## 3 Results and Discussion
### Off-Design Performance  
By changing the static pressure of the third stage impeller outlet, the turbine designed was analyzed. Nine kinds of non-design conditions are analyzed for outlet static pressure of 7.5 MPa, 8 MPa, 9 MPa, 10 MPa, 11 MPa, 12 MPa, 13 MPa, 13.5 MPa and 14 MPa. The variation curve of turbine output power with outlet static pressure is shown in Figure 11. It can be found that the curve shows a monotonous decreasing trend because when the outlet pressure of the turbine increases, the inlet and outlet expansion ratios of the turbine decrease, and the flow capacity decreases, resulting in a decrease in the mass flow rate of the throughflow portion. Meanwhile, the increase of turbine outlet pressure makes the enthalpy of the outlet working fluid larger, and the enthalpy drops of the whole turbine at the inlet and outlet are decreased. The output power of the turbine is proportional to the mass flow and the inlet and outlet enthalpy drop. Therefore, the turbine's working capacity will gradually decrease as the outlet pressure increases.  
The variation curve of total-total efficiency with mass flow rate is shown in Figure 12. It can be found from the diagram that when mass flow rate is less than 184.3 kg/s under design conditions, the total-total efficiency increases slightly with the decrease of mass flow rate. When the mass flow rate is about 164 kg/s, the turbine has the highest total-total efficiency of 92.12%, which is about 0.5% higher than that under design conditions. With the continuous decrease of the mass flow rate, the turbine efficiency decreases gradually in the range of 115 kg/s to 164 kg/s, and the change curve is relatively smooth. When the mass flow rate is less than 115 kg/s, the expansion ratio is too small and the outlet pressure becomes larger, which leads to gas reflux at the outlet of the turbine. Turbine efficiency becomes very sensitive to the change of mass flow rate, thus small flow rate changes will lead to a significant reduction of turbine efficiency. In order to keep the carbon dioxide in supercritical state in the turbine, the minimum pressure at the outlet is set to 7.5 MPa in off-design condition analysis. At this time, the maximum flow capacity of the turbine is reached, which is 201.3 kg/s. When the flow rate ranges from 184.3 kg/s to 201.3 kg/s, the turbine efficiency decreases with the increase of mass flow rate. Generally speaking, the designed S-CO\({}_{2}\) three-stage axial turbine can operate steadily  
Figure 11: The variation curve of turbine output power with outlet static pressure.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Thermal Design** & **Aerodynamic Analysis** \\ \hline Flow rate/kg\(\cdot\)s\({}^{-1}\) & 185 & 184 \\ Efficiency/\% & 85 (estimated efficiency) & 91.60 (total-total efficiency) \\ Output power/MW & 10 & 10.37 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance parameters.  
and efficiently in the range of mass flow from 115 kg/s to 201.3 kg/s (i.e., its output power ranges from 16.2% to 155.9%). This means the designed turbine has excellent performance with wide range of off-design operation. Therefore it can be adapted to the variable condition characteristics of solar power generation system affected by geographical distribution, seasonal variation and day-night alternation to some extent.