# Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine
## 3 Optimization of the Low-Pressure-Stage Centrifugal Compressor  
An optimized design system [18] was adopted to optimize the aerodynamic layout of the low-pressure-stage centrifugal compressor. A comparison of the parameters of the original and optimized designs is shown in Table 1. The geometric impeller parameters after optimization changed minimally and, mainly due to a slight increase in the outlet width, \(b_{2}\), the efficiency of the optimized design increased by approximately 0.3% compared with the original design. This result shows that the impeller parameters are set reasonably in the original design. After optimization, the outlet efficiency of the vaned diffuser was 2.29% higher than that of the original design. This finding indicates that the mismatch between the diffuser and impeller mainly leads to the low efficiency in the original design. For the vane-less diffuser, pressure can be increased by increasing diameter ratio \(D_{3}/D_{2}\). However, if the increase in the diameter ratio is overly large, the efficiency of the entire stage would decrease. Thus, the ratio of \(D_{3}/D_{2}\) = 1.05:1.2 is recommended. In the original design, the diameter ratio, \(D_{3}/D_{2}\), is 1.34, which is much higher than the recommended value. In the optimized design, \(D_{3}/D_{2}\) is 1.1, which is within the reasonable design range. Thus, the loss in the vane-less diffuser was significantly reduced, leading to an increase in the efficiency of the entire stage. Figure 6: Performance curve of the high-pressure-stage centrifugal compressor. The 1D optimization results showed it was necessary to reduce \(D_{3}/D_{2}\) to improve the efficiency of the entire stage of the low-pressure-stage centrifugal compressor. When \(D_{3}/D_{2}\) was reduced, if the original shape of the vanes was still used in the vaned diffuser, the throat area of the vaned diffuser decreased, as shown in optimized design 1 in Figure 7. Then, the chock mass flow of the vaned diffuser decreased to have an influence on the matching of the diffuser and impeller. In order to improve the performance of the entire stage after optimization, it is necessary to analyze the matching of the diffuser and impeller. To achieve the best matching performance of the diffuser and impeller, the design ratio, \({A_{d}}^{*}/{A_{i}}^{*}\), should be as close to the theoretical level as possible [19]. The ratio of design \({A_{d}}^{*}/{A_{i}}^{*}\) to theoretical \({A_{d}}^{*}/{A_{i}}^{*}\) is 1.161 in the original design as shown in Table 2. It indicates that the chock mass flow of the vaned diffuser is larger than that of the impeller. When the vaned diffuser is moved toward the impeller, the ratio of design \({A_{d}}^{*}/{A_{i}}^{*}\) to theoretical \({A_{d}}^{*}/{A_{i}}^{*}\) would be decreased to 0.922. The choke area decreased significantly to make the chock mass flow in the vaned diffuser much lower than that of the impeller, which cannot meet the design requirements. Therefore, it is necessary to redesign the vaned diffuser to leave the chock mass flow of the unit unchanged when the diameter ratio \(D_{3}/D_{2}\) is reduced. Considering all factors, the original vaned diffuser was replaced by a tandem vaned diffuser as shown in optimized design 2 in Figure 7. By using the optimized method, the ratio of design \({A_{d}}^{*}/{A_{i}}^{*}\) to theoretical \({A_{d}}^{*}/{A_{i}}^{*}\) was 1.043, which is closer to 1 and indicates the better matching of the diffuser and impeller. The throat area of the vaned diffuser was slightly larger than that of the impeller, which made the choke mass flow of the optimized design consistent with that of the original design. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Optimized Design** & **Original Design** \\ \hline \(D_{18}\) (m) & 0.075 & 0.082 \\ \(D_{1t}\) (m) & 0.190 & 0.202 \\ \(D_{2}\) (m) & 0.326 & 0.326 \\ \  
The steady simulations were performed using the commercial software Numeca. The Spalart-Allmaras (SA) turbulence model was used.