CFD-DEM Investigation on Pressure Drops of Heterogeneous Alternative-Layer Particle Beds for Low-Carbon Operating Blast Furnaces

Abstract

Low-carbon operation technologies of the blast furnace (BF) are crucial for reducing carbon dioxide emissions from the steelmaking industry. The variation characteristic of permeability and structure in a BF lumpy zone has a critical impact on achieving low-carbon operations. Still, their influences have not been fully understood, and related studies are very limited. To solve the problem of the deteriorating permeability of blast furnaces after lowering the coke ratio, this study aims to provide insights into the pressure drop of the lumpy zone in an ironmaking BF based on computational fluid dynamics coupled with the discrete element method (CFD-DEM) model. The study systematically investigates the influence of different packing configurations on permeability using a heterogeneous alternating-layer (HAL) packed bed. After the model was validated by comparing the simulation’s results with ones calculated by the Ergun equation, it was used to investigate the effects of the number of layers, coke-mixing ratio, nut coke replacement ratio, and particle-size ratio on the structure, void fraction variation, and pressure drop of the HAL packed bed. The results reveal the effect of these factors on the permeability of the lumpy zone, providing fundamental guidance towards low-carbon operations of BFs.

1. Introduction

Ironmaking blast furnaces (BFs) are still an essential process for steel production in the foreseeable future [1,2], although some alternative approaches [3,4], such as hydrogen-based direct reduction processes [5], are innovatively proposed. The lumpy zone of BFs is essentially a heterogeneous alternative-layer (HAL) packed bed (see Figure 1, which is illustrated above the yellow line), and its permeability heavily affects fluid flow, heat and mass transfer, and thus the efficiency of the process. For example, for an industrial BF of 4000 m³ with a column height of 25 m from the tuyere to the BF’s top, the typical pressure drop is in the range of 1.5~2.0 atm, wherein the pressure drop in the lumpy zone accounts for about 20%, and deep insight into it is of great significance to reduce the pressure drop for stable production. In particular, under the background of low-carbon operating BF, when some innovative technologies are applied, such as mixing charges of ore and coke, nut additions into ore layers, changing the particle size ratio between layers, and so on, a deeper understanding of the variation characteristic of permeability and structure in a HAL packed bed is vital to achieve low-carbon operation targets, reduce pressure drops, lower the consumption of fuel, increase the efficiency of production, immigrate CO₂ emissions [6,7], and also provide a basis for optimizing industrial operations.

Some low-carbon operations for a BF have been reported [8,9,10,11,12,13,14,15,16,17,18,19]. Watakabe et al. [8] reported that the permeability would increase with the increase in coke-mixing ratios. Babich et al. [9] used model experiments to reveal the influence of nut coke on permeability. Guha et al. [10] reported that the interfacial resistance in the layered packed structure significantly contributed to the overall pressure drop in their experiments. Mousa et al. [11] showed that the permeability increased with the increase in mixed nut coke into the ore layer of a blast furnace. Yu et al. [12] showed the validity of the simulation by comparing the results of discrete element models (DEM) and experimental measurements of the percolation behavior of pellets in the coke layer during the charging process and revealed the influence of the properties of the particles on permeability. Liu et al. [13] studied the flow rate, interface numbers, and layer thickness, revealing the existence and variation patterns of interfacial resistance and its significant effect on the total pressure drop. Allen et al. [14] investigated the effects of particle shape, diameter distribution, packing structure, and roughness effects on pressure drops in a packed bed. Mitra et al. [15] found that the mixed layers of coke and pellets show lower voids than the alternative layers charged. Ichikawa et al. [16] investigated the effect of the coke layer’s thickness on permeability, concluding that pressure drops increase as the coke layer’s thickness decreases. Terui et al. [17] studied the effect of the particle diameter ratio between layers. The results showed that reducing the particle diameter ratio of coke to a sinter ore could result in a uniform coke distribution in the mixed layer. Li et al. [18] pointed out that bed’s permeability was closely related to the distribution features of ore and coke granularities in the lumpy zone of a BF. Li et al. [19] derived the effect of the number of interfaces on the pressure drop based on a heterogeneous particle-packed bed model containing interfaces by an in-depth study of the mechanism of interfacial resistance loss. However, until now, only a few studies concentrated on the effect of these low-carbon operations on pressure drops or permeability, and it is inadequately understood or incompletely documented due to the limits of sensor technology and the painful cost of in situ experiments at high temperatures and hazardous conditions for HAL packed beds or ironmaking BFs.

