Influence of Variable-Diameter Structure on Gas–Solid Heat Transfer in Vertical Shaft Cooler

Abstract

In order to improve the heat transfer between high-temperature sinter and cooling gas in a vertical shaft cooler, a new furnace type with variable-diameter structure was proposed, and the influence of variable-diameter structure on gas–solid heat transfer in vertical-shaft cooler was studied by CFD-DEM coupling method in the current work. The results show that variable-diameter structure can increase the quantity of low-temperature sinter as well as the outlet cooling gas temperature, and can improve the uniformity of sinter and cooling gas temperature along the width, at the cost of significantly increasing the cooling gas pressure. By changing the parameters of the variable-diameter structure, it was found that a smaller width of the vertical section or a larger angle of the contraction section led to a better sinter–gas heat transfer. The influence of vertical section width on cooling gas pressure was more obvious. It is suggested that when designing and using the vertical shaft cooler with variable-diameter structure, consideration should be given to the effect of sinter–gas heat exchange and the pressure of cooling gas. Furthermore, the occurrence of material blockage and excessive equipment height should be avoided.

1. Introduction

The energy consumption of the sintering process accounts for about 12%~15% of the total energy consumption of the whole iron and steel production process in China, second only to the iron-making process, and about 19% higher than the international benchmark [1,2]. The recovery of sintering waste heat has become an important way to reduce energy consumption and improve energy efficiency in the sintering process, which is of great significance for iron and steel enterprises in the achievement of low-carbon and clean production. The sensible heat of sinter, which is of high quality and large quantity and is easily carried by air medium, accounts for 35%~40% of the total heat output of a sintering machine, and has become the focus of sintering waste heat recovery. At present, sensible-heat recovery in sintering is mainly carried out on annular coolers in China’s iron and steel enterprises. These have the disadvantages of high air consumption, high air-leakage rate, more dust escape and low sensible-heat-recovery efficiency. In view of the above shortcomings, scholars have proposed the vertical recovery process for sinter sensible heat, using dry-quenching technology for reference [3]. Its core lies in the countercurrent heat exchange between high-temperature sinter and cooling air in the vertical shaft cooler.

For the solid–gas heat-transfer characteristics in the vertical shaft cooler, significant research has been conducted. In terms of experimental research, Feng [4] and Huang [5] each used self-made experimental devices to study the effects of the apparent velocity of cooling air and particle size on the gas–solid overall heat-transfer coefficient, and obtained the Nusselt experimental correlation. Zheng [6] obtained Nusselt experimental correlation of gas–solid volume heat-transfer coefficient through experimental research, and found that particle diameter and cooling air flow have more significant effects on it than sinter flow rate and cooling section height. In terms of simulation research, Xu [7] established a two-dimensional steady-state model based on porous media theory and local thermal non-equilibrium model to study the influence of air flow, sinter flow and sinter particle size on gas–solid heat-transfer process. With exergy-destruction minimization as the goal, the above parameters were optimized using the multi-objective genetic algorithm backpropagation (BP) neural network. Feng [8] took maximum enthalpy exergy of cooling air as the goal, optimized the inner diameter and height of the vertical shaft cooler as well as the temperature and flow of the inlet cooling air, and proposed that for the vertical shaft cooler matched with the 360 m² sintering machine, the appropriate values of the above parameters were 9 m, 8 m, 353 K and 180 kg/s, respectively. Zhang [9] further considered the influence of the inner diameter and height of the vertical shaft cooler and the mass flow of sinter and cooling air on exergy, energy consumption and dimensionless exergy consumption. The results showed that the factor with the most influence on dimensionless exergy consumption was the inner diameter of the vertical shaft cooler, followed in order by cooling air flow, height of the vertical shaft cooler and sinter flow. In addition, many researchers [10,11,12] have used analytical methods to study the above contents and obtained similar conclusions.

