# Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine
## 5 Coupling Calculations of the Original and Optimized Designs
### 100% Load  
Figure 14 shows the meridional streamline chart at 100% load and illustrates a large separation vortex in the vane-less diffuser in the original design. In the optimized design, the separation vortex disappeared in the vane-less diffuser with the decrease in diameter ratio, \(D_{3}/D_{2}\). The flow condition at the vaned diffuser inlet improved. Therefore, a separation area was not observed in the vaned diffuser. Figure 15 shows the Mach number distribution in different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 100% load. An obvious backflow was observed at the vaned diffuser inlet in the original design at 10% span because the diameter ratio was large, and the separation vortex in the vane-less diffuser worsened the flow condition at the vaned diffuser inlet. The overall flow in the vaned diffuser was good with no obvious vortex. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \begin{tabular}{c} **100\% Load** \\ **Original** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Optimized** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Relative** \\ **Error** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **90\% Load** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Optimized** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Relative** \\ **Error** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **60\% Load** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Optimized** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Relative** \\ **Design** \\ \end{tabular}  & \ \begin{tabular}{c} **Optimized** \\ **Design** \\ \end{tabular}  & \begin{tabular}{c} **Relative** \\ **Error** \\ \end{tabular}  \\ \hline Low-pressure stage & 4.24 & 4.41 & 4.01\% & 3.64 & 3.83 & 5.22\% & 2.58 & 2.64 & 2.33\% \\ \hline Low-pressure stage efficiency & 0.793 & 0.822 & 2.90\% & 0.797 & 0.830 & 3.30\% & 0.783 & 0.831 & 4.80\% \\ \hline High-pressure stage & 2.574 & 2.68 &  
Figure 14: Meridional streamline at 100% load. Figure 15: Mach number distribution at different spans of the original and optimized designs of the low-pressure-stage centrifugal compressor at 100% load. In the optimized design, the diameter ratio of the vane-less diffuser decreased, and the flow was uniform without separation due to the use of the tandem diffuser. Therefore, the vaned diffuser inlet was in a good condition without backflow. An obvious low-speed area was observed at the end of the second-row diffuser, and no obvious separation was observed in the passage. The inlet flow was not affected and had no backflow at 50% span because the vaned diffuser inlet flow was far from the vane-less diffuser separation area. The gas flow in the vaned diffuser was stable, and a large separation area appeared at the vaned diffuser outlet. In the optimized design, a high Mach number area existed in the diffuser inlet on the first row because the vaned diffuser inlet was close to the impeller. A large low-speed area was observed in the diffuser end on the second row, similar to the 10% span. At 90% span, the separation area inside the vaned diffuser had no influence on the vaned diffuser inlet flow in the original design, and the inlet condition was improved. The flow showed significant deceleration in the vaned diffuser, and the Mach number in the middle of the vaned diffuser dropped to approximately 0.2. The low-speed area at the vaned diffuser outlet expanded further and occupied approximately 80% of the flow passage. In the optimized design, the flow deceleration process was obvious in the vaned diffuser, and the Mach number at the outlet dropped to below 0.2. However, the flow in the passage was stable with no obvious separation phenomenon. In general, in the original design, the flow condition was affected by the separation area in the vaneless diffuser, and the Mach number distribution was completely different at different spans.