On the other hand, computational simulation technology has become an increasingly crucial tool in recent years. Several modeling strategies have been extensively used to simulate fluid–solid multiphase systems, including a two-fluid model (TFM) [20] and computational fluid dynamics combined with DEM (CFD-DEM) [21]. TFM assumes solid granules and fluids as two interpenetrating continuums with a variable to describe the occupying volume. At the same time, the CFD-DEM method manages the particle phase as discrete elements, which is closer to the physical nature of particles. As a result, CFD-DEM has proven to capture most of the macro- and micro-characteristics of packed beds on a particle scale. For example, Neuwirth et al. [22] examined the validation of CFD-DEM simulation via tracking the motion of particles in a rotor granulator and found the results obtained by the model were similar to experimental ones, manifesting that the CFD-DEM model can more precisely simulate granular phenomena. Jajcevic et al. [23] reported that CFD-DEM could be used for numerical simulations of a large number of particles. Yu et al. [24] revealed that DEM using a sphere-shaped particle with calibrated coefficients might reasonably predict the behaviors of irregular particles of different sizes. Furthermore, Wei et al. [25] showed that the measured DEM parameters have sufficient accuracies by comparing the DEM simulation’s results with the experimentally measured data. Vijayan et al. [26] showed that CFD-DEM could accurately and efficiently investigate packing processes, including particle-stacking structure and density and size ratio effects. Mondal et al. [27] studied gas-flow features and temperature-distribution characteristics in the upper part of the blast furnace by CFD-DEM, and the results showed that CFD-DEM accurately revealed the momentum and heat transfer between the gas–solid two-phase flow.

This study aims to investigate the effect of innovative low-carbon operating techniques on the pressure drop or permeability of the HAL-packed bed for the lumpy zone of the ironmaking blast furnace using the CFD-DEM simulation. First, the established CFD-DEM model was calibrated and validated. Then, the effects of different variables and structures induced by low-carbon operations for a BF, such as alternative-layer numbers in a fixed height, a ratio of coke mixing into ore layer, nut coke replacement ratio, and particle size ratio between adjacent layers, on the stock column’s structure, void fraction variation, and the pressure drop of the HAL packed bed were investigated in detail. The simulation’s results can help guide low-carbon BF production in improving their permeability.

2. Model Description

2.1. DEM for Particles Phase

The collection of granular materials consists of mesoscopic particles, and DEM tracks each particle via a force–displacement relationship that can be separated into rotational and translational motions [19,28], as exemplified in Figure 2. The superiority of DEM compared to TFM is not only that it can obtain the macroscopic information of the collection but also that it precisely elaborates microscopic motion details of individual particles. The translational and rotational motions of each particle i with radius R_i, mass m_i, and moment of inertia I_i are governed by the following equations, respectively:

$$m_i\frac{d^2{x}_i}{d{t}^2}+\eta \frac{d{x}_i}{dt}+K{x}_i+F_{\mathrm{v},i}+F_{\mathrm{s},i}=0$$

(1)

$$I_i\frac{d^2{\theta }_i}{d{t}^2}+{\eta }_{\mathrm{r}}\frac{d{\theta }_i}{dt}+K_{\mathrm{r}}{\theta }_i=0$$

