Numerical Approach to Comprehend for Effect of Melts Physical Properties on Iron-slag Separation Behaviour in Self-reducing Pellet

Abstract

A smooth iron-slag separation during ironmaking process is necessary for the steel refining process, even in case of “Zero Carbon Ironmaking”. For a fundamental comprehension of the effect of the physical properties of the melts on the iron-slag separation behaviour, a numerical approach with a practical multi-interfacial smoothed particle hydrodynamics (SPH) simulation for the tracking of the iron-slag separation behaviour is undertaken in this study.

Experimental values for iron-slag separation conditions from a previous work and estimated physical properties from literature were used for the numerical analysis. The CLS-SPH method was able to reproduce the iron-slag separation behaviour where iron aggregated in a unitary sphere and the slag discharged onto the iron surface. A less viscous slag may reduce the negative impact on the separation. A slag with a high surface tension enables the slags to agglomerate and decreases the number of elements that may disturb the iron agglomeration. A highly dense slag has a strong influence on the variation of the iron-slag interface due to a larger momentum. The interfacial tension showed no obvious effect on the separation behaviour in the range of experimental values considered in this study.

1. Introduction

As the steel industry advances toward the adoption of the “Zero carbon emission” approach, the suppression of greenhouse gas emission from ironmaking process has emerged as one of the most important issues to be tackled. One of the promising technologies for the suppression of CO₂ emission is hydrogen ironmaking, such as the COURSE50 project.¹⁾ The utilization ratio of the direct reduced iron in electric arc furnace process has shown a simultaneous increase because of its environmental efficiency as well as a shortage of high-quality scrap. Gas-based direct reduction processes²⁾ such as MIDREX or ENEGIRON are becoming increasingly reasonable due to the impact of the shale gas. Further, the processes may shift their reducing agents from natural gas to hydrogen gas in a bid to approach “Zero Carbon Ironmaking” globally. However, the produced iron has to be melted for refining. The melted iron additionally needs to be separated from the slag components to produce high-quality steel products. In the ironmaking process, carbon plays the role of not only the heat source and reducing agent, but also of a carburizing agent. Carburization reaction is necessary for lowering the temperature of iron melting to enable energy saving. Hydrogen has been studied in the literature as an alternative agent for reduction and heat supply.^3,4,5,6,7,8)

Meanwhile, no other agent can replace carbon without compromising on the quality of the hot metal. From this point of view, a certain amount of carbon is necessary to smoothen the separation, even in “Zero Carbon Ironmaking”. Discussions about iron-slag separation are mainly confined to the refining process. Iwamasa and Fruehan⁹⁾ discussed the separation behaviour of metal from slag phase with the help of a cold model experiment and a high temperature in-situ observation using the X-ray diffraction (XRD) technique. They reported that slags of low viscosities and low densities are favourable for faster metal droplet settling times. Based on this report, Fruehan’s group¹⁰⁾ further discussed the iron-slag separation behaviour in a trough of blast furnace.

Usually, iron-slag separation around the cohesive zone of a blast furnace in an ironmaking process is prominently investigated. The beginning of the formation of the molten slag in the iron bearing burden layer is the trigger to form a gas-impermeable cohesive zone. Through the cohesive zone, melts of slag and iron are separated and gathered until an amount sufficient enough to drip from the bottom of the zone is collected. This formation of a cohesive zone was well discussed with the help of a reduction test under load.^11,12,13) These reports included an evaluation of gas permeability as well. The gas permeability in the cohesive zone is one of the most important factors for the blast furnace operation. The results indicated that the formation of the molten slag has a dominant effect on the packed bed macro-structure, which is important for the gas permeability.

Even if “Zero Carbon Ironmaking” is deemed to be the future of steel making, a self- reducing pellet, such as a carbon composite agglomerate, remains one of the most promising solutions for the mitigation of CO₂ emission. In the self-reducing pellet, the average distance between iron ores and coals is much lesser than the distance between these particles when the ore and coal are charged by the conventional layer-by-layer method. This proximity of ore to coal in the pellet leads to a coupling reaction¹⁴⁾ and a reduction of the mass transfer resistance, thus enhancing the reaction rate. The pellet also needs the iron-slag separation to occur for the process to proceed to the refining step. Hence, the separation behaviour has often been studied as a key factor for control over the reaction in the pellet.^{15,16,17,18,19,20,21,22,23,24,25,26)} Matsumura et al.¹⁵⁾ reported reduction behaviour of the self-reducing pellet during heating up to 1500°C which reproduced the rotary hearth furnace condition. This report concluded that the iron melting due to the carburization reaction is the dominant controlling factor for the iron-slag separation.

Matsui et al.¹⁶⁾ reported the effect of minerals of iron ore, while Wibow et al.¹⁷⁾ and Chapman et al.¹⁸⁾ mentioned the effect of ash, on carburization. Both the studies indicated that the easy melting of mineral and ash is advantageous for the carburization reaction. Kim et al.¹⁹⁾ investigated the effect of slag wetting on the coke and iron phases in the iron-slag separation, with the help of in-situ observation with confocal laser microscopy and computational simulation based on a phase-field method. This study reported that the increment of the interfacial tension of the Fe–C melt/molten slag was the driving force behind the separation of the molten slag from the melt.

The self-reducing pellet has the great advantage that enables the utilization of low- grade iron ores such as ore fines, magnetite ores, and high Al₂O₃ ores. C. R. Borra et al.²⁰⁾ focused on the utilization of high Al₂O₃ iron ore for coal-based DRI processes and it was seen that the alumina content required a high temperature for the iron-slag separation. J. O. Park et al.^21,22) reported the effect of CaO addition as one of the counter measures for the high Al₂O₃- containing iron ore. They concluded that the reduction of the pellet with a highly basic slag with a low SiO₂ content slowed the slag melting, resulting in a delayed separation of metal and slag.

In our previous research,^17,23,24,25) an in-situ observation with confocal laser microscopy at high temperature was used to analyse the effect of slag melting on the iron-slag separation. It was concluded that this separation behaviour was dominated largely by the agglomeration of the liquid iron phase, and the residual solid iron phase and/or solid slag phase basically prevented the separation.²³⁾ However, the influence of the physical properties of the metal and slag melts on the separation was not clarified.

Hence, with an aim to focus on this influence, a numerical approach with practical multi- interfacial smoothed particle hydrodynamics (SPH) simulation²⁶⁾ for tracking the separation of two immiscible liