Introduction

Vanadium–titanium magnetite (VTM) is a symbiotic composite ore rich in iron, vanadium, titanium, and other valuable elements,[1,2] and it is also a mineral resource distributed worldwide. However, the VTM is considered a refractory mineral, indicating its difficulty in comprehensive utilization—effective separation and recovery for iron, vanadium, and titanium are significant. At present, the traditional blast furnace process and rotary kiln–electric furnace (RKEF) process for VTM smelting have been developed. Although molten iron can be obtained by smelting VTM with traditional blast furnace process, and vanadium slag can be recovered by blowing air into molten iron, there are many problems in practical production, causing low recovery efficiency of vanadium (about 70 pct) and scarce titanium recovered.[3,4,5] As for the RKEF process, it has been proved relatively mature by South Africa Haveld Company and New Zealand Iron and Steel Company with practical production for years. The vanadium-containing molten iron can be produced well, and vanadium slag can be obtained from it.[6,7] However, it suffers from the same drawbacks, and the titanium-containing slag cannot be further utilized. Therefore, comprehensive utilization of VTM has long drawn a lot of attention in the steel industry, and some new smelting processes for VTM have been developed.[8,9,10,11] To solve the current situation of difficult utilization of VTM, a new sodium smelting process was proposed, and projects on a pilot scale and an expended scale consuming 50,000 tons of VTM annually were built in Hengshui, Hebei Province, respectively.[12,13] By combining of pyrometallurgy and hydrometallurgy, the new sodium smelting process can complete the separation and recovery of vanadium, iron, and titanium in VTM and maximize the resource value of VTM.[14] The key to sodium smelting technology is smelting reduction.[15,16] With the alkaline added, this novel process achieves direct reduction of VTM by one-step carbothermic reduction in the furnace and obtains high-quality pig iron and highly valuable slag.[17]

With wide adaptability for raw materials and short process flow, the oxygen-rich side-blow bath smelting furnace (OSBF) can be used to treat various iron-bearing materials. It has been reported that a variety of iron-bearing materials such as blast furnace slag, converter dust, iron ore, and vanadium-bearing slag have been successfully smelted in the Romelt furnace (a kind of OSBF) with a bed area of 20 m2.[18] The Romelt process has been commercialized, and a plant has been constructed in Myanmar for pig iron production.[19] As of now, few industrial applications for VTM smelting with OSBF has been carried out. Related fundamental investigation and feasibility verification of the process have been performed by our group. The OSBF where the smelting reduction of iron ore and the separation of slag/molten iron occur is the central equipment of this technology.[20] During the smelting process, the oxygen-enriched air is blown into the high-temperature melt at high velocity via the tuyeres through the side wall. The melt is vigorously stirred to facilitate the smelting reaction and the separation of slag and molten iron. The multiphase flow of gas–slag–metal in the smelting process has a significant impact on the material mixing, chemical reaction, and slag–metal separation in the furnace, which determines the smelting efficiency.[21,22] However, the challenges of in situ measurement and direct monitoring of multiphase flow remain due to the high temperature and corrosivity of slag in the smelting process.[23] At present, physical model and numerical simulation have been mainly employed to study the behavior of multiphase flow in the metallurgical smelting process. The former investigates the gas–liquid multiphase flow in a reactor with reduced size proportionally. Although the morphology of bubbles can be observed in part, the acquired parameters are insufficient enough to quantitatively describe the multiphase flow in the bath. Plus, this method designs and implements experiments in terms of equal Froude number; therefore, the effect of viscosity and surface tension on gas–liquid multiphase flow is ignored. When it comes to numerical simulation, it can override the above disadvantage using computational fluid dynamics (CFD) to study multiphase flow in metallurgical processes.

