## 4 Results and Discussion
### Rotor Optimization Results  
Both T-100 rotor optimization and T-100 re rotor optimization evolved for 35 generations and took nine days on a workstation with two CPUs (main frequency 2.4 GHz, total 16 compute cores). A single evaluation including CFD and CSM analysis took approximately 25 min. Table 3 shows the performance at every design stage for comparison. It can be seen that the increase of the total-to-static efficiency achieved in the rotor optimization for T-100 and T-100 re turbine are 0.7% and 1.2%, respectively. Comparing T-100 re optimized design with T-100 baseline design, the total-to-static efficiency has been increased by 2.2%. According to Table 3, T-100 rotor weighs 1.31 kg after the preliminary design, and 1.12 kg after the rotor optimization, so 14.5% of the weight is cut down. The T-100 re rotor weighs 0.96 kg after the preliminary design, and 0.82 kg after the rotor optimization, so 14.6% of the weight is cut down. Comparing T-100 re optimized design with T-100 baseline design again, the rotor weight decreases by 0.49 kg (37.4%). Both rotors are available regarding the stress level. Figure 11 shows the 2-D objective space obtained from T-100 rotor optimization after 35 generations. Each symbol represents a radial turbine design which has been analyzed successfully by the CFD and CSM solver as the rotor optimization adopts the accurate optimization strategy. The designs that satisfy all constraints are indicated with a green color, the baseline design from the very beginning is presented by a blue square, and the baseline design after the nozzle optimization is by a light blue delta. It can be seen that most designs were generated with a higher total-to-static efficiency and a lower weight compared to the baseline design. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Objectives**} & \multicolumn{2}{c}{**Preliminary Design**} & \multirow{2}{*}{**Nozzle Opt.**} & \multirow{2}{*}{**Rotor Opt.**} \\ \cline{2-2} \cline{4-5}  & **Mean Line** & & & \\ \hline T-100 \(\eta_{ls}\) [-] & 0.864 (exp.) & 0.874 & 0.875 & 0.882 \\ T-100 re \(\eta_{ls}\) [-] & 0.874 & 0.883 & 0.884 & 0.896 \\ T-100 \(W\) [kg] & 1.31 & - & - & 1.12 \\ T-100 re \(W\) [kg] & 0.96 & - & - & 0.82 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparison between T-100 and T-100 re turbines after rotor optimization. Figure 10: Comparison of T-100 re nozzle profiles. However, most designs violate the equivalent stress constraint (Figure 12), the apparent Pareto front towards the lower left-hand corner in Figure 11 can be considered as the pure aerodynamic Pareto optimal solutions. Only seven individuals satisfy all constraints, which also demonstrates the highly conflicting relationship between the total-to-static efficiency and the equivalent stress. In the constraint-satisfied solutions, the four individuals generated in the early phase of the optimization (Gen 3-9 in Figure 11) are not competitive, so only the three individuals generated in the later phase (Gen 21-28) can be considered as the optimal solutions. In T-100 rotor optimization, the individual from Gen 22 is selected as the best trade-off solution (selected optimum), because it has the lowest weight (1.12 kg), the lowest stress (649 MPa), and higher efficiency of 88.2%, which is quite close to the best achieved (88.3% at Gen 28). The total-to-static efficiency increases by 0.7%, and the rotor weight decreases by 14.5%. The maximum stress is lower  
Figure 11: Change of rotor weight along with total-to-static efficiency (T-100). Figure 12: Change of equivalent stress along with total-to-static efficiency (T-100). than the maximum allowable stress (684 MPa), and the change of mass flow rate is 0.13%, which is acceptable. Figures 13 and 14 show the 2-D objective space obtained from T-100 re rotor optimization. It can be seen from Figure 14 that most individuals violate the equivalent stress constraint too, so the apparent Pareto front cannot be considered as trade-off solutions.