**1. Introduction**

In a blast furnace (BF), the raceway is formed by airflow wherein the particles circulate. The combustion of coke and injected fuels in the raceway supplies gas and heat for the critical endothermic reduction of iron ores and for iron smelting [1]. Therefore, the raceway characteristics directly affect the primary distribution of gas and heat inside the BF. Some previous studies have used empirical size characteristics of the raceway to predict the combustion of pulverized coal and the gas flow distribution, which may considerably differ from those of the actual BF raceway [2–4]. The raceway depth directly affects the burnout rate of pulverized coal and determines the airflow distribution in the center of the blast furnace. The flow pattern will determine the strength of gas–solid mixing and the rate of coke consumption, thereby further affecting the smelting efficiency of the blast furnace. Therefore, it is necessary to understand the evolution process and physical characteristics of the raceway.

Investigations of the BF raceway phenomenon and its characteristics can be carried out via three methods: theoretical analysis, experimental testing, and numerical modeling. In theoretical analyses, some studies analyzed the raceway size on the basis of the force balance of the raceway boundary in different spatial dimensions [5–8]. The phenomenon of raceway hysteresis was explained, together with the effects of chemical reactions, blast velocity, material layer porosity, particle diameter, and other factors. However, this method treats the raceway as a circle or a sphere and disregards the force between the particles. Thus, it can be considered a relatively inaccurate method.

In experimental testing, the microwave reflection method was used to study the formation and depth of the BF raceway during production [9]. The effects of tuyere diameter, air volume, and coal injection on the depth of the raceway zone were investigated. In contrast, considering that the complex environment, in terms of high temperature and pressure in the raceway, implies significant difficulties for direct research, most researchers used cold models to study the formation and physical characteristics of the raceway [10–16]. However, it was challenging for the researchers to experimentally obtain dynamic information and accurately measure the raceway characteristics in three-dimensional (3D) space through experimental testing.

With the advancement of computers, numerical modeling has become a more popular method. A combined computational fluid dynamics and discrete element method (CFD-DEM) was developed [17–23]. The effects of different variables on the raceway were investigated. Nonetheless, previous CFD-DEM-based studies generally used two-dimensional (2D) or pseudo 3D models and small sizes with certain divergences from actual conditions. Hilton et al. [24] and Lichtenegger et al. [25] used the CFD-DEM method to investigate the effect of particle properties on the evolution of the raceway in 3D packed beds. However, these previously reported approaches were computationally expensive. Also, these approaches did not facilitate quantitative analysis of the raceway or the investigation of raceway physical characteristics.

However, the gas–solid flow model based on CFD can achieve high efficiency at low computational cost. The shape and size of the raceway was studied in a 2D state using a transient or steady model based on CFD [26–28]. Rangarajan et al. [29] extensively studied the influence of the operating conditions on raceway properties using a two-fluid model. Based on CFD modeling technology, research on coupling fuel combustion and raceway formation has been carried out, and a lot of information about combustion and gas distribution has been obtained [30–36]. However, no details on constitutive relations, the surface area of the raceway, or the evolution of the raceway penetration depth in a short time interval can be found in these articles.

In this study, we developed an industrial-scale blast furnace 3D slot model based on a transient Eulerian multiphase flow model (EMFM). The influence of the chemical reaction in the BF on the raceway characteristics is mainly reflected in the change in gas flow [26]. For simplicity, we did not set the combustion reaction or heat transfer, but we set the initial bed solid packing fraction to be less than the maximum volume fraction as an approximate replacement. The evolution process and flow pattern of the raceway are revealed. The depth, height, width, and surface area of the raceway were predicted, providing detailed information and theoretical guidance for the process of gas injection into packed beds in industrial processes.
