. Table 6 is presented as a summary and to aid the experim enter in selecting suitable techniques for measurement of various temperatures in electronics cooling problems,

5.6

For further study

The general subject of temperature measurement is covered in a number of excellent books, Temperature Measurement by .Michalski et al. (1991) covers the field in great detail, from an engineering point of view, with many practical exam ples and a host of supporting calcu­ lations. Extensive practical information is also presented in Temperature M easurement in Engineering , Vols, 1 and II by Baker ef al, (1975). Excellent general descriptions of engi­ neering temperature measurements are also given in Fundamentals of Temperature, Pressure, and Flow Measurements by Benedict (1984) and by Goldstein and Chang in the Handbook o f Heat Transfer Applications, For a more fundamental or laboratory view of temperature measurement, the book Temperature by Quinn (1983) is a valuable source. For fundamentals of heat transfer, a good elementary treatment is Introduction to Heat Transfen 2nd edition by Incropera and

Chapter five:

Temperature measurement in electronics cooling

Table 6

209

Suggested Measurement Techniques for Electronic Cooling Problems

Measurement

Technique and sensor

Comments

IC or heated device temperature

1. Device sensor on IC if available 2. Fiberoptic probe 3. IR imaging or liquid crystal

IC package surface temperature

1. Thermocouple (type K o r T) 2. IR

Substrate temperature

1. Integral resistor 2. Thermocouple (type K o r T) 3. Fiberoptic probe 4. IR or liquid crystal

PC board temperature

1. Thermocouple 2. IR or liquid crystal 3. Fiberoptic probe

Air temperature

1. Thermocouple

Fluid coolant temperature

1. Thermocouple

If a device sensor is available it will usually produce the highest accuracy measurement of device temperature. The fiberoptic probe is useful but will have a contact resistance error associated with it. IR and liquid crystal techniques produce a useful temperature map. A good low resistance thermocouple attachment is critical if an accurate package temperature is to be measured. IR imaging is useful to obtain an idea about the temperature distribution on the package in order to place the thermocouple in a near isothermal region. The presence of high thermal gradients may make this a difficult measurement. Both the probe and the thermocouple may be affected by high thermal contact resistance. IR and/or liquid crystal measurements will be useful to define the magnitude of these gradients. A thermocouple should be attached with conducting epoxy and imbedded in the board if possible. Board thermal gradients are usually reasonably small in magnitude, making precise probe placement not too much of a problem. See section on fluid measurements above for comments on use of thermocouples in air temperature measurements. Thermocouple should be located in well mixed fluid region.

DeWitt (1990). A more advanced treatment which has been referenced in this work is

Analysis o f Heat and Mass Transfer by Eckert and Drake (1992). Perhaps the m ost thorough discussion of electronic cooling is contained in the threevolume series Advances in Thermal Modeling o f Electronic Components and Systems by BarCohen and Kraus (1993). Although the emphasis is on modeling, there are many experi­ mental results presented. O f particular interest is a rather thorough bibliography, compiled by R. E. Simons, of papers published on heat transfer in electronic equipment, including papers on thermal m easurements and sensing, for the years 1986-1989. One of the best sources on practical techniques associated with electronics cooling measurements is the Proceedings o f the Semiconductor Thermal and Temperature Measurement Symposium (SEMI-THERM). This topical conference started in 1984 and has been held annually since that time. Frequently, short courses at this conference, such as Experimental Methods and Measurements in Electronics Thermal Control by R. J. Moffat (1992), provide a wealth of practical "how -to" information. Many current papers on experim ental m easurem ents in electronics cooling are con­ tained in the ASM E Journal o f Electronic Packaging and the IEEE Transactions on Compo­ nents , Hybrids , and Manufacturing Technology. There are also m any papers in the past IEEE

Thermal measurements in electronics cooling

210

Proceedings o f the Electronic Components and Technology Conference (ECTC). This annual conference usually has one or two sessions devoted to electronics cooling.

Acknowledgment The author would like to thank Dan Barton for making available workshop material he has presented on IR thermal techniques and fluorescent thermographic imaging.

5.7

Defining terms Am bient temperature: The temperature of the medium, usually air or another cooling fluid, to which heat is transferred from the electronic system or assembly. It is hard to define this term rigorously or in complete generality It is usually defined by a specific temperature measurement for a given experiment. An example would be the inlet air temperature in a wind tunnel experiment with a circuit board in the tunnel. Base-em itter voltage, V BE: The base-em itter voltage represents the voltage drop across the temperature sensitive diode. W hen the diode is biased in its forward or "o n " direction, it supports a current with a voltage drop w hich is a weak function of current and varies approximately linearly with temperature. Black body: A material w hich is a perfect emitter (or absorber) of infrared radiation, with an emittance equal to unity. Some materials such as certain flat black paints and carbon black approach e = 1. Artificial black bodies are cavity structures which trap incident radiation efficiently. Conduction: A m echanism of heat transfer in w hich heat is transferred through either direct contact of bodies at different temperatures or through a body with a temper­ ature gradient. Convection: A heat transfer mechanism in which heat is transferred from a hot body to a moving fluid as a result of mass motion of the fluid over the body. D*: The "d ee-star" function w hich is related to the spectral or detector response function for an infrared optical detector. It is a figure of merit for a detector w hich is approximately independent of the detector area and frequency bandwidth and hence can be used to compare different detectors. Distribution function: A mathematical function specifying the relative frequency with which a group of identical entities are distributed with respect to some variable. If there are N identical entities with the property x and a distribution function f(x), then the num ber of entities w ith the property in the range x to x + dx is f(x)dx. Electrical resistivity: A material property w hich gives the electrical resistance of a unit length of a material with a unit cross section area. It has units of Q m. Emittance: The emittance or em issivity of a material is a number, e, which measures the relative efficiency with which a body will emit or radiate thermal energy to a surrounding environment at a lower temperature, e is defined such that 0 < e < 1, with e = 0 corresponding to a non-em itter (perfect reflector) and e = 1 corresponding to a perfect emitter or black body. For a more precise definition see, for example, Eckert and Drake (1972, chap. 15). Fluorescence: A process in w hich an atom absorbs a photon at one wavelength and then drops or decays to an interim state by em itting a photon at a longer wavelength and lower energy. Heat transfer coefficient: A number specifying how much heat is transferred per unit area and unit time across an interface or region when a unit temperature difference occurs across the interface or region.

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211

Heat Transfer: A process in w hich energy flows from a body with a high temperature to a body at a lower temperature. Heat transfer can occur by conduction, convection, or radiation. Infrared radiometry: The process of obtaining a temperature map or thermal image of a sample by observing the infrared radiated electromagnetic energy emitted by the sample. With a suitable detector and signal processing, this measurement yields a num ber w hich is proportional to the absolute temperature of the sample at each sample point. Junction to am bient thermal resistance: The temperature rise of a power producing device above the ambient temperature per unit pow er input into the device, ex­ pressed in °C/W. This is a somewhat imprecise term but is in common use in the electronics cooling community. The imprecision arises from the fact that neither the terms junction nor ambient may be precisely and uniquely defined. The junction commonly refers to the p-n junction of the diode used for device thermometry, but this junction may not be at the hottest location on the die under test. Similarly, the ambient temperature may be defined somewhat arbitrarily (see ambient tempera­ ture). Kelvin (four-terminal) configuration: An electrical measurement configuration used to accurately measure the resistance or current-voltage relation of an electrical device. Two terminals are used for supplying current to the device and the other two term inals for measuring the voltage across the device. Current and voltage term inals of the same polarity are connected right at the device by the manufacturer. In this geometry, the measured device voltage is not affected by the voltage drops across resistances in the current source leads. Liquid crystals: These are organic compounds which can flow and yet maintain their characteristic molecular orientations. The molecular alignment can affect the optical reflectivity of the liquid crystal and it can be affected or controlled by temperature and electric field. M odulation: A technique w hich is used in optical detection systems to reduce the effect of noise generated detector current. The incoming radiation is modulated or chopped at some frequency f and the detector output current is measured within a small bandwidth or frequency interval about f. Noise produced at frequencies outside this bandw idth w ill not contribute to the measured signal. Photoelectric detectors: Detectors used to measure the intensity of incident electro­ magnetic radiation. They are semiconductors w hich absorb radiation within a cer­ tain wavelength interval. The absorbed electromagnetic energy generates electric currents in the semiconductor w hich are detected with suitable circuitry, providing an output signal which is a function of the temperature associated with the incident thermal radiation. Probe: The portion of a thermal sensor whose temperature controls the output of the sensor. The balance of a sensor consists of the sensor body, electrical leads, and an amplifier/readout unit. Radiation: A heat transfer mechanism in which thermal energy is transported by infrared radiation emitted by a hot body and received by a cooler body. Resistance thermom eter (RTD): A thermometer or resistance temperature detector whose probe is a temperature sensitive electrical resistor. The body consists of the leadwires, usually four, and the probe case. Sample: The portion of a system for which the temperature is being measured. Seebeck coefficient: A temperature-dependent material property which gives the rate of change or derivative of the open circuit voltage with respect to temperature for a piece of the m aterial with ends held at two different temperatures. Since it is defined as a derivative, it does not depend on the magnitude of the reference

Thermal measurements in electronics cooling

212

temperature, only on the temperature of the end whose voltage is being measured with respect to the reference. Semiconductor devices: These are common structures, made in semiconducting m a­ terials by ion doping or implantation, insulating and conducting film deposition, and photolithographic definition of these films. Among the most common devices used for therm om etry are the bipolar junction transistor, the junction diode, and the metal-oxide-sem iconductor (MOS) field effect transistor. Sensor system: A complete thermal m easurement system, as shown in Figure 4. It consists of a probe which is sensitive to temperature, a sensor body, and an amplifier or readout unit. Specific heat: A material property w hich gives the temperature rise in a thermally isolated piece of the material per unit mass for a unit energy input. The specific heat is usually measured at constant pressure and has units of J/kg-K. Spectral response function: A function of wavelength, D(^), characterizing how well a given detector can sense incident infrared radiant energy. It is the reciprocal of the noise equivalent power, w hich is the smallest amount of radiant power which could theoretically be detected. This is an amount of power w hich would produce a detector current equal to the intrinsic detector noise generated current. Surface tem perature: The temperature at a surface or interface between two different materials. Frequently there is a very high thermal gradient normal to the surface so that the temperature at the geometric surface may be quite different from that at nearby points in a norm al direction. System: The system is defined to be either a complete electronic assembly or a subassembly under test. An example of a system would be a whole personal computer and the surrounding air. Another example would be a circuit board from a personal computer mounted in a wind tunnel together with the air flowing over the board. A third example would be an IC package and the cooling block on which it is mounted, including the coolant flowing through the block. Temperature: A property of a body or system proportional to the average energy of the particles in the system. If the temperatures of two systems are equal, they will not exchange heat when brought into contact. Thermal conductance: A number giving the total heat flux or pow er in W flowing through a body or region with a unit temperature difference across the region. Thermal resistance: The inverse of the thermal conductance, it gives the temperature drop across a body or region when a thermal net heat flux or power of 1 W flows through the region. Thermochrom ic paints: These are paints whose color or optical reflectance properties are a function of temperature. Depending on the specific paint, the color change may be reversible or irreversible and it may also be a function of the heating rate. Therm ocouple bead: The tip or temperature sensitive joint of a thermocouple. It may be a physical bead such as a weld or solder region or a part of the sheath which is joined to the two thermocouple legs. Thermocouples: A type of temperature sensor made with wires of two different materials. The probe is the joint betw een the two different wires. The wires are each connected to extension wires, one of which has a reference temperature junction. The temperature sensitive parameter is the open circuit voltage developed in the circuit.

References ASTM (American Society for Testing and Materials), Committee E20, Manual on the Use of Thermo­ couples in Temperature Measurement, 4th ed., ASTM, Philadelphia, 1993.

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Azar, K., Benson, J. R., and Manno, V. P, Liquid Crystal Imaging for Temperature Measurement of Electronic Devices, Proc. 7th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, IEEE, 1991, pp. 23-33. Baker, H. Dean, Ryder, E. A., and Baker, N. H., Temperature Measurement in Engineering; Vol. 1, Omega Press, Stamford, CT, 1975. Bar-Cohen, A. and Kraus, A. D., Advances in Thermal Modeling of Electronic Components and Systems, Vol. 1, Hemisphere Publishing, New York, 1988; Vol. 2, ASME Press, New York, 1990; Vol. 3, ASME Press, New York, 1993. Barnes Engineering Co., Handbook of Infrared Radiation Measurement, Barnes Eng. Co., Stamford, CT, 1983. Benedict, R. P , Fundamentals of Temperature, Pressure, and Flow Measurements, 3rd Ed., John Wiley & Sons, New York, 1984. Bentley, J. P , Principles of Measurement Systems, 2nd ed., John Wiley & Sons, New York, 1988. Dereniak, E. L. and Crowe, D. G., Optical Radiation Detectors, John Wiley & Sons, New York, 1984, pp. 32-58. Eckert, E. R. G. and Drake R. M., Jr., 1972, Analysis of Heat and Mass Transfer, McGraw-Hill, New York, 1972. Eckert, E. R. G. and Goldstein, R. J., Measurements in Heat Transfer, 2nd ed., McGraw-Hill, New York, 1976. Ellison, G. N., Thermal Computations in Electronic Equipment, Van Nostrand Reinhold, New York, 1984. Hewlett Packard, Application Note 290, Practical Temperature Measurements, 1988. Incropera, F. P. and DeWitt, D. P., Introduction to Heat Transfer, 2nd ed., John Wiley & Sons, New York, 1990. Lide, D. R., CRC Handbook of Chemistry and Physics, 75th ed., CRC Press, Boca Raton, FL, 1994. Luxtron Corp., Model 755 Technical Reference and Service Manual, Luxtron Corp., Mountain View, CA. Michalski, L., Eckersdorf, K., and McGhee, J., Temperature Measurement, John Wiley & Sons, New York, 1991. Moffat, R. J., Experimental Methods and Measurements in Electronics Thermal Control, (presented as a short course at the Eighth SemiTherm Symposium on Semiconductor Temperature and Thermal Management), Moffatt Thermosciences Inc., 1992. National Instruments, "Measuring Temperature with RTDs, Application Note 046, 1995; Measuring Temperature with Thermocouples — a Tutorial, Application Note 043, 1995. Nishiguchi, M., Fujihira, M., Miki, A., and Nishizawa, H., Precisional Comparison of Surface Tem­ perature Measurement Techniques for GaAs ICs, Proc. 7th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, IEEE, 1991, pp. 34-38. O Mathuna, S. C., Fremont, T., Koschnick, W., and O'Connor, L., 1993, "Test Chips, Test Systems and Thermal Test Chips for Multichip Modules in the ESPIRIT-APACHIP Project, Proc. 9th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, IEEE, pp. 117-126. Oettinger, F. F., Thermal evaluation of VLSI packages using test chips — a critical review, Solid State Technol, Feb., 169-178, 1984. Oettinger, F. F. and Blackburn, D. L., Thermal Resistance Measurements, NIST Special Publication 400-86, U.S. Dept, of Commerce, Washington, D.C., 1990. OMEGA Engineering, The Temperature Handbook, OMEGA Engineering Inc., Stamford, CT, 1991. Quinn, T. J., Temperature, Academic Press, London, 1983. Reif, F., Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965. Rohsenow, W. M., Hartnett, J. P., and Ganic, E. N., Handbook of Heat Transfer Applications, 2nd ed., McGraw-Hill, New York, 1985. Sears, F. W., An Introduction to Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics, Addison-Wesley, Reading, MA, 1953. Siegal, B. S., Implementation of Thermal Transient Testing in Production Applications, Semiconduc­ tor Thermal and Temperature Measurement Symposium (Semitherm), Southwest Seminars, paper B.5, CS Communications, Tempe, AZ, 1986. Sofia, J. W., Analysis of thermal transient data with synthesized dynamic models for semiconductor devices, IEEE Trans. Components, Packaging Manuf. Technol., 18(A), 39, 1995.

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Sun, Mv Wickersheim, K., and Kim, J., Improved Surface Temperature Measurement Techniques for Use in Conjunction with Electronics Processing and Testing, Proc. 1985 Semiconductor Thermal and Temperature Measurement Symposium (Semitherm), Southwest Seminars, paper A.4, CS Communications, Tempe, AZ, 1985. Sweet, J. N., Peterson, D. W., Chu, D., Bainbridge, B. L., Gassman, R. A., and Reber, C. A., Analysis and Measurement of Thermal Resistance in a 3-Dimensional Silicon Multichip Module Popu­ lated with Assembly Test Chips, Proc. 9th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, IEEE, 1993, pp. 1-7. Sweet, J. N., Peterson, D. W., and Emerson, J. A., Liquid Encapsulant and Uniaxial Stress Measure­ ment with the ATC04 Assembly Test Chip, Proc. 44th Electronic Components and Technology Conference, IEEE, 1994. Verster, T. C., The silicon transistor as a temperature sensor, Temperature, Its Measurement and Control in Science and Industry, Vol. 4, Plumb, H. B., Ed., Instrument Society of America, Pittsburgh, 1972.

chapter six

Measuring pressure in electronic systems George A. Pender 6.1 6.2 6.3

Introduction.......................................................................................................................................216 Pressure m easurem ent...................................................................................................................216 Pressure measuring in strum ents...............................................................................................219 6.3.1 M anom eters........................................................................................................................ 219 6.3.2 Dial g a g es........................................................................................................................... 221 6.3.3 Electronic tran sd u cers....................................................................................................221 6.3.3.1 Flush diaphragm transducers..................................................................... 221 6.3.3.2 Silicon-based pressure transducers........................................................... 222 6.3.4 S y stem s................................................................................................................................223 6.4 Calibration of pressure measuring instrum ents.............................................. 223 6.5 Data acquisition/measurement system erro rs..................................................................... 223 6.5.1 M anom eters........................................................................................................................ 223 6.5.2 Dial g a g es........................................................................................................................... 225 6.5.3 Electronic tran sd ucers.................................................................................................... 225 6.5.3.1 Temperature resp on se....................................................................................225 6.5.3.2 Frequency resp on se........................................................................................ 226 6.5.3.3 Media com patibility........................................................................................ 226 6.5.3.4 M ounting effects............................................................................................... 226 6.5.3.5 M agnetic fields.................................................................................................. 226 6.5.4 Periodic com parison to pressure stan dard.............................................................. 226 6.5.5 Pressure tap erro r.............................................................................................................227 6.5.6 Spatial error in AC pressure m easurem ents...........................................................227 6.5.7 Data acquisition system s................................................................................................227 6.5.7.1 Cable effects.......................................................................................................227 6.5.7.2 A m plifiers........................................................................................................... 228 6.5.7.3 E xcitation .......................................................................................................228 6.5.7.4 Electrical n o ise .................................................................................................. 228 6.5.7.5 Digitizing erro rs............................................................................................... 229 6.5.7.6 Analog filtering................................................................................................. 230 6.6 Measuring pressure in a typical application........................................................................ 231 6.7 How-to list for pressure m easurem ent....................................................................................233 6.8 Defined term s....................................................................................................................................237 References................................................................................................................................................... 241 Appendix: for further inform ation.................................................................................................... 241 0-8493-3279-6/97/$0.00+$.50 © 1997 by CRC Press LLC

? 1 5

216

Thermal measurements in electronics cooling

6.1

Introduction

In the pressure measurement continuum from the vacuum of outer space to the crushing pressure required to transform graphite into diamond, only a tiny fraction of that contin­ uum is used for pressure m easurements in the cooling of electronic systems. This tiny fraction, however, has great utility in m easuring the pressure drops generated and in determ ining the presence and amplitude of vortices and wakes in turbulent flow. Spoilers, baffles, and deflectors are all being used to increase the contribution of turbulence to heat transport. As the need for more energy-efficient cooling grows, the need for m easuring the turbulence in pressure at each source of heat generation will follow. To characterize a cooling system, pressure instruments measure: • • • • • • • • • •

The pressure drop across channels in electronic circuit card assemblies Differential pressure across Pitot tubes, orifice plates, and venturi tubes Intake to exhaust pressure drop in forced convection cooling systems The amplitude and frequency of turbulence components Pressure drop across heat exchangers Pressure build-up in sealed cooling systems utilizing boiling/condensation of liq­ uids Pressure drop across in-line filters Pressure in circulating pumps Barometric pressure used in data correction for hot wire anemometers Static pressure level in cooling system control loops

Pressure measurem ent and the instruments that serve these applications are the subject of this chapter.

