## 2 Computational Model and Numerical Algorithm
### Numerical Algorithm  
The three-dimensional Large Eddy Simulation (LES) equations [17; 18] coupled with dynamic Smagorinsky subgrid model are employed for numerical simulation of the aerodynamics on wing and flap configuration. The commercial CFD program ANSYS FLUENT 19.1 is used to simulate the flow field. LES method directly calculates the turbulent motion larger than the grid scale through the unsteady Navier-Stokes (NS) equations, while the influence  
Figure 1: Schematic diagram of wing and flap configuration. Figure 2: Anechoic wind tunnel and 63-channel phased array for experiment. of small-scale vortices on large-scale vortices is reflected through subgrid model [19; 20]. In LES method, two parts are divided for instantaneous variable \(\varphi\), given by  
\[\varphi=\overline{\varphi}+\varphi^{\delta} \tag{1}\]  
where \(\overline{\varphi}\) is the large-scale average component, which is processed using a filter function \(\overline{\varphi}=\int_{D}\varphi D(x,x^{\delta})\mathrm{d}x^{\delta}\). \(D\) is the flow region, \(x\) is the spatial coordinate in the filtered large-scale space, \(x\)' is the spatial coordinate in the actual flow region, and \(D\) (\(x\), \(x\)) determines the scale of the solved vortex. \(\varphi^{\delta}\) represents the small-scale components. The unsteady NS equation is processed by the filter function \(D(x,x^{\delta})\), and the following can be obtained:  
\[\frac{\partial}{\partial t}(\rho\overline{u}_{i})+\frac{\partial}{\partial x _{j}}\big{(}\rho\overline{u}_{i}\overline{u}_{j}\big{)}=\quad\frac{\partial \overline{p}}{\partial x_{i}}+\frac{\partial}{\partial x_{j}}\bigg{(}\mu\frac {\partial\overline{u}_{i}}{\partial x_{j}}\bigg{)}\quad\frac{\partial\tau_{ij} }{\partial x_{j}} \tag{2}\]  
\[\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x_{i}}(\rho\overline {u})=0 \tag{3}\]  
where \(\tau_{ij}\) is the subgrid scale stress, referred to as SGS stress, which reflects the influence of small-scale vortex motion on the NS equation. According to Smagorinsky model, SGS stress was given by  
\[\tau_{ij}\quad\frac{1}{3}\tau_{kk}=\quad 2\mu_{i}\overline{S}_{ij} \tag{4}\]  
where \(\mu_{t}=\big{(}C_{s}\Delta\big{)}^{2}\big{|}\overline{S}\big{|}\) is the turbulent viscosity at the sublattice scale. \[\overline{S}_{ij}=\frac{1}{2}\bigg{(}\frac{\partial\overline{u}_{i}}{\partial x _{j}}+\frac{\partial\overline{u}_{j}}{\partial x_{i}}\bigg{)} \tag{5}\]  
\[\bigg{|}\overline{S}\bigg{|}=\sqrt{2\overline{S}_{ij}\overline{S}_{ij}} \tag{6}\]  
\[\Delta=\big{(}\Delta_{x}\Delta_{y}\Delta_{z}\big{)}^{1/3} \tag{7}\]  
where \(\Delta_{x}\) represents the grid size along the x-axis, and \(C_{S}\) is Smagorinsky constant. The sound source term is calculated by unsteady CFD, and then the sound propagation characteristics are obtained by acoustic analogy method. The calculation methods of sound propagation characteristics mainly include [PERSON] acoustic analogy equation [21], [PERSON]'s acoustic analogy equation [22], FW-H acoustic analogy equation [23], and Kirchhoff integral method [24]. The FW-H acoustic analogy equation is used in present paper. The FW-H acoustic analogy method is based on the near-field flow solution, which is used as the sound source signal, and the aerodynamic noise at the far-field observation point is obtained by integrating the FW-H formula, given by  
\[\begin{array}{ll}\bigg{(}\frac{1}{\partial^{2}}\frac{\partial^{2}}{\partial ^{2}}&\frac{\partial^{2}}{\partial x_{i}^{2}}\bigg{)}\,p^{\delta}(x,l)&=\frac {\partial}{\partial t}\,\tau[\rho_{0}\
u_{n}+\rho(u_{n}\quad\
u_{n})]\delta(f )g\\ &\frac{\partial}{\partial x_{i}}\bigg{\{}\bigg{[} \begin{array}{cc}&\rho_{l,j}^{\delta}&\eta_{j}+\rho u_{l}(u_{n}\quad\
u_{n})\end{array}