Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK̄/■̄) is the ratio of the turbulent to mean strain time scale. While low‐order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two‐equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

1.
K. G.
Wilson
, “
Renormalization group and critical phenomena
,”
Phys. Rev. B
4
,
3174
(
1971
).
2.
V.
Yakhot
and
S. A.
Orszag
, “
Renormalization group analysis of turbulence
,”
J. Sci. Comput.
1
,
3
(
1986
).
3.
J.
Smagorinsky
, “
General circulation experiments with the primitive equations
,”
Mon. Weather Rev.
91
,
99
(
1963
).
4.
K.
Hanjalic
and
B. E.
Launder
, “
A Reynolds stress model of turbulence and its application to thin shear flows
,”
J. Fluid Mech.
52
,
609
(
1972
).
5.
L. M. Smith and W. C. Reynolds, “Progress in understanding the renormalization group skewness and K-ε models,” Annual Research Briefs—1990 (Center for Turbulence Research, Stanford University, Stanford, CA, 1991), p. 51.
6.
L. M.
Smith
and
W. C.
Reynolds
, “
On the Yakhot-Orszag renormalization group method for deriving turbulence statistics and models
,”
Phys. Fluids A
4
,
364
(
1992
).
7.
V.
Yakhot
and
L. M.
Smith
, “
The renormalization group, the ε-expansion and derivation of turbulence models
,”
J. Sci. Comput.
7
,
35
(
1992
).
8.
C. G.
Speziale
,
T. B.
Gatski
, and
N.
Fitzmaurice
, “
An analysis of RNG based turbulence models for homogeneous shear flow
,”
Phys. Fluids A
3
,
2278
(
1991
).
9.
R.
Rubinstein
and
J. M.
Barton
, “
Nonlinear Reynolds stress models and the renormalization group
,”
Phys. Fluids A
2
,
1472
(
1990
).
10.
C. G.
Speziale
, “
On nonlinear K-l and K-ε models of turbulence
,”
J. Fluid Mech.
178
,
459
(
1987
).
11.
A. N.
Kolmogorov
, “
The equations of turbulent motion in an incompressible fluid
,”
Izv. Acad Sci. USSR Phys.
6
,
56
(
1942
).
12.
J. L.
Lumley
, “
Computational modeling of turbulent flows
,”
Adv. Appl. Mech.
18
,
123
(
1978
).
13.
W. C. Reynolds, “Fundamentals of turbulence for turbulence modeling and simulation,” Lecture Notes for von Kármán Institute, AGARD Lecture Series No. 86 (NATO, New York, 1987), p. 1.
14.
B. E.
Launder
and
D. B.
Spalding
, “
The numerical computation of turbulent flows
,”
Comput. Methods Appl. Mech. Eng.
3
,
269
(
1974
).
15.
B. E.
Launder
,
G. J.
Reece
, and
W.
Rodi
, “
Progress in the development of a Reynolds stress turbulence closure
,”
J. Fluid Mech.
68
,
537
(
1975
).
16.
H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, Cambridge, MA, 1972).
17.
C. G.
Speziale
, “
Analytical methods for the development of Reynolds-stress closures in turbulence
,”
Annu. Rev. Fluid Mech.
23
,
107
(
1991
).
18.
P. A.
Durbin
and
C. G.
Speziale
, “
Local anisotropy in strained turbulence at high Reynolds numbers
,”
ASME J. Fluids Eng.
113
,
707
(
1991
).
19.
P. A. Durbin, “Turbulence closure modeling near rigid boundaries,” in Ref. 5, p. 3.
20.
A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (MIT Press, Cambridge, MA, 1975), Vol. 2.
21.
P.
Rosenau
, “
Extending hydrodynamics via the regularization of the Chapman-Enskog expansion
,”
Phys. Rev. A
40
,
7193
(
1989
).
22.
V. C.
Patel
,
W.
Rodi
, and
G.
Scheuerer
, “
Turbulence models for near-wall and low Reynolds number flows: A review
,”
AIAA J.
23
,
1308
(
1985
).
23.
J. Bardina, J. H. Ferziger, and W. C. Reynolds, “Improved turbulence models based on large-eddy simulation of homogeneous, incompressible turbulent flows,” Stanford University Technical Report No. TF-19, 1983.
24.
S.
Tavoularis
and
S. J.
Corrsin
, “
Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient: Part I
,”
J. Fluid Mech.
104
,
311
(
1981
).
25.
M. M. Rogers, P. Moin, and W. C. Reynolds, “The structure and modeling of the hydrodynamic and passive scalar fields in homogeneous turbulent shear flow,” Stanford University Technical Report No. TF-25, 1986.
26.
S. C.
Crow
, “
Viscoelastic properties of fine grained incompressible turbulence
,”
J. Fluid Mech.
33
,
1
(
1968
).
27.
J.
Kim
,
S. J.
Kline
, and
J. P.
Johnston
, “
Investigation of a reattaching shear layer: Flow over a backward facing step
,”
ASME J. Fluids Eng.
102
,
302
(
1980
).
28.
J. Eaton and J. P. Johnston, “Turbulent flow reattachment: An experimental study of the flow and structure behind a backward facing step,” Stanford University Technical Report No. MD-39, 1980.
29.
S.
Thangam
and
C. G.
Speziale
, “
Turbulent flow past a backward facing step: A critical evaluation of two-equation models
,”
AIAA J.
30
,
1314
(
1992
).
30.
R. Abid, C. G. Speziale, and S. Thangam, “Application of a new K-τ model to near-wall turbulent flows,” AIAA Paper No. 91-0614, 1991.
31.
G. Karniadakis, A. Yakhot, S. Rakib, S. Orszag, and V. Yakhot, “Spectral element RNG simulations of turbulent flows in complex geometries,” Proceedings of the Seventh Symposium on Turbulent Shear Flows, Stanford University, Paper No. 7.2, 1989.
32.
C. G. Speziale and S. Thangam, “Analysis of RNG based turbulence models for separated flows,” to appear in Int. J. Eng. Sci.
33.
J.
Bardina
,
J. H.
Ferziger
, and
R. S.
Rogallo
, “
Effect of rotation on isotropic turbulence: Computation and modeling
,”
J. Fluid Mech.
154
,
321
(
1985
).
34.
C. G.
Speziale
and
N.
Mac Giolla Mhuiris
, “
Scaling laws for homogeneous turbulent shear flows in a rotating frame
,”
Phys. Fluids A
1
,
294
(
1989
).
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