One–equation turbulence model based on ϵ–equation

A one–equation variant of a two–equation k-ϵ turbulence model based on the mean dissipation–rate ϵ–equation is constructed to account for the distinct 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_a = uv/k is devised as a function of local variables without resorting to a constant √C_μ = 0.3. An anisotropic function f_k is embedded with R_a to reduce its magnitude in the near–wall region. Consequently, the parameter R_a entering the turbulence production P_k is supposed to prevent the overestimation of P_k in flow regions where non–equilibrium effects may result in a misalignment between turbulent stress and mean strain–rate with a linear eddy–viscosity model. The Bradshaw–relation R_a and the coefficients of length-scale determining terms are calibrated against the fully developed turbulent channel flow; they yield good predictions. A comparative assessment of the present model with the Spalart–Allmaras (SA) one–equation model and the shear stress transport (SST) k–ω model is provided for well–documented simple and non–equilibrium turbulent flows.