(2)

in which t is the time; x_i and θ_i represent the translational displacement and the rotational angle, respectively; η and K are the ith particle’s damping coefficient and stiffness, respectively; F_v,i is the body force, similarly to gravitational force m_ig; F_s,i is the surface force acting on the particle, similarly to the fluid-particle interphase drag force; the subscript r denotes the action caused by the rolling effect. Furthermore, when only focusing on interactions between particles, the above equations can be reduced as follows:

$$m_i\frac{d{v}_i}{dt}={\displaystyle \sum _{j=1}^{k_i}(F_{\mathrm{n},ij}+F_{\mathrm{t},ij})+m_{i}g}+F_{\mathrm{fp},i}$$

(3)

$$I_i\frac{d{\mathsf{\omega }}_i}{dt}={\displaystyle \sum _{j=1}^{k_i}(M_{\mathrm{t},ij}+M_{\mathrm{r},ij})}$$

(4)

where F_c,i is the ith particle acting on the particle–particle or particle–wall contact force, and it can be decomposed into two components: F_n,ij in the normal direction and F_t,ij in the tangential direction between entities i and j. F_fp,_i is the fluid–particle interactional force; M_t,ij and M_r,ij are torques that are raised by the tangential force and rolling resistance force, respectively; v_i and ω_i denote the ith particle’s translational and angular velocities. The specific formulas [29,30,31] of these items are listed in

Table 1. The specific formula for each force and torque acting on particle i.

Forces and Torques	Symbol	Equations
Normal force: elastic component	Fen,ij	−Knδn	$K_{\mathrm{n}}=\frac{4}{3}{E}^{*}\sqrt{R^{*}\left|{\mathsf{\delta }}_{\mathrm{n}}\right|}$
Normal force: damping component	Fdn,ij	$-{\eta }_n{V}_{n,ij}$	${\eta }_n=-2\sqrt{\frac{5}{4}}\mathsf{\beta }\sqrt{m^{*}{K}_{\mathrm{n}}}$
Tangential force: elastic component	Fet,ij	−Ktδt	$K_{\mathrm{t}}={8\mathrm{G}}^{*}\sqrt{R^{*}\left|{\mathsf{\delta }}_{\mathrm{n}}\right|}$
Tangential force: damping component	Fdt,ij	$-{\eta }_t{V}_{t,ij}$	${\eta }_{\mathrm{t}}=-2\sqrt{\frac{5}{6}}\mathsf{\beta }\sqrt{m^{*}{K}_{\mathrm{t}}}$
Torque: tangential force arising part	Mt,ij	R*n × (Fet,ij + Fdt,ij)
Torque: rolling resistance arising part	Mr,ij	−Krθr θr < = θ0 M0 θr > θ0	$K_{\mathrm{r}}=\frac{K_{\mathrm{n}}{B}^2}{12}$ $M_0=\frac{n\times \left(F_{\mathrm{en}}+F_{\mathrm{dn}}\right)B^2}{6}$

. It should be mentioned that each particle may experience net actions by multiple interactions induced by multiple particles in an instant, and they are summed up until the kth particle that is contacting with the current ith particle. In addition, the Coulomb-type friction law must be applied when the tangential force meets relationship |F_t,ij| < = μ_s|F_n,ij| and wherein μ_s denotes the sliding friction coefficient.

