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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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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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