Some effects of shock-induced separation of turbulent boundary layers in transonic flow past aerofoils

Abstract

The effects of shock-induced separation of turbulent boundary layers on two-dimensional aerofoils are introduced by considering the development of the surface-pressure distribution and flow pattern as the free-stream speed is increased in the transonic range (defined as that for which regions of supersonic flow exist on the aerofoils but are limited in chordwise extent). The progressive rearward extension of the supersonic flow, as the terminating shocks move rearwards over the surfaces, is an essential feature of this development. Unless the incidence and thickness of an aerofoil at lift are both very small, the upper-surface shock, at some stage in its movement, induces a boundary-layer separation which tends to reduce the pressure rise through the shock. The consequences of this are usually not serious until the shock fails to re-establish subsonic flow immediately downstream. At that stage, however, the 'bubble' of separated flow begins to expand rapidly towards the trailing edge and beyond, and in so doing to exert a dominating influence on the development of the overall flow, i.e., on the actual and relative rates of shock movement, or flow development, on the two surfaces. This influence wanes as soon as either the lower surface shock reaches the trailing edge or a centred supersonic expansion occurs there; the bubble finally collapses when the upper-surface shock moves on to the trailing edge. The physical nature of the overall flow and the mechanism by which separation affects its development so strongly are described qualitatively. The picture presented has been made as complete as possible, even though this involves some ideas which must be regarded as speculative, in the hope that it might form a tentative basis for more rigorous treatments or for extension of the work.to swept-back and finite wings. Considerations of the flow at the trailing edge of the aerofoil and downstream along the wake figure prominently in the description, and the pressure at the trailing-edge position is used extensively.