A wall function for turbulent compressible boundary layer flow

Here we propose a method to develop a wall function for a turbulent compressible boundary layer flow. We reduce the governing equations of motion to a lower-order form through application of shock-layer and boundary layer analysis of the compressible RANS equations. The equations are closed using the Spalart-Allmaras one equation model. We derive the governing equations for an idealized high Mach number flow over an insulated plate with Pr = Pr_T = 1. The equations yield a wall function for turbulent compressible boundary layer flows that have potential to improve upon the more commonly used wall function presented by Van Driest.