To summarize, in view of the sinter–gas heat-transfer characteristics, the research mainly focuses on optimizing the operating parameters and structural parameters, while research on the optimization and improvement of the vertical shaft cooler type is rarely reported [13]. Based on this, on the basis of the vertical structure, a new vertical shaft cooler with variable-diameter structure with additional contraction section, vertical section and expansion section is proposed in this paper. The CFD-DEM coupling model is used to calculate the sinter–gas heat-transfer process. The heat-transfer effects of the variable diameter structure and the vertical structure are compared, based on the sinter and cooling air temperature as well as their distribution uniformity and cooling air pressure drop. At the same time, the vertical section width and the angle of the contraction section of the variable diameter structure are optimized, in order to obtain a new vertical shaft cooler type that can improve sinter–gas heat transfer.

2. Model Description

2.1. Particle Phase Governing Equations

In the CFD-DEM coupling model, the discrete element method under the Lagrangian framework is used to solve the motion and heat transfer of a single particle. Its governing equations are as follows:

$$m_i\frac{d{\mathit{v}}_i}{dt}={\displaystyle \sum _{j=1}^{k_i}({\mathit{F}}_{cn,ij}+{\mathit{F}}_{dn,ij}+{\mathit{F}}_{ct,ij}+{\mathit{F}}_{dt,ij})+{\mathit{F}}_{pf,i}+m_i\mathit{g}}$$

(1)

$${\mathit{I}}_i\frac{d{\mathit{\omega }}_i}{dt}={\displaystyle \sum _{j=1}^{k_i}({\mathit{M}}_{t,}{}_{ij}+{\mathit{M}}_{r,}{}_{ij})}$$

(2)

$$m_i{c}_i\frac{d{{\rm T}}_i}{dt}={\mathit{Q}}_{c,i}+{\displaystyle \sum _{j=1}^{k_i}{\mathit{Q}}_{i,j}}$$

(3)

where m_i denotes the mass of particle i; I_i denotes the rotational inertia of particle i; v_i denotes the transitional velocity of particle i; ω_i denotes the angular velocity of particle i; t denotes time; k_i denotes the number of particles in contact with particle i; F_cn,ij denotes the normal contact force between particle i and particle j; F_dn,ij denotes the normal damping force between particle i and particle j; F_ct,ij denotes the tangential contact force between particle i and particle j; F_dt,ij denotes the tangential damping force between particle i and particle j; F_pf,i denotes the fluid force on particle i; m_ig denotes the gravity of particle i; M_t,ij denotes the tangential force torque between particle i and particle j; M_r,ij denotes the rolling friction torque between particle i and particle j; c_i denotes the specific heat of particle i; Q_c,i denotes the convective heat-transfer flow between particle i and fluid; and Q_c,i denotes the heat conduction flow of particle i and particle j. The specific expressions of all forces and torques in the above formula are shown in [14], and the calculation of heat conduction between particles is shown in [15].

2.2. Fluid Phase Governing Equations

The flow and heat transfer of fluid between particles are calculated by the continuity equation, the Navier–Stokes equation and the energy conservation equation based on local average variables, and the forms are as follows:

$$\frac{\partial \epsilon {\rho }_f}{\partial t}+\nabla ·\left(\epsilon {\rho }_f{\mathit{u}}_f\right)=0$$

(4)

$$\frac{\partial \epsilon {\rho }_f{\mathit{u}}_f}{\partial t}+\nabla ·\left(\epsilon {\rho }_f{\mathit{u}}_f{\mathit{u}}_f\right)=-\nabla p+\nabla ·\left(\epsilon {\mu }_f\nabla {\mathit{u}}_f\right)+\epsilon {\rho }_f\mathit{g}-{\mathit{F}}_{pf}$$

(5)

$$\frac{\partial \epsilon {\rho }_f{c}_f{T}_f}{\partial t}+\nabla ·\left(\epsilon {\rho }_f{\mathit{u}}_f{c}_f{T}_f\right)=\nabla ·\left({\Gamma }_f\nabla T_f\right)+{\mathit{Q}}_c$$

(6)

where ε, ρ_f, u_f, p, μ_f, F_pf, c_f, T_f, Γ and Qc denote the fluid phase’s volume fraction, density, velocity, pressure, viscosity, force exerted by the particles, specific heat, temperature, thermal conductivity and convective heat-transfer flow with particles.

