Study of laminar separation in the vicinity of the point of piecewise-constant pressure distribution over the wall

Abstract

A family of two-dimensional divergent channels with piecewise-constant velocity and pressure distributions over the wall is considered. The method of matched asymptotic expansions is applied to study the two-dimensional viscous incompressible flow at high but subcritical Reynolds numbers in the vicinity of a pressure jump point on the channel wall. It is shown that if the pressure difference is of the order O(Re−1/4), then in the vicinity of this point a classical region of interaction between the viscous boundary layer on the wall and the outer inviscid flow occurs. The problem formulated for the interaction region is solved numerically. The asymptotic values of the pressure difference corresponding to separationless flow are determined and the separation flow patterns are constructed.