*3.1. Raceway Evolution Characteristics*

Raceway evolution is an important phenomenon, particularly reblowing, which occurs after a temporary wind break in an ironmaking BF. To accurately analyze the evolution process and physical characteristics of the raceway, the boundary of the raceway was previously defined by the values of isostatic stress and solid or gas volume fractions [24–27]. In this study, when the solid volume fraction was less than 0.5, the frictional pressure was 0, and the solid motion was mainly affected by collision. Therefore, the boundary of the raceway was defined as a solid volume fraction of 0.5.

As depicted in Figure 2, at an injection velocity of 150 m/s, the penetration depth of the raceway reached a peak at 1 s, at a value of 0.783 m, and it stabilized at 9 s, at a value of 0.386 m. At an injection velocity of 200 m/s, the penetration depth reached 0.982 m at 1.1 s and then decreased to 0.460 m at 25 s. At 250 m/s, the penetration depth increased to a peak of 1.143 m at 1.5 s and achieved a stable value of 0.631 m at 40 s. At 300 m/s, the penetration depth reached a peak of 1.327 m at 1.7 s and stabilized at 1.109 m at 47.5 s. The evolution process of the raceway can be divided into three stages: (1) rapid expansion, (2) slow contraction, and (3) gradual stabilization. In Stage 1, the penetration depth of the raceway increases rapidly in the early stages of gas injection. The higher the injection velocity, the faster the increase in the penetration depth. Then, in Stage 2, as the particles descend and congregate, the penetration depth decreases slowly after reaching the peak. In Stage 3, the raceway stabilizes.

**Figure 2.** Evolution of penetration depth in the raceway: (**a**) 0–2 s and (**b**) 2–50 s.

A typical blast velocity is close to 250 m/s in a small BF tuyere. Figure 3 depicts the evolution of the raceway. When air was injected through the tuyere, the expansion of the depth of the raceway was more obvious. When the peak was reached, the height changes of the raceway were more obvious. Finally, the raceway stabilized at 40 s. This trend was due to the fact that when the solid phase interacted with the gas phase, the initial solid volume fraction changed toward the maximum limiting volume fraction and eventually stabilized. This created a particle circulation zone attributed to the balance between the drag of the blast and the gravity and pressure of the particles.

**Figure 3.** Time evolution of the solid volume fraction for Case 3.

### *3.2. Raceway Size Characteristics*

Different BF operating conditions led to different raceway physical characteristics, which were mainly reflected by their size. Figure 4 shows that the shape of the raceway after it stabilizes is an upturned bag at high blast velocity. In an actual BF, this provides enough space for the combustion of pulverized coal and coke, thereby improving production efficiency.

**Figure 4.** Raceway shapes after they stabilize at different blast velocities: (**a**) 150 m/s; (**b**) 200 m/s; (**c**) 250 m/s; (**d**) 300 m/s.

The blast velocity increase was obviously beneficial for increasing the depth, height, and surface area of the raceway, while the width was slightly increased, as depicted in Figure 5. The size of the raceway was not linearly related to the blast velocity. When the blast velocity was increased from 150 m/s to 300 m/s, the surface area of the raceway increased from 0.194 m2 to 1.644 m2, and the depth increased from 0.386 m to 1.109 m. This was due to the increased gas kinetic energy because of the increased blast volume and velocity. Therefore, increasing the blast velocity is very effective for increasing the depth of the raceway in order to develop the central gas flow in an actual BF.

**Figure 5.** Effect of blast velocity on the raceway size.

#### *3.3. Pressure Distribution*

Figure 6a shows that the gas pressure was high in the raceway and decreased as it approached the outlet of the particle bed. In contrast, the solid granular pressure was considerably low in the raceway and at the boundary of the raceway. It is noteworthy that the solid granular pressure reached a local peak at the boundary of the raceway, where gas injection resistance was the highest, as depicted in Figure 6b.

