1.3 Flow Regimes Based on Mach Number#
The Mach number determines the qualitative behavior of a flow field and its interaction with surrounding geometry. Compressible flow regimes are classified as follows:
Subsonic Flow (\(M < 1\))
Pressure disturbances can propagate upstream.
For \(M < 0.3\), compressibility is negligible.
Governing equations are elliptic in nature.
Typically smooth and predictable flow.
Transonic Flow (\(0.8 < M < 1.2\))
Contains both subsonic and supersonic zones.
Local shock waves and flow separation are common.
Highly sensitive to geometry and operating conditions.
Mixed-type governing equations (elliptic + hyperbolic).
Supersonic Flow (\(M > 1\))
Disturbances cannot propagate upstream.
Shock waves and expansion fans dominate flow structure.
Governing equations are hyperbolic.
Strong compressibility effects present.
Hypersonic Flow (\(M > 5\))
Exhibits strong shock–boundary layer interactions.
Significant high-temperature effects:
Vibrational excitation
Molecular dissociation
Chemical reactions
Requires thermochemical and viscous modeling.
Flow Regime
Regime |
Mach Number |
Key Characteristics |
|---|---|---|
Subsonic |
\(M < 1\) |
No shocks, upstream communication, low compressibility |
Transonic |
\(0.8 < M < 1.2\) |
Local shocks, sensitivity, mixed-type PDEs |
Supersonic |
\(M > 1\) |
Shock waves, expansion fans, hyperbolic behavior |
Hypersonic |
\(M > 5\) |
Strong shocks, high-temperature effects, real-gas physics –> |