Table Of ContentExperimental Heat Transfer, 
Fluid Mechanics 
and Thermodynamics 
1993 
Proceedings of the Third World Conference on 
Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 
Honolulu, Hawaii, USA, 31 October-5 November,  1993 
Editors 
M.D. Kelleher  R.K. Shah 
Naval Postgraduate  School  Harrison Division, GM 
Monterey, CA, USA  Lockport, NY, USA 
K.R. Sreenivasan  Y. Joshi 
Yale University  Naval Postgraduate  School 
New  Haven, CT, USA  Monterey, CA, USA 
Volume 1 
1993 
ELSEVIER 
AMSTERDAM • LONDON • NEW YORK • TOKYO
ELSEVIER SCIENCE PUBLISHERS B.V. 
Sara Burgerhartstraat 25 
P.O. Box 211,1000 AE Amsterdam, The Netherlands 
Library  of  Congress  CatalogIng-ln-PublIcatlon  Data 
rtorld Conference on Experimental Heat Transfer, Fluid Mechanics, and 
Thermodynamics  (3rd : 1993 : Honolulu, Hawaii) 
Experimental  heat transfer, fluid  mechanics, and thermodynamics 
1993 : proceedings of the Third  World Conference on Experimental 
Heat Transfer, Fluid Mechanics, and Thermodynamics, Honolulu, 
Hawaii, USA, 31 October-5 November 1993 /  editors, M.D. Kelleher ... 
[et al .]. 
p.  cm. —  (Elsevier series in thermal and  fluid sciences) 
Includes bibliographical references and index. 
ISBN 0-444-81619-4 
1. Fluid  mechanics—Congresses.  2. Heat—Transmission-
-Congresses.  3. Thermodynamics—Congresses.  I. Kelleher, Matthew 
D.  II. Title.  III. Series. 
QC138.W67  1993 
621 .402'2—dc20  93-32073 
CIP 
ISBN: 0 444 81619  4 
©1993  ELSEVIER SCIENCE PUBLISHERS B.V. All rights reserved. 
No part of this publication  may be reproduced, stored in a retrieval system or transmitted  in any form or by any means, electronic, 
mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher,  Elsevier Science Publishers 
B.V., Copyright & Permissions Department, P.O. Box 521,1000 AM Amsterdam, The Netherlands. 
Special regulations for readers in the U.S.A. -  This publication  has been registered with the Copyright Clearance Center Inc.   (CCC), 
Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of  this  publication 
may  be made in the  U.S.A. All other copyright questions, including  photocopying  outside  of the  U.S.A., should  be referred to  the 
copright owner, Elsevier Science Publishers B.V., unless otherwise specified. 
No responsibility  is assumed by the publisher for any injury and/or damage to persons or property as a matter of products   liability, 
negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. 
This book is printed on acid-free paper. 
Printed in The Netherlands.
V 
PREFACE 
This Volume contains papers presented at the 3rd World Conference on Experimental Heat 
Transfer, Fluid Mechanics and Thermodynamics, held in Honolulu, Hawaii during October 31-
November  5,  1993.  Specifically  the  volume  contains  the  texts of  the  Plenary Lecture, 
Nusselt-Reynolds  Prize  Lecture, seven  Keynote  Lectures,  21  Invited  Lectures,  and  195 
Contributed Papers. The number of the papers and the variety of subjects addressed attest to the 
continued vitality and vigor of experimental work.  The papers cover a broad spectrum from the 
experimental investigation of complex fundamental physical phenomena to the study o fpractical 
devices and applications. 
A decade ago there were those who predicted that large scale computational codes would 
go a long way toward eliminating the need for experiments.  What has emerged though is the 
true nature of the symbiotic relationship between experimental and computational simulation. 
Computation can provide the  direction  for the  conduct  of  efficient  experimentation  while 
experimentation is necessary to verify complex computational codes and for complex situations 
for which no reasonably accurate numerical analysis is possible.  Also, physical experiments still 
possess unsurpassed advantages as a tool for exploring and discovering new physical phenomena. 