With the extensive application of CFD in metallurgy, it has been developed into an effective method to reveal and predict the flow field, temperature, and concentration distribution in a smelting furnace.[24,25] The multiphase flow behavior during various metallurgical smelting processes has drawn a lot of attention and has been investigated using this method. However, few works have been reported to shed light on the side-blow smelting process, let alone side-blow bath smelting ironmaking. Zhang et al.[26] studied the gas–liquid multiphase movement, the slag/air fluctuation, the flow field distribution, and the effect of gas flow rate on the mean slag velocity in the copper smelting process of the Vanyukov furnace. Liu et al.[27] compared three different turbulence models (the Standard k-ε model, the Realizable k-ε model, and the SST k-ω model) in the simulation of gas–liquid multiphase flow in the side-blown bath by combining physical model and numerical simulation. They concluded that the numerical results with the Realizable k-ε turbulence model are the closest to the experiment for the penetration depth, the surface fluctuation height, and the bubble scale. Xiao et al.[28] studied the flow field distribution and gas–liquid stirring of the copper smelting process and proposed three improved gas injection modes to enhance circulation flow in a side-blown copper smelting furnace. Zhao et al.[29] studied the variation of bubble shape in the side-blown furnace. They explored the effect of tuyeres arrangement spacing on the phase distribution and splash behavior of the molten pool. However, most of the very present simulation studies on the side-blown smelting process are about nonferrous metallurgy, which has greatly promoted the understanding of multiphase flow in the side-blown furnace. Owing to the different operating conditions and physical parameters between nonferrous metallurgy and iron-making process, especially the gas flow rate, slag density, and surface tension, which are the main parameters affecting the multiphase flow status in the bath, therefore the conclusions obtained from the nonferrous metallurgy don’t apply to the iron-making process. In addition, those previous simulation studies on the bath smelting process mainly employed the VOF model, but it suffers from difficulty in accurately predicting the radius of curvature of the interface in a region where the volume ratio is discontinuous. Therefore, the necessity for an improvement in the VOF model was recognized to track the interface more accurately between gas, slag, and metal. Besides, some studies performed short flow duration or 2D model for saving computational resources; these results remain inadequate. Therefore, it is imperative to systematically explore the multiphase flow behavior during the iron smelting process in OSBF and the effects of operating conditions and physical parameters on the smelting process.

In the present work, a 3D simulation model with a bed area of 5.4 m2 was established to describe the behavior of multiphase flow during the ironmaking process in OSBF based on the project in expended scale consuming 50,000 tons of iron ore annually fabricated by our group. The multiphase flow characteristics in OSBF were obtained through numerical simulation. In addition, the effects of primary air flow, slag thickness, and slag viscosity on the smelting process were also studied, and the range of operating conditions suitable for industrial production was also concluded. The present results are expected to provide theoretical guidance for the design and operation of OSBF.

Mathematical Model

In this section, the calculation models are introduced detailly. To simplify the calculations, several assumptions were made as follows:

  1. (1)

    The influence of solid feeding on the smelting process is negligible, and the initial state is static.

  2. (2)

    The effect of chemical reactions and changes in temperature field is not taken into consideration.

  3. (3)

    Fluids are incompressible and viscous, with constant physical and chemical properties.

  4. (4)

    There is no penetration and slip on the wall of the bath, and the standard wall function is used in the boundary layer near the wall.

Multiphase Model

Based on different treatments for gas phase, the simulation methods of gas–liquid multiphase flow in the metallurgical process are divided into Euler–Euler method and Euler–Lagrange method.[30,31] When it comes to the latter, the conservation of mass and momentum equations of the liquid phase shall be solved in the Euler reference system; while the particles or bubbles are considered dispersed phase, and their motion trajectory is described by the force balance in the Lagrange reference system. Nevertheless, it’s difficult for this method to track clear gas–liquid interface and to obtain accurate flow field distribution at a high velocity of gas; however, the VOF model based on Euler–Euler method can do, even in a wider range of gas velocity.[32] In the VOF model, different phases are regarded as non-penetrating continuum mathematically, and one set of equations is used to solve the conservation of mass and momentum equations of each phase.

The VOF model assumes that there is no interpenetration between each fluid phase. It is necessary for each additional phase to introduce an additional phase volume fraction, and the sum of them in each calculation cell shall be 1. In a certain calculation cell, there are three possibilities for the volume fraction (α) of the qth fluid:αq = 0: there is no qth fluid in the cell;αq = 1: the cell is full of qth fluid;

0 < αq < 1: the cell contains the phase interface between the qth fluid and other fluids.

All fluids share only one set of momentum equations for the VOF model, and the α is recorded in each calculation cell of the whole flow field during the calculation process. The phase interface is tracked by solving the continuity equation for the α of one or more phases. For the qth fluid, the continuity equation is given as follows:

$$\frac{\partial }{\partial t}\left( {\alpha_{q} \rho_{q} } \right) + \nabla \cdot \left( {\alpha_{q} \rho_{q} \overrightarrow {u}_{q} } \right) = 0$$
$$\sum\limits_{q = 1}^{n} {\alpha_{q} = 1}$$

All fluid phases in the whole region share a single momentum equation, and its velocity field is shared among all phases. The momentum equation depends on the α of all phases through the properties ρ and μ, and it gives:

$$\frac{\partial }{\partial t}\left( {\rho \overrightarrow {u} } \right) + \nabla \cdot \left( {\rho \overrightarrow {u} \overrightarrow {u} } \right) = - \nabla p + \nabla \cdot \left[ {\mu \left( {\nabla \overrightarrow {u} + \nabla \overrightarrow {u}^{T} } \right)} \right] + \rho \overrightarrow {g} + \overrightarrow {F}$$

