Boundary layers with suction or injection

Abstract

Approximate integral equations are derived for the compressible laminar boundary layer with arbitrary pressure gradient and arbitrary suction or injection velocity through a porous wall, Reasonable agreement is obtained when particular solutions to the integral equations are compared with solutions by previous authors. Experiments in an incompressible turbulent boundary layer over a porous surface reveal two laws for the inner and cuter regions; laws which correlate previous experimental results. The lams are used to calculate shear distributions and variations of skin friction with Reynolds number and enable Preston tubes to be used to estimate skin friction over a porous surface. The outer region theory is extended to boundary layers in small pressure gradients and at separation. The only universal functions required are obtained from zero pressure gradient flow. No other constants are used to calculate the mean velocity profiles for boundary layers in small pressure gradients, with suction or injection and at separation or reattachment. The theory agrees with the available experimental results for turbulent boundary layers in energy equilibrium. Experiments in folly developed pipe flow show haw the mean flow is altered when there is suction through a porous section of the pipe. An approximate theory for the inner region compares reasonably well with the experiments for small suction velocities.