Panel Methods in Fluid Mechanics with Emphasis on Aerodynamics: Proceedings of the Third GAMM-Seminar Kiel, January 16 to 18, 1987

271 Pages·1988·9.64 MB·German

by  H. W. M. Hoeijmakers (auth.)

Notes on Numerical Fluid Mechanics
Josef Ballmann · Richard Eppler
Wolfgang Hackbusch H rsg.
Panel Methods in
Fluid Mechanics
with Emphasis on
Aerodynamics
Proceedings of the Third GAMM-
Seminar Kiel, January 16 to 18, 1987
Josef Ballmann
Richard Eppler
Wolfgang Hackbusch (Eds.)
Panel Methods
in Fluid Mechanics
with Emphasis
on Aerodynamics
Notes on Numerical Fluid Mechanics
Volume 21
Series Editors: Ernst Heinrich Hirschel, MUnchen
Keith William Morton, Oxford
Earll M. Murman, M.I.T., Cambridge
Maurizio Pandolfi, Torino
Arthur Rizzi, Stockholm
Bernard Roux, Marseille
(Addressesofthe Editors:seelast page)
Volume 1 BoundaryAlgorithmsforMultidimensional Inviscid Hyperbolic Flows
(K.Fòrster.Ed.)
Volume 2 Proceedings ofthe Third GAMM·Conferenceon Numerical Methodsin Fluid
Mechanics (E.H.Hirschel,Ed.) (outofprint]
Volume3 Numerical MethodsfortheComputationof Inviscid Transonic FlowswithShock
Waves(A.Rizzi/H.Viviand, Eds.)
Volume4 ShearFlowinSurface-OrientedCoordinates (E.H.Hirschel/W.Kordulla)
Volume5 Proceedingsofthe Fourth GAMM-Conferenceon Numerical Methodsin Fluid
Mechanics (H.Viviand, Ed.) (outofprint)
Volume6 Numerical Methods in Laminar FlamePropagation (N.Peters/J.Warnatz. Eds.l
Volume7 ProceedingsoftheFifth GAMM-Conferenceon Numerical Methods in Fluid
Mechanics (M.Pandolfi/R.Piva.Eds.)
Volume8 VectorizationofComputerProgramswith Applications toCornputational Fluid
Oynamics(W.Gentzsch)
Volume9 Analysisof Laminar FlowoveraBackward Facing Step (Ken Morgan/J.Periaux/
F.Thomasset,Eds.]
Volume 10 EfficientSolutions ofEllipticSystems (W.Hackbusch, Ed.)
Volume 11 Advancesin Multi·Grid Methods(D.Braess/W.Hackbusch/U.Trottenberg.Eds.)
Volume 12 TheEfficient UseofVectorComputerswith Emphasison Cornputational Fluid
Oynamics (W.Schiinauer/W.Gentzsch, Eds.)
Volume 13 Proceedingsofthe Sixth GAMM-Conference on Numerical Methodsin Fluid
Mechanics (O.Rues/W.Kordulla.Eds.] (outofprimI
Volume 14 FiniteApproximationsin Fluid Mechanics (E.H.Hirschel, Ed.]
Volume 15 Oirectand Large EddySimulation ofTurbulence (U.Schumann/R.Friedrich, Eds.)
Volume16 Numerica! Techniques in Continuum Mechanics (W.Hackbusch/K.Witsch, Eds.)
Volume 17 Research in Numerical Fluid Dynamics (P.Wesseling.Ed.)
Volume 18 Numerical Simulation ofCompressible Navier·StokesFlows 1M.O.Bristeau/
R.Glowinski/J.Periaux/H.Viviand, Eds.)
Volume 19 Three-OimensionalTurbulent Boundary Layers- Calculationsand Experiments
(B.vanden Berg/O.A.Humphreys/E.Krause/J.P.F.Lindhoutl
Volume20 Proceedingsofthe Seventh GAMM-Conferenceon Numerica! Methodsin Fluid
Mechanics (M.Deville, Ed.)(in preparationl
Volume 21 Panel Methods in Fluid Mechanicswith Emphasison Aerodynamics (J.Ballmann/
R.Eppler/W.Hackbusch,Eds.l
Josef Ballmann . Richard Eppler
Wolfgang Hackbusch (Eds.)
Panel Methods
in Fluid Mechanics
with Emphasis
on Aerodynamics
Proceedings of the Third GAMM-Seminar
Kiel, January 16 to 18,1987
Springer Fachmedien Wiesbaden
CIP-Titelaufnahmeder Deutschen Bibliothek
Panel methodsinfluid mechanicswithemphasis
onaerodynamics: Kiel, January 16- 18,1987/
Josef Ballmann ...(ed.l. - Braunschweig;
Wiesbaden:Vieweg,1988
(Proceedingsof the ...GAMM seminar;3)
(Noteson numericalfluid mechanics;Vol. 21)
NE: Ballmann,Josef[Hrsg.J;Gesellschaftfür
Angewandte Mathematik und Mechanik:
Proceedingsof the ...;2.GT
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ISSN 0179-9614
ISBN978-3-528-08095-2 ISBN978-3-663-13997-3 (eBook)
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Foreword
The GAMM Committee l'orEfficient Numerìcal l\1ethods l'or Partial Differential
Equations (GAMM FachausschuB"Effiziente Numerische Verf'ahren fìir Partielle
Differentialgleichungen") organizes conferences and serninars on subjects
concerning the algorithmic treatment of partial differential equation problerns.