The fluid properties in the momentum equation are determined by component phases in each cell. For an n-phase system, the density can be given by

$$\rho = \sum\limits_{q = 1}^{n} {\alpha_{q} \rho_{q} }$$

Other properties for this system can be calculated in this manner. For example, in a gas–liquid two-phase system, the density and viscosity can be given by

$$\rho = \rho_{g} \alpha_{g} + \rho_{l} \left( {1 - \alpha_{g} } \right)$$
$$\mu = \mu_{g} \alpha_{g} + \mu_{l} \left( {1 - \alpha_{g} } \right)$$

The phases interface is tracked by a geometric reconstruction scheme in the VOF model, and it performs a piecewise linear method to represent the interface between fluids. The VOF method tracks the α of a particular phase in each cell rather than the interface itself. However, its spatial derivatives cannot be calculated accurately owing to the discontinuity of the interface volume fraction. Therefore, the Level Set function is introduced to enhance interface tracking.[33] The Level Set function φ is defined by

$$\varphi \left( {x,t} \right) = \left\{ \begin{gathered} \begin{array}{ll} { - 1} & {{\text{if}}\;{\text{the}}\;{\text{primary}}\;{\text{phase}}\;{\text{in}}\;{\text{the}}\;{\text{cell}}} \\ \end{array} \hfill \\ 0\begin{array}{*{20}c} {} & {{\text{at}}\;{\text{the}}\;{\text{interface}}} \\ \end{array} \hfill \\ \begin{array}{*{20}c} 1 & {{\text{if}}\;{\text{the}}\;{\text{second}}\;{\text{phase}}\;{\text{in}}\;{\text{the}}\;{\text{cell}}} \\ \end{array} \hfill \\ \end{gathered} \right.$$
$$\frac{\partial \varphi }{{\partial t}} + \nabla \cdot \left( {\overrightarrow {u} \varphi } \right) = 0$$

In the CLSVOF model, the surface tension is given in the form of source term due to the introduction of Level Set method in VOF model. Tension surface is modified by the Heaviside function and is included as a volumetric source term in the momentum equation[34]:

$$\overrightarrow {F}_{\text{sf}} = 2H\sigma \kappa \delta \left( \varphi \right)\overrightarrow {n}$$
$$H_{\varphi } = \left\{ \begin{gathered} \begin{array}{ll} 0 & {{\text{if}}\;\varphi < - \delta } \\ \end{array} \hfill \\ \begin{array}{*{20}c} {\frac{1}{2}\left[ {1 + \frac{\varphi }{\delta } + \frac{1}{\pi }\sin \left( {\frac{\pi \varphi }{\delta }} \right)} \right]} & {{\text{if}}\;\varphi \le \delta } \\ \end{array} \hfill \\ \begin{array}{*{20}c} 1 & {{\text{if}}\;\varphi > \delta } \\ \end{array} \hfill \\ \end{gathered} \right.$$
$$\overrightarrow {n} = \left. {\frac{\nabla \varphi }{{\left| {\nabla \varphi } \right|}}} \right|_{\varphi = 0} ,\quad \kappa = - \nabla \cdot \left. {\frac{\nabla \varphi }{{\left| {\nabla \varphi } \right|}}} \right|_{\varphi = 0}$$

The spatial gradients of Level Set function can be accurately calculated due to its smoothness and continuity—this produces accurate estimates of interface curvature and surface tension force caused by the curvature. Therefore, the CLSVOF can accurately determine the interface and ensure mass conservation, and the obtained physical quantities have good continuity near the interface.

Turbulence Model

A suitable turbulence model is the key to study the particle migration and mixing phenomenon in fluid. The simplest complete turbulence model is the two-equation model. The form of equations is similar. The length and time scale of turbulence are determined by solving two independent transport equations of turbulent kinetic energy k and turbulent energy dissipation rate ε. The main differences between them are: (1) the calculation method of turbulent viscosity; (2) the Prandtl number that controls turbulent diffusion of k and ε; (3) generation and destruction terms in the ε equation. In present work, the Realizable k–ε turbulence model was determined and chosen to perform calculations by experimental comparison. Compared to the Standard k–ε turbulence model, it increases the vortex viscosity for turbulence on the one hand, and it adds a new transport equation for diffusivity on the other hand.[35,36]