As demonstrated in Figure 7, the gas pressure remained relatively stable up to 0.4 m from the front end of the tuyere because there were fewer particles and low resistance. At a distance equal to or greater than 0.4 m, the air pressure rapidly increased because the gas was subjected to increased particle resistance after deep penetration into the particle bed, and the pressure decreased because the gas velocity decreased and there was further particle resistance. The solid granular pressure in the raceway is close to 0. Near the boundary of the raceway, due to the interaction gas and solid, the solid granular pressure changes drastically, increasing first and then decreasing. However, it slowly increases in the end because the solid were constricted by the wall.

**Figure 6.** (**a**) Gas pressure and (**b**) solid granular pressure for Case 3 in the symmetry plane at 40 s.

**Figure 7.** Gas pressure and solid granular pressure for Case 3 on the axis of the tuyere at 40 s.

#### *3.4. Flow Pattern*

As depicted in Figures 8a and 9a, the gas in the raceway can be divided into a jet zone and an anti-clockwise flow zone. However, the gas flowed into the particle bed from the boundary of the raceway and did not form a large circulation area. This was due to the injection of high-speed gas into the tuyere, which limited gas circulation in the jet zone. Additionally, the gas had a weak anti-clockwise circulation flow at the edge of the tuyere. This is inconsistent with previous results in which the gas studied according to the CFD-DEM model was divided into anti-clockwise or clockwise circulation or a plume-like flow [21].

**Figure 8.** The symmetry plane of Case 3 at 40 s: (**a**) gas velocity streamline; (**b**) solid velocity streamline.

**Figure 9.** The tuyere level plane of Case 3 at 40 s: (**a**) gas velocity streamline; (**b**) solid velocity streamline.

The particles were clearly circulating anti-clockwise in the raceway, as depicted in Figure 8b. This was mainly due to the higher resistance of the solid particles along the axis of the tuyere and the lower pressure on the upper part of the particle bed. Below the tuyere, two clockwise particle circulation zones were formed, but the movement speed was considerably low. This was because the gas was affected by the solid resistance and the forces on the bottom and the wall. This reduced the gas flow velocity in the lower part of the packed bed, resulting in lower resistance. The source of particles in the solid jet area mainly derived from the upper part of the raceway particles, which also caused the upper particles in the particle bed to move downwards. In the horizontal direction, although there were also two anti-clockwise circulating flows to provide particles for the raceway, as depicted in Figure 9b, their velocities were extremely low. Therefore, the BF raceway was not a single-cycle flow as previously reported [21], but an extremely complex multi-cycle flow with gas–solid interaction. The circulation pattern near the tuyere may have a negative impact on the life of the tuyere.

The gas was injected from the tuyere along the axial direction of the tuyere. Owing to the resistance of the solid particles, the gas velocity rapidly decreased until it reached a value of 0.443 m/s at the wall surface, as depicted in Figure 10. The drag of the gas affected the particles. The particle velocity increased rapidly and maintained a relatively stable value in the middle part of the raceway. However, near the boundary of the raceway (α*<sup>s</sup>* → 0.5), the particle collision viscosity increased because of the increased particle volume fraction, which considerably reduced the particle velocity. External to the raceway boundary and with an increase in the particle friction viscosity and a decrease in the gas drag, the particle velocity was reduced to a value close to 0.

**Figure 10.** Gas and solid velocity along the axis of the tuyere for Case 3 at 40 s.

#### **4. Conclusions**

A 3D transient EMFM was developed to study the evolution and physical characteristics of the raceway in the packed particle bed of an ironmaking BF. The constitutive relation of the gas and solid phases was comprehensively considered in the model. The main conclusions of this study are as follows:


**Author Contributions:** Investigation, X.P., H.Z., and J.W.; methodology, X.P. and H.Z.; resources, Q.X.; data curation, X.P.; Formal analysis, X.P. and J.W.; writing—original draft preparation, X.P.; writing—review and editing, X.P. and J.W.; project administration, Q.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China, grant number U1960205, and supported by the National Key Research and Development Program, grant number 2016YFB0601304.

**Acknowledgments:** The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (No. U1960205) and the National Key Research and Development Program (No. 2016YFB0601304).

**Conflicts of Interest:** The authors declare no conflict of interest.
