Near-wall behavior of RANS turbulence models and implications for wall functions

The paper proposes a novel wall-function formulation applicable to any RANS turbulence model. It is based on the assumption of wall layer universality, applied to the entire model. The approach is implemented via tables for the turbulence quantities and the friction velocity uτ. The influence of numerical errors on the wall-function solution is investigated and improvements are proposed. Numerical results are presented for a flat plate boundary layer at zero pressure gradient and for a flow with pressure gradient driven separation. The behavior of RANS turbulence models in the near wall region is also analyzed. The models considered are: Spalart-Allmaras, k-ω, k-g and v2-f. The analysis of the v2-f model resulted in new analytical solutions in the viscous sublayer and logarithmic layer. The analytical solutions for the Spalart-Allmaras model can be used directly as a simple wall function.