Model-Based Analysis of Factors A ﬀ ecting the Burden Layer Structure in the Blast Furnace Shaft

: The distribution of burden layers in an ironmaking blast furnace strongly inﬂuences the conditions in the upper part of the process. The bed permeability largely depends on the distribution of ore and coke in the lumpy zone, which a ﬀ ects the radial gas ﬂow distribution in the shaft. Along with the continuous advancement of technology, more information about the internal conditions of the blast furnace can be obtained through advanced measurement equipment, including 2D proﬁles and 3D surface maps of the top burden surface. However, the change of layer structure along with the burden descent cannot be directly measured. A mathematical model predicting the burden distribution and the internal layer structure during the descending process is established in this paper. The accuracy of the burden distribution model is veriﬁed by a comparison with experimental results. A sensitivity study was undertaken to clarify the role of some factors on the arising layer distribution, including the descent-rate distribution, the initial burden surface proﬁle, and the charging direction through the charging matrix. The ﬁndings can be used as a theoretical basis to guide plant operations for optimizing the charging.


Introduction
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

Mathematical Model
The mathematical model developed considers the process of burden formation in the BF with the bell-less charging system [26] (cf. Figure 1), by including five fundamental steps: free falling of particles from the hopper onto the chute, particle sliding along the chute, free falling from the chute tip, burden surface formation, and burden layer descent.
Metals 2019, 9,1003 3 of 18 particles from the hopper onto the chute, particle sliding along the chute, free falling from the chute tip, burden surface formation, and burden layer descent.

Free Falling from the Hopper onto the Chute
Particles of the burden material stored in the hopper fall onto the rotating chute through the down-comer. This motion is simplified by assuming that the flow of bulk stream is similar to the one of an individual particle, which is stationary when leaving the hopper and gains an exit velocity V0 along the direction of the chute: = , cos 2 (ℎ + sin ); = coke, ore where a correction coefficient, k_ (1,i), is introduced to take into account the collision of the falling particles, which has been neglected in previous studies.

Sliding along the Chute
When the bulk stream strikes the chute, the velocity component perpendicular to the chute is assumed to be lost and all the particles slide along the chute over an effective distance, depending on the chute inclination ( = − / sin ). Along this distance, the forces on each individual particle include the gravity force ( = ), centrifugal force ( = sin ), counteracting force ( = sin − sin cos ), and frictional force corresponding to the sliding between the particle and chute inner wall ( = = sin ( − cos )). The resulting net force is thus = cos − sin ( − cos ); = coke, ore The velocity at the end of chute is then obtained as = + sin (sin + cos ) + 2 (cos + sin ) ; = coke, ore

Free Falling from the Hopper onto the Chute
Particles of the burden material stored in the hopper fall onto the rotating chute through the down-comer. This motion is simplified by assuming that the flow of bulk stream is similar to the one of an individual particle, which is stationary when leaving the hopper and gains an exit velocity V 0 along the direction of the chute: where a correction coefficient, k_(1,i), is introduced to take into account the collision of the falling particles, which has been neglected in previous studies.

Sliding along the Chute
When the bulk stream strikes the chute, the velocity component perpendicular to the chute is assumed to be lost and all the particles slide along the chute over an effective distance, depending on the chute inclination (l = L − d/ sin α). Along this distance, the forces on each individual particle include the gravity force (G i = m i g), centrifugal force (C i = m i ω 2 l sin α), counteracting force (N i = m i g sin α − m i ω 2 l sin α cos α), and frictional force corresponding to the sliding between the particle and chute inner wall (f i = µ i N i = µ i m i sin α g − ω 2 l cos α ). The resulting net force is thus The velocity at the end of chute is then obtained as

