fluid_mechanics

590 Chapter 11 ■ Compressible Flow
When the point source and the fluid are stationary, the pressure wave pattern is symmetrical
1Fig. 11.3a2 and an observer anywhere in the pressure field would hear the same sound frequency
from the point source. When the velocity of the point source 1or the fluid2 is very small in comparison
with the speed of sound, the pressure wave pattern will still be nearly symmetrical. The
speed of sound in an incompressible fluid is infinitely large. Thus, the stationary point source and
stationary fluid situation are representative of incompressible flows. For truly incompressible flows,
the communication of pressure information throughout the flow field is unrestricted and instantaneous
1c 2.
F l u i d s i n t h e N e w s
Pistol shrimp confound blast detectors Authorities are on the
trail of fishermen in Southeast Asia and along Africa’s east
coast who illegally blast coral reefs to rubble to increase their
catch. Researchers at Hong Kong University of Science and
Technology have developed a method of using underwater microphones
(hydrophones) to pick up the noise from such blasts.
One complicating factor in the development of such a system is
the noise produced by the claw-clicking pistol shrimp that live
on the reefs. The third right appendage of the 2-in.-long pistol
shrimp is adapted into a huge claw with a moveable finger that
can be snapped shut with so much force that the resulting sound
waves kill or stun nearby prey. When near the hydrophones, the
shrimp can generate short-range shock waves that are bigger
than the signal from a distant blast. By recognizing the differences
between the signatures of the sound from an explosion
and that of the pistol shrimp “blast,” the scientists can differentiate
between the two and pinpoint the location of the illegal
blasts.
V11.2 Jet noise
90
a
60
a
30
0
1 1.5 2 2.5 3
Ma
When the point source moves in fluid at rest 1or when fluid moves past a stationary point
source2, the pressure wave patterns vary in asymmetry, with the extent of asymmetry depending
on the ratio of the point source 1or fluid2 velocity and the speed of sound. When Vc 6 1, the wave
pattern is similar to the one shown in Fig. 11.3b. This flow is considered subsonic and compressible.
A stationary observer will hear a different sound frequency coming from the point source depending
on where the observer is relative to the source because the wave pattern is asymmetrical.
We call this phenomenon the Doppler effect. Pressure information can still travel unrestricted
throughout the flow field, but not symmetrically or instantaneously.
When Vc 1, pressure waves are not present ahead of the moving point source. The flow
is sonic. If you were positioned to the left of the moving point source, you would not hear the
point source until it was coincident with your location. For flow moving past a stationary point
source at the speed of sound 1Vc 12, the pressure waves are all tangent to a plane that is perpendicular
to the flow and that passes through the point source. The concentration of pressure
waves in this tangent plane suggests the formation of a significant pressure variation across the
plane. This plane is often called a Mach wave. Note that communication of pressure information
is restricted to the region of flow downstream of the Mach wave. The region of flow upstream of
the Mach wave is called the zone of silence and the region of flow downstream of the tangent plane
is called the zone of action.
When V 7 c, the flow is supersonic and the pressure wave pattern resembles the one depicted
in Fig. 11.3d. A cone 1Mach cone2 that is tangent to the pressure waves can be constructed
to represent the Mach wave that separates the zone of silence from the zone of action
in this case. The communication of pressure information is restricted to the zone of action.
From the sketch of Fig. 11.3d, we can see that the angle of this cone, a, is given by
sin a c V
1 Ma
(11.39)
V11.3 Speed boat
This relationship between Mach number, Ma, and Mach cone angle, a, shown by the figure in
the margin, is valid for Vc 7 1 only. The concentration of pressure waves at the surface of
the Mach cone suggests a significant pressure, and thus density, variation across the cone surface.
(See the photograph at the beginning of this chapter.) An abrupt density change can be
visualized in a flow field by using special optics. Examples of flow visualization methods include
the schlieren, shadowgraph, and interferometer techniques 1see Ref. 42. A schlieren photo
of a flow for which V 7 c is shown in Fig. 11.4. The air flow through the row of compressor
blade airfoils is as shown with the arrow. The flow enters supersonically 1Ma 1 1.142 and