Stability of the Boundary Layer with Internal Heat Release and Gas Injection through a Porous Wall

Abstract

The problem of stability of a subsonic boundary layer is solved under the conditions of heat supply inside the boundary layer with injection of a homogeneous gas through a porous plate that partially simulates the problem of stability of a boundary layer with diffuse combustion. Two-dimensional waves are the most growing waves over the entire range of investigated parameters. It is found that in the case of a fixed norm of heat supply the maximum temperature in the boundary layer increases with the Reynolds number, i.e., with increase in the distance from the leading plate edge. This is in agreement with available experiments and calculations of parameters of the boundary layer with diffuse combustion. In this case the dependence of the degrees of amplification on the Reynolds number, which are maximum in the frequency, is nonmonotonic. It is shown that gas injection with heat supply destabilizes the boundary layer, as it occurs without heat supply. On the other hand, the stabilizing role of heat supply is also shown under the conditions of gas injection through a porous wall. As the frequency of growing wave increases, the phase velocity tends to the velocity at the generalized inflection point. Despite fairly large degrees of growing, the Gaster relation is valid. In accordance with this relation the spatial degree of amplification is equal to the temporal degree of amplification divided by the group velocity.