The papers contained in this volume reflect the ingenuity and originality of experimental 
work in the areas of fluid mechanics, heat transfer and thermodynamics.  A quick perusal of the 
papers also indicates that the quality of work is not limited by geography.  The contributors to 
the Volume come from 27 countries  and provide an indication of how well the worldwide 
scientific community is networked. 
The two previous Conferences were held m Dubrovnik, Yugoslavia. The first was held in 
September 1988, and the second in June 1991.  In an effort to reflect the trul yworldwide nature 
of the participants of the Conference, the Scientific  Committee at the Firs tWorld Conference 
in  1988  had decided  to move  the  conference  location  worldwide after the  Second  World 
conference.  Accordingly, the venue has been moved to the USA this time. 
An attempt has been made to use a uniform outline and method of presentation of each 
paper.  The International System of Units (SI) is used throughout the proceedings.  All keynote 
papers are included first followed by all invited papers.  Contributed papers are grouped in 
appropriate sections to provide better access to readers. In addition to the Table of Contents at 
the beginning of the proceedings, an author index is included at the end of the volume. 
We are grateful to the lead scientists of this conference, experts in the area of thermal and 
fluid science, for their contributions in coordinating the evaluation of contributed papers and 
maintaining the high quality of research papers presented in this proceedings.  We especially 
acknowledge the professional help of over 700 reviewers from all over the world for selection 
of papers and suggestions for improvement of the content of accepted papers published in the 
proceedings.
vi 
The sponsorship of the following professional societies and institutions also contributed to 
the success of the conference: 
.  American Society of Mechanical Engineers 
.  American Institute of Chemical Engineers 
.  National Committee of Heat and Mass Transfer, Russia 
.  The Society of Chemical Engineers, Japan 
.  Regional Centre of Energy, Heat and Mass Transfer for 
Asia and the Pacific 
Finally, we greatly appreciate the cooperation provided by Ms. Inez van der Heide of 
Elsevier Science Publishers B.V. for her preparation of this fine proceedings in a very timely 
manner. 
The Editors
vii
SCIENTIFIC COMMITTEE 
Conference Chairman 
M.D. Kelleher 
Naval Postgraduate School 
Monterey, CA, USA 
Conference Vice-chairman 
K.R. Sreenivasan 
Yale University 
New Haven, CT, USA 
Assistant Program Chairman 
Y. Joshi 
Naval Postgraduate School 
Monterey, CA, USA 
Conference Scientific Secretary 
R.K. Shah 
Harrison Division, GMC 
Lockport, NY, USA 
Local Organizing Committee Chairman 
P. Cheng 
Univeristy of  Hawaii 
Honolulu, Hawaii, USA 
LEAD  SCIENTISTS 
P.J. Catania, International Energy Foundation, Regina, Canada 
G.P. Celata, ENEA Casaccia, Roma, Italy 
J.C. Chen, Lehigh University, Bethleham, PA, USA 
Dr. T. Choi, Korea Institute of Machinery & Metals, Kyungnam, S. Korea 
G.R. Cunnington, Jr., Lockheed Missiles & Space Co., Palo Alto, CA, USA 
D.S. Dolling, University of Texas at Austin, Austin, TX, USA 
L.J. Fang, Industrial Technology Res. Inst., Hsinchu, Taiwan, China 
M. Gharib, California Institute of Technology, Pasadena, CA, USA 
P.J. Heggs, University of Bradford, Bradford, United Kingdom 
L.A. Kennedy, Ohio State University, Columbus, OH, USA 
V.V. Klimenko, Moscow Power Engineering Institute, Moscow, Russia 
D. G. KrOger, University of Stellenbosch,  Stellenbosch, South Africa 
M. Lance, Ecole Centrale de Lyon, Ecully, France 
