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Research Papers: Fundamental Issues and Canonical Flows

Sensitization of a Transition-Sensitive Linear Eddy-Viscosity Model to Rotation and Curvature Effects

[+] Author and Article Information
Varun Chitta

Department of Mechanical Engineering,
Center for Advanced Vehicular Systems (CAVS),
Mississippi State University,
Mississippi State, MS 39762
e-mail: vc217@msstate.edu

Tej P. Dhakal

Department of Mechanical Engineering,
Center for Advanced Vehicular Systems (CAVS),
Mississippi State University,
Mississippi State, MS 39762
e-mail: tpd22@msstate.edu

D. Keith Walters

Department of Mechanical Engineering,
Center for Advanced Vehicular Systems (CAVS),
Mississippi State University,
Mississippi State, MS 39762
e-mail: walters@cavs.msstate.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 19, 2013; final manuscript received September 17, 2014; published online January 14, 2015. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 137(3), 031207 (Mar 01, 2015) (14 pages) Paper No: FE-13-1565; doi: 10.1115/1.4028627 History: Received September 19, 2013; Revised September 17, 2014; Online January 14, 2015

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.

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References

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.
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. [CrossRef]
Steelant, J., and Dick, E., 2000, “Modeling of Laminar-Turbulent Transition for High Freestream Turbulence,” ASME J. Fluids Eng., 123(1), pp. 22–30. [CrossRef]
Wang, C., and Perot, B., 2002, “Prediction of Turbulent Transition in Boundary Layers Using the Turbulent Potential Model,” J. Turbul., 3, pp. 1–15. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Dhakal, T. P., and Walters, D. K., 2011, “A Three-Equation Variant of the SST kω Model Sensitized to Rotation and Curvature Effects,” ASME J. Fluids Eng., 133(11), p. 111201. [CrossRef]
Gatski, T. B., and Speziale, C. G., 1993, “On Explicit Algebraic Stress Models for Complex Turbulent Flows,” J. Fluid Mech., 254, pp. 59–78. [CrossRef]
Girimaji, S. S., 1997, “A Galilean Invariant Explicit Algebraic Reynolds Stress Model for Turbulent Curved Flows,” Phys. Fluids, 9(4), pp. 1067–1077. [CrossRef]
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. [CrossRef]
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. [CrossRef]
ANSYS, ANSYS Fluent Theory Guide 14.0, ANSYS, Inc., Canonsburg, PA.
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Coupland, J., 1990, “ERCOFTAC Special Interest Group on Laminar to Turbulent Transition and Retransition: T3A and T3B Test Cases,” Technical Report No. A309514.
Schlichting, H., and Klaus, G., 2000, Boundary Layer Theory, Springer, New York. [CrossRef]
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. [CrossRef]
Roshko, A., 1961, “Experiments on the Flow Past a Circular Cylinder at Very High Reynolds Number,” J. Fluid Mech., 10(3), pp. 345–356. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Chitta, V., and Walters, D. K., 2012, “Prediction of Aerodynamic Characteristics of an Elliptic Airfoil at Low Reynolds Number,” ASME Paper No. FEDSM2012-72389. [CrossRef]
Schubauer, G. B., 1939, “Air Flow in the Boundary Layer of an Elliptic Cylinder,” National Advisory Committee for Aeronautics, Report No. 652.
Lin, J. C. M., and Pauley, L. L., 1996, “Low-Reynolds-Number Separation on an Airfoil,” AIAA J., 34(8), pp. 1570–1577. [CrossRef]
Tani, I., 1964, “Low-Speed Flows Involving Bubble Separations,” Prog. Aerosp. Sci., 5, pp. 70–103. [CrossRef]
Kwon, K., and Park, S. O., 2005, “Aerodynamic Characteristics of an Elliptic Airfoil at Low Reynolds Number,” J. Aircraft, 42(6), pp. 1642–1644. [CrossRef]

Figures

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Fig. 1

Example grid sensitivity study for circular cylinder test case at ReD = 104

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Fig. 2

Schematic representation of fully developed rotating turbulent channel flow test case

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Fig. 3

Mean velocity profiles for nonrotating (Ro = 0) channel flow case comparing new model with DNS data [20]

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Fig. 4

Mean velocity profiles for rotating (Ro = 0.5) channel flow case

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Fig. 5

TKE profiles for rotating (Ro = 0.5) channel flow case

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Fig. 6

Turbulent shear stress profiles for rotating (Ro = 0.5) channel flow case

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Fig. 7

(a) Computational domain and boundary conditions used for ZPG flat plate test case and (b) close-up of grid near flat plate LE

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Fig. 8

Streamwise decay of freestream turbulence intensity (Tu) for test case T3A, compared to experimental data [21]

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Fig. 9

Streamwise distribution of skin friction coefficient (Cf) for each of the three flat plate cases: (a) T3A−, (b) T3A, and (c) T3B

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Fig. 10

Normalized profiles of: (a) mean velocity (U), (b) total fluctuation kinetic energy (kTOT), (c) LKE (kL), and (d) TKE (kT) in pretransitional, transitional, and turbulent regions of boundary layer in test case T3A

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Fig. 11

Computational grid, boundary conditions, and close-up of mesh near the surface of circular cylinder test case for flow ReD = 107

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Fig. 12

Time-averaged TKE along the top of the cylinder for (a) ReD = 106 and (b) ReD = 107

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Fig. 13

Time-averaged streamwise velocity distribution along the top of the cylinder for (a) ReD = 106 and (b) ReD = 107

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Fig. 14

Time-averaged drag coefficient curves for all turbulent models used in this study and in comparison with experimental results [22]

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Fig. 15

Time-averaged pressure coefficient distribution along the top of the cylinder at ReD = 3.6 × 106 in comparison with experiments [26]. Discrepancy in the CP profile can be attributed to the delayed prediction of flow separation point by new model.

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Fig. 16

Mean velocity contours of circular cylinder for the new model at various Reynolds numbers

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Fig. 17

Computational domain for elliptic airfoil test case and close-up of mesh in the vicinity of the LE highlighting the multitopology grid

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Fig. 18

(a) Lift coefficient (cl) and (b) drag coefficient (cd) curves for elliptic airfoil plotted as a function of angle of attack (α)

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Fig. 19

Time-averaged pressure coefficient profiles over elliptic airfoil for the new model in comparison with curvature-sensitive SST k–ω–v2 model and experimental results [32]

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Fig. 20

TKE distributions around elliptic airfoil test case from the new model at (a) α = 0 deg, (b) α = 3 deg, (c) α = 6 deg, and (d) α = 9 deg

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Fig. 21

Mean velocity contours of elliptic airfoil at α = 6 deg for (a) new model and (b) curvature-sensitive SST k–ω–v2. LSB is observed on the suction surface near LE for the new model.

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Fig. 22

Mean velocity contours of elliptic airfoil at α = 9 deg for (a) new model and (b) curvature-sensitive SST k–ω–v2

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