## 3 Numerical Validation  
According to the experimental data performed by [PERSON] [25] on pressure distribution, the numerical results obtained by CFD code are verified. Y+ is the main indicator for grid analysis, which plays an important role in turbulence modeling: it determines the height of the first cell normal to the wall. In this study, the height of the first cell is refined to obtain a Y+ value of approximately 1.0 to confirm the numerical accuracy. The X+ and Z+ estimations are 100 and 150 according to the length and width of the first cell, respectively. Similar grid scales can be referred to in the aerodynamic and aeroacoustics analysis of high-lift configuration using LES method [26]. The structural grids and the zoom-in view of the leading edge and trailing edge are shown in Figure 3. The parameters of mesh configuration are listed in Table 2. \begin{table}
\begin{tabular}{l l} \hline Total amount of cells & 41.4 million \\ \hline Span-wise Resolution & 85 cells \\ \hline Initial height of the first cell near the wall & 0.05 mm \\ \hline Streamwise resolution along the wing & 480 cells \\ \hline Streamwise resolution along the flap & 150 cells \\ \hline Boundary layer resolution of the wing & 60 cells \\ \hline Boundary layer resolution of the flap & 60 cells \\ \hline Vertical resolution in the leading edge of the wing & 60 cells \\ \hline \end{tabular}
\end{table} 
Table 2: Mesh configuration. Figure 3: Structural meshes of wing and flap configuration: (**a**) the whole view; (**b**) zoom-in view near the leading edge; (**c**) zoom-in view near the flap. In the numerical simulation, the implicit dual time-stepping approach was used to solve the unsteady flow field. To predict noise with frequency below 10 kHz in noise analysis, and according to the maximum frequency calculation formula \(F=1/2\Delta t\), the time step \(\Delta t\) was set to 5 10 5 s.  
Comprehensively considering the computational accuracy and efficiency of numerical simulation, according to the research experience of relevant researchers [27], the spanwise width of the model was set to 0.4 times of the flap chord length. The porous surface has an important influence on the analysis of noise [28]. Turbulence and vortices in the wake region are mainly quadrupole sound sources, which have little effect on the far-field noise at low speed. In this paper, the influence of dipole sound source is mainly considered, and the noise integral surface is directly taken on the solid wall. After the flow field is obtained by steady calculation, the mean values were obtained in last 5 s of the unsteady simulation process. The comparison of the mean pressure distributions along the surface between the numerical simulation and experimental results from the VALIANT database is presented in Figure 4. Figure 4a shows that there is a pressure rise at the upper trailing surface of the main wing, which is due to the block effect from the flap. Certain deviations could be observed here between the numerical results and experimental results, which could also be found in the research by [PERSON] [29] and NUMECA [29]. Basically, the pressure coefficients on the surface of wing and flap from numerical simulations agree well with the experimental results. The z-direction vorticity contours calculated by the numerical approach are shown in Figure 5. Small vortex structures form at the regions where the pressure coefficient is high, and the flow becomes more chaotic. The wake of the wing has a great influence on the upper surface of the flap, which makes the flow on the upper surface of the airfoil separate rapidly. Figure 6 shows the iso-surfaces of Q-criterion. The vortex structures on the upper and lower surfaces of the airfoil are significantly less than that on the flap, since the flow on the airfoil surface is less disturbed and there is basically no flow separation.