# Numerical Simulation and Parameter Optimization of Air Slide Based on CFD-DEM
## 4 Experimental Results and Discussion
### Orthogonal Experimental Analysis  
Through single-factor experiments, the influence of each parameter on the evaluation indicators was obtained, along with an analysis of the underlying causes for these variations. Considering the potential interactions among these factors, orthogonal experimental design was subsequently employed based on the single-factor tests to further investigate the possible multi-factor interactions affecting both conveying ratio and stability, thereby facilitating parameter optimization. The orthogonal experiment considered the following three factors: chute inclination angle (\(\theta\)), inlet air velocity (\(v\)), and porosity (\(\varphi\)), analyzing the effects of different factor-level combinations on the two evaluation indicators. The orthogonal array and corresponding results are presented in Tables 3 and 4, respectively. To more intuitively illustrate the degree of influence of these three factors on the two evaluation indicators, range analysis was conducted, as shown in Figure 13.  
Figure 12: Experimental results under varying chute inclination angles. (a) Effect on conveying ratio. (b) Effect on surface fluctuation. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Level**} & \multicolumn{3}{c}{**Factor**} \\ \cline{2-4}  & \(\mathbf{v(A)/(m/s)}\) & \(\mathbf{\varphi(B)/(\%)}\) & \(\mathbf{\theta(C)/(^{\circ})}\) \\ \hline
1 & 1.4 & 37.84 & 5 \\
2 & 1.6 & 47.24 & 6 \\
3 & 1.8 & 50.60 & 7 \\
4 & 2.0 & 58.13 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Factor levels in orthogonal experiments. Analysis of Figure 13a reveals that through comparative range analysis of each influencing factor on the two indicators, the primary-to-secondary ranking of the three factors affecting the conveying ratio is permeable baffle porosity \(>\) inlet air velocity \(>\) chute inclination angle. Figure 13b demonstrates that the ranking of factors influencing surface fluctuation difference is as follows: inlet air velocity \(>\) baffle porosity \(>\) chute inclination angle. The observed trend variations differ from those in the single-factor analysis due to the presence of a strong correlation between the two indicators. The trend variations are consistent with the trend variations in the single-factor analysis due to the presence of a strong correlation between the two indicators. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{3}{c}{**Factor**} & \multicolumn{3}{c}{**Metric**} \\ \cline{2-5}  & **A/m/s** & **B/\%** & **C/\({}^{\circ}\)** & **Conveying Ratio** & **Surface Fluctuation** \\  & & & & **\%** & **mm** \\ \hline
1 & 1.4 & 37.84 & 5 & 94.867 & 3.133 \\
2 & 1.4 & 47.24 & 6 & 89.286 & 3.675 \\
3 & 1.4 & 50.60 & 7 & 85.326 & 3.219 \\
4 & 1.4 & 58.13 & 8 & 77.060 & 2.838 \\
5 & 1.6 & 37.84 & 6 & 97.225 & 5.695 \\
6 & 1.6 & 47.24 & 7 & 90.112 & 3.840 \\
7 & 1.6 & 50.60 & 8 & 91.738 & 5.262 \\
8 & 1.6 & 58.13 & 5 & 77.630 & 2.822 \\
9 & 1.8 & 37.84 & 7 & 92.111 & 4.992 \\
10 & 1.8 & 47.24 & 8 & 96.685 & 3.198 \\
11 & 1.8 & 50.60 & 5 & 93.391 & 3.544 \\
12 & 1.8 & 58.13 & 6 & 88.078 & 3.702 \\
13 & 2.0 & 37.84 & 8 & 92.338 & 3.631 \\
14 & 2.0 & 47.24 & 5 & 96.542 & 4.122 \\
15 & 2.0 & 50.60 & 6 & 91.188 & 4.099 \\
16 & 2.0 & 58.13 & 7 & 86.138 & 4.127 \\ \hline K11 & 86.635 & 94.135 & 90.607 & & \\ K12 & 89.176 & 93.156 & 91.444 & & \\ K13 & 92.566 & 90.411 & 88.422 & & \\ K14 & 89.176 & 82.226 & 89.455 & & the conveying ratio \\ R1 & 5.931 & 11.909 & 3.022 & & \\ Optimal level & A3 & B1 & C2 & & \\ \hline K21 & 3.216 & 4.363 & 3.405 & & \\ K22 & 4.405 & 3.709 & 4.293 & & \\ K23 & 3.859 & 4.031 & 4.045 & & \\ K24 & 3.995 & 3.372 & 3.732 & & the surface fluctuation \\ R2 & 1.189 & 0.991 & 0.887 & & \\ Optimal level & A1 & B4 & C1 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Orthogonal experimental design with results and range analysis. Figure 13: Range analysis of orthogonal experiment results. (**a**) Conveying ratio. (**b**) Surface fluctuation. to inherent interactions among the three factors.