## 3 Simulation Conditions
### Model Scaling
According to the equality of the Reynolds numbers between the prototype and the model, the inlet velocity of the scaled model was calculated to obtain the gas velocity distribution inside the vertical cooling furnace under different scaling conditions, as shown in Figure 2. It can be seen that after the calculation domain was reduced, the gas velocity distribution cloud map was similar. To quantitatively compare the distribution of the gas velocity along the transverse direction, the ratio of the gas velocity at each point on different height planes L1-L4 to the average gas velocity on the plane was extracted as a dimensionless velocity, and the distribution of dimensionless velocity on L1\(\sim\)L4 was plotted, as shown in Figure 3. On plane L3, the gas velocity curves corresponding to three scaling factors were very similar to the prototype. On plane L2, the dimensionless velocity corresponding to the scaling factor of 0.6 was generally higher, and the velocity curve was also significantly different from the prototype. On planes L1 and L4, the velocity curve corresponding to the scaling factor of 0.7 was even closer to the prototype. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Scaling** & **Width** & **Width–Diameter** & **Upper Limit of** & **Particle Size** & **Particle Diameter** & **Particle Number** & **Voidage** & **Average Diameter(mm)** \\ \hline
1.0 & 2400 & 16 & 150 & 15:1 & 366,060 & 0.395 & 22.39 \\
0.8 & 1920 & 16 & 120 & 12:1 & 181,663 & 0.415 & 22.43 \\
0.7 & 1380 & 16 & 105 & 10.5:1 & 121,893 & 0.418 & 22.50 \\
0.6 & 1440 & 16 & 90 & 9:1 & 75,929 & 0.423 & 22.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Model scaling settings. Combined with the comparative results of the particle number, voidage, and gas velocity distribution, it was necessary to take into consideration both the simulation accuracy and the calculation cost; the scaling factor was determined to be 0.7. In addition, from the distribution of gas velocity in the furnace cavity, there was almost no air flow distribution in the conical section at the bottom of the furnace cavity, indicating that gas-solid heat transfer did not occur in this area. Therefore, the particles in this area were ignored in order to further reduce the number of particles and improve the calculation efficiency. The final computational domain is shown in Figure 4a. The computational domain was meshed using tetrahedral cells. Due to the dense packing of particles, the mesh size could be even lower than 3 times the maximum particle diameter without compromising the grid independence of the particle volume fraction calculation. Therefore, the minimum mesh size was set to be 1.5 times the maximum particle diameter. The edge vent cowl tuyere and center vent cowl tuyere were set as velocity inlets. The wall above the center vent cowl was set as the symmetrical surface. The outlet plane of the distribution pipe was set to the pressure outlet, and the rest of the wall was set to wall, as shown in Figure 4b. Figure 3: Gas velocity distributions on L1–L4. (**a**) L1; (**b**) L2; (**c**) L3; (**d**) L4. Figure 2: Gas velocity distribution under different scaling factors: (**a**) 1.0; (**b**) 0.8; (**c**) 0.7; (**d**) 0.6.