An eddy viscosity model with elliptic relaxation approach

An extended version of the isotropic k – ϵ model accompanied by an elliptic relaxation approach to account for the distinct effects of low-Reynolds number (LRN) and wall proximity is proposed. To demonstrate the internal consistency of the elliptic relaxation approach with the characteristic length scale, both the Kolmogorov and hybrid length scales are introduced. The model incorporates a secondary source term to amplify the level of dissipation in nonequilibrium flow regions, thus reducing the kinetic energy and length scale magnitudes to improve prediction of adverse pressure gradient flows, involving flow separation and reattachment. The eddy viscosity formulation maintains the positivity of normal Reynolds stresses and the Schwarz’ inequality for turbulent shear stresses. The model coefficients/functions preserve the anisotropic characteristics of turbulence. The model is validated against a few well-documented flow cases, yielding predictions in good agreement with the direct numerical simulation (DNS) and experimental data. Comparisons indicate that the present model offers considerable improvement over the standard eddy viscosity formulation.