The volume fraction of the fluid phase in a grid cell is calculated using the sampling point method. First, Monte Carlo method is used to generate a certain number of sampling points located in and around a single particle to characterize the volume of particles. Next, the volume of particles is determined based on the number of sampling points in the grid. The calculation equation for the volume fraction is as follows:

$$\epsilon =1-\frac{1}{V}·{\displaystyle \sum _{i=1}^n\frac{n_c}{N}{V}_i}$$

(7)

where V, n and n_c represent the volume, the number of particles and the number of sample points in the grid cell, respectively; N is the total number of sample points; V_i is the volume of particle i.

The force of the particles acting on the fluid in the grid cell is the sum of all the particle forces in the grid. The calculation equation is as follows:

$${\mathit{F}}_{pf}=\frac{{\displaystyle \sum _{i=1}^n{\mathit{F}}_{pf,i}}}{V}$$

(8)

The convective heat-transfer flow of fluid and particles in the grid cell is the sum of the heat-transfer flow of all particles in the grid, and its calculation equation is:

$${\mathit{Q}}_c=\frac{{\displaystyle \sum _{i=1}^n{\mathit{Q}}_{c,i}}}{V}$$

(9)

2.3. Fluid-Particle Interaction

The gas–solid interaction principally involves drag force. In this paper, the Ergun and Wen & Yu drag models [16] are used to describe the drag force on particles. The calculation equation for F_pf,i are as follows:

$${\mathit{F}}_{pf,i}=\frac{\beta V_i}{1-\epsilon }\left({\mathit{u}}_f-{\mathit{v}}_i\right)$$

(10)

$$\beta =\{\begin{array}{l}\frac{150{(1-\epsilon )}^2{\mu }_f}{\epsilon d_i^2}+\frac{1.75(1-\epsilon ){\rho }_f\left|{\mathit{u}}_f-{\mathit{v}}_i\right|}{d_i} \left(\epsilon <0.8\right)\\ \frac{3}{4}{C}_d\frac{\left(1-\epsilon \right){\epsilon }^{-1.65}{\rho }_f\left|{\mathit{u}}_f-{\mathit{v}}_i\right|}{d_i} \left(\epsilon \ge 0.8\right)\end{array}$$

(11)

$$C_d=\{\begin{array}{ll}\frac{24}{\mathrm{Re}}& \left(\mathrm{Re}\le 0.5\right)\\ \frac{24}{\mathrm{Re}}\left(1.0+0.15{\mathrm{Re}}^{0.687}\right)& \left(0.5<\mathrm{Re}\le 1000\right)\\ 0.44& \left(\mathrm{Re}>1000\right)\end{array}$$

(12)

$$\mathrm{Re}=\frac{{\rho }_f{d}_i\epsilon \left|{\mathit{u}}_f-{\mathit{v}}_i\right|}{{\mu }_f}$$

(13)

where d_i denotes the diameter of particle i.

The convective heat transfer between the particle phase and the fluid phase is described by the Ranz–Marshall model, and its accuracy has been verified [15,17,18]. The specific calculation formulae of Q_c,i are as follows:

$$Nu=\frac{h_{conv}{d}_i}{{\Gamma }_f}$$

(14)

$$Nu=2+0.6R{e}_p^{1/2}{\mathrm{Pr}}^{1/3}$$

(15)

$$R{e}_p=\frac{\mathrm{Re}}{\epsilon }$$

(16)

$$\mathrm{Pr}=\frac{c_f{\mu }_f}{{\Gamma }_f}$$

(17)

$${\mathit{Q}}_{c,i}=\pi d_i^2{h}_{conv}(T_i-T_f)$$

(18)

where Pr is the Prandtl number of the fluid phase; h_conv represents the convective heat-transfer coefficient between the fluid phase and particle i.