6.2

Pressure measurement

Pressure is defined, in technical terms, as a stress, Le. force per unit area. It has been a most useful concept for the measurem ent of fluids, both stationary and in motion. The first m easurement of pressure was made in 1643 using a manometer (a useful device today as well). It was noted that an evacuated column of mercury contained in a glass tube, its open end immersed in a dish of mercury (Hg), repeatedly sank to a level of some 76 cm (such a device is now called a m ercury barometer). It was reasoned that the weight of the Earth's air m aintained the m ercury at that height. The force on the mercury column due to the Earth's gravitational field was F = mg = pVg = phAg m g P V h A

= = = = = =

(1)

mass of Hg gravitational constant density of Hg volume of Hg height of column of Hg area of Hg

Since the forces were in equilibrium, the force imposed on the m ercury dish due to the Earth's blanket of air (atmospheric force) had to equal the force exerted by gravity on the mercury column, so

Chapter six:

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217

Atmospheric force = p h A g

(2)

and since pressure was defined as force per unit area, the atmospheric pressure was Atmospheric pressure = Atmospheric force/area = p g h

(3)

Since p and g were known constants, the atmospheric pressure could be measured by the height of the liquid column. Initial confirmation of this theory was made by measuring the mercury column level on top of a mountain, where a difference of 76 mm (3 in.) was detected for an elevation change of 914 m (3000 ft) (Benedict, 1984). It was soon observed that the level of the liquid in a m anom eter was independent of the size and shape of its confining boundaries. This observation led to the further realization that a pressure applied to a confined liquid was transferred undiminished throughout the liquid to all bounding surfaces (Pascal's law). These two fundamental principles led to the development of m odem pressure measuring instruments, since the measurement of pressure in any liquid could be indicated by the elastic deformation of any container of the liquid. Bourdon tubes, bellows, and diaphragms all deformed when pressurized, and their displacement was proportional to the amount of pressure exerted by the liquid. M odem electronic manometers and pressure transducers used for pressure measurement are all based on this definition of pressure, i.e. they measure pressure as an induced stress. Following the initial discoveries using mercury manometers, the observed similarity between gas and liquid in response to pressure was key to the development of the kinetic theory of gases. The pressure of a gas in a closed container was thought to result from the continuous impact of large numbers of molecules on the container walls. This theory was soon borne out by experimentation, since pressure m easurement at any point in a closed container of gas yielded identical results. The development of the theory enabled pressure to be defined in terms of the kinetic energy of molecules and its relation to temperature (Pendlebury, 1985). p = 2 E = MC^ = qRT 3V where

P E V M C2 q R T

3V

V

= absolute pressure = kinetic energy of molecules = volume = total mass of the gas = average value of the square of the molecular velocities = num ber of moles of gas = gas constant = absolute temperature

In the m easurement of vacuum, i.e. very low pressure, the force imparted by the gas molecules is in many cases too small to result in any measurable displacement of a pressure sensing element. As a result, measurement devices have been developed which do not measure pressure directly (these are referred to as inferential pressure transducers); they measure physical characteristics of the gas w hich are proportional to the pressure, and with suitable corrections, can be equated to the pressure. These inferential pressure mea­ suring devices are used extensively in high vacuum systems but their usage in electronic cooling systems is limited; the reader is referred to Berman (1985) for a comprehensive review of their capabilities.

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Thermal measurements in electronics cooling

In the SI system, pressure is measured in pascal (or newton/m2), in the metric system it is gram/cm2, and in the English system pressure is measured in pounds per square inch (abbreviated as psi). See Table 7 for pressure unit conversions, psi is further delineated by adding a suffix which denotes the reference. Differential — psid in the English system where the d suffix denotes differential, i.e. a pressure difference between two points is measured. There are many measurements where the individual value of the two pressures is of little or no concern, but the differential pressure may be vital. For example, a clogged filter has the potential to reduce the operating efficiency of the system, but only the differential pressure across the filter, not the individual pressures, is of concern. All pressure measure­ ments of fluids are differential, but when the reference pressure is defined a priori, specific nam es have been assigned as noted below. Absolute — psia in the English system where the a suffix denotes absolute, which means that the pressure m easurement is being made referenced to a total vacuum. A total vacuum may be defined as a volume at zero pressure, i.e. there are no atoms present to exert a force against the walls of the container. Psia devices are most com m only used in pressure measurem ent where the atmospheric pressure will be changing during the measurement, e.g. rockets. Gage — psig in the English system where the g suffix denotes gage , which means that the reference pressure is local atmospheric pressure (gauge is a variation of gage). Since atmospheric pressure is a function of altitude, humidity, wind, etc., the absolute value of the pressure can only be determined if local atmospheric pressure is known. Sealed — psis in the English system where the s denotes sealed, which represents a device w ith the reference pressure cavity sealed at standard (or Normal) atmospheric pressure. Sealed pressure sensing devices are usually chosen to prevent the huge zero offset (essentially full scale) in the electrical output of a 103 kPa (15 psia) absolute transducer which occurs since barometric (atmospheric) pressure is about 101 kPa (14.7 psia). True psis devices should be avoided whenever possible because the trapped gas at 101 kPa (14.7 psia) makes an excellent therm ometer via Charles' gas law. Simulated psis devices with a reference vacuum and an electrical offset are usable, as they are really psia devices. Line — this term commonly is defined as the pressure existing simultaneously on both sides of a sensing element, e.g. a diaphragm. Common mode pressure is now synonymous with line pressure. See Defined Terms in Section 6.8 for the rigorous definition of line pressure. Henri de Pitot developed the procedures for measuring fluid flow in 1732, and these basic procedures are still in use today. W hen measuring pressure under flow conditions, there are two complementary measurements w hich must be made to describe the (incom­ pressible) flow: the static pressure and the total pressure. Note that dynamic pressure (also called impact pressure or velocity pressure) is the difference between total and static pressure. Figure 1 illustrates the concept. Under laminar flow conditions, both the static and dynamic pressures are steady state. In turbulent flow conditions, the pressures are changing with time, and m easurements in the kilohertz range are often required in order to quantify the turbulent parameters. Depending on containm ent and boundary conditions, the pressure m easured in the m iddle of the flow (point A), and the boundary of the flow (point B), m ay be significantly different. Since high flow rates generate low pressure areas (a basic law of physics attributed to Bernoulli), negative, i.e. subatm ospheric, pressures may be observed. Except in conditions of lam inar flow, the static pressure m easurem ent at point "A " will

Chapter six:

Figure 1

M easuring pressure in electronic systems

Fluid flow diagram.

219

ILLUSTRATIONS BY GARY CLEVELAND 1996

have turbulent com ponents and it is necessary to average the pressure readings over an elapsed period of tim e, e.g. 30 s. Since dynamic pressure is the difference between total and static pressure, the static and total pressure tubes may be plumbed to a differential pressure indicator which then reads out the dynamic pressure directly The velocity of the fluid may be derived from Bernoulli's equation for incompressible, steady state flow:

where

v pd p

= fluid velocity = dynamic pressure = fluid density

In addition to pressure associated with duct or pipe flow, pressure associated with acoustic noise is also a point of interest in electronic systems. Forced air cooling of enclosures is certain to generate acoustic energy, i.e. periodic, low amplitude pressure pulsations. The measurem ent of amplitude and frequency of this acoustic energy is nec­ essary in some applications to control the resulting acoustic noise and vibration (see Chapter 12). With the advent of thermoacoustic cooling, there is also a requirement for pressure measurem ent of the acoustic generator, and the generator's acoustic level falls neatly into the norm al operating range of a condenser microphone.

6.3

Pressure measuring instruments

The three major types of pressure measuring instruments are manometers, dial gages, and electronic transducers. Table 1 tabulates the salient features. 6 .3 .2

M a n o m e te r s

If a liquid is poured into an open U-shaped tube, the liquid level in each side will be the same, as in Figure 2a. If pressure is applied to one side, that level will go down and the level on the other side will rise (the pressure being applied is balanced by the weight of

220

Thermal measurements in electronics cooling

Table 1 Types of Pressure Measuring Instruments

Characteristic

Manometer

Pressure range

fO 1 kPa (0,25 in, HXMO0 in, tig) 0.25 Pa {0.001 in, HO) to Accuracy range 2% full scale Frequency response < 10 Hz No Electronic output Temperature range -62°C to +66°C Media compatibility Gas Cost (U.S.) $100-42000

Dial gage

Electronic transducer

62 Pa-700 MPa (0.01-100,000 psi) G.066%-5% full scale

25 Pa-700 MPa (0,004-100,000 psi) O,0O3%“3% full scale

< 10 Hz No -32°C to +54°C Gas or liquid $10-$3000

DC to 1 MHz Yes -27FC to +40Q°C Gas or liquid $50-410,000

the liquid column), as in Figure 2b. This difference between the two levels is called the pressure head and is proportional to the pressure applied and the density of the liquid. Although the LRube manometer is the simplest form of manometer, it is the recognized standard for the measurement of low pressure. If one side of the manometer is connected to an unknown pressure., and the other side is left open to atmosphere, the manometer indicates gage pressure, positive or negative (vacuum). Differential pressure is measured by connecting each leg of the manometer to the two different pressures. Absolute pressure is measured by evacuating one side; a barometer is a specialized manometer with a reference vacuum so it responds to atmo­ spheric pressure. M anom eters are commercially available in U-tube, well-type, and inclined tube configurations (see Figure 2 and Table 2). For both the well-type and inclined manometers, the pressure is indicated directly by the scale, whereas the U-tube manometer requires reading the scale on both legs, The m echanical advantage provided by the inclined manometer increases the fluid displacem ent for a given pressure which enables lower pressure changes to be detected. The inclined water manometer is used extensively in pressure measurement for forced air cooling of electronic systems.

Figure 2

Types of manometers.

Chapter six:

M easuring pressure in electronic systems

221

Table 2 Types of Manometers Type U-tube Well Inclined

Full scale range 500 Pa-339 kPa (2 in. H2O-100 in. Hg) 1 kPa-339 kPa (4 in. H2O-100 in. Hg) 62 Pa-5 kPa (0.25 in. H2O-20 in. H2Q)

Accuracy range 0.25 Pa (0.001 in. H20 ) 2% of full scale 0.01% of full scale-2% of full scale 0.025% of full Scale-1 % of full scale

Manometers are available in ranges from 62 Pa to 339 kPa with accuracy to 0.25 Pa (0.001 in. H20 ) . While manometers are highly accurate and sufficiently sensitive to the low pressures encountered in gas media cooling applications, they lack the capability for remote reading and recording of the indicated pressures. They also have very limited frequency response. Further information on liquid column manometers can be found in Berman (1985).

632

D ia l g a g e s

A pressure sensing element, such as a bourdon tube, is mechanically attached to a pointer which rotates against a graduated dial as pressure deforms the sensing element. These gages are available in ranges from 62 Pa to 700 MPa (0.25 in. H20 to 100,000 psi), with accuracy to 0.066% of full scale. Dial gages have two m ajor limitations for use in cooling system pressure measurement; no remote reading/recording capability and limited frequency response.

6 3 3 E lectro n ic T ran sd u cers When a novel mechanical to electrical transduction principle attains commercial viability, it is often first applied to pressure transducers. Table 3 lists the major different pressure sensing elements, in addition to the different transduction principles which are utilized in electronic transducers available today. Since any of the pressure sensing elements noted in the left column of the table can be combined with any of the electrical transduction principles on the right column of the table, a large variety of pressure transducers is available to choose from. Note that none of the sensing elements listed are inferential, i.e. all of these sensing elements respond to pressure as an induced stress and the measured pressure is therefore not a function of the chemical composition or physical characteristics of the fluid. Electronic pressure transducers are available in full scale ranges from 25 Pa to 700 MPa (0.004 psi to 100,000 psi), with accuracy as good as 0.003% of full scale. For a comprehensive review of the various sensing elements and mechanical/electrical transduction principles used in pressure transducers, the reader is referred to Norton, (1982), Allocca and Stuart, (1984), Fraden, (1993), Neubert, (1975), Sinclair, (1988), and Tandeske, (1991). 6.3.3.2 Flush diaphragm transducers Flush diaphragm transducers are required to make high-frequency m easurements of tur­ bulence intensity since transducers with recessed diaphragms or attached tubing have limited frequency response due to Helmholtz or organ-pipe resonance in the cavity. All three of the configurations shown in Figure 3 have flush diaphragms but the recently available flatpack configuration (see Figure 3b) provides minimum disturbance of the flow coupled with ease of mounting, e.g. the flatpack unit can be adhesively mounted to a cooling fin (see Section 6.S.3.4 for recommended mounting techniques). For extremely low pressure amplitudes, only condenser microphones/hydrophones have the required sen­ sitivity, e.g. 1 mV/Pa (6.9 V/psi) for a 3.2 mm (0.125 in.) diameter device.

222

Thermal measurements in electronics cooling

Table 3 Types of Electronic Transducers

Figum- 3

Pressure sensing elements

Electrical transduction principle

Bourdon tube, Helical Oshaped Spiral Twisted Bellows, metal Capsule, metal Diaphragm, Metal, (flat or corrugated) Silicon Ceramic Tube, metal (radial tube expansion) Membrane, elastomer

Resistance, Metal wtrewound Plastic Cermet Bulk Force balance (Servo) Strain gage, Deposited (thin) film Bonded foil Unbonded wire Bonded semiconducto r Ditfused semieonduetor Capacitance (condenser) Reluctance Inductance Eddy current Differential transformer (LVDT) Vibrating (resonant) Tube Wire Beam Diaphragm Piezoelectric P hotoelec trie /fi her op dc Magne tos triciive

MinIalure si Iieon-ba sod press ure t ransduce rs. {Shown 2< actua 1 size),

6332

Low accuracy pressure transducers

For low accuracy pressure measurement requirements, such as measuring the differential pressure across filters to detect clogging, silicon-based pressure transducers developed for the automotive industry are likely candidates. These automotive pressure transducers fea­ ture high sensitivity, good temperature performance, and outstanding performance/price ratio. Media compatibility is always an issue for silicon diaphragm transducers, and some precautions may be required (see Section 6.53,3), These transducers are available from many sources, reference 1 7,18, 28, 28, and 39 of Table 6.

Chapter six:

6 .3 .4

M easuring pressure in electronic systems

223

S y stem s

Complete air data measurement systems which measure pressure, air flow, velocity, and temperature all in one package have been developed for the HVAC (heating, ventilating, and air conditioning) market. These systems are of lower accuracy than instruments used in research, but may be completely adequate for many industrial applications. Sources are noted in 5 ,2 1 ,2 9 , and 41 of Table 6. Silicon diaphragm transducers specifically designed for low pressure measurem ent are available from sources 2 and 10 of Table 6.

6.4

Calibration of pressure measuring instruments

All pressure m easuring devices should be periodically calibrated to verify their accuracy. Manometers, precision dial gages, and high accuracy electronic transducers are usually on an annual recalibration cycle. Lower accuracy (e.g. 1%) instruments are usually cali­ brated every 6 months. For the highest attainable accuracy, zero and span calibrations are made periodically during the test using electronic or mechanical scanning methodology (see Section 6.5.4). The calibration of a test pressure instrument should be accomplished over the pressure and temperature ranges expected in the test. A ten point calibration over the pressure range anticipated is sufficient to characterize the device (any deviation from straight line linearity can be curve matched using a polynomial expansion). Placing the transducer in a precision controlled temperature chamber (such as a Delta 9000 series environmental chamber, reference 7 of Table 6), and measuring the transducer's output at the extremes of the expected temperature range quantifies thermal zero and sensitivity errors which enable correction factors to be generated. A manometer is calibrated by applying a gas pressure (normally dry nitrogen) sim ul­ taneously to the test manometer and a precision U-type manometer such as a Hook gage. The calibration includes draining the manometer, cleaning the tubing, and replacing the liquid. Calibration includes error correction for fluid density change with temperature as well as local gravity (see Section 6.5.1). A dial gage is norm ally calibrated by applying a gas or liquid pressure simultaneously to the test gage and a dead weight tester. A dead weight tester (sometimes called a piston gage) is a precision instrument consisting of a piston in a cylinder which is loaded by weights. Each weight applies a precisely known incremental force, and the piston transmits the force into a gas or liquid to pressurize the dial gage. An electronic transducer with DC response is calibrated by applying a gas or liquid pressure simultaneously to the test transducer and a precision manometer, or dead weight tester, depending on the range. An electronic transducer with only AC response (such as a piezoelectric or condenser microphone/hydrophone) is calibrated by applying an electrodynam ically generated acoustic pressure wave of known amplitude simultaneously to the test transducer and a precision condenser microphone. A typical calibration is performed in an anechoic cham ­ ber using normal incident plane progressive sound waves at a sound pressure level (SPL) of about 120 dB re 0.00002 Pa from 20 Hz to 20 kHz. An alternate calibration technique involves creating a step function input utilizing a dead weight tester and a quick dump valve, reference (ANSI B88.1-1971).

6.5 6.5.1

Data acquisition/measurement system errors Manometers

To achieve the inherent accuracy of a manometer, a few precautions are necessary:

Thermal measurements in electronics cooling

224

1. The liquid must remain clean. Any visual evidence of contamination of the liquid is sufficient reason to clean out the tubing and replace the liquid. Contaminants in the liquid affect the wetting of the liquid to the tubing w hich distorts the profile of the meniscus. 2. A correction factor for the change in density of the liquid as a function of temper­ ature must be applied to the readings. Density of mercury is corrected from p = 13.556786 [1 - 0.0001818 (T - 15.5556)]

(6)

Density of water is corrected from p = 0.9998395 + 6.7982999 x 10~5 (T) - 9.1060255 x lO^6 (T2) + 1.0052729 x 10~7 (T3) - 1.1267135 x 10-9 (T4) + 6.5917956 x 10~12 (T5) (7) where p is in gram/cm3 and T is in °C (Meriam, 1992). Since the temperatures established for standard density are 0°C for mercury and 4°C for water, an error of about 0.4% of reading for m ercury and about 0.3% of reading for water will occur at normal room temperatures, unless the above corrections are applied. Ratioing the densities simplifies the correction factor, because h0 = (h t)£ -

(8)

Po

where

h0 ht Pt PQ

= the corrected height to standard temperature = height of liquid at the ambient temperature = density of liquid at the ambient temperature = density of liquid at standard temperature

3. Since the earth is not a perfect sphere of homogeneous density, a correction factor for the local value of gravity must be applied to calibrations performed using the earth's field, i.e., the reported sensitivities must be referenced to standard gravity. NIST (National Institute of Standards and Technology, formerly National Bureau of Standards) uses the value of 980.665 cm /sec2 as the standard "g ." g = ({978.03185 (1 + 0.005278895 sin2 (o) + 0.000023462 sin4 (o))} - {0.0003086 x h)) cm/sec2

(9)

where o is the latitude and h is the elevation above sea level in meters. This is the International Gravity Formula 1967. Altitude and latitude for any location can be obtained from the United States Department of the Interior Geological Survey, 7.5 minute Series (Topographic). An altitude uncertainty of 100 m causes a 0.003% error, and a latitude error of 1 degree corresponds to an error of approximately 0.01% (Sill, 1990). As an example, for San Juan Capistrano, California the variables are h = 85 m; latitude = 33.5208; measured gravity anomaly = -5 5 x 10-3 cm/s2 which yields a value of 979.527 cm /s2. Without taking the local g value into consideration, all measurements made in San Juan Capistrano that are directly proportional to the earth's gravity are in error by -0.116% . There is an additional correction which can be made if the local gravity anomaly is known. The local gravity anomaly can be estimated from the gravity map in Vanicek and Krakiwsky (1986) but measurement by a service such as the United States Air Force Defense Mapping Agency yields superior results.

