Numerical and Physical Aspects of Aerodynamic Flows III

486 Pages·1986·11.95 MB·English

by  Tuncer Cebeci

Proceedings of a Symposium on
Numerical and
Physical Aspects of
Aerodynamic Flows III
Numerical and
Physical Aspects of
Aerodynamic Flows III
Edited by Tu ncer Cebeci
With 265 Illustrations
Springer-Verlag
New York Berlin Heidelberg Tokyo
Tuncer Cebeci
Douglas Aircraft Company
Long Beach, CA 90846
U.S.A.
and
California State University
Long Beach, CA 90840
U.S.A.
Library of Congress Cataloging in Publication Data
Symposium on Numerical and Physical Aspects of
Aerodynamic Flows (3rd: 1985: California State
University at Long Beach)
Numerical and physical aspects of aerodynamic
flows III.
"Proceedings of a Symposium on Numerical and
Physical Aspects of Aerodynamic Flows III" - Half t. p.
Symposium held at the California State University at
Long Beach from 21 to 24 January 1985.
Bibliography: p.
I. Aerodynamics-Congresses. I. Cebeci, Tuncer.
II. Title. II. Title: Proceedings of a Symposium on
Numerical and Physical Aspects of Aerodynamic Flows III.
TL570.S94 1985 629.132'3 86-1757
© 1986 by Springer-Verlag New York Inc.
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ISBN-13: 978-1-4612-9362-0 e-TSBN-13: 978-1-4612-4926-9
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Preface
The Third Symposium on Numerical and Physical Aspects of Aerodynamic
Flows, like its immediate predecessor, was organized with emphasis on the
calculation of flows relevant to aircraft, ships, and missiles. Fifty-five papers
and 20 brief communications were presented at the Symposium, which was
held at the California State University at Long Beach from 21 to 24 January
1985. A panel discussion was chaired by A. M. O. Smith and includeq state
ments by T. T. Huang, C. E. lobe, l. Nielsen, and C. K. Forester on priorities
for future research. The first lecture in memory of Professor Keith Stewartson
was delivered by J. T. Stuart and is reproduced in this volume together with
a selection of the papers presented at the Symposium.
In Volume II of this series, papers were selected so as to provide a clear
indication of the range of procedures available to represent two-dimensional
flows, their physical foundation, and their predictive ability. In this volume,
the emphasis is on three-dimensional flows with a section of five papers
concerned with unsteady flows and a section of seven papers on three
dimensional flows: The papers deal mainly with calculation methods and
encompass subsonic and transonic, attached and separated flows. The selec
tion has been made so as to fulfill the same purpose for three-dimensional
flows as did Volume II for two-dimensional flows. A section of nine papers
is included to supplement the information of Volume II by describing recent
developments, and especially those concerned with procedures which involve
interaction of solutions to inviscid-flow and boundary-layer equations. It is
likely that these interactive procedures will be increasingly applied to flows
involving thick boundary layers and separated flow, and it is appropriate that
v
VI Preface
they are considered here, especially since they will soon be developed for
application to three-dimensional flows. This section of two-dimensional flows
precedes those on three-dimensional flows and is itself preceded by a review
paper, prepared especially to put the content of the volume in the wider
context of current research into aerodynamic flows, and a section of those
papers dealing with stability and transition and including the Stewartson
Memorial lecture.
The papers are similar to those presented at the Symposium but have been
improved as a consequence of suggestions made by session chairmen, the
authors, and myself. In most cases, they have been shortened to meet the
requirements of the publisher and to improve the general conciseness of
presentation; in a few, additional material has been included. In all cases, the
authors completed the required modifications in good time and it is a pleasure
to acknowledge their help in producing the volume. Copies of the soft-bound
collection of all the papers presented at the Symposium, including those not
published here, can be obtained from Dr. Hillar Unt, Chairman of the
Mechanical Engineering Department of the California State University at
Long Beach.
The Symposium was made possible partly by financial support provided
to the California State University by NASA Ames Research Center, the U.S.
Army Research Office (ARO), the National Science Foundation (NSF),
the Office of Naval Research (ONR) , the Naval Sea Systems Command
(NAV SEA), and by the cooperation of authors, session chairmen, partici
pants, and colleagues at the University. Particular thanks are due to V. L.
Peterson of NASA Ames, R. E. Singleton of ARO, G. K. Lea of NSF, R. E.