3. Simulation Conditions

The vertical shaft cooler uses a dry quenching coke oven for reference, so its core heat-exchange zone can be approximately abstracted as a vertical structure. In this paper, a quasi-3D flat model was established, derived from the vertical shaft cooler with rectangular cross-section at Meishan Iron and Steel Co., Ltd. Then the contraction section, vertical section and expansion section were added on the basis of the vertical structure, so as to obtain the variable-diameter structure. The two structures are shown in Figure 1a. The above structures were divided into 10 bins from the bottom to the top to quantitatively study sinter temperature distribution. At the same time, three vertical lines, shown in Figure 1b as lines 1–3, were set in the center and middle area of the furnace cavity to study the cooling air temperature and pressure distribution. Hexahedral mesh was used to divide the computational domain. To ensure the accuracy of particle volume fraction, the size of a single grid was larger than the particle diameter [19]. For sinter, the top and bottom faces were set as particle factory and insulation wall, respectively, while for cooling air, they were set as pressure outlet and speed inlet, respectively. The front and rear walls were set as periodic boundaries, and the rest were set as insulation walls. The specific grid division is shown in Figure 1c. As the downward-moving speed of sinter in the vertical shaft cooler is nearly three orders of magnitude lower than the apparent flow velocity of cooling gas, it was simplified as a fixed bed for sinter–gas heat-transfer calculation.

The physical and simulation parameters were selected based on reference [15]. See

Table 1. Material properties and simulation parameters.

Parameters		Values	Parameters	Values
Poisson’s ratio	Sinter–Sinter	0.13	Rolling friction	3.5 × 10−4
	Sinter–Wall	0.3	Thermal conductivity, W/(m·K)	8.0
Density, kg·m−3	Sinter	2.96 × 103	Specific heat, J/(kg·K)	700
	Wall	7.8 × 103	Particle number	1200
Shear modulus, Pa	Sinter	1.46 × 109	Particle diameter, m	0.035
	Wall	7 × 1010	Particle initial temperature, K	723
Static friction	Sinter	0.15	Air initial temperature, K	393
	Wall	0.13	Air velocity, m·s−1	2
Restitution coefficient		0.25

for the specific values. Several examples were set according to different structural parameters. Case 0 referred to vertical structure and Cases 1~5 referred to variable-diameter structure. See

Table 2. Operating conditions.

	h	w	α
Case 0	-	-	-
Case 1	5 di	6 di	60°
Case 2	5 di	7 di	60°
Case 3	5 di	8 di	60°
Case 4	5 di	6 di	65°
Case 5	5 di	6 di	70°

for specific settings, where d_i is the diameter of a sinter particle.

The simulation process was as follows: first, a specific number of sinter particles were generated through the particle factory, and then they were naturally accumulated under the action of gravity. After the sinter became static, cooling air was introduced from the bottom for gas–solid counter-current heat transfer. After 10 s, the calculation was completed and the data were processed. EDEM2020 and ANSYS fluent2020 were used for the coupling calculation in this paper.

4. Results and Discussion

4.1. Influence of Variable-Diameter Structure on Sinter–Gas Heat Transfer

4.1.1. Sinter Temperature Distribution

The relationship between sinter temperature and quantity proportion was measured to demonstrate the cooling effect of sinter, as shown in Figure 2. It can be seen that in the two temperature ranges [711,713) and [718,720], the quantity of sinter accounts for 21.92%, 7.5%, 22% and 9.08%, respectively, with little difference between them. For the two lower temperature ranges [713,714) and [714,715), the proportion of sinter in the vertical structure is only 9.92% and 12%, respectively, while that in the variable-diameter structure is 17.5% and 20.25%, respectively, with an increase of 76.41% and 68.75%. It shows that under the conditions of a variable-diameter structure, more sinter is cooled to the two temperature ranges [713,714) and [714,715). For [715,718) with higher temperature, the sinter quantity in the vertical structure accounted for 48.66% in total, while that in the variable-diameter structure was only 31.17%, a relative decrease of 35.94%, indicating that the number of sinter particles in the above higher temperature ranges decreased significantly when the variable-diameter structure was used. Therefore, it can be concluded that the cooling effect of sinter is better when the variable-diameter structure is used.

