# A Review on Two-Phase Volumetric Expanders and Their Applications
## 2 General Principles of the Two-Phase Volumetric Expanders
### Impact of Two-Phase Flow on Performances of Volumetric Expanders  
The magnitude of the under-expansion or over-expansion losses, internal fluid leakages, pressure losses introduced in the valves or ports, heat transfer losses, and friction losses is emphasized by the presence of a two-phase flow. This encouraged some authors to assess how a two-phase fluid impacts the performances of a volumetric expander. In 2006, [PERSON] et al. [6] conducted experimental tests on a modified reciprocating axial piston working with CO\({}_{2}\). They found that the high speed (1000 rpm) preventeda thermodynamic equilibrium being reached during the expansion in the two-phase region, thus, causing a sharp pressure drop that decreased the area of the pressure-volume diagram. Their results indicated how this effect is emphasized with the decrease in suction quality, as shown by a reduction in the isentropic efficiency from 24% to 15%. In 2015, [PERSON] et al. [20] experimentally investigated a two-phase reciprocating axial piston expander with water as a working fluid. They stated that the increase in the piston velocity diminished the adiabatic efficiency from 95 to 80%. In 2017, [PERSON] et al. [21] carried out experimental research to fill the knowledge gap concerning the fundamental aspects of the two-phase expansion with non-equilibrium effects. They concluded that fast acting inlet valves were necessary to obtain significant results and that the dead volume is responsible of pre-expansion losses, as it occurs in reciprocating machines. In 2019, [PERSON] et al. [23] proposed an experimental validated numerical model of a two-phase volumetric expander to consider how the suction valves affected the performances of the machine. They found that the pressure losses through the valves appeared as an isenthalpic process that led to the separation of the vapor and liquid phases within the working chamber. This aspect is relevant when the expander receives a liquid or a vapor-liquid mixture at the inlet ports, since the corresponding pressure drop increases the quality of the mixture. Moreover, to the best of the author's knowledge, two-phase volumetric machines operating with a fluid in the two-phase region under a fixed pressure ratio are characterized by the possibility of changing their SVFR for the same BVR and timing. This consideration relies on the value of the inlet quality that determines the specific volume at the suction for the same pressure level. Consequently, the same device may perform a more or less complete expansion for the same pressure ratio, thus, exhibiting different isentropic efficiency. Nonetheless, this behaviour also depends on other circumstances, such as the pressure losses through the ports, whose magnitude depends on the density. Another aspect that affects a two-phase expander occurs when the inlet vapor is single-phase, since the pressure reduction in the expansion differs depending on whether this last one occurs through the saturated liquid or saturated vapor line. [PERSON] et al. [6] highlighted this behaviour by testing a volumetric expansion device with CO\({}_{2}\) as a working fluid (Figure 3a). They noted that the expansion through the left-hand side of the critical point caused a sharper pressure drop (Figure 3d) than the case in which the expansion occurred through the saturated vapor line (on the right-hand side of the critical point). This last case exhibited a pressure drop that was smoother and more similar to a complete expansion in the superheated region (Figure 3b,c). As a result, the corresponding indicated cycles varied and resulted in different isentropic efficiencies whose smaller value appeared for the expansion through the saturated liquid line. This study suggested that the initial quality value as the fluid becomes two-phase contributes to determining the isentropic efficiency value of the device. Finally, the geometry of the device and the volume variation of the operating chamber seems to affect the tolerance of the machine to the liquid phase.