A multicomponent real-fluid fully compressible four-equation model for two-phase flow with phase change

A fully compressible four-equation model for multicomponent two-phase flow coupled with a real-fluid phase equilibrium-solver is suggested. It is composed of two mass, one momentum, and one energy balance equations under the mechanical and thermal equilibrium assumptions. The multicomponent characteristics in both liquid and gas phases are considered. The thermodynamic properties are computed using a composite equation of state (EoS), in which each phase follows its own Peng-Robinson (PR) EoS in its range of convexity, and the two-phase mixtures are connected with a set of algebraic equilibrium constraints. The drawback of complex speed of the sound region for the two-phase mixture is avoided using this composite EoS. The phase change is computed using a phase equilibrium-solver, in which the phase stability is examined by the Tangent Plane Distance approach; an isoenergetic-isochoric flash including an isothermal-isobaric flash is applied to determine the phase change. This four-equation model has been implemented into an in-house IFP-C3D software. Extensive comparisons between the four-equation model predictions, experimental measurements in flash boiling cases, and available numerical results were carried out, and good agreements have been obtained. The results demonstrated that this four-equation model can simulate the phase change and capture most real-fluid behaviors for multicomponent two-phase flows. Finally, this validated model was applied to investigate the behaviors of n-dodecane/nitrogen mixtures in one-dimensional shock and double-expansion tubes. The complex wave patterns were unraveled, and the effects of dissolved nitrogen and the volume translation in PR EoS on the wave evolutions were revealed. A three-dimensional transcritical fuel injection is finally simulated to highlight the performance of the proposed four-equation model for multidimensional flows.