# Numerical Simulation and Parameter Optimization of Air Slide Based on CFD-DEM
## 4 Experimental Results and Discussion
### Multi-Index Orthogonal Test Weight Analysis  
Through range analysis of the orthogonal experiments above, it was found that all three factors significantly influence the evaluation indicators, and the optimal parameter combinations for each of the two evaluation indicators were determined. To achieve the goal of optimizing the chute design, it is necessary to identify a common optimal parameter combination that satisfies both evaluation indicators. Therefore, a matrix analysis method was employed to assess the influence of factor levels on the weights of experimental results. Following the methodology described in the reference, a matrix analysis model was constructed, and the experimental data from Table 4 were incorporated into the calculations. The detailed computational procedure is as follows:  
\[M_{1} = \begin{bmatrix}86.635&0&0\\ 89.176&0&0\\ 92.566&0&0\\ 89.176&0&0\\ 0&94.135&0\\ 0&93.156&0\\ 0&90.411&0\\ 0&82.266&0\\ 0&0&90.607\\ 0&0&91.444\\ 0&0&88.422\\ 0&0&89.455\end{bmatrix},\] \[T_{1} = \begin{bmatrix}0.0028&0&0\\ 0&0.0028&0\\ 0&0&0.0028\end{bmatrix},\] \[S_{1} = \begin{bmatrix}\frac{5.931}{20.826}\\ \frac{11.909}{20.826}\\ \frac{3.002}{20.826}\\ \frac{3.002}{20.826}\end{bmatrix},\] \[W_{1} = M_{1}\cdot T_{1}\cdot S_{1} \tag{4}\]  
where \(M_{1}\) is the test indicator layer matrix; \(T_{1}\) is the factor layer matrix; \(S_{1}\) is the level layer matrix; and \(W_{1}\) is the weight matrix of indicator values.  
According to the matrix analysis method, when evaluating indicators where smaller values are preferable, the \(K_{ij}\) values in the test indicator layer matrix \(M_{2}\) should be taken as \(1/K_{ij}\). The calculation methods for the factor layer matrix \(T_{2}\) and level layer matrix \(S_{2}\) follow the same principle as Equation (4). The total weight matrix \(W\) is then computed as shown in Equation (5).  
\[W=\frac{w1+w2}{2}=\frac{1}{2}\times\begin{bmatrix}0.691\\ 0.771\\ 0.738\\ 0.711\\ 1.507\\ 1.448\\ 1.317\\ 0.366\\ 0.369\\ 0.357\\ 0.361\end{bmatrix}+\frac{1}{2}\begin{bmatrix}0.007835\\ 0.005721\\ 0.006530\\ 0.006308\\ 0.004814\\ 0.005663\\ 0.005210\\ 0.005661\\ 0.005711\\ 0.00577\\ 0.005661\end{bmatrix}+\begin{bmatrix}0.007835\\ 0.05721\\ 0.006530\\ 0.006308\\ 0.004814\\ 0.005663\\ 0.005210\\ 0.005210\\ 0.006228\\ 0.005711\\ 0.00577\\ 0.005661\end{bmatrix}+\begin{bmatrix}0.349335\\ 0.358409\\ 0.372330\\ 0.05663\\ 0.055710\\ 0.005577\\ 0.05663\\ 0.005210\\ 0.006228\\ 0.005711\\ 0.00577\\ 0.005661\end{bmatrix}+\begin{bmatrix}0.349335\\ 0.358409\\ 0.372330\\ 0.358702\\ 0.0756023\\ 0.0748611\\ 0.0726403\\ 0.0661392\\ 0.185737\\ 0.187001\\ 0.181229\\ 0.183356\end{bmatrix}+\begin{bmatrix}A1\\ A2\\ A3\\ A4\\ B1\\ B3\\ B4\\ C2\\ C3\\ C4\end{bmatrix} \tag{5}\]  
The matrix analysis results from Equation (5) reveal the following comprehensive influence ranking of the three factors on the evaluation indicators: B > A > C, indicating that permeable baffle porosity exerts greater influence than inlet air velocity, which in turn surpasses chute inclination angle. Further analysis of Equation (5) demonstrates the following among different levels: for factor B (porosity), level B1 carries the highest weight; for factor A (air velocity), level A3 shows maximum influence; and for factor C (inclination angle), level C2 dominates. The comprehensive weight evaluation identifies A3B1C2 as the optimal multi-objective parameter combination for the air slide operation. Simulation tests under this optimal configuration yielded a conveying ratio of 96.52% and a surface fluctuation of 4.39 mm. Comparative analysis with orthogonal experiment results shows both performance metrics maintain relatively high values, confirming that the two key performance indicators of the air slide cannot be simultaneously optimized to their respective peak levels.