## 5 Optimal Design of Four Kinds of Axial Compressors
### CFD Verification  
The aerodynamic performance of the aforementioned four types of compressors will be illustrated by NUMECA.  
As Table 5 displays, the predicted total pressure ratio and adiabatic efficiency of the 4-stage compressor have converged with the node number of 6,009,601, which will be used in this work. The computational grid is demonstrated in Figure 12.  
Table 6 presents a comparison between detailed design results and CFD prediction of the 4-stage, 5-stage, 6-stage, and 7-stage compressors. The maximum relative errors between the design results and CFD prediction are 1.70%, 1.02%, and 1.92% for adiabatic efficiency, total pressure ratio, and mass flow rate, respectively. The CFD simulation confirms that the design adiabatic efficiencies increase 0.80%, 2.44%, 0.56%, and 1.34% for the 4-stage, 5-stage, 6-stage, and 7-stage compressors after optimization, respectively.  
Figure 12: Computational grid of the 4-stage compressor.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multicolumn{3}{c}{**Node Number**} \\ \cline{2-4}  & **4,507,617** & **6,009,601** & **9,186,193** \\ \hline Total pressure ratio & 3.89 & 3.90 & 3.90 \\ Adiabatic efficiency & 81.35\% & 81.39\% & 81.38\% \\ Mass flow rate(kg/s) & 180.64 & 180.68 & 179.71 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Grid independency examination.  
Figure 13 displays total pressure along the row-wise direction for CFD prediction and optimal design intention of four kinds of compressors at design conditions. It could be concluded that the developed method can accurately predict total pressure ratio.  
Figure 14 presents rotor 1 outlet total pressure for CFD prediction and optimal design results of four kinds of compressors. The results of the comparative studies indicate a pretty good consistency of the stage match in the main flow region.  
Overall, the developed method is sufficient for the optimization of 4-stage, 5-stage, 6-stage, and 7-stage compressor configuration. The preliminary optimal design consumed a few minutes and the detailed throughflow design only needed several seconds on a PC. The optimal design results were verified with the CFD prediction. Each CFD calculation used four cores in parallel on a PC and required about 2 h to 3 h before reaching sufficient convergence for 4-stage, 5-stage, 6-stage, and 7-stage axial-flow compressors. Throughflow-based optimization and three-dimensional blade optimization will be conducted in future.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Number of Stages**} & \multicolumn{4}{c}{**Initial**} & \multicolumn{2}{c}{**Optimal**} \\ \cline{3-8}  & & **Design** & **CFD** & **Errors** & **Design** & **CFD** & **Errors** \\ \hline \multirow{4}{*}{Total pressure ratio} & 4-stage & 3.94 & 3.90 & 1.02\% & 3.94 & 3.92 & 0.51\% \\  & 5-stage & 3.94 & 3.94 & 0.00\% & 3.94 & 3.93 & 0.25\% \\  & 6-stage & 3.94 & 3.96 & 0.51\% & 3.94 & 3.90 & 1.02\% \\  & 7-stage & 3.94 & 3.97 & 0.76\% & 3.94 & 3.93 & 0.25\% \\ \hline \multirow{4}{*}{Adiabatic efficiency} & 4-stage & 80.31\% & 81.39\% & 1.34\% & 83.51\% & 82.19\% & 1.58\% \\  & 5-stage & 83.95\% & 83.61\% & 0.41\% & 84.69\% & 86.05\% & 1.61\% \\  & 6-stage & 83.10\% & 84.51\% & 1.70\% & 85.97\% & 85.07\% & 1.05\% \\  & 7-stage & 84.14\% & 85.32\% & 1.40\% & 86.15\% & 86.66\% & 0.59\% \\ \hline \multirow{4}{*}{Mass flow rate (kg/s)} & 4-stage & 179.08 & 180.68 & 0.89\% & 179.08 & 181.68 & 1.45\% \\  & 5-stage & 179.08 & 178.86 & 0.12\% & 179.08 & 182.59 & 1.96\% \\ \cline{1-1}  & 6-stage & 179.08 & 181.52 & 1.36\% & 179.08 & 182.26 & 1.78\% \\ \cline{1-1}  & 7-stage & 179.08 & 182.23 & 1.76\% & 179.08 & 182.51 & 1.92\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The design results and CFD prediction of four compressors.  
Figure 13: Rowwise total pressure.