A modified one-equation turbulence model based on k-equation

An approach to reducing the two-equation k-ǫ model to a one-equation model based on the k-equation is proposed to account for the distinct effects of low-Reynolds number (LRN) and wall proximity. The dissipation rate ǫ is evaluated with an algebraically prescribed length scale having only one adjustable coefficient. The stress-intensity ratio R_b = u₁u₂/k is devised as a function of local variables without resorting to a constant C_μ = 0.3. The key parameter R_b entering the turbulence production Pk prevents presum-ably the overestimation of P_k in flow regions where non-equilibrium effects could result in a misalignment between turbulent stress and mean strain-rate with a linear eddy-viscosity model. An anisotropic function f_k is for-mulated to enhance the dissipation in the near-wall region. The Bradshaw-relation R_b and the coefficient of dissipation term are calibrated against the fully developed turbulent channel flow; however 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.