## 3 Simulation Conditions
### Simulation Process  
1. Set a virtual buffer bin (not drawn) above the computational domain, with its bottom connected to the top of the computational domain. Calculate the accumulation process of constant mass particles in the buffer bin using the discrete element method. This is because when the fixed-bed heat transfer model is used, the particle size composition and the mass fraction of each particle size section should be consistent. If the particles are generated and accumulated directly in the calculation domain, the characteristics of a wide particle size distribution and the random generation of particles will cause differences in the mass and composition of particles contained in different Venturi furnace types, thereby affecting the gas-solid heat transfer.
2. Discharge the particles from the buffer bin into the computational domain. According to the material distribution characteristics in the vertical cooling furnace [25], the segregation of particles in the furnace is the most severe in the initial stage of discharge. As the discharge progresses, the distribution segregation of materials is alleviated. In order to shorten the discharge time and make the particle distribution in Venturi furnaces with different structures relatively consistent, the entry mode of particles was changed so that the particles entered directly from the top of the calculation domain.
3. Complete the accumulation of particles within the computational domain. Then, set the particle velocity to 0 m/s and delete the buffer bin. Subsequently, introduce the cooling gas from the edge and center vent cowl for the gas-solid heat transfer coupling calculation. After 2 s of heat exchange, stop the calculation and perform data processing. According to the operation data of the Meishan Steel vertical cooling furnace, the entry temperatures of the sinter and the cooling gas were set to 773 K and 393 K, respectively. The qualitative temperature of both was the average of the temperature in and out of the vertical cooling furnace, and the qualitative temperatures of the sinter and the cooling gas were calculated to be 613 K and 483 K, respectively. The physical property parameters at the qualitative temperature were obtained by introducing the physical property parameter calculation formulas in Refs. [26; 27; 28]. See Table 4 for details.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \multirow{2}{*}{\begin{tabular}{c} **Scaling** \\ **Factor** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Specific Heat** \\ **Capacity** \\ **(J/kg-K)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **(W/m-K)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Density** \\ **(kg-m-3)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Dynamic** \\ **Viscosity** \\ **(kg/m-s)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Inlet** \\ **Temperature** \\ **(K)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Particle** \\ **Mass** \\ **(kg)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Superficial** \\ **Velocity** \\ **(m-s-1)** \\ \end{tabular} } \\ \hline Cooling gas & 1034.04 & 0.0382 & 0.726 & 2.64 \(\times\) 10\({}^{-5}\) & 393 & – & 3.203 \\ Sinter & 817.36 & 8 & 2600 & – & 773 & 2400 & – \\ \hline \end{tabular}
\end{table}
Table 4: Simulation parameter settings.  
Figure 4: Computational domain and grid division. (**a**) Computational domain; (**b**) grid division.