A new scalar eddy-viscosity turbulence model is proposed, designed to exhibit physically correct responses to flow transition, streamline curvature, and system rotation effects. The eddy-viscosity model (EVM) developed herein is based on the k–ω framework and employs four transport equations. The transport equation for a structural variable (v2) from a curvature-sensitive Shear Stress Transport (SST) k–ω–v2 model, analogous to the transverse turbulent velocity scale, is added to the three-equation transition-sensitive k–kL–ω model. The physical effects of rotation and curvature (RC) enter the model through the added transport equation. The new model is implemented into a commercial computational fluid dynamics (CFD) solver and is tested on a number of flow problems involving flow transition and streamline curvature effects. The results obtained from the test cases presented here are compared with available experimental data and several other Reynolds-Averaged Navier-Stokes (RANS) based turbulence models. For the cases tested, the new model successfully resolves both flow transition and streamline curvature effects with reasonable engineering accuracy, for only a small increase in computational cost. The results suggest that the model has potential as a practical tool for the prediction of flow transition and curvature effects over blunt bodies.

References

1.
Savill
,
A. M.
,
1993
, “
Some Recent Progress in the Turbulence Modeling of By-Pass Transition
,”
Near-Wall Turbulent Flows
,
R. M. C.
So
,
C. G.
Speziale
, and
B. E.
Launder
, eds.,
Elsevier
,
Amsterdam, The Netherlands
, pp.
829
848
.
2.
Suzen
,
Y. B.
, and
Huang
,
P. G.
,
2000
, “
Modeling of Flow Transition Using an Intermittency Transport Equation
,”
ASME J. Fluids Eng.
,
122
(
2
), pp.
273
284
.10.1115/1.483255
3.
Steelant
,
J.
, and
Dick
,
E.
,
2000
, “
Modeling of Laminar-Turbulent Transition for High Freestream Turbulence
,”
ASME J. Fluids Eng.
,
123
(
1
), pp.
22
30
.10.1115/1.1340623
4.
Wang
,
C.
, and
Perot
,
B.
,
2002
, “
Prediction of Turbulent Transition in Boundary Layers Using the Turbulent Potential Model
,”
J. Turbul.
,
3
, pp.
1
15
.10.1088/1468-5248/3/1/022
5.
Walters
,
D. K.
, and
Leylek
,
J. H.
,
2004
, “
A New Model for Boundary Layer Transition Using a Single-Point RANS Approach
,”
ASME J. Turbomach.
,
126
(
1
), pp.
193
202
.10.1115/1.1622709
6.
Menter
,
F. R.
,
Langtry
,
R. B.
,
Likki
,
S. R.
,
Suzen
,
Y. B.
,
Huang
,
P. G.
, and
Volker
,
S.
,
2004
, “
A Correlation-Based Transition Model Using Local Variables—Part I: Model Formulation
,”
ASME J. Turbomach.
,
128
(
3
), pp.
413
422
.10.1115/1.2184352
7.
Walters
,
D. K.
, and
Cokljat
,
D.
,
2008
, “
A Three-Equation Eddy-Viscosity Model for Reynolds-Averaged Navier–Stokes Simulations of Transitional Flow
,”
ASME J. Fluids Eng.
,
130
(
12
), p.
121401
.10.1115/1.2979230
8.
Muck
,
K. C.
,
Hoffman
,
P. H.
, and
Bradshaw
,
P.
,
1985
, “
The Effect of Convex Surface Curvature on Turbulent Boundary Layers
,”
J. Fluid Mech.
,
161
, pp.
347
369
.10.1017/S002211208500297X
9.
Shur
,
M. L.
,
Strelets
,
M. K.
,
Travin
,
A. K.
, and
Spalart
,
P. R.
,
2000
, “
Turbulence Modeling in Rotating and Curved Channels: Assessing the Spalart–Shur Correction
,”
AIAA J.
,
38
(
5
), pp.
784
792
.10.2514/2.1058
10.
York
,
W. D.
,
Walters
,
D. K.
, and
Leylek
,
J. H.
,
2009
, “
A Simple and Robust Linear Eddy-Viscosity Formulation for Curved and Rotating Flows
,”
Int. J. Numer. Methods Heat Fluid Flow
,
19
(
6
), pp.
745
776
.10.1108/09615530910972995
11.
Pettersson-Reif
,
B. A.
,
Durbin
,
P. A.
, and
Ooi
,
A.
,
1999
, “
Modeling Rotational Effects in Eddy-Viscosity Closures
,”
Int. J. Heat Fluid Flow
,
20
(
6
), pp.
563
573
.10.1016/S0142-727X(99)00056-9
12.
Dhakal
,
T. P.
, and
Walters
,
D. K.
,
2011
, “
A Three-Equation Variant of the SST k–ω Model Sensitized to Rotation and Curvature Effects
,”
ASME J. Fluids Eng.
,
133
(
11
), p.
111201
.10.1115/1.4004940
13.
Gatski
,
T. B.
, and
Speziale
,
C. G.
,
1993
, “
On Explicit Algebraic Stress Models for Complex Turbulent Flows
,”
J. Fluid Mech.
,
254
, pp.
