A New Unified Form of Universal Wall Function (Advances in Applied Mathematics and Mechanics, 2024)
A new form of universal wall function is proposed in this work, which canbe applied to a variety of eddy viscosity models including one-equation models andtwo-equation models. The new wall function approximates the analytical results of theSpalart-Allmaras turbulence model in the near wall region of the zero pressure gradient incompressible turbulent boundary layer. This approximate form can be appliedas a unified eddy-viscosity-based wall function and a concise unified wall function ofvelocity distribution is proposed after integration. On this basis, the grid Reynoldsnumber is introduced and a function for judging the position of the first layer grid isgiven. The new wall function is validated using the NACA0012 and the axisymmetricseparated boundary layer. It is proved that the wall function is accurate and universal,and the grid requirements are lower in applications.