A scalar anisotropy model for turbulent eddy viscosity

A three-equation eddy-viscosity turbulence model using transport equations for the turbulent kinetic energy (k), dissipation rate (ϵ), and a scalar measure of the Reynolds-stress anisotropy is described. Away from walls, where the turbulence anisotropy goes to zero, the model naturally reverts to the isotropic k–ϵ formulation, with only a slightly modified value of the eddy-viscosity coefficient. This leverages the predictive capability of k–ϵ for free shear flows, while still providing accurate predictions of wall-bounded flows without resorting to wall-damping functions. The computed model predictions are compared against experimental Reynolds-stress measurements for a zero-pressure-gradient flat-plate boundary layer, a planar mixing-layer, and the separated flow over periodic hills. Further, the computed results show improvements over standard one- and two-equation models, most notably for the smooth-body separation and recirculation encountered in the flow over periodic hills.