Computational fluid-dynamic modelling of two-phase compressible flows of carbon dioxide in supercritical conditions

Compressible two-phase flows of carbon dioxide in supercritical thermodynamic conditions are encountered in many applications, e.g. ejectors for refrigeration and compressors for power production and carbon capture and sequestration to name a few. Alongside the phase change, transonic/supersonic flow regimes and non-ideal effects also add additional complexities in the simulations of such flows. In this work, we investigate cavitating and condensing flows of carbon dioxide via numerical simulations based on the two-fluid concept, applying both a mixture model and a barotropic model. In the mixture model, the phase change is modelled with an extra transport equation for the mass of the dispersed phase and a source term introduced via a penalty formulation. The barotropic model reproduces the pressure-density relation of the mixture along the upstream isentrope. Both the models assume thermodynamic and mechanical equilibrium between phases and exclude meta-stability effects. All results are compared against experimental data taken from literature and the main numerical issues of the models are discussed in detail. The agreement between the simulations and the experiments is remarkable qualitatively and quantitatively, resulting in the range 2%-4% for pressure and below 1% for temperature in terms of weighted mean absolute percentage error for supercritical expansions, even though suggesting a further margin of improvement in the physical modelling, especially for subcritical expansions. Finally, we show that the barotropic model yields comparable predictions of the expansion processes at a lower computational cost and with an improved solver robustness.