Here, $\frac{1}{E^{*}}=\frac{{(1-{\mathsf{\nu }}_i)}^2}{E_i}+\frac{{(1-{\mathsf{\nu }}_j)}^2}{E_j}$, $\frac{1}{G^{*}}=\frac{{2(2+\mathsf{\nu }}_i\left)\right(1-{\mathsf{\nu }}_i)}{E_i}+\frac{{2(2+\mathsf{\nu }}_j\left)\right(1-{\mathsf{\nu }}_j)}{E_j}$, $\frac{1}{R^{\ast }}=\frac{1}{R_i}+\frac{1}{R_j}$, $\frac{1}{m^{\ast }}=\frac{1}{m_i}+\frac{1}{m_j}$, $\mathsf{\beta }=\frac{\ln \left(\mathrm{e}\right)}{\sqrt{{\ln }^2\left(\mathrm{e}\right)+{\mathsf{\pi }}^2}}$, ${\delta }_{\mathrm{n}}=\left[\left(R_i+R_j\right)-|x_i-x_j|\right]n$, ${\mathrm{V}}_{n,ij}=({\mathrm{V}}_{ij}\cdot \mathrm{n})\cdot \mathrm{n}$, ${\mathrm{V}}_{t,ij}=({\mathrm{V}}_{ij}\times \mathrm{n})\times \mathrm{n}$, ${\mathrm{V}}_{ij}={\mathrm{V}}_j-{\mathrm{V}}_i+{\mathsf{\omega }}_j\times {\mathrm{R}}_j-{\mathsf{\omega }}_i\times {\mathrm{R}}_i$, and $n=\frac{x_j-x_i}{|x_j-x_i|}$. Young’s Modulus is denoted by E; Poisson ratio is denoted by ν; B represents a contact width that can be calculated via φR*, and φ is a parameter related to the particle shape; δ_t is the tangential overlap.

2.2. CFD for Fluid Phase

The governing equations for the fluid phase can be written as follows:

$$\frac{\partial }{\partial t}(\epsilon {\rho }_{\mathrm{f}})+\nabla \cdot (\epsilon {\rho }_{\mathrm{f}}{u}_{\mathrm{f}})=0$$

(5)

$$\frac{\partial }{\partial t}(\epsilon {\rho }_{\mathrm{f}})+\nabla \cdot (\epsilon {\rho }_{\mathrm{f}}{u}_{\mathrm{f}}{u}_{\mathrm{f}})=-\epsilon \nabla p_{\mathrm{f}}+\epsilon {\mu }_{\mathrm{f}}{\nabla }^2{u}_{\mathrm{f}}+\epsilon {\rho }_{\mathrm{f}}g-\frac{{\displaystyle \sum _{i=1}^{k_V}{F}_{\mathrm{fp},i}}}{\Delta V}$$

(6)

where ε is the porosity of the bed, and ρ_f, u_f, p_f, and μ_f, are the density, apparent velocity, pressure, and dynamic viscosity of the fluid, respectively. F_p is the force of particles acting on the fluid.

2.3. Coupling of CFD and DEM

The CFD and DEM coupling scheme is detailed in Figure 3, and the heat transfer model was also coded in this procedure. In this program, the DEM is implemented based on the open-source code LIGGGHTS [21,32]. The program considers the motion of the particles and the heat transfer between them, and the CFD implementation uses OpenFOAM [33]. At each time step, the positions, velocities, and temperatures of individual particles calculated by the DEM module will be pushed to the CFD module. Consequently, the CFD module can compute the porosity and volume fraction occupied by particles and interaction force in each computational cell. In this study, the DEM module passed the information to the CFD module every time it reached 1000 steps. Then, CFD solves the equations of velocity, pressure, and temperature fields; furthermore, the interactional forces between the fluid and individual particles, as well as local heat exchange, can be obtained. Incorporating the resultant forces into the DEM procedure makes it closed, thus implementing a step advancement of the Newton equation, completing the motion of the individual particles for the next time step. Additionally, it should be stressed that the established model included the heat-transfer module to consider behaviors of the cohesive zone, but it was not used, and the subsequent discussion in this study is based on isothermal simulations.

2.4. Computational Details

In this paper, a cylindrical geometric model (shown in Figure 4) is used to validate the permeability and pressure drop law of a HAL packed bed. The diameter of the cylinder is 1 m, and the height is 9 m. The grid size used in this study is slightly larger than the particle size to meet the CFD-DEM’s simulation requirements; thus, the model has a grid cell of about 113,400. The particles in the study are assumed as spherical particles. The gas inlet is at the bottom of the packed bed, and the particles were poured from the top into the bed according to the planned configuration to form a target HAL packed bed. The specific parameter settings used in the simulations are shown in

Table 2. Computational conditions and material properties.