Chapter six:

6.5.2

M easuring pressure in electronic systems

225

Dial gages

A major source of error in a dial gage is the inability of the human eye to discern the precise location of the pointer. In a precision dial gage, a mirrored scale eliminates the parallax error, but two operators may read a slightly different pressure as they attempt to interpolate betw een the scale markings. Since the construction of a dial gage includes mechanical linkages, pressure hysteresis errors are normally larger than encountered in other pressure instruments.

6.5.3

Electronic transducers

For specialized pressure m easurements made in electronic cooling systems, where the transducer may be used over a small fraction of its rated pressure range, the performance characteristics noted below deserve particular attention. Note that electronic transducers specifically designed for low pressure m easurement are also known as micromanometers, digital manometers, or electronic manometers.

6.5.3.1

Temperature response

A change in the electrical output as a function of temperature is usually the largest source of error for electronic pressure transducers. For DC pressure (steady, unfluctuating pres­ sure) measurement, temperature errors may be accounted for and eliminated by periodic sampling and comparison to a pressure standard. Where periodic comparison to a pressure standard is not practical, as in measurement of AC pressure (fluctuating or modulated pressure) using miniature silicon-based transducers, it is necessary to eliminate DC cou­ pling to the device, because a thermally induced shift in the zero may saturate the amplifier unless AC coupled (e.g., for an amplifier with 10 Vpk maximum output, only a 1 mV change in the zero is required to saturate the amplifier when used at X10 000 gain). Transducer signal conditioners often include an AC coupled input stage, or a simple DC blocking RC filter may be constructed as shown in Figure 4.

Figure 4

AC coupling schematic.

(10)

where

fc R C ET E0

= 3 dB down frequency in Hz = Resistance in ohms = Capacitance in farads = Excitation voltage = O utput voltage

Thermal measurements in electronics cooling

226

6 .5 .3 2

Frequency response

Frequency response for an undamped pressure transducer is usually limited to about 1/5 of the natural frequency (fn) (see Figure 5) since the amplitude is up about 5% at 1/5 of fn. If the sensing element of the transducer is recessed in a cavity, the frequency response is limited by the Helmholtz resonance, reference pp. 23-26 of Goldstein (1983). FR EQ U EN CY

Figure 5

R E SPO N SE

Frequency response for undamped transducer.

6.5 .3 .3 M edia com patibility Media com patibility of the transducer m ust be considered. Particularly in water cooled systems, the compatibility of materials in the test transducer must be established. For extreme media com patibility problems, metal diaphragms (particularly stainless steel) are used, or buffer solutions such as silicone oil (e.g., Dow Com ing DC200, 100 cs) are used to isolate the corrosive media from the pressure sensor. In applications with questionable media, contact the manufacturer, since diaphragm coatings are available to increase resis­ tance to m any chemicals.

6.5.3.4

M ounting effects

M ounting effects/case strain affect all electronic transducers to some degree since total isolation of the pressure sensing element from its surrounding case is not possible. The m ost com m only experienced error is a change in output when the unit is mounted. For a miniature pressure transducer, mounting the unit with an RTV (room temperature vulcanizing) adhesive, such as Dow Corning 738 or 3145, is usually sufficient to reduce the m ounting error to within acceptable limits. The RTV thickness should be at least 0.08 mm (0.003 in.) thick to achieve an acceptable level of strain isolation.

6.5.3.5

M agnetic field s

M agnetic fields have negligible effect on m ost types of pressure transducers. However, some transduction methods, such as variable reluctance or LVDT (linear variable differ­ ential transformer), may be susceptible to magnetic fields depending on design and con­ struction. Also, condenser and piezoelectric m icrophones/hydrophones may be extremely sensitive to magnetic fields, depending on the diaphragm material.

6.5.4

Periodic comparison to pressure standard

Perhaps the single m ost im portant contribution to accuracy in pressure measurements is to make periodic comparisons to a pressure standard during the test. By periodic com ­ parisons (e.g., every 120 s) to a known pressure standard such as a manometer, dead weight tester, or electronic transducer, accurate measurement of very low pressure, e.g.,

Chapter six:

M easuring pressure in electronic systems

227

1 Pa (0.00014 psi), can be made using a 34 kPa (5 psi) full scale pressure transducer. During each complete sequence of m easurements, a reference pressure measurement for both zero and span is performed. These reference pressure measurements enable the data acquisition system to correct the data in essentially real time and provide pressure measurement accuracy far beyond the capability of the test transducer since repeatable errors, such as temperature, are eliminated. See 32 and 36 of Table 6 for manufacturers of commercial pressure scanning systems. W henever scanning techniques are used for DC pressure measurement, the data acquisition system should be program m ed to time-average the data since there will always be some fluctuations occurring in the flow — true laminar flow being a laboratory curiosity. A time-averaging duration of 10 to 30 s has been used successfully.

6.5.5

Pressure tap error

The geometry of pressure taps used to measure static pressure can introduce an error in the range of ±1%. Optim um design of pressure taps for static pressure measurement is described in G. E. M attingly's chapter Volume Flow Measurements in Goldstein (1983). In addition, when turbulence is present, the indicated static pressure is too high by the factor (p. 301, Goldstein, 1983):

where p = fluid density and v = rms magnitude of the turbulence velocity component normal to the orifice.

6.5.6

Spatial error in AC pressure measurements

To reduce the spatial error in sensitivity which is proportional to the diaphragm diameter (e.g., a -5 % error occurs for a 10 kHz pressure wave traversing a 3 mm (0.12 in.) diaphragm [Wilson, 1991]), flush diaphragm units must have the smallest possible diameter; only a silicon-based transducer or condenser m icrophone meets this criterion. Improvement in spatial resolution through the use of pin-holes and acoustic resonators is described in W.K. Blake's chapter Differential Pressure Measurement in Goldstein (1983).

6.5.7

Data acquisition systems

The readout and recording system may include meters, oscilloscopes, analyzers, and recorders, w hich receive their inputs from the excitation-transducer-amplifier system. All of these ancillary instruments, including the interconnecting cables, have electronic char­ acteristics which may have significant effects on the accuracy of the data. The sections below address the major sources of error contributed by data acquisition components, and these errors are in addition to any error in the output of the transducer.

6.5.7.1

Cable effects

Long, i.e., greater than 30 m (100 ft), cable lines severely affect data transmission. The resistance of the wires in the cable reduces the excitation voltage and increases loading error. The capacitance of the wires affects the amplitude and phase of AC signals, and can create a slewing error in the readout equipment. And, of course, the longer the cable lines, the more noise is picked up, and the worse the signal-to-noise (SNR) ratio. W hen long cable lines are unavoidable, see Wilson (1991) for techniques w hich have been developed to ensure accuracy of the transmitted data.

Thermal measurements in electronics cooling

228

6 .5 7 .2

Am plifiers

Condenser microphones/hydrophones and piezoelectric transducers are high impedance devices that require specialized electronic signal conditioning to convert their output signal to low impedance, which is then suitable for input to DVMs, oscilloscopes, A/D converters, etc. For a condenser microphone, the required signal conditioner is called a preamplifier and is normally remote from the transducer. For a piezoelectric transducer, the required signal conditioner is referred to as a charge amplifier, w hich can be remote or internal to the transducer. Silicon-based transducers are commonly configured as a 4 active-arm W heatstone bridge. Since the W heatstone bridge configuration provides a high level, low impedance voltage output, it can be used directly with electronic measuring instruments. However, to achieve the benefits inherent in a W heatstone bridge output, a specialized bridge signal conditioner should be used to process the signal, or at the very minimum, care must be taken to preserve the differential nature of the output signal, i.e., neither of the two output leads can be connected to circuit ground.

6 .5 .7 3

Excitation

Stability and low noise in the excitation (= supply) voltage to the transducer is key to satisfactory performance. Many pressure transducers have a built in voltage regulator to reduce the dependence on the excitation supplied by the user — but note that there are still m easurable zero and span errors in the transducer's output when the excitation voltage level changes. Self-generating transducer types, such as piezoelectric, require no external excitation for operation, but they do require specialized amplifiers (see Section 6.5.7.2) to condition the output. Excitation voltage is particularly im portant for a W heatstone bridge strain gage or potentiometric transducer, because the output from the transducer is directly proportional to the excitation voltage. If the excitation voltage is electrically noisy or drifts with time, these defects w ill similarly appear on the output of the transducer. W hen using transducers w ithout internal voltage regulation, it is common to monitor the excitation voltage con­ tinuously during the test and make a correction for any deviation, e.g., if a Wheatstone bridge transducer has a sensitivity of 23.2 mV/psi at 10.000 V, but the test is performed at 10.042 V, the sensitivity is corrected to

(23.2 mV/psi) = 23.3 mV/psi v /F } 10.000 V /F

(12)

W henever possible, excitation to a transducer is best supplied by a signal conditioner specifically designed for that particular type of transducer. In addition to providing a stable, low-noise excitation, a transducer signal conditioner provides zero adjustment, excitation level adjustment, variable gain, low-noise amplification, and a selection of electronic filters. Three manufacturers of transducer signal conditioners are listed in 12, 30, and 45 of Table 6 .

6 .5 7 .4

Electrical noise

Each com ponent in a m easurement system contributes in some way to the total system noise. Noise also originates from external sources and is superimposed on the excitation and/or signal leads of the transducer, or interconnecting cables. Transducer noise is usually not a factor, typically being 5 microvolts rms for siliconbased transducers. In high gain applications (very applicable to gas cooling systems) the am plifier's noise and the electrical noise pickup in the cabling are the dominant factors. To minimize amplifier noise, use the amplifier contained in a transducer signal conditioner since these amplifiers feature very low noise semiconductors on the input stage. To reduce

Chapter six:

M easuring pressure in electronic systems

229

electrical noise pickup in the cabling, use twisted wires, preferably even twisted and shielded pairs (one shielded pair for the excitation leads, and one shielded pair for the signal leads) for the transducer cable and any extension cables. The electrical circuitry contained within a transducer is usually insulated from the case. This permits grounding the case of the transducer to earth ground, w hich provides shielding of the internal circuitry from external electrical noise (e.g., 60 Hz AC line voltage). In some transducer designs the case is electrically connected to circuit ground, and for these specific transducers it is m andatory that the case be totally insulated (including the m ounting bolts) from earth ground. Following the guidelines below reduces the susceptibility of any measurement system to electrical noise: • • • • • • • • • • • • • • • • • • • • • • • •

Attach circuit ground to earth ground at only one point in the measurement system Insulate metal cases of all equipment from circuit ground Connect metal cases of all equipment to earth ground Separate the low level signal leads from the high level signal leads Keep signal and earth ground leads as short as possible Route low signal leads close to chassis (= earth ground) Route earth ground leads away from circuit ground leads Maintain sym m etry whenever possible; keep leads and cables of equal length Use differential inputs that have a high common mode rejection ratio Keep all cable lengths as short as possible Enclose noise generators in a metal case Route excitation and signal leads as far as possible from noise sources Install line filters before input into the next portion of the system Maintain the m axim um distance possible between digital and analog circuits M aintain leads and connections in an isothermal environment Place ground lead betw een low level and high level signal leads in connectors Continue the shield through the splice of cable extensions Carry shield on signal leads through connectors on a separate pin Minimize the length of leads extending beyond the cable shield Use shielded, twisted pair leads below 100 kHz Use coaxial cable for frequencies above 100 kHz Connect only one end of the cable shield to earth ground Use low-pass filters to suppress unwanted high-frequency signals Use a 60 Hz notch filter to reduce interference when making DC measurements (Sheingold, 1980)

Amplitude of the lowest signal of interest should be at least twice the noise amplitude. W hen the above precautions have proven insufficient to attenuate electrical noise, it is necessary to utilize specialized noise reduction techniques which have been developed by Ott (1976) and Morrison (1977; 1984).

6.5.7.5

D igitizing errors

W henever an analog signal is digitized, the errors created by digitizing are added to all of the other errors in the system. The two most com mon digitizing errors are aliasing and accuracy errors. Aliasing error, which is only applicable to AC data,is covered in Section 6.S.7.6. The accuracy error for the digitizing process is determined by the size, in bits, of each sample or word of data. In terms of positive-to-negative full scale (which is the definition of full scale output or FSO), a digitizer's accuracy can be expressed as

Thermal measurements in electronics cooling

230

Accuracy = ~ ^ /'°FSO

(13)

where n is the number of bits. Since the number of bits has to be spread over the full scale range, the accuracy of the reading is seriously reduced when the amplitude is only a small percentage of the range. For example, consider the 8-bit digitizing of a 1 V full scale output. At 1 V, the limitation on accuracy from digitizing is 4 mV or 0.4% of the signal, but for an output signal of only 8 mV, the lim itation on accuracy from digitizing is the same 4 mV, which now represents 50% of the signal. Increasing the gain of the analog amplifier to provide a peak output near the full scale level of the digitizer, or using a 16- or 32-bit digitizer, greatly reduces the significance of this scaling error. 6.5 .7 .6 A nalog filterin g For AC pressure data transmission, analog filters may be necessary before the amplification stage to reduce resonant frequency content from the transducer, and before the A/D converter to prevent an aliasing error when the data are digitized. W hen an analog filter is used to reduce resonant frequency output from an undamped transducer, the cut-off frequency is com m only set at half of the resonant frequency (fn), (see Section 6.5.3.2). Passive analog filters (i.e., filters not incorporating transistors or ICs) which consist of simple RC or RLC circuits, are com monly used to filter out (or attenuate) a resonant frequency output. Note that in m ost transducer signal conditioners, the analog filter stage is after the am plification stage, w hich severely limits its usefulness to reduce resonant frequency content in the signal. A mechanical analogy is possible; installing a pressure snubber (a small orifice acts as a low pass filter to a fluid) in line with the pressure sensing element accomplishes the same result. If AC data are to be digitized, an analog filter must be installed before the A/D converter to prevent aliasing errors. An aliasing (false) frequency is generated when highfrequency data are sampled (digitized) at a lower frequency as shown in Figure 6. To prevent aliasing, the filter cut-off frequency should be set at 1/5 of the digitization rate. The analog filter in transducer signal conditioners may be used as an anti-aliasing filter, and m any analog multiplexers already include anti-aliasing filters. For a source of anti­ aliasing filters, see 33 of Table 6.

Figure 6

Aliasing diagram.

Chapter six:

M easuring pressure in electronic systems

231

All analog filters create phase shift, and where it is an important criterion (e.g., in a control loop), the type of filtering, Butterworth, Bessel, elliptical, etc., must be considered since each type has different phase shift characteristics.

6.6 Measuring pressure in a typical application Forced convection cooling continues to gain in importance as current density in electronics increases, and package size decreases. Flow of the fluid in a forced convection system is due to the pressure difference between the intake and exhaust; the fluid flows from the high pressure area to the low pressure area. To minimize the size, weight, cost, noise, and power requirements of the fan, blower, or pump, it is necessary to measure or calculate the static pressure drop across the entire system, i.e., the differential pressure between the intake and the exhaust. In Figure 7, the differential pressure m easured betw een points A and G represents the total pressure drop across the system. In an air cooled system, this pressure drop is quite sm all, perhaps 250 Pa (1 in. H20 ) . To optim ize the cooling efficiency of the system, the forced convection source generates a m axim um flow rate, with m inim um pressure drop. Since any forced convection system has some unavoidable pressure losses, such as orifice restrictions, obstructions, bends, duct wall friction, filters, heat exchangers, and turbulence, the design of the cooling system can only be optim ized if the forced convection source provides sufficient mass flow to remove the electrically generated heat, while generating sufficient pressure to overcom e the frictional losses that occur as the coolant flows through the system. Determ ination of the optim um fan size (called sizing the fan) requires m easuring the pressure drop across the entire system, calculating the flow rate required to dissipate the electrically generated heat, and then locating a fan with the required pressure/flow characteristics. A detailed procedure for sizing a fan is given by Steinberg (1991). Since the pressure drop across the entire system is the sum of the individual pressure drops of the serial subsystems (parallel flow paths are not considered here), it is instructive to measure the pressure drop across each part of the system to determine where the major pressure losses occur. Note that pressure drops measured in some parts of the system may be negligible, e.g., 0.7 Pa (0.003 in. H20 ) . In the portions of the system where heat dissi­ pation is high (as betw een points E and F), it may be necessary to generate turbulence via spoilers to decrease thermal resistance or to use deflectors to increase the air flow. Gen­ erating turbulence or diverting the fluid flow to areas requiring high thermal transfer rates minim izes the size, and power requirements, of the forced convection generator. In Figure 7, the pressure taps or ports (called tappings in the UK) are metal tubes with the tube entry norm al to the flow so that only static pressure is measured. Multiple taps are manifolded together, or holes are drilled in the tubes normal to the flow, to generate a pneumatic average for the static pressure level. The differential pressure betw een points A B C D E F A

and and and and and and and

B C D E F G G

measures measures measures measures measures measures measures

the the the the the the the

pressure pressure pressure pressure pressure pressure pressure

drop drop drop drop drop drop drop

of the intake plenum across a filter in a typical channel across a heat exchanger in an area of high heat dissipation of the exhaust plenum for the entire system

Thermal measurements in electronics cooling

Figure 7

Electronics enclosure diagram.

Flexible tubing (e.g., Tygon®) is attached to the metal tube for each pressure tap, and the tubing is brought outside of the enclosure where the tube is attached to a manometer, a dial gage, or an electronic pressure transducer. The type of pressure measuring device used (see Table 4) depends on range, accuracy, and electronic recording requirements. The pressure characteristics of turbulence, in absolute pressure (psia), am measured on the cooling fins (see detail A of Figure 7) of the largest heat source. Silicon-based pressure transducers of the flatpack configuration from Table 5 are used to make the measurement. In Figure 8, the electronic equipment required to m ake both the DC and AC pressure measurem ents for a typical forced air convection cooling system are described. The EXT data channel uses electrically operated valves to connect sequentially the pressure trans­ ducers to a known precision pressure source. Components of a typical personal computerbased data acquisition system are shown, and many of these electronic instruments are available as plug-in boards. The AC data channel includes a low pass analog filter which is only necessary if there is sufficiently high frequency input to excite the resonance of the pressure sensing element (e.g., diaphragm).

Chapter six:

M easuring pressure in e k x fn m k systems

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Pressure measurement system block diagram.

How-to list for pressure measurement 1„ Determine how many different pressure m easurements are required to characterize the system* 2, Determine the frequency response required for each measurement. 'For DC pressure data, manometers, dial gages, and electronic transducers are all suitable (see Table 4). For AC pressure data, electronic transducers, with their attendant signal condi­ tioning and recording devices, are required (see Table 5). 3. D eterm ine the highest pressure expected for each m easurem ent, Use the lowest range instrum ent for the application to increase the accuracy of the measurem ent. 4. Determine if the data are to be electronically recorded or analyzed, 5, Determine the level of accuracy desired for each measurement. 6. Determine the uncertainty in each measurement by analyzing each source of error. If necessary, reduce or eliminate the source of error by pretest calibration, use of a temperature controlled environment, etc. 7, Determine m edia compatibility. Particularly when using a liquid co o la n t it may be necessary to contact the m anufacturer to confirm appropriateness of the in­ strum ent.

Thermal measurements in electronics cooling

234

8 . Calibrate the measuring device(s) using a precision standard, or use a comparison scanning technique throughout the test (reference Section 6.5.4). 9. Determine if the observed pressure measurement is in close agreement with expec­ tations. If there is a large divergence, it may be necessary to use a measuring instrument of different range, accuracy, or frequency response.

