A Simple Analytical Velocity Profile for a Turbulent High-Speed Boundary Layer Over a Flat Plate

An analytical function for a turbulent boundary-layer velocity profile is proposed to describe turbulent, wall-bounded, external incompressible and compressible flows. The profile is shown to satisfy (1) endpoint boundary conditions both in value and slope, (2) have physical behavior in all four turbulent regions, and (3) provide estimation of physical quantities, such as viscous lengthscales, momentum thickness, and a wake lengthscale. The profile is shown to fit experimental data well. The profile is used in conjunction with a model based on mixing length in the log region to define profile fit parameters and calculate the friction factor and boundary-layer thickness as a function of the streamwise coordinate on a flat plate. The model uses friction factor as the independent variable to simplify calculations.