Item	Symbol	Value	Unit
Diameter of coke	dc	0.08	m
Diameter of nut coke	dn	0.025	m
Density of coke or nut coke	ρc	1050.0	kg/m3
Friction coefficient of coke or nut coke	ecf	0.43	-
Friction coefficient of coke and nut coke	ecnf	0.43	-
Restitution coefficient of coke	ecr	0.3	-
Restitution coefficient of coke and nut coke	ecnr	0.3	-
Poisson coefficient of coke	vc	0.22	-
Diameter of ore	do	0.045	m
Density of ore	ρo	3950.0	kg/m3
Friction coefficient of ore	eof	0.43	-
Friction coefficient of ore and coke or nut coke	eocf	0.43	-
Restitution coefficient of ore	eor	0.3	-
Restitution coefficient of ore and coke or nut coke	ecnr	0.3	-
Poisson coefficient of ore	vo	0.22	-
Diameter of container	D	2	m
Height of container	H	9	m
Friction coefficient of the container wall	ewf	0.43	-
Restitution coefficient of the container wall	ewr	0.3	-
Poisson coefficient of the container wall	vw	0.24	-

below. Here, it should be noted that we simplified the particle size’s distribution in which the actual ore and granular coke in an industrial BF were used, and only one size with respect to the round particles for each material was used. Although this simplification may be a slight variation in quantitative terms, the fundamental law should be consistent and valid.

The list of material properties that will be used in the following simulation is shown in Table 2.

3. Model Validation

A validation of the model is essential for the reliability and accuracy of simulation results. Considering that the Ergun equation is widely used to address the pressure drop of the packed bed with the same particle size, the Ergun equation is as follows.

$$-\frac{\mathsf{\Delta }P}{\mathsf{\Delta }L}=\frac{150{\mu }_{\mathrm{f}}{\left(1-\epsilon \right)}^2{u}_{\mathrm{f}}}{{\epsilon }^3{D}_{\mathrm{p}}^2}+\frac{1.75\left(1-\epsilon \right)u_{\mathrm{f}}^2}{{\epsilon }^3{D}_{\mathrm{P}}}$$

(7)

In the above equation, ΔP is the pressure drop, Pa; L is the packed bed height, m; ε is the packed bed void ratio; D_p is the equivalent sphere diameter of the furnace charge, m where the following is the case.

$$\epsilon =1-{\epsilon }_{\mathrm{s}}$$

(8)

$${\epsilon }_{\mathrm{s}}=\frac{V_{\mathrm{s}}}{V_{\mathrm{b}}}$$

(9)

In Equations (7) and (8), ε_s is the volume fraction of the solid; vs. is the volume of the solid, m³; V_b is the volume of the packed bed, m³. Moreover, the equation is written in a vector form as follows.

$$-\frac{dp}{dx}=\frac{1}{\kappa }\cdot \left({\mu }_{\mathrm{f}}\cdot {\mathit{u}}_{\mathrm{f}}\right)+\beta \cdot \left(\rho \cdot {\mathit{u}}_{\mathrm{f}}^2\right)$$

(10)

Among them, we have the following.

$$\kappa =\frac{150{\left(1-\epsilon \right)}^2}{{\epsilon }^3{D}_{\mathrm{p}}^2}$$

(11)

$$\beta =\frac{1.75\left(1-\epsilon \right)}{{\epsilon }^3{D}_{\mathrm{P}}}$$

(12)

It should be stressed that the Ergun equation often deviated for calculating pressure drops in heterogeneous packed beds, and many researchers have to correct the Ergun equation based on their experimental data or by adding empirical formulas. Therefore, in this study, a uniformly sized coke particle was chosen to verify the accuracy of the established CFD-DEM. The simulation results were compared with those calculated by the Ergun equation under the same conditions. The validation procedure considers changing the particle’s size in the DEM module and the inlet velocity in the CFD module.

