# A Review on Two-Phase Volumetric Expanders and Their Applications
## 9 Conclusions  
This work has provided an overview of the state-of-the-art aspects that characterize volumetric expanders fueled with a pure substance in the two-phase state to fill the gaps in the scientific literature where the contributions appear scarce. As a result, we attempted to identify the critical points that deserve more attention to improve the performances of these systems through numerical and experimental analysis. The following points summarize the main conclusions drawn from several papers published in the literature in the last thirty years about ORC and heat pump applications in which the expander operates with a two-phase fluid:  
* Flash expansion in a variable chamber volume needs to be further analyzed by numerical and experimental studies because it affects the operation of a two-phase device. In detail, the thermal disequilibrium between the vapor and liquid phases seems crucial because it penalizes the efficiency of the machines. As a result, the two-phase fluid must consist of the vapor phase containing fine liquid particles uniformly dispersed to improve the efficiency of the expander. The literature suggested that this aspect deserves further numerical and experimental investigations;
* To the best of the authors' knowledge, two-phase volumetric machines operating with a fixed pressure ratio allow for the changing of their SVFR for the same BVR and timing. As a result, the expansion can be complete or incomplete in the same device for the same pressure ratio, thus, resulting in a different isentropic efficiency. Consequently, some experimental or numerical analysis might be developed to confirm or rebut this conjecture;
* Improving two-phase volumetric machines requires optimization of the shape of valves and ports to reduce the pressure drop and reduce leaks and friction losses. In detail, the passage of the fluid through the valves causes flashing effects;
* Scroll and twin-screw expanders exhibit comparable volumetric and isentropic efficiency in which the maximum values of the latter are between 0.7 and 0.8. Scroll devices are employed for a few up to a dozen of kilowatt, while twin screw systems cover higher power output. Nonetheless, twin screw machines seem to be the most suitable for commercial applications because of their better compatibility with the liquid phase;  
Figure 22: Power output for different expansion devices under two-phase conditions, showing heat pump and cooling (**left**), and power production (**right**). Vane expanders represent other machines tested as two-phase expanders in a power range below 1 kW, but most reach an isentropic efficiency within 0.15-0.62 and exhibit difficulty reducing friction and leaks;
* Piston machines provide a broader range for isentropic efficiency because they are available in various kinematic architectures that result in different performances. Although some authors suggest that the liquid phase involves some issues in piston expanders, the literature has proposed them as machines suitable for transcritical CO2 vapor compression refrigeration cycles. Reciprocating piston systems exhibit an isentropic efficiency from 0.10-0.70 depending on the operating conditions. This range diminishes for rolling and swinging piston systems whose most of their isentropic efficiencies fall between 0.30 to 0.60. Nonetheless, other studies aim to propose the free piston expander as a two-phase machine suitable for ORC applications because its isentropic efficiency falls between 0.65-0.70, at least in the expansion of single-phase flow. Consequently, an investigation of a free piston machine operating in the two-phase region may be developed to assess the performance of this system. Future research should elaborate on detailed mathematical models of two-phase volumetric expanders, including the heat transfer phenomena between vapor and liquid phases, which could affect the isentropic efficiency of these machines.