When a gas is flowing over a body, or a body is moving in the fluid, disturbances will
be generated.
These disturbances will propagate within the flow and interact with other parts of the
body.
Such flow disturbances are called waves and their motion is referred to as wave motion.
The wave motion has a significant effect on the dynamics of gas flow because it can profoundly
affect the forces and thermal loads on the body in the flow environment.
In general, the wave motion in compressible flows is complicated and its fundamental physics
and mechanisms need to be understood and correctly described by predictive methods.
For this purpose, the one-dimensional governing equations of gas dynamics and derived relations
will be utilized for the analysis of wave motion in this course.
But before diving into these mathematical formulations and equations, let us first talk about the basic
features of two different compressible waves, that are - shock waves and expansion waves.
As mentioned earlier, compressible waves are essentially the disturbances in the flow.
The shock wave is a type of flow disturbance that propagates through the gas faster than
the local speed of sound.
Consider an object moving through a fluid at a supersonic speed.
Waves due to the motion of this object cannot affect upstream because they propagate at
the speed of sound and are therefore slower than the object itself.
As a result, these waves coalesce a short distance in front of the object and form a
very thin wave front.
This is called a shock wave or simply a shock.
The lag of wave fronts behind the object restricts these waves into a cone-shaped region, which
is called a Mach cone.
The wave fronts at the edge of this Mach cone coalesce into a shock wave that is the downstream
part of the front, or bow, shock.
Now, if you are standing outside of the Mach cone, you will not hear any sound.
This region is called the zone of silence.
There are three different types of shock waves.
The normal shocks are oriented perpendicular to the flow direction whereas the oblique
shocks are inclined with the flow.
A bow shock is generally positioned upstream, away from the stagnation point of the body,
and arcs away from its position as an oblique shock.
Please note that more than one type of shock waves can appear simultaneously in the flow.
Let us now look the fundamental characteristics of shock waves.
Firstly, the thickness of a shock wave is very small.
According to the measurements, a typical thickness of a shock is on the order of magnitude of
the mean free path of molecules.
Moreover, Shock waves result in a sudden change in flow properties across them.
For example, the magnitude of static properties such as pressure, temperature and density
increase sharply across the shocks and so does the flow entropy.
On the contrary, the Mach number and total pressure of the flow decreases suddenly downstream
of the shock.
Because of this reason, the shock waves are treated as discontinuities in the continuum
description of gas dynamics.
Besides supersonic flow, a sudden release of energy is another mechanism of generating
a shock wave.
In this scenario, the energy is dissipated into the ambient environment through an expanding
shock.
A subsonic flow is present at the downstream side of the shock.
One typical example of this type of shock is blast waves that are created by massive explosions.
However, the released energy does not have to be huge to generate a shock.
It just needs to be released suddenly, for instance, within a few microseconds.
One interesting example is the “popping” sound you hear when popping an air balloon
or stomping on a packaging air pillow.
That popping sound is the shock wave hitting your eardrums.
A similar example is the bursting sound or shock wave generated when a firecracker suddenly
explodes.
Another type of compressible wave we are going to cover in this lesson is the expansion wave.
Expansion waves, also frequently called expansion fans, are formed when a supersonic flow meets
a sudden expanding area.
For example when the flow turns around a convex corner.
As the flow turns away from itself, a series of expansion waves are formed at the corner
and expands away like a fan.
Just like shock waves, the flow properties change at the downstream side of the expansion
fan.
As we can see the Mach number increases but at the same time, the static pressure, temperature,
and density decrease.
The expansion fan is basically a mechanism for supersonic flow to expand without “violating” laws
of thermodynamics.
So, in this lesson we covered the basic concepts of waves in compressible flows and two different
compressible waves, i.e., shocks and expansion waves were described.
We will get into more details on these waves in the following lessons of this course.