Table 4 Pressure instrument

Instruments for DC Pressure Measurement Full scale range (lowest to highest)

Hook gage

Best accuracy

Sources (see Table 6)

0.25 Pa (0.001 in. of H20 ) 0.025% of FS

10

Manometer, inclined Manometer, Utube/well-type Digital pressure calibrator Digital pressure controller Electronic transducer

500 Pa-6 kPa (2 in. H20 - 2 4 in. H20 ) 62 Pa-5 kPa (0.25 in. H2O-20 in. H20 ) 1-339 kPa (4 in. H2O-100 in. Hg) 6.9 kPa-17.2 MPa (1-2500 psi) 500 Pa-17.2 MPa (0.07-2500 psi) 25 Pa-200 MPa (0.004-30,000 psi)

0.01% of FS

10, 25

0.003% of FS

35

0.01% of FS

Electronic transducer

345 Pa-200 MPa (0.05-30,000 psi)

0.1% of FS

Dial gage

62 Pa -700 MPa (0.01-100,000 psi)

0.066% of FS

5, 8, 24, 35, 36 9, 11, 15, 16, 25, 27, 32, 47 4, 6, 14, 15, 16, 32, 34, 37, 38, 40, 43, 44, 46 5, 10, 15, 48

Table 5 Type of transducer Microphone, condenser Microphone, piezoelectric Transducer, silicon Transducer, flatpack Transducer, piezoelectric

0.05% of FS

10, 25

Transducers for AC Pressure Measurement

Resolution 0.007 Pa (0.000001 psi) 0.2 Pa (0.00003 psi) 0.2 Pa (0.00003 psi) 2.7 Pa (0.0004 psi) 34 Pa (0.005 psi)

Range 7 kPa (1 psi) 14 kPa (2 psi) 14 kPa (2 psi) 100 kPa (15 psi) 700 kPa (100 psi)

Frequency response

Sources (Table 6)

6 Hz-140 kHz

1, 3, 23

0.05 Hz-2.6 kHz

12, 20, 31 9, 12,13, 19, 22 12, 13, 22, 42 12, 20, 31

0-14 kHz 0-30 kHz 0.5 H z-50 kHz

Chapter six:

M easuring pressure in electronic systems

Table 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

235

Manufacturers of Pressure Instruments

ACO Pacific, Inc. 2604 Read Ave, Belmont CA 94002 AutoTran, Inc. 11543 K-Tel Drive, Minnetonka, MN 55343 Bruel & Kjaer Instruments, Inc. (B&K) 185 Forest St., Marlborough, MA 01752-3093 CEC Instruments 955 Overland Ct., San Dimas, CA 91773 Davis Instrumentation Mfg. Co., Inc. Seton Business Center, 4701 Mt. Hope Drive, Baltimore, MD 21215 Daytronic Corporation 2589 Corporate Place, Miamisburg, OH 45342 Delta Design, Inc. 5775 Kearny Villa Road, San Diego, CA 92123 DH Instruments 1905 West Third Street, Tempe, AZ 85281 Druck Incorporated 4 Dunham Drive, New Fairfield, CT 06812 Dwyer Instruments Inc. P.O. Box 373, Michigan City, IN 46360 Eaton Consolidated Controls 15 Durant Avenue, Bethel, CT 06801 Endevco Corporation 30700 Rancho Viejo Road, San Juan Capistrano, CA 92675 Entran Devices, Inc. 10 Washington Ave., Fairfield, NJ 07004 Gulton-Statham Transducers, Inc. 1664 Whittier Ave, Costa Mesa, CA 92627 Heise Instrument Division, Dresser Industries 250 East Main St., Stratford, CT 06497 Honeywell Solid State Electronics Center 12001 Hwy 55, Plymouth, MN 55441 IC Sensors 1701 McCarthy Blvd., Milpitas, CA 95035-7416 Kavlico Corp. 14501 Los Angeles Ave., Moorpark, CA 93031 Keller PSI, Inc. 503 Vista Bella, #11, Oceanside, CA 92057 Kistler Instrument Corp. 75 John Glenn Dr., Amherst, NY 14228-2171 Kobold Instruments, Inc. 1810 Parkway View Drive, Pittsburgh, PA 15205 Kulite Semiconductor Products, Inc. One Willow Tree Rd., Leonia, NJ 07605 Larson*Davis Laboratories 1681 West 820 North, Provo, UT 84601 Mensor Corporation 2230 IH-35 South, San Marcos, TX 78666

Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX

415 595-8588 415 591-2891 612 933-3323 612 933-3114 508 481-7737 508 624-0503 909 394-4410 909 394-4400 800 368-2516 800 433-9971 513 866-3300 513 866-3327 619 292-5000 619 277-7884 602 967-1555 602 968-3574 203 746-0400 203 746-2494 219 879-8000 219 872-9057 203 796-6068 203 796-6313 714 493-8181 714 661-7231 800 635-0650 201 227-6865 714 642-2400 714 642-9490 203 378-8281 203 385-0357 612 954-2093 612 954-2051 800 767-1888 408 432-7322 805 523-2000 805 523-7125 619 967-6066 619 967-0563 716 691-5100 716 691-5226 412 788-2830 412 788-4890 201 461-0900 201 461-0990 801 375-0177 801 375-0182 512 396-4200 512 396-1820

236

Thermal measurements in electronics cooling

Table 6 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Manufacturers of Pressure Instruments (continued)

Meriam Instrument 10920 Madison Avenue, Cleveland, OH 44102 Micro Switch, a Honeywell Division 11 West Spring Street, Freeport, IL 61032 MKS Instruments, Inc. Six Shattuck Road, Andover, MA 01810 Motorola Semiconductor P.O. Box 2953, Phoenix, AZ 85062-2953 Omega Engineering, Inc. P.O Box 2284, Stamford, CT 06906 Pacific Instruments, Inc. 215 Mason Circle, Concord, CA 94520 PCB Piezotronics, Inc. 3425 Walden Avenue, Depew, NY 14043-2495 Pressure Systems, Inc. 34 Research Drive, Hampton, VA 23666 RC Electronics Inc. 6464-T Hollister Ave., Santa Barbara, CA 93117-3110 Rosemount 14300 Judicial Road, Burnsville, MN 55337 Ruska Instrument Corporation P.O. Box 630009, Houston, TX 77263-0009 Scanivalve Corp. 1722 North Madson St., Liberty Lake, WA 99019 Sensotec Inc. 1200 Chesapeake Ave, Columbus, OH 43212 Sensotron, Inc. 5881 Engineer Dr., Huntington Beach, CA 92649 Sensym Inc. 1804 McCarthy Blvd., Milpitas, CA 95035 Setra Systems, Inc. 45 Nagog Park, Acton, MA 01720 Shortridge Instruments, Inc. 7855 East Redfield Road, Scottsdale, AZ 85260 Soltec Corp. 12977 Arroyo St., San Fernando, CA 91340 Tavis Corp. 3636 Highway 49, Mariposa, CA 95338 Teledyne Taber 455 Bryant St., North Tonawanda, NY 14120 Unholtz-Dickie Corp. 6 Brookside Drive, Wallingford, CT 06492 Validyne Engineering Corp. 8626 Wilbur Avenue, Northridge, CA 91324-4498 Volumetries, Inc. 3010 Rollie Gates Drive, Paso Robles, CA 93446 Wallace & Tieman, Inc. 25-T Main Street, Belleville, NJ 07109-3057

Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX Phone FAX

216 281-1100 216 281-0228 815 235-6847 815 235-6545 800 227-8766 508 975-0093 602 244-4556 602 244-5738 800 826-6342 203 359-7700 510 827-9010 510 827-9023 716 684-0001 716 684-0001 804 865-1243 804 766-2644 805 685-7770 805 685-5853 612 681-8921 612 681-8909 713 975-0547 713 975-6338 509 891-9970 509 891-9481 614 486-7723 614 486-0506 714 893-1514 714 894-3123 408 954-1100 408 954-9458 508 263-1400 508 264-0292 602 991-6744 602 443-1267 800 423-2344 818 365-7839 209 966-2027 209 966-4930 716 694-4000 716 694-1450 203 265-3929 203 265-2690 818 886-2057 818 886-6512 805 239-0110 805 239-2381 800 628-0897 201 759-5218

Chapter six:

Table 7 Atm 1 Atm = 1 psi = 1 bar 1 pascal = 1 in. H20 = 1 in. Hg =

237

M easuring pressure in electronic systems

1 6.80456 x 9.86923 x 9.86923 x 2.45832 x 3.34211 x

Pressure Unit Conversions bar

psi

pascal

1.01325 101325 14.6960 10-2 1 6.89472 x lO"2 6894.72 10-1 14.5039 1 1 xlO 5 10-6 1.45039 x 1(H 1 x 10-5 1 10-3 3.61275 x lO-2 2.49089 x 10-3 249.089 lO-2 4.91157 x 10-1 3.38639 x lO-2 3386.39

in. H20

in. Hg

406.782 27.6797 401.463 4.01463 x 1(h3 1 13.5951

29.9212 2.03601 29.5300 2.95300 x 1(H 7.35559 x lO"2 1

1 bar = 106 dyne/cm 2 = 105 pascal (newton/m2) 1 torr = 1 mmHg = 133.322 Pa (ISO/DIS 3529/1, 1981) Conversions based on 1 Normal Atmosphere = 101325 Pa (CIPM, 1954) 1 in. Hg

= 3386.39 Pa (ISO/DIS 3529/1, 1981)

1 in. H20

= 249.089 Pa (ISO/DIS 3529/1, 1981)

1 psi

= 6894.72 Pa (Berman, 1985)

Table adapted from NBS Monograph 8.

6.8

Defined terms

Absolute pressure Absolute pressure transducer AC pressure Accuracy

Aliasing error

Analog output

Anemometer Atmospheric pressure

Barometric pressure Bourdon tube Calibration

Capsule

The pressure measured relative to a total (or com ­ plete) vacuum. A transducer that has an internal reference chamber sealed under a total (or nearly total) vacuum. A fluctuating (modulated) pressure. The ratio of the maximum error to the output, or to the fu ll sca le o u tp u t, w h ic h e v e r is sp ecified , expressed in percent. M any m anufacturers define accuracy as the algebraic sum of the errors for nonlinearity, hysteresis, and non-repeatability (either in RSS or maximum), and for some instruments, tem­ perature is included as well. False frequencies are created when analog signals are digitized at a sampling rate lower than the frequency of the data. Output w hich is a continuous function of the m ea­ surand, as opposed to digital output w hich is a series of discrete quantities representing the measurand. An instrument used to measure the velocity of an air stream. The pressure exerted by the weight of the earth's atmosphere w hich changes with geographic location, altitude, and weather. See Atmospheric pressure. A pressure sensing element consisting of a flattened and curved tube which straightens when pressurized. The comparison of a transducer's output to the out­ put of a reference standard when subjected to the identical measurand. A pressure sensing element consisting of two metallic diaphragms joined at their peripheries. Similar to a single element bellows.

238 Charge amplifier

Com m on mode pressure

Com m on mode rejection

dB

Damping

DC pressure Dead weight tester Diaphragm Differential pressure Dynamic pressure

Excitation Fluid Flush diaphragm

Frequency response

Full scale range Full scale output (FSO)

Gage pressure

Gage pressure transducer

Thermal measurements in electronics cooling A charge to voltage converter w hich converts a high impedance output into a low impedance output, with or without gain. The lowest pressure existing simultaneously on both sides of a differential pressure transducer. Also called static pressure by some pressure transducer manu­ facturers. The ability of a differential amplifier to reject common mode voltages, expressed as a ratio of signal gain to com m on mode gain, in dB. Abbreviation for decibel, a unit of measurement in acoustics equal to one tenth of a BEL. dB is used in many other disciplines to designate the common log­ arithm of a ratio of values. The reduction of response under oscillating condi­ tions via energy dissipation. Usually specified as the ratio to critical damping (critical damping yields zero overshoot to a step function input). A steady, unfluctuating pressure. A pressure standard using a piston/cylinder appara­ tus loaded with weights. Also called piston gage. The sensing membrane which is deflected when pres­ sure is applied. The difference in pressure between two m easurement points. Same as impact pressure or velocity pressure. Confus­ ing terminology, because " dynam ic" pressure is also used to describe a pressure change as a function of time, e.g., turbulence in flow, sound in acoustics, etc. The voltage or current applied to the input terminals of a transducer. A gas or liquid. The two states are interchangeable as a function of temperature and pressure. A type of transducer characterized by the absence of a cavity between the front of the transducer and the pressure sensing diaphragm. Flush diaphragm trans­ ducers are designed to optimize the response to fluc­ tuating pressures. The range of frequencies over w hich the transducer's electrical output will follow a varying mechanical input within specified limits. The m axim u m m easu rand that a tran sd u cer is designed to measure within its specifications. The algebraic difference betw een the electrical output at minimum full scale range and maximum full scale range. The pressure above, or below, ambient (local) atm o­ spheric pressure. Can be converted to absolute pres­ sure by adding the actual atm ospheric pressure value. A transducer which measures pressure relative to the ambient (or local) atmospheric pressure.

Chapter six:

M easuring pressure in electronic systems

Gain

Hysteresis

Impact pressure

Line pressure

Loading error Measurand

Micromanometer

Natural frequency

Noise Phase shift Piezoelectric

Pressure head

Pressure drop

Psi Psia Psid

239

The amplitude of the transfer function between the output and input. Gain is often a function of fre­ quency, and must be so specified. Applies to either pressure or temperature. The m ax­ imum difference, expressed in percent of full scale, between output readings for the same measurand point; one output reading obtained while increasing, the other output reading obtained while decreasing, the measurand. The pressure in a moving fluid which is exerted par­ allel to the direction of flow, caused by the inertia of the fluid. Also called dynamic pressure or velocity pressure. The absolute pressure existing on the low side of a differential pressure transducer. The term is com ­ monly used to mean the lowest pressure comm on to both ports which is more accurately called the com­ mon mode pressure. An error in the transducer's output caused by the load impedance of the readout device. The physical or chem ical quantity w hich is being measured, e.g., pressure, load, weight, acceleration, etc. Any type pressure m easuring device used in the range of 0.13 to 6650 Pa (0.0005 to 26.7 in. H20 ) . Current usage of this term is limited to electronic transducers. For an undamped mechanical system, the natural fre­ quency is the frequency of free (unforced) oscillation. For a damped m echanical system, the natural fre­ quency is defined by the 90° phase shift between input and output. An unwanted electrical output which is unrelated to the desired signal. The phase angle between the output AC signal and the applied AC signal. A self-generating transduction system which relies on the attribute of some crystalline materials to gen­ erate an electrical charge when mechanically stressed (the process is reversible). The pressure resulting from the weight of a column of liquid. The term is often generalized to mean any pressure measured with a manometer, e.g., velocity head and static head. In fluid flow, a pressure difference exists whenever the velocity changes; this pressure difference between inlet and outlet is referred to as a pressure drop. The term is entirely analogous to the electrical term volt­ age drop which occurs across an impedance. Abbreviation for pounds per square inch. Abbreviation for pounds per square inch, absolute. Abbreviation for pounds per square inch, differential.

240 Psig Psis Reference pressure Resonant frequency

Sealed (or sealed gage) pressure

Self-generating

Sensing element Sensitivity

Slewing error

Snubber Sound pressure level (SPL) Span

Stagnation pressure Standard pressure Static pressure

Therm oacoustic refrigeration

Total pressure

Thermal measurements in electronics cooling Abbreviation for pounds per square inch, gage. Abbreviation for pounds per square inch, sealed. The pressure relative to which another pressure is measured. The frequency at which a transducer responds with m axim um output am plitude. Resonant frequency and natural frequency are the same value for an undamped mechanical system. Pressure measured with reference to the pressure in a sealed container; the container is usually within the transducer. A type of transducer which provides an electrical output without externally applied excitation voltage or current, e.g., piezoelectric, thermoelectric, etc. The part of the transducer which responds to the measurand. The ratio of change in transducer output to a change in the value of the measurand, i.e., the slope of the output/input curve. Specified sensitivity is usually averaged over the full scale range of the measurand, and therefore the sensitivity for small portions of the full scale range may be m arkedly different than the sensitivity determined from full scale. An error created in an AC signal measurement when the measuring device cannot respond as fast as the signal is changing. A small orifice inserted into a fluid line to attenuate high frequency amplitudes. The ratio of the rms sound pressure to a specified reference pressure, expressed in dB. The algebraic difference betw een the limits of the range from m inimum full scale to m axim um full scale. See Total pressure. Pressure of one Normal atmosphere (101325 Pa), see Table 7. The pressure of a fluid which is exerted norm al to the direction along which it flows. "Static" pressure is also used to describe a nonfluctuating pressure. An acoustic exciter is used to set up standing waves in a gas; the gas warms up as it moves toward the high pressure portion of the wave and cools off as it oscillates back toward the low pressure region. The cooled portion is then conducted to the desired loca­ tion. The sum of the static pressure and the impact pres­ sure. Same as stagnation pressure. Total Pressure also has an entirely different meaning when it is defined as the sum of the partial pressures which each gas would exert if it occupied the containing vessel alone.

Chapter six:

M easuring pressure in electronic systems

Transducer

Undamped Vacuum

241

A device that converts energy from one form to another. The term is generally applied to devices that convert a physical or chemical characteristic like pres­ sure, temperature, humidity, etc. into an electrical sig­ nal. Now commonly referred to as a sensor. A mechanical system exhibiting negligible damping. Pressures below atmospheric pressure.

References Allocca, J.A. and Stuart, A., Transducers, Theory and Applications, Reston Publishing, Reston, VA, 1984. ANSI B88.1-1971. A Guide for the Dynamic Calibration o f Pressure Transducers, American Society of Mechanical Engineers, 1972. Benedict, R.P., Fundamentals o f Temperature, Pressure, and Flow Measurements, John Wiley & Sons, New York, 1984. Berman, A., Total Pressure Measurements in Vacuum Technology, Academic Press, Orlando, FL, 1985. Bryer, D. W. and Pankhurst, R.C., Pressure Probe Methods fo r Determining Wind Speed and Flow Direction, Her Majesty's Stationery Office, London, England, 1971. Fraden, J., AIP Handbook o f Modern Sensors, American Institute of Physics, New York, 1993. Goldstein, R.J., Fluid Mechanics Measurement, Hemisphere Publishing, New York, 1983. Meriam Instruments, General Installation, Operation and Maintenance Instructions fo r Meriam Manom­ eters; File No. 022C:440-11, Meriam, Cleveland, OH, 1992. Morrison, R., Grounding and Shielding Techniques in Instrumentation, John Wiley & Sons, New York, 1977. Morrison, R., Instrumentation Fundamentals and Applications, John Wiley & Sons, New York, 1984. Neubert, H.K.P., Instrument Transducers, Clarendon Press, Oxford, England, 1975. Norton, H.N., Sensor and Analyzer Handbook, Prentice-Hall, Englewood Cliffs, NJ, 1982. Ott, H.W., Noise Reduction Techniques in Electronic Systems, John Wiley & Sons, New York, 1976. Pendlebury, J.M., Kinetic Theory, Adam Hilger Ltd., Bristol, England, 1985. Sheingold, D.H., Transducer Interfacing Handbook, Analog Devices, Norwood, MA, 1980. Sill, R.D., Local Gravity, Endevco, San Juan Capistrano, CA, 1990, (unpublished). Sinclair, I.R., Sensors and Transducers, BSP Professional Books, Boston, MA, 1988. Steinberg, D.S., Cooling Techniques fo r Electronic Equipment, John Wiley & Sons, New York, 1991. Tandeske, D., Pressure Sensors, Marcel Dekker, New York, 1991. Vanicek, P. and Krakiwsky, E.J., Geodesy: the Concepts, p. 76-82, Elsevier, New York, 1986. Wilson, J., Dynamic Pressure Measurement Technology, Endevco, San Juan Capistrano, CA, 1991, (un­ published).

