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Research Papers: Fundamental Issues and Canonical Flows

# A Three-Equation Variant of the SST k-ω Model Sensitized to Rotation and Curvature Effects

[+] Author and Article Information
Tej P. Dhakal

Department of Mechanical Engineering, Center for Advanced Vehicular Systems,  MS State University, MS State, MS 39762tpd22@msstate.edu

D. Keith Walters

Department of Mechanical Engineering, Center for Advanced Vehicular Systems,  MS State University, MS State, MS 39762walters@cavs.msstate.edu

J. Fluids Eng 133(11), 111201 (Oct 13, 2011) (9 pages) doi:10.1115/1.4004940 History: Received November 08, 2010; Revised August 18, 2011; Published October 13, 2011; Online October 13, 2011

## Abstract

A new variant of the SST k-ω model sensitized to system rotation and streamline curvature is presented. The new model is based on a direct simplification of the Reynolds stress model under weak equilibrium assumptions [York , 2009, “A Simple and Robust Linear Eddy-Viscosity Formulation for Curved and Rotating Flows,” International Journal for Numerical Methods in Heat and Fluid Flow, 19 (6), pp. 745–776]. An additional transport equation for a transverse turbulent velocity scale is added to enhance stability and incorporate history effects. The added scalar transport equation introduces the physical effects of curvature and rotation on turbulence structure via a modified rotation rate vector. The modified rotation rate is based on the material rotation rate of the mean strain-rate based coordinate system proposed by Wallin and Johansson (2002, “Modeling Streamline Curvature Effects in Explicit Algebraic Reynolds Stress Turbulence Models,” International Journal of Heat and Fluid Flow, 23 , pp. 721–730). The eddy viscosity is redefined based on the new turbulent velocity scale, similar to previously documented k-ɛ-$υ2$ model formulations (Durbin, 1991, “Near-Wall Turbulence Closure Modeling without Damping Functions,” Theoretical and Computational Fluid Dynamics, 3 , pp. 1–13). The new model is calibrated based on rotating homogeneous turbulent shear flow and is assessed on a number of generic test cases involving rotation and/or curvature effects. Results are compared to both the standard SST k-ω model and a recently proposed curvature-corrected version (Smirnov and Menter, 2009, “Sensitization of the SST Turbulence Model to Rotation and Curvature by Applying the Spalart-Shur Correction Term,” ASME Journal of Turbomachinery, 131 , pp. 1–8). For the test cases presented here, the new model provides reasonable engineering accuracy without compromising stability and efficiency, and with only a small increase in computational cost.

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Copyright © 2011 by American Society of Mechanical Engineers
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## Figures

Figure 9

Turbulent shear stress profile across the rotating channel at Ro = 0.5

Figure 10

Computational domain and mesh for 2D U-bend test case

Figure 11

Velocity profile at θ = 90° in U bend

Figure 12

Turbulent kinetic energy profile at θ = 90° in U bend

Figure 13

Velocity profile at θ = 180° in U bend

Figure 14

Turbulent kinetic energy profile at θ = 180° in U bend

Figure 15

Skin friction coefficient along the inner wall of the U bend

Figure 18

Computational geometry for impinging jet

Figure 19

Impinging jet Nusselt number profiles

Figure 1

Bifurcation diagram for the SST k-ω-υ2 model

Figure 2

Grid sensitivity test on 2D U-bend flow for two different grids

Figure 3

Convergence history of normalized turbulent kinetic energy

Figure 4

Temporal behavior of turbulent kinetic energy for rotating homogeneous turbulence in plane shear under different frame rotation rates

Figure 5

Schematic diagram of fully developed rotating channel flow with channel height H

Figure 6

Mean velocity profile in a nonrotating channel flow

Figure 7

Mean velocity profile for a rotating channel flow Ro = 0.5

Figure 8

Turbulent kinetic energy profile for channel flow rotating at Ro = 0.5

Figure 16

Pressure coefficient plot for flow over cylinder, [circo], Experiment (Achenbach, 1968), Re = 4.0 × 106 ; simulation, Re = 3.6 × 106 ; —, SST k-ω-υ2 ; —, SST k-ω; -··-, SST-CC

Figure 17

Skin friction coefficient plot for flow over cylinder, Re = 3.6 × 106 ; [circo], experiment (Achenbach, 1968); ♦, 2D DES (Travin 1999); —, SST k-ω-υ2 ; —, SST k-ω; -··-, SST-CC

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