# 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 Geometric Characteristics  
In comparison to constant-lead twin-screw machines, dual-lead machines exhibit distinct variations in the chamber volume curve, ports, blowhole, contact line, tip sealing line and end-face sealing line. These variations significantly impact the thermodynamic performance of screw machines (see Section 3.2). However, the calculation methods for these geometric characteristics are nearly identical for both constant-lead and dual-lead twin-screw machines, and hence are not reiterated in this paper. To compare the geometric characteristics of a TSE with different dual-lead curves, various values were assigned to \(L_{HP}\) and \(\tau_{HP}\) as presented in Table 3, when the rotor length was set as 110 mm with a wrap angle of 220\({}^{\circ}\) and a built-in volume ratio of 2.6. Case #1 represented the control group with constant-lead rotors. Cases #2 and #3 had an equal length for the HP rotor segment, but the rotor lead of the HP rotor segment in case #2 was far lower than that in case #3. Compared to case #2, case #4 had the same lead but a longer length for the HP rotor segment. Figure 5 illustrates the variation in the chamber volume with the rotating angle of a male rotor for the four cases in Table 3. Due to the limited overall wrap angle, each case reached a maximum chamber volume of 140.6 cm\({}^{3}\) when the LP port was just open. The built-in volume ratio of the TSE was 2.6, and thus, the chamber volume was 54.4 cm\({}^{3}\) when the combined axial and radial HP port was closed. However, there were visible differences in the rotating angle at the suction end for TSEs with different dual-lead parameters, as indicated by the intersection point between the orange line and chamber volume curves in Figure 5, since lead curves significantly affect the expansion rate. Case #4 exhibited the largest rotating angle at the suction end of 189\({}^{\circ}\), surpassing that of the constant-lead rotors (case #1) by 43\({}^{\circ}\), indicating the longest suction time, as shown in Figure 6a. In contrast, case #3 had the shortest rotating angle at the suction end of 130\({}^{\circ}\), which was lower than that of case #1 by 16\({}^{\circ}\). Furthermore, it can be observed from Figure 6b that case #4 consistently exhibited the largest suction area at each chamber volume during the suction process, with the largest suction area being twice as large as that of case #1. Therefore, it can be concluded \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case No.** & \(L_{HP}\), mm & \(\tau_{HP}\), \({}^{\circ}\) & \(T_{HP}\), mm & \(L_{LP}\), mm & \(\tau_{LP}\), \({}^{\circ}\) & \(T_{LP}\), mm & **Rotor Structure** \\ \hline \hline \#1 & 110 & 220 & 180 & - & - & - \\ \hline \#2 & 30 & 90 & 120 & 80 & 130 & 221.5 \\ \hline \#3 & 30 & 40 & 270 & 80 & 180 & 160 \\ \hline \#4 & 60 & 180 & 120 & 50 & 40 & 450 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Main rotor parameters of TSEs with different dual-lead curve parameters. that reducing the lead and increasing the length of the HP rotor segment would result in an extended rotating angle at the suction end and a significantly enlarged suction area. The variable-lead curves would also influence the leakage area via the leakage paths, further affecting the leakage characteristics of the TSEs. Figure 7 illustrates the variation in the leakage area via several leakage paths with the rotating angle and chamber volume. It can be observed that the leakage duration through any leakage path was the same for the four cases, as it was determined by the geometric properties of the screw rotors. However, there were sometimes significant differences in the terms of the corresponding chamber volume at which the leakage started via a blowhole, and ended via a rotor tip and HP end face, respectively. For instance, the leakage via a blowhole for both of cases #2 and #4 started at the same chamber volume of about 23 cm\({}^{3}\).