# Optimization of a Centrifugal Compressor Using the Design of Experiment Technique
## 6 Results and Discussions  
### Effective Parameter Identification  
The performance of each design point is evaluated by total pressure ratio and total to total isentropic efficiency from compressor inlet to the diffuser outlet. Pressure ratio is calculated by means of following relation:  
\[Pr=\left[\int P_{03}d\hat{m}/\hat{m}\right]/P_{00} \tag{9}\]  
In which the numerator is mass flow average of total pressure at the diffuser outlet. Using pressure ratio, the isentropic efficiency is calculated using Equation (10). \[\eta_{tt}=T_{00}\left(Pr^{(\gamma-1)/\gamma}-1\right)/(T_{03}-T_{00}) \tag{10}\]  
The normal probability plots for stage I contains 32 runs are shown in Figures 8 and 9 for the effects on \(\eta_{tt}\) and \(Pr\) respectively. Among the five investigating parameters in this stage, as is expected, the impeller meridional geometry, as defined by \(M_{1}\) to \(M_{4}\) contains the main parameters. The diffuser inlet curvature varied by \(M_{5}\), has a negligible effect on both efficiency and pressure ratio. However the results shows that the two parameters \(M_{1}\) and \(M_{4}\) which adjust the hub and shroud profile at the impeller outlet respectively have the most significant effect in comparison to the others. Among the two factor interaction effects, the \(M_{1}M_{4}\) is apart from line in Figure 8. Both the \(M_{1}M_{4}\) and \(M_{2}M_{3}\) points in Figure 9 show that they play an important role in total pressure ratio in this case. Generally the main effects and the low order interactions are dominant and the higher order interactions are usually negligible [5]. As the \(M_{1}\) to \(M_{4}\) main effects are positives, this means that each parameter at high level solely improves the efficiency and pressure ratio. It should be noted that the high level for these parameters are considered in a way that the flow passage width increases. Whereas when both \(M_{1}\) and \(M_{4}\) at the high levels or both at the low level, efficiency and pressure ratio decrease as it has a negative value. The same analysis is true for both \(M_{2}\) and \(M_{3}\) on the pressure ratio. When both \(M_{1}\) and \(M_{4}\) or both \(M_{2}\) and \(M_{3}\) are considered at high levels, it means that respectively the flow passage at the outlet or at the inlet, becomes wide and when they are at the low levels it narrows the flow passage. Therefore increasing or decreasing flow passage area by simultaneously changing the hub and shroud curves is deleterious to the performance. Figure 8: Normal probability plots for stage I showing effects on efficiency (total to total). In the same way, the normal probability plots for stage II, contains 16 runs, are extracted. Figures 10 and 11 are shown to investigate the effects of blade angle distribution on \(\eta_{tt}\) and \(Pr\) respectively. As seen in Figure 10, \(B_{1}\), \(B_{2}\), \(B_{3}B_{4}\) and also all two-factor interactions with \(B_{2}\) are apart from the straight line; however the other effects do not lie along the line and can be considered as significant as the mentioned ones. Whereas in Figure 10, \(B_{1}\) to \(B_{3}\) clearly are the dominant factors in pressure ratio. The \(B_{1}\) factor is representative for \(\beta\) angle distribution slope at the inlet for hub. The value of its effect on the isentropic efficiency (Figure 10) is positive however its effect on pressure ratio (Figure 11) is negative. This means that increasing \(B_{1}\), increases the efficiency and reduces the pressure ratio. Increasing the \(B_{1}\) value is equivalent to decreasing the blade curvature as it defines the angle variation (Figure 4). The \(B_{2}\) value also shows the same effect on the pressure ratio. By considering two-factor interactions \(B_{2}B_{3}\) and \(B_{3}B_{4}\) on the efficiency, it is clear that, the efficiency will improve when the hub and shro  
Figure 10: Normal probability plots for stage II showing effects on efficiency (total to total). Figure 9: Normal probability plots for stage I showing effects on pressure ratio.