## 3 Results and Discussions
### Effects of Stator Openings on Cycle and Turbine Performances  
First, the effects of stator openings on turbine efficiency are investigated as shown in Figure 7. All engine operating points present a similar trend, where turbine efficiency increases, reaching a maximum value at P3, then decreases at P3 as shown in Figure 7a. At P1, the 60% opening presents substantially higher turbine efficiency with 57.5%, while P3 presents the lowest turbine efficiency with a value of 42.4%. The 30% opening presents the lowest turbine efficiency because of the excessive heat for the low mass flow rates of the exhaust gas as shown in Table 1. In other words, the mass flow rate of the working fluid decreases at low openings. Therefore, the excessive heat results in an extremely superheated fluid at the turbine inlet. Moreover, radial turbine losses (tip clearance and incidence, as shown in Table 2) increase at higher turbine inlet temperatures, which deteriorates the turbine efficiency as per Equation (30). Regarding stator openings, the 100% opening is not always favorable due to the increased fluid capacity that requires more heat to be fully vaporized.  
Figure 7c depicts the behavior of turbine power with different stator openings and various engine operating points. It is clear that the 100% opening is superior for all the investigated engine points. This is expected, since turbine power is directly related to the mass flow rate and the enthalpy drop through the turbine. P3 with a 100% stator opening presents the highest turbine power with 18.5 kW. The 30% and 60% stator openings present maximum values of 12.60 and 16 kW, respectively. Again, as the mass flow rate decreases, the turbine power decreases according to Equation (18). Figure 7c shows that the 30 and 60% throat openings present comparable turbine power at engine point P2. This is due to the comparable exhaust temperatures as per Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Loss** & **Equation** \\ \hline Incidence Loss & \(\Delta h_{incidence}=\frac{1}{2}[W_{4}\text{sin}\left(\beta_{4}-\beta_{4 opt} \right)]^{n}\) \\ Passage Loss & \(\Delta h_{\text{passage}}=\frac{1}{2}\left(2f_{t}\frac{L}{L_{\text{th}}} \overline{W}^{2}+\frac{n_{\text{c}}G_{\text{s}}^{2}}{F_{\text{c}}Z_{\text{s} }}\right)\) \\ Tip Clearance Loss & \(\Delta h_{\text{tip}}=\frac{U_{\text{s}}^{3}Z_{\text{s}}}{8\pi^{2}}\left(K_{ \text{a}}\varepsilon_{\text{a}}C_{\text{a}}+K_{\text{rf}}\varepsilon_{\text{r }}C_{\text{r}}+K_{\text{a}\pi}\sqrt{\left(\varepsilon_{\text{a}}\varepsilon_ {\text{r}}C_{\text{a}}C_{\text{r}}\right)}\right)\) \\ Windage Loss & \(\Delta h_{\text{windage}}=k_{\text{rf}}\frac{\
abla h_{\text{rf}}^{4}G_{\text{s} }^{2}}{2n_{\text{rf}}}\) \\ Exit Energy Loss & \(\Delta h_{\text{exit}}=\frac{1}{2}C_{\text{s}}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Losses model across the radial turbine stage.  
The effects of stator openings on the thermal efficiency are depicted in Figure 7b. The cycle thermal efficiency is directly related to turbine power and the absorbed heat in the evaporator. Thermal efficiency follows the trend of turbine power qualitatively. As per Equation (6), the cycle thermal efficiency is a function of turbine power. As the turbine power increases, the cycle thermal efficiency increases. As already depicted in Figure 7c, the turbine power increases and, hence, the cycle efficiency increases. The 100% opening presents the highest thermal efficiency for all the engine operating points, followed by the 60% opening. The maximum thermal efficiency of the system is 13.8% and obtained at P3, with a 100% opening. The lowest thermal efficiency is 0.4% and presented by engine operating point P1 with a 30% stator opening.  
Figure 7: Effects of stator opening on (**a**) turbine efficiency, (**b**) turbine power, and (**c**) cycle thermal efficiency at different engine operating points.