A.I. Leontiev, Moscow Higher Technical School, Moscow, Russia
viii 
L. Martfti, Institute of Atomic Energy Research, Budapest, Hungary 
L.F. Melo, University of Minho, Braga, Portugal 
Y. Miyake, Osaka University, Osaka, Japan 
A.K. Mohanty,'Indian Institute of Technology, Kharagpur, India 
P.H. Oosthuizen, Queen's University, Kingston, Canada 
E. Payko$, Middle East Technical University, Ankara, Turkey 
A. Pollard, Queen's University, Kingston, Canada 
AT.  Prata, Universidade Federal de Santa Catarina, Florian6polis, SC, Brazil 
K. Rehme, Kernforschungszentrum Karlsruhe GmbH, Karlsruhe, Germany 
D.P.  Sekuli6, University of Novi Sad, Novi Sad, Yugoslavia 
B. Sund6n, Chalmers University of Technology, GOteborg, Sweden 
I. Tanasawa, University of Tokyo, Tokyo, Japan 
P.R. Viswanath, National Aeronautical Laboratory, Bangalore, India 
M.C. Welsh, CSIRO Div. of Building, Construction, and Engineering, Highett, Australia 
S.M.  Yang, Shanghai Jiaotong University, Sanghai, China 
A.A. Zukauskas, Lithuanian Academy of Sciences, Vilnius, Lithuania 
ASSEMBLY OF WORLD  CONFERENCES 
Officers 
R.K. Shah, President 
Harrison Division, GMC, Lockport, NY, USA 
J.F. Keffer, Vice President 
University of Toronto, Toronto, Canada 
T. Aihara, Member 
Tohoku University, Sendai, Japan 
J. Bataille, Member 
Ecole Centrale de Lyon, Ecully, France 
E.N. GaniC, Secretary General 
University of Sarajevo, Sarajevo, Bosnia-Herzegovina 
General Members 
J.S.M. Botterill, UK  R. Letan, Israel 
P.J.  Catania, Canada  Y. Miyake, Japan 
G.P.  Celata, Italy  A.K. Mohanty, India 
T. Choi, S. Korea  W. Nakayama, Japan 
M. Cumo, Italy  E. Payko?, Turkey 
J.E. Fackrell, UK  A. Pollard, Canada 
L.J. Fang, Taiwan, China  A.T. Prata, Brazil 
M. Giot, Belgium  K. Rehme, Germany 
Z.Y. Guo, Beijing, China  V.M.K. Sastri, India 
M.D. Kelleher, USA  K.R. Sreenivasan, USA 
V.V. Klimenko, Russia  M.C. Welsh, Australia 
Y. Kurosaki, Japan  K.T. Yang, USA 
A. Leontiev, Russia
Experimental  Heat  Transfer,  Fluid  Mechanics  and  Thermodynamics  1993 
M.D.  Kelleher et al.  (Editors) 
1993  Elsevier Science Publishers  B.V.  3 
THE  CHANGING  ROLES  OF  EXPERIMENTAL  AND  COMPUTATIONAL  FLUID  MECHANICS 
AJ.  Strazisar 
NASA  Lewis Research Center, Cleveland, OH 44135  U.S.A. 
ABSTRACT 
When computational fluid mechanics was in its infancy,  the complexity of our experimental, theoretical, and nu
experiments and theoretical  analysis were often  the pri merical methods - it is a rare individual who is expert in all 
mary approaches used to study flow physics.  Numeri three. The field of fluid and thermal sciences has therefore 
cal simulations were performed after an experiment was  been divided by natural forces into two "camps", exper
complete,  and the measured, theoretical,  and numerical  imental and theoretical/analytic/computational.  In addi
results were compared to assess the accuracy of the nu tion, the very organization of our research laboratories, in 
merical results. As numerical simulation techniques have  which there are quite often separate "test" and "numerical 
matured, computational, analytic, and experimental efforts  analysis" groups, continues to foster this situation.  Be
have become equal partners in fluid mechanics research.  cause of these facts, the integration of experimental and 
Today numerical simulations are being used to guide the  computational approaches in a particular investigation  is 
design of experimental hardware, to determine those ar not something which naturally "happens" - it must be pro-
eas of the flow field in which to concentrate the measure actively sought by one camp or the other. 
