# Multidisciplinary Design Optimization of Cooling Turbine Blade: An Integrated Approach with R/ICSM
## 4 Optimization Results and Discussion
### Detail Analysis of Disciplines  
Figure 14 presents a comparison of the von Mises stress distribution of the first stage rotor blade between the initial and enhanced schemes. Compared to the initial design, the improved blade exhibits an increased maximum von Mises stress, with its location shifting from the root extension near the trailing edge of the blade pressure surface to the root of the blade pressure surface. The underlying cause of this change is the expansion of the cross-sectional area of the blade above the root post-optimization, whereas the cross-sectional area of the blade root remains unaltered. Consequently, there is a higher mass situated above the blade root, resulting in amplified centrifugal force and subsequently elevated stress levels at the blade root. Table 3 presents the energy loss coefficients for each row of the blade in both the initial and optimized schemes. The data indicate that the energy loss for the first-stage stator blade experienced a slight increase, whereas the energy loss for the subsequent blade rows decreased. Notably, the energy loss for the first-stage rotor blade saw the most  
Figure 14: Von Mises stress distribution first stage rotor blade. (**a**) Initial scheme; (**b**) optimized scheme. Figure 13: Comparison of the three-dimensional model of the first-stage rotor blade before and after optimization. significant reduction, with a decrease of 14.57%. Consequently, the subsequent discussion will concentrate on analyzing the flow field of the first-stage rotor blade. Figure 15 illustrates the spanwise distribution of the energy loss coefficient for the first-stage rotor blade in both the initial and enhanced schemes. Comparing the two plans, it is evident that the enhanced scheme shows minimal changes in losses in areas below 50% blade height, slightly increased losses in areas between 50% and 58% blade height, and notably reduced losses in areas above 58% blade height. Figure 16 presents the entropy distribution at the outlet of the first-stage rotor blade in the initial and enhanced schemes. The following observations can be made: (1) the improved scheme significantly reduces the area of high energy losses; (2) consistent with the results in Figure 15, losses remain relatively unchanged below 50% blade height, while there is a significant decrease in losses above 58% blade height; and (3) the improved plan slightly shifts the high-loss areas downwards, resulting in a slight increase in losses between 50% and 58% of the blade height. Figures 17-19 display the relative Mach number distribution at the 10%, 55%, and 90% blade height cross-sections for the first-stage rotor blade in the initial and improved schemes. Key observations include the following: (1) the improved scheme reduces the highest Mach number at each blade height section; (2) the initial scheme exhibits a large low-speed zone at the trailing edge of the suction surface at the 90% blade height section, which is eliminated in the improved scheme; and (3) at the 55% blade height section, there is a slight increase in the low-speed zone at the trailing edge in the improved scheme. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Blade** & \begin{tabular}{c} **First-Stage** \\ **Stator Blade** \\ \end{tabular} & \begin{tabular}{c} **First-Stage** \\ **Rotor Blade** \\ \end{tabular} & \
\begin{tabular}{c} **Second-Stage** \\ **Stator Blade** \\ \end{tabular} &
\begin{tabular}{c} **Second-Stage** \\ **Rotor Blade** \\ \end{tabular} \\ \hline Initial & 0.0593 & 0.1221 & 0.0709 & 0.0690 \\ \hline Optimized & 0.0595 & 0.1043 & 0.0689 & 0.0685 \\ \hline Rate & 0.42\% & \(-14.57\%\) & \(-2.71\%\) & \(-0.78\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The energy loss coefficient of each row blade before and after optimization. Figure 15: Spanwise distribution of the coefficient of energy loss for the first-stage turbine blade before and after optimization. Figure 16: Comparison of entropy distribution at the outlet of the first-stage rotor blade before and after optimization.