# Surrogate-Based Optimization of a Centrifugal Pump with
## 6 Results and Discussion
On the suction side a lower \(c_{f}\) distribution for the optimal geometry confirms a reduction of the losses. Figure 17 shows the static pressure at mid-span for the baseline (left) and optimized geometry (right). The pressure contours for the baseline are characterized by a low pressure area near the leading edge, which is completely removed in the optimal geometry, reducing also the cavitation problems. Figure 18 shows the velocity contours with streamlines at the plane \(z=5\) mm for the baseline (left) and optimized geometry (right). The small zone of acceleration near the leading edge of the suction side, probably motivated by a not correct blade inlet angle, is removed, and a smoother acceleration is visible in the blade channel. Finally, the wake near the trailing edge is reduced and the velocity distribution at the impeller outlet is more uniform. The flow in the meridional channel is analyzed in Figure 19. The velocity contours show a more uniform distribution along the span in the inlet pipe and inside the impeller for the optimal geometry. This is obtained with a modification of the hub and shroud profile, as shown in Figure 15. In particular, the reduction of the section at the end of the inlet pipe avoids the stall at the hub. Moreover, at the impeller outlet the velocity peak is reduced and the velocity distribution is more uniform along the blade height. Finally, the flow field in the volute is analyzed. In particular, Figures 20 and 21 show the pressure and velocity contours with streamlines in a plane at \(z=4\) mm. The pressure contours are quite similar for both baseline and optimized geometries. However, the latter shows a reduction of the low pressure zone at the volute tongue. The velocity contours show smaller values in the optimized geometry for the increased cross-section area (see Figure 22). Moreover, the small recirculation zone after the volute tongue is removed in the optimal geometry. Figure 16: _Cont._  
Figure 13:0 Pressure coefficient (**a**) and skin friction coefficient (**b**) along the blade for the baseline and the optimized geometry. Figure 13:1 Static pressure field in the blade to blade view at 50% of the span for the baseline (**a**) and optimized (**b**) geometries. Figure 13:2 Velocity field in the meridional channel for the baseline (**a**) and the optimized (**b**) geometries. Figure 13:3 Velocity contours and streamline in the plane \(z=5\) mm for the baseline (**a**) and the optimized (**b**) geometries. Figure 13:4 Static pressure field in the volume at \(z=4\) mm for the baseline (**a**) and the optimized (**b**) geometries. Figure 13:5 Velocity field and streamlines in the volume at \(z=4\) mm for the baseline (**a**) and the optimized (**b**) geometries. The distribution of the velocity vectors for the baseline and optimized geometry is displayed in Figure 23 for a plane at \(z=5\) mm. A small recirculation zone is evident near the leading edge of the baseline geometry, while the optimized geometry is characterized by a smooth distribution of the vectors. Figure 13:6 Velocity field at the solute outlet for the baseline (**a**) and the optimized (**b**) geometries. A comparison of the baseline and the optimal design in terms of the static pressure rise, \(\Delta p\), total pressure rise, \(\Delta p_{t}\) and hydraulic efficiency is reported in Figure 13:7 Moreover, also single components, i.e., impeller, vaneless diffuser and volute, are compared. The global efficiency is increased by 3%; this improvement has been obtained decreasing the power absorbed by the impeller, and slightly the total pressure rise. The impeller torque \(C\) (and the power at the impeller \(W\)) is reduced by 11% in the optimal design, and its efficiency, \(\eta_{imp}=\dot{Q}\Delta p_{t,imp}/\text{W}\), is increased by 3%. The reduction of \(C\) can be ascribed to the decrease of the blade loading, as shown in Figure 16 by the \(c_{P}\) distribution, and of the losses.