Free Falling from the Chute Tip
Upon leaving the chute tip, the velocity of the bulk stream in the furnace throat is decomposed into three components in the vertical direction (V r = V 1 sin α), horizontal direction (V y = V 1 cos α), and rotation direction (V z = ω l sin α). The distance from the stream center to the symmetric plane of the hopper (cf. Figure 1) can be expressed as with the specific time expressed as where a correction coefficient, k_(2,i), is introduced to consider the effect of drag due to the ascending gas. The distances L r and L z (cf. Figure 1) are given as with reference to the axes, and the trajectory of the bulk stream in the free board is therefore derived as

Burden Surface Formation
If the top surface of the burden in the BF is known at the moment when the bulk stream falls from the chute tip, the impact point can be obtained as the intersection of the top surface with the trajectory of the bulk stream. The impact point is then used as the radial coordinate for the apex of the burden layer to be formed. The surface of the newly formed layer can thus be shaped with the impact point and the repose angle (RA) of each specific material to be charged [11,14]. It should be kept in mind that the aforementioned RA is different from the so-called natural repose angle because the former one usually depends on the constraints associated with the furnace wall, the shape of the initial burden surface, and the ascending gas. Additionally, the RA varies as charging proceeds, thus leading to different growth mechanisms of the burden layer. The RAs are calculated as Other details concerning the treatments of the formation of the burden layer can be found in [12].

Burden Layer Descent
The behavior of burden descent in the BF has been studied extensively and intensively in the literature [1,3,6,11,12,[27][28][29][30][31]. The path lines of the solid in the BF can be generally assumed as depicted in Figure 2, where plug flow is the main solid flow pattern in the upper and middle zones (i.e., lumpy zone), while a slight convergent flow and a dead man zone dominate in the lower bosh zone. In the current work, the classical central radiation approach [27,28] that generally reflects the solid flow pattern in the BF lumpy zone is adopted to track each individual burden layer as it descends. It can be seen from the figure that materials charged into a certain radial region (e.g., 0.4 R-0.6 R) will preserve their relative radial position and continue to descend along the shaded area in the figure, thus gradually stretching in the horizontal direction. As the volume of a layer is assumed to remain constant, the layer gradually becomes thinner upon descent. A function (cf. Equation (11)) was built to allow for a specified radial distribution of the burden descent rate and to update the positions of the edges of the layers during the descent, thus tracking the layers.
These five fundamental steps, as well as their mathematical description, form the basis for the present model of the BF burden distribution, which is designed as three modules: a burden charging module, a descending module, and a layer structure module. Figure 3 shows a flowchart that outlines the working principles of the modules. was built to allow for a specified radial distribution of the burden descent rate and to update the positions of the edges of the layers during the descent, thus tracking the layers.
These five fundamental steps, as well as their mathematical description, form the basis for the present model of the BF burden distribution, which is designed as three modules: a burden charging module, a descending module, and a layer structure module. Figure 3 shows a flowchart that outlines the working principles of the modules. In a normal calculation, a base bed is initiated in the simulated region. After entering the charging matrix and some other parameters required, a dump is "charged" by turning on the module of burden charging, which estimates the layer formed on top of the initial bed. Then, the module of burden descending is triggered and the bed is lowered slowly at the bottom, followed by the descent of the overlaying layers, until the stock line (at a given radial position) is below a given set point (i.e., similar to the logics built based on radar signals in the real process). Then, the dump layer is charged, the procedure is repeated, and so on, until a quasi-stationary state is reached, and local information on the ore-to-coke ratio and volume fraction of the burden is extracted using the module of the burden structure.

Initial and Boundary Conditions
As outlined in the calculation flow chart of Figure 3, the input boundary parameters include the furnace geometry parameters, the physical property parameters of the burden materials, the charging  In a normal calculation, a base bed is initiated in the simulated region. After entering the charging matrix and some other parameters required, a dump is "charged" by turning on the module of burden charging, which estimates the layer formed on top of the initial bed. Then, the module of burden descending is triggered and the bed is lowered slowly at the bottom, followed by the descent of the overlaying layers, until the stock line (at a given radial position) is below a given set point (i.e., similar to the logics built based on radar signals in the real process). Then, the dump layer is charged, the procedure is repeated, and so on, until a quasi-stationary state is reached, and local information on the ore-to-coke ratio and volume fraction of the burden is extracted using the module of the burden structure.

