Matching Inviscid/Boundary Layer Flowfields

Abstract

New boundary-layer equations are developed and the solutions match all the boundary-layer properties, except for the normal velocity, exactly with the corresponding inviscid properties. The numerical procedure solves tridiagonal matrices at each marching station. As part of the solution an inviscid transpiration velocity at the surface is calculated from the boundary-layer solution. This transpiration velocity could be used as a boundary condition to calculate a new inviscid solution. If the inviscid/boundary layer solutions are iterated, then the normal velocity from the boundary layer solution will match the inviscid values exactly. Solutions are calculated for shear flows over a flat plate. Results from the present method compared well with Navier-Stokes solutions for incompressible constant shear flow and sinusoidal shear flow. Iterations of the inviscid/boundary layer solutions were not necessary. Compressible flow of an exponential shear at Mach 4 was calculated for cold, adiabatic, and hot walls. It was found that inviscid shear flows have a significant effect on skin friction and heating rates. The present method should yield accurate boundary-layer solutions at Reynolds numbers lower than the traditional boundary-layer equations.