**2. Experimental**

A 1/3-scale experimental burden distribution simulator, which is shown in Figure 1, was used herein. It is a bell-less-type blast furnace and it has approximately a 3.7-m throat diameter and approximately a 10-m height. Furthermore, it has a surge hopper, parallel hoppers, and a discharging funnel. A horseshoe-shaped rotating chute with a length of 1.7 m is installed at the top of the furnace. A blower and a discharging unit are installed at the bottom of the furnace to assess the effects of the gas flow and the burden descending. Figure 2 shows the detailed schematic illustration of the experimental apparatus.

**Figure 1.** Picture of the 1/3-scale experimental burden distribution simulator.

**Figure 2.** Schematic illustration of the 1/3-scele experimental burden distribution simulator.

Sinter particles were conveyed to the top of the experimental blast furnace via a surge hopper, one of the parallel hoppers, and a discharging funnel, as shown in Figure 2. The sinter, which were sieved in the range 5–20 mm (*d*<sup>50</sup> = 11.4 mm), were used in this charging test. The particle size distribution is shown in Figure 3. In total, 5500 kg of sinter was charged into the experimental blast furnace during 15 rotations at 13.4 rpm. Table 1 shows a charging pattern of coke and ore dumps. The gas was not blown in this experiment to simplify the phenomena.

**Figure 3.** Distribution of the particle diameter of the sinter.


**Table 1.** Charging conditions for the rotating chute.

Subsequent to charging, a burden surface profile was measured with a laser distance meter. Moreover, the burden was dug up using a vacuum cleaner to obtain the ore to coke mass ratio (O/C) and the particle size distribution. The area that was dug up was rectangular (200 mm × 262 mm) from the furnace wall to its center for seven divisions, and the digging-up depth was every 50 mm, as shown in Figure 4. This was carefully performed to avoid breaking the particle-packing structure. The burden was removed by a large vacuum cleaner, except for the sampling area, before digging up. That is to say, the sampling area became the highest in the burden. The digging up was carried out from the highest position, thus collapse did not occur. Subsequently, the particles were sieved and weighed. The sinter particles, which were discharged from the funnel, were also sampled to check the particle size segregation during conveying to the top of the furnace. This gave the time evolution of the particle size distribution that was used as input of the DEM calculation.

**Figure 4.** Schematic illustration of the digging-up operation.

#### **3. Simulation**

#### *3.1. Discrete Element Method*

DEM is one of the most popular and reliable simulation methods for the numerical analysis of particle behavior. This simulation method comprises an idea for determining the kinematic force to each finite-sized particle. The key calculation of DEM comprises three steps; i.e., (1) contact detection, (2) calculation of forces, and (3) updating the trajectories, and these processes are looped until *t* = *t*max. The contact between two particles is given using Voigt model, which consists of a spring dashpot and a slider for the friction in the tangential component. The contact forces, **F***n* and **F***t*, are calculated using:

$$\mathbf{F}\_{n,ij} = \left(\mathbf{K}\_{n} \Delta \mu\_{n,ij} + \eta\_{n} \frac{\Delta \mu\_{n,ij}}{\Delta t}\right) \mathbf{n}\_{ij\prime} \tag{1}$$

 

$$\mathbf{F}\_{t,ij} = \min \left\{ \mu \left| \mathbf{F}\_{n,ij} \right| \mathbf{t}\_{ij}, \left[ K\_t \left( \Delta u\_{t,ij} + \Delta \phi\_{ij} \right) + \eta\_t \left( \frac{\Delta u\_{t,ij} + \Delta \phi\_{ij}}{\Delta t} \right) \right] \mathbf{t}\_{ij} \right\}, \tag{2}$$

where *K* and η are the spring and damping coefficients, Δ*u* and Δϕ are the relative translational displacement of the gravitational center between two particles and the relative displacement at the contact point caused by the particle rotation, μ is the frictional coefficient, and **n***ij* and **t***ij* denote the unit vector from *i*-th particle to the *j*-th one in the normal and the tangential components. The subscript "*n*" and "*t*" denote the normal and the tangential components. The translational and rotational motions of each particle are updated using:

$$
\dot{\mathbf{v}} = \frac{\sum \mathbf{F}}{m},
\tag{3}
$$

$$
\dot{\boldsymbol{\omega}} = \frac{\boldsymbol{\Sigma} \cdot \mathbf{M}}{I},
\tag{4}
$$

where **v** is the vector of a particle velocity, **F** is the contact force acting on a particle, *m* and *g* are the mass of a particle and the gravitational acceleration, ω is the vector of the angular velocity, and **M** and *I* are the moment caused by the tangential force and the moment of inertia. ɘ

The shape of granular material in DEM is usually assumed to be spherical to simplify the contact detection and the calculation of the contact force, although the shape of the sinter particle is not spherical. The best solution for considering the particle shape in DEM is to model the exact particle shape using polyhedra. However, this calculation is extremely laborious, and it is unsuitable for the simulation of particle flow in the ironmaking process where the number of particles could be in the billions. Thus, the effect of the particle shape on the motion was considered by setting a proper rolling friction for the particle, and it is given by:

$$\mathbf{M}\_{r,i} = -\frac{3}{8} a\_i b |\mathbf{F}\_{\text{ll}}| \frac{\omega\_i}{|\omega\_i|} \,\text{\AA} \tag{5}$$

where *b* is the radius of the contact area and α*<sup>i</sup>* is the coefficient of the rolling friction. Every particle has different α*i*, because the shapes of the sinter are totally different from each other. Its distribution is related with the rollability of the particle [16], and it is shown in Figure 5. The method of having different rolling friction provides a significant agreement with the experimental results [16]; therefore, this method was applied here.

**Figure 5.** Distribution of the coefficient of the rolling friction [16].