Figure 3 shows the distribution of sinter temperature in the two furnace structures. The sinter temperature at the bottom was low, while that at the top was high. It can be seen from further observation that the height of the area occupied by blue particles in the two furnace types was basically the same. However, there was a great difference in the height of the area occupied by cyan and green particles. When using the variable-diameter structure, the height of this area was much higher. In the width direction, for vertical structure, the sinter temperature distribution at the bottom of the bed was relatively uniform. With the increase in the bed height, the temperature of the sinter at the sidewall was gradually lower than that in the central area, resulting in an inverted-V-type temperature distribution, which continued to the surface of the bed. As for the variable-diameter structure, the difference between the sinter temperature in the sidewall area and the central area was reduced, alleviating the temperature segregation, thus forming a horizontal distribution. This distribution also extended to the surface of the material layer.

In order to quantitatively study sinter temperature distribution, the two furnace types were divided into 10 bins along the height direction, and the average temperature and coefficient of variation of sinter temperature in each bin were counted. The results are shown in Figure 4.

In Figure 4a, it can be seen that the sinter temperature was basically the same in Bins 1 and 2 of the two structures, while in Bins 3~8, the sinter temperature of the variable-diameter structure was lower than that of the vertical structure. This is because the furnace volume was reduced after adopting the variable-diameter structure, resulting in an increase in the height of the bed formed by stacking the same amount of sinter. When the height was limited to Bin 8, the quantity of sinter used to provide heat in the variable-diameter structure was less than that in the vertical structure. Moreover, as the width of the furnace cavity decreased, the gas velocity increased, which improved the sinter–gas convection heat-transfer coefficient, resulting in an increase in the sensible heat carried by the cooling air. This enabled the sinter in the variable-diameter structure to be cooled to a lower temperature.

The sinter temperature difference in the corresponding areas of the two structures increased first and then decreased. This can be explained by the fact that the average width (AW) determines the gas flow velocity with equal height and thickness. Bin 3 (AW = 326.68 mm) and Bin 4 (AW = 237.28 mm) basically corresponded to the contraction section of the variable-diameter structure. As the shrinkage effect of Bin 4 was more obvious, the gas velocity was higher, the number of particles was smaller, and the sinter temperature drop was greater, resulting in an increase in sinter temperature difference. Bin 5 (AW = 210 mm) corresponded to the vertical section. The gas flow rate in this zone further increased, and the number of sinter particles continued to decrease, so the temperature difference continued to increase. Bin 6 (AW = 211.35 mm) included most vertical segments and a small number of expansion segments. In this area, the gas velocity began to decrease, and the number of sinter particles began to increase, making the temperature difference begin to decrease. Bin 7 (AW = 274.66 mm) corresponded to the expansion section and the width of Bin 8 (AW = 346.29 mm) returned to normal. The gas velocity in these two bins gradually decreased, and the number of sinter particles gradually increased. Therefore, the sinter temperature increased significantly, making the temperature difference continue to decrease.

Figure 4b gives the coefficient of variation of sinter temperature in different bins of the two structures. It can be seen that the coefficient of variation in the vertical structure was greater than that in the variable-diameter structure in the other bins except the bottom, Bin 1, indicating that the sinter temperature in the variable-diameter structure was more evenly distributed along the width direction. Due to the wall effect of vertical structure, the cooling effect of the sinter in this area was better than that in the center of the bed, resulting in uneven cooling of the sinter along the width, thus increasing the coefficient of variation of the sinter temperature. As the vertical structure could not destroy the wall effect and eliminate the sidewall airflow channel, the coefficient of variation was relatively large in the whole range of material layer height. Using the variable-diameter structure, thanks to the blocking effect of the contraction section, while the gas moved upward, it tended to flow to the center of the furnace cavity. At the same time, the narrower gas flow channel gradually reduced the number of sinter particles in the width direction and increased the contact heat transfer between sinter and cooling gas, and thus improved the uniformity of sinter temperature distribution. In the vertical section, the width of the gas flow channel was the narrowest, which reduced the temperature range. In the expansion section, the gas flow channel became wider and the uneven distribution of sinter temperature along the width was improved, while for the material layer above the expansion section, the sinter was basically loosely stacked, and the gas velocity distribution was relatively uniform, so that the sinter cooled evenly and the coefficient of variation was low.

