Some boundary-layer effects in supersonic flow

A few comments may now be made about the qualitative effects on boundary-layer flow of shock waves that may be generated in the mainstream adjacent to the surface of a body. A normal shock in a supersonic stream invariably reduces the Mach number to a subsonic value and this speed reduction is associated with a very rapid increase in pressure, density and temperature.

For an aerofoil operating in a transonic regime, the mainstream flow just outside the boundary layer accelerates from a subsonic speed near the leading edge to sonic

speed at some point near the subsonic-peak-suction position. At this point, the streamlines in the local mainstream will be parallel and the effect of the aerofoil surface curvature will be to cause the streamlines to begin to diverge downstream. Now the characteristics of a supersonic stream are such that this divergence is accompanied by an increase in Mach number, with a consequent decrease in pres­sure. Clearly, this state of affairs cannot be maintained, because the local mainstream flow must become subsonic again at a higher pressure by the time it reaches the undisturbed free-stream conditions downstream of the trailing edge. The only mechan­ism available for producing the necessary retardation of the flow is a shock wave, which will set itself up approximately normal to the flow in the supersonic region of the mainstream; the streamwise position and intensity (which will vary with distance from the surface) of the shock must be such that just the right conditions are established behind it, so that the resulting mainstream approaches ambient conditions far down­stream. However, this simple picture of a near-normal shock requirement is compli­cated by the presence of the aerofoil boundary layer, an appreciable thickness of which must be flowing at subsonic speed regardless of the mainstream flow speed. Because of this, the rapid pressure rise at the shock, which cannot be propagated upstream in the supersonic regions of flow, can be so propagated in the subsonic region of the boundary layer. As a result, the rapid pressure rise associated with the shock becomes diffused near the base of the boundary layer and appears in the form of a progressive pressure rise starting at some appreciable distance upstream of the incident shock. The length of this upstream diffusion depends on whether the boundary layer is laminar or turbulent. In a laminar boundary layer the length may be as much as one hundred times the nominal general thickness (6) at the shock, but for a turbulent layer it is usually nearer ten times the boundary-layer thickness. This difference can be explained by the fact that, compared with a turbulent boundary layer, a larger part of the laminar boundary – layer flow near the surface is at relatively low speed, so that the pressure disturbance can propagate upstream more rapidly and over a greater depth.

It has already been pointed out in Sections 7.2.6 and 7.4 that an adverse pressure gradient in the boundary layer will at least cause thickening of the layer and may well cause separation. The latter effect is more probable in the laminar boundary layer and an additional possibility in this type of boundary layer is that transition to turbulence may be provoked. There are thus several possibilities, each of which may affect the external flow in different ways.