An integral method for analyzing incompressible two dimensional turbulent boundary layers with separation

An integral method is proposed for analyzing incompressible two dimensional turbulent boundary layers with flow separation based on the inner variable theory. Utilizing the law-of-the-wall and wake, the integration of continuity and momentum equations across the boundary layer gives a differential equation in terms of the wake parameter and the shear velocity. With the aid of an empirical correlation between the wake parameter and the pressure gradient parameter, derived from the experimental data of several separated and near separating flows, the above equation is reduced to a single ordinary differential equation in skin friction. Predictions have been made for a wide range of flows and satisfactory agreement is observed between the theory and the experimental measurements. The method is practically insensitive to the separation point singularity and calculation proceeds smoothly through the separation point into the reverse flow region without any numerical instability. Various degrees of refinement are possible for this theory and they are summarized in the text.