Figure 5 shows pressure drop variations over time. The simulated value fluctuates continuously with time, while the calculated value of the Ergun equation does not change with time. It can be seen that the simulated value constantly fluctuates up and down around the estimated value of the Ergun equation.

Figure 6 illustrates the variation of the pressure drop for different particle diameters. The packed bed’s pressure drop decreases with increasing particle size, and the simulated values follow the same trend as the pressure drop curve obtained from the classical Ergun equation calculation.

Table 3. Comparison of pressure drop with different coke diameters from the Ergun equation and simulations.

Items	Case 1	Case 2	Case 3	Case 4	Case 5
dp (m)	0.06	0.08	0.10	0.12	0.14
The calculated value of the Ergun equation (Pa)	3.68	1.98	1.28	0.92	0.64
Averaged values of simulations (Pa)	3.48	1.97	1.20	0.98	0.62
Error (%)	5.43	0.51	6.25	6.52	3.13

below provides the values of pressure drop calculated by the Ergun equation and simulated pressure drop for different particle sizes. Combining Figure 6 and Table 3, an agreement can be achieved using CFD-DEM simulations.

Figure 7 shows pressure drop variations of the packed bed with respect to time for an initial gas velocity of 0.68 m/s. Again, it can be observed that most simulated values are close to the calculated values of the Ergun equation, and the simulated values always fluctuate up and down around the calculated values of the Ergun equation.

Figure 8 compares the pressure drop variation obtained from the packed bed simulation and the Ergun equation calculation for the initial velocity of the gas from 0.28 m/s to 0.68 m/s. Again, the pressure drop increases with increasing inlet velocities. The pressure-drop curves of the simulated and calculated values from the simulation and the Ergun equation almost follow the same variation trend.

Table 4. Comparison of pressure drop with different gas velocities from the Ergun equation and simulations.

Items	Case 1	Case 2	Case 3	Case 4	Case 5
uf (m/s)	0.28	0.38	0.48	0.58	0.68
The calculated value of the Ergun equation (Pa)	0.58	0.87	1.20	1.57	1.98
Simulated values (Pa)	0.59	0.88	1.21	1.59	2.00
Error (%)	1.72	1.15	0.83	1.27	1.01

provides the calculated and simulated pressure drops of the Ergun equation for different gas velocities. Table 4 shows that the values of simulated and Ergun equation calculation results are in good agreement. In summary, the simulation results of the established CFD-DEM model agree well with the calculated results of the Ergun equation, and the model is validated.

4. Results and Discussion

4.1. Effect of Layers Number

Considering different charging batch weights will result in a different number of layered packed structures, e.g., at a fixed height; even the charged overall weight of the ore and coke particles remains constant, but the layer numbers or interface numbers are varied. However, their changes and their effects on pressure drops or permeability are not fully understood.

Figure 9 provides several typical configurations for HAL packed beds with different layer numbers. Although, in different cases, each type of particle with respect to the number or overall weight is the same, it can be observed that the height of these columns decreases slightly, and the thickness of each bed becomes thin as the number of layers increases. This is because the small-sized ore particles will enter gaps between the coke particles around the interface, and the voids or holes in the interfaces are filled so that the gas cannot pass through properly. Furthermore, Figure 10a shows the pressure distribution of the two-layer column, and it can be seen that the pressure-drop loss at the interface is greater than the one at the bulk layer. Moreover, the variation in pressure drop at the interface with height is provided quantitatively in Figure 10b, which shows more clearly that the pressure loss at the interface varies drastically. Figure 11 demonstrates the cross-section of stock columns with a different number of layers for visualizing the void fraction’s distribution. As the interface’s numbers increases, the void fraction of the overall packed bed will gradually lower. As a result, the pressure drop at the interfaces is greater than the bulk layer. Consequently, as observed in Figure 12, the pressure drop increases due to an increase in the layer’s numbers, leading to an increase in the interface’s number. Thus, the more interfaces there are, the higher the pressure drop of the column, and the less permeable the column will become. Additionally, the pressure drop per meter modeled by this study is in the range of 1200~1600 Pa/m, and it is consistent with the practical data of industrial BFs.

