Consistently formulated eddy-viscosity coefficient for k-equation model

An approach to devising a consistency formulation for Pk/ϵ(production-to-dissipation ratio) is proposed to obtain a non-singular C_μ(coefficient of eddy-viscosity) embedded in the one-equation model based on the turbulent kinetic energy k. The dissipation rate ε is evaluated with an algebraically prescribed length scale having only one adjustable coefficient, accompanied by an anisotropic function qϵ enhancing the dissipation in non-equilibrium flow regions. The model accounts for the distinct effects of low Reynolds number (LRN) and wall proximity. The stress-intensity ratio R_b = u1u2/k is formulated as a function of local variables without resorting to a constant √C^* _μ= 0.3. The parameters R_b and Pk/ϵ entering the turbulence production P_k prevents presumably 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. 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. Finally, the current model provides a proposal to compute free shear flows.