The integral method for turbulent momentum boundary layers on a porous plate with uniform blowing and suction

Abstract:

The turbulent boundary layer with injection and suction is of fundamental interest for the analytical research in the field of transpiration or film cooling, which has an important theoretical significance. The momentum boundary layer is divided into the viscous sublayer and turbulent core zone for steady turbulent flows on a porous flat plate, and the velocity distributions in the two zones are approximated by the cubic polynomial and 1/5 power functions, respectively. An integral method is used to recast the momentum equations into the integro-differential equation groups, and the analytical solutions of velocity boundary layers through the permeable surfaces are obtained by employing the fourth-order Runge-Kutta method. Following the foregoing analytical results, the profile of skin friction factor on the wall is also obtained. It is showed that the proposed analytical solutions have a satisfactory agreement with the existing experimental measurements carried out respectively by Whitten and Blackwell, and also with the empirical formula of Kays.