## 3 Simulation Conditions
### Model Scaling  
Under the above simulation conditions, the number of particles accumulated in the slot model reached 3.66 \(\times\) 10\({}^{4}\). The efficiency of the DEM-CFD coupling calculation was \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Particle Size (mm)** & **10–25** & **25–40** & **40–80** & **80–150** \\ \hline Mass fraction (\%) & 20 & 35 & 30 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Sinter particle size distribution and mass fraction. Figure 1: Existing furnace type and Venturi furnace type. (**a**) Existing furnace type; (**b**) single bin; (**c**) Venturi furnace type; (**d**) structure parameters of Venturi furnace; (**e**) slot model. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Parameters** & **Poisson’s Ratio** & **Density (kg\(\cdot\)m\({}^{-3}\))** & \begin{tabular}{c} **Shear Modulus (Mg)** \\ \end{tabular} & \begin{tabular}{c} **Restitution** \\ **Coefficient** \\ **Coefficient** \\ \end{tabular} & \
\begin{tabular}{c} **Coefficient** \\ **of Sliding** \\ **Friction** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient** \\ **of Rolling** \\ **Friction** \\ \end{tabular} \\ \hline Sinter & 0.25 & 2.6 \(\times\) 10\({}^{3}\) & 3.5 \(\times\) 10\({}^{1}\) & – & – & – \\ Wall & 0.30 & 7.8 \(\times\) 10\({}^{3}\) & 7.0 \(\times\) 10\({}^{4}\) & – & – & – \\ Sinter–sinter & – & – & – & 0.25 & 0.38 & 0.08 \\ Sinter–wall & – & – & – & 0.20 & 0.45 & 0.16 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation parameters. low due to the large number of particles. Therefore, the method of scaling the physical model was proposed to further improve the computational efficiency. Firstly, the different structural parameters of the Venturi furnace resulted in different height-diameter ratios. And different height-diameter ratios often correspond to different optimal gas-solid ratios. Therefore, under the same gas-to-solid ratio, it may be the case that this gas-to-solid ratio had a better heat transfer effect for one type of Venturi structure, but a worse effect for another, resulting in a comparison between better and worse heat transfer effects. Considering the large adjustable range of the sinter capacity and the cold air flow rate in the Meishan Steel vertical cooling furnace, in order to eliminate the influence of the gas-solid heat transfer caused by the gas-solid ratio, the fixed-bed heat transfer mode was proposed in this study. At this time, the particles did not move except for the accumulation process. Therefore, the thickness of the slot model was reduced to 3 times [23] the maximum particle size (450 mm). Secondly, the physical model was reduced by introducing a scaling factor. Only the upper limit of particle size was reduced, and the rest of the particle size and the mass fraction were kept unchanged. Thus, the number of particles was reduced while the characteristics of a wide particle size distribution were maintained. Thirdly, the physical model and the upper limit of particle size used the same scaling factor, so the width-diameter ratio of the slot model remained unchanged. See Table 3 for detailed scaling. It can be seen from Table 3 that with the above scaling method, the particle size ratio was still basically maintained at about 10:1; that is, the particles were still basically widely distributed. Therefore, the scaled sinter packed bed could still simulate the filling effect of relatively small particles in the large particle gap. The number of sinter particles decreased significantly, which improved the calculation efficiency. The maximum variation range of the average voidage was only 7%, while the average particle size hardly changed. The gas velocity distribution in the furnace after scaling was further studied to determine the appropriate scaling factor. In this study, the particles were densely packed and moved down slowly, and the particle size used in the reduction model was close to that of the actual furnace. Therefore, the Reynolds number [24] was selected to determine the inlet gas velocity of the scaled model.