# Optimization of a Centrifugal Compressor Using the Design of Experiment Technique
## 6 Results and Discussions
### Effective Parameter Identification
In conclusion for the case II investigation, \(B_{1}\) and \(B_{2}\) can be considered as the most dominant factors and both efficiency and pressure ratio will improve by controlling the angle difference between hub and shroud in the defined ranges. To better capture the effects of blade angle distribution on the fluid behavior, the streamlines for the original case and the case with \(\{B_{1}^{+}B_{2}^{+}B_{3}^{+}B_{4}^{-}\}\) which is shows the best efficiency are shown in Figure 12. The streamlines for one main impeller and splitter passage are shown at span 0.8 where the effect of shroud curvature which is controlled by \(B_{3}\) and \(B_{4}\) could be realized. The streamlines show that how the blade angle adjustment could lead to guide the flow through the passage following the blade where the fluid intensify is escaping from the tip clearance at that span. The blade outlet angle at hub and shroud for the case with \(B_{2}^{+}\) and \(B_{4}^{-}\) has the lowest difference among the test cases and it gives the most uniform flow in the span-wise direction. Similarly, the normal probability plots for isentropic efficiency and pressure ratio are shown in Figures 13 and 14 respectively for stage III. The plots show that moving \(I_{1}\) along the hub curve toward the outlet increases the pressure ratio and decreases the efficiency; however moving \(I_{3}\) toward the outlet results in pressure ratio and efficiency improvement. When both \(I_{1}\) and \(I_{2}\) are moving simultaneously toward the inlet or outlet, it also results in the performance increasing, whereas moving \(I_{2}\) towards the outlet leads to an unconventional incline at impeller inlet and reduces the pressure ratio. Figure 15 shows passage streamlines for two cases named \(A\) and \(B\) which their configuration are \(\{I_{1}^{+}I_{2}^{-}I_{3}^{-}I_{4}^{+}\}\) and \(\{I_{1}^{-}I_{2}^{-}I_{3}^{+}I_{4}^{-}\}\) respectively. In Case \(A\) with \(I_{3}^{-}\) and \(I_{4}^{+}\) the splitter at hub starts earlier and it has longer length but at shroud it has short length. Case \(B\) has \(I_{3}^{+}\) and \(I_{4}^{-}\) which means shorter hub and  
Figure 11: Normal probability plots for stage II showing effects on pressure ratio. Figure 12: Streamlines of the original case (left) versus case \(\{B_{1}^{+}B_{2}^{+}B_{3}^{+}B_{4}^{-}\}\) (right) at span = 0.8.  
longer shroud in comparison with Case \(A\). It can be seen that in Case A the longer length at span 0.1 helps the flow to follow the splitter curvature earlier. At mid span (\(S=0.5\)) two cases show nearly the same behavior; however near the shroud, the flow cannot follow the blade curvatures in Case \(A\). The flow in Case \(B\) is guided around the splitters with limited circulation. The flow structure describes how the losses in cases with \(I_{3}^{+}\) and \(I_{4}^{-}\) configuration i.e. Case B are minimized and how it results in higher efficiency. It should be mentioned that the splitter with longer length in Case A adds additional friction loss. Figure 14: Normal probability plots for stage III showing effects on pressure ratio. \[\eta_{tt}=T_{00}\left(Pr^{(\gamma-1)/\gamma}-1\right)/(T_{03}-T_{00}) \tag{10}\]0 Normal probability plots for stage III showing effects on efficiency (total to total).