A Mathematical Model For the Simulation of Two-phase Compression in Thermal Non-equilibrum

When a pure refrigerant in a two-phase state undergoes a reduction of volume, the volume of the vapour phase is going to follow closely the total reduction of volume, while the liquid phase volume variation is negligible in comparison to this total reduction. This variation of
vapour volume induces a rise in temperature, creating a thermal disequilibrium between the two phases, whereas the mechanical equilibrium is maintained. Heat transfer, condensation and evaporation are thereby going to occur between the two phases, leading to variations in pressure that are difficult to predict. In this paper, a mathematical model for simulating a two-phase compression (or expansion) assuming a thermal non-equilibrium is proposed. This model is intended to be used as a core model for the simulation of displacement compressors using deterministic modelling. The model is applied to a piston-cylinder setup simulating a simple variation of volume over time, as well as a resting phase allowing to reach a final state in both thermal and mechanical equilibrium. External heat transfers and leakages are considered in the equations but will be set at zero in the simulation. The simulated fluid is the refrigerant R1233zd(E). The results of this application are discussed in terms of work consumption and isentropic efficiency, showing that irreversibilities are unavoidable when working in thermal non-equilibrium.