Appendix: For further information Scientific Journals — The following two journals specialize in measurement technology appropriate to pressure measurem ent in cooling systems: 1. Measurement Science and Technology is a monthly journal dedicated to the theory, practice, and application of measurement in physics, chemistry, engineering, and the environmental and life sciences from inception to commercial exploitation. Its scope includes measuring instruments and sensors, measurement techniques, as­ sociated signal processing, and control systems. Published by:

Institute of Physics Publishing Ltd. Techno House, Redcliffe Way Bristol BS1 6NX, UK Phone 0117 929-7481 FAX 0117 929-4318

Thermal measurements in electronics cooling

242

2. Wind Engineering is a bim onthly journal w hich publishes papers on all aspects of wind energy systems, including measurem ent methods and related economic and environmental topics. Published by:

Multi-Science Publishing Company, Ltd. 107 High Street Brentwood Essex CM14 4RX, England

Technical Magazines — The following four magazines primarily serve the transducer community: 1. Sensors, the Journal o f Machine Perception is a monthly publication which is almost exclusively dedicated to modern transducer technology, and publishes a Buyer's Guide that is available on disk with full search, sort, and output capabilities. Published by:

Helmers Publishing, Inc. 174 Concord Street P.O. Box 874 Peterborough, NH 03458-0874 Phone 603 924-9631 FAX 603 924-7408

2. Measurement & Control is a bim onthly publication which is predominantly dedicated to transducers and m easurement systems, and publishes m any tutorials on m ea­ surem ent technology. Published by:

Measurements and Data Corporation 2994 West Liberty Avenue Pittsburgh, PA 15216 Phone 412 343-9666 FAX 412 343-9685

3. Instrumentation & Control Systems is a monthly publication with heavy emphasis on com puterized data acquisition. Published by:

Chilton Company One Chilton Way Radnor, PA 19089 Phone 610 964-4000

4. NASA Tech Briefs is an official m onthly publication by NASA which often has technical briefs concerning the latest techniques in the measurement of pressure in aeronautical wind tunnels. Published by:

Associated Business Publications Co., Ltd. 41 East 42nd Street New York, NY 10017-5391

chapter seven

Measuring thermal conductivity and diffusivity J . E. Graebner

7.1

Introduction............................................. 243 244 7.1.1 Materials of in terest...................................................................... 7.1.2 Thermal quantities of interest...................................................................................... 244 7.1.3 Example: Measuring thermal conductivity of multilayer boards.................... 245 7.1.4 Choosing a measurement technique...........................................................................245 7.2 Detailed description of four m easurement techniques.................................................... 247 7.2.1 Long bar with steady h eatin g....................................................................................... 247 7.2.2 Long bar with periodic h eatin g....................................................................................249 7.2.3 Three-omega m ethod.......................................................................................................252 7.2.4 Flash m ethod...................................................................................................................... 254 7.3 Brief descriptions of other techniques................................................................................... 257 7.3.1 Steady-state heating......................................................................................................... 257 7.3.1.1 Radiating b a r....................... 257 7.3.1.2 Radial heat flow, solid cylinder orp la te ...................................................257 7.3.1.3 Line-heated thin p la te ................................................................................... 258 7.3.1.4 Bridge method for film on su bstrate............................................ 258 7.3.1.5 Transient D C ....................... 258 7.3.2 Periodic heating.......................... 260 7.3.3 Pulsed h ea tin g ................................................................................................................... 260 7.3.3.1 Transient thermal g ra tin g .............................................................................260 7.3.3.2 Converging w a v e ............................................................................................ 262 7.3.3.3 Photothermal reflectance...............................................................................262 7.4 Com parison of all tech niq u es...................................................................................................263 7.5 Com m ercial vendors.................................................................................................................... 267 7.6 Sum m ary........................................................................................................................................... 267 7.7 D efinitions........................................................................................................................................268 R eferences................................................................................................................................................... 269

7.1 Introduction Successful therm al design of electronic com ponents and circuits requires accurate know l­ edge of the therm al properties of the various m aterials involved. Such knowledge is not always available, especially for new m aterials. Even for relatively w ell-docum ented 0-8493-3279-6/97/$0.00+$.50 © 1997 by CRC Press LLC

243

Thermal measurements in electronics cooling

244

m aterials, there is often a large range of values from different laboratories because of variations in the m aterials and/or inaccuracies in the experim ental techniques* In this chapter we discuss many of the techniques available for m easuring therm al properties for the m aterials that are useful in the construction of electronic devices and circuits.

711

Materials of interest

The list of materials includes many familiar substances such as single-crystal silicon, copper and other metals, fiberglass, epoxies, molding compounds, and ceramics. Com bi­ nations of the above materials are often encountered in a single component; a well-known example is the use of copper, fiberglass, and epoxy in printed wiring boards. Thin films can be important thermally, especially in the analysis of devices on a microscopic scale. Finally, the interfaces between components are a potential source of serious thermal resistance, but are often ignored for lack of reliable data. Thermal measurements are therefore im portant to thermal design engineers across the entire electronics industry, from microscopic devices to large enclosures.

712

Thermal quantities of interest

The primary quantities governing the flow of heat are the thermal conductivity k and the thermal diffusivity a . k and a are related by a = k/(pC), where p is the mass density and C is the heat capacity per unit mass, i.e., the specific heat. The regimes governed by k and a are easily separated in terms of the time dependence of the problem: k governs the static temperature distribution (arising from any steady component of heating) while a governs the dynamic temperature distribution (arising from non-steady, time-dependent heating). In some cases, the heat capacity per unit volume (pC) is known, so that measurement of k provides im m ediate knowledge of a , or vice versa. Generally pC is not known before­ hand, and one m ust either measure it (or estimate it if high accuracy is not required) or make certain to choose a technique that measures the desired quantity — k or a . For the purposes of this chapter, we suggest that k is the important quantity for thermal manage­ ment on length scales usually encountered with devices/boards. One would expect dynamic effects ( a ) to be important only when analyzing extremely local and rapidly changing heat loads in the immediate vicinity of the active area of a device, i.e., on a micron length scale. Thermal conduction through solid material near room temperature typically accounts for 20% to 80% of the total heat transfer. Fleat can also be carried away from hot spots by (1) thermal radiation to the surroundings, and (2) thermal conduction and convection in the surrounding fluid. In general, it is because of these two alternative paths for heat flow that k is a difficult quantity to measure, and we discuss them briefly below. Thermal radiation is the electromagnetic radiation given off by any material whose temperature is above absolute zero. It covers a wide spectrum of wavelengths (-0.1 to 100 pm) and is governed by a basic physical law with only one material-dependent factor, e, the emissivity. Crudely speaking, e for metals depends inversely on how "shiny" the material is, particularly in the infrared part of the spectrum. For many materials, the emissivity depends directly on how "black" the surface appears. Depending on the mate­ rial, e can range over several orders of m agnitude, from a maximum of 1.0 for an ideal black body to low values of - 0.02 for some highly polished metals. Thermal loss to a surrounding fluid is more complicated physically because it includes several m echanisms: (1) simple thermal conduction through a stable fluid, (2) extra con­ duction due to rolls and other gravitational instabilities (natural convection) w hich provide cooler fluid flowing past an object, and (3) forced convection of fluid past the object with the use of fluid movers (e.g., fans), resulting in either laminar or turbulent flow. These

Chapter seven:

M easuring thermal conductivity and diffusivity

245

three mechanism s are usually lumped together approximately (Carslaw and Jaeger, 1959) by writing down a heat flux that depends on some low power of AT, the temperature difference betw een the hot object and the surroundings, with a proportionality constant determined em pirically

7.1.3

Example: Measuring thermal conductivity of multilayer boards

To illustrate how some of these quantities can be obtained, we describe measurements (Azar and Graebner, 1996) of a sample of printed wiring board (PWB). The specimen (1 cm x 5 cm x 0.1 cm) is cut from a standard 6-layer, 0.1 cm thick PWB which has a number of layers of Cu foil sandwiched between layers of fiberglass-epoxy. An electrical resistance heater wire is attached with epoxy as a thermal transfer agent at one end and the sample is thermally grounded to a copper block by clamping at the other end. The heat is applied uniform ly across one end and the thermal grounding is done as uniformly as possible across the other end (see below) so that the heat flow at all points is uniform ly parallel to the long direction of the sample. This restriction to low-dimensional heat flow (in this case, one-dimensional) simplifies the analysis enormously and is a profitable approach in many thermal m easurement problems. The steady thermal gradient generated by steady heater power Q is measured by the therm ocouples (Figure 1). The slight upward curvature that is observed in the temperature profile, and the dependence of the profile on the presence or absence of air and radiation shielding, are indicative of loss of heat through the surfaces of the sample to the surround­ ings (see below). In the absence of such loss, the temperature profile would be a single straight line of constant slope AT/Ax - S, and the thermal conductivity could be calculated according to the equation k = Q/(SA)

(1)

where A is the cross-sectional area (0.1 cm2) of the sample perpendicular to the direction of heat flow. The presence of curvature necessitates a more detailed analysis (see below, Section 7.2.1) that allows measurement of the surface heat loss coefficient h, as well as a more accurate value of k than would be obtained from a straight-line approximation to the data in Figure 1.

71A

Choosing a measurement technique

As will becom e clear in the discussion below (Sections 7.2 and 7.3), many techniques are available for measuring the various thermal quantities (Maglic et al., 1984). Each technique has its own requirements for sample size and shape, degree of accuracy, cost, complexity, etc. We list here some of the criteria to be considered when choosing a m easurement technique, either in setting one up from scratch or purchasing a commercial m easurement system. 1. W hat is the quantity for w hich data are desired: k, a, £, h? If the specific heat is not known or not readily m easurable by, for example, differential scanning calo­ rimetry, one must be careful not to measure a if the desired quantity is actually k. Also, combinations of the thermal quantities sometimes need to be measured, such as k and h; this requirement can restrict the choices available. 2. W hat are the size and shape of the sample? M ost measurement techniques have a preferred range for these variables, and if possible it may be advantageous to cut or mold the material into an optimum shape for a particular technique.

Thermal measurements in electronics cooling

246

Position (cm) Figure 1

Data for measuring the in-plane thermal conductivity kj| of a sample (inset) of printed wiring board with many vias. The 12 thermocouples, attached along the center line of the sample, are used to measure the gradient generated by a heater at the free end. Copper wire looped through holes at either end is used to improve thermal contact of the sample to both the heater wire and thermal ground. The lines through the data indicate the fit of a model discussed in the text. The lower set of data is obtained with an atmosphere of air around the sample; the upper set is obtained with a vacuum and radiation shields placed around the sample. (From Azar, K. and Graebner, J. E., Semitherm Proc., 1996, 169-182. ©IEEE 1996. With permission.)

3. Is the conductivity or diffusivity expected to be anisotropic for the material under consideration? In other words, is the conduction of heat expected to be easier in one direction than in another? This can be caused by nonuniform microstructure such as that found in printed wiring boards. Many techniques apply heat flow in only one direction. 4. W hat is the expected range of the thermal variable to be measured? Some techniques are better suited for low conductivity material than for high, or vice versa. 5. W hat degree of accuracy is required? Techniques vary considerably in accuracy 6 . W hat tem perature range is desired? Som e techniques function well only near room tem perature, while others are especially useful at either high or low tem ­ peratures. 7. W hat is the available budget? System costs range over more than an order of magnitude. 8 . W hat technical skill is available? M easurement techniques vary widely in the ease of setup and/or operation. O utstanding features or limitations of the various techniques described below are collected in Section 7.4. Several references may be of special interest to the reader. The physics of thermal transport in solids is described in a classic treatment by Berman (1976). A very detailed collection of solutions to the diffusion equation, under many different boundary conditions in time and space, is given by Carslaw and Jaeger (1959). Two extensive surveys of measurem ent techniques are available, edited by Tye (1969) and by Maglic, Cezairliyan, and Peletsky (1984). Finally, there are several collections of data for the thermal properties of solids (Touloukian et al., 1970; CINDAS 1995).

Chapter seven:

7.2

Measuring thermal conductivity and diffusivity

247

Detailed description of four measurement techniques

Four different techniques for measuring k and/or a will be described in sufficient detail to allow a person with a technical background to set up the apparatus and obtain data. Expertise can be achieved by experience and further study of the technical literature. The techniques have been selected for their relative simplicity in construction and use, and to demonstrate a variety of sample requirements and measured quantities.

7.2.1

Long bar with steady heating

The m ost traditional method of measuring thermal conductivity uses a bar-shaped sample with one dimension significantly longer than the other two, as shown in Figure 1. This choice of sample shape facilitates one-dimensional heat flow. In order to make good thermal contact with the embedded Cu layers in this sample of PWB, a line of approxi­ mately ten holes (0.060 cm. diameter) was drilled across the sample at either end and Cu wire (0.025 cm. diameter) was threaded through the holes, which were then filled with alumina-powder-containing epoxy. A heater consisting of -2 5 cm of 0.0025 cm. diameter Manganin wire was wound through the Cu wire at one end of the sample and buried in more epoxy for thermal contact. Fine-wire thermocouples (0.005 cm diameter, type E) were epoxied into holes drilled along a center line of the sample. Again, the holes were used to provide good contact to the embedded Cu layers. Styrofoam and aluminized Mylar (0.001 in. Mylar with an evaporated thin film of Al on one surface) above and below the sample served as thermal insulation to resist the loss of heat to the surroundings by air convection or by radiation. The apparatus was placed in a vacuum chamber capable of achieving a pressure of 10-5 Torr. Typical temperature profiles with power Q dissipated in the heater are shown in Figure 1. If the slope AT/Ax were constant, the thermal conductivity could be calculated from the general expression for one-dimensional heat flow with no surface loss, Equation 1, as pointed out above. However, the pronounced upward curvature of the data, especially with an atmosphere of air and no radiation insulation, indicates considerable loss of heat by radiation and convection. Inclusion of a surface loss term linear in the temperature difference AT between sample and surroundings (Carslaw and Jaeger, 1959) produces a modified heat balance equation: the one-dimensional Laplace equation, 92 T/9x2 = 0, becom es k92 T / 9 x 2 = hP AT /A, where P is the perimeter around area A and h is the surface heat loss coefficient (energy per unit time per unit surface area per unit temperature difference). The linear dependence on AT is approximately valid for temperature differ­ ences that are small compared with the absolute temperature. If both radiation and con­ vection are present, h = hrad + hconv, where hrad = 4aeT3 and the absolute temperature T is measured in degrees Kelvin. Here a is the Stefan-Boltzmann constant (a = 5.67 x 10-8 W /m 2K4) and e is the surface emissivity. At room temperature with maximum emissivity (e = 1.0), ^ = 6.1 W m“2°C_1. Convective loss in still air often gives a value for hconv which is of the same order of magnitude as hrad. The solution to this equation (Carslaw and Jaeger, 1959) describes the temperature profile along a sample with its ends at temperatures T1 and T2 and with an outward heat flux at the surface given by hAT: w x = Tj sinh p(L - x) + T2 sinh px sinhpL where jx is a measure of the im portance of surface loss relative to bulk conduction: p = (Ph/Aic)1/2

(3)

248

Thermal measurements in electronics cooling

jjt1 is the length of sample for w hich the conductance along the sample is equal to the conductance out through the surface. Equation 2 can be fitted to the data (Figure 1) and the conductivity can be calculated from the fitting parameters |it, T lr and T2: QslnhHL (iA(T2 cosh (J.L - T j) One interpretation of this analysis is that Equation 2 allows one to extrapolate the tem­ perature distribution to the position of the heater to obtain the correct slope to use in Equation 1. If a straight line is fit to the data, its slope will always be lower than the slope near the heater; the straight line will therefore give too large a value for the conductivity. Failure to account for surface loss of heat is probably the most common error in thermal conductivity measurements. The uncertainty in the value of k obtained with Equations 2 and 4 is estimated to be ±5% to 10% if the sample dimensions are known within a few percent. For the sample shown in Figure 1, w ith inhomogeneities such as copper vias, the value of k given by Equation 4 should be taken as an average over the whole sample. Deviations of the data from the smooth curves are well outside the expected accuracy of thermocouples (at least -0.01 K) and are attributed to real variations in the local conduc­ tivity. Fitting the vacuum data in Figure 1 with Equation 2 yields a value of k = 14.4 W m_1 K_1 with [i = 12.8 m -1. As expected, the data with an atmosphere of air present and no insulation give a m uch higher value for [i = 29.3 m_1, but unexpectedly the value of k is also somewhat (15%) higher. The reason for the higher value undoubtedly lies in the sim plicity of the assumption of a linear dependence of the heat loss on temperature difference, and we choose the value in vacuum and with radiation shielding (lower surface loss) as being the more accurate. This example shows the importance of providing a vacuum and radiation shielding around the sample for accurate results. We also note that a straight-line analysis of the two data sets (disregarding heat loss through the surface) would provide very poor fits to the data and would result in two values for k w hich differ from each other by roughly a factor of 2, and both values of k would be significantly higher than the correct value. The value of ji = 29.3 m_1 can be used to calculate h = 8.4 W /m 2°C for the surface heat transfer coefficient. This value can be compared with h = 6.1 W /m2°C calculated for radiation loss alone with an emissivity of 1.0. If the actual em issivity is not much less than -0 .5 , this result indicates that the heat loss by radiation is comparable to the heat loss by conduction/convection through the residual gas and thermal insulation material. If the conduction/convection heat loss could be reduced nearly to zero, say by using a higher vacuum and removing the thermal insulation material to provide an environment at a fixed temperature, the value of h could in principle be used to obtain a value for the em issivity A common mistake made by novices in thermal measurements is to assume that the effects of radiative losses can be reduced by using extremely small temperature differences, AT. However, because AT is typically a few degrees, which is usually small compared to the absolute temperature T(K), the radiative heat flux is accurately proportional to PAT. As the heat conducted through the sample by ordinary conduction is also proportional to the first pow er of AT, the ratio of radiated to conducted heat flux is independent of AT. Thus, no advantage with respect to radiative loss is gained by decreasing AT. On the other hand, convective heat loss is sometimes observed to follow a slightly higher-than-linear dependence on AT, and in this case it might be advantageous to keep AT small, i.e., no larger than required for an acceptable signal-to-noise ratio.

