# Potential Evaluation of Twin-Screw Air Expanders with Dual-Lead Rotors Used in PEMFC Systems
## 3 Results and Discussion
### Effects of the Geometric Parameters on the Thermodynamic Performance
#### 3.2.1 Effect of the Lead and Length of an HP Rotor Segment on the Thermodynamic Performance  
The influence of the lead and length of an HP rotor segment on the expander's performance was simulated using a fixed rotor length of 110 mm, wrap angle of 220\({}^{\circ}\) and built-in volume ratio of 2.6. Figure 8 illustrates the influence of the lead and length of an HP rotor segment on \(p\)-\(V\) diagrams, suction pressure loss and indicated power of the expander. It is evident that the smaller lead and longer length of the HP rotor segment within the simulated parameter ranges leads to a lower suction pressure loss (Figure 8b), which means that the air pressure during the suction process is reductively smaller than the inlet pressure. It could be found that the suction pressure loss in the case of \(T_{\text{HP}}\) = 90 mm and \(L_{\text{HP}}\) = 50 mm was lower than the constant-lead case by about 38 kPa. This further caused the increment in the indicated power by 25.4% (Figure 8c). The improvement can be attributed to an enlarged suction area caused by the smaller lead and longer length of the HP rotor segment, as shown in Figure 6. In addition, the largest suction pressure loss and lowest indicated power occurred at the largest lead along with the longest length of the HP rotor segment. When the length of the HP rotor segment was relatively small, it could not contribute to the reduction in the suction pressure loss and increment in the \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline inlet pressure, kPa & 400 \\ inlet temperature, \({}^{\circ}\)C & 90 \\ outlet pressure, kPa & 100 \\ rotating speed of a male rotor, rpm & 10,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Operating conditions of TSEs. Figure 7: Variation in leakage area via several leakage paths with rotating angle and chamber volume. (**a**) Leakage area via blowhole; (**b**) Leakage area via contact line; (**c**) Leakage area via rotor tip; (**d**) Leakage area via HP end face. indicated power compared with the constant-lead rotors, even though the lead of the HP rotor segment was also small, which can be observed by comparing the \(p\)-\(V\) diagrams of the case of \(T_{\text{HP}}\) = 90 mm, \(L_{\text{HP}}\) = 20 mm and the case of \(T_{\text{HP}}\) = 180 mm. It should be noted that for a given small lead of the HP rotor segment, the maximum allowable length of the HP rotor segment is limited by the wrap angle. For example, when \(T_{\text{HP}}\) = 90 mm and \(L_{\text{HP}}\) = 60 mm, the wrap angle of the HP rotor segment was 240\({}^{\circ}\), exceeding the overall wrap angle of 220\({}^{\circ}\). The larger suction pressure loss was caused by the inadequate suction, and thus would lead to the lower mass flowrate and filling factor, as Figure 9 shows. Therefore, the smallest lead with the longest length of the HP rotor segment (\(T_{\text{HP}}\) = 90 mm and \(L_{\text{HP}}\) = 50 mm) yielded the highest mass flowrate of 212.1 g/s and filling factor of 1.53, which were approximately 45% higher than those of the constant-lead case. In addition, the filling factor exceeded 1, also indicating the severe leakage in the suction process, negatively impacting the expander's performance. Although a larger mass flowrate entering the expander increased the indicated power, it did not result in an improvement in the isentropic indicated efficiency as depicted in Figure 9c. It can be observed from Figure 9c that the high isentropic indicated efficiency primarily concentrated near the constant-lead case. The maximum isentropic indicated efficiency of 0.6626 occurred at \(T_{\text{HP}}\) = 150 mm and \(L_{\text{HP}}\) = 60 mm, surpassing the constant-lead case by 0.3%. Both a smaller and larger lead with a longer length of the HP rotor segment led to a decrease in the isentropic indicated efficiency. One possible explanation for this phenomenon is that the smaller or larger lead with a longer length of the HP rotor segment resulted in a significant mismatch between the internal and external pressure ratios.