Thermodynamics

852 | ThermodynamicsFIGURE 17–36Schlieren image of a small model ofthe space shuttle Orbiter being testedat Mach 3 in the supersonic windtunnel of the Penn State GasDynamics Lab. Several oblique shocksare seen in the air surrounding thespacecraft.Photo by G. S. Settles, Penn State University. Usedby permission.bObliqueshockMa 1Ma 1Ma 2FIGURE 17–37An oblique shock of shock angle bformed by a slender, two-dimensionalwedge of half-angle d. The flow isturned by deflection angle udownstream of the shock, and theMach number decreases.duOblique ShocksNot all shock waves are normal shocks (perpendicular to the flow direction).For example, when the space shuttle travels at supersonic speedsthrough the atmosphere, it produces a complicated shock pattern consistingof inclined shock waves called oblique shocks (Fig. 17–36). As you cansee, some portions of an oblique shock are curved, while other portions arestraight.First, we consider straight oblique shocks, like that produced when a uniformsupersonic flow (Ma 1 1) impinges on a slender, two-dimensionalwedge of half-angle d (Fig. 17–37). Since information about the wedgecannot travel upstream in a supersonic flow, the fluid “knows” nothingabout the wedge until it hits the nose. At that point, since the fluid cannotflow through the wedge, it turns suddenly through an angle called theturning angle or deflection angle u. The result is a straight oblique shockwave, aligned at shock angle or wave angle b, measured relative to theoncoming flow (Fig. 17–38). To conserve mass, b must obviously begreater than d. Since the Reynolds number of supersonic flows is typicallylarge, the boundary layer growing along the wedge is very thin, and weignore its effects. The flow therefore turns by the same angle as the wedge;namely, deflection angle u is equal to wedge half-angle d. If we take intoaccount the displacement thickness effect of the boundary layer, the deflectionangle u of the oblique shock turns out to be slightly greater thanwedge half-angle d.Like normal shocks, the Mach number decreases across an oblique shock,and oblique shocks are possible only if the upstream flow is supersonic.However, unlike normal shocks, in which the downstream Mach number isalways subsonic, Ma 2 downstream of an oblique shock can be subsonic,sonic, or supersonic, depending on the upstream Mach number Ma 1 and theturning angle.