The two flrst sernìnars "Efficient Solution of Elliptic Systems" 098S) and
"Efficient Numerical Methods in Continuum Mechanìcs" (986) were followed
by a third one, co-organized together with the GAMM Committee l'or Dlscre
tizing Methods in Solid Mechanics and the special research project SFB 2S
"Vortex Flows in Aeronaut.ìcs" at the R\VTH Aachen, sponsor-ed by the
Deutsche Forschungsgemeinschaft CDFGl.
During the lastdecades PaneI Methods and Boundary Element Methods became
a very efficient tool to selve numerìcally the integrai equations with surface
or boundary singularity distributions in Aerodynamics and in Continuum
Mechanics. First designed l'or elliptic problems with linear partial dìfferent.ial
equations, the different variants of the methods now apply to nonlinearities
introduced by free vortex sheets or compressible flows and to time-dependent
problems as wave propagation and non-stationary Flows.
The seminar was attended by 47 scientists l'rom IO countrles. A greater part
of the 22 papers presented at the seminar concerned the different approaches
l'orst.atlonaryand non-stationary subsonic potential flows around aerodynamic
configurations and propellers, inc1uding inverse methods l'or design problems.
Othercontributions dealt with hybrid mcthods l'or subsonic f'lows with ernbcd
ded supersonic regions and weak shocks, panel methods l'or linearized super-:
sonic flows and boundary element methods l'or th:-ee-dimensional viscous
flows. l'or flows through porous media and transìent loading by pressure
waves.
An ìncrease of the efficiency and accuracy of panel methods was achieved,e.g.
by multi-grid methods with panel-c1ustering. by new error estimates in
solving the integrai equations and by realizing the applicability of the
Fredholrn-Radon method l'or dornains with corners.
The editors and organizers of the seminar would like to thank the land
Schleswig-Holstein and the DFG far their support.
Decernber 1987
J. Ballmann
R. Eppler
W. Hackbusch
c o
N T E N T S
Page
H.W.M.HOEIJMAKERS: Panel Methods in Aerodynamies; Some
Highlights .
H.ANTES: Time Domain Boundary Element Solutions of Hyper-
bolie Equations for 2-D Transient Wave Propagation 35
E.BRUCH, S.GRILLI: Computation of the Transient Flow in
Zoned Anisotropie Porous Media by the Boundary Eiement
Method . 43
L.FORNASIER: HISSS - a Higher-Order Panel Method for
Subsonie and Supersonie Attaehed Flow About Arbitrary
Configurations . 52
F.K.HEBEKER: Charaeteristies and Boundary Elements for
Threedimensionai Nonstationary Navier Stokes Flow 71
J.L.HESS, W.O.VALAREZO: Applieation of an Advaneed Panei
Method to Aerodynamie Problems of Aireraft Design 79
H.JAKOB: The Predietion of Transonie Interferenee Flow
by Means of a Hybrid Method 91
O.A.KANDIL, H.HU: Integrai Equation Solution for Tran-
sonie and Subsonie Aerodynamies 101
E.KATZER: Steady and Unsteady Potential Fiows Around
Axisymmetrie Bodies and Ring Airfoiis 110
J.KRAL, W.WENDLAND: On the Applieability af the Fred
~olm-Radon Method in Potential Theory and the Panel Me-
thod . 120
K.KUBRyNSKI: A Subsonie Panel Method for Design of 3-Di
mensional Complex Configurations with Speeified Pressure
Distribution . 137
P.LOTSTEDT: Evaluation of a Higher Order Panel Program
for Subsonie Flow 147
B.MASKEW: Caleuiation of Flow Charaeteristies for Gene-
rai Configurations Using Panel Methods . 156
Z.P.NOWAK: Panel Ciustering Teehnique for Lifting Poten-
tiai Fiows in the Three Spaee Dimensions . 166
E.L.ORTIZ: Singuiarity Treatment in the Bidimensionai
Tau Method with an Applieation to Probiems Defined on L-
Shaped Domain~ . 179
J.RYAN, T.H.LE, Y.~10RCHOISNE: A Fourier Bour.dary Condi-
tion for PaneI, Met;lOd 188
Page
J.SARANEN: On the Effect af Numerical Quadratures in
Salving Baundary Integral Equations . . . . . . . . 196
H.SCHIPPERS: On the Evaluation af Aerodynamic Influence
Caefficients . . . . . . . . . . . . . . . 210
J.SCHONE: A Daublet Paint Methad far the Calculatian af
Unsteady Propeller Aeradynamics 220
R.VOSS: Calculation af Unsteady Transanic Flow About Os-
cillating Wings by a Field Panel Methad 232
S.WAGNER, CH.URBAN, R.BEHR: A Vortex-Lattice Method for
the Calculation af Wing-Vortex Interaction in Subsanic
Flow . . . . . . . . . . . . . . . . . . . . . . . . .. 243
P.WIEMER, K.HAAG, J.BALLMANN: Appraximatian of Free and
Baunded Vortex Sheets at Delta Wings . . . . . . . . .. 252
List af Participants . . . . . . . . . . . . . . . . . . 261
PANEL METHODS IN AERODYNAMICS;
SOME HIGHLIGHTS
H.W.M. Hoeijmakers
National Aerospace Laboratory NLR
Anthony Fokkerweg 2, 1059 CM Amsterdam, The Netherlands
SUMMARY
A survey is presented of several aspects of the use and further devel
opment of panel methods in aerodynamics. Aspects discussed include possible
types of boundary conditions, low versus higher-order formulations, simula
tion of subsonic and supersonic flow and modeling of wakes as well as of
leading-edge vortex separation. Aiso discussed are computational aspects of
panel methods and possible directions for new developments. The latter in
clude the extension of the domain of applicability to compressible flow and
the coupling with viscous flow methods, as well as ways to improve the effi
ciency of the panel method.
