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.