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

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 et al., 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.