Initial and Boundary Conditions
As outlined in the calculation flow chart of Figure 3, the input boundary parameters include the furnace geometry parameters, the physical property parameters of the burden materials, the charging matrix, the shape of the initial burden surface, and the descent-rate profile. For a specific BF, the first two parameter sets are fixed, while the other three are decided by the operators. Table 1 shows an example of a charging matrix, which reports the different materials charged, the "dump size" (expressed as mass), and how the different rings of burden are charged by the chute. Practically always, for the convenience of the operator, the chute angle is discretized into a number (typically 10-12) of settings, and the number of rings for each chute setting is reported. In addition to this information, a stand has to be taken on the charging level (stock line level at the moment of charging) and the chute direction (wall to center, or center to wall). Table 1. Charging matrix of the illustration case. The charging direction (here wall → center) and charging level (here, z = −1.4 m) have to be specified. The final column refers to the layer colors in Figure 6.

Effect of Burden Descent-Rate Distribution and Initial Surface
Profile meter measurements [2,[27][28][29] have indicated that the burden descent rate is usually larger in the peripheral area than in the central area. Different burden descent models have been proposed [13,24,30,31]. In this paper, a classical "central radiation method" [12,31] was adopted to study the burden descent. Even though the model may consider an arbitrary distribution of the descent rate, in the examples to be illustrated, we use the three relative descent-rate distributions depicted in Figure 4.
The shape of the initial burden surface has a significant influence on the distribution of the material layers. Therefore, to replicate the state under a stable operation, the model has to be run a sufficient number of passes (periods or batches) through the charging program to eliminate the effect of the initial state. As an example, three kinds of initial burden surface profiles are shown in Figure 5, which will be used to illustrate the effect. These initial states can be characterized by the size of the plateau part, which, in the first case, extends over the whole radius and, in the second case, represents half of the radius, while the final case shows no plateau. sufficient number of passes (periods or batches) through the charging program to eliminate the effect of the initial state. As an example, three kinds of initial burden surface profiles are shown in Figure  5, which will be used to illustrate the effect. These initial states can be characterized by the size of the plateau part, which, in the first case, extends over the whole radius and, in the second case, represents half of the radius, while the final case shows no plateau.  In order to illustrate the model, the cases shown in Table 2 were studied to investigate the influence of the initial burden surface and the descent-rate profile on the arising layer structure in the shaft, using the three descent-rate profiles of Figure 4 and three initial burden surfaces of Figure 5. In the cases studied, the charging matrix of Table 1   material layers. Therefore, to replicate the state under a stable operation, the model has to be run a sufficient number of passes (periods or batches) through the charging program to eliminate the effect of the initial state. As an example, three kinds of initial burden surface profiles are shown in Figure  5, which will be used to illustrate the effect. These initial states can be characterized by the size of the plateau part, which, in the first case, extends over the whole radius and, in the second case, represents half of the radius, while the final case shows no plateau.  In order to illustrate the model, the cases shown in Table 2 were studied to investigate the influence of the initial burden surface and the descent-rate profile on the arising layer structure in the shaft, using the three descent-rate profiles of Figure 4 and three initial burden surfaces of Figure 5. In the cases studied, the charging matrix of Table 1 was applied, charging a new dump when the burden surface at the point of the (simulated) radar reached the set point (z = 1.4 m) indicated by the green In order to illustrate the model, the cases shown in Table 2 were studied to investigate the influence of the initial burden surface and the descent-rate profile on the arising layer structure in the shaft, using the three descent-rate profiles of Figure 4 and three initial burden surfaces of Figure 5. In the cases studied, the charging matrix of Table 1 was applied, charging a new dump when the burden surface at the point of the (simulated) radar reached the set point (z = 1.4 m) indicated by the green solid circle at the end of the dashed vertical line in Figure 5. Denoting the descent rates by 1-3 and the initial surfaces by a-c, the nine investigated cases will be abbreviated as follows: CaseA2c, for instance, denotes the system where the rings are charged from the wall to the center (labelled A) using the middle burden descent-rate pattern of Figure 4 and the V-shaped initial burden surface profile of Figure 5. The charging program was repeated for six passes to make the distribution of upper layers reach a quasi-stationary state, leading to a state where the initial bed had descended to the z ≈ 8 m level in the shaft. The effects of different initial burden surfaces and descent-rate profiles on the layer structure in the upper shaft are shown in Figure 6, where the yellow arrowed dashed line represents that the descent distance (at the radial position of the radar) of the bed is the same in the nine cases. The top panels of the figure show the resulting layer structure for the case with a uniform descent rate and the central panels represent the results for the case where the descent rate varies moderately in the radial direction, while the bottom panels represent the results for the most extreme descent-rate distribution (labelled 1-3 in Figure 4). Correspondingly, the left, middle, and right panels of Figure 6 depict the effect of the initial burden surface shape, from the horizontal case to the V-shaped case (labelled a-c in Figure 5).
As the results on all panel rows show, for the same burden descent-rate distribution, the influence of the initial surface profile on the burden distribution gradually decays, and recurring layer patterns occur after about four passes through the charging program. Therefore, the topmost layers (Center coke/Coke/Ore) are identical in the three figures.
If the initial burden surface profile is same (i.e., moving along the columns in Figure 6), compared with the uniform descent-rate profile (top panels), the slope of the burden top surface near the furnace center decreases with the increase of the relative descent rate at the sidewall, and the slope of the ore and coke layer further decreases along with the descent in the shaft, accompanied by the increase in furnace diameter. The green arrowed lines in the middle column highlight how the shape of the upper part of the coke layer (formed by the first two coke dumps in the charging sequence) is affected by the descent-rate distribution. The shape of the upper part of the coke layer forms a center hopper and edge plateau according to the axially symmetric principle when the descent rate is uniform for Case A1b. As the relative descent rate increases linearly from the center to the wall, the shape is transformed into a center plateau and edge hopper shape for Case A2b or an Λ shape for Case A3b during the descending process.
An example of the gradual changes experienced in the burden top surface profile and in the radial ore/coke distribution is depicted in Figure 7, which shows the conditions for Case A1c. It can be seen that the top-layer profile rapidly converges: Figure 7a indicates that the layer profile only changes marginally after two passes through the charging program. The difference volume ∆V between the top surfaces after two consecutive passes through the charging program can be taken as a criterion used to judge whether the burden distribution has reached a (quasi-)stationary state. The changes in volume, ∆V, between two such consecutive batches, are reported in the upper left part of Figure 7a. The second batch is ∆V = 19.11 m 3 larger than the first one and the third is 4.28 m 3 smaller than the second one, but the difference between the sixth and fifth batch is only ∆V = 0.08 m 3 , i.e., completely marginal. Therefore, one may use a condition, e.g., |∆V| < 0.2 m 3 , as an indication that a quasi-stationary condition has been reached in the model. The corresponding changes in the ore/coke thickness ratio distribution are shown in Figure 7b. The ore/coke ratio of the first batch is fundamentally different from that of the latter ones, which are seen to rapidly converge. The reason for the large change experienced between the first two batches is, naturally, that the initial burden profile differs from that corresponding to the quasi-stationary state. the central panels represent the results for the case where the descent rate varies moderately in the radial direction, while the bottom panels represent the results for the most extreme descent-rate distribution (labelled 1-3 in Figure 4). Correspondingly, the left, middle, and right panels of Figure 6 depict the effect of the initial burden surface shape, from the horizontal case to the V-shaped case (labelled a-c in Figure 5).

