As an object moves through a gas, the gas molecules near the object
are disturbed and move around the object.
Aerodynamic
forces are generated between the gas and the object and the
magnitude of these forces depend on many factors associated
with the object and the gas. The
speed of the object relative to the gas
introduces many significant effects.
We characterize the speed of the object by
a non-dimensional number called the
Mach number;
the Mach number is the ratio of the speed of the
object to the
speed of sound
in the gas. The speed of "sound" is actually the
speed of transmission for small,
isentropic
disturbances in the gas.
As shown on the figure,
the physical state of the gas depends on the Mach number of the object.
In our discussions, we will use the Mach number of the object and
the Mach number of the flow interchangeably.
If we travel with the object as it moves through the air, the
air moves past the object at the speed of the object. So, the
Mach number of the object and the Mach number of the flow are
the same number.
For a moving flow of gas,
there are several different values of the
temperature of the gas.
The static temperature
is the temperature of the gas if it had no ordered motion
and was not flowing.
From
kinetic theory,
static temperature is related to the average kinetic energy
of the random motion of the molecules of the gas. The value
of the static temperature of air depends on the
altitude.
For a moving flow, there is a dynamic temperature
associated with the kinetic energy of ordered motion of the flow
in the same way that the static temperature is related to the
kinetic energy of the random motion of the molecules.
The total temperature is
the sum of the static temperature and the dynamic temperature.
and the value of total temperature depends on the Mach number of the flow.
If the moving flow is isentropically brought to
a halt on the body, we measure a stagnation temperature.
The stagnation temperature is important because it is the temperature
that occurs at a stagnation point on the object.
Because the total temperature does not change through a
shock wave, the stagnation temperature and
and the total temperature have the same value at a stagnation point.
The red line on the figure shows the general trend of the
stagnation temperature of air as a function of the Mach number.
A more detailed relation for Mach numbers from zero to
eight is shown on a
separate page.
In the process of slowing the flow, the gas is heated due to
the kinetic energy of flow. The amount of the heating depends
on the
specific heat capacity
of the gas.
If the specific heat capacity is a constant value, the gas is said
to be calorically perfect and if the specific heat capacity
changes, the gas is said to be calorically imperfect.
At subsonic and low supersonic
Mach numbers, air is calorically perfect.
But under low hypersonic conditions, air is
calorically imperfect.
Derived flow variables, like the
speed of sound and the
isentropic flow relations
are slightly different for a calorically imperfect gas
than the conditions predicted for a calorically perfect gas
as described below.
On this page, we have indicated some important real gas effects
that occur as the Mach number of the flow increases.
Air
is a mixture of gases with the major
components
being diatomic nitrogen and diatomic oxygen.
For very low Mach numbers, the
density
of the air is a constant. But as the Mach number
increases into the supersonic regime,
some of the energy associated with the motion of the object
compresses
the gas and changes the density from its static value.
Compressibility effects,
such as
shock waves, are
present in supersonic airflows.
As the Mach number increases into the low hypersonic regime, some of the energy
of the flow excites the vibrational modes of the diatomic
molecules. The molecules vibrate as illustrated in this computer
model:
Click on the slider bar, hold the mouse button down and drag to the
right to increase the temperature.
Both the nitrogen and the oxygen experience vibrational excitation. There
are mathematical models determined from statistical mechanics and the
As the Mach and temperature are further increased, some of the energy
of the flow goes into breaking the
molecular bonds holding the diatomic nitrogen and oxygen.
We then have a mixture of dissociated atomic nitrogen and
oxygen which is both calorically imperfect and thermally imperfect.
A gas that follows the ideal
equation of state is said to be
thermally perfect and a gas that does not follow the ideal
equation of state is thermally imperfect.
With even more speed and temperature, some of the electrons surrounding
the nitrogen and oxygen atoms are stripped free to produce a mixture of
ionized nitrogen, oxygen, and free electrons. The resulting
plasma
can conduct an electric current and is influenced by electro-magnetic forces.
