## 2 **Introduction**  
The energy consumption of the sintering process in China accounts for about 15% of the entire iron and steel industry, second only to the ironmaking process. The recovery of sintering waste heat is an important means to reduce the energy consumption and improve the energy efficiency in the sintering process. At present, the recovery rate of sintering waste heat in China is low, only about 40% [1]. Sintering waste heat mainly includes two parts: sintering flue gas waste heat and sintering ore sensible heat, accounting for about 27% and 45% [2] of the total sintering heat expenditure, respectively. Compared to the waste heat from sintering flue gas, the amount of sensible heat in sintering ore is large, the quality is high, and it is easily carried by air, making it a key focus for the recovery of the waste heat resources from sintering. At present, the sensible heat recovery of sinter is mainly carried out in a ring cooler. Statistics show that only 42% of the sensible heat of sinter can be recovered. As much as 32% of the waste heat of medium- and low-temperature flue gas is released directly. The ring-cooling process inevitably has some disadvantages, such as a large amount of air leakage and the unorganized discharge of dust. Based on this, and inspired by coke dry quenching (CDQ) technology [3], relevant scholars put forward the sinter sensible heat vertical recovery process [4], which changes the heat transfer mode, transforming gas-solid cross-flow horizontal ring cooling into vertical gas-solid countercurrent vertical cooling. Theoretically, the outlet gas temperature can be maintained at a higher level of 400-500 \({}^{\circ}\)C. This is expected to increase the sensible heat recovery from 40% to 80%. A vertical cooling furnace is the core piece of equipment of the sinter sensible heat vertical recovery process, and its furnace structure has an important influence on the countercurrent heat transfer between the high-temperature sinter and the cooling gas in the furnace. Therefore, it is necessary to study the structure of vertical cooling furnaces and the range of reasonable parameters. Due to the sinter sensible heat vertical recovery process being put forward with reference to CDQ technology, the design of a vertical cooling furnace often refers to a type of dry quenching furnace. The appropriate parameters have been studied by relevant scholars. [PERSON] [5] established a two-dimensional steady-state model based on porous media theory and the local thermal non-equilibrium model and, with the goal of minimum loss, used the multi-objective genetic algorithm of a backpropagation (BP) neural network to propose a suitable height-diameter ratio and gas-solid ratio for a given size of a vertical cooling furnace. Taking the maximum enthalpy exergy of the outlet cooling gas as the target, [PERSON] [6; 7] optimized the inner diameter and height of a vertical cooling furnace, the inlet cooling gas temperature, the flow rate, and the particle size of the sinter and put forward the appropriate values of the corresponding parameters for a vertical cooling furnace matched with a 360 m\({}^{2}\) sintering machine. Taking the exergy value and exergy efficiency of hot gas as indices, [PERSON] [8] obtained suitable parameters such as the height-diameter ratio, the volume, and the temperature of the cooling gas, which formed a suitable model for a vertical cooling furnace. [PERSON] [9] studied the effects of the gas-solid ratio, the cooling height, and the diameter on the gas-solid heat transfer in a vertical cooling furnace with the target of hot flue gas exergy and obtained the appropriate structure and process parameters of the studied object. [PERSON] [10] took into account the effects of the inner diameter and the height of the vertical cooling furnace and the mass flow rate of the sinter and the cooling air on the enthalpy of the outlet cooling air, the fan energy consumption, and the dimensionless exergy loss and obtained the appropriate structure and process parameters.