A Provisional Analysis of Turbulent Boundary Layers with Injection

Abstract

SUMMARY Prandtl's analysis of the incompressible turbulent boundary layer over a flat plate is extended in this report to include the effect of uniform, transverse fluid injection. The nondimensional parameters characterizing such a flow are deduced by dimensional reasoning. A velocity profile is generated by considering the flow over a plane wall; this distribution reduces to the universal log law when the mass transfer is zero. The expression also serves to relate the local skin friction to the boundary-layer thickness. When these relationships are used in conjunction with the von Karman integral, the problem becomes mathematically specified. Since only a limited amount of experimental data is available, it is necessary to assign to certain parameters that arise in the velocity profile the constant values they have for no mass transfer. When more measurements are completed, it may be possible to adjust these parameters as or if required. The results give the variation of average skin-friction coefficient with the injection ratio and the Reynolds Number based on the streamwise coordinate. The agreement between these results and the experimental data available is found to be satisfactory. The significant reductions in skin friction, and therefore in heat trans­ fer, to be realized with small rates of injection are indicated.