INTRODUCTION
The computation of the aerodynamic characteristics of aircraft config
urations has been carried out by panel methods since the mid 1960's,
following the pioneering work of Hess &Smith [1) and Rubbert &Saaris [2).
But even before the availability of large-scale digitaI computers work was
done on surface singularity methods, notably in Germany by Prager [3 J and
Martensen [4J. Panel methods are presently the only computational aero
dynamic tools that have been developed to an extent that they are routinely
used in the aerospace industry for the analysis of the subsonic and super
sonic flow about real-life, complex aircraft configurations. Panel methods
have also been us~d for the analysis of the flow about propellers, auto
mobiles, submarines, shiphulls, sails, etc. Panel methods have been used so
heavily because of their ability to provide for complex configurations lin
ear potential flow solutions of engineering accuracy at reasonable expense.
The latter applies to the computer resources required for running the com
puter code as well as to the manhour cost involved in preparing the input.
The relatively easy input requirement of panel methods, very important
from a user's point of view, is directly related to the circumstance that a
discretization is required for the surface.of the 3D configuration only.
This ·is considered to be an order of magnitude simpler than the volume dis
cretization of the space around the configuration generally needed for
finite-difference and finite-element methods.
It may be noted that in aircraft development projects the application
of panel methods is gradually shifting from the final design phase towards
the preliminary design phase, primarily due to:
- the increase in computer power, decrease of its costs and improvement of
turn-around times,
- modern data handling techniques,
- availability of graphic displays for visualizing geometry and flow solu-
tion.
Several panel methods, e.g. Ref. [5], [6), [7), have been developed
and are in use in the aerospace industry that are variations on the ap
proach described in Refs. [1) and [2). Other investigators extended the
panel method to linearized supersonic flow, e.g. Refs. [8], [9]. Because
most of these "first-generation" panel methods do have some restrictions
concerning their geometrie and aerodynamic modeling capabilities and re
quire improvement of their computational efficiency several efforts have
been undertaken to develop a "second-generation" panel method, e.g. Refs.
[10]-[18].
M>Mcrit
ONSET BOUNOARY-LAYER
SEPARATION
FLlGHTENVELOPE
CRUISE
MACH NUMBER
SUBSONICTRANSPORT
CONFIGURATION
Fig. l Domain of applicability of panel method (adapted from [27])
The major drawback of the present panel methods is that their range of
applicability is restricted to linear potential flow, i.e. nonlinear com
pressibility effects are not accounted for and the important case of local
regions of supercritical flow and shock waves cannot be treated. The latter
occur in the high speed region in a large portion of the flow field and
possibly at low speeds (at the larger incidences used in start and landing)
in smaller portions of the flow field. To account for such regions of
supercritical flow would require the use of a transonic finite-difference
code on a spatial grid covering the entire space around the configuration.
However, up to the present time the spatial grid generation problem has not
been solved satisfactorily for complex configurations as configurations
with extended slats and flaps. In addition, the computer resources required
for present-day finite difference codes are quite substantial.
A second drawback of current panel methods is that the computational
effort, and cost, is proportional to N2, or even N3, where N is the number
of panels. This implies that the method becomes rapidly impractical for N
of the order of 2000-5000, panel numbers required for the resolution re
quired for the coupling with boundary-layer methods. It is also an exper
ience of the practise of applying panel methods that this number of panels
is often quite easily "consumed", so that compromises have to be sought
regarding resolution and accuracy.
In the present lecture an overview is given of several aspects related
to the formulation and use of panel methods and the possibilities for ex
tending the domain of applicability and improving the computational effi
ciency. The discussion deals primarily with methods for the steady flow
about three-dimensional configurations. It is based on the literature on
the subject and on past and current NLR research. The latter is aimed at
the development of a higher-order panel method (AEROPAN) and of a panel
method (PDAERO) to be used in preliminary design studies.
2