One-equation turbulence model based on k/ϵ

A one–equation variant of a k-ϵ turbulence model based on the mean turbulent time scale T = k/ϵ–equation is developed to account for the effects of low–Reynolds number (LRN) and wall proximity. The turbulent kinetic energy k is evaluated with an algebraically prescribed length scale having only one adjustable coefficient. The stress–intensity ratio R_b= uv/k is devised as a function of local variables without resorting to a constant √Cµ = 0.3. An anisotropic function f_kis embedded in the eddy-viscosity µT to reduce its magnitude in the near–wall region. In this model, the parameter R_bincluded in the turbulence production P_kprevents the overestimation of P_kin flow regions where non–equilibrium effects may result in a misalignment between the turbulent stress and mean strain–rate common in a linear eddy–viscosity model. The Bradshaw–relation R_band the coefficients in the length-scale determining terms are calibrated using the DNS data for the fully developed turbulent channel flow. A comparative assessment of the accuracy of the present model compared to the the Spalart–Allmaras (SA) one–equation model and the shear stress transport (SST) k–ω model is conducted for well–documented simple equilibrium and non–equilibrium turbulent flows.