## 3 Simulation Analysis
### Simulation Analysis: Effect of Flow Field on Wavefront  
In accordance with the design introduced above, we gridded the flow field in the beam expanding system; the result is shown in Figure 3.  
In such a simulation, the airflow is mainly used to observe the spread of airflow expelled after the beam expanding system. For the flow field simulation, we used Fluent (CFD calculation software) for calculations. For simulation purposes, we set the calculation parameters as shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline
**Project** & **Number of Rows** & **Number of Holes Per Row** \\ \hline Plan A & 4 & 90 \\ Plan B & 8 & 90 \\ Plan C & 16 & 90 \\ \hline \end{tabular}
\end{table} 
Table 1: Initial simulation schemes. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value** \\ \hline Material & Ideal gas \\ Model & Realisable \(k-\varepsilon\) \\ Inlet & Mass flow rate \\ Mass flow rate & 0.1 kg/s \\ \hline \end{tabular}
\end{table} 
Table 2: Settings of the computational fluid dynamics (CFD) software. Figure 3: Simulation model of the beam expanding system. Figure 2: Simulation model of the beam expanding system. As shown in these figures, the flow field in the beam expanding system gradually improves as the number of inlet rows increases. When there are only four rows of air holes, there are two obvious large eddies in front of the main mirror, and there are several small eddies near the air intakes and in front of the third mirror. The directions of the velocity vectors at the inlet holes are obvious. As seen from the density contour map, the density contour lines in the beam expanding system are dense with multiple centres. This indicates that the flow field is rather disordered in this state. The fluid density gradient is large, and the gradient directions are disorderly. When the number of air inlet rows is increased to eight, several small eddies around the air intakes merge into several large eddies. At the same time, the directions of the velocity vectors at the inlet holes are weakened. From the density contour map,  
By observing the velocity vector diagram for plan D, it is found that the weak eddy currents near the inlet holes are significantly reduced compared with plan C. The eddies in front of the third mirror change from two obvious eddies to a single weak eddy. The density contour lines are obviously sparser, indicating that the flow field in the beam expanding system tends to be simpler and the density gradient is decreased (Figure 7). When the number of holes per row is increased to 360, the flow field vortex in front of the third mirror essentially disappears, and those eddies in front of the main mirror are significantly weakened. The density contour lines of the flow field tend to be simple and sparse, indicating that the flow field in the beam expanding system is simple and that the density field distribution is highly uniform. Below, we analyse the last three plans from the perspective of the wavefront aberration. Following the ray tracing process described in Section 2.2 above, we conducted ray tracing analyses of the optical paths in the beam expanding system. The PV (peak-to-valley) and RMS of wavefront aberration under these three plans are listed in Table 4. By comparing the wavefront aberrations of a beam passing through the beam expanding system, we can clearly see that plan D is significantly superior to plan C. This finding indicates that when the number of holes per row is 180, the flow state in the beam expanding system is better than it is with 90 holes per row. By comparing plan D with plan E, we can see that when the number of holes in a single row is further increased, and the further improvement in the wavefront aberration is significantly weaker. Thus, an increase in the number of holes per row from 180 to 360 has little effect on the wavefront aberration. However, from Figure 8, we can clearly see that the 4 th-order Zernike coefficient under plan E is increased compared with that under plan D, whereas the 22 nd-order coefficient is significantly decreased.