4.1.2. Cooling Gas Temperature and Pressure Distribution

The cooling gas temperature distribution in the two structures is shown in Figure 5. For the vertical structure, at the same bed height, the gas temperature at the sidewall was lower than that at the center, making the horizontal distribution uniformity of gas temperature poor. The reason for this was that the wall effect made the gas velocity near the wall higher, which not only enhanced the cooling of the sinter and lowered its temperature, but was also able to quickly remove the heat obtained from the sinter, thus making the cooling gas temperature at the wall lower. With the adoption of the variable-diameter structure, the wall effect can be reduced, and the uniformity of the gas temperature distribution along the width direction can also be greatly improved.

The cooling gas temperature on line 1–3 was measured to quantitatively study its distribution along the height direction, as shown in Figure 6a. Below 0.7 m, the gas temperature in the variable-diameter structure was always lower than that in the vertical structure, due to the low sinter temperature in the structure. However, under the conditions of the vertical structure, the area above 0.7 m was a free space, so the cooling gas temperature basically remained unchanged. For the variable-diameter structure, the length of the sinter–gas heat-exchange section was extended due to the increase in the bed height. Although the cooling gas temperature was relatively low, the temperature difference between the cooling gas and the sinter above the expansion section increased, which was instrumental in the sinter–gas heat exchange, making the cooling gas temperature higher than the temperature at the sidewall of the vertical structure and close to the temperature at its center. The relationship between the outlet gas temperature of the two structures and the cooling time is shown in Figure 6b. We can see that with the vertical structure, the maximum cooling gas temperature was 603.91 K, while with the variable-diameter structure, the maximum cooling gas temperature reached 611.76 K, an increase of 7.85 K. Moreover, it was observed that the temperature curve of Case 1 was always above Case 0, indicating that the gas outlet temperature of Case 1 was higher during the simulation period. Under the same conditions with regard to other influencing factors, it can be considered that the variable-diameter structure can improve the sinter–gas convection heat transfer and increase the heat carried by the outlet cooling gas.

The cooling gas pressure distributions of the vertical structure and the variable-diameter structure are shown in Figure 7a. With the vertical structure, the maximum pressure was 1334 Pa, while for the variable-diameter structure, it was 2176 Pa. The gas pressure increased by 63.12%, which indicates that the use of variable-diameter structure required the configuration of higher-power fans. Figure 7b shows the distribution of cooling gas pressure drop within the equal material layer thickness (0.056 m), which measured the power required for cooling gas to pass through the material layer. In the case of the vertical structure, the value changed little within the range of ~0.6 m in material layer height, indicating that the power required was basically unchanged; For the variable-diameter structure, the value gradually increased before entering the vertical section. This meant that it became gradually more difficult for cooling air to pass through the material layer, and it also indicated that the upper sinter hindered the upward flow of the cooling gas below it. This obstruction was able to avoid the phenomenon of the cooling gas quickly escaping from the wall due to the wall effect, increase the uniformity of the cooling gas distribution in the material layer, improve the contact heat-transfer conditions of the sinter–gas so as to improve the utilization efficiency of the cooling gas and the sinter–gas heat-transfer effect.

4.2. Parameter Optimization of Variable-Diameter Structure

As a new type of sinter vertical shaft cooler, the variable-diameter structure involves many structural parameters. Next, this study selected the vertical section width and contraction section angles to study their influence on the sinter–gas heat transfer, and optimized the values of the above parameters.

