# A Review on Two-Phase Volumetric Expanders and Their Applications
## 7 Two-Phase Piston Expander
### Literature Review of Two-Phase Piston Expander  
The analysis of the two-phase piston expanders mainly addressed developing their applications in CO\({}_{2}\) transcritical vapor compression refrigeration cycles, as suggested by Table 4.  
In 2004, [PERSON] et al. [72] developed a two-phase rolling piston expander considering several aspects, such as sealing, friction losses, and timing of the intake. Experimental tests were carried out at an inlet pressure of 7.34 MPa with a rotating speed between 600-2200 rpm, obtaining the isentropic efficiency of 0.32. In 2005, [PERSON] et al. [73] developed a two-phase three-stage expander based on a free piston architecture. This machine was experimentally tested between a suction pressure of 80 MPa and a discharge pressure of about 50 MPa. They suggested that the expansion in the two-phase region did not cause any problems, and the isentropic efficiency was in the range of 0.65-0.70, depending on the operating conditions. In 2005, [PERSON] et al. [74; 75] built a two-phase reciprocating axial piston machine by modifying a commercial small four-stroke, two-piston gasoline engine in which the displacement of each cylinder measured 13.26 cm\({}^{3}\). However, the original crankshaft was modified to obtain a proper out-of-phase firing that limited the mechanical inertia. This solution ensured that the piston in the expansion stroke drove the other piston through the exhaust stroke. Other modifications concerned the valves and the cylinder head to provide acceptable volumetric efficiency and a proper BVR. This expander was lubricated by oil and provided an isentropic efficiency of about 0.10 under a pressure ratio of 2.07 for a rotating speed 114-120 rpm. The low efficiency probably depended on the leaks from the working chamber. In 2006, [PERSON] et al. [76] proposed a two-phase two-stage two-cylinder rolling piston expander, whose main characteristic was the removal of the suction valve to ensure a continuous expansion process. The authors elaborated a numerical model of this machine to assess the forces on the crankshaft, the flow velocity, and the shape of the pressure-volume  
Figure 17: Two-phase free piston expander, showing the principle of operation [71]. diagram. In the numerical model, the first and second expansion unit displacements were 0.49 and 1.29 cm\({}^{3}\), respectively, while the boundary conditions were an inlet pressure of 9 MPa, an inlet temperature of 35 \({}^{\circ}\)C and a discharge pressure of 3.48 MPa. The results indicated that the pressure decreased slowly in the expansion when the CO\({}_{2}\) entered the vapor-liquid two-phase region. Nonetheless, this study did not report any values for the isentropic efficiency. In 2009, [PERSON] et al. [77] investigated the potentialities of a two-phase rolling piston expander by developing and testing a prototype that consisted of one cylinder with a particular suction system and reached a peak of isentropic efficiency of 0.587. The last analysis associated with the implementation of the two-phase piston expanders in CO\({}_{2}\) vapor compression refrigeration cycles was carried out in 2010 by [PERSON] et al. [78]. They proposed a two-phase rolling piston expander designed for an inlet pressure of 9 MPa, an inlet temperature of 35 \({}^{\circ}\)C, a discharge pressure of 3.9 MPa, and a rotating speed of 1500 rpm The experimental results revealed that this machine exhibited an isentropic efficiency that increased from 0.30 at around 600 rpm to 0.45 at 1500 rpm. However, a further increase in the rotating speed up to 1800 rpm caused a reduction in the isentropic efficiency, which became 0.42. An additional application of the two-phase piston expanders was related to the power cycles. The review in this field is described as follows. In 2016, [PERSON] et al. [77] proposed a free piston device with a linear generator as suitable for ORC systems thanks to some advantages, such as compactness and flexibility. In 2019, [PERSON] et al.