Whitehead of ONR, L. Pasiuk of NAVSEA, and H. Unt of the University.
The content of the volume was decid~d after extensive discussions, especially
with J. H. Whitelaw. The editing process benefited considerably from the
efforts of Nancy Barela and Sue Schimke and it is a pleasure to acknowledge
their help.
Long Beach, California TUNCER CEBECI
August 1985
Contents
General Review
Calculation Methods for Aerodynamic Flows-A Review
T. Cebeci and J. H. Whitelaw .................................. .
PART 1. Stability and Transition
1. Stewartson Memorial Lecture: Hydrodynamic Stability and
Turbulent Transition
J. T. Stuart. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2. Transition Calculations in Three-Dimensional Flows
R. Michel, E. Coustols, and D. Arnal. . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3. Transitional Spot Formation Rate in Two-Dimensional Boundary
Layers
R. Narasimha and J. Dey. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
PART 2. Two-Dimensional Flows
4. The Computation of Viscid-Inv iscid Interaction on Airfoils with
Separated Flow
R. E. Melnik and J. W. Brook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5. Laminar Separation Studied as an Airfoil Problem
H. K. Cheng and C. J. Lee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Vll
Vlll Contents
6. A Quasi-simultaneous Finite Difference Approach for Strongly
Interacting Flow
D. E. Edwards and J. E. Carter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
7. Newton Solution of Coupled Euler and Boundary-Layer Equations
M. Drela, M. Giles, and W. T. Thompkins, Jr. . . . . . . . . . . . . . . . . . . . 143
8. Aerofoils at Low Reynolds Numbers-Prediction and Experiment
P. M. Render, J. L. Stollery, and B. R. Williams................. 155
9. Comparison ofInteractive and Navier-Stokes Calculations of
Separating Boundary-Layer Flows
D. Adair, B. E. Thompson, J. H. Whitelaw, and B. R. Williams..... 168
10. Significance of the Thin-Layer Navier-Stokes Approximation
F. G. Blottner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
11. A Comparison ofInteractive Boundary-Layer and Thin-Layer
Navier-Stokes Procedures
U. Mehta, K. C. Chang, and T. Cebeci ......................... 198
12. Development of a Navier-Stokes Analysis to Investigate the
Mechanism of Shock -Wa ve-Boundary-Layer Interactions
D. V. Roscoe, H. J. Gibeling, H. McDonald, and S. J. Shamroth. . . . 216
PART 3. Unsteady Flows
13. Unsteady Airfoil Boundary Layers-Experiment and Computation
P. F. Lorber and E. E. Covert. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
14. A Viscous-Inviscid Interaction Method for Computing Unsteady
Transonic Separation
J. C. Le Balleur and P. Girodroux-Lavigne. . . . . . . . . . . . . . . . . . . . . . 252
15. Computations of Separated Subsonic and Transonic Flow about
Airfoils in Unsteady Motion
R. Houwink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
16. Massive Separation and Dynamic Stall on a Cusped Trailing-Edge
Airfoil
A. P. Rothmayer and R. T. Davis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
17. Analysis of Two-Dimensional Incompressible Flow Past Airfoils
Using Unsteady Navier-Stokes Equations
K. N. Ghia, G. A. Osswald, and U. Ghia........................ 318
PART 4. Three-Dimensional Flows
18. Computation of Velocity and Pressure Variation Across
Axisymmetric Thick Turbulent Stern Flows
T. T. Huang and M.-S. Chang................................ 341
Contents ix
19. Inverse-Mode Solution of the Three-Dimensional Boundary-Layer
Equations about a Shiplike Hull
J. Piquet and M. Visonneau . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
20. Prediction of Dynamic Separation Characteristics Using a
Time-Stepping Viscid-Inviscid Approach
B. Maskew and F. A. Dvorak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
21. Computation of Turbulent Separated Flows over Wings
J. C. Wai,J. C. Baillie, and H. Yoshihara. . . . . . . . . . . . . . . . . . . . . . . 397
22. An Interactive Scheme for Three-Dimensional Transonic Flows
T. Cebeci, L. T. Chen, and K. C. Chang. . . . . . . . . . . . . . . . . . . . . . . . 412
23. x-Marching Methods to Solve the Navier-Stokes Equations in
Two-and Three-Dimensional Flows
J. Cousteix, X. de Saint-Victor, and R. Houdeville. . . . . . . . . . . . . . . . 432
24. Computation of Three-Dimensional Flows with Shock-Wave
Turbulent-Boundary-Layer Interaction
C. C. Horstman, M. I. Kussoy, and W. K. Lockman..... ......... 449
References 465
Calculation Methods for Aerodynamic
Flows-a Review*
Tuncer Cebecit and J. H. Whitelawt
1 Introductory Remarks
The present volume has been arranged so as to emphasize present abilities to
calculate flows involving three independent variables and, at the same time to
provide a background of the two-dimensional approaches upon which they
are based. In the earlier review by Cebeci, Stewartson, and Whitelaw [1], two
dimensional flows were considered in some detail, and the corresponding
volume included 22 papers which described related calculation methods and
their achievements. Thus, the following section makes clear the background of
advances which have been made since the Symposium of [1], and Sections 3
and 4 review the present status of unsteady three-dimensional methods. In
each section new results are reported where they help to clarify the abilities
of calculation methods.
