A proper distribution of burden materials in an ironmaking blast furnace (BF) has been commonly recognized as a basic prerequisite for an appropriate distribution of burden permeability, which, in turn, facilitates the distribution of the ascending gas originating in the raceways. The radial gas distribution is one of the key factors that determine the utilization of both thermal and chemical energy embodied in the gas phase. As a result, the burden distribution plays an important role in the overall performance of the BF, and, in particular, in the fuel rate and productivity [
1]. After screening the burden material, which mainly includes iron oxides (commonly referred to as “ore”, but consisting of sinter, pellets, or lump ore), coke and flux are supplied in separate dumps. In modern BFs, the (Paul Wurth) bell-less charging system is applied, where a dump is split into rings charged at desired radial coordinates by a rotating chute. The bell-less charging technology provides a set of advantages over the traditional bell-type charging system, including higher circumferential uniformity, reduced grain size segregation, less pushing effects, and a high flexibility in the design of burden layers. It is still worth noting that the initial burden layers formed by the bell-less charging system are strongly affected by the initial burden surface profile in the BF throat and, furthermore, that the layers undergo changes as the burden descends, thus reshaping every layer. Therefore, it is important to clarify the governing mechanisms underlying the formation and reshaping process during and after burden charging in order to be able to design efficient charging programs and to make appropriate adjustments of the burden distribution to increase the efficiency of the BF operation.
In modern BFs, the top gas temperature and composition are routinely measured, often across one or two diagonals of the throat by above-burden probes. Information about the initial burden level is usually obtained locally by using mechanical stock rods or sometimes even more advanced techniques, such as laser or radar sensors. The thermal profile of the burden surface may furthermore be measured by IR cameras [
2]. In the lumpy zone where the burden descends, direct measuring or monitoring techniques are still limited to in-burden probes that can occasionally measure the radial distribution of gas temperature and composition. Because of the hostile environment, on-line sensors cannot be permanently placed in this region of the BF. As a consequence, most of the studies on the conditions of the burden in the lumpy zone [
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23] have been based on laboratory-scale experiments or mathematical modeling. Such studies have, e.g., [
3,
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5], presented correlations between the charging pattern and the burden structure in the lumpy zone. However, since direct measurements of the layers in the shaft are lacking, the modeling results have usually only been verified for the top layers in the throat or indirectly through gas temperature and composition measurements in the throat. Compared with physical experiments, mathematical modeling [
3] has gained popularity due to its lower cost and higher flexibility. The mathematical modeling approaches [
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5] regarding the BF burden distribution (corresponding to the bell-less charging system) can basically be categorized as volume-based simplified models or classical (continuum) force models [
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14], data-driven models [
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16], or hybrid models [
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18], as well as the more computationally expensive models based of the discrete element method (DEM) [
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23]. Among these models, the classical force model has advantages in terms of its simple model formulation and fast computation, which are readily suitable for online implementation. Over the years, the classical force model has been continuously improved by different researchers (groups). In order to consider the non-uniform distribution of the burden descending speed, Fu et al. [
24] extended the classical force model by assuming a potential flow of burden and that the boundary profile of each individual layer was polygonal. A more practical burden descending speed with different ore-to-coke ratios has been predicted and an online version of the model has been developed and utilized in some operating BFs [
13]. Extensive efforts have also been put into estimating the effects of charging patterns on the burden trajectory, burden surface profile, and position of each layer in the descending process [
11,
12]. As for the charging pattern, however, the influence of charging direction (i.e., inward charging from the wall to center or outward charging from the center to wall) is yet to be clarified, even though some industrial trials of changing the charging direction have shown promising results [
12]. In addition, it should be pointed out that the repose angle of each burden material was given a specific value in those models reported. This seems to be questionable, since the repose angle may vary owing to the change of chute angle, the non-uniform descending of the burden surface, and the blocking and rebounding effect of the non-flat burden surface and furnace wall.
Based on the above reviews, a mathematical model using the Polygonal Line (PL) method of the burden surface profile has been verified in a reduced-scale (1:10) experiment [
12] and applied for the automatic generation of charging programs satisfying certain criteria concerning the radial distribution of the burden [
25]. In the present work, a more comprehensive mathematical model based on the aforementioned PL method has been developed and further extended by adding functions to analyse the influence of different boundary conditions, such as the initial burden surface, the descending velocity profile, and the charging direction (inward and outward). Finally, some conclusions and suggestions for future work are presented.