Case A2a Case A2b Case A2c
Case A3a Case A3b Case A3c Figure 6. Effect of burden descent-rate distribution (rows) and initial burden surface (columns) on the arising burden layer structure for the charging program of Table 1.
As the results on all panel rows show, for the same burden descent-rate distribution, the influence of the initial surface profile on the burden distribution gradually decays, and recurring layer patterns occur after about four passes through the charging program. Therefore, the topmost Figure 6. Effect of burden descent-rate distribution (rows) and initial burden surface (columns) on the arising burden layer structure for the charging program of Table 1. completely marginal. Therefore, one may use a condition, e.g., |∆V| < 0.2 m , as an indication that a quasi-stationary condition has been reached in the model. The corresponding changes in the ore/coke thickness ratio distribution are shown in Figure 7b. The ore/coke ratio of the first batch is fundamentally different from that of the latter ones, which are seen to rapidly converge. The reason for the large change experienced between the first two batches is, naturally, that the initial burden profile differs from that corresponding to the quasi-stationary state. Therefore, in the calculation of the burden distribution for a charging matrix, a sufficient number of passes through the charging program is needed to stabilize the system. Otherwise, the result may be misleading and differ considerably for the true conditions. Based on the above results, it may be concluded that the effects of the initial burden surface and the descent-rate profile should be considered in simulations and physical experiments.

Effect of Charging Direction
The direction in which the chute moves when rings of a burden dump are formed on the burden surface, here called the charging direction, is either outward from the center to the wall (C → W) or inward from the wall to the center (C → W). Furthermore, charging programs may be designed where a mixed charging direction is applied, i.e., charging some dumps in one direction and some in the other. The effect of the charging direction on the arising burden layer structure is smaller for charging programs where the dump size is small, since there are fewer rings. However, as the BFs grow in size, the dump size increases gradually, and therefore also the number of rings in the charging program, which emphasizes the effect of the charging direction. Here, the effect is illustrated by four simulations, where the charging matrix of Table 1 is applied using a uniform descent-layer distribution and the initial burden surface with a plateau at the wall. Table 3 presents the conditions denoted by Cases A1b-D1b. Therefore, in the calculation of the burden distribution for a charging matrix, a sufficient number of passes through the charging program is needed to stabilize the system. Otherwise, the result may be misleading and differ considerably for the true conditions. Based on the above results, it may be concluded that the effects of the initial burden surface and the descent-rate profile should be considered in simulations and physical experiments.

Effect of Charging Direction
The direction in which the chute moves when rings of a burden dump are formed on the burden surface, here called the charging direction, is either outward from the center to the wall (C → W) or inward from the wall to the center (C → W). Furthermore, charging programs may be designed where a mixed charging direction is applied, i.e., charging some dumps in one direction and some in the other. The effect of the charging direction on the arising burden layer structure is smaller for charging programs where the dump size is small, since there are fewer rings. However, as the BFs grow in size, the dump size increases gradually, and therefore also the number of rings in the charging program, which emphasizes the effect of the charging direction. Here, the effect is illustrated by four simulations, where the charging matrix of Table 1 is applied using a uniform descent-layer distribution and the initial burden surface with a plateau at the wall. Table 3 presents the conditions denoted by Cases A1b-D1b. Table 3. Cases studied employed to illustrate the effect of the charging direction.