The transport equations for k and ε in the Realizable k-ε model[37] are:

$$\frac{\partial }{\partial t}\left( {\rho k} \right) + \frac{\partial }{{\partial X_{j} }}\left( {\rho ku_{j} } \right) = \frac{\partial }{{\partial X_{j} }}\left[ {\left( {\mu + \frac{{\mu_{t} }}{{\sigma_{k} }}} \right)\frac{\partial k}{{\partial X_{j} }}} \right] + G_{k} + G_{b} - \rho \varepsilon$$

and

$$\frac{\partial }{\partial t}\left( {\rho \varepsilon } \right) + \frac{\partial }{{\partial X_{j} }}\left( {\rho \varepsilon u_{j} } \right) = \frac{\partial }{{\partial X_{j} }}\left[ {\left( {\mu + \frac{{\mu_{t} }}{{\sigma_{\varepsilon } }}} \right)\frac{\partial \varepsilon }{{\partial X_{j} }}} \right] + \rho C_{1} S\varepsilon - \rho C_{2} \frac{{\varepsilon^{2} }}{{k + \sqrt {v\varepsilon } }} + C_{1\varepsilon } \frac{\varepsilon }{k}C_{3\varepsilon } G_{b}$$

where \(C_{1} = \max \left[ {0.43,\;\frac{\eta }{\eta + 5}} \right]\), \(\eta = S\frac{k}{\varepsilon }\), \(S = \sqrt {2S_{ij} S_{ij} }\), \(\mu_{t} = \rho C_{\mu } \frac{{k^{2} }}{\varepsilon }\) unlike in other k-ε models, Cμ in the Realizable k-ε model is no longer constant, and it is computed from

$$C_{\mu } = \frac{1}{{A_{0} + A_{{\text{s}}} \frac{{kU^{*} }}{\varepsilon }}}$$

where

\(U^{*} = \sqrt {S_{ij} S_{ij} + \widetilde{\Omega }_{ij} \widetilde{\Omega }_{ij} }\), \(\widetilde{\Omega }_{ij} = \Omega_{ij} - 2\varepsilon_{ij} k\omega_{k}\), \(\Omega_{ij} = \overline{\Omega }_{ij} - \varepsilon_{ij} k\omega_{k}\).

The model constants are.

A0 = 4.04, C1ε = 1.44, C2ε = 1.92, C2 = 1.9, σk = 1.0, σε = 1.2.

Geometric Model and Numerical Procedure

Geometry and Mesh Model

The structure of OSBF is shown in Figure 1. Two rows of tuyeres are on each side of the wall, which are arranged opposite each other in the OSBF. The position of primary tuyeres (6 pairs) is lower than that of the secondary tuyeres (5 pairs). The primary tuyeres are immersed in the slag layer, and the oxygen-enriched air injected through them generates violent agitation in the slag layer where the smelting reaction occurs, which is the main character of the OSBF. Compressed air is blown into the secondary tuyeres to burn the combustible gas generated during the smelting process. The molten bath consists of molten iron layer (red area) and slag layer (yellow area). The rest above the liquid level of the bath is gas phase. The flue gas is discharged from the top of furnace, and the outlet pressure is − 358 Pa.

Fig. 1
figure 1

Schematic diagram of the OSBF. 1, Feed inlet; 2, Feed inlet; 3, Slag layer; 4, Iron layer; 5, Molten iron outlet; 6, Flue gas outlet; 7, Secondary tuyeres; 8, Primary tuyeres; 9, Slag outlet

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According to the size of the OSBF in the practical project, a 1:1 three-dimensional geometric model was established, as shown in Figure 2(a), and the meshed model is shown in Figure 2(b). The structured mesh was adopted for calculation, and the number of meshes was approximately 350,000. Considering the large flow velocity near the tuyeres, the meshes near them and the bath area of concern were locally densified, while the meshes near the flue gas outlet was sparse. All of the above were to ensure the calculation accuracy and speed up the calculation simultaneously, and thus the convergence efficiency during the calculation was improved.

Fig. 2
figure 2

Geometric model (a) and meshed model (b) of the OSBF

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Numerical Setup and Boundary Conditions

In the calculations, SIMPLE arithmetic was adopted to solve the velocity–pressure coupling equation with the transient mode. The spatial discretization for momentum and velocity adopted the second-order upwind scheme, and the turbulence and Level Set function adopted the first-order upwind scheme. The convergence was determined by monitoring the residuals of continuity equation, and they were set as 0.001. The CLSVOF model was employed for multiphase flow simulation, and Realizable k-ε was adopted for turbulence model. These models have been used in some studies and were verified by experiments in another research.[23,26,27,28,29] Variable time step was used for calculation; the initial time step was set to 10−5, and the maximum number of iterations in each time step was 20. The maximum Courant number was controlled to be less than 2 for a good balance between simulation accuracy and calculation cost. Model dimensions, operating conditions, and physical properties data are listed in Table I.

