An anisotropic two-equation model is developed through a novel technique that involves the representation of the energy spectrum and invariance based scaling. In this approach the effect of rotation is used to modify the energy spectrum, while the influence of swirl is modeled based on scaling laws. The resulting generalized two-equation turbulence model is validated for several benchmark turbulent flows with swirl and curvature.

1.
Speziale
,
C. G.
, 1991, “
Analytical Methods for the Development of Reynolds Stress Closures in Turbulence
,”
Annu. Rev. Fluid Mech.
0066-4189,
23
, pp.
107
157
.
2.
Lumley
,
J. L.
, 1970, “
Toward a Turbulent Constitutive Relation
,”
J. Fluid Mech.
0022-1120,
41
, pp.
413
434
.
3.
Speziale
,
C. G.
, 1987, “
On Nonlinear K−L and K−ε Models of Turbulence
,”
J. Fluid Mech.
0022-1120,
178
, pp.
459
475
.
4.
Reynolds
,
W. C.
, 1976, “
Computation of Turbulent Flows
,”
Annu. Rev. Fluid Mech.
0066-4189,
8
, pp.
183
208
.
5.
Hanjalić
,
K.
, and
Launder
,
B. E.
, 1972, “
A Reynolds Stress Model of Turbulent and its Application to Thin Shear Flow
,”
J. Fluid Mech.
0022-1120,
52
, pp.
609
638
.
6.
Pope
,
S. B.
, 1975, “
A More General Effective-Viscosity Hypothesis
,”
J. Fluid Mech.
0022-1120,
72
, pp.
331
340
.
7.
Thangam
,
S.
,
Wang
,
X.
, and
Zhou
,
Y.
, 1999, “
Development of a Turbulence Model Based on the Energy Spectrum for Flows Involving Rotation
,”
Phys. Fluids
1070-6631,
11
, pp.
2225
2234
.
8.
Zeman
,
O.
, 1994, “
A Note on the Spectra and Decay of Rotating Homogeneous Turbulence
,”
Phys. Fluids
1070-6631,
6
, pp.
3221
3223
.
9.
Zhou
,
Y.
, 1995, “
A Phenomenological Treatment of Rotating Turbulence
,”
Phys. Fluids
1070-6631,
7
, pp.
2092
2094
.
10.
Lumley
,
J. L.
, 1978, “
Computational Modeling of Turbulent Flows
,”
Adv. Appl. Mech.
0065-2156,
18
, pp.
123
176
.
11.
Speziale
,
C. G.
,
Sarkar
,
S.
, and
Gatski
,
T. B.
, 1991, “
Modeling the Pressure-Strain Correlation of Turbulence: An Invariant Dynamical Systems Approach
,”
J. Fluid Mech.
0022-1120,
227
, pp.
245
272
.
12.
Pope
,
S. B.
, 1983, “
Consistent Modeling of Scalar in Turbulent Flows
,”
Phys. Fluids
0031-9171,
26
(
2
), pp.
404
408
.
13.
Gatski
,
T. B.
, and
Speziale
,
C. G.
, 1993, “
On Explicit Algebraic Stress Models for Complex Turbulent Flows
,”
J. Fluid Mech.
0022-1120,
254
, pp.
59
78
.
14.
Imao
,
S.
, and
Itoh
,
M.
, 1996, “
Turbulent Characteristics of the Flow in an Axially Rotating Pipe
,”
Int. J. Heat Fluid Flow
0142-727X,
17
, pp.
445
451
.
15.
Kitoh
,
O.
, 1991, “
Experimental Study of Turbulent Swirling Flow in a Straight Pipe
,”
J. Fluid Mech.
0022-1120,
225
, pp.
445
479
.
16.
Yakhot
,
V.
,
Orszag
,
S. A.
,
Thangam
,
S.
,
Gatski
,
T. B.
, and
Speziale
,
C. G.
, 1992, “
Development of Turbulence Models for Shear Flows by a Double Expansion Technique
,”
Phys. Fluids A
0899-8213,
4
, pp.
1510
1520
.
17.
Ribeiro
,
M. M.
, and
Whitelaw
,
J. H.
, 1980, “
Coaxial Jets With and Without Swirl
,”
J. Fluid Mech.
0022-1120,
96
, pp.
769
795
.
18.
Sislian
,
J. P.
, and
Cusworth
,
R. A.
, 1986, “
Measurements of Mean Velocity and Turbulent Intensities in a Free Isothermal Swirling Jet
,”
AIAA J.
0001-1452,
24
, pp.