4.2. Effect of Coke Mixing Ratio

In order to lower reducing-agent usage and mitigate CO₂ emissions, high reactivity coke and/or nut coke mixed-charge technologies were reported [8,9,11], wherein partial coke that originally should be charging into the coke layer or nut coke that was not used in a BF was mixed and charged with the ore layer. However, the mechanism of preferable permeability must be clarified to design a favorable packed bed structure. The mixing ratio as a core parameter plays a vital role in this process. Therefore, the pressure drop variation via changing the coke and nut coke mixed ratio in the ore layer is discussed in this section and the following section, respectively.

Figure 13 shows several typical stock column structures with different coke mixed ratios. Herein, the total number of particles for all cases has not changed, and only the number of coke particles mixed into the ore layer has changed. The height of these columns is visually the same as each other. However, from a quantitative view, the height of the column mixed with 0% coke in the ore layer is the highest, and the one mixed with 100% coke in the ore layer is the lowest. That is to say that the porosity of the entire packed bed slightly increases when the mixing ratio increases. Figure 14 shows the pressure drop, thus, declined with the increase in the coke mixed ratio. It can be observed that there is an obvious correspondence between the void fraction and pressure drop or that the void fraction is inversely related to the pressure drop. According to Figure 15, the void fraction of the coke layer is much larger than the void fraction of the ore layer, and mixing coke in the ore layer improves the void fraction of the ore layer. With the increase in the coke-mixing ratio, the stock column becomes more and more uniform, the interface region turns gradually indistinct, and the influence brought by the interface effect lowers and improves the overall permeability of the column. Consequently, the pressure drop decreases with the increase in the coke-mixing ratio, as shown in Figure 14.

4.3. Effect of Nut Coke Replacing Ratio

The particle size of coke particles in a blast furnace is generally 40–60 mm, and small nut coke with a particle size of less than 40 mm is discarded. In the modern ironmaking practice, it is well-recognized that adding small nut coke into the ore layer can optimize the charge’s structure and improve the permeability of the cohesive zone. However, it is unknown how adding nut coke particles affects pressure drops in the lumpy zone. Therefore, in this study, we designed a certain amount of nut coke that was added to the ore layer and replaced the partial coke in the original coke layer, but we kept the total mass constant in the furnace.

Figure 16 shows the stock column structure under different nut coke mixing ratios. Moreover, we can see that with the increase in the number of coke particles in the ore layer, the coke layer gradually becomes thinner. Additionally, the bed’s height decreases with the increase in replacement ratios, leading to a decrease in the porosity of the column and a reduction in bed permeability. This is because the nut coke particles are smaller than the coke and ore particles, which will fill the gap between the larger ore particles, resulting in the entire ore layer’s particles stacking more closely. Furthermore, Figure 17 shows pressure drop variances with different nut coke mixing ratios. It can be observed from Figure 17 that the pressure drop per unit height increases obviously with the increase in nut coke–ore layer mixing ratio. In particular, when the replacement proportion is low, the pressure drop increases significantly; thus, it is necessary to pay attention to the pressure in the blast furnace to avoid the problem of lower burden blockage that has an equivalent effect on the nut coke mixing addition. However, in the production practice of a blast furnace, it is impossible to replace a large number of large-size coke with small-size nut coke, and it is even impossible to replace 100% coke with nut coke. Therefore, the nut coke mixed ratio of 100% is only used as a research reference, which has little significance for actual production applications. When adding nut coke, it should be considered that nut coke affects not only the lumpy zone but also the cohesive zone in improving permeability and production efficiency.