Material
Center Coke Coke Mixed Ore In order to eliminate the effect of the initial burden surface profile in the illustration, four additional passes through the charging programs were included. The arising burden layer distributions for the cases are shown in Figure 8. For the purpose of illustration, the results are divided into two parts, where the zone spanned by the green arrowed line represents the dynamic region where a stable burden surface is established, and the region spanned by the dashed yellow line represents the quasi-stationary state. Analyzing the region spanned by the yellow dashed lines in the figure, the effects of the charging directions on the arising burden-layer structure can be explored.
Analyzing the region spanned by the yellow dashed lines in Figure 8, the effects of four cases with different charging directions on the arising burden-layer structure can be analyzed. The figure clearly shows that the charging direction plays a very important role in the distribution of the layers. Comparing Case A1b and Case B1b (cf. Figure 8a,b), where the only difference is the charging direction of the ore rings, the burden distribution changes substantially: from a case with a rather uniform distribution of ore and coke, the pattern changes to a distribution where clearly more coke is charged into the central region, while the share of ore increases in the outer part of the shaft. This would lead to considerable changes in the gas distribution, partly due to changes in the gas permeability in the lumpy zone and partly due to changes in the coke slits in the cohesive zone.
The change between Case A1b and Case C1b, where the charging direction is flipped, leads to more dramatic changes in the burden distribution (cf. Figure 8c): the center coke and the following coke dump are split into two almost distinct parts due to the separating action of the ore layer, the apex of which falls between the two coke layers. This gives rise to a rather extreme distribution, with very little coke in the intermediate region and very little ore in the peripheral region. The effect on the coke slits is expected to be even more dramatic, forcing the gas to the central and peripheral region.
Finally, the case with an opposite charging direction, from the center to the wall, for all dumps (Figure 8d), gives rise to a relatively uniform distribution of ore and coke over the radius, but still with a fundamentally different layer formation than in Case A1b.
A detailed scrutiny of the rings and layers shows how the charging order affects the gradually stacked layer structure and how this influences the outcome if the layer is formed from the center to the wall or from the wall to the center, due to the overlapping effect of the rings. It is also interesting to note that the surface of the ore layer is practically equal in Cases A1b and C1b, as well as in Cases B1b and D1b. Therefore, for these pairs, coke is charged on the same burden surface (cf. Figure 9), but the internal structures of the cases in a pair are fundamentally different. This is seen in Figure 10, which presents the radial ore/coke layer thickness distribution. This graph shows that the base case (Case A1b) gives rise to a relatively uniform distribution, followed by Case D1b and Case B1b, while Case C1b is the clearly most non-uniform one.
Even though the examples presented concern a simple three-dump charging program, the options provided by changing the charging direction highlighted the inherent flexibility in the design of charging programs that aim at obtaining a desired layer structure. Summarizing the findings, the design of charging programs is a very complicated process and different burden distributions may arise, even though the burden surface profile for certain dumps is identical.  Even though the examples presented concern a simple three-dump charging program, the options provided by changing the charging direction highlighted the inherent flexibility in the design of charging programs that aim at obtaining a desired layer structure. Summarizing the findings, the design of charging programs is a very complicated process and different burden distributions may arise, even though the burden surface profile for certain dumps is identical.

Validation of the Model
In order to validate the model, it was applied to data from a real BF operated with pellets and coke as the main burden materials. In this furnace, the burden surface profile is measured by a 3D top scanner every 20 s. The results from one day of operation will be illustrated, where the furnace was run under the nine-dump charging program presented in Table 4. The charging program consisted of a three-dump subsequence (Coke/Pellets/Pellets + Coke), which was repeated three options provided by changing the charging direction highlighted the inherent flexibility in the design of charging programs that aim at obtaining a desired layer structure. Summarizing the findings, the design of charging programs is a very complicated process and different burden distributions may arise, even though the burden surface profile for certain dumps is identical.

Validation of the Model
In order to validate the model, it was applied to data from a real BF operated with pellets and coke as the main burden materials. In this furnace, the burden surface profile is measured by a 3D top scanner every 20 s. The results from one day of operation will be illustrated, where the furnace was run under the nine-dump charging program presented in Table 4. The charging program consisted of a three-dump subsequence (Coke/Pellets/Pellets + Coke), which was repeated three

