Handbook of Compressible Aerodynamics

Chapter 14

Oblique Shock Wave and Shock Polar

14.1. General solution

Based on the results obtained for the normal shock, we will reconsider the problem of oblique shock (see Figure 13.3). We recall the equations given in the previous chapter:

We note that in these equations (except the second), the only intervention is by the normal components V_n1 and V_n2 of the upstream and downstream velocities. Thus, written with normal velocities, the oblique shock equations are identical to the equations of the normal shock. It is thus possible to use relations established for the normal shock under the condition that we consider the flow arriving normally at the shock wave. In particular, the upstream Mach number here is the normal Mach number, defined from the component V_n1 :

In a similar way, the downstream Mach number M₂ is replaced by the normal Mach number, so that:

We remember that σ is the shock angle with respect to the upstream velocity and φ the deflection of the velocity vector across the shock. Without repeating them all, the formulas giving the variations of various quantities become:

The relation between the normal Mach numbers:

which gives:

where the downstream normal Mach ...