## 3 Multi-Objective Aerodynamic Design Optimisation of Centrifugal Impeller
### Optimisation Results and Analysis
#### 3.6.3 Flow Field Analysis  
Figure 13 shows the entropy contour of the S3 section before and after the optimisation of the rated operating condition. After optimisation, the high entropy areas in channels I and II, A, B, C and D are reduced, and the losses are significantly reduced. The reason for the decrease of inlet loss is that the shock wave at the blade inlet is weakened due to the better matching of the inlet attack angle. Figure 14 shows the entropy contour of the S3 section before and after the optimisation of the common operating condition. The entropy value of A, B, C, D, E and F is obviously reduced after optimisation, given that the incidence angle and blade geometry are better matched, making the acceleration section of the blade inlet shorter and acceleration slower. This is beneficial to reduce the loss. As can be seen from Figures 10-12, the top of the flow channel between the pressure surface of the main blade and the suction surface of the splitter blade becomes narrower. Further, the back-bending angle is increased after optimisation, which reduces the pressure expansion angle and reduces the return loss. This is the main reason for the reduction of the top \begin{table}
\begin{tabular}{c c c c c} \hline
**100,000** & **Mass Flow** & **Total Pressure Ratio** & **Isentropic Efficiency** & **Comprehensive Surge Margin 1** \\
**rpm** & **(g/s)** & & & \\ \hline Original & 118.32 & 2.70 & 83.54\% & 19.4\% \\ Optimised & 128.76 & 2.72 & 84.83\% & 25.6\% \\
**Relative change** & **+8.8\%** & **0.74\%** & **+1.29\%** & **+6.2\%** \\ \hline \end{tabular}  
* _Comprehensive surge margin_ \(=\left(\frac{p_{\text{S}}\times Md}{\text{P}\times Md}-1\right)\times 100\%\), _PS_: total pressure at the surge point; _Pd_: total pressure at design point; _MS_: mass flow at the surge point; _Md_: mass flow at the design point.  
\end{table} 
Table 7: Comparison of the performance at the design point before and after optimisation (rated operating condition). Figure 12: Aerodynamic performance curve at different conditions before and after optimisation. clearance and loss at the outlet of the rated and common operating conditions and the increase of efficiency. This is the main reason for the reduction of tip and outlet losses. Figure 15 shows the isentropic efficiency changes along the span-wise at the downstream outlet for different operating conditions before and after optimisation. It can be seen that the most significant efficiency improvement is roughly in the area of 80% in the span-wise direction. As such, the flow field structure at the 80% height (H) of the impeller was chosen as the focus of the analysis. Figure 16 shows the static pressure distribution on the blade surface at the 80% height of the impeller before and after the optimisation of the rated operating condition. Figure 17 shows the relative Mach number contour on the B2B surface at the 80% height of the impeller before and after the optimisation of the rated operating condition. After optimisation, the positive angle of the attack at the inlet is reduced, the matching of airflow is improved, the area and maximum value of the high relative Mach number of the front edge A and B of the main blade suction are reduced, and the shock loss at the inlet is reduced. At the same time, the loss of the interaction between the shockwave and the boundary layer is reduced, which makes the flow separation in the latter half of the suction surface move backwards. Further, the separation area is reduced, and the separation loss is  
Figure 14: Entropy contour of the S3 cross-section before and after optimisation (common operating condition). Figure 13: Entropy contour of the S3 cross-section before and after optimisation (rated operating condition). reduced. The decrease of the positive angle of attack also increases the flow area, which increases the mass flow after optimisation. The static surface pressure of the suction surface of the main blade and splitter blade is significantly reduced, increasing the relative Mach number in the C, D and E regions.