One of the illustrations used in a current Comsol Multiphysics ad.
visualizes flow in a duct.
High-Mach Number Fluid Flow
The new High-Mach Number Fluid Flow interface applies when the flow
velocity is large enough to introduce significant changes in the density
and temperature of the fluid; the thermodynamic properties of the fluid
are coupled. Appreciable changes in the fluid properties are encountered
as the flow velocity approaches, or exceeds, the speed sound. As a rule
of thumb, velocities greater than 0.3 times the speed of sound are
considered to be high Mach number flows. Important applications include:
nozzles, pipe networks, valves, and aerodynamic phenomena
The picture shows a benchmark model for turbulent compressible flow in a
two-dimensional converging-diverging diffuser (Sajben diffuser). The
flow enters the diffuser at a velocity of Ma = 0.46, accelerates through
the converging part, and reaches supersonic conditions at the throat of
the diffuser. The supersonic flow is terminated with a shock in the
diverging part, after which the flow is subsonically decelerated.