A New Unified Form of Universal Wall Function

A new form of universal wall function is proposed in this work, which can be applied to a variety of eddy viscosity models including one-equation models and two-equation models. The new wall function approximates the analytical results of the Spalart-Allmaras turbulence model in the near wall region of the zero pressure gradient incompressible turbulent boundary layer. This approximate form can be applied as a unified eddy-viscosity-based wall function and a concise unified wall function of velocity distribution is proposed after integration. On this basis, the grid Reynolds number is introduced and a function for judging the position of the first layer grid is given. The new wall function is validated using the NACA0012 and the axisymmetric separated boundary layer. It is proved that the wall function is accurate and universal, and the grid requirements are lower in applications.