Exploring k and eps with R–Equation Model Using Elliptic Relaxation Function

Authors: Rahman, M.M., Wallin, S.W., Siikonen, T.
Document Type: Article
Pubstate: Published
Journal: Flow Turbulence and Combustion
Year: 2012


An extended version of the isotropic R–equation model accompanied by an elliptic relaxation approach to account for the distinct effects of low-Reynolds number (LRN) and wall proximity is proposed. The turbulent kinetic energy k and the dissipation rate epsilon are evaluated using the R (=k^2) transport equation together with some empirical relations. 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 in the sense that they are sensitized to rotational and nonequilibrium flows. 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 some improvement over the Spalart–Allmaras one–equation model and competitiveness with the SST k–omega model.