INVERSE APPROACH SOLUTION FOR TURBULENT BOUNDARY LAYERS SUBJECTED TO ARBITRARY PRESSURE GRADIENTS

Abstract

This paper deals with the study of the turbulent boundary layer development on two dimensional flows subjected to steady incompressible oncoming stream. In the turbulent flow, the boundary layer is divided into two layers, a wall layer and an outer layer. It is well known that the wall layer is universal but the outer layer depends on the pressure gradient. The outer layer is modeled as a nonlinear turbulent wake and consequently a constant eddy viscosity model for Clauser is adopted. The outer layer problem is shown to be governed by the classical Falkner – Skan equation for the laminar wake, the difference being in a turbulent condition which requires a finite stress at its inner boundary instead of zero stress in laminar flows. For the computations it was convenient to convert the above direct problem (for a given stress, find the slip velocity at the wall) to an inverse problem (given the slip velocity at the wall find the stress). Riley & Weidman (1989) dealt with the solution of the above inverse problem, but had not however covered the entire range of solutions. In the present work a much wider range solution to the inverse problem using a finite domain transformation is obtained by Runge-Kutta method. The results are displayed graphically and discussed critically. The solution of the inner and outer layers put together describes the turbulent boundary layer subjected to arbitrary pressure gradients.