# A New Flow Control Method of Slat-Grid Channel-Coupled Configuration on High-Lift Device
## 5 Influence Analysis of Design Parameters  
In order to further clarify the design method of grid-slat configuration, the influence of each parameter on lift-drag coefficient and lift-drag ratio is analyzed according to the calculation results under the different design parameters calculated in the optimization process. First, the Pearson correlation coefficient [29] is selected to calculate and analyze the correlation between design parameters, lift-drag coefficient and lift-drag ratio, as shown in Table 4. The results show that the five design parameters are significantly related to the lift-drag ratio \(K\), where \(x_{1}\), \(k_{3}\), \(k_{6}\) are positively correlated with \(K\), \(y_{3}\), \(y_{6}\) are negatively correlated with \(K\).  
[PERSON]'s formula [30] is:  
\[\rho_{X,Y}=\frac{\text{cov}(X,Y)}{\sigma_{X}\sigma_{Y}}=\frac{E(XY)-E(X)E(Y)}{ \sqrt{E(X^{2})-\left(E(X)\right)^{2}}-\sqrt{E(Y^{2})-\left(E(Y)\right)^{2}}} \tag{6}\]  
where \(\text{cov}(X,Y)\) is the covariance of \(X\) and \(Y\), and \(\sigma_{X}\), \(\sigma_{Y}\) is the standard deviation of \(X\) and \(Y\), respectively.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{\(\mathbf{x_{1}}\)} & \(\mathbf{x_{2}}\) & \(\mathbf{y_{2}}\) & \(\mathbf{y_{3}}\) & \(\mathbf{k_{3}}\) \\ \hline \multirow{2}{*}{\(Cl\)} & Pearson correlation & 0.036 & \(-\)0.048 & \(-\)0.097 & \(-\)0.164 ** & 123 * \\ \cline{2-6}  & Sig. (2-tailed) & 0.500 & 0.373 & 0.070 & 0.002 & 0.021 \\ \hline \multirow{2}{*}{\(Cd\)} & Pearson correlation & \(-\)0.113 * & 0.010 & \(-\)0.028 & 0.260 ** & \(-\)0.277 ** \\ \cline{2-6}  & Sig. (2-tailed) & 0.034 & 0.857 & 0.607 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{\(K\)} & Pearson correlation & 0.112 * & \(-\)0.019 & 0.004 & \(-\)0.300 ** & 0.305 ** \\ \cline{2-6}  & Sig. (2-tailed) & 0.036 & 0.720 & 0.948 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{\(Cl\)} & \multicolumn{2}{c}{\(\mathbf{x_{4}}\)} & \(\mathbf{x_{5}}\) & \(\mathbf{y_{5}}\) & \(\mathbf{y_{6}}\) & \(\mathbf{k_{6}}\) \\ \hline \multirow{2}{*}{\(Cl\)} & Pearson correlation & 0.063 & 0.109 * & 0.174 ** & \(-\)0.123 * & 0.287 ** \\ \cline{2-6}  & Sig. (2-tailed) & 0.241 & 0.041 & 0.001 & 0.021 & 0.000 \\ \hline \multirow{2}{*}{\(Cd\)} & Pearson correlation & 0.007 & 0.082 & \(-\)0.017 & 0.279 ** & \(-\)0.240 ** \\ \cline{2-6}  & Sig. (2-tailed) & 0.902 & 0.123 & 0.747 & 0.000 & 0.000 \\ \hline \multirow{2}{*}{\(K\)} & Pearson correlation & 0.000 & \(-\)0.055 & 0.057 & \(-\)0.308 ** & 0.311 ** \\ \cline{2-6}  & Sig. (2-tailed) & 0.997 & 0.302 & 0.284 & 0.000 & 0.000 \\ \hline \hline \end{tabular}  
* *. At 0.01 level (2-tailed), the correlation is significant. *. At 0.05 level (2-tailed), the correlation is significant.  
\end{table}
Table 4: The correlation analysis results between design parameters and lift-drag coefficient.  
Figure 11: Comparison of pressure coefficient between the original airfoil and optimal grid-slat configuration at different attack angle.  
This shows that within the given range of variables, the shape of the slot changes with the change in five design parameters, which will greatly change the flow field. The change of \(x_{1}\) results in the change of seam entry position, while the change of the other four design parameters \(y_{3}\), \(y_{6}\), \(k_{3}\) and \(k_{6}\) results in the change in seam shape. The design parameter \(x_{1}\) is positively correlated, indicating that the lift force is better when the inlet position of the slot is closer to the right. The design parameters \(k_{3}\) and \(k_{6}\) are positively correlated, indicating that as the expansion degree of the slot increases, the acceleration degree of the slot to the flow is greater, and the lift force is better.