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NASA Contractor Report 187460
ICASE Report 90-76
ICASE
TOWARD THE LARGE-EDDY SIMULATION OF
COMPRESSIBLE TURBULENT FLOWS
(NASA-CR-187460) TOWARD THE LARGE-EO_Y
_[MIJLATTON OF CnMORESS[_LE TURBULENT FLOWS
Final Repork (ICASF) 46 p CSCL 20D
G. Erlebacher
M. Y. Hussaini
C. G. Speziale
T. A. Zang
N91-13050
Unclds
G3/34 03i_013
Contract No. NAS1-18605
October 1990
Institute for Computer Applications in Science and Engineering
NASA Langley Research Center
Hampton, Virginia 23665-5225
Operated by the Universities Space Research Association
National Aeronaulics and
Space Adminislralion
Langley Research Center
Hampton, Virginia 23665-5225
TOWARD THE LARGE-EDDY SIMULATION OF
COMPRESSIBLE TURBULENT FLOWST
G. Erlebacher $
ICASE, NASA Langley Research Center
M. Y. Hussaini t
ICASE, NASA Langley Research Center
C. G. Speziale$
ICASE, NASA Langley Research Center
T. A. Zang
NASA Langley Research Center
Hampton, VA 23665
ABSTRACT
New subgrid-scale models for the large-eddy simulation of compressible turbulent flows are
developed and tested based on the Favre-filtered equations of motion for an ideal gas. A
compressible generalization of the linear combination of the Smagorinsky model and scale-
similarity model, in terms of Favre-filtered fields, is obtained for the subgrid-scale stress ten-
sor. An analogous thermal linear combination model is also developed for the subgrid-scale
heat flux vector. The two dimensionless constants associated with these subgrid-scale models
are obtained by correlating with the results of direct numerical simulations of compressible
isotropic turbulence performed on a 963 grid using Fourier collocation methods. Extensive
comparisons between the direct and modeled subgrid-scale fields are provided in order to val-
idate the models. A large-eddy simulation of the decay of compressible isotropic turbulence
- conducted on a coarse 323 grid - is shown to yield results that are in excellent agreement
with the fine grid direct simulation. Future applications of these compressible subgrid-scale
models to the large-eddy simulation of more complex supersonic flows are discussed briefly.
tThis report supersedes ICASE Report No. 87-20
tThis research was supported by the National Aeronautics and Space Administration under NASA Con-
tract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in
Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23865.
1. Introduction
The direct numericalsimulationof turbulent flowsat the high Reynoldsnumbersencountered
in problemsof technologicalimportance is all but impossibleas a result of the wide range
of scalesthat are present. Consequently,the solutions to such problems must invariably
be based on some form of turbulence modeling. Traditional turbulence models based on
Reynolds averages have had only limited success since the large scales of the turbulence
- which contain most of the energy - are highly dependent on the geometry of the flow
being considered. Experience has indicated that such models usually break down when a
variety of turbulent flows are considered (Lumley 1983). The small scales are more universal
in character, and serve mainly as a source for dissipation. Hence, it can be argued that a
better understanding of turbulent flows could be achieved if just the small scales are modeled
while the large scales are calculated (Deardorff 1970). This is the fundamental idea behind
large-eddy simulations.
During the past decade, considerable progress has been made in the large-eddy simulation
of incompressible turbulent flows. This effort has shed new light on the physics of turbulence.
The earliest work relied heavily on the use of the Reynolds averaging assumption to elim-
inate the Leonard and cross stresses while the Reynolds stresses were computed using the
Smagorinsky model (Deardorff 1970, Leonard 1974, Reynolds 1976). More recent large-eddy
simulations have been based on the direct calculation of the Leonard stresses with models
provided for the cross and Reynolds subgrid-scale stresses in order to enhance the numerical
accuracy (see Biringen and Reynolds 1981, Bardlna Ferziger and Reynolds 1983). However,
among these newer models, only the Bardina, Ferziger and Reynolds (1983) model, with a
Bardina constant of 1.0, satisfies the important physical constraint of Galilean invariance
(Speziale 1985). The underlying physical concepts, fundamental numerical algorithms, and
comprehensive historical data behind the recent field of large-eddy simulation have been
presented in articles by Schumann (1975), Voke and Collins (1983) and Rogallo and Moin
(1984). More recently, work on the subgrid-scale modeling of transition to turbulence of ini-
tially laminar incompressible flows has begun (Piomelli, Zang, Speziale and Hussaini 1990).
Several large-eddy simulations have been performed and initial results are promising.
Despite the intensive research effort that has been devoted to the large-eddy simulation
of incompressible flows as outlined above, it appears that no large-eddy simulation of a
compressible turbulent flow has yet been attempted. Of course, such work could have im-
portant technological applications in the analysis of turbulent supersonic flows, where shock
waves are generated, and in turbulent flows within combustion chambers. The prerequisite
for carrying out such computations is the development of suitable subgrid-scale models for
compressible turbulent flows. With the exception of the recent work of Yoshizawa (1986)
and Speziale et al. (1988), few, if any, studies along these lines appear to have been pub-
lished. The subgrid-scale models of ¥oshizawa are only suitable for slightly compressible
turbulent flows since they made use of an asymptotic expansion about an incompressible
state. Recently however, Dahlburg, Zang and Dahlburg (1990) have performed an extensive