303
309
.
19.
Murakami
,
M.
, and
Kikuyama
,
K.
, 1989, “
Turbulent Flow in Axially Rotating Pipes
,”
ASME J. Fluids Eng.
0098-2202,
102
, pp.
97
103
.
20.
Lavan
,
Z.
,
Nielsen
,
H.
, and
Fejer
,
A. A.
, 1969, “
Separation and Flow Reversal in Swirling Flows in Circular Duct
,”
Phys. Fluids
0031-9171,
12
, pp.
1747
1756
.
21.
Speziale
,
C. G.
,
Younis
,
B. A.
, and
Berger
,
S. A.
, 2000, “
Analysis and Modeling of Turbulent Flow in an Axially Rotating Pipe
,”
J. Fluid Mech.
0022-1120,
407
, pp.
1
26
.
22.
Poroseva
,
S. V.
,
Kassinos
,
C. A.
,
Langer
,
C. A.
, and
Reynolds
,
W. C.
, 2002, “
Structure-Based Turbulence Model: Application to a Rotating Pipe Flow
,”
Phys. Fluids
1070-6631,
14
, pp.
1523
1532
.
23.
Hirai
,
S.
,
Takagi
,
T.
, and
Matsumoto
,
M.
, 1988, “
Predictions of the Laminarization Phenomena in an Axially Rotating Pipe Flow
,”
ASME J. Fluids Eng.
0098-2202,
110
, pp.
425
430
.
24.
Younis
,
B. A.
, and
Gibson
,
M. M.
, 1986, “
Calculation of Swirling Jet With a Reynolds Stress Closure
,”
Phys. Fluids
0031-9171,
29
(
1
), pp.
38
47
.
25.
Muck
,
K. C.
,
Hoffmann
,
P. H.
, and
Bradshaw
,
P.
, 1985, “
The Effect of Convex Surface Curvature on Turbulent Boundary Layers
,”
J. Fluid Mech.
0022-1120,
161
, pp.
347
369
.
26.
Gillis
,
J. C.
, and
Johnston
,
J. P.
, 1983, “
Turbulent Boundary-Layer Flow and Structure on a Convex Wall and its Redevelopment on a Flat Wall
,”
J. Fluid Mech.
0022-1120,
135
, pp.
123
153
.
27.
Hoffmann
,
P. H.
,
Much
,
K. C.
, and
Bradshaw
,
P.
, 1985, “
The Effect of Concave Surface Curvature on Turbulent Boundary Layers
,”
J. Fluid Mech.
0022-1120,
161
, pp.
371
403
.
28.
Gibson
,
M. M.
,
Jones
,
W. P.
, and
Younis
,
B. A.
, 1981, “
Calculations of Turbulent Boundary Layers on Curved Surfaces
,”
Phys. Fluids
0031-9171,
24
, pp.
386
395
.
29.
Irwin
,
H. P. A. H.
, and
Smith
,
P. A.
, 1975, “
Prediction of the Effect of Streamline Curvature on Turbulence
,”
Phys. Fluids
0031-9171,
18
, pp.
624
630
.
30.
Rodi
,
W.
, and
Scheuerer
,
G.
, 1983, “
Calculation of Curved Shear Layers With Two-Equation Turbulence Models
,”
Phys. Fluids
0031-9171,
26
(
6
), pp.
1422
1436
.
31.
Girimaji
,
S. S.
, 1997, “
A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Curved Flows
,”
Phys. Fluids
1070-6631,
9
, pp.
1067
1077
.
32.
Lilley
,
D. G.
, and
Rhode
,
D. L.
, 1982, “
A Computer Code for Swirling Turbulent Axisymmetric Recirculating Flows in Practical Isothermal Combustor Geometries
,” NASA Contractor Report No. 3442.
33.
Durbin
,
P. A.
, 1993, “
A Reynolds Stress Model for Near-Wall Turbulence
,”
J. Fluid Mech.
0022-1120,
249
, pp.
465
498
.
34.
Eskinazi
,
S.
, and
Yeh
,
H.
, 1956, “
An Investigation of Fully Developed Turbulent Flows in a Curved Channel
,”
J. Aeronaut. Sci.
0095-9812,
23
, Jan., pp.
23
75
.
35.
Younis
,
B. A.
,
Speziale
,
C. G.
, and
Berger
,
S. A.
, 1998, “
Accounting for Effects of a System Rotation on the Pressure-Strain Correlation
,”
AIAA J.
0001-1452,
36
, pp.
1746
1748
.
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