## 2 Methods
### CFD Method
#### 2.1.2 Rotor 67 Simulation  
NASA Rotor 67 [33] is a low-aspect-ratio transonic axial-flow fan rotor with experimental data that was used as the reference design. Table 1 shows the primary features of Rotor 67. Note that the observed tip clearance was 0.061 cm rather than the designed value of 0.101 cm [33].  
Figure 1: Overall structure of the artificial intelligence design framework, with a hierarchical structure. The CFD manager calculates the operating characteristics of rotors in multiple threads, extracts the performance, and manages the data.  
Different grids were calculated, with node numbers of 0.8 M, 1.2 M, 1.6 M, and 2.0 M. The setting \(y^{+}=1\) was specified for all grids, and the 1.2 M grid was shown in Figure 2. The calculated operating characteristics and the experimental results are plotted in Figure 3. The pressure ratio and efficiency fit the experimental data well for the medium (1.2 M) and fine (1.6 M and 2.0 M) meshes, while the coarse mesh deviated from the experimental values. The calculated shock mass flow rate was 34.3 kg/s, slightly less than the experimental value and considered acceptable.  
Physically, rotating stall is an unsteady process, but the rotor was analyzed at steady state. Thus, some of the time-averaged features or convergence criteria could approximately indicate the 'numerical stall point' [15; 34; 35]. The calculation was considered converged if the adiabatic efficiency variation was less than 0.04% per 100 iterations and was regarded as stalled if it did not converge. The calculated stall mass flow was about 93% for the grids with 1.2 M, 1.6 M, and 2.0 M nodes. Due to the insufficient special resolution, CFD cases with 0.8 M grid were harder to diverge and obtained a lower stall mass flow rate numerically. Moreover, the pressure ratio and efficiency were also changed since the 0.8 M  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Rotational speed (rpm) & 16,043 & Relative tip Mach number & 1.3 \\ Tip clearance (cm) & 0.101 & Mass flow rate (kg/s) & 33.25 \\ Number of blades & 22 & Pressure ratio & 1.63 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of Rotor 67 [33].  
Figure 3: Operating characteristics of NASA Rotor 67 with 0.8 M, 1.2 M, 1.6 M, and 2.0 M grids.  
Figure 2: The multiblock structured O–H grid with 1.2 M nodes.  
grid captured fewer flow details. The near stall mass flow rate and the pressure ratio at \(\dot{m}=0.97\) of different grids were plotted in Figure 4, showing that the results changed only slightly at grid numbers larger than 1.2 M. Thus, the grid independency was acceptable, and the 1.2 M grid was selected. The shock wave structure of different spans is shown in Figure 5. The calculated shock wave showed similar features to the experiment [33]. An oblique shock wave was identified at the leading edge of the blades, and normal shock waves were found in the passages.  
Figure 4: The near stall mass flow rate and the pressure ratio at \(\dot{m}=0.97\).  
Figure 5: Relative Mach number distribution of the experimental [33] and CFD results: (**a**) 90% span of the experimental (left) and simulated (right) results; (**b**) 70% span of the experimental (left) and simulated (right) results. Red dotted line is to denote the shock wave.  
The pressure ratio and temperature ratio distributions of the near-peak efficiency are plotted in Figure 6. The CFD results fit the experimental results well. The CFD tools and methods were confirmed to give suitable results and were then applied to generate and evaluate the rotor geometries generated by agents.