Table I Geometrical Dimensions, Operational Parameters and Material Properties in Industrial OSBF
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Mesh Independence Test

The calculation accuracy and the suitable number of meshes can be determined by verifying flow velocity on an interface at a specific time when other calculation conditions remain constant. The models with different numbers of meshes under the same calculation conditions were simulated to verify the mesh independence. The numbers of meshes were about 150,000, 250,000, 350,000, and 450,000, respectively. A straight line (line 1) was established in the middle of the cross-Sect. (0.2 m below the bath liquid level, z = 0.75 m), as shown in Figure 3. The velocity distribution on line 1 of several models with different mesh numbers was obtained. It can be observed from Figure 4 that the difference between flow velocities of melt with different mesh numbers decreases with the number of meshes increasing. The calculation results of model with 350,000 meshes and that with 450,000 meshes are close, and the flow velocity error of the bath is 3.67 pct. In addition, the variation of gas holdup and fluid velocity within 1 s for the models with different mesh numbers was also compared. As shown in Figure 5, the calculation results with fewer meshes deviate significantly, while the difference between the calculation results with 350,000 and 450,000 grids decreases. The relative errors of gas holdup and fluid velocity calculated by the two groups within the first second are 3.84 and 3.77 pct, respectively, which are acceptable for the flow simulation in such a large reactor. However, more meshes require more computational resources and time. Therefore, the mesh number of 350,000 was selected for subsequent simulation calculation.

Fig. 3
figure 3

Position of line 1 in the bath

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Fig. 4
figure 4

Velocity distribution on line 1 calculated by models with different mesh numbers

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Fig. 5
figure 5

Gas hold-up (a) and flow velocity (b) of the fluid in the bath within 1 s

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Results and Discussion

Characteristics of Gas–Slag–Metal Three-Phase Flow

The gas holdup in the bath was analyzed by monitoring the calculation process in real-time. When the primary air flow was 3516 Nm3 h−1, the gas holdup in the bath increased gradually with the injection time; then, it tended to be stable after 20 s, which is about 27 pct, as shown in Figure 6. Actually, the flow duration calculated was 25 s. It can be considered that the side-blown smelting process in the bath has reached dynamic equilibrium. The calculation results under other different primary air flows are similar to that under 3516 Nm3 h−1. Therefore, 25 s was selected as the flow duration simulated. The characteristics of gas–slag–metal multiphase flow was analyzed by the slag phase distribution, flow field distribution, and flow status analysis for the XZ and XY sections of the bath.

Fig. 6
figure 6

Variation of gas holdup with time in the bath

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Slag phase distribution

Figure 7 shows the variation of isosurface distribution of slag phase with time. There are about three stages in general after the gas is blown into the slag layer, which are the bubble-floating stage, gas-stirring stage, and slag droplet formation stage. Firstly, during the bubble-floating stage, the gas blown into the bath formed large hemispherical bubbles near the tuyeres, then the latter floated upward rapidly due to the buoyancy. The bottom of the bubbles was concave, and mushroom-shaped bubbles were observed. As the bubbles kept floating, the concave on the bottom became deeper, and the horizontal range of floating bubbles became larger. The bath surface bulging with the bubbles floating. The slag layer at the top of the bubbles became thinner, and the bulge part became higher; finally, the bubbles broke through the slag layer and ruptured. Subsequently, during the gas-stirring stage, big bubbles ruptured, and the splashed slag droplets dropped down. Then, the surrounding slag poured in and filled the space occupied by the original bubbles, which caused violent turbulence in the upper slag layer. With the gas blown into the bath continuously, the turbulence became more violent, and the turbulence also spread from top to bottom. Meanwhile, the gas holdup in the bath was also increasing, and the range of slag layer without gas became smaller. As injection time went by, the smelting process engaged in the slag droplet formation stage. The slag layer above the tuyeres in the bath was gradually dispersed under the gas-blowing circumstance, and a large number of slag droplets were generated. The splashing and falling of slag droplets resulted in the violent stirring of the slag layer, and the gas holdup in the bath gradually increased and then stabilized. Thus, the smelting process was in a dynamic steady state.

Fig. 7
figure 7

Slag phase distribution in molten bath at different time

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Figure 8 shows the slag phase distribution of each section in the vertical direction in the furnace after the smelting process reached steady state. It can be seen from the OSBF that the volume fraction of slag phase on the section of Y = 3 m rarely exceeds 0.2, demonstrating most gas phase here and few slag drops splashing out of the bath. It increases in turn at the sections of Y = 2.3 m and Y = 1.8 m, indicating the increased splashing slag drops near the bath surface. The section of Y = 1.3 m is bath surface, where the volume fraction of slag phase increases significantly and the slag phase is evenly distributed, indicating that the gas and slag mix well. The volume fraction of slag phase rises to about 0.4 at Y = 1.1 m, indicating that a large amount of gas phase is mixed in the slag here, and these two phases can react better. The tuyeres are located at the section of Y = 0.8 m, where a large amount of gas phase is mixed into the slag, and there are also some slag clusters with large volume fraction of slag phase. The section of Y = 0.5 m is slag–iron interface, where the volume fraction of slag phase is about 0.5, meaning slight fluctuation of the interface. In summary, one can see that the slag–metal interface remains stable with subtle fluctuation during the whole smelting process. In the slag layer abreast of and above primary tuyeres, the gas and slag were mixed evenly. Splashed slag droplets were formed in the area above the bath, and their number decreased with the distance to the bath surface increasing.

