Curvature Correction for Turbulent Diffusion Inside a Differential Reynolds-Stress Model

A correction of the turbulent diffusion terms inside a Reynolds-stress model for mean-streamline curvature is presented. The correction is based on work by Zeman and is reformulated in this work to be applicable in general CFD codes. For this purpose, a new and grid-point local gradient Richardson number is derived which is used within the correction term in order to characterize mean-streamline curvature. These quantities are verified for a channel with U-turn and delta wing vortex. The final correction term was finally applied to these test cases: The overall effect of the correction term on the local Reynolds stresses depends the relative effect of diffusion on the turbulent kinetic energy balance. In this sense, no effect on the solution of the mean flow field was observed for the channel test case, whereas lower values of turbulent kinetic energy appear for the delta wing vortex.