4.4. Effect of Particle Size Ratio

The particle size ratio between layers is one of the main influencing factors that lead to a variation in pressure drops in the Ergun equation. In this study, for the sake of simplicity, we fixed the radius of coke particles to 40 mm and changed the radius of sinter ore particles (15, 20, 25, 30, 35, and 40 mm) to investigate the effect of the particle size’s ratio.

Figure 18 shows the structure of the packed bed under the condition of particle size ratios. It is clearly seen that with the increase in sinter particle size, the ore’s layer thickness increases, and the overall height of the column increases, although the total charging mass is fixed for all cases. Moreover, by combining Figure 18 and Figure 19, we found that the interfaces between the coke layer and the sintered ore layer are not clear when the particle size ratio is relatively large. When a layer of coke particles is charged, the small size ore particles fall into the gaps of the coke layer consisting of the larger size coke. The contact between the coke and the ore will be closer and the void fraction will be reduced. As the particle size ratio further decreases, it can be seen that this situation is enhanced, and the interface between the sinter and coke layers becomes more pronounced; the void fraction in the bed becomes larger, and its height thus increases. Figure 20 shows a comparison of the pressure drop with different particle size ratios, finding that the pressure drop remarkably decreases as the particle’s size ratio decreases. As the particle’s size ratio decreases, the pressure drop tends to fall more and more gently. The pressure drop is at its lowest when the particle size ratio is 1. When screening the charging granular for ironmaking BF practices, the particle size ratio cannot be too large. Otherwise, the permeability of the blast furnace will seriously deteriorate and reduce production efficiencies.

5. Conclusions

A CFD-DEM model was used to investigate the permeability of a heterogeneous alternative layer packed bed with different structures with respect to applications in the lumpy zone in ironmaking BFs to understand innovative low-carbon operations technologies. Simulations studied the effects of the layer numbers, coke mixing ratio, nut coke replacing ratio, and particle size ratio on stock column structure, void fraction variation, and the pressure drop of the HAL packed bed, and the following conclusions were obtained.

• The increase of the layer numbers in a fixed height of the bed implies a decrease in a single-layer thickness and an increase in interface numbers, wherein some original voids around the interface region are filled with smaller-sized ore particles, resulting in a smaller void at the interface; thus, an increase in the pressure drop of the packed bed, resulting in a deterioration in permeability.
• As the coke mixing ratio increases, the amount of coke mixed into the sintered ore layer increases, and the overall void ratio and permeability of the packed bed improved, which shows that the pressure drop of the bed decreases with the increase in the coke mixing ratio, and permeability improved significantly.
• Considering the case of nut coke replacing coke and blending into the sintered ore layer, with the nut coke’s replacement ratio increase, the sintered ore layer that was blended by the small and medium particle size, and nut coke forms a smaller void ratio structure compared to the pure sintered ore layer, resulting in a higher pressure drop. In particular, when the amount of nut coke blended is large, it will lead to a considerable pressure drop and significant deterioration in the permeability in the lumpy zone of a BF. Additionally, considering that it brings a beneficial effect in the cohesive zone of a BF, a 20% mixing ratio of nut coke is a preferable option.
• When the particle size ratio (ore/coke) increases, the small-size sintered ore around the ore-coke interface that could originally enter the coke layer is not easily penetrated the interface into the voids due to an increase in its particle size, leading to a decrease in the interface pressure and an improvement in permeability with the increase in the particle’s size ratio. The closer the particle size ratio is to 1, the more improved the permeability of the furnace and the lower the pressure drop.

Finally, we want to emphasize that this study represents an initial exploration towards a deeper insight into the permeability characteristics of BFs after applying low-carbon operations. Moreover, the established model appears to be a good starting point for further extension, e.g., considering the polydisperse size particle for ore and coke granular and including the cohesive zone and industrial applications.