Compressible flows are typically characterized by the total
pressure 
and total
temperature 
of the flow.
For an ideal gas, these quantities can be related to the static pressure
and temperature by the following:
 | (1–29) |
For constant 
, Equation 1–29 reduces
to
 | (1–30) |
 | (1–31) |
These relationships describe the variation of the static pressure
and temperature in the flow as the velocity (Mach number) changes
under isentropic conditions. For example, given a pressure ratio from
inlet to exit (total to static), Equation 1–30 can
be used to estimate the exit Mach number that would exist in a one-dimensional
isentropic flow. For air, Equation 1–30 predicts
a choked flow (Mach number of 1.0) at an isentropic pressure ratio, 
,
of 0.5283. This choked flow condition will be established at the point
of minimum flow area (for example, in the throat of a nozzle). In
the subsequent area expansion the flow may either accelerate to a
supersonic flow in which the pressure will continue to drop, or return
to subsonic flow conditions, decelerating with a pressure rise. If
a supersonic flow is exposed to an imposed pressure increase, a shock
will occur, with a sudden pressure rise and deceleration accomplished
across the shock.
Compressible flows are described by the standard continuity and momentum equations solved by Ansys Fluent, and you do not need to enable any special physical models (other than the compressible treatment of density as detailed below). The energy equation solved by Ansys Fluent correctly incorporates the coupling between the flow velocity and the static temperature, and should be enabled whenever you are solving a compressible flow. In addition, if you are using the pressure-based solver, you should enable the viscous dissipation terms in Equation 5–1, which become important in high-Mach-number flows.
For compressible flows, the ideal gas law is written in the following form:
 | (1–32) |
where 
is the operating
pressure defined in the Operating Conditions Dialog Box, 
is the local static pressure
relative to the operating pressure, 
is the universal gas constant,
and 
is the molecular weight. The
temperature, 
, will be computed from the energy equation.
Some compressible flow problems involve fluids that do not behave as ideal gases. For example, flow under very high-pressure conditions cannot typically be modeled accurately using the ideal-gas assumption. Therefore, the real gas model described in Real Gas Models in the User's Guide should be used instead.