ment effort, and to complement measurements in studying  In  the past, experimental and analytic approaches to 
flow physics.  The changing roles of experimental, ana problems were often done separately. The interaction be
lytical, and computational research will be traced by re tween the two approaches consisted of comparing results 
viewing several investigations  in which these approaches  when both efforts were complete, and learning from the re
were used in varying degrees.  A case will be made for  sults. This "open loop" way of doing business has changed 
maintaining a high degree of interaction between these ap markedly over the past forty years.  I believe that this 
proaches throughout the course of an investigation.  The  change has been driven by the significant advances which 
development of prototype computing systems designed to  have occurred in both analysis  and measurement capa
enhance the integration of numerical simulations and flow  bility.  During this time, instrumentation  has progressed 
physics experiments will also be described.  from pitot probes and thermocouples to high-response in
struments (such as hot-wires and semiconductor pressure 
INTRODUCTION  transducers) and to non-intrusive optical techniques (such 
The  importance of using experimental  measurements,  as laser anemometry and laser-based spectroscopy). Anal
mathematical analysis, and numerical methods to investi ysis approaches have moved from the realm of approxima
gate fluid mechanics problems has long been recognized.  tion methods to the realm of computational fluid mechan
Most of us are introduced to this concept during our for ics, which in itself has moved from the solution of invis-
mal  education.  Graduate programs of study in fluid and  cid equations to the solution of the full three- dimensional 
thermal sciences include strong emphasis on pure and ap Navier-Stokes equations. These advances now necessitate 
plied mathematics and, in more recent times, on numerical  a new way of doing business, in which computations and 
methods as well.  Graduate students who perform an ex experiments are conducted concurrently during an inves
periment for their dissertation research are often encour tigation.  For example, the experimentalist needs to know 
aged by their professors to either perform some analysis  "Where should I concentrate my measurements?  Is there 
of the problem on their own or to compare their mea likely to be separated flow in the corner of the model?" 
sured results with theoretical,  analytic, or computational  The  analyst can answer "Yes, I predict separation will oc
results generated by other researchers.  Conversely, stu cur,  but I don't trust my transition model.  Can you tell 
dents who pursue an analytic approach to a problem are  me where the flow separates?  My predicted separation 
often encouraged to compare their results to experimen point varies as I change the parameters in my transition 
tal measurements in order to assess the accuracy of their  model and I'd like to know which settings yield the best 
results.  agreement with your measurements". 
In  our professional careers we tend to specialize in one  The  roles of analysis and experiments in fluid mechan
approach or the other. This is in large part necessitated by  ics research will be examined by reviewing several differ-
4 
ter a close interaction between the three disciplines will 
also be described. 
BOUNDARY LAYER STABILITY — A STUDY OF 
INDEPENDENT  INVESTIGATIONS 
The first example which I would like to examine con
sists of several investigations dealing with the stability of 
laminar boundary layers to small disturbances. These in
vestigations were carried out over a period of 40 years by 
different research groups. Taken as a whole, they repre
Understanding of Flow Physics  sent what I call an "open loop" type of interaction between 
Accurate Predictive Capability 
computations, modelling, and experiments in that much of 
Figure 1 Schematic model of an integrated approach  the work progressed in serial fashion rather than concur
to fluid mechanics research.  rently.  Before describing the separate investigations,  a 
little background information is in order. 
