Numerical investigation of two-dimensional turbulent boundary-layer compressible flow with adverse pressure gradient and heat and mass transfer

Abstract

The effect of heat and mass transfer on the steady turbulent compressible boundary-layer flow with adverse pressure gradient are numerically studied. The Reynolds-averaged boundary-layer equations and their boundary conditions are transformed, in a suitable form for numerical solution, by using the compressible version of the Falkner-Skan transformation and the resulting coupled and nonlinear system of partial differential equations is solved using the Keller's-box method and a modified version of it. For the eddy kinematic viscosity the model developed by Cebeci and Smith is employed whereas for the turbulent Prandlt number model a modification of the extended Kays and Crawford's model is used. Numerical calculations are carried out for the case of air, at about free stream temperature of 300°K, and for a linearly retarded flow, known as Howarth's flow when the porous limiting surface is adiabatic, heated or cooled. The porous surface is subjected to a continuous or localized suction/injection velocity and the influence of this velocity as well as of the free-stream Mach number and of the heat-transfer parameter on the turbulent boundary-layer and the separation point is examined. It is hoped that in the absence of detailed investigations into this problem, the obtained results, presented in the figures, are very interesting and give a clearer insight into the mechanism of controlling a turbulent boundary-layer compressible flow.