# A Review on Two-Phase Volumetric Expanders and Their Applications
## 6 Two-Phase Vane Expander
### Literature Review of Two-Phase Vane Expander  
The investigations of the two-phase vane expanders mainly aimed to further their applications in CO\({}_{2}\) transcritical vapor compression refrigeration cycles. The following Table 3 summarizes the main performances provided in the literature. Figure 14: Two-phase vane expander, with principle of operation (**a**) [12] and leakage pathways (**b**) [59]. In the late 2000s, [PERSON] et al. provided the main contribution to the analysis of the two-phase vane expanders in the applications of CO\({}_{2}\) transcritical vapor compression refrigeration cycles. They investigated the volumetric performance of a vane expander prototype by identifying five possible paths for the leaks [61]. This prototype was a double-acting type, i.e., two symmetric expansion chambers working in parallel where each of them had its own suction port and discharge port so that there were two suction ports and two discharge ports in total, and it employed seven vanes. The results indicated an increase in the volumetric efficiency from 0.10 at 500 rpm up to 0.6 at 3000 rpm, and that the leakage from the inlet to the outlet port was higher than the leakage from the end cover. The same authors in [61] improved this original vane expander by making some modifications and then tested it. The average experimental conditions were an inlet pressure of 8.05 MPa, inlet temperature of 35.2 \({}^{\circ}\)C, outlet pressure of 4.77 MPa, and an outlet temperature of 12.08 \({}^{\circ}\)C, under which conditions the machine delivered a power of 0.375 kW for a rotating speed of 710 rpm. In a further study, the same researchers [62] experimentally tested the same prototype to investigate the impact of springs in the vane slots. The device operated under an inlet pressure from 7.5 to 9.0 MPa for temperatures from 32.4 to 44.3 \({}^{\circ}\)C and a discharge pressure in the range of 4.8-6.4 MPa, in which the discharge temperature was the saturation temperature. These tests showed that the volumetric efficiency had a maximum value of 0.29 at a rotational velocity equal to 1000 rpm, while the maximum isentropic efficiency was 0.23 at 800 rpm. The authors concluded that the inlet gas flow was responsible for the loss of contact between the vane and the stator. For this reason, they highlighted the importance of the springs to improve the volumetric efficiency by limiting the leaks. Finally, the same authors [63] elaborated and validated the mathematical model of the vane dynamics. The results showed that the arrangement of springs in the slot underneath the vane proved to be beneficial in maintaining a tight contact between the vane and the cylinder wall and, thus, improved the working processes of the expander. In the same period, [PERSON] et al. [64] experimentally investigated a prototype with a chamber volume of 64 mm\({}^{3}\) at the expansion process start and a built-in expansion volume ratio of 2. The inlet and outlet pressures were of 9.1 MPa and of 4.1 MPa, respectively. The measured mechanical, volumetric, and total efficiencies were 0.95, 0.7, and 0.6, respectively, at an outlet temperature of 40 \({}^{\circ}\)C and a rotational velocity of 2000 rpm.