Fig. 8
figure 8

Slag phase distribution on different height sections of the OSBF

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Flow field distribution

The velocity distribution in the Y-axis direction was analyzed under the steady melting condition. As shown in Figure 9, there were some small high-speed vortices in the bath area above the primary tuyeres due to the primary air injection, resulting in strong turbulence of melt and uniform mixing of gas and slag. The flow velocity in the molten iron layer was low, which was less than 0.1 m/s. This can retard the corrosion of the hearth lining and is conducive to the separation of slag and iron. Besides, the secondary air blown into the furnace resulted in a high-speed turbulent region near the secondary tuyeres. The secondary air injected from opposite furnace sides collided in the reactor, forming downward airflow. This can inhibit the splashing of slag droplets and lower the splashing height.

Fig. 9
figure 9

Velocity contour in the Y-axis direction of the OSBF

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The gas movement track shown in Figure 10 confirms this. The primary air can be blown into the bath, causing violent stirring of molten slag. The colliding secondary air generates vortices, which restrict the splashing of slag droplets.

Fig. 10
figure 10

Velocity streamline of the OSBF

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Flow status analysis of XZ section in the bath

Gas holdup, flow velocity, and turbulent kinetic energy of each level in the Y-axis section of the bath (as shown in Figure 11(a)) were analyzed after the smelting process is steady.

Fig. 11
figure 11

Characteristics of gas–liquid multiphase flow at different heights (a) in bath, (b) Gas holdup; (c) Velocity; (d) Turbulence kinetic energy

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The average flow velocity of the layer below the slag–metal interface (Y = 0.5 m) was low. There was no gas mixing in the molten iron, and its turbulent kinetic energy was small, meaning that there was no violent turbulence in the iron layer. In the slag layer above the slag–metal interface, especially at the primary tuyeres (Y = 0.8 m), the flow velocity of melt increased, and the gas holdup increased rapidly, leading to the increased turbulent kinetic energy and the violent turbulence in the slag layer. In addition, when the primary air flow is different, it also shows a similar characteristic.

Flow status analysis of XY section in the bath

Flow status in the Z-axis section of the bath were analyzed after the smelting process was steady. As shown in Figure 12, the gas holdup of each level along the Z-axis direction in the bath varies little, indicating that the primary air was evenly mixed in the slag layer, and it played an important part in slag layer mixing. When the primary air flow was 3516 Nm3 h−1, the gas holdup of the bath reached the maximum. As the velocity distribution and turbulent kinetic energy distribution are shown in Figure 12(c) and Figure 12(d), respectively, the degree of turbulence was relatively uniform in most bath areas except the area close to the wall. The degree of turbulence of the melt intensified with the primary air flow increasing.

Fig. 12
figure 12

Characteristics of gas–liquid multiphase flow at Z-axis section (a) of the bath, (b) Gas holdup; (c) Velocity; (d) Turbulence kinetic energy

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Effect of Primary Air Flow on Flow Status of the Bath

The characteristics of the gas–liquid multiphase flow in the bath with different primary air flow were studied. The analysis indexes consist of the gas holdup of the bath, the average velocity of the slag layer, the average velocity of the molten iron layer, and splashing height of the slag droplets, which are important parameters reflecting the smelting status of the bath in the practical smelting process. Higher gas holdup of the bath represents larger gas–liquid interaction area and greater gas phase concentration, which is conducive to the metallurgical reaction in the bath; larger average velocity of slag represents more violent stirring and better mixing effect between gas and liquid phase. As for the velocity of molten iron layer, it affects the service life of OSBF. Violent turbulence of molten iron leads to severe erosion of hearth lining and fluctuation of slag–metal interface; the latter is prone to draw the slag into the iron layer, which is harmful to the separation of slag and iron. Thus, the molten iron layer should be kept stable during the smelting process. The splashing height of slag droplets is regarded as a restrictive condition. When it is beyond the secondary tuyeres, the slag droplets tend to be cooled down on the furnace wall, resulting in nodulation and blockage of the secondary tuyeres and feed inlets. However, a certain splashing height is required during the smelting to effectively transfer the heat generated in the secondary combustion region.