The inclusion of three papers which address the subject of transition re
quires no justification. Considerable experimental effort has been expended
but has not, so far, allowed the development of a method for representing the
transition process in other than a very limited range of flows. This is especially
disappointing in that the extrapolation of wind-tunnel experience to flight
conditions frequently requires the ability to understand the role of transition
• This paper was prepared under the National Science Foundation Grant MEA-80l8565.
tDepartment of Mechanical Engineering, California State University, Long Beach, CA 90840.
!Department of Mechanical Engineering, Imperial College, London SW7 2BX.
2 Tuncer Cebeci and J. H. Whitelaw
and to represent it in design methods. The three papers include the Stewarts on
Memorial Lecture of J. T. Stuart, which provides a review of hydrodynamic
stability and its relationship to transition. The papers by Michel, Coustols,
and Arnal and by Narasimha and Dey are both concerned with modeling the
transition region which is necessary for low-Reynolds-number flows. The
importance of transition is demonstrated, by example, in the following three
sections, which show that it can severely limit the accuracy of predicted
results, especially for airfoil flows at high angles of attack.
Perhaps the main arguments underlying current research into calculation
methods, apart from the questions raised by the transition processes, concern
the relative merits of different forms of the Navier-Stokes equations and the
extent to which time-averaged equations can represent turbulent flows. In the
context of aerodynamic flow, the controversies are made more difficult by the
knowledge that lift forces are usually much more dependent upon the inviscid
regions offlow, and on the corresponding inviscid-flow equations, than on the
viscous regions which form boundary layers. Thus the correct solution of the
inviscid-flow equations is of primary importance and the solution of forms of
the boundary-layer equations with assumptions for Reynolds stresses is of
lesser importance to the determination of lift. In the calculation of drag,
however, the viscous-flow equations are essential and must be formulated and
solved so that overall drag can be determined, if possible, to an accuracy of
better than 1% . The boundary condition at the so-called edge of the boundary
layer can be determined from a solution of the inviscid-flow equations, but
interaction with the solution of the boundary-layer equations is required to
ensure that the mutual influence of the inviscid and viscous regions are
properly represented.
An alternative to interaction between solutions of in viscid and viscous-flow
equations is to solve the Navier-Stokes equations, and various forms have
been proposed. In general, these equations are averaged and represent convec
tive, diffusive, and pressure forces throughout a solution domain which
encompasses the body under consideration and all regions of the surrounding
flow which are considered to be influenced by the body. Two particularly
noteworthy forms are the two-dimensional, full Navier-Stokes equations and
their thin-shear-Iayer counterpart: the former comprises two momentum
equations each with a pressure gradient and two turbulent diffusion terms,
and the latter also comprises two momentum equations each with a pressure
gradient term but with one diffusion term. Both forms have been examined in
some detail, particularly at the NASA Ames Research Center, and are repre
sented in the papers of this volume. The basis of the thin-layer approach is
carefully considered in Blottner's paper of Part 2. It is evident that the higher
order equations do not provide a panacea, since they can be limited in
accuracy by numerical assumptions and the available storage and cost of
computer facilities. Indeed, present evidence suggests that the inaccuracies
associated with the use of boundary-layer equations may be less than those
associated with the numerical solution of higher-order forms, even where
large regions of flow separation are involved.