## 4 Results and Discussion  
### Orthogonal Experimental Design  
An orthogonal experiment is an efficient experimental method that uses an orthogonal table to arrange and analyze multi-factor experiments scientifically and to find the optimal level combination. It has the advantages of a smaller number of experiments, a uniform distribution of data points, a simple method, and strong reliability of the conclusions. According to the results of the analysis in the previous section, the structure of Venturi furnaces involves four factors: the width \(w\) and length \(l\) of the vertical part, the contraction angle of the contraction part \(\beta\), and the expansion angle of the expansion part \(\alpha\).  
The smaller the vertical section width \(w\), the faster the cooling gas and sinter velocities, which increases the gas-solid heat transfer coefficient but also causes an increase in the pressure drop of the cooling gas passing through the region. However, the more important impact is the increased risk of sinter sticking. Ref. [29] points out that for spherical particles, the diameter of the circular discharge port should not be less than 6-8 or 6-10 times the maximum particle size. At the same time, for the convenience of equipment installation, the width of the upper center vent cow should not be too small. The final value range of \(w\) was determined to be 1.0-1.2 m, which means the values were 1.0 m, 1.1 m, and 1.2 m.  
The longer the length \(l\) of the vertical section, the longer the distance for gas to exchange heat with the sinter at a higher speed, which is beneficial for increasing the heat exchange capacity between gases and solids in the furnace but also leads to an increase in the pressure drop of gas passing through the material layer. The thickness of the material layer of the existing circular cooler is usually 0.76 m. In view of this, the length \(l\) of the vertical part was set to 0.7 m, 0.5 m, and 0.3 m.  
The contraction angle \(\beta\) of the contraction part was equivalent to the half-top angle of the silo structure. Compared with the gas velocity, this value had a greater influence on the integrity of the downward movement of the sinter. Ref. [30] points out that under the condition of certain material parameters, the key factor determining whether the flow in the silo presents a funnel flow or a mass flow is the half-top angle of the silo, and it gives the formula for calculating the maximum half-top angle required to maintain the mass flow. According to the physical parameters provided in Ref. [31], the maximum half-top angle obtained using the above formula is 16.5\({}^{\circ}\). Based on this, appropriate adjustments were made to obtain the values for \(\beta\) of 18\({}^{\circ}\), 16\({}^{\circ}\), and 14\({}^{\circ}\).  
The expansion angle \(\alpha\) of the expansion part was equivalent to the residual angle of the blast furnace shaft. If \(\alpha\) is too small, the effect of increasing the width of the furnace cavity will not be significant, while too great a value will increase the width of the furnace cavity too violently, resulting in the loose accumulation of particles on the side wall, thus increasing its voidage. Therefore, the expansion angle \(\alpha\) was set to 13\({}^{\circ}\), 15\({}^{\circ}\), and 17\({}^{\circ}\).  
Based on the above parameters and their values, the L9 (3\({}^{\circ}\)) orthogonal table was selected to arrange the orthogonal experimental plan, as shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Levels**} & \multicolumn{4}{c}{**Factors**} \\ \cline{2-5}  & \(w\)/m & \(l\)/m & \(\beta l^{c}\) & \(\alpha l^{c}\) \\ \hline
1 & 1.0 & 0.3 & 14 & 13 \\
2 & 1.1 & 0.5 & 16 & 15 \\
3 & 1.2 & 0.7 & 18 & 17 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental factors and levels.