1. Introduction
The BF (blast furnace) is the most important smelting reactor involving complex mass transfer, momentum transfer, heat transfer, and chemical reactions between gas and granular materials in the ironmaking industry [
1]. There is a general awareness that the burden distribution is vital to the operation of a BF. To be specific, the burden distribution determines the gas flow distribution, gas permeability, and CO utilization, thus significantly impacting the emission reduction, energy saving, efficiency, yield and quality of molten iron, and stability, safety, and durability of the blast furnace [
2]. In general, the burden distribution in a BF is largely determined by the charging process of coke and iron ore involving complicated particle dynamics. Therefore, investigating the charging process and obtaining a preferred burden distribution within the BF should be not only of academic interest, but also of significance for practical applications.
The charging process is a typical particulate system. Just as in the investigation of particulate systems, both experimental studies and numerical simulations are the frequently used methods for studying the charging process and burden distribution. In the published experimental investigations, both full-scale and reduced-scale blast furnaces have been studied, and different detection means (e.g., horizontal bar measurement, material box method, mechanical sounding method, image processing technique, metal grid measurement, and laser measurement technology) have been introduced for extracting the information of the charging process and burden distribution (e.g., the burden profile, charging trajectory, and filling point) [
3]. For example, Kajiwara et al. [
4] experimentally investigated the charging behaviors, burden distribution, and mixing of charging material in a full-scale apparatus Kashima No. 2 BF using the mechanical sounding method, sampling box method, and a magnetometer. Lu et al. [
5] studied the descending behavior of solid flow in a laboratory-scale experimental BF. Using an industrial BF at a one-tenth scale, Hattori et al. [
6] experimentally explored the effect of throat diameter on the burden distribution and particle size distribution. Then, a simulation model for predicting the burden distribution in the BF was proposed on the basis of the experimental results. Jimenez et al. [
7] also carried out a charging process experiment in an industrial BF at a one-tenth scale to study a particular charging pattern and the gas flow effect.
With the great effort made in the corresponding experimental investigations, many interesting findings have been yielded, contributing greatly to a better comprehension of the rules of the charging process and burden distribution. In addition, various empirical correlations have also been developed for predicting the burden movement on the basis of the experimental results [
3,
8]. However, the ability of experimental studies to investigate the charging process should be quite constrained. Specifically, the BF could be viewed as a “black box”, whereby the interior behaviors of burden materials should be quite difficult to be measured by experiment, resulting from the opaque nature of a BF. Moreover, the proposed empirical correlations generally lack universality. With the proliferation of computing power and technology, on the other hand, numerical simulations have become a powerful alternative for exploring discrete granular systems. Among the various numerical methods, the DEM (discrete element method), first proposed by Cundall and Strack [
9], has received extensive attention due to its ability to directly track individual particles and its potential for obtaining abundant particle-level information, which can be of significant importance for better understanding the burden behaviors in a BF.
Due to the superiority of DEM in processing particulate systems, there has been growing interest in applying DEM to investigate the charging process and burden distribution in a BF. For instance, Wei et al. [
10] used two different DEM packages (EDEM and LIGGGHTS) to demonstrate the ability of DEM in simulating the charging system by comparing the mass fraction distribution and burden distribution between the simulation and experiment results. The capability of DEM was also validated in the investigation of Mio et al. [
11] by comparing the velocity and trajectory of particles through a rotating chute between simulations and experiments, in which the particle velocity and particle trajectory in the experiments were extracted using a high-speed camera and pressure-sensitive sheet. By means of DEM, Ho et al. [
12] emphatically analyzed the force structures of granular materials for deeply understanding the fundamentals of the formation of burden piles. In the study of Zhang et al. [
13], the impact of the chute inclination angle on the size segregation and burden profile was numerically explored during the charging process in a BF using the serial-hopper-type bell-less charging system. A similar investigation was also conducted by Mio et al. [
14], in which the effect of the chute angle on the flow behavior and particle segregation was presented. Xu et al. [
15] further evaluated the effect of the cross-section shape (including semicircular and rectangular types) of the rotating chute on burden distribution and granular flow during the charging process of a bell-less top BF using DEM. Using DEM, Zhou et al. [
16] focused on the movement trend and velocity distribution law of coke in the chute. In the research of Mio et al. [
17], the melting behavior and combustion of the burden material were modeled by introducing a shrinking particle model into DEM, and then they observed the particle pulsating flow and collapse of the coke layer at the top of a BF. Kou et al. [
18] further numerically investigated the influences of sinter amount, rotation speed, and chute angle on the size segregation and coke collapse. Kurosawa et al. [
19] also simulated particle shrinking in a BF but using a different method, where a large overlap between particles was allowed by introducing a quite small Young’s modulus in the DEM. Using an experiment and DEM, Yu et al. [
20] thoroughly investigated the interparticle percolation segregation during burden descent in a BF.
In the past, spherical particles were the most frequently used in DEM investigations of charging processes and burden distribution, e.g., the above-cited literature, because the spheres possess perfect symmetry, which can greatly reduce the difficulty in establishing the DEM model and bring excellent calculation efficiency. Nevertheless, most particles encountered in practical applications are non-spherical, and the particle shape can significantly impact the burden behavior in the BF [
21]. To utilize the advantage of spherical particles, a rolling friction model was devised for simulating non-spherical particles using the DEM, where the effects of particle shape were quantified using spherical particles with suitable rolling friction [
22,
23]. This approach has been used in the DEM investigations of burden movement in the BF [
21,
24]. The simulation results indicated that spherical particles with a reasonable rolling friction can properly reproduce the burden behavior in some cases [
24]. However, the rolling friction model would be more suitable for quite small particles considering the importance of the actual shape for larger particles; hence, using the rolling friction model remains insufficient to fully describe the influence of particle shape in the BF [
21]. Furthermore, this model also lacks a solid theoretical foundation in determining the value of rolling friction, whereby it can be viewed as a “tunable parameter” [
22,
25].
Due to the aforementioned limitations of the rolling friction model, the non-spherical particle model (e.g., the multi-sphere model [
26,
27,
28,
29], polyhedral model [
30,
31,
32,
33], and super-ellipsoid model [
34,
35,
36,
37]) should be the most used in the DEM to describe the irregular shape of particles [
25,
38,
39]. To the best of our knowledge, the multi-sphere model should be adopted most frequently to approximate the non-spherical particles in DEM studies of a BF. Specifically, coke particles have generally been constructed using a multi-sphere model, whereas iron ore pellets have mostly been represented by spheres in DEM investigations of burden behaviors in a BF [
40,
41,
42,
43,
44,
45]. Some of these investigations also examined the effect of particle shape on the charging behavior and burden distribution [
40,
44,
45], and the apparent shape effects could be observed. In addition, the multi-sphere DEM model has also often been combined with computational fluid dynamics to study a BF involving fluid flow and heat transfer [
1,
46,
47,
48,
49]. In the investigations of Xia et al. [
24] and Govender et al. [
21], the polyhedral model was applied to construct non-spherical particles, and the different effects of spheres and polyhedrons on the charging behavior and burden topography were effortlessly observed. The ability of the super-ellipsoid model to reasonably reproduce the burden charging was demonstrated by Xia et al. [
50].
These non-spherical particle shape models indisputably have their own flaws and admirable points in terms of modeling difficulty, simulation accuracy, and computational efficiency [
25,
38,
39,
51]. Furthermore, the influence of adopting different particle shape models on the flow dynamics of particle systems generally cannot be ignored [
28,
29]. According to the above discussion, the corresponding published investigations mainly focused on directly using the particle shape model to simulate the flow of non-spherical particles in the BF so as to suitably match the actual application, while the effect of particle shape was also explored in some studies. However, how the particle shape model affects the burden behavior was rarely investigated, and the influence of particle shape model on the particle behavior in a BF remains poorly understood. Accordingly, the goal of this study was to evaluate the impact of applying different particle shape models on the DEM simulations of charging processes and burden distribution in a BF. For this purpose, the DEM using a multi-sphere model, polyhedral model, and super-ellipsoid model was first developed. Experiments involving the charging of non-spherical particles in a lab-scale bell-less top BF were subsequently conducted, and DEM simulations using different particle models corresponding to the experimental conditions were also performed. Lastly, the simulation accuracy and computational efficiency of different particle models were examined on the basis of the experimental and simulation results.