Detached Shock Wave in Front of a Blunt Body

The curved bow shock which stands in front of a blunt body in a supersonic flow is sketched in Figure 8.1. We are now in a position to better understand the properties of this bow shock, as follows.

The flow in Figure 8.1 is sketched in more detail in Figure 9.21. Here, the shock wave stands a distance 8 in front of the nose of the blunt body; 8 is defined as the shock detachment distance. At point a, the shock wave is normal to the upstream flow; hence, point a corresponds to a normal shock wave. Away from point a, the shock wave gradually becomes curved and weaker, eventually evolving into a Mach wave at large distances from the body (illustrated by point e in Figure 9.21).

A curved bow shock wave is one of the instances in nature when you can observe all possible oblique shock solutions at once for a given freestream Mach number M|. This takes place between points a and e. To see this more clearly, consider the в-Р-М diagram sketched in Figure 9.22 in conjunction with Figure 9.21. In Figure 9.22, point a corresponds to the normal shock, and point e corresponds to the Mach wave. Slightly above the centerline, at point b in Figure 9.21, the shock is oblique but pertains to the strong shock-wave solution in Figure 9.22. The flow is deflected slightly upward behind the shock at point b. As we move further along the shock, the wave angle becomes more oblique, and the flow deflection increases until we encounter point c. Point c on the bow shock corresponds to the maximum deflection angle shown in Figure 9.22. Above point c, from c to e, all points on the shock correspond to the weak shock solution. Slightly above point c, at point c’, the flow behind the shock becomes sonic. From a to c the flow is subsonic behind the bow shock; from c’ to e, it is supersonic. Hence, the flow field between the curved bow shock and the blunt body is a mixed region of both subsonic and supersonic flow. The dividing line between the subsonic and supersonic regions is called the sonic line, shown as the dashed line in Figure 9.21.

The shape of the detached shock wave, its detachment distance <5, and the com­plete flow field between the shock and the body depend on M and the size and shape

of the body. The solution of this flow field is not trivial. Indeed, the supersonic blunt – body problem was a major focus for supersonic aerodynamicists during the 1950s and 1960s, spurred by the need to understand the high-speed flow over blunt-nosed missiles and reentry bodies. Indeed, it was not until the late 1960s that truly suffi­cient numerical techniques became available for satisfactory engineering solutions of supersonic blunt-body flows. These modem techniques are discussed in Chapter 13.