## 5 Conclusions  
1. A scaling factor was introduced to scale the physical model; only the upper limit of particle size was reduced, and the rest of the particle size and mass fraction remained unchanged. The scaling factor for the physical model was the same as the upper limit of granularity. Based on the results of a comparison of the particle quantity, porosity, and gas flow velocity distribution, the scaling factor was determined to be 0.7 to balance the simulation accuracy and computational cost.
2. From the perspective of preventing material jamming, improving material flow integrity, facilitating installation, and reducing cooling gas pressure drop, the selection range of the structural parameters of a Meishan Steel Venturi shaft cooling furnace was determined.
3. The results of the orthogonal experiments were as follows: For the sensible heat recovery, the width \(w\) of the vertical part had the greatest influence, followed by the contraction angle \(\beta\) and the expansion angle \(\alpha\), and their effects were similar. The length \(l\) of the vertical part had the least influence. For the pressure drop, the structural parameter with the greatest influence was still \(w\). The next were \(\beta\) and \(l\), and the effects of the two were also similar. The influence of \(\alpha\) was the smallest.
4. The higher the sensible heat recovery, the greater the gas pressure drop, but there was a difference in the trend of the two with the change in structural parameters. From the perspective of balancing the sensible heat recovery and the gas pressure drop, the appropriate structure parameters for the Venturi furnace were as follows: \(w=1.1\) m, \(\beta=16^{\circ}\), \(\alpha=13^{\circ}\), and \(l=0.5\) m.
5. The fluidity of the material in the Venturi furnace with the above parameter combination was verified, and it was found that the _MFI_ of the particles in the vertical section decreased to 0.43. After the wall friction experienced by the particles in the central area of the vertical section was increased, the _MFI_ increased to 0.7, indicating that the integrity of the sinter flow in this furnace type can also be guaranteed.
6. The results can provide theoretical guidance for the improvement of Meishan Steel vertical cooling furnaces. Of course, for the sake of comparison, this study maintained the existing operating parameters of Meishan Steel vertical cooling furnaces. Further research can be conducted on the operating parameters corresponding to the Venturi furnace type.  
Conceptualization, H.L.; data curation, T.Q.; funding acquisition, H.L.; investigation, H.L.; methodology, T.Q.; project administration, H.L.; resources, H.L.; software, T.Q.; supervision, Y.Z.; writing--original draft preparation, T.Q.; writing--review and editing, H.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key R&D Program of China (grant number 2022 YFE0208100) and the Fundamental Research Funds for the Central Universities (grant number N2225022), and the APC was funded by 2022 YFE0208100.  
Not applicable.  
The data are contained within the article.  
The authors sincerely acknowledge the anonymous reviewers for their insights and comments, which further improved the quality of the manuscript.  
The authors declare no conflict of interest.