The flow parameters during the smelting process varied with time, and there was an initialization effect that should be eliminated. The average value of the last 10 s was adopted for comparison. Figure 13 shows the variation tendency of flow characteristics in the bath with the primary air flow. It can be observed that the gas holdup in the bath increases with the increase of primary air flow, and then it peaks the first local maximum when the primary air flow is 3516 Nm3 h−1; subsequently, it decreases first and then increases with the latter increasing, and then it reaches the second local maximum which is absolute maximum at the primary air flow of 4834 Nm3 h−1. After the primary air flow exceeds 4834 Nm3 h−1, the gas holdup declines slightly again. As the gas flow rate increases, two peaks appear in the gas holdup variation, which is due to the change in the pattern of rising bubbles in the slag. The occurrence of the gas injected into the slag is mainly individual large bubbles when the gas flow rate is below 3516 Nm3 h−1. With the gas flow rate increasing, the bubbles detached from the tuyere elongate and form a slender bubble string, generating a short-circuit channel, where the gas flows out quickly, resulting in a slight decrease in the gas holdup. Subsequently, with the increase in gas flow rate, the bubble string becomes thicker, and the gas holdup increases. When the gas flow rate becomes larger, the thicker bubble string starts to break up, thus decreasing the gas holdup again. Larger gas holdup in the bath means that more gas is mixed into the slag layer, which is more conducive to the stirring for the bath and the smelting reaction in the slag layer. The velocity of slag layer increases with the primary air flow increasing, signifying that the turbulence of slag layer becomes more violent and the effect of gas–liquid mixing is strengthened with the rise in primary air flow. The velocity of molten iron increase with the increase in primary air flow as well. Therefore, the service life of the OSBF also decreases with the increase of primary air flow. In addition, with the increase of primary air flow, the splashing height of molten slag also increases, and it is above the secondary tuyeres when the primary air flow reaches 4834 Nm3 h−1. In this situation, the splashing slag droplets will be cooled down by the secondary air and then solidify on the furnace wall, causing further production accidents. Therefore, in the light of production security, the splashing height should be lower than 3.8 m, that is, the primary air flow should be under 4000 Nm3 h−1. Taking all the above into consideration, the appropriate primary air flow of 3000–4000 Nm3 h−1 is recommended.

Fig. 13
figure 13

Effect of primary air flow on gas–liquid multiphase flow in the bath, (a) Gas holdup; (b) Velocity of slag; (c) Velocity of iron; (d) Splash height of slag droplet

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As shown in Figure 14, the splashing height of slag droplets under different primary air flow was analyzed; obviously, it increases as the gas flow increases. When the primary air flow exceeds 4834 Nm3 h−1, the splashing height of slag droplets is above the secondary tuyeres, which will lead to the nodulation of the secondary tuyeres. This is detrimental to the stable operation of the furnace. Therefore, the operation range of primary air flow should not be higher than 4000 Nm3 h−1.

Fig. 14
figure 14

Splashing height of slag drops in the furnace with different primary air flow rate

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Effect of Slag Layer Thickness on Flow Status of the Bath

The thickness of the slag layer in the bath is related to the feeding operation conditions, and it is also a key parameter in the design and operation of the OSBF. The appropriate thickness of slag layer is capable of the improvement of smelting efficiency and the increase in output. Therefore, it is necessary to explore the effect of the thickness of slag layer on the smelting process. When the primary air flow is 3516 Nm3 h−1, the flow status of slag and iron layer are both in good condition. Subsequently, under the primary air flow of 3516 Nm3 h−1, the appropriate slag layer thickness in the bath was investigated.

Figure 15 shows the flow characteristics in the bath with different thicknesses of slag layer. The gas holdup in the bath increases with the increase of the slag layer thickness. When the slag layer thickness exceeds 0.9 m, the gas holdup in the bath is at a high level, greater than 27 pct. This is due to the fact that the increase in the thickness of slag layer leads to the increase in the distance from the primary tuyeres where gas is blown into to the surface of the bath, and the bubbles volume increases owing to the decrease in pressure during the upward process. When the slag layer thickness is 0.9–1.0 m, the gas holdup in the bath is relatively larger, indicating better gas–slag mixing efficiency. The velocity of the slag layer decreases with the thickness of slag layer increasing. This can be explained by the increment in the pressure arising from the thicker slag layer. Due to the higher pressure, the turbulence of the molten slag caused by the primary air becomes milder, causing a poor mixing effect on the bath. The thickness of slag layer has little effect on the velocity of the iron layer, and it fluctuates in a low-velocity range with the thickness of slag layer increasing. The splashing height of slag increases as the thickness of slag layer increases. With the slag layer thickness increasing, the residence time (acceleration time) of gas bubbles would be longer, and thus the kinetic energy would be greater, resulting in a higher splashing height after breaking through the slag layer. In addition, as the thickness increases, the rising bubbles become larger when breaking through the slag layer, also causing higher droplet splash. When the thickness of slag layer exceeds 1 m, the splashing height of slag droplets is higher than 3.8 m, which is a height limit. Therefore, the appropriate recommended value of slag layer thickness is 0.8–1.0 m.

