# A New Flow Control Method of Slat-Grid Channel-Coupled Configuration on High-Lift Device
## 4 Optimization Example and Analysis  
Through optimization design, the values of design variables are shown in Table 3, and the configuration at this time is shown in Figure 7a. The grid-slat configuration plays a role in increasing lift and reducing drag through calculations. Figure 7b-d show the comparison of the lift coefficient, drag coefficient and lift-drag ratio between the original airfoil and the new configuration at different angles of attack. The simulation and optimization results show that the lift coefficient increases by 3.3%, the drag coefficient decreases by 12.7%, and the lift-drag ratio increases by 18.4% of the optimal configuration compared with the original airfoil at an angle of attack of 16.3\({}^{\circ}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **Grid Cell** & **Lift Coefficient** \\ \hline Case1 & 28,947 & 3.14498 \\ \hline Case2 & 40,792 & 3.13469 \\ \hline Case3 & 61,923 & 3.144985 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Grid independence verification. Figure 7: Numerical simulation comparison between original airfoil and optimal configuration. (**a**) Lift coefficient of slat; (**b**) Total lift coefficient; (**c**) Drag Coefficient; (**d**) Lift-drag ratio. In order to further clarify the mechanism of increasing lift and reducing drag of grid-slat configuration, Figure 8 describes the total lift coefficients of the original airfoil and the optimized airfoil at different angles of attack. The lift coefficients, extracted separately from the slats, show that the configuration not only improves the lift of the slat itself but also improves the lift of the main wing. The simulation results of the original airfoil and the optimized configuration at four typical angles of attack (\(\alpha=8^{\circ},16.3^{\circ},19^{\circ},22.36^{\circ}\)) are compared and analyzed. The development process of wake flow is shown in Figure 9. For the original airfoil at an angle of attack of \(22.36^{\circ}\), the wake flow area generated by the separation bubble is strongly mixed with the slot jet and the boundary layer of the main wing section, so that the rear section of the main airfoil and trailing-edge flap are in the mixed wake flow area. After optimization, the separation of grid-slat configuration is weakened, and the wake area is greatly reduced. Superimposed contour plots of velocity magnitude and instantaneous streamlines at different angles are shown in Figure 10. Although the jet velocity has not yet reached the peak value, the velocities near the upper trailing edge are improved to varying degrees. The downstream flow-separated area near the upper trailing edge becomes a flow-attached area. Figure 11 shows the surface pressure coefficient Cp of the original airfoil and the optimized layout under two operating conditions. For the convenience of differentiation, blue represents the original airfoil and red represents the optimal grid-slat configuration. The negative pressure value in the figure represents the suction on the upper surface of the wing. The positive pressure value represents the pressure on the lower surface of the wing. The pressure surface curve is located below the suction surface curve, indicating that the pressure on the lower surface is greater than that on the upper surface, which means the lift of the airfoil is positive [27; 28]. The area enclosed by the pressure coefficient curve can roughly reflect the lift coefficient. As is shown in Figure 11a, at an angle of attack of \(19^{\circ}\), each suction peak of optimized configuration for each wing is slightly higher than that of the original wing, while the pressure surface curve is basically the same, so the optimal grid-slat configuration has a higher lift. As can be seen in Figure 11b, the suction peak of the original airfoil decreases sharply, and the area enclosed by the pressure coefficient curve decreases. However, the pressure coefficient curve of the optimized configuration is significantly different from that of the original airfoil, indicating that stall status had not been reached.