Table Of ContentTurbulent Shear Flows 3
Selected Papers from the Third International
Symposium on Turbulent Shear Flows,
The University of California, Davis, September 9-11, 1981
Editors:
L. 1. S. Bradbury E Durst B. E. Launder
E W Schmidt 1. H. Whitelaw
With 244 Figures
Springer-Verlag Berlin Heidelberg New York 1982
Leslie 1. S. Bradbury
Department of Mechanical Engineering, University of Surrey,
Guildford, Surrey GU2 5XH, England
Franz Durst
Sonderforschungsbereich 80 der Universitiit Karlsruhe, KaiserstraBe 12,
D-7500 Karlsruhe 1, Fed. Rep. of Germany
Brian E. Launder
Department of Mechanical Engineering, University of Manchester,
Institute of Science and Technology, PO Box 88,
Manchester M60 1QD, England
Frank W. Schmidt
Mechnical Engineering Department, The Pennsylvania State University,
University Park, PA 16802, USA
James H. Whitelaw
Department of Mechanical Engineering, Imperial College of Science and
Technology, Exhibition Road, London SW7 2BX, England
ISBN-13 :978-3-642-95412-2 e-ISBN-13 :978-3-642-9541 0-8
DOl: 10.1007/978-3-642-95410-8
Library of Congress Cataloging in Publication Data. International Symposium on Turbulent Shear Flows
(3rd: 1981: University of California, Davis). Turbulent shear flows 3. Bibliography: p. Includes index.
1. Shear flow -Congresses. 2. Turbulence-Congresses. I. Bradbury, L. J. S. (Leslie John Stanley), 1936-.
II. Title TA357.I59 1981 620.1'064 82-16916
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Preface
In spite of intensive efforts over many decades, the problem of turbulence remains as
challenging as ever and the number of papers, books and conferences on this topic con
tinues to grow. As experimental techniques and computing power have developed, the
breadth of investigations into the structure and development of turbulent flows has in
creased to encompass many diverse fields of application in engineering, physics, biolo
gy and so on. As a consequence, it is now very difficult for a single research worker to
keep in touch with the many developments that are taking place in turbulence. One of
the few opportunities for obtaining some overall view of the subject arises from large
international symposia on turbulence and, although they have some drawbacks, it is
this opportunity that is one of their main merits.
The International Symposium on Turbulent Shear Flows has now been held on
three occasions and they seem to be established as a major opportunity for papers on a
very diverse range of topics to be presented at a single meeting. This volume is a collec
tion of papers from the third symposium that was held at the University of California,
Davis from 9-11 September 1981. The papers are divided into four sections entitled
Wall Flows, Scalar Transport, Recirculating Flows and Fundamentals. This collection
represents about a third of the total number of papers presented. Inevitably, there is
some uneveness in the coverage of various sections but, nevertheless, the selection is
reasonably representative of the range of papers presented. As with previous volumes,
each section is preceded by a brief introductory article whose purpose is to make some
general observations about the various sections and to fit the individual papers into the
context of the general topic.
As with the earlier symposia, we would like to acknowledge the financial support
of the Research Offices of the United States Army, Navy, and Air Force and the Na
tional Science Foundation. We would also like to thank the many individuals at the
University of California, Davis who helped with both organising and running the con
ference and express again our appreciation to the Fluids Engineering and Heat Transfer
Divisions of the American Society of Mechanical Engineers for their assistance with
publicity.
