Equation of State

The equations of state are constitutive relations that describe the relation between the density and the internal energy to the two basic thermodynamic variables pressure and temperature.

Simcenter STAR-CCM+ provides various Equation of State models to compute the density and the density derivatives with respect to temperature and pressure. For example, the Ideal Gas model calculates the density using the ideal gas equation. However, at high pressure and low temperature, the p-v-T behavior of real gases deviates from that predicted by the ideal gas equation. This change of behavior results from the molecules of the gas taking up a significant portion of the total volume as the gas density increases. In addition, intermolecular attractive forces become increasingly important. For this reason, Simcenter STAR-CCM+ provides various Real Gas models that allow you to take into account non-ideal behavior such as compressibility effects, variable specific heat, van der Waals forces, and non-equilibrium thermodynamic effects. The real gas models are suitable for modeling complex chemistry combustion applications at high pressures and low temperatures in transcritical and supercritical environments, such as in liquid rocket engines. These applications can have flow regions in which the equation of state departs substantially from ideal gas behavior.

Thermal non-equilibrium occurs at high temperatures and low densities, where the vibrational/electronic energy modes become active yet the density is low enough such that equilibration does not occur. Examples of problems include high-speed atmospheric re-entry flows and nozzles. For problems in this regime, Simcenter STAR-CCM+ provides a Thermal Non-Equilibrium model that allows you to capture temperature profiles and heating accurately. The principal application for this model is hypersonic flows (mainly atmospheric re-entry). Nozzle flows where the effects of vibrational freezing are important can also be simulated.