Compressible Flows

Compressibility effects are encountered in gas flows at high velocity and/or in which there are large pressure variations. When the flow velocity approaches or exceeds the speed of sound in the gas or when the pressure change in the system (Δp/p) is large, the variation of the gas density with pressure has a significant impact on the flow velocity, pressure, and temperature.

Compressible flows can be characterized by the value of the Mach number (M≡u/c, where c is the speed of sound in the gas). When the Mach number is less than 1.0, the flow is termed subsonic. At Mach numbers much less than 1.0 (M 0.1 or so), compressibility effects are negligible and the variation of the gas density with pressure can safely be ignored in your flow modeling. As the Mach number approaches 1.0 (which is referred to as the transonic flow regime), compressibility effects become important. When the Mach number exceeds 1.0, the flow is termed supersonic, and may contain shocks and expansion fans which can impact the flow pattern significantly.

Compressible flows are described by the standard continuity and momentum equations and the treatment of density as detailed below.

The compressible form of the gas law (the ideal gas law) is written in the following form:

ρ=(pop+p)/(RT/Mw)

Where pop is the operating pressure, p is the local static pressure relative to the operating pressure, R is the universal gas constant, and Mw is the molecular weight. The temperature, T, will be computed from the energy equation.

Guidelines and Best Practices

  • Discovery provides compressible flow modeling capabilities for subsonic internal flows. However, there may be cases where the flow becomes transonic or supersonic due to a flow constriction in the fluid domain. You can use Discovery to solve internal flow applications such as high-speed gas flows or gas flows with large temperature variations, flows through orifices or other flow constrictions, and exhaust systems with high temperature ranges. External aerodynamics applications, supersonic and hypersonic flows, and compressible liquids should be avoided.
  • For simulations including multiple fluids, all gases in the simulation will be treated as compressible using variable density with the ideal gas law. All liquids in a simulation with multiple fluids are treated as incompressible, regardless of whether compressibility is turned on.
  • Buoyancy is not compatible with compressible flow. Turn off the Include buoyancy selection in the Gravity HUD to solve a compressible flow simulation.
  • Mass flow rate specification at a flow inlet is not supported in compressible flow simulations in Explore. You can specify pressure at the flow inlet, switch to incompressible flow, or use the Refine stage instead.
  • Mass flow rate specification at a flow outlet is not supported in compressible flow simulations in Explore. You can specify pressure at the flow outlet or use the Refine stage instead.
  • Velocity specification at a flow inlet is not supported in compressible flow simulations. You can specify pressure at the flow inlet instead (or mass flow rate in Refine), or switch to incompressible flow.
  • Velocity specification at a flow outlet is not supported in compressible flow simulations in Explore. You can specify pressure at the flow outlet or use the Refine stage instead.
  • In Refine, if a domain with a compressible fluid is excluded from the simulation, after subsequent inclusion it is incompressible.