The task of reviewing and selecting papers was carried out by a papers committee
and an advisory committee many of whose members later performed sterling work as
chairmen of technical sessions at the conference and who also have been a valuable
source of helpful criticism. Their work has been greatly appreciated. The committees
consisted of:
RJ. Adrian, University of Urbana, Urbana, L.H. Back, Jet Propulsion Lab., Pasadena,
USA Calif., USA
J.C. Andre, EERN/GMD, 92100 Boulogne, H.A. Becker, Queen's University
France Kingston, Ont., Canada
v
R. Borghi, O.N.E.R.A., France P.N. Joubert, University of Melbourne,
S. Corrsin, The John Hopkins University, Melbourne, Australia
Baltimore, Md., USA J. Laufer, University of Southern
J.J. Domingos, University of Lisbon, California, Calif., USA
Lisbon, Portugal A. Libby, University of California, San
C. du Pont Donaldson, ARAP, Princeton, Diego, Calif., USA
N.J., USA J.L. Lumley, Cornell University, Ithaca,
R. Dumas, Institut de Mecanique Statisti N.Y., USA
que de la Turbulence, Marseilles, O. Martynenko, Heat and Mass Transfer
France Institute, Minsk, USSR
H. Fiedler, Technische UniversWit Berlin, J. Mathieu, Ecole Centrale de Lyon,
Berlin, Fed. Rep. of Germany Ecully, France
I.S. Gartshore, University of British H. McDonald, Scientific Research Asso
Columbia, Canada ciates Inc., Glastonbury, Conn., USA
V.W. Goldschmidt, Purdue University, W. Y. Mori, Tokyo Institute of Technology,
Lafayette, Ind., USA Tokyo, Japan
A.D. Gosman, Imperial College, London, K. Owen, Owen International, Palo Alto,
U.K. Calif., USA
R. GUnther, Universitat Karlsruhe, Karls W.C. Reynolds, Stanford University,
ruhe, Fed. Rep. of Germany Stanford, Calif., USA
K. Hanjalic, Masinski Fakultet, Sarajevo, W. Rodi, Universitat Karlsruhe, Karlsruhe,
Yugoslavia Fed. Rep. of Germany
T.J. Hanratty, University of Illinois, M.W. Rubesin, NASA Ames Research
Urbana-Champaign, 111., USA Center, Calif., USA
RJ. Herring, NCAR, Boulder, Colo., USA A.K. Runchal, Dames & Moore, Los
A.K.M.F. Hussain, University of Houston, Angeles, Calif., USA
Texas, USA I. Wygnanski, Tel-Aviv, Israel
W.P. Jones, Imperial College London, U.K. J.e. Wyngaard, CIRES, Boulder, Colo.,
USA
Finally, it is a pleasure to record our thanks to the authors for meeting the various
deadlines we set and to Springer Verlag for their help in producing this third vol
ume in the series.
Karlsruhe, June 1982 The Editors
VI
Contents
Part I Wall Flows
Introductory Remarks. By H. Eckelmann 3
Measurements of the Periodic Velocity Oscillations Near the Wall in Unsteady
Turbulent Channel Flow. By G. Binder and J.L. Kueny (With 9 Figures) . . . . . 6
A Dynamical and Visual Study on the Oscillatory Turbulent Boundary Layer
By T. Hayashi and M. Ohashi (With 19 Figures) . . . . . . . . . . . . . . . . . . . . . . .. 18
Dynamics of an Unsteady Turbulent Boundary Layer. By P.G. Parikh,
R. Jayaraman, and W.C. Reynolds (With 14 Figures) . . . . . . . . . . . . . . . . . . .. 34
Influence of Strouhal Number on the Structure of Flat Plate Turbulent Boundary
Layer. By J. Cousteix, J. Javelle, and R. Houdeville (With 10 Figures) ..... '. 46
A Theoretical Model of the Coherent Structure of the Turbulent Boundary
Layer in Zero Pressure Gradient
By Z. Zhang and G.M.Lilley (With 8 Figures) ........................ " 60
The Mechanism of Turbulent Mass Transfer at a Boundary
By J.A. Campbell and T.J. Hanratty (With 6 Figures) ................... 73
Measurements in the Heated Turbulent Boundary Layer on a Mildly Curved
Convex Surface. By M.M. Gibson, C.A. Verriopoulos, and Y. Nagano
(With 9 Figures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80
Part II Scalar Transport
Introductory Remarks. By. K.N.C. Bray 93
A Test of Gradient Transport and Its Generalizations
By K.R. Sreenivasan, S. Tavoularis, and S. Corrsin (With 13 Figures) ...... " 96
Calculations of Velocity-Scalar Joint pdf's. By S.B. Pope (With 8 Figures) 113
Aerosol Formation in a Mixing Layer
By S.V. Sherikar and R. Chevray (With 6 Figures) . . . . . . . . . . . . . . . . . . . . .. 124
The Role of Coherent Structures in the Development of a Uniformly Strained
Turbulent Wake. By J.G. Kawall and J.F. Keffer (With 18 Figures) ........ ' 132
Investigations on a Reaction Model for Turbulent Diffusion Flames
By H. Eickhoff and K. Grethe (With 8 Figures) ........................ 146
