Development of a One-Equation Turbulence Model based on Epsilon-Equation

Abstract

A one-equation variant of a two-equation k-ǫ turbulence model based on the mean dissipation-rate ǫ-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.