Fig. 15
figure 15

Effect of slag layer thickness on gas–liquid multiphase flow in the bath, (a) Gas holdup; (b) Velocity of slag; (c) Velocity of iron; (d) Splash height of slag droplet

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Effect of Slag Viscosity on Flow Status of the Bath

The slag viscosity is an important control parameter for the OSBF, since it varies significantly with temperature and slag composition during the smelting process. Ito and Fruehan[39] quantitatively studied the foaming characteristics of CaO–SiO2–FeO slag through experiments, which were described with foaming index. The empirical formula between foaming index and viscosity was obtained through dimensional analysis.[40] It was considered that the foaming index increased with the increase in slag viscosity, and the height of foam in practical operation was predicted to be 3–5 m. However, slag viscosity may vary from 0.01 to 0.2 Pa s by adding sodium salt additives during the OSBF process for VTM, which is significantly lower than that of calcium-based slag. Improper slag viscosity is prone to cause production accidents, such as foam slag. Therefore, the effect of slag viscosity on gas–liquid multiphase flow during the smelting process was studied. When the primary air flow and the slag layer thickness are 3516 Nm3 h−1 and 0.8 m, respectively, the flow status in the furnace for different slag viscosity is simulated, and Figure 16 depicts the results. It can be seen that the gas holdup in the bath decreases with the increase in slag viscosity. This is because the bubbles in the slag are not preferable to break into small bubbles as the slag viscosity increases, and fewer small bubbles retain in the slag, resulting in the lower gas holdup in the bath. The surface of small bubbles retained in the slag is the main place for gas–liquid reaction, and fewer small bubbles can further lead to poor smelting effect. The average velocity of slag layer increases with the increment in slag viscosity. It peaks the maximum when the slag viscosity is 0.13 Pa s, and it then decreases with the increase in slag viscosity. It shows that the kinetic energy brought by the primary air is more consumed in the slag layer after the slag viscosity increases, resulting in the intensification of turbulence in the slag layer. With the increase in slag viscosity, the average velocity of the iron layer increases first and then decreases. When it exceeds 0.04 Pa s, the velocity of iron layer decreases with the viscosity of slag. This is also because the increase in slag viscosity improves the kinetic energy consumption of slag layer, which reduces the kinetic energy transferred to molten iron. The slag viscosity has little effect on the splashing height of slag droplets, which means that lower viscosity has little effect on foam height. When the slag viscosity is 0.01 Pa s, the splashing height is 3.62 m; when the former exceeds 0.04 Pa s, the latter fluctuates around 3.5 m with the increase in the former. The maximum splashing height of slag droplets is smaller than 3.8 m, indicating no foam slag accident. In general, it can be considered that lower slag viscosity is conducive to higher smelting efficiency. The smelting process can be carried out normally with the slag viscosity increasing from 0.01 to 0.2 Pa s.

Fig. 16
figure 16

Effect of slag viscosity on gas–liquid multiphase flow in the bath, (a) Gas holdup; (b) Velocity of slag; (c) Velocity of iron; (d) Splash height of slag droplet

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Conclusions

A numerical calculation model was established to simulate the smelting process of VTM by the OSBF. The central conclusions are listed as follows:

  1. (1)

    The primary air causes violent stirring for slag layer, and a large amount of gas is mixed with slag. The interface between slag and iron is relatively steady, and the velocity of the iron layer below the slag-iron interface is slow (< 0.05 m/s). The turbulence of molten iron is weak, which can reduce the erosion of hearth refractory, and this is conducive to the separation of slag and iron.

  2. (2)

    When the primary air flow is 3516 Nm3 h−1, the gas holdup, slag layer velocity, iron layer velocity, and splashing height of slag droplets are at a high level, indicating that the gas and slag in the bath are evenly mixed under this condition, which is conducive to the smelting process. It can be considered that the suitable operation range of primary air is 3000–4000 Nm3 h−1.

  3. (3)

    With the increase in the slag layer thickness, the turbulence of the slag layer becomes weaker, and the splashing height of slag droplets increases, which is harmful to the smelting process. The appropriate slag layer thickness is 0.8–1.0 m.

  4. (4)

    The broken small bubbles in the slag become less with the increase in slag viscosity, and the gas holdup in the bath decreases, which leads to the poor smelting effect. It was proved that the smelting process could be performed normally as the slag viscosity increased from 0.01 to 0.2 Pa s.