# Analysis and Improvement of a Two-Stage Centrifugal Compressor Used in an MW-Level Gas Turbine
## 4 Optimized Design of the High-Pressure-Stage Centrifugal Compressor  
The optimized design system [18] was adopted to optimize the aerodynamic layout of the high-pressure-stage centrifugal compressor. Table 3 shows a comparison of the parameters of the original and optimized designs. The geometric parameters after optimization changed only slightly, and the efficiency of the optimized design increased by approximately 0.2% compared with the original design. This finding shows that the impeller parameters are set reasonably in the original design. After optimization, the efficiency of the vaned diffuser outlet was 2.61% higher than that of the original design. This result indicates that the mismatch between the diffuser and impeller mainly lead to the low efficiency in the original design. Compared with the value of the divergent angle, \(2\theta\), in the original design, the value in the optimized design decreased significantly. The divergent angle is defined as follows:  
\[\tan\theta=\frac{D_{4}-D_{3}}{2L}.\]  
For the diffuser design, \(2\theta\) should be less than 12\({}^{\circ}\) to avoid gas over-expansion and separation. The experimental results showed that the loss coefficient of the vaned diffuser is related to the divergent angle. In general, the loss was minimal when \(2\theta=6^{\circ}\), and gradually increased with the growth of \(2\theta\). If the value of \(2\theta\) is too large, it could be reduced by increasing the diameter and number of blades. By contrast, the increase in diameter and blade number increased the loss in flow passage. Therefore, the influence of various parameters on the performance of the diffuser should be considered comprehensively in the design. In the original design, the large divergent angle increases the loss in  
Figure 9: Inlet attack angle distribution of the vaned diffuser in the optimized design. the vaned diffuser, which, in turn, leads to the low efficiency of the entire stage. In the optimized design, the divergent angle was effectively reduced, and the efficiency of the unit was improved by increasing the blade number and length. The divergent angle was reduced in the 1D optimized design system by increasing the blade number and length, as shown in Figure 10b, and the efficiency of the design was improved. This optimization method reduced the throat area of the vaned diffuser and changed the matching characteristics of the vaned diffuser and impeller. Therefore, it is necessary to make an optimized design on the matching characteristics of the impeller and vaned diffuser. The ratio of design \({A_{d}}^{*}/{A_{i}}^{*}\) to theoretical \({A_{d}}^{*}/{A_{i}}^{*}\) is 1.09 in the original design as shown in Table 4. It indicates that the chock mass flow of the vaned diffuser is larger than that of impeller. When the number of blades is increased and the blade diffuser is moved close to the impeller, the ratio of design \({A_{d}}^{*}/{A_{i}}^{*}\) to theoretical \({A_{d}}^{*}/{A_{i}}^{*}\) would be decreased to 0.948. The choke area decreased significantly to make the chock mass flow in the vaned diffuser much lower than that of impeller, which cannot meet the design requirements. Therefore, it is necessary to redesign the vaned diffuser to leave the chock  
Figure 10: Geometric structure of the vaned diffuser. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Optimized Design** & **Original Design** \\ \hline \(D_{\text{1s}}\) (m) & 0.071 & 0.073 \\ \(D_{\text{1t}}\) (m) & 0.192 & 0.134 \\ \(D_{\text{2}}\) (m) & 0.252 & 0.252 \\ \(L_{\text{2}}\) (m) & 0.057 & 0.058 \\ \(b_{\text{2}}\) (m) & 0.0956 & 0.00948 \\ \(D_{\text{3}}\) (m) & 0.274 & 0.282 \\ \(D_{\text{4}}\) (m) & 0.392 & 0.388 \\ \(D_{\text{3}}/D_{\text{2}}\) & 1.09 & 1.12 \\ \(2\theta\) & 11.9 & 15.7 \\ \(Z\) & 20 & 17 \\ \(\eta_{\text{2}}\) & 95.47\% & 95.24\% \\ \(\eta_{\text{3}}\) & 92.88\% & 92.37\% \\ \(\eta_{\text{4}}\) & 84.12\% & 82.29\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the parameters of the optimized and original designs.