The only application for un-swept wings in supersonic flight is in military hardware such as missiles that have no take-off and landing requirements. The wings and other flight surfaces are normally very small and used only once.
The basic sections that are used are the double wedge shown in figure 14-14 and the double arc.
I have drawn the wave pattern for a double wedge in figure 14-22 for about Mach 2. There is a shock wave off the leading edge and a compression wave from the trailing edge and expansion waves off the apexes. The bow shock wave and the trailing edge compression waves are generated in different ways as we have seen with the bullet. They are now not conical like that for a bullet but shaped like a folded piece of paper.
At the apex the flow breaks away but the inevitable pressure gradient that forms just after the apex bends the flow progressively in the expansion wave. Then the compression wave at the trailing edge forms in the collision between two flows along the after part of the wing.
I
have drawn this double wedge wing at zero angle of attack but, if the wing is
to lift it will have to be set at some small angle to the flight path and that
will make the flow pattern asymmetrical.
It is not at all a suitable shape for subsonic lift, nor are the acoustic waves desirable for either civil or military use. Thin wings, that might be seen as derivations from subsonic wing sections, have been designed for “ordinary” supersonic flight.