4.2.1. Vertical Section Width

Cases 1~3 were used to study the effect of vertical section width on sinter–gas heat transfer. Figure 8 illustrates the distribution of sinter and cooling gas temperature and cooling gas pressure along the vertical direction. With the decrease in the vertical section width, the sinter temperature in each bin decreased. For cooling gas, in most of the middle and lower regions, the temperature also decreased; however, it increased in the upper region, making the outlet gas temperature rise. In addition, the cooling gas pressure also showed an upward trend. The reasons were as follows: The decrease in the vertical section width reduced the amount of sinter and increased the gas flow rate, resulting in the decrease in sinter temperature in each bin and in the cooling gas temperature in most of the middle and lower areas. However, the length of the heat-exchange section and the temperature difference between the sinter bed above the expansion section and the cooling gas increased with the decrease in the vertical section width, which made the cooling gas temperature in the upper area rise, thus increasing the outlet gas temperature. The reduction in the vertical section width also led to the increase in the blocking effect of the contraction section on the cooling gas, so that the cooling gas pressure increased.

Therefore, it is recommended to set a smaller vertical section width when using the variable-diameter structure to improve the sinter–gas heat transfer. At the same time, the pressure increase of the cooling gas should also be taken into account. In addition, the width should not affect the normal downward movement of the sinter to prevent the occurrence of blocking.

4.2.2. Contraction Section Angle

Cases 1, 4 and 5 were set to study the influence of contraction section angle on sinter–gas heat transfer. Figure 9 shows the distribution of sinter and cooling gas temperature and cooling gas pressure along the vertical direction. With the increase in the angle, the variation trends of the sinter temperature, cooling gas temperature and pressure was similar to the effect of reducing the vertical section. The difference was that with the increase in contraction-section angle, the sinter temperature could still maintain a rapid decline in the contraction section and the vertical section. This was because changing the angle only meant that the variable-diameter structure could still be maintained. Moreover, the increase in the angle increased contraction-section length. On the one hand, the number of sinter particles in the corresponding area were reduced. On the other hand, the acceleration area of the cooling gas velocity was extended, making the sinter temperature drop further in the above sections. The increase in the contraction-section length also increased the bed height, which increased the cooling gas pressure. However, the increase in the angle also slowed down the change rate of the contraction-section width, which reduced its blocking effect on the flow of the cooling gas, and finally caused a small increase in the cooling gas pressure.

Increasing the contraction-section angle was able to increase the outlet cooling gas temperature and reduce sinter temperature, but also made the variable-diameter structure higher. Therefore, when selecting the contraction-section angle, full consideration should be given to whether the site has height restrictions.

5. Conclusions and Future Perspectives

The CFD-DEM model was used to study the influence of variable-diameter structure on sinter–gas heat transfer in a vertical shaft cooler from the temperature distribution and uniformity of sinter and cooling gas, as well as cooling gas pressure drop. The vertical section width and contraction section angle of the variable-diameter structure were optimized, and the conclusions are as follows:

(1)

Compared with the vertical structure, the variable-diameter structure can improve the sinter–gas contact characteristics and the utilization efficiency of cooling gas at the cost of increasing the pressure drop of cooling gas, so as to strengthen the sinter–gas convection heat transfer and increase the amount of low-temperature sinter as well as the outlet cooling gas temperature. Additionally, it increases the uniformity of the temperature distribution of sinter and cooling gas along the width direction. Hence the variable-diameter structure can become a new type of sinter vertical shaft cooler.

(2)

A smaller vertical section width leads to a better sinter–gas heat transfer. However, when selecting the vertical section width, the pressure drop of the cooling gas should be taken into account. Additionally, the occurrence of blocking should also be avoided.

(3)

Although it increases the height of the variable-diameter structure, a greater contraction section angle results in a better sinter–gas heat transfer. Therefore, it is necessary to consider whether there is a height limit on site.

In future work, the influence of sinter particle size distribution, the distribution mode and the flow pattern of sinter and cooling gas will be taken into account to further investigate the influence of variable-diameter structure on sinter–gas heat transfer.