# A Review on Two-Phase Volumetric Expanders and Their Applications
## 2 General Principles of the Two-Phase Volumetric Expanders
### Flush Evaporation Fundamentals in Volumetric Two-Phase Expanders  
Flash evaporation is a phase change that occurs when a fluid in the liquid phase or a fluid constituted by both liquid and vapor phases suddenly undergoes a pressure reduction below its saturation pressure, thus, increasing the vapor quality. Two-phase expanders experience flashing phenomena during the intake and expansion processes because of their pressure reductions. A characteristic aspect of flashing phenomena in volumetric machines is that the volume of the flashing chamber varies over time. This aspect is crucial since the literature has only investigated flash evaporation in constant volume chambers (static flashing) or  
Figure 2: Under-expansion (**left**) and over-expansion (**right**). flashing in which the liquid film initially moves (circulatory flashing). Nonetheless, there is a lack of studies about flashing into variable volume chambers. According to our best knowledge, [PERSON] and [PERSON] are the only ones that attempted to investigate flash evaporation in volumetric machines [20,21]. They confirmed that flash evaporation is a non-equilibrium process because it entails the formation of bubbles that increase in number and size. The non-equilibrium state depends on several physical aspects, such as atomization, nucleation, phase change, two-phase flow, droplet formation, and velocity. The atomization transforms the liquid phase into droplets by a breakup process that consists of two steps. The first is the creation of large droplets, while the second is the further breakup of these wider droplets into smaller droplets (secondary breakup). Bubble nucleation is the other process that can be homogeneous or heterogeneous depending on whether the bubbles appear anywhere in the liquid or exclusively at the interface between the liquid and solid surfaces of the machine. The growth of these bubbles is due to the reception of the latent heat provided by the surrounding liquid, whose temperature diminishes because of the sensible heat loss. This mechanism stops when the temperature of the liquid reaches a saturation temperature corresponding to the existing pressure. All these considerations suggest that the mass flow rate of the generated vapor can be found as the product of the liquid-vapor interfacial area and the net heat flux of this interface divided by the latent heat of the evaporation. Nonetheless, [PERSON] [20] proposed an agitation factor that replaces the liquid-vapor interfacial area and summarizes the non-equilibrium effects. [PERSON] avoided the difficulties due to the modelling of flash evaporation by using a homogeneous relaxation model to predict vapor generation [21]. However, both authors underlined that the velocity with which the volume deforms is crucial because it determines the pressure reduction and the flashing time, thus, influencing flash evaporation. Moreover, the thermal disequilibrium between the vapor and liquid phases during the two-phase expansion process penalizes the efficiency of the machines. Indeed, the pressure change causes a high volume (or density) variation for the vapor phase, resulting in high temperature variation. Conversely, the pressure change implies a negligible volume/density/temperature variation of the liquid phase. In other words, high efficiency of two-phase expanders can be obtained only in the presence of thermal equilibrium during two-phase expansion process, i.e., the temperature equality of the two phases thanks to adequate heat exchange between them. Thus, the two-phase fluid must consist of the vapor phase where fine liquid particles are uniformly dispersed [2]. As a result, the design of two-phase expanders requires the availability of numerical models capable of accurate predictions about the behaviour of a two-phase flow. For this aim, [PERSON] et al. [22] summarized the potential numerical techniques to describe the thermodynamic state of two-phase flows.