I come to the end of this chapter thinking that it is not really satisfactory. I have committed myself to writing a textbook and I cannot omit this chapter on supersonic flow. I had expected the physics to just point me in the right direction but it does not. So let me spell out what I am concerned about.
The first is that I do not know whether the behaviour of a flow of air at supersonic speed round a stationary model in a supersonic tunnel is the same as the behaviour of air when a body moves at the same supersonic speed through still air. The flow in a supersonic wind tunnel takes place in a convergent-divergent nozzle and the working section is a part of the divergence. If a model is installed in the working section there will inevitably be a shock wave formed at the forward end whatever shape it may be. Suppose that the nose is fairly blunt. The shock wave will span the whole section produce the same result as a plane shock wave in an unobstructed nozzle and the whole of the model will be in subsonic flow and no other shock wave can form subsequently. This does not preclude the formation of compression and expansion waves in high-speed, subsonic flow. Now suppose that the nose is pointed. The shock wave that would form would be like the wave round the bullet and may well decay into an acoustic wave before it reaches the tunnel walls. In the immediate vicinity of the model the flow through the shock wave at right angles to the wave will change to be subsonic but this will not happen in the acoustic wave. I think that this leaves the flow in an interesting condition that may or may not lead to the shock wave extending right across the working section and reducing all the flow to subsonic flow. This would not happen in the case of the same object moving through still air.
There is always the possibility that I have misinterpreted the Schlieren pictures and that there is no acoustic wave but a shock wave extending through the still air but the mechanics of that idea seems to be quite untenable as it would involve so much energy.
I have a second problem. Imagine a supersonic aeroplane flying at its design speed. A shock wave will form at its nose whatever that may be. Suppose that it is a pitôt tube and the shock wave will be small compared to the shock wave that would form on the nose of the fuselage in the absence of the pitôt tube. Do we get two shock waves if there is a pitôt tube? Certainly, just behind the nose of the pitôt tube, the flow will be less than where is the local temperature but it will soon decay to an acoustic wave. Then a second shock wave could form on the nose of the fuselage and this will be of a much larger size. What I cannot decide is whether this second wave affects the engine intake ducts. Do they working subsonic or supersonic flow?
To a reader this end piece may seem to be unusual but I cannot find any way to resolve these problems but I can alter this text easily in the event of authoritative information.