# A New Flow Control Method of Slat-Grid Channel-Coupled Configuration on High-Lift Device
## 3 Verification  
Calculation Method and Verification of Aerodynamic Characteristics of the Multi-Section Airfoil 30P30N  
In the present simulation, the flow field was assumed to be described by the 2D Reynolds-averaged Navier-Stokes (RANS) equations. The turbulence model adopted was the \(k-\omega\) SST model. This turbulence model uses the damping function in the vortex viscosity model. It is more accurate at simulating the aerodynamic characteristics and pressure distribution of multi-section airfoil [21; 22]. This has wide applicability and good prediction performance for separation flows with high-lift configurations.  
The \(k-\omega\)_SST_ model formula is given as:  
\[\begin{array}{l}\mu_{t}=\frac{\rho a_{1}k}{\max(a_{1}\omega(\omega)T_{2})}\\ \frac{\partial(\omega k)}{\partial t}+u_{i}\frac{\partial(\omega k)}{\partial x _{i}}=P_{k}-\beta_{k}\rho k\omega+\frac{\partial}{\partial x_{i}}\Big{[} \Big{(}\mu_{l}+\frac{k_{l}}{\sigma_{k}}\Big{)}\frac{\partial k}{\partial x_ {i}}\Big{]}\\ \frac{\partial(\omega\omega)}{\partial t}+u_{i}\frac{\partial(\omega\omega)}{ \partial x_{i}}=C_{\omega}P_{\omega}-\beta_{\omega}\rho\omega^{2}+\frac{ \partial}{\partial x_{i}}\Big{[}\Big{(}\mu_{l}+\frac{k_{l}}{\sigma_{\omega}} \Big{)}\frac{\partial\omega}{\partial x_{i}}\Big{]}+2\rho(1-F_{1})\frac{1}{ \sigma_{\omega}\omega}\frac{1}{\omega}\frac{\partial k}{\partial x_{i}}\frac {\partial\omega}{\partial x_{i}}\\ \end{array} \tag{4}\]  
The modified \(k-\omega\) SST turbulence model constructs the model coefficient in the vortex viscosity coefficient of the equation as the following equation:  
\[\alpha^{*}=\alpha_{\infty}^{*}\left[\frac{\alpha_{0}^{*}+\frac{\text{Re}_{t}} {\text{R}_{k}}}{1+\frac{\text{Re}_{t}}{\text{R}_{k}}}\right] \tag{5}\]  
where \(\text{Re}_{t}=\rho\kappa/\mu\omega\) is the turbulent Reynolds number.  
A numerical simulation of the 30P30N airfoil is taken as an example to verify the numerical simulation method of the two-dimensional lifting device adopted in this paper. The multi-section airfoil 30P30N of the high-lift device is widely used by CFD workers [23; 24]. The deflection angle of the leading-edge slat and trailing-edge flap of this airfoil is \(30^{\circ}\), the  
Figure 2: Optimization flow chart of grid-slat configuration.  
slot width of the leading-edge slat is 2.95%, and the overhang is \(-2.5\%\). The trailing-edge flap slot width is 1.27%, and the extension is 0.25% [23], as shown in Figure 3.  
The comparative test data are the wind tunnel test results of McDonnell Douglas Aerospace and NASA Langley [25; 26]. According to actual wind tunnel test conditions, the attack angles of the incoming flow are \(-0.17^{\circ}\sim 21^{\circ}\). The Reynolds number is \(~{}9\times 10^{6}\). The Mach number is 0.2. All the calculations provided here were obtained using the coupled solver of Fluent code. A second-order upwind difference scheme was chosen for momentum and turbulent kinetic energy, respectively. The incoming flow pressure is the standard atmospheric pressure. The mesh is generated as shown in Figure 4. For the component grid, we used a hybrid mesh with 40,792 cells. Wall spacing of the first layer is \(1.71\times 10^{-3}\), which satisfies \(y+\leq 1\).  
In the process of calculation, we monitored the convergence of residuals on the one hand, and found that the energy item decreases to \(10^{-9}\) and other residuals except the energy item decrease to \(10^{-4}\). On the other hand, the calculation results cl or cd basically do not change with the increase in iteration steps. In Figure 5a, it seems that good agreement is achieved by comparing the calculated lift coefficient of the airfoil with the wind tunnel test results and that the deviation is large only near the stall angle of attack. As shown in Figure 5c,d, the surface pressure coefficients distribution of the main wing and flap coincide very well, and the pressure coefficients of the slats are basically consistent with the experimental data.