VII
Part III Recirculating Flows
Introductory Remarks. By I.P. Castro 157
Low Frequency Unsteadiness of a Reattaching Turbulent Shear Layer
By J.K. Eaton and J.P. Johnston (With 6 Figures) ...................... 162
Turbulent Shear Flow Behind Hemisphere-Cylinder Placed on Ground Plane
By S. Okamoto (With 35 Figures) .................................. 171
Experimental Investigations in Transonic Highly Separated, Turbulent Flow
By A. Fracy, V. Mercier, and R. Leblanc (With 9 Figures) ............... 186
Turbulent Flow Induced by a Jet in a Cavity-Measurements and 3D Numerical
Simulation. By F. Baron, J.P. Benque, and Y. Coeffe (With 6 Figures) ...... 195
The Assessment of Numerical Diffusion in Upwind Difference Calculations
of Turbulent Recirculating Flows
By J.1. McGuirk, A.M.K.P. Taylor, and J.H. Whitelaw (With 9 Figures) ...... 206
Turbulent and Mean Flow Measurements in an Incompressible Axisymmetric
Boundary Layer with Incipient Separation
By P. Dengel, H.H. Fernholz, and J.-D. Vagt (With 13 Figures) ............ 225
Part IV Fundamentals
Introductory Remarks. By J. Lumley 239
Pressure Effects on Triple Correlations in Turbulent Convective Flows
By J .-C. Andre, P. Lacamlre, and K. Traore (With 4 Figures) .............. 243
A Model of Three-Dimensional Transfer in Non-Isotropic Homogeneous
Turbulence. By J.-P. Bertoglio (With 11 Figures) ....................... 253
A Theoretical Study of Radiative Cooling in Homogeneous and Isotropic
Turbulence. By D. Schertzer and O. Simonin (With 6 Figures) ............. 262
Second Order Closure for Variable Density Free Shear Layer
By D. Vandromme and W. Kollmann (With 6 Figures) .................. 275
The Turbulence Modelling of Variable Density Flows - A Mixed-Weighted Decom
position. By H. Ha Minh, B.E. Launder, and J. MacInnes (With 4 Figures) .... 291
Direct Simulation of Homogeneous Turbulent Shear Flows on the Illiac IV
Computer: Applications to Compressible and Incompressible Modelling
By W.1. Feiereisen, E. Shirani, J.H. Ferziger, and W.e. Reynolds
(With 7 Figures) ............................................... 309
Index o/Contributors .............................................. 321
VIII
Part I
Wall Flows
Introductory Remarks
Helmut Eckelmann
Max-Planck-Institut fijr Stromungsforschung, BottingerstraBe 4-8
D-3400 Gottingen, Fed. Rep. of Germany
Wall flows, which mean in this context wall bounded turbulent flows, can generally be
classified into two main groups; external flows which arise around bodies (boundary
layers) and internal flows which arise through a space confined by walls (pipes and chan
nels). Although both groups exhibit a difference - the boundary layer thickness increases
in streamwise direction whereas in pipes and channels the flow remains restricted to the
space confined by the walls - both flows show a common behaviour in the vicinity of the
wall. They both have a viscous sublayer, a buffer layer and for both the law of the wall
is valid in the inner region. The key for the understanding of wall bounded turbulent
flow should therefore be searched in the region close to the wall. The viscous sublayer
is very thin and experimentally not accessible in most of the flows. The buffer layer,
which is in most practical cases thick enough for experimental investigations, is in the
opinion of the writer, the region which one should look at.
This chapter contains a selection of papers on wall flows which were presented at the
3rd Symposium on Turbulent Shear Flows held at the University of California at Davis.
The major parts of the papers describe experimental work and one of them deals with a
theoretical model of the turbulent boundary layer and calculations on this model which
lead to longitudinal vortices occuring in the buffer laver. Such vortices were first observed
experimental by Bakewell and Lumley (1967). One of the papers is both numerical and
experimental and deals with calculations and experimental investigations obtained in a
pipe flow.
The first four papers in this chapter deal with unsteady wall bounded turbulent flows,
a subject which is very important for many engineering applications. Recently Carr
(1981a) reviewed this flow type. The many laminar, transitional and turbulent unsteady
flow experiments that have been performed are fully referenced in a AGARDograph by
Carr (1981 b).