Chapter seven:

M easuring thermal conductivity and diffusivity

249

The thermal and electrical properties of the heater and its electrical leads must be chosen carefully to avoid inaccuracies in Q . The leads must be long and thin enough so that the thermal resistance along them is 100 times higher than the thermal resistance along the sample, if 1% accuracy is desired. The electrical resistance of the heater should then be chosen as 100 times the electrical resistance of the leads, to assure that 99% of the electrical energy is dissipated in the heater. The presence of surface heat loss can be detected and corrected for by another steadystate technique (Graebner et al., 1994) which uses two heaters, one at the free end of the sample and one near the grounded end, as well as three thermocouples. The second heater, when operated alone, provides a very sensitive test for the presence of surface heat loss. For a hom ogeneous sample with accurately measured dimensions, a vacuum environment, and radiation shielding, an accuracy of 1% or better in k is possible with the two-heater technique. In a different approach to measuring k|( for a board or plate (Vanlaer and Lasance, 1994), the sample can be packed in material such as foam with a known (previously measured) thermal conductivity The uncertain surface loss due to radiation and/or con­ vection is then replaced with a possibly better-controlled loss of heat through the foam to thermal ground. This approach reduces the need to work in a vacuum chamber. The advantage of the long heated bar geometry (with one dimension much larger than the other two) is that one-dimensional heat flow is easily obtained, thus justifying the use of an equation as simple as Equation 1. The same simple flow can be obtained by using a sample with one dim ension much shorter than the other two, provided that heat can be introduced and extracted uniform ly over the large faces. This might be called the short-bar or through-the-thickness plate geometry. The disadvantage of this plate geom ­ etry is that thermometry is not easily accomplished. One solution is the use of high-spatialresolution infrared imaging at the edge of the sample. This is particularly useful in certain cases where the material under test is not uniform. An example is the case of printed wiring board (PWB) with buried layers of copper foil (Azar and Graebner, 1996), for which this geometry provides a through-the-thickness conductivity k± of the board (Figure 2). To make the measurement, a 1 cm2 sample of PWB is sandwiched with Ag-epoxy between two 1 cm2 blocks of Cu; one block of Cu is attached to thermal ground, the other is provided with an electrical heater. With known heat flowing through the sample, the temperature profile along one edge is recorded with a m oving single infrared detector (Figure 2) or with an infrared camera. The measured slope can be used with the known heat flow and the cross-sectional area perpendicular to the heat flow (1 cm2) to calculate k via Equation 1. The slope in the glass-epoxy is easily distinguished from the (near-zero) slope in each of the Cu layers. Furthermore, the data can be examined for faulty interfaces between adjacent layers by looking for a jump in temperature at an interface. None is observed, indicating good-quality interfaces, i.e., no gaps or regions of partial contact. The short-bar technique is therefore very useful for measuring k ± for individual layers in the PWB. Even for a hom ogeneous but anisotropic material, it serves as a complement to the long-bar technique which measures k|(. A related technique uses two blocks of reference material placed on either side of the sample, between the sample and the Cu blocks. If the conductivity of the reference material is known, the conductivity of the sample can be calculated from the gradients in the sample and the reference materials. 7 .2 .2

L o n g b a r w ith p e r io d ic h ea tin g

Rather than using steady heating of a long bar, it is sometimes useful to set up thermal waves by applying time-dependent heat to the sample. The analysis of thermal waves generated by periodic heating is a technique pioneered by Angstrom in the 19th century

Thermal measurements in electronics cooling

250

x (mm) Data for measuring the through-the-thickness thermal conductivity k of a sample of printed wiring hoard. Hie 1 cm2 sample (shown as rectangular in the inset) is sandwiched between two copper blocks (cross-hatched) with silver-filled epoxy. A heater on one block generates a flow of heat through the sample to the other block, which is thermally grounded, The temperature is measured by an infrared defector focused on a smalt spot (-30pm diameter) that is scanned across the edge of the sample. The line through the data is a fit to the data using a model which assumes a constant k = 0,25 W/mK in the glass-epoxy and 400 W/mK in the four copper layers embedded in the sample, indicated by vertical shaded bands near x = 1.8 mm and 2.4 mm, (From Azat; K, and Graebner, f, E., Semitherm Pmc,, 1996, 169-182, ©IEEE 1996, With permission,) Figure. 2

(Angstrdm, 1861,1863), It has appeared in many modifications (Carslaw and jaeger, 1959; Maglic et al., 1984), By studying the diffusive motion of thermal waves, one can determine the thermal diffusion length 5-r = (2 a / to p 2 for a heating frequency to, thus determining the thermal diffusivity a. If the absolute power input is also known, and if there is no loss of heat by radiation or convection, both the diffusivity and the specific heat may be obtained, allowing a determination of the thermal conductivity. If a non-contact heating technique is used, making it difficult to determine pC, a value must be assumed for pC in order to convert the measured a into k. Heat loss by radiation/convection must be taken into account for the case of periodic heating, as for the case of steady heating, but the problem of surface heat loss can be largely avoided by supplying heat at a sufficiently high frequency. The selection of an appropriate heating frequency is guided by the fol­ lowing analysis. Most treatments of this experimental technique assume a long hat which is heated at one end and which loses heat by radiation or conduction through a surrounding gas, and possibly through direct contact with thermal ground at the other end. The time-dependent heat balance equation has an extra term (Carslaw and Jaeger, 1959) to account for the loss of heat through the surface:

pC

dl

3 2T

hP

dt" ~ K 3 xt ~ "A

T

The heat applied at one end, Q (t)., appears separately as a boundary condition, and h (W co r2°C~l) is the conductance per unit area between sample and thermal bath. P is the perim eter around area A = ZVV. One can define (Salamon et al,, 1974) a relaxation time to

Chapter seven:

the bath, Tb =

M easuring thermal conductivity and diffusivity

~

' w^ere

and width W, with Z «

251

approximation is for a thin sample of thickness Z

W. It is convenient to supply a sinusoidal heat input at one end

of the sample: Q (0,t) = Q 0 sincot, by applying a time-varying electrical current to a heater attached to that end of the sample. The general solution to Equation 5 can be obtained in closed form for several simple cases. Choosing the operating frequency co ( = 2ni) sets the thermal diffusion length = (a/7if)1/2 for the measurement of a given material (a given a). By choosing f, we can decide to operate in any of three frequency regimes, corresponding to different relationships among three quantities: (1) the thermal diffusion length (2) the total sample length, and (3) the length for which heat loss to the bath is competitive with conduction along the sample. The m ost important regime for m easurements is usually the high-frequency regime (Salamon et al., 1974): Tb-1 «

co, or equivalently hW 8T «

KZW/&P

(6)

In this regime, a length dj of the sample has a much higher thermal conductance along its length (kZ W /^) than through its surface to thermal ground (hW8T). Under these conditions, the effects of surface loss via the gas or radiation can be ignored. The solution is given approximately by the simple expression: T(x, t) = T e - * sin(ft)t - x /8 T - 0) + Tmean(x)

(7)

where T0 = Q 0/2coZpC. The constant phase shift 0 is a result of the boundary condition appearing as a sinusoidal heat flux, not a sinusoidal temperature. The thermal wave of Equation 7 has a period 2 7r/co in time and 2 7i8p in distance, and is very strongly attenuated as a function of position. At a distance of one wavelength from the heater, x = 27r8T, the prefactor attenuates the sinusoid by a factor of e~2n - 0.002. By measuring either the phase or the amplitude of the temperature oscillations as a function of position near the heater, one can obtain a. Measurement of the phase as a function of position yields the phase velocity vp = co8r = (2coa)1/2, from w hich a is determined. Measurement of the amplitude as a function of position yields the thermal length 8T directly, from which a is determined. If absolute measurements of heat input Q 0 and temperature T0 are made, and if surface losses are negligible, the specific heat pC can be determined from the absolute amplitude of the thermal waves. However, many of the most commonly used versions of this approach apply heat by radiation and therefore do not measure the power input accu­ rately; hence, only a is measured. If it is not possible or convenient to work at a sufficiently high frequency (sufficiently small 8 p) to avoid problems due to surface heat loss, it is still possible to measure a accurately by any of three techniques: (1) measuring phase and amplitude simultaneously at two positions (Angstrom, 1861, 1863; Sidles and Danielson, 1954; Abeles et al., I960); (2) measuring phase at two frequencies and two positions (King, 1915); or (3) m easuring amplitude at two frequencies and two positions (Starr, 1937). By taking the proper ratios, the effect of surface heat loss is cancelled out for any of these three approaches. The simplest case is the first: the thermal diffusivity is given by a = coL2/(2 0) over the surface of a sem i­ infinite body initially at a zero reference temperature, the equation for the surface tem­ perature history is

T(t) = (2q(t)/k)^at/7i = 2q(t) t Jt(kpcp)

(21a)

Using DuhameTs Convolution Integrals, the time-varying heat flux can be obtained from a m easured temperature history by using the following equation (Jones, 1977):

(21b)

Chapter eight:

Heat flu x measurements: theory and applications

299

As long as the temperature range is appropriately limited, the thermal inertia |^kpcp j of the material is relatively constant. Then, Equation 21b is a linear equation and processing can be done with an analog circuit for the active measurements or with a simple numerical scheme for m easurements made with any of the temperature sensors (thermocouples, thin film resistance therm om eters, liquid crystals, or thermographic phosphors). In electronics cooling, applications of the thermally thick case generally occur over a short period of time inside a component, such as a power transistor, a silicon controlled rectifier, or a thick film component where the size of the heat source is small compared with that of the substrate. In Blackburn and Berning, 1982, the junction temperature of a pow er MOSFET was measured by first bringing the transistor up to operating temperature and then switching betw een the operating current levels and a much lower measurement current. The periodic excitation was nominally a square wave with a 99% duty cycle at operating pow er (heating) levels and 1% at measurement (cooling) levels. Varying the pow er dissipation changes the heat flux out of the active region of the transistor. Based on the size of the junction, the transient temperature response was approximated by a semi-infinite body solution (Equation 21a). To correct for nonthermal switching transients, the decay histories of three TSEPs were compared to the expected Vt decay of the junction temperature based on one-dimensional heat conduction for a thermally thick body. W hen the variation of the TSEP followed the expected Vt variation, any nontherm al switching transients were assumed to have disappeared. For the power MOSFETs being studied, the one-dimensional case was expected to last for 250 psec. Equation 21b can be used with the temperature history to estimate the heat transfer from the active region if the thermal inertia parameter (i.e., ykpcp (W- Vs /m2-K)) of the MOSFET material is known. Assum ing the drain region is silicon with a nom inal thermal diffusivity of 7*106 pm 2/s, the region would have to be approximately 100 pm thick to satisfy the criteria of Fourier number < 0.2 (based on the thickness) to allow the use of Equation 21b. Alternatively, the thermal inertia parameter can be estimated from Equation 21b if T(t) and q(t) are known. One possible approach for determining q(t) is to measure the power dissipation. Least squares techniques can be used for param eter estimation because the equation is linear. Discussions related to measuring the thermal inertia param ­ eter by periodically exciting the active junction are given in Examples 3 and 10. Keltner et al. (1988), used pulse heating of a platinum resistance thermometer (1 mm by 10 mm) to measure the thermal inertia parameter of a M ACOR glass ceramic material, see Figure 7. In this experiment, a three-dimensional transient heat conduction model was used to remove the one-dimensional conduction time constraint and to compensate for edge effects resulting from the small size. Multidim ensional heat transfer models enable the analysis of surface temperature m easurements over longer time periods (Beck et al., 1985b; Keltner et al., 1988); the longer times permit a wider variety of geometries and excitation waveform s to provide data for a wider range of electronics applications. M ul­ tidimensional models provide a more accurate means of relating temperature and heat flux; they can also be used to relax the assumption of uniform temperature or heat flux in analyses (Beck et al., 1992). Example 8: Heat flux measurements using one-dimensional and three-dimensional models for thermal diffusion Blackburn and Berning (1982), used an infrared camera to measure temperatures over the surface of a power M OSFET for comparison with their TSEP measurements. Although no actual size was given, the num ber of pixels (each 25 pm square) in an infrared photo

Thermal measurements in electronics c

■Umfam&jf. Surteet

Sami Infinite

mm

Early

Analytical Analytical Analytical

Analytical Series Series

Element Solytteas Middle

Late Analytical Expressions

flHej l a*** fpd 1 Late » Ct .m ° L *Cg' bk iio T jr " •C2

Modeling a thin film heat flux sensor, indicates the junction was approximately I 1/* mm by 2 mm. Micro­ electronic fabrication processes develop active features with dim en­ sions less than 1 pm, this small size eliminates the use of infrared cam eras for m easuring the temperature, because the feature is small­ er than the wavelength of the infrared radiation. The small size severely limits the time for which one-dimensional heat transfer approximations are valid for analyzing the data. Compare the use of one-dimensional (semi-infinite or thermally thick assumption) and three-dimensional models for 1 mm and 1 pm power dissipating features on a silicon substrate. The thermal diffusivity of silicon is approximately 7*106 pm2/s. Equation 21a describes the surface temperature response of a semi-infinite body with a uniformly heated surface; Beck et a i, 1985b, modified this for a heated square on the surface to

at ......v 1 + fta2 rca

. at

2 i at 3 \m 2

The first term on the right-hand side is the one-dimensional solution for a semi-infinite body. The second and third terms are the correc­ tions for the finite size in two dimensions, T h e Fourier number, at/ a2, is based on the ha If-width of the feature. The 250 psec period used in Blackburn and Bem ing (1982), would give a Fourier number = 0.002 for the 1 mm feature. For estimating the junction temperature at the end of this period, the difference between using the one-dimensional solution (Equation 21a) and the multidimensional solution (Equation 22) would be approximately

2V2%.

Chapter eight:

Heat flu x measurements: theory and applications

301

For a Fourier number of 0.1 used as a limit in true one-dimen­ sional cases, the correction for the finite size effects is almost 20%; this corresponds to real times of approximately 14 msec for a 1 mm feature and 14 nsec for a 1 pm feature. Using a one-dimensional approximation for even these short time periods would introduce a significant error in the estimated temperatures or heat fluxes for these devices. For small features, the very short times can increase problems with nontherm al switching transients in a TSEP measure­ ment; as a result, these types of measurements may be easier if smooth functions, such as sine waves, are used for excitation instead of square waves. W hen the temperature m easurement location is some distance away from the surface or if multiple measurem ent locations are used, then estimating the heat flux from the temperature m easurements is often done with a numerical technique known as inverse heat conduction analysis (Beck et al., 1985a; Blackwell et al., 1987). In inverse heat con­ duction codes, temperature histories from one or more locations in the body are used to estimate boundary conditions, such as surface temperature or heat flux. These topics are beyond the scope of this chapter.

8.5.3

,

Transient and/or steady-state temperature gradient based sensors

Temperature gradient-based sensors use multiple temperature sensors mounted on oppo­ site sides of a known thermal resistance to measure heat flux. Three types of sensors have been used for measuring the temperature gradient: • Thermopiles, which are a number of thermocouples connected in series • M ultiple thin-film resistance thermometers • Thermographic phosphors Temperature gradient sensors are widely used for making either conduction or con­ vection heat transfer measurements. The sensors are normally fabricated using a dielectric material as the thermal resistance element between the temperature sensors. A constant trade-off in gradient sensors is between the sensitivity which increases linearly with the thickness (L) for a given material, the response time which increases with L2, and the frequency response which decreases with L2 (Ortolano and Hines, 1983). Another factor in m easurement uncertainty is distortion of the heat flow caused by the sensor (ASTM, 1983, for embedded sensors and Baba et al., 1985, for surface sensors). These points are examined in Examples 9 and 11. Temperature gradient heat flux sensors can be used as transient or quasi-steadystate devices. The difference betw een transient and steady-state applications is the m ethod of converting the tem perature gradient into a heat flux. For steady-state m ea­ surem ents or quasi-steady-state m easurem ents such as monotonic or low frequency periodic heating, the conversion uses a calibration constant based on an experim entally obtained conduction therm al resistance, see Equation 4. In the m onotonic heating case such as a step change, the tem peratures of the two sensors track with a basically constant offset related to the tim e constant, after an initial transient period. The calibration constant can be used for periodic heating where the period is longer than the nom inal response tim e of the sensor. For higher frequency periodic heating, attenuation and phase shift between the two temperature m easurements (described in Equations 10a and 10b) can require the use of analog or numerical processing to obtain the heat flux; the analysis is based on the diffusion

Thermal measurements in electronics cooling

302

equation (Equation 8a) as with the thermal diffusion measurements. This analysis is possible if the two temperature m easurements are independent; it should not be used with thermopile sensors. The specific routine depends on the characteristic time of vari­ ations of the heat flux phenomena and the thermal penetration time of the thermal resistance layer in the sensor. W hen using data from both temperature sensors, the highest frequencies that can be measured are limited by attenuation of the signal between the two temperature measurem ent locations. Above these frequencies, the front temperature sen­ sor can be used in the thermal diffusion sensor mode; thermopiles can be used in this mode because the cold junction temperature does not vary during the fluctuation period.

8.5.3.1

Therm opiles

Therm opile-based sensors use a number of thermocouples connected in series. Thermo­ piles are the most common type of temperature gradient sensor. They can be calibrated to provide a direct indication of the heat flux for steady-state or slowly varying conditions. Thermopiles should not be used for fluctuating or periodic heat transfer measurements at frequencies where attenuation between the hot and cold junctions is significant, because the hot and cold junction temperature m easurements cannot be separated due to the series wiring of the multiple thermocouples. Therm opiles can be used in a diffusion mode at higher frequencies, where there is total attenuation (>99%) at the second or cold junction location, see Equation 10a. There are a number of designs of thermopile-based sensors. One of the oldest designs is the Schm idt-Boelter gauge (Jacob, 1954; Kidd and Nelson, 1995). Various interpretations of the original design are routinely used in a variety of applications ranging for building heat loss (ASTM, 1983) to fire safety testing (Keltner and Moya, 1989). Some of these sensors can be built into simulated electronic components; others are flexible enough to fit curved surfaces. For higher heat flux levels (up to 10 W /cm 2), Kidd and Nelson (1995) describe a design based on a 0.5 mm anodized alum inum plate (See Figure 8a). To fabricate the sensor, a constantan wire is wrapped around the plate. Copper is electroplated onto half of each turn of the wire to form a plated thermocouple (Pesko, et al., 1972). A 25-tum sensor provides a sensitivity of approximately 0.1 mV/(kW /m2). The thermopile element is potted with a high temperature epoxy (Stycast 2762). The 95% response time is less than 1 s. The peak operating temperature of this design is approximately 300°C. Another common design uses a flexible plastic film, such as Kapton, for the thermal resistance element (Ortolano and Hines, 1983). These sensors are generally attached to a surface with an adhesive. Two sensor designs are shown in Figure 8b. Kapton film designs typically have a lower temperature range than the Schmidt-Boelter designs; the maximum operating temperature is 260°C. Example 9: Installation errors for temperature gradient sensors In Azar and Moffat (1991) a Kapton thermopile sensor (RdF Corp. Model No. 20450-3) was used to measure the heat transfer off the top surface of the aluminum blocks. Does the sensor installation alter the heat transfer? The top of the aluminum block is 25 mm x 25 mm; the sensor dimensions were 7.5 mm x 12.7 mm x 0.3 mm. The nominal sensi­ tivity of the sensor is 0.634 m V/(W /cm2). The unit thermal conduc­ tion resistance from Equation 4 is thus L/k= 0.03 cm/0.0014 W /cm-K = 21.4 K/W /cm2

Chapter eight:

Heat flax measurements, theon? and apt it r * is

Figure S (a) Schema tic of a Schmidt-Bod ter thermopile sensor; (b) photographs of Kapton film design thermopile sensors, (Figure 8a used with the permission of Arnold Engineering Development Center, Tuilahoma, TN, Figure 8b used with the permission of RdF Corporation, Hudson, NH3 where L is the sensor thickness and k is the thermal conductivity of Kapton, The maximum power dissipation for a single aluminum block was 3 W. If all of tiiis energy went out the exposed surfaces of a block, the heat flux would be 0.24 W/em2, The expected output of the thermopile would be (115 mV (this provides a first setting for the data acquisition system). Based on the thermal resistance of the sensor and a heat flux of 0.24 W /cm 2, the temperature drop across the sensor due to conduction will be approximately 5 K (21.4*0,24). The analysis in Example 5 indicates the temperature within the aluminum blocks is uniform. Installation of the sensor should not change this because the Biot number « 0.1, As a result, the temper­ ature on the exposed surface of the sensor will be different from the surface temperature of the aluminum blocks. According to Baba et al. (1983b the operational or installation error created by the change in the local thermal resistance is given by an analysis that evaluates the effect of changing the local thermal resistance over a circular disk on the surface of a semi-infinite body, The change in the heat transfer through the sensor is given by q/q0 = he/h0/(l a- (l\ Jh Q- 1) x N) where \\ is the effective heat transfer coefficient with the sensor installed and h, is the original heat transfer coefficient. The effective heat transfer coefficient is defined by the sum of the conductive, convective, and radiative effects of the sensor

(23)

Thermal measurements in electronics cooling he = (L /k s) + (hconv + hrad)

(24)

and N is a parameter derived from a Green's function analysis. The parameter N is given as a function of a Biot modulus based on the sensor radius, P = r x h0/kal For this example, the rectangular sensor is replaced by an equivalent area disk (r = 5.5 mm). From above, the conductive resistance L/ks = 21 K/(W /cm2). Azar and M offat (1991) give an average value of the total heat transfer coefficient of = 0.0023 W /cm2-K; this value has both radiative and convective components. From Example 4, the radiative portion of the heat transfer coefficient was estimated to be hrad - 0.00081 x es. The emissivity, es, of Kapton is approximately 0.5 (Ortolano and Hines, 1983). Then the convective portion of the co­ efficient is hconv = 0.0019 W /cm2-K. Using these numbers in Equation 24 gives an effective heat transfer coefficient of he = 0.0022 W /cm2K. Using Equation 12b, the radiation coefficient for unpolished alu­ minum is approximately 0.0001. Assuming the convective portion of the heat transfer coefficient was not changed by the sensor instal­ lation, the total heat transfer coefficient for the aluminum, ho, would be 0.002 W /cm2-K. For this application, P = 0.55 cm * 0.002 W /cm 2-K/1.9 W /cm-K = 0.00058 A graph in Baba et al. (1985) indicates the parameter N is ap­ proximately zero for this value of the parameter P. From Equation 23, the m easurement error introduced by the sensor is approximately q/q0 = he/h0 = 0.0023/0.002 = 1.15 The analysis indicates the sensor installation actually increases the local heat transfer by 15% as a result of the higher emissivity of Kapton compared to aluminum. This type of error or uncertainty m ight be reduced in several ways. The Kapton film could be applied to the entire top surface; this would change the overall thermal resistance on the top of the blocks but eliminate the variation across the surface. Aluminum foil (dull-side up) could be glued to the thermopile surface to eliminate the different emissivities; adding aluminum foil and adhesive would increase the overall thermal resistance of the sensor. Both the block and the sensor could be painted to provide uniform emissivity; the paint could introduce an error between the experim ent and the actual application. The analysis in Baba et al. (1985) presumed a semi-infinite wall. A more detailed analysis would account for the finite dimensions (both lateral and thickness) of the aluminum blocks. An analysis of this type is given in Wesley (1979); however, it is not as easy to use and does not provide results for small values of the Biot modulus.

