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u
July 1881
NASA Techniol Memorandum 81309
(NASA-TH-813011) NOdEBICAL INVESTIGATION OF
N81
-30385
T08BOLBNT CHANNEL FLCW (NASA) 73 p
HC 104
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Numerical Investigation of
Turbulent Channel Flow
Parviz Moin and John Kim
MASA
National Aeronautics and
Space Administration
NASA Technical Memorandum 81309
r
Numerical Investigation of
Turbulent Channel Flow
Parviz Moin
John Kum, Stanford University, Stanford, Califo
►
nia and
Ames Research Center, Moffett Field. California
1^_-.
PJASA
Ames Research Center
K
11 MICAL IRIIBSTA"TIN OF 1URSULBMT CU ML FUN
Parvia Moir*and John M*
Department of Mechanical
ineerUS
Stanford University, Stanford
$
CA 94305
Fully developed turbulent channel flow has been simulated americally at
. Reynolds number 19800, based on centerline velocity and channel half width.
The large-scale flow field has been obtained by directly integrating the fil-
tered, three-dimensional, tine-dependent, Davies-Stokes equations. The small-
scale field motions were simulated through an eddy viscosity model. The
calculations were carried out on the ILLIAC IV computer with up to 516,096
grid points.
The computed flow field was used to study the statistical properties of
the flow as
well as
its
time-dependent
features.
The agreement of
the
computed mean velocity
profile,
turbulence
statistics,
and detailed
flow
structures with experimental data is good.
The resolvable portion of
the
statistical
correlations
appearing
in
the
Reynolds
stress
equations
are
calculated.
Particular attention is given
to the examination of the
flow
structure in
the vicinity of the wall.
I. I
ntroduction
Large-eddy simulation (LBS) is a relatively new approach to the calcula-
tion of turbulent flows. The basic idea stems from two experimental observa-
tions. First, the large-scale structure of turbulent flows varies greatly
from flow to flow (e.g., jets vs. boundary layers) and consequently is diffi-
cult, if not impossible, to model in a general way. Second, the small-scale
turbulence structures are nearly isotropic, very universal in character
(Chapman, 1979) and hence such sore amenable to general modeling. In LBS,
one actually calculates the large-scale notions in a time-dependent, three-
*Portions of this work were carried out while the authors held NRC
.';
Research Associateships at Ames Research Center.
A
^
dimensional computation, using for the large-scale field dynamical equations
that incorporate simple models for small-scale turbulence. Only the part of
the turbulence field with scales that are small relative to overall dimensions
of the flow field is modeled. This is in contrast to phenomenological turbu-
lence modeling, in which all the deviations from the mean velocity profile are
•
r
modeled.
A typical LES calculation for wall-bounded turbulent flows imposes a
great demand on computer speed and memory. At present, therefore, the use of
LES for practical engineering applications is admittedly uneconomical. How-
ever, for simple flows, such calculations are just within reach of the largest
present computers. The information generated by these computations can in
turn be used as a powerful research tool In studies of the structure and
dynamics of turbulence. In addition, the various correlations that can be
obtained from the computed large-scale flow field may be used iv developing
phenomenological turbulence models for complex flows. These are the consid-
erations that motivate the present development of the LES method.
The first application of LES was made by Deardorff (1510), whu simulated
a turbulent channel flow at an indefinitely large Reynolds number. In this
pioneering work he showed that three
-
dimensional computation of turbulence (at
least for simple flows) is feasible. Using only 6
,
720 grid points, he was
able to predict several features of turbulent channel flow with a fair amount
of success. Of particular significance was the demonstration of the potential
of LES for use in basic studies of turbulence.
Following Deardorff
'
s work, Schumann
(
1973, 1975) also calculated turbu-
lent channel flow and extended the method to cylindrical geometries
(
annuli).
He used up to ten times more grid points (65,536) than Deardorff and an
improved subgrid scale (SGS) model. In addition to dividing SGS stresses into
2