Validation of the Model
In order to validate the model, it was applied to data from a real BF operated with pellets and coke as the main burden materials. In this furnace, the burden surface profile is measured by a 3D top scanner every 20 s. The results from one day of operation will be illustrated, where the furnace was run under the nine-dump charging program presented in Table 4. The charging program consisted of a three-dump subsequence (Coke/Pellets/Pellets + Coke), which was repeated three times, with the main difference being that the first two dumps in the first subsequence were charged from the center to the wall, while all other dumps were charged from the wall to the center.
The top scanner data for the day was preprocessed to yield estimates of the average radial burden surface profile before and after each dump, with the results shown in Figure 11. The corresponding results of the simulation model are presented in Figure 12, which shows that the model has been able to reconstruct the layer distribution fairly well: the three dumps of the first subsequence (Dumps 1-3) are seen to distribute differently, due to the different charging directions employed for the first two dumps. The different distributions of these layers are also clearly seen in the profiles from the top scanner. The latter two subsequences, in turn, give rise to almost identical results, which is expected due their strong similarities. Overall, despite some discrepancies, the model is seen to be quite successful in predicting the distribution of burden layers in the top of the throat. The simulated layer distribution for the last three passes through the charging program is depicted in Figure 13. The figure shows how the layers gradually get thinner and how their angles decrease along with the descent in the furnace. The results of the model can thus be used to track the layers deeply into the BF and could also be used as a starting point for computational fluid dynamics (CFD) simulations of the thermal and flow conditions in the shaft. model is seen to be quite successful in predicting the distribution of burden layers in the top of the throat. The simulated layer distribution for the last three passes through the charging program is depicted in Figure 13. The figure shows how the layers gradually get thinner and how their angles decrease along with the descent in the furnace. The results of the model can thus be used to track the layers deeply into the BF and could also be used as a starting point for computational fluid dynamics (CFD) simulations of the thermal and flow conditions in the shaft. Figure 11. Average radial stock profile before (red) and after (blue) each dump reconstructed from top scanner data.      Table 4.

Conclusions and Future Perspectives
A model of charging, burden distribution, and burden descent in the BF shaft has been developed. The model calculates the burden stream trajectory under different chute angles, solves the distribution of rings on the burden surface, and simulates the descent of the layers. The charging matrix, initial burden surface, burden descent-rate distribution, and chute direction during charging can be specified and the model estimates the arising layer structure. The model, which has been validated by a comparison of its results with top scanner information from an operating BF, has been applied to study the effect of some user-specified parameters in order to gain a better understanding of the complex engineering system at hand. On the basis of the results, some conclusions can be drawn, as follows: • Compared with previous versions of the model [12], a sub-model was established for calculating the stable burden top surface using an arbitrary initial surface, which yields information about the conditions in the shaft under a quasi-stationary state. The calculation results showed that the initial burden surface typically affects the results for about five dumps, after which asymptotic behavior of the radial layer distribution will be reached; • The effect of different radial descent-rate profiles on the arising burden layer structure has been analyzed, and it has been demonstrated that the distribution plays an important role in the internal layers in the shaft, but only marginally affects the radial distribution of the top layers in the throat; • The charging direction, i.e., the direction in which the chute moves (center to wall, or wall to center) when the rings of a dump are distributed on the burden surface plays a key role. This strong effect is due to the material overlapping, which becomes accentuated in a large BF with large dump sizes, where each dump is split into several rings. By changing the direction, fundamentally different layer distributions can be obtained.
In the future, the model will be applied for multiple purposes, including the design of charging programs fulfilling requirements set on the arising burden distribution. Another use of the model would be to apply it to an on-line simulation of charged layers in the shaft, tracking their position with time. In this way, one may realize an intelligent soft sensor by which the shaft state may be monitored and visualized for better understanding and control. It would also be interesting to explore the possibilities of an automatic combination of signals from a top scanner with the model of layer descent in the bed, particularly after disturbances (e.g., slips) that upset the burden distribution in the furnace. Yet another option is to extend the model to consider heat transfer and gas flow in the lumpy zone. length of the chute m m mass of the particle k N counteracting force N R throat radius m t time of particle movement in free board s u descent rate along the vertical direction -V 0 exit velocity along the direction of chute m/s V 1 velocity at the end of chute m/s α chute angle in the vertical direction rad ω rotation speed of the chute rad/s µ friction factor between material and chute β repose angle rad Subscript i ore or coke rc center to particle stream (cf. Figure 1) in inner repose angle min minimum max maximum out outer repose angle r horizontal (radial) direction y vertical (altitudinal) direction z rotation (tangential) direction -