(25)

Chapter eight:

Heat flu x measurements: theory and applications

305

The basic conclusion drawn from this example is that installation of this sensor, with thermal properties that are significantly different from the properties of the underlying aluminum substrate, will per­ turb the heat transfer and affect the measurement. W hile methods are available for m inimizing the radiation heat transfer effect, any changes may introduce other measurement uncertainties. A third type of therm opile design uses semiconductor processing techniques to develop very small sensor areas and typically incorporate a surface temperature sensor with the heat flux sensor. The small thickness provides very fast time response at a cost of reduced sensitivity due to the small temperature difference. This can be offset by increasing the number of thermopile elements. Hager et al. (1993) reported a 96-junction sensor design with a 3 mm x 3 mm area. The sensitivity was 15.5 (iV/W/cm2 with a response time of approximately 20 (isec.

8 .5 3 .2

Multiple thin film designs

M ultiple thin film designs typically use platinum resistance thermometers for the hot and cold temperature m easurements (Epstein et al. 1986; Doorley and Oldfield, 1987). Some of the uses and problems are similar to the other designs; however, there are major advantages. Although the instrumentation is more complex, separate temperature m ea­ surements are provided by the two thin films. This allows these sensors to be used for heat flux measurements in either temperature gradient or thermal diffusion modes. The temperature gradient m easurements are useful for steady-state or slowly varying condi­ tions that are representative of many electronics cooling applications. Epstein et al. (1986) indicate a dual-film sensor mounted on a 25 (im thick polyamide resistance layer functions as a gradient gauge up to 20 Hz (see Example 10). Although transient, convective heat transfer m easurements are generally not necessary in electronics cooling applications, Epstein et al. (1986) provide some insight into the heat transfer measurement process. Between 20 and 1500 Hz, the data analysis of the dual film sensor is based on an analog solution of the transient heat conduction equation within the 25 pm thick polyamide film; a logarithmically distributed resistance-capacitance net­ work was used to process the temperature measurements. For frequencies above 1500 Hz, the front surface sensor was used as a diffusion-based surface measurement; the analysis is described in the prior section. Another analysis for multilayer gauges on both thick and thin plates is given in Doorley and Oldfield (1987). Using resistance thermometers instead of thermocouples provides another advantage. A technique known as transient thermal resistance testing (TTRT) provides the capability for checking the integrity and performance of both the sensor and the installation (Kerlin et al., 1978; Keltner et al., 1988; Cole and Beck, 1988). TTRT uses a combination of loopcurrent step response (LCSR) tests to interrogate the sensor, and transient response models to interpret the sensor response to this controlled input. An example application for evaluating the installation of a wire wound resistance temperature detector with an epoxy is given in Keltner et al. (1983). In some cases, the LCSR techniques can be used to estimate the thermal properties of the component to w hich the sensor is attached (Kerlin et al., 1978; Keltner et al., 1988; Cole and Beck, 1988; Scott et al., 1994). Another application uses one sensor as a heater to check the other sensor. Example 10: Transient response characteristics of dual thin film sensors Consider the use of a dual thin film sensor for a fluctuating heat transfer m easurement; this might be due to vortex shedding from

Thermal measurements in electronics cooling

306

components in forced convection or buoyancy driven instabilities in natural convection. W hat are the response characteristics of 25 pm thick, Kapton sensors for the measurements at 1, 2, 10, and 20 Hz? Epstein et al. (1986) used dual platinum resistance sensors on a 25 pm thick polyamide film, such as Kapton. This sensor was indi­ cated to respond as a gradient type of heat flux gauge from DC to 20 Hz, when mounted on an aluminum substrate. The indicated thermal diffusivity of the polyamide film was 0.0012 cm2/s. For a step change in the heat flux at the surface, the thermal penetration time (Fo - 0.05) between the first and second sensors is 0.26 msec. For periodic heat transfer, the amplitude ratio between the surface temperature sensor and the in-depth temperature sensor is given in Equation 10a as A(x)/A(0) = exp(-x^o>/2a) and the phase lag is given in Equation 10b as iHerroi Heating Coisillfepi

Radiation or Stagnation Flow (T^ « I0CNT)

Figure W

Actual temperature and heat

f lu x

distributions for Gardon gauges.

mode) should be avoided; an example of such a ease would occur for a gauge mounted in the top of the aluminum blocks in the experiment by Azar and Moffat (1991). The asymmetric heating produced by shearing flow greatly increases the measurement uncer­ tainty. An experimental evaluation of the output in both shear flow and stagnation flow modes is given by Brookley and Liller (1994). In addition to the large uncertainties, it shows the gauges are nonlinear in the shear flow mode.

8SA 2

Gardon gauge: applications summary

* Convective heat flux measurement applications should use a convective calibration constant. The m anufacturer's calibration normally uses a radiative source; calibra­ tion constants are different for radiation and stagnation flow convection heat trans­ fer, ♦ Gardon gauges slumld not be used in shear flows. • If the source temperatures and thus the spectral distribution of the radiant energy in the calibration and the experim ent are significantly different, the spectral absorp­ tivity of the coating should be evaluated to determine potential errors in radiant heat flux measurements, * The potential for boundary layer disturbances and coolant temperature effects should be evaluated,

8S A 3

Flow calorimetry

Flow calorimetry is an integral technique in that heat transfer is measured over the entire flow path. It is not used for local measurements. The basic principle in flow calorimetry is to measure the temperature rise and mass flow rate of a well-characterized fluid. The heat transfer is then calculated from Q = cp(dm/dt)AT

(26)

This approach works best with liquids, which are easier to mix to obtain a uniform, or well-stirred, temperature; the temperature measurement errors and uncertainties are usually smaller w ith liquids. To obtain adequate sensitivity (i.e., temperature rise), flow calorimetry is generally used in system s with high power dissipation. In Peterson et al. (1994), flow calorimetry was used to measure the contact resistance of a cold chuck used to hold a m ultichip module. In electronics, applications have ranged from main frame com puter modules to large silicon controlled rectifiers to radar power transistors.

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310

8 .5 .5

P o w e r d iss ip a tio n -b a sed sen so rs

Although dissipation measurements have a variety of applications, the basic principle involves relating the power dissipation, usually electrical, to another parameter. It has been used to measure the conduction resistance by relating the power dissipation to the temperature rise of a heated spot (Beck et al., 1993; Keltner et al., 1988; Negus et al., 1989). It has been used to measure heat transfer coefficients in conjugate heat transfer problems (Cole and Beck, 1988). It has been used to measure the effective or local thermal properties of a material (Keltner et al., 1988; Garnier et al., 1992; Scott et al., 1994). Transient m ea­ surements of this type usually provide estimates of the thermal inertia of the mate­ rial |^/kpcp

j

from early time m easurements (i.e., small Fourier number), while later time

m easurements are used to estimate the thermal conductivity (k). Power dissipation (i.e., heat transfer) is used in hot-wire and hot-film anemometry to measure velocity and turbulent fluctuations. An example application of these sensors in electronics cooling would be mapping the cooling air velocity distribution inside an enclosure. For hot-wire anemometers, there are two modes of operation, constant current and constant temperature. In the constant current mode, the device acts as a resistance thermometer. The temperature fluctuations are related to velocity fluctuations in the flow, which affect the heat transfer. As shown in Example 6, the velocity is one component in the Reynolds num ber which is one of the dimensionless groups used in Equation 16 to correlate convective heat transfer. In the constant temperature mode, a feedback-controlled circuit is used to vary the current. The current fluctuations are then related to the velocity fluctuations. For hot-wire anemometers, first-order or differential compensation is used to reduce thermal inertia effects and extend the effective frequency response range, just like thermocouples. A 5 |im platinum wire has an upper frequency limit of 50 kHz (Jones, 1977). A hot-film anemometer is a heat transfer sensor which has a relatively simple design compared to most microelectronic components. A conjugate analysis for a sensor with a rectangular heat source on the surface of a dielectric substrate is given in Cole and Beck (1988). These sensors are used for measuring velocity and for studying shear flows or jet cooling in applications such as electronics. A hot-film anemometer developed by HyCal Engineering uses two platinum films. One is used to measure heat transfer and through it velocity. The second one is used to compensate for temperature (density) effects on m easurements of air velocity. The device has an operating velocity range of 0.0004 to 40 m/s and a response time of less than 150 msec.

8.6

Calibration of sensors

As mentioned at the beginning of this chapter, heat flux is not a prim ary physical param ­ eter. Calibrations of the heat flux sensors described in this chapter generally require specialized equipm ent; one exception is thin film, resistance temperature detectors. Depending on the specific sensor, the equipment could include blackbody radiation sources, em issom eters or reflectometers for surface radiative properties, differential scan­ ning calorimetry for specific heat measurements, thermal comparators for conductivity measurements, wind tunnels, and so on. The purpose of this section is to describe the calibration methods as an aid to the reader becoming an informed user. The sensor manufacturers are a good source of inform ation for their specific products and provide applications specific consulting as part of their service.

Chapter eight:

8.6 .1

Heat flu x measurements: theory and applications

311

S te a d y -sta te sen so rs 8 .6 1 .1

Gardon gauges

The normal calibration method uses a radiant source. The heat flux from a black body (or gray body) radiator of known dimensions is related to its absolute temperature (see Equation 11). A calibration is developed for a transfer standard gauge as a function of the radiative heat flux, which is calculated from an optical pyrometer temperature measure­ ment. The transfer standard and the gauge to be calibrated are then exposed to the same source. The output of the gauge being calibrated is used to drive the y-axis of an XY plotter and the transfer standard is used to drive the x-axis. According to an American Society for Testing and Materials (ASTM) standard for Gardon gauges, the accuracy is expected to be ±3% ; this is possible in a single laboratory. The Federal Aviation Administration has sponsored a round-robin calibration of Gardon gauges; unpublished results of calibrations by the three manufacturers, the Federal Aviation Administration, and the National Insti­ tute of Standards and Technology indicated an interlaboratory standard deviation of approximately 10% (Johnson, 1995). Borrell and Diller (1987) developed a convective heat transfer calibration method using a free jet wind tunnel design. Heat flux gauges can be calibrated in a stagnation flow condition in the jet. Convective heat transfer coefficients up to 200 W /m2-K were devel­ oped. The estimated uncertainty was ±7.5%.

8 .6 1 2

Temperature gradient gauges

These gauges are often calibrated in a m anner sim ilar to Gardon gauges. For exam ple, M edtherm uses a radiant source to calibrate Schm idt-Boelter therm opiles. RdF Corpo­ ration m ounts a Kapton film therm opile on a slug calorim eter and then exposes it to a radiant source; the calibration is developed by relating the output of the therm opile sensor and the heat transfer calculated from the response of the slug calorim eter (Equa­ tion 14). Another approach for calibrating thermopiles uses a thermal comparator, which is designed to measure the thermal conductivity of materials. The comparator provides one­ dimensional heat transfer through a stack of different materials. There is insulation around the edges of the stack. The gauge is mounted between two high thermal conductivity plates. The temperatures of the plates are used to define the boundary conditions for the sensor. In another part of the stack, the temperature drop across a layer of standard m aterial w ith a known thermal resistance is used to calculate the heat flux. Another part of the calibration process involves a determination of any temperature dependence of the gauge sensitivity. For thermopile gauges, this can be done by running calibrations at different temperatures, as in the comparator. Another approach measures thermal conductivity of the gauge material as a function of temperature and uses it with the temperature-dependent sensitivity of the thermopile, w hich depends on the type of thermocouples used, to calculate an overall temperature effect.

8 .6 2

T ran sien t sen so rs 8 .6 2 1

Slug calorim eters

An ideal calibration of a slug calorimeter can be provided by measuring the mass of the calorimeter, the specific heat of the material, and the surface area that is exposed to heating. Loss factors, such as heat loss through the mounting insulation or lead wires, must be developed to correct the ideal calibration and reduce errors. These can be obtained by exposing the calorim eter to a known thermal source.

Thermal measurements in electronics cooling

322

8 .6 2 .2

Surface tem perature sensors

These calibrations require the output of the temperature sensor and the thermal properties of the substrate material. The actual calibration steps depend on whether the sensor uses a thermocouple or a resistance thermometer. For resistance thermometers, the sensor output as a function of temperature is determined from a steady-state measurement in an

j

oven or a constant temperature bath. The properties of the substrate material |^kpcp and the characteristics of the installation, such as an adhesive, can be determined from a power dissipation measurement (Keltner et al., 1988) or by exposing it to a known heat source, such as a laser (Epstein et al., 1986). For a thermocouple, the output as a function of

j

temperature is obtained from standard tables. The thermal inertia |^kpcp of the substrate must be measured by other methods. Example 11: Designing a heat flux measurement application Different pieces of the inform ation necessary to design the experi­ ment described in Azar and M offat (1991) have been given in other examples earlier in the chapter. To try to demonstrate the entire process of developing an experim ental application to measure heat transfer from either an actual or a simulated component, this exam­ ple will use that earlier inform ation and supplement it. Table 5

Designing a Heat Flux Measurement

Design step

Purpose

Estimate temperature and heat flux levels Evaluate the transient response of the sensor

Selecting a sensor with adequate sensitivity and operating range Ensure the measurement can capture transient events of interest Set the sampling rate to prevent aliasing Ensure thermal or mechanical interactions with the flow do not alter the heat transfer Ensure the thermal characteristics of the sensor do not alter the heat transfer process Ensure calibration accounts for temperature changes in the sensitivity Different techniques affect the calculated heat transfer coefficients and uncertainties Is there a better way?

Evaluate installation effects on measurement errors and uncertainties Evaluate temperature effects on measurement uncertainties Evaluate reference temperature effects Consider alternate approaches

8 .6 2 .3

Estim ating tem perature and heat flu x

Assume the configuration described in Azar and M offat (1991) is an electronics enclosure in w hich convective heat transfer information is needed for a component. The top surface of the component is a 25 by 25 mm plate. A n initial estimate of the local heat transfer is obtained from a correlation given in Eckert and Drake (1972): Nux = 0.332 Rex1/2Pr1/3

(27)

For a velocity of 1.5 m/s and an air temperature of 40°C, the local Reynolds number at the center of the plate is given by

Chapter eight:

Heat flu x measurements: theory and applications Rex = Vx/v = 1.5 (m/s)*0.0125 (m )/17*l(H (m2/s) -1100

313 (28)

Note, the inlet flow velocity has been used for this calculation because local velocity measurements are not available. At 40°C/ the Prandtl number of air is approximately 0.7. This gives a local Nusselt num ber of 9.8. The estimated local heat transfer coefficient is then hx = Nux*(k/x) = 9.8^(0.027 W /m-K)/(0.0125 m) = 21 W /m 2-K Remember, turbulence might increase this value by up to 50%. The power dissipation is 3 W. Assuming there is convective heat transfer off the top surface and the edges, the average power dissipation will be 0.24 W /cm 2. The estimated surface temperature rise of the blocks is obtained from Equation 2. AT - Q/hA - 3 (W)/21 (W/m2-K)*0.00126 (m2) - 113 K This estimate assumes all of the power is dissipated out the top and edges. (The experi­ mental values from Azar and Moffat, 1991, were approximately 50% lower due to con­ duction heat transfer into the printed circuit board.) A thermopile sensor has been found that has a sensitivity of 634 jiV/(W /cm 2). The product of the average heat flux and the thermopile sensitivity indicates an output of 152 pV. An available data acquisition system has a 12-bit analog to digital converter; this provides a resolution of 1 part in 4096. If the system voltmeter has a 1 mV range, the least significant bit will equal 0.24 pV. This provides a resolution of 0.00038 W /cm2 or 0.16%.

8 .6 2 .4

Transient response characteristics

The 63% response time of the sensor is given as 0.4 s. For the adhesively bonded film sensors, the response time is calculated from x = 4L2pcp/;i2k (seconds)

(29)

(Ortolano and Hines, 1983). This equation can be rearranged to give Fo = ax/L2 - 0.4 which is 80% of the more conservative value of 0.5 quoted in Luikov (1968) to ensure the hot and cold junction surfaces are rising at the same rate. The full transient solution for convective heat transfer to a flat plate is an infinite series, where each term is a product of an exponential and a trigonometric term. If only the first term of the solution is used, then the sensor is assumed to respond as a firstorder, low-pass system. Equation 18 shows the response time and the break frequency are related. The response time of 0.4 s indicates a break frequency of 0.41 Hz. As long as events of interest are at frequencies lower than the break frequency, the sensor's transient response characteristics should not have a major impact on the m easurements (see Exam­ ple 10 for a more detailed discussion). A sampling rate on the data acquisition system of 1 Hz or more will minimize aliasing effects.

8 .6 2 .5

Installation effects

Another concern is the potential effect the sensor might have on the flow field. One of these is purely m echanical; how does the thickness of the sensor compare to the boundary layer thickness and will it mechanically trip the boundary layer? The other concern is thermal; is the surface temperature of the sensor different enough from the aluminum to

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314

cause thermal tripping? Either type of tripping w ill increase the local heat transfer coef­ ficient. The boundary layer thickness is given by (Incropera and DeWitt, 1985, p. 291): 8 = 5x/.^Re~ = 0.0019 m = 1.9 mm

(30)

where Rex is from Equation 28 and x is the distance from the leading edge of the plate. The sensor thickness is 0.3 mm, w hich is less than the boundary layer thickness. The installation should not mechanically trip the boundary layer. The conduction resistance of the sensor is 0.0021 K/W /m2 or 21 K/W /cm2. The temperature drop across the sensor is estimated from AT = q/R = 0.24 W /cm 2/21 K/(W /cm2) ~ 5 K In Example 5, the aluminum blocks were shown to be isothermal (this would not be the case for plastic cases which have low conductivity); therefore, the surface temperature of the sensor will be lower than the surface temperature of the block. If this temperature difference occurred as a step discontinuity at the edge of the sensor, it would probably initiate the development of a new thermal boundary layer (i.e., trip the boundary layer) and increase the local heat transfer coefficient (Eckert and Drake, 1972, p. 316). The high thermal conductivity of the alum inum blocks might smooth it out slightly. Another approach m ight be to cover the entire top surface of the block with a Kapton film to eliminate the potential temperature discontinuity; Example 9 indicated this will increase the total heat transfer from the top surface.

