373
11
Hypersonic Flow
Introduction
Hypersonic ow was loosely dened in Chapter 1 as ow in which the Mach number is
greater than about 5. No real reasons were given at that point as to why supersonic ows
at high Mach numbers were different from those at lower Mach numbers. However, it is
the very existence of these differences that really denes hypersonic ow. The nature of
these hypersonic ow phenomena, and therefore the real denition of “hypersonic ow,”
will be presented in the next section.
Hypersonic ows have, up to the present, mainly been associated with the reentry of
orbiting and other high altitude bodies into the atmosphere. For example, a typical Mach
number with altitude variation for a reentering satellite is shown in Figure 11.1. It will be
seen from this gure that because of the high velocity that the craft had to possess to keep
it in orbit, very high Mach numbers—values that are well into the hypersonic range—exist
during reentry.
Discussions and studies of passenger aircraft that can y at hypersonic speeds at
high altitudes have also been undertaken. A typical proposed such vehicle is shown in
Figure 11.2.
This chapter, which presents a brief introduction to hypersonic ow, is the rst of three
interrelated chapters. One of the characteristics of hypersonic ow is the presence of so-
called high-temperature gas effects, and these effects will be discussed more fully in the
next chapter. Hypersonic ow is also conventionally associated with high altitudes where
the air density is very low, and “low-density ows” will be discussed in Chapter 13.
Characteristics of Hypersonic Flow
As mentioned above, hypersonic ows are usually loosely described as ows at very high
Mach numbers, say greater than about 5. However, the real denition of hypersonic ows
is that they are ows at such high Mach numbers that phenomena occur that do not exist
at low supersonic Mach numbers. These phenomena are discussed in this section.
One of the characteristics of hypersonic ow is the presence of an interaction between
the oblique shock wave generated at the leading edge of the body and the boundary layer
on the surface of the body. Consider the oblique shock wave formed at the leading edge of
a wedge in a supersonic ow as shown in Figure 11.3.
374 Introduction to Compressible Fluid Flow
100
80
60
40
20
0
0
5
10
15
20
25
30
M
Altitude (m × 10
3
)
FIGURE 11.1
Typical variation of Mach number with altitude during reentry.
FIGURE 11.2
Proposed hypersonic passenger aircraft. (Copyright © Boeing.)
Shock wave
We
dge
M
FIGURE 11.3
Flow over a wedge.
375Hypersonic Flow
As the Mach number increases, the shock angle decreases and the shock therefore lies
very close to the surface at high Mach numbers. This is illustrated in Figure 11.4.
Because the shock wave lies close to the surface at high Mach numbers, there is an inter-
action between the shock wave and the boundary layer on the wedge surface. To illustrate
this shock wave–boundary layer interaction, consider the ow of air over a wedge having
a half-angle of 5° at various Mach numbers. The shock angle for any selected value of
M can be obtained from the oblique shock relations or charts or using the software (see
Chapter 6). The angle between the shock wave and the wedge surface is then given by the
difference between the shock angle and the wedge half-angle. The variation of this angle
with Mach number is shown in Figure 11.5.
It will be seen from Figure 11.5 that as the Mach number increases, the shock wave lies
closer and closer to the surface. Further, hypersonic ow normally only exists at relatively
High Mach number
Low Mach number
MM
FIGURE 11.4
Shock angle at low and high supersonic Mach number ow over a wedge.
20
15
10
5
0
0
5
10
15
20
Angle between shock wave and surface
Mach number
Turning angle = 5°
FIGURE 11.5
Variation of angle between shock wave and wedge surface with Mach number for ow over a wedge.
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