The development of supersonic flow over an aerofoil

So far we have discussed supersonic flow at a relatively high Mach number but ignored the complicated processes necessarily involved in accelerating from subsonic to supersonic speed. We now return to our aerofoil problem in order to illustrate some of the important things which occur during this process.

Figure 5.18 shows photographs of an aerofoil at various Mach numbers from fully subsonic to fully supersonic. The photographs were taken using an optical system which shows shock waves as a dark band and expansion waves as a light coloured area. This system, which is extensively used in high speed wind-tunnel testing, is known as a schlieren system.

Because of the thickness of aerofoil, the flow is speeded up over the top and bottom surfaces. Thus the flow will eventually become supersonic in these regions, although the free stream is still subsonic. The flow is decelerated from its locally supersonic speed by a shock wave (Fig. 5.18(b)). The local super­sonic patches on the top and bottom of the aerofoil grow in extent as the free stream speed is increased, and the strength of the shock wave also gets greater.

It can also be seen from the schlieren photographs (Fig. 5.18(b)) that the pre­sence of the shock waves leads to boundary layer separation, about which more will be said in the following section.

As the free-stream Mach number is increased further, the shock wave moves further back as well as increasing in strength. As the free-stream flow just becomes supersonic, another shock wave starts to appear upstream of the aerofoil forming the bow shock wave mentioned previously. This bow shock wave gets progressively nearer to the nose of the aerofoil as the Mach number is increased and the typical flow for a fully supersonic aerofoil shown in Fig. 5.18(c) is obtained.