It is generally accepted that transition from laminar to 
ent investigations  in which each approach has been used  turbulent flow within a boundary layer occurs in several 
in varying degrees. This topic has been discussed by sev stages.  If the free stream disturbance levels are suffi
eral previous authors. Dunham [1] and Lakshminarayana  ciently small, they will excite the normal modes of the 
[2]  have recently examined the role of computations in  laminar boundary layer, which are often  referred to as 
fluid mechanics research directed at turbomachinery. At  Tollmien-Schlichting (TS) waves. These waves are small-
the 2nd World Conference on Experimental Heat Trans amplitude, two-dimensional disturbances whose behavior 
fer,  Fluid Mechanics and Thermodynamics, Bergles [3]  is described by the Orr- Sommerfeld equations  [5].  If 
discussed the role of experiments in fluid mechanics re the TS waves decay, then the boundary layer will remain 
search. In a review which addressed both analysis and ex laminar and the flow will be "stable".  If the TS waves 
periments, Horlock [4] has pointed out that there are really  grow sufficiently strong (an "unstable" situation), they can 
six possible interactions between theoretical (T), computa trigger non-linear disturbances which in turn can lead to 
tional (C) and experimental (E) research, which he labelled  the formation of turbulent spots and eventually to a com
as the T/C, C/T, T/E, E/T, C/E, and E/C interactions.  pletely turbulent flow. Understanding the stability of the 
In place of Horlock's "theoretical" category, I would  boundary layer as evidenced by the behavior of TS waves 
like to introduce the concept of flow physics modelling.  is therefore an important component of understanding the 
Flow physics models are simplified mathematical repre larger phenomena of boundary layer transition. 
sentations of real flow physics.  These models are tightly  The Orr-Sommerfeld equations are derived from the full 
coupled to both experimental and computational research.  Navier-Stokes equations  by making several  simplifying 
The  formulation of such models is often based upon ob assumptions (see Schlichting [5]). One of these assump
servations drawn from experimental measurements.  The  tions is that a flat plate boundary layer can be modelled 
models serve to simplify the computational approach to  as a parallel flow, i.e.  that the streamwise velocity, U, is 
a particular problem because the flow physics which they  only a function of the distance normal to the plate, y, and 
account for does not have to be solved computationally.  is independent of the streamwise distance, x. This is ob
A classic example of flow physics modelling is the tur viously a good model when the length Reynolds number 
bulence modelling approach used in the solution of the  is large and the boundary layer is relatively thin, which 
Reynolds-averaged Navier-Stokes equations, wherein tur is often  the case. 
bulent mixing is modelled as a simple diffusion process.  Analytic  solutions  of  the  Orr-Sommerfeld equations 
I believe that a modern approach to research in the fluid  were first achieved by Tollmien [6] and Schlichting [7] 
and thermal sciences should be structured as shown in Fig in the early 1930's.  In 1940, a key experiment was per
ure  1.  The key feature of such an approach is the close  formed in a flat plate boundary layer in air by Schubauer 
interaction between experimental, analytic, and modelling  and  Skramstad [8]. This team had designed and built a 
disciplines.  The benefits which can be realized from such  wind tunnel with very low turbulence intensity (0.02%) 
an approach will be demonstrated by reviewing several re in order to  study boundary layer transition.  The low 
search efforts in which the degree of coupling between the  free-stream disturbance environment in this tunnel enabled 
three disciplines varied.  In reviewing these examples, a  them to detect TS waves which were triggered by free-
case will be made for the fact that modern fluid mechanics  stream disturbances.  This discovery was  accomplished 
research can reap substantial benefits from a strong inter using hot wire anemometers to measure the unsteady ve
action between analysis, computations, and experiments.  locity within the boundary layer. In order to more easily 
The design of two prototype computer systems which fos study the TS waves, Schubauer and Skramstad then added
5 
420  1- low Reynolds numbers, they do bracket the experimental 
data. In addition, Schubauer and Skramstad noted that the 
Data,  Schubauer&  unstable disturbances which they found at low Reynolds 
Skramstad  numbers and high frequencies were extremely weak and 
difficult to measure, which lead to larger experimental un
300  4- certainty in the (Re, F) coordinates of the neutral points in 
this region in Figure 2. Based on the agreement between 
Tollmlen 
6 measured and predicted results for several other charac
Fx  io 4-
teristics of the disturbances, Schlichting himself declared 
Schlichting  in his textbook that "The experimental results show such 
180  4- complete agreement with the theory of stability of lami
nar flows that the latter may now be regarded as a verified 
Stable  component of fluid mechanics" [5]. 
