# A Review on Two-Phase Volumetric Expanders and Their Applications
## 7 Two-Phase Piston Expander
### Literature Review of Two-Phase Piston Expander
[23] simulated a TFC operating with water as a working fluid and implemented a two-phase reciprocating axial piston expander whose volume measured 4.9 \(\times\) 10\({}^{-3}\) m\({}^{3}\). Their simulations considered inlet and condensation temperatures of 373 K and 303 K, respectively, and a rotating speed of between 200 and 1500 rpm. They found a decrease in the isentropic efficiency from around 0.70 to 0.58 or 0.33 when the rotating speed grew. The magnitude of such a reduction depended on the inlet operating conditions. In 2021, [PERSON] et al. [79] proposed the use of a two-phase reciprocating axial piston expander in a Rankine cycle to recover the waste heat from a truck engine. The experimental results allowed for a semi-empirical model of the expander to be calibrated. The simulations based on a rotating speed of 1000 rpm and superheating of 60 K predicted isentropic efficiencies in the range 0.10-0.50 depending on the working fluid. Nonetheless, the expansion in the two-phase region caused a lack of fit for the expander power due to the high leakage. Finally, a series of projects carried out by Libertine recalled these advantages to develop two-phase free-piston systems for ORC applications [80; 81]. A further application of the two-phase piston expanders was associated to the CO\({}_{2}\) heat pump cycles. The review in this field is described as follows. In 2006, [PERSON] et al. [82] proposed a two-phase swing piston expander that operated between an inlet pressure of 10 MPa and a discharge pressure of 4 MPa. The tests indicated that the isentropic efficiency was in the range 0.33-0.44 at a load of 500 W and ranged from 0.28 to 0.44 for a set of rotating speeds between 1400-1800 rpm. The authors claimed that these isentropic efficiency values were attractive compared to the corresponding provided by a two-phase rolling piston expander that they had developed before, whose maximum isentropic efficiency was 0.29. In 2008, [PERSON] et al. [83] tested a two-phase two-stage swing piston expander at an inlet pressure of 9.4 MPa, discharge pressure of 3.4 MPa, inlet temperature of 30 \({}^{\circ}\)C, and a rotating speed in the range 40-90 rps. The results indicated that the isentropic efficiency and volumetric efficiency were 0.59 and 0.98, respectively. In 2008, [PERSON] et al. [84] developed a two-phase two-stage rolling piston expander whose optimized prototypes provided an isentropic efficiency of 0.60. Later, [PERSON] et al. [85] introduced a radial reciprocating piston expander that consisted of four cylinders, each of which had a displacement of 96.2 mm\({}^{3}\). This machine was designed to replace the throttling valve in refrigeration cycles based on CO\({}_{2}\). For this reason, it was experimentally tested between an inlet pressure of 8.5 MPa and an exhaust pressure of 3.2 MPa for rotating speed between 180-400 rpm. The authors stated that the total efficiency was about 0.4 and claimed that this value was acceptable for a small expander. In 2017, [PERSON] et al. [86] proposed a reciprocating radial piston expander working with R134a, having nine cylinders and a total displacement of 102 cm\({}^{3}\). The test conditions were as follows: the inlet pressure was between 10 and 16 bar, temperatures ranged from 40 to 60 \({}^{\circ}\)C, and the outlet pressure was between 3.5 and 5.6 bar. The machine was tested at 500 rpm with a quality that grew from 0 to 0.8. The results highlighted that a rise in the inlet quality reduced the friction losses and increased the expansion ratio for a given rotating speed and inlet temperature. The increase in the rotational speed diminished the volumetric efficiency of the machine, thus, meaning a worse filling of the working chamber. However, higher rotational speeds seemed to entail irrelevant effects on the expansion of the fluid.