# Effect of Vaneless Diffuser Shape on Performance of Centrifugal Compressor
## 3 Result and Discussion  
### Aerodynamic Performance Analysis  
The ratio of actual flow conditions to design flow conditions is defined as relative mass flow \(\varphi/\varphi_{\text{D}}\). It can be known from Table 3 that under the design conditions and 0.6 relative mass flow conditions, the whole stage pressure ratio can be increased through reducing diffuser width and the best effect on the pressure ratio improvement can be achieved by convergence of the vaneless diffuser width from the shroud side. However, the convergence of the diffuser width under the 1.125 relative mass flow condition causes the pressure ratio of the centrifugal compressor to decrease. This phenomenon is similar to the experimental results in literature [9], indicating that the positive effect cannot be achieved in making use of the convergence of the vaneless diffuser width under all conditions.  
In order to investigate which part of the centrifugal compressor is affected by the convergent diffuser width, the inlet and outlet pressure ratios of the impeller and the diffuser are extracted, as  
Figure 3: Comparison of calculated and experimental total pressure ratios.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Relative Mass Flow \(\varphi/\varphi_{\text{D}}\)** & **Vaneless Diffuser Shape** & **Press Ratio p/p\({}_{1}\)** \\ \hline
1.125 & Parallel & 1.914 \\
1.125 & Convergence from shroud & 1.905 \\
1.125 & Convergence from hub & 1.903 \\
1.125 & Convergence from shroud and hub equally & 1.904 \\
1.0 & Parallel & 1.931 \\
1.0 & Convergence from shroud & 1.970 \\
1.0 & Convergence from hub & 1.964 \\
1.0 & Convergence from shroud and hub equally & 1.967 \\
0.6 & Parallel & 2.309 \\
0.6 & Convergence from shroud & 2.342 \\
0.6 & Convergence from hub & 2.339 \\
0.6 & Convergence from shroud and hub equally & 2.341 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Total-to-total pressure ratio of centrifugal compressor.  
shown in Table 4. The convergence of the vaneless diffuser width can increase the impeller outlet pressure and has little effect on the change of the vaneless diffuser pressure ratio. Furthermore, it can be found that when the relative mass flow is 1.125, the impeller pressure ratio with convergent diffuser increases slightly but the pressure ratio of the convergent diffuser decreases compared with parallel wall diffuser case. This may be the reason for the convergence of the diffuser width but the increase of the centrifugal compressor pressure ratio in the near choking condition.  
Table 5 shows the isentropic efficiency of centrifugal compressors with different diffuser shapes under multiple operating conditions. Isentropic efficiency is the ratio of the isentropic power of the compressor to the actual power required by the compressor. It can be concluded from Table 5 that all three convergent shape vaneless diffusers improve the isentropic efficiency of centrifugal compressors. The maximum isentropic efficiency can be reached by converging the diffuser wall from the hub side at 1.125 and 1.0 relative mass flow conditions and from shroud side at 0.6 relative mass flow condition. The change of isentropic efficiency in the shape of the vaneless diffuser is also consistent with the experimental phenomenon in literature [9].