32.A. Turbulence modeling for Reynolds-averaged Navier-Stokes equations.

This lecture starts with an introduction to turbulence modeling approach. We present the concepts of time and ensemble averaging, mean values, and fluctuations of variables. Next, the Reynolds-averaged Navier-Stokes equations, Reynolds stresses, and turbulent scalar fluxes are presented. We then introduce the most widely used concept of turbulence modeling – the eddy-viscosity approach. To compute the eddy (or turbulent) viscosity we need to determine the velocity and the length scale of turbulence. Many turbulence models require the computation of turbulent kinetic energy, from which the velocity scale is determined. We present the exact equation for it, and the models for terms which include additional unknowns. Turbulence models from the k-epsilon family require the solution of an additional equation for the dissipation rate of turbulent kinetic energy, which is used to determine the length scale. Another family of models solves the equation for another variable, omega, to compute the length scale. Both equations and their modeling are presented. Finally, the Reynolds-stress class of models is briefly described. These models solve equations for Reynolds stresses and turbulent scalar fluxes. This leads to a significantly higher computing effort than in the case of two-equation models, which is magnified by slower convergence due to the stiffness of equation system. You can download this video, the transcript of its soundtrack, and the PowerPoint presentation file from this site: https://sie.ag/6a3r6J You are also encouraged to participate in the discussion by posting comments, questions, and suggestions for improvements in the dedicated space for "The Perić Lectures on CFD" at the above site.