A Simple, Accurate Integral Solution for Accelerating Turbulent Boundary Layers With Transpiration

Abstract

The inner law for transpired turbulent boundary layers is used as the velocity profile in the integral form of the x momentum equation. The resulting ordinary differential equation is solved numerically for the skin friction coefficient, as well as boundary layer thicknesses, as a function of position along the surface. Predicted skin friction coefficients are compared to experimental data and exhibit reasonably good agreement with the data for a variety of different cases. These include blowing and suction, with constant blowing fractions F for both mild and severe acceleration. Results are also presented for more complicated cases where F varies with x along the surface.