*3.2. CFD Results*

The pressure pattern as the operation of the scroll evolves with the conditions described in Section 2.3 is reported in Figure 5. The filling procedure of the high-pressure chamber can be noticed passing from Figure 5a–d. Further, the good operation in proximity of the design point is proven by the pressure of the chamber before the opening of the discharge port (Figure 5d shows the pressure distribution of a few degrees before the actual opening): the pressure in the chamber is slightly above the output value, and therefore, no under or overexpansion is recorded. The minimum pressure reached in the domain is slightly above 8 bar and reached downstream the working chamber sealing clearance. In such areas, the flow becomes chocked as reported in Reference [34]. The simulation catches well such phenomena and proves to be robust and stable also in case of transonic problems.

**Figure 5.** Pressure pattern evolution during the operation of the expander: (**a**) 0◦, (**b**) 90◦, (**c**) 180◦, and (**d**) 270◦.

Another interesting result shows the deflection from the ideal behaviour of the refrigerant during the operation and is reported in Figure 6. The maximum deflection from 1 is found in the inlet chamber and is roughly 15%. As a general remark, the real gas effects lower (Z tends to 1) as the fluid goes through the gaps and increase in the bulk of the chambers.

**Figure 6.** Compressibility factor for R134a during the operation of the expander.

Regarding the performance of the scroll, Figure 7 reports the mass flow rate that is processed over an entire revolution of the machine. Under the conditions investigated, the machine processes 27.5 g/s. It should be kept in mind that only a portion of the entire thickness is included. The value obtained is in line with other investigation of the current machine [47]. It is possible to estimate also the VFM (Volumetric Flow Matching Ratio), as the theoretical volume is isolated by the scroll over the CFD-calculated volume flow operated by the scroll. The resulting VFM is of 1.23. This value is perfectly in line with typical values of VFM, that ranges from 1.07 to 1.3 [53]. The imbalance in the mass with the current setup is of the order of 0.1%, that is remarkably good considering the application and the presence of two ACMIs (Arbitrary Coupling Mesh Interfaces). The outflow shows high pulsations with respect to the inlet, and the amplitude of the oscillation is of roughly 80% of the average value.

**Figure 7.** Flow rate variation over a revolution of the shaft.

With regards to the output that can be extracted from the machine, as reported in Figure 8, the power varies over a period from less than 50 W to almost 250 W, with an average of 149.2 W. This value has been calculated as the product between the mechanical torque and the rotational speed (2000 rpm). This is perfectly in line with what has been found in the previous simulation and with the nameplate power of the machine (that is 1 kW, very close to 7 times the actual power). The average internal isentropic efficiency of the machine is therefore 41%, that is typical for this kind of applications [53]. This value has been calculated as the ratio of the average power produced by the expander and the power that it would produce if the expansion of the fluid was isentropic.

A final remark regards the impact of the gaps in the volumetric efficiency. To help in visualizing the relative importance of the gaps, Figure 9 reports the flow field in a constant-span plane. It can be clearly seen how the velocity in clearances is remarkably high with respect to the bulk of the working chambers. An interesting remark regards the different speeds that are reached in the two gaps of each pocket: the higher Mach numbers are obtained in the second gap, closer to the outlet port. From Figure 9, it can also be seen that the high speed traces downstream the gaps are the ones in which the real gas effects are lower (as can be noticed by comparison with Figure 6).

**Figure 8.** Power variation over a revolution of the shaft.

**Figure 9.** Velocity distribution in the domain: The arrow size is scaled by the local velocity magnitude.
