# A Review on Two-Phase Volumetric Expanders and Their Applications
## 3 Two-Phase Volumetric Expanders Applications
Figure 4: T-s diagram of vapor compression refrigeration cycle. Here, 3–4a is the throttling valve, and 3–4b is the two-phase expander. On the other hand, a two-phase expander can be used in the trilateral flash cycle (TFC, Figure 6 [25]). In the heat exchanger, the working fluid receives the thermal power transferred by the heat source, leaving in the saturated or subcooled liquid phase. The electricity production takes place in the two-phase expander, where the working fluid exits in the wet vapor phase, dry saturated phase, or superheated vapor phase. In cases of a single-phase heat source, the mean temperature difference in the heat exchanger can be modest. Thus, the low thermal irreversibility implies the production of substantial electric power and high cycle thermodynamic efficiency. The difficulty arises at higher heat source temperatures, where the volume ratio of expansion of the working fluid is too large to be realized in one stage of a two-phase expander. In particular, the second stage of a two-phase expander may then need to be too large to be cost-effective, or may be beyond current manufacturing limits. The Smith cycle shown in Figure 7 [24] was proposed to overcome the problems associated with the need for two stages of a two-phase expander for the TFC at high heat source temperatures (180-210 \({}^{\circ}\)C). The first expansion stage takes place in the two-phase expander (2-3), whereas the second expansion stage occurs in the single-phase expander (3\"-4\"). The working fluid at the two-phase expander outlet (point 3) is separated in the saturated liquid phase (point 3\") and dry saturated vapor phase (point 3\"). Figure 5: T–s diagram of transcritical vapor compression refrigeration cycle. Figure 6: T–s diagram of the trilateral flash cycle [25]. Similarly to the Smith cycle, the organic double-flash cycle adopts the separation between the liquid and vapor phases (Figure 8). In particular, this takes place in points 4 and 8. Thus, the two-phase expanders (3-4) and (7-8) are used, whereas the expansion processes (5-6) and (10-11) take place in single-phase expanders and the expansion process (9-12) occurs in the throttling valve [26]. Another application of the two-phase expander is the wet vapor ORC. In particular, the working fluid is in the wet vapor phase at the expander inlet and it is in the wet vapor phase, dry saturated vapor phase, or superheated vapor phase at the expander outlet. Figure 9[24] shows a wet vapor ORC (cycle 1-2'-3'-4) and a traditional ORC (cycle 1-2-3-3'-4). In the wet vapor ORC, the evaporation temperature can be higher with the same input thermal power. This can imply greater electric power production per unit of mass flow rate of the working fluid and, as such, higher cycle thermodynamic efficiency. Organic fluids are used in the wet vapor ORC cycle. Conversely, different working fluids (e.g., water) are used in the wet vapor Rankine cycle. Figure 8: T–s diagram of organic double-flash cycle [26]. Figure 7: T–s diagram of Smith cycle [24]. Recently, the application of two-phase expanders and two-phase compressors was proposed in an innovative combined cooling, heating, and power (CCHP) thermodynamic cycle (Figure 10). It consists of the first subcircuit (1-2-2*-3-4-5-5*-6-7-8) and second subcircuit (1-9-10-11-12), where the first and second part of the working fluid mass flow rate circulate after partition in the split (point 1). The supply of electric power to the end-user takes place thanks the expansion processes (4-5, 5*-6, 7-8 and 9-10), whereas the supply to the end-user of heating power and cooling power occur through the condenser (6-7) and evaporator (10-11), respectively [27; 28; 29]. Two-phase expanders can also be used in the high-temperature heat pumps, constituted by two (top and bottom) vapor compression cycles (Figure 11). In particular, in the evaporator of the bottom cycle, the working fluid (ammonia) receives low-temperature thermal power from a heat source.