Displacement Effects on the Laminar Mixing of Two Parallel Streams

Abstract

SummaryAn analytical study is made of the laminar mixing of two semi-infinite streams that are initially parallel. The equations governing the mixing process and the boundary conditions are derived by application of the perturbation technique. The “missing” correct third boundary condition is shown to be the condition that the pressures of the inviscid upper and lower streams due to the displacement thicknesses be balanced across the mixing layer. A general procedure for solution of the mixing problems is established by means of a transformation of the mixing-layer equations and two boundary conditions.As an example, the laminar mixing of two parallel uniform streams of both incompressible and compressible fluids is solved. It is shown that the profiles of v are entirely different from those based on the approximate third boundary condition. The improved profiles are in excellent agreement with the experimental data.