8.6. 2.6 Temperature effects The estimated temperature rise of 113 K could affect the sensitivity of the thermopile in two ways. For example, the thermal conductivity of Kapton increases by approximately 5% for a 50 K temperature rise. The AT across the sensor and thus the output is inversely proportional to the thermal conductivity for a constant heat flux (see Equation 3). Standard tables show the sensitivity (or Seebeck coefficient) of the type K thermocouples used in the selected thermopile sensor does not change significantly from 41 jaV/K over the range from 25 to 75°C. (This might not be the case for other types of thermopiles. In some cases, the type of thermocouple can be chosen to offset thermal conductivity effects and reduce sensitivity changes.) 8 .6 .2 .7 R eference tem perature effects Some aspects of measuring the reference temperature used in calculating the heat transfer coefficient have been discussed in Examples 6 and 7. Azar and Moffat, (1991) used three different reference temperatures to calculate heat transfer coefficients. These were the inlet air temperature, a local temperature estimated from the power dissipation upstream of a measurement location, and a power-off component temperature, which was obtained by turning off the power to individual components. For the first two methods, the mean value of the heat transfer coefficient in one row was 15.6 W /m2-K with a variation of ±24%. For the power-off method, the calculated value of h was 22.5 W /m2-K ±5%. (The power-off method might not be applicable in an experiment with an actual circuit board where an individual component cannot be turned off.) The results demonstrate that experiment design can affect both the level and the uncertainty of the heat transfer coefficient.

8 .6 2 .8

A lternate approaches

All of the discussion in this example has assumed that a steady-state measurem ent is the best approach. Example 5 shows the blocks in this experiment could be used as slug

Chapter eight:

Heat flu x measurements: theory and applications

315

calorimeters to measure the heat transfer. Given the size of the aluminum blocks, the thermal capacity (pcpV = density * specific heat * volume) is approximately 100 J/K. If pow er was turned on and all of the blocks were stabilized at a uniform temperature (say 125°C) before initiating the flow at 1.5 m/s and 25°C, then a transient measurement could be made. Assum ing a heat transfer coefficient of 0.0021 W /cm2-K along with a total area (top and edges) of 12.6 cm2, the rate of temperature change is obtained from Equation 14 Q = pcp V(AT/At) = hA(Ts - Tf) to give 0.027 K/s. This small signal change, ~1 pV/s for a type K thermocouple, suggests the use of a higher resolution sensor, such as a thermistor or a resistance thermometer. If the power is left on when the flow starts, the energy input must be accounted for in the calculations. (A platinum resistance thermometer could be used to simultaneously heat the block and provide the higher sensitivity.) The calculations in this example are typical of what is required in designing an experim ent and estim ating the errors and uncertainties in the measurements. These same types of calculation can be used as a means of checking experimental results.

8.7

Summary

A variety of techniques for measuring convective, conductive, and radiative heat transfer in both transient and steady-state conditions have been described. Examples have been presented for specific aspects of these measurements. The final example attempted to work through the design of an experiment from end to end. The examples are intended to demonstrate an important point; in measuring heat flux, there is no silver bullet or universal solution. The measurements must be designed to suit the individual tasks in order to provide accurate results. In m ost cases, calibration of heat flux sensors is difficult without specialized equip­ ment. Resistance thermometer-based designs (e.g., thin film heat flux sensors) are an exception. If the tem perature-resistance curve of the sensor is known, a loop-current-step response test can be used to calibrate it (Keltner et al., 1988) in a fashion similar to the technique used for m easuring the temperature of a transistor junction inside a microcircuit (Blackburn and Berning, 1982). Due to the relatively low temperatures involved in electronics applications, temper­ ature-related drift (aging) should not pose a problem for heat flux sensors. Recalibration of most heat flux sensors should not be necessary unless the sensor has been used outside its operating limits. Radiation heat flux sensors often need to be calibrated to account for changes in the high absorptivity surface coating, w hich tends to be fragile and is easily damaged. However, it is a good practice to periodically check the sensor installation. In Peterson et al. (1994), the initial thermal resistance of a silver-filled, thermoplastic adhesive used to bond test chips to a silicon substrate was twice as high as the estimate based on material properties. During the experiment, it continued to increase.

8.8 Nomenclature A Bi f3db p 1 or L

Area (m2) Biot number (Equation 13) Break frequency (Equation 18) Density (kg/m3) Depth or thickness or length (m)

Thermal measurements in electronics cooling

316

Diameter (m) Emissivity Fourier number (Equation 8b) Frequency (radians/s) Heat flux (kW/m2) Heat transfer (kW) Heat transfer coefficient (kW/m2-K) Mass (kg) Nusselt number Power (kW) Prandtl number Radiation configuration factor Radius Reynolds number Specific heat (J/kg-K) Stefan-Boltzmann constant (5.67*10^ W /m 2-K4) Temperature (K) Temperature difference (K) Therm al conductivity (W/m-K) Thermal diffusivity (m2/s)

d e Fo CO

q Q h m Nu P Pr

Fl-2 a Re cp

o T AT k a

Thermal inertia

vkpc.> R AX t X V V

8.9

Thermal resistance (K/W) (see Equations 2, 4, and 11) Thickness (m) Time (s) Time constant (s) Velocity (m/s) Volume (m3)

Definition of terms

Absorptivity (emissivity)

Advection Assem bly test chips (ATC)

Biot num ber

Break frequency

Characteristic length

Fourier number

Fraction of the radiation absorbed (emitted) by a surface as compared to am ount absorbed (emitted) by a perfect absorber (emitter), which is known as a black body Energy transport due to bulk motion of a fluid A special purpose test chip that includes heaters, p-n diodes for temperature measurements, and other sen­ sors A dimensionless number, which is the ratio of the ther­ mal resistance within a solid to the thermal resistance at the surface of the solid (Equation 13) The frequency at which the output of a first-order, lowpass sensor is one-half the amplitude of the excitation (also known as the half-power or 3db down frequency) A concept used to describe the m ost representative dim ension of a body in the analysis of conduction and convection heat transfer A dimensionless time used to indicate the speed of heat­ ing or cooling of a solid (Equation 8b) (also defined as the ratio of the heat conduction rate to the rate of ther­ mal energy storage in a solid)

Chapter eight:

Heat flu x measurements: theory and applications

Heat flux Heat transfer coefficient Inverse heat conduction

N usselt number Radiation configuration factor Thermal capacitance Thermal inertia Thermal resistance Thermal contact resistance

Thermal spreading resistance

Thermally thick plate

317

Heat flow/unit area/unit time A calculated number which is the quotient of the heat flux and the temperature difference A type of thermal analysis where the temperatures and heat fluxes at the surface of a solid (i.e., the boundary conditions) are calculated from internal temperature m easurements Dimensionless temperature gradient at the surface of a solid The fraction of the radiant energy emitted by one surface that strikes another surface. (0 < F^

^

10 10

(10)

Plot i= l

As an example, combining two sound pressure levels of 70 dB each results in a sound pressure level of 73 dB. Sound powers are added directly For example, three equal sound power levels (Wu W2, W3) of 1 pW each (L ^ = = 6.0 B) add to 3 pW. In terms of sound power level, the levels are combined on a logarithmic basis using

L wtot= l o g I

1 0 Lwi

(11)

i= l

In this example, the total sound power level LVVtot is 6.5 B.

12.4 Experimental procedures for determination of the noise emissions of a personal computer The following procedure outlines the noise emission m easurement process for a single personal computer. Table 1 gives a list of equipment required for the measurement. This equipment can, of course, be used to measure the noise emissions of any source. In a personal computer, the noise sources are generally one or more AMDs and the hard disk drive. If only the AMD noise is of interest, one must, of course, disable the hard disk during the measurements. The acoustical information obtained from these measurements

Thermal measurements in electronics cooling

434

Table 1

Equipment Needed for Determination of Sound Power Level

Device or facility

Function

Hemi-anechoic room or reverberation room Microphone(s), preamplifiers), and cable(s)

Required for determination of sound power level from measurement of sound pressure level One or more sets used in an array to measure the sound pressure level on a measurement surface in a hemi-anechoic room; one microphone mounted on a rotating boom to measure space average sound pressure level in a reverberation room Used in a reverberation room for moving a microphone along a specified path; used in a hemi-anechoic room (different boom design) if measurements are made using coaxial circular paths Required to calibrate the instrument system used to determine sound pressure level Required to switch between microphones when an array of microphones is used Required to determine the sound pressure level, A-weighted and in octave or one third octave bands Required to determine sound intensity if a hemi-anechoic room or reverberation room is not available for the measurements Required for determination of the sound power level of air-moving devices made according to ISO 10302 Required for determination of the static pressure inside the test plenum described above Required for the measurement of the rotational speed of an airmoving device

Rotating boom

Calibrator Multiplexer Sound level meter/ spectrum analyzer Sound intensity analyzer Test plenum Static pressure measurement device Speed measurement device

is useful in rank ordering noise sources and evaluating various potential noise reduction techniques. Another use for this information is in obtaining noise emission values needed for a product noise declaration (see ISO 9296). A noise declaration is a statistical statement of typical and maximum (upper limit) noise levels provided by the manufacturer of a computer or other information technology equipment to a customer. A noise declaration is typically based on acoustical data obtained from a sample of several production units. See Table 2 for Swedish limits on declared sound power values on computer and business equipment. To determine the sound power of a personal computer, the following steps should be followed: • Install the computer in a test chamber • Calibrate the measurem ent system • Measure the background sound pressure level and determine the background sound power level • Power on and warm up the equipm ent to be tested • Determine the computer sound pow er levels in operating and idle modes • Measure the sound pressure levels produced by the computer at the operator's position and at bystander positions • Perform a discrete tone and impulsive noise analysis at the operator's position These seven steps are described in more detail below. 1. Install the personal computer system in the test chamber. As discussed earlier in this chapter, the test chamber may be a hemi-anechoic room or a reverberation room. Install the personal computer in accordance with ISO 7779 on the floor of a

Chapter twelve:

Table 2

Acoustical noise measurement and control in electronic systems

435

Swedish Recommended Upper Limits for Declared Sound Power Level Values

Product category Category I Equipment for use in dedicated rooms Category II Equipment for use in general business areas

Category III Equipment for use in quiet office areas

Recommended upper limit sound power level in bels I^ad Operating L w a d Idling

Product description A. All products

A. Fully formed character typewriters and printers B. Printers and copiers more than 4 m distance from workstations C. Tabletop printers and tabletop copiers D. Processors, controllers, disk and tape drives, etc. (more than 4 m distant from workstations) E. Processors, controllers, disk and tape drives, etc. (Less than 4 m from workstations) A. Printers, typewriters, and plotters B. Keyboards D. Floor-standing processors E. Tabletop processors, controllers, system units including built-in disk drives and/or tapes, display units with fans F. Display units (no moving parts)

7.0 + K

7.0 + K

7.2

5.5

7.0

6.5

7.0

5.5

7.0

7.0

6.8

6.6

6.5 6.2 6.0 5.8

5.0 N /A 5.5 5.0

4.5

4.5

Note: Technical standard 26:3. Statskontoret, Swedish Agency for Administrative Development, Stockholm, Sweden. First day of validity: 1993-05-01. In case of conflict, the Swedish text prevails over the English text in the table. K = lg (S /S 0) where S0 is equal to one square meter, and S is the footprint in square meters, i.e., the projection in square meters of the machine on the floor. If S < 3 square meters, use S ~ 3. The calculated value of the recommended upper limit may be rounded to the nearest upper 0.1 bel.

Table 3 Relative Response Values for the A-Weighting Network at the Center Frequencies of the Octave Bands from 125 to 8000 Hz Octave band center frequency Hz

index, i

Relative response values, Ri, of the Aweighting curve dB

125 250 500 1000 2000 4000 8000

1 2 3 4 5 6 7

-16.1 -8.6 -3.2 0 +1.2 +1.0 -1.1

hem i-anechoic chamber or a reverberation room for determination of sound power levels (see step 5 for reverberation room and step 6 for hemi-anechoic room sound power determination methods). A variety of ISO-standardized measurement meth­ ods can be used in either test environment. One of the most accurate methods is

Thermal measurements in electronics cooling

436

2.

3.

4. 5.

6.

7.

the use of a rotating m icrophone array on coaxial circular paths for determining the surface sound pressure level on a hemispherical measurement surface. Such an array is described in ISO 3744. Sound power levels can be computed directly from the average surface sound pressure level. Calibrate the measurement system and check the frequency response. Calibration and frequency response should be checked on a weekly basis, or just prior to and after a set of m easurements is completed. Single-frequency or multifrequency cal­ ibrators are available from several manufacturers. A multifrequency calibrator such as the Briiel & Kjaer Type 4226 is useful in determining overall system frequency response as well as providing a reference signal for calibration. M easure the background sound pressure and determine the background sound power level. These measurements are made with the personal computer system turned off. It is recommended that the background or residual noise level of the instrum entation and test chamber be determined prior to the test. This is done by m aking a sound power level and sound pressure level measurement with the microphones in place but w ith no noise source powered on. This will highlight any instrum entation or connection problems at low signal levels that may not have been apparent when calibrating in step 2, which is normally done using a relatively high signal level. The background levels are also necessary for comparison with the measured personal computer noise levels to ensure that the minimum requirements for signal-to-noise ratio are m et (see sections 5.7.3 and 6.7.3 of ISO 7779). Pow er up and warm up the equipment so that all initialization is complete and it is operating in the steady state before acquiring any data. Determine the personal computer sound power levels in idle and operating modes. There are normally at least two distinct modes of operation: idle mode and oper­ ating mode. Idle mode refers to the personal computer in a power-on state and ready to receive commands, and operating mode indicates that the disk drive(s) are being exercised to simulate storage and retrieval of data. See ISO 7779, Annex C for further details of modes of operation. Sound power determination in a hemianechoic chamber normally entails acquiring a space- and time-average m easure­ m ent of the sound pressure level on the measurement surface. Averaging time will depend on the particular m icrophone arrangement; several alternative arrays are specified in ISO 7779. For a five-microphone coaxial circular path array, an averag­ ing time of 32 s per m icrophone is often used since that corresponds to the period of rotation of the array when using a Briiel & Kjaer 3923 rotating microphone boom. M easure the personal computer sound pressure levels in idle and operating modes. Desktop units should be placed on a standard test table (see ISO 7779, Annex A). With the personal computer in the same modes of operation as in step 4 above, the bystander and operator position sound pressure levels should be measured. Al­ though sound power can be determined in either a reverberation room or a hemianechoic chamber, sound pressure determinations must be done in the latter (see ISO 7779 section 7). Typically four bystander positions are specified (1 m from the side of the personal computer, centered on each side, and 1.5 m above the floor) and one operator position. Since the microphones are stationary during the m ea­ surement, an averaging time of approximately 8 to 16 s may be used. Measurement duration should be extended when a mode of operation is cyclical, for example, a certain seek pattern for the hard disk. In this case, at least three operating cycles must be included in each measurement. Perform a discrete tone analysis at the operator position. The existence of discrete frequency tones in the spectrum often requires that an additional measurement be performed to assess the prominence of the tone(s). Tonal prominence is related to annoyance and the psychoacoustics of how discrete tones are perceived in the

Chapter twelve:

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presence of noise. Annex D of ISO 7779 specifies the detailed procedure. The quantity obtained from the measurement is termed the tone-to-noise ratio, or ALT. W hen ALT exceeds a value of 6 dB, the tone is considered prominent. The discrete tone analysis is complex, and is a special procedure to be followed for computer and business equipment. The procedures are not covered in detail in this article; see ISO 7779 for the procedures to be followed for both discrete tones and impulsive noise.

12.5 Limit values for sound power levels The wide variety of electronic equipment cooled by AMDs makes it impossible to specify a set of limit values for sound power level which are applicable to all equipment. However, there are two sets of requirements which have been adopted in Europe for data processing equipment. In Germany, the German Institute for Quality Assurance (RAL) has been authorized to grant the environmental logo Blue Angel to certain products, including workplace computers and workstations consisting of a system unit, keyboard, and m on­ itor. These environmental requirements are mostly concerned with recycling; there are, however, acoustical requirements specified. A "non-official" translation of the acoustical requirements into the English language reads In accordance with section 3.2.5 of ISO 9296, the "declared sound power level, LwAd, of the components, measured when idling and multiplied by 10, must not be more than 48 dB(A). In other condi­ tions of operation (access to diskette or hard disk) the maximum value m ust not exceed 55 dB(A). The measurements are to be per­ formed in accordance with DIN EN 2 7779. The multiplication by 10 mentioned in the above paragraph is required for the conversion from bels (as specified in ISO 9296) to decibels. The measurements are to be made by an independent "test house," or by an applicant whose test facilities and procedures have been certified by an independent certification body in accordance with a European stan­ dard EN 2 9000 or ISO 9000. In Sweden, Statskontoret Technical Standard 26:3 specifies recommended upper limits for the noise emissions of computer and business equipment. These requirements are summarized in Table 3.

12.6 Air-moving device characteristics 1 2 .6 .1

Types o f air-m oving devices

The m ost common types of small AMDs are centrifugal blowers, axial flow fans , propeller fans , and motorized impellers. These units are usually sold as a complete assembly, including a motor and, where used, a scroll. The type of device selected depends not only on its ability to deliver the required air flow and its acoustical characteristics, but also cost, reliability, and potential applications across multiple products. Centrifugal blowers are often arranged in pairs (a duplex blower) as illustrated in Figure 2. However, small low-profile DC blowers are becoming available for use in spaceconstrained applications. A typical axial flow fan which has a diameter of 175 mm is shown in Figure 3. Many units sold have the motor integrated into the hub of the fan. These devices can range in size from several meters in diameter for large scale airconditioning applications to 25-^0 mm for "spot cooling" applications in electronic equipment.

Thermal measurements in electronics cooling

Figure 2 A typical duplex centrifugal blower (From Mating, G. C , Jr. and Boggess, A. L., in Handbook o f Acoustical Measurements ami Noise Control, 3rd ed,, Harris, C, M , Ed,, McGraw-Hill, Mew York, 1991, chap. 44, With permission,)

Figure 3

A typical axial-flow fan with packaged motor (From Maling, G, C,, Jr. and Boggess, A* L , in Handbook o f Acoustical Measurements and Noise Control, 3rd ed., Harris, C. M., Ed., McGrawHill, New York, 1991, chap, 4 4 With permission,) Motorized im pellers usually have an impeller sim ilar to that of a centrifugal blower (often with fewer blades, however). It is common to have a motor built into the hub of a

Chapter heeler

Figure 4

Acoustical noice measurement a ad control in electronic cisterns

439

A typical motorized impeller. The motor is often built into the huh of the impeller.

motorized im peller A sketch of a motorized impeller is shown in Figure 4. A typical propeller fan is shown in Figure 5. The general characteristics of several types of small AMDs and representative noise emission data have been given elsewhere (Maling and Boggess, 1991). A laminar flow fan is a device which consists of a series of closely spaced spinning disks that move air by m eans of viscous drag forces rather than the lift forces generally associated with the blades on other types of AMDs. The interdisk spacing is chosen to ensure laminar flow, thereby reducing the aerodynamic noise generation due to turbu­ lence. There have been some applications of laminar flow fans in the U.K. (Merry and Glegg, 1984}, but they are not widely available as commercial products, and are not discussed in this chapter It has been found, however, that spinning disks near heat sinks can produce a significant improvement in the heat transfer from the heat sink (Maling, 1994), and such air movers may have cooling applications in the future.

Figure 5 A typical propeller fan, (From Mating, G. C , Jr. and Boggess, A, L.# in Handbook o f Acoustical Measurement* and Noise Control f 3rd ed,, Harris, C M,, Ed,, McGraw-Hill. New York, 199], chap, 44, With permission.)

Thermal measurements in electronics cooling

440

22.6.2

Air performance

The air performance of a small AMD is defined by a graph of static pressure rise across the device vs. the volumetric air flow rate through it. Air performance is usually measured with the device mounted on a standard air flow test chamber as specified in ASHRAE standard 51-1985. The flow of air is allowed to expand into a plenum, and the static pressure rise, P, of the device is determined as a function of the volumetric flow rate, Q, of air. Ideally, the rotational speed of the AMD, N, is held constant during the measure­ ments, but in practical situations variations in speed occur as the static pressure and air flow rate are varied while the fan motor input voltage is held constant. Typical air per­ formance curves for a blower and an axial flow fan are shown in Figure 6. W hen the speed of the AMD changes with flow, a curve of speed vs. air flow is often provided as a supplem entary plot.

A ir flow in cfm

100

200

OtN X

C aA > x