Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Oblique Shocks

Not all shock waves are normal shocks (perpendicular to the flow direc-

tion). For example, when the space shuttle travels at supersonic speeds

through the atmosphere, it produces a complicated shock pattern consisting

of inclined shock waves called oblique shocks(Fig. 17–36). As you can

see, some portions of an oblique shock are curved, while other portions are

straight.

First, we consider straight oblique shocks, like that produced when a uni-

form supersonic flow (Ma 1 
1) impinges on a slender, two-dimensional

wedge of half-angle d(Fig. 17–37). Since information about the wedge

cannot travel upstream in a supersonic flow, the fluid “knows” nothing

about the wedge until it hits the nose. At that point, since the fluid cannot

flow throughthe wedge, it turns suddenly through an angle called the

turning angleor deflection angleu. The result is a straight oblique shock

wave, aligned at shock angleor wave angleb, measured relative to the

oncoming flow (Fig. 17–38). To conserve mass, b must obviously be

greater than d. Since the Reynolds number of supersonic flows is typically

large, the boundary layer growing along the wedge is very thin, and we

ignore its effects. The flow therefore turns by the same angle as the wedge;

namely, deflection angle uis equal to wedge half-angle d. If we take into

account the displacement thickness effect of the boundary layer, the deflec-

tion angle uof the oblique shock turns out to be slightly greater than

wedge 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 is

always subsonic, Ma 2 downstream of an oblique shock can be subsonic,

sonic, or supersonic, depending on the upstream Mach number Ma 1 and the

turning angle.

852 | Thermodynamics

FIGURE 17–36

Schlieren image of a small model of

the space shuttle Orbiterbeing tested

at Mach 3 in the supersonic wind

tunnel of the Penn State Gas

Dynamics Lab. Several oblique shocks

are seen in the air surrounding the

spacecraft.

Photo by G. S. Settles, Penn State University. Used

by permission.

d

b

u

Ma 1

Ma 1

Ma 2

Oblique

shock

FIGURE 17–37

An oblique shock of shock angleb

formed by a slender, two-dimensional

wedge of half-angle d. The flow is

turned by deflection angleu

downstream of the shock, and the

Mach number decreases.

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