During the 1950's and 1960's the solution of the Orr-
Sommerfeld  equations  was  further pursued using ana
60  4- lytic approaches and, with the aid of computers, finite-
Stable 
difference techniques  as well.  These solutions were dis
cussed by Jordinson [9], who also solved the equations 
»
 4A 0n0   ^  800  1200  numerically on a computer.  The maximum unstable fre
quencies and the lowest Reynolds number for which the 
boundary layer is unstable, (termed the minimum critical 
Figure 2 Comparison of analytically predicted boundary 
Reynolds number, Remc)  are summarized in Table 1 for a 
layer neutral stability characteristics  [6,7] to 
number of these investigations.  Since the numerical solu
measured neutral stability characteristics [8]. 
tions obtained by several additional investigators all gave 
exactly the same results, there was a general feeling that 
a thin vibrating ribbon placed near the plate surface to in
the numerical solutions were more accurate than the ear
troduce small- amplitude two-dimensional harmonic dis
lier analytic solutions of the Orr-Sommerfeld equation. 
turbances into the boundary layer at known frequencies. 
They then mapped the growth and decay of these distur Table 1 Comparison of measured and predicted 
bances as they moved downstream and thus experimen properties of the neutral stability curve at 
tally established the stability characteristics of the laminar 
low Reynolds number. 
boundary layer. Figure 2 is a comparison of their exper
imental results with the calculations  of Schlichting  and  Source  Approach  FnuuXW6 
Tollmien. This figure is called a neutral stability diagram.  Tollmein,  1931  Analytic  420  <300 
The ordinate is the non-dimensional frequency of the dis
Schlichting  1933  Analytic  575  178 
turbance and the abscissa is the displacement thickness 
Reynolds number. The solid lines in Figure 2 are the an Lin,  1945  Analytic  425  345 
alytical solutions, while the broken lines are curves fared  Shen,  1954  Analytic  425  345 
through the neutral points  measured by Schubauer and  Wazzan,  1968  Numerical  520  245 
Skramstad.  The data points and analytical results define 
Jordinson,  1970  Numerical  520  245 
the neutral points of the boundary layer, which are the loci 
of disturbances that neither grow nor decay. The boundary  Schubauer  1940  Exp  400  400 
layer is stable to disturbances which fall outside the neu
tral curve (in other words these disturbances will decay).  Jordinson was one of a team of researchers at the Uni
The boundary layer is unstable to disturbances which fall  versity of Edinburgh who were performing an integrated 
inside the neutral curve - these disturbances will grow and  experimental and computational investigation into why the 
are therefore potentially dangerous in that they can lead  computed and measured stability characteristics were dif
to transition.  ferent at low Reynolds numbers. In another phase of the 
The agreement between experiment and theory shown  computational  effort,  Barry and Ross  [10] added terms 
in Figure 2 was taken to be quite good by Schubauer  to the Orr-Sommerfeld equation which accounted for the 
and Skramstad.  The agreement between theory and ex growth of boundary layer thickness with streamwise dis
periment at frequencies  below  180 is clear.  Although  tance and used a modified version of Jordinson's program 
the analytic solutions do not agree with one another at  to numerically  solve  the equations.  In so doing, they 
low Reynolds numbers, they do bracket the experimental  hoped to determine if the parallel flow assumption was 
data. In addition, Schubauer and Skramstad noted that the  invalid at low Reynolds numbers and thus the cause of the
6 
420 
•  SchEuxbpaeureirm &e Snktsr amstad  •  F =  86xl06 
A  Ross et al 
T  Wortmann  24 
Strazisar et al  Non-parallel 
*  Kachanov et al  prediction  X. 