59
78
.10.1017/S0022112093002034
14.
Girimaji
,
S. S.
,
1997
, “
A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Turbulent Curved Flows
,”
Phys. Fluids
,
9
(
4
), pp.
1067
1077
.10.1063/1.869200
15.
Wallin
,
S.
, and
Johansson
,
A. V.
,
2002
, “
Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models
,”
Int. J. Heat Fluid Flow
,
23
(
5
), pp.
721
730
.10.1016/S0142-727X(02)00168-6
16.
Gatski
,
T. B.
, and
Jongen
,
T.
,
2000
, “
Nonlinear Eddy Viscosity and Algebraic Stress Models for Solving Complex Turbulent Flows
,”
Prog. Aerosp. Sci.
,
36
(
8
), pp.
655
682
.10.1016/S0376-0421(00)00012-9
17.
ANSYS
,
ANSYS Fluent Theory Guide 14.0
,
ANSYS, Inc.
,
Canonsburg, PA
.
18.
Matsubara
,
M.
, and
Alfredsson
,
P. H.
,
1996
, “
Experimental Study of Heat and Momentum Transfer in Rotating Channel Flow
,”
Phys. Fluids
,
8
(
11
), pp.
2964
2973
.10.1063/1.869074
19.
Smirnov
,
P. E.
, and
Menter
,
F. R.
,
2009
, “
Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart–Shur Correction Term
,”
ASME J. Turbomach.
,
131
(
4
), p.
041010
.10.1115/1.3070573
20.
Kristoffersen
,
R.
, and
Andersson
,
H. I.
,
1993
, “
Direct Simulations of Low-Reynolds-Number Turbulent Flow in a Rotating Channel
,”
J. Fluid Mech.
,
256
, pp.
163
197
.10.1017/S0022112093002757
21.
Coupland
,
J.
,
1990
, “
ERCOFTAC Special Interest Group on Laminar to Turbulent Transition and Retransition: T3A and T3B Test Cases
,” Technical Report No. A309514.
22.
Schlichting
,
H.
, and
Klaus
,
G.
,
2000
,
Boundary Layer Theory
,
Springer
,
New York
.10.1007/978-3-642-85829-1
23.
Zdravkovich
,
M. M.
,
1990
, “
Conceptual Overview of Laminar and Turbulent Flows Past Smooth and Rough Circular Cylinders
,”
J. Wind Eng. Ind. Aerodyn.
,
33
(
1–2
), pp.
53
62
.10.1016/0167-6105(90)90020-D
24.
Roshko
,
A.
,
1961
, “
Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number
,”
J. Fluid Mech.
,
10
(
3
), pp.
345
356
.10.1017/S0022112061000950
25.
Holloway
,
D. S.
,
Walters
,
D. K.
, and
Leylek
,
J. H.
,
2004
, “
Prediction of Unsteady, Separated Boundary Layer Over a Blunt Body for Laminar, Turbulent, and Transitional Flow
,”
Int. J. Numer. Methods Fluids
,
45
(
12
), pp.
1291
1315
.10.1002/fld.739
26.
Achenbach
,
E.
,
1968
, “
Distribution of Local Pressure and Skin Friction Around a Circular Cylinder in Cross-Flow up to Re=5 × 106
,”
J. Fluid Mech.
,
34
(
4
), pp.
625
639
.10.1017/S0022112068002120
27.
Chitta
,
V.
,
Dhakal
,
T. P.
, and
Walters
,
D. K.
,
2012
, “
Prediction of Aerodynamic Characteristics for Elliptic Airfoils in Unmanned Aerial Vehicle Applications
,”
Low Reynolds Number Aerodynamics and Transition
,
M. S.
Genc
, eds.,
Intech
,
Rijeka, Croatia
, pp.
59
78
.10.5772/33312
28.
Chitta
,
V.
, and
Walters
,
D. K.
,
2012
, “
Prediction of Aerodynamic Characteristics of an Elliptic Airfoil at Low Reynolds Number
,”
ASME
Paper No. FEDSM2012-72389. 10.1115/FEDSM2012-72389
29.
Schubauer
,
G. B.
,
1939
, “
Air Flow in the Boundary Layer of an Elliptic Cylinder
,” National Advisory Committee for Aeronautics, Report No. 652.
30.
Lin
,
J. C. M.
, and
Pauley
,
L. L.
,
1996
, “
Low-Reynolds-Number Separation on an Airfoil
,”
AIAA J.
,
34
(
8
), pp.
1570
1577
.10.2514/3.13273
31.
Tani
,
I.
,
1964
, “
Low-Speed Flows Involving Bubble Separations
,”
Prog. Aerosp. Sci.
,
5
, pp.
70
103
.10.1016/0376-0421(64)90004-1
32.
Kwon
,
K.
, and
Park
,
S. O.
,
2005
, “
Aerodynamic Characteristics of an Elliptic Airfoil at Low Reynolds Number
,”
J. Aircraft
,
42
(
6
), pp.
1642
1644
.10.2514/1.16740
You do not currently have access to this content.