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Shock Reflection

Reflection of shock wave from the wall is mainly of two types, regular reflection and irregular or Mach reflection. These reflection patterns are shown in Fig. 1 and Fig. 2.

The shock that originates from the corner of the compression wedge makes an angle β with the free stream velocity vector. Flow behind this shock gets deflected by angle θ and becomes parallel to the wedge. However, when the shock hits the top wall, the part of the flow which was parallel to the top wall, upstream of the shock, also gets deflected by angle θ. Hence the flow downstream of the shock does not remain parallel to the top wall. This contradicts the necessary condition of formation of shock; hence the primary shock gets reflected from the top wall to cancel out the deflection of the flow and to make it parallel to the wall. In this process shock reflection can be observed as the reflection of light ray, however the incident and reflection angle of shock are dependent on shock upstream Mach number. Therefore this reflection is called as the regular reflection. Typical pressure deflection diagram for the streamline ABC is shown in Fig. 3.

Providing equal and opposite deflection to the flow as that provided by incident shock is the objective of reflected shock. However possibility of such a deflection behind the reflected shock depends on the Mach number behind the incident shock or Mach number upstream to the reflected shock (in region B of Fig. 3). If the deflection required is more than the maximum possible deflection for that Mach number then the reflection of shock does not remain as regular reflection since the reflected shock gets detached from the wall.

Mach Reflection

Typical Mach reflection situation is shown in Fig 2. Let’s understand the reason for deviation from regular reflection to Mach reflection. We know from Fig. 1 that the presence of reflected shock is mainly to deflect the flow in region B and make it parallel with the wall. The amount of this flow deflection expected from the reflected shock is same as that from the primary or incident shock. However, regular reflection ensures that this deflection is less than the maximum possible defection corresponding to the Mach number in region B in the same figure. A situation has been shown in Fig. 3 which shows the possibility of where the expected deflection using reflected shock more than the maximum deflection possible corresponding to Mach number in region B.

Therefore, since reflected shock cannot provide the necessary deflection to the flow so as to make it parallel to the wall, the incident or primary shock does not reflect like the ray of light or regular reflection. This is the main reason for the Mach reflection shown in Fig 2.