300  +  Non-parallel flow 
prediction  ^-Parallel 
prediction 
b • Parallel flow 
FxlO |  prediction 
600  1000 
Re  1 4 00 
180  + 
Figure 4 Comparison of measured and calculated growth 
of a disturbance of frequency F=86xl0~~6  as a 
function of streamwise distance [13]. 
alytic solution of the governing equations tractable, was 
60  + 
too restrictive  at low Reynolds numbers.  In retrospect, 
the earlier attempt to include non-parallel effects made by 
Barry and Ross had failed because they had included only 
400  800  1200  some of the non-parallel effects. 
Re  The  results shown in Figure 3 might lead one to con
clude that non-parallel effects are only significant at low 
Figure 3 Comparison of measured boundary layer  Reynolds number and high frequency, since the parallel 
neutral stability points to the neutral stability  and  non-parallel neutral curves are quite similar for dis
curves determined using parallel and  turbance frequencies less than F=120xl0~6.  Further ev
non-parallel flow calculations [13].  idence that the non-parallel effects are important even at 
higher Reynolds numbers can be seen in Figure 4, which 
observed discrepancy. In the experimental effort, Ross et  compares the predicted and measured log of the distur
al.  [11] repeated Schubauer and Skramstad's experiment.  bance amplitude for a frequency  of  F=86  xlO"6  as a 
The  numerical results displayed only a slight difference  function of streamwise distance (expressed as the displace
when the non-parallel effects were included — Remc  was  ment thickness Reynolds number).  Note that the results 
7
reduced from 520 to 500 and Z ,^  increased from 245 to  in Figure 4 represent a cross-sectional  cut through Figure 
260x10^.  On the other hand, the experimental results  3 along a horizontal line at F=86  xlO"6. 
were in complete agreement with those of Schubauer and  This example is representative  of the way in which 
Skramstad.  At this point, the cause of the experimental  much or our fluid mechanics research is conducted. It rep
and  numerical discrepancies was still unresolved.  resents a sound investigative  approach in which analytic 
In the early 1970's, several additional, independent ex and  experimental investigations  were conducted by inde
perimental and numerical efforts followed. Each new ex pendent groups.  Researchers learned from one another 
perimental investigation verified the fact that the minimum  over time and achieved progress toward the ultimate goal 
critical Reynolds number for a flat plate laminar bound of gaining insight into a particular aspect of fluid physics. 
ary  layer is Remc=  400.  This body of evidence spurred  The  experimental measurements, which were conducted 
continuing efforts to understand this phenomena from a  in the actual non-parallel flow, ultimately showed that the 
theoretical point of view. Significant progress was finally  attempt to "model" the boundary layer as a parallel flow 
achieved by Saric and Nayfeh [12,13] who included all  was  too restrictive. This fact was not immediately obvious 
of the non-parallel flow terms in the governing equations  for  two reasons.  First, the measurements departed from 
and  then solved the equations using the method of multiple  parallel-flow predictions in a region in which the mea
scales.  Their analytic results with the non-parallel terms  surements were difficult to acquire. There was therefore a 
included and neglected are compared to the experimen lack of confidence in the early measurements which only 
tal results from five independent investigations  in Figure  disappeared when the measurements were verified during 
3.  When all non-parallel effects are included, the calcu follow-on independent investigations.  Second, the early 
lated minimum critical Reynolds number is 400.  From  parallel-flow  computational  results  were misleading be
this comparison it is evident that the parallel-flow model,  cause they agreed closely  with one another, which was 
adopted almost forty years earlier in order to make the an- taken as a confirmation of the parallel-flow theory, when