The Turbulent Boundary Layer With Mass Transfer and Pressure Gradient

Abstract

An analysis of the incompressible, turbulent boundary layer, including the combined effects of mass transfer and pressure gradient is presented in this paper. An integral method employing the integral mechanical energy equation forms the basis of the analysis. Stevenson’s velocity profiles are used to obtain the functional dependence of the integral properties and also obtain a skin-friction law. A definition of an equilibrium flow with mass transfer and pressure gradient is given in order to evaluate the dissipation integral (CD) which appears in the integral mechanical energy equation. This definition requires a pressure gradient parameter similar to Clauser’s βT with a modification to include the effect of mass transfer to be held constant. An expression for CD in the case of equilibrium turbulent flows is then obtained which depends directly on this new pressure gradient parameter (βT*). In order to treat the general case of nonequilibrium flows, this expression for CD is uncoupled from βT*, through the use of a single empirical curve fit of the existing no mass transfer equilibrium flow data relating βT to the Clauser shape parameter. In addition to unhooking CD from the pressure gradient parameter, several specified variations in mass transfer rate are assumed in order to obtain an expression for CD which is not a function of the mass transfer rate derivative. The numerical results are found to be weakly dependent on which of these variations is used. Comparisons of the numerical results with a wide variety of experimental data, including cases where the blowing rate and pressure are varying simultaneously, show good agreement. In addition, several problems with discontinuities in blowing or suction are solved and seem to be in good agreement with the data.