In a turbulent channel flow with forced velocity oscillations of small amplitude Bin
der and Kueny made measurements over a wide range of frequencies. They found that
both mean flow and mean turbulent intensity are not affected by the forced oscillations.
The phase averaged stream wise turbulent intensity is not simply proportional to the am
plitude of the velocity oscillations but depends on the wall distance and the oscillation
frequency. The ratio of Stokes thicknessy211/w (where W = 2rrf) to viscous length II/ur
(II being the kinematic viscosity of the fluid and ur the friction velocity) becomes an
important parameter for this problem.
In a large oscillating water tunnel which is in principle a water filled U-tube Hayashi
and Ohashi investigated the unsteady turbulent boundary layer with a hot-film probe and
by a flow visualization technique that uses a thin milk layer on the wall. The hot film mea
surements yielded that the velocity phase leads that of the wave amplitude by about ISo;
3
in addition, both Reynolds stress and turbulent energy were found to be larger in the de
celeration than in the acceleration period of the free stream period. The visual studies
showed that the disturbances at the wall lag behind the free stream velocity maximum.
The response of a turbulent boundary layer to oscillations of the free stream velocity
was studied by Parikh, Jayaraman and Reynolds and by Cousteix, Javelle and Houdeville.
The first authors confirmed the results of Binder and Kueny that both mean velocity and
mean turbulence intensity were unaffected by the imposed oscillations. In addition they
found that the boundary layer thickness and Reynolds stress distribution across the
boundary layer becomes frozen over the oscillation cycle at their mean values. The
frequencies in this experiment ranged from zero to approximately the bursting frequency
fB which corresponds due to measurements of Rao et al. (1971) to a Strouhal number
fB6jU"" of about 0.2. Cousteix et al. also found that the mean flow field was not affected
by the unsteady effects. They interpreted this by assuming that the boundary layer
responds to the perturbations induced by the pulsation of the external flow as a mechani
cal system with a small damping.
Zhang and Lilley present a theoretical model of the coherent structure of the tur
bulent boundary layer with zero pressure gradient. They show that a self-generating
coherent structure arises in the calculation with their model. For a given initial disturbance
amplitude Zhang and Lilley obtained strong streamwise vortices occurring periodically with
opposite sign in the spanwise direction of the flow. The non-dimensional wave length of
a counter-rotating vortex pair was found to be of the order of 100 v/ur over a wide range
of Reynolds numbers, a result which is in good agreement with the experimental investiga
tions of Lee et al. (1974), Blackwelder and Eckelmann (1979) and KrepUn and Eckelmann
(1979) who all had evidence for counter-rotating streamwise vortices occuring frequently
in the wall region wall of bounded turbulent flow. The distance between two counter
rotating vortices was experimentally determined to be of the order of 50 v/ur. As early as
1959 Kline and Rundstadler speculated that the low speed streaks having a spacing of
about 100 v/ur are related to an organized vortical structure in the wall region.
The mechanism of turbulent mass transfer at a solid surface was investigated by
Campbell and Hanratty. From the mass balance equation the fluctuating concentration
field was calculated by using measured values of the fluctuating velocity field. They
found that at large Schmidt numbers the concentration boundary layer close to the
surface acts as a filter in such a way that only velocity fluctuations of much lower fre
quency than the most energetic velocity fluctuations are effective in transporting mass.
With increasing Schmidt number smaller and smaller fractions of turbulence energy are
effective in determining the magnitude of the mass transfer coefficient.
The third paper in this chapter by Gibson, Verri0poulos and Nagano is concerned
with the effects of longitudinal curvature on turbulent heat transfer, a problem which
had been given little attention in the past. More is known about effects of such curvature
on the turbulent boundary layer. The AGARDograph by Bradshaw (1973) fully reviewed
this subject up to that time. The paper of Gibson et al. reports measurements of mean
velocity, mean temperature and surface heat flux in a boundary layer growing on a
mildly curved convex plate for which the radius of curvature R is about 100 times the
boundary layer thickness 6. The main result of this investigation is that the curvature
depresses the surface heat flux more than it depresses the skin friction, i.e., with increasing
length Reynolds number the Stanton number falls more rapidly from flat plate values
than does the skin friction coefficient.
4
