On slot injection into a supersonic laminar boundary layer

Abstract

The structure of a supersonic laminar boundary layer near a flat plate is examined when fluid is injected into it, normal to the surface, with velocity O (∊ 3 U * ∞ ) over a distance O (∊ 3 L). Here U * ∞ is the undisturbed velocity of the fluid, L is the plate length and ∊ -8 is a representative Reynolds number of the flow. It is found that the pressure rises upstream of the injection region and that in all the cases fully computed the blowing takes place in a favourable pressure gradient. Afterwards the pressure rises to its undisturbed value. Further incomplete studies suggest that in more extreme conditions, e. g. longer slots, the pressure gradient can be adverse just downstream of the start of the blow and that separation can even occur there. The analytical discussion rests heavily on the notion of the triple-deck, a subdivision of the boundary layer suitable for investigating its response to sudden changes in boundary conditions. Extensive numerical work is also required and the methods devised fail when the boundary layer separates at the onset of the blow. The relation between this type of injection and weak plate injection where the blowing velocity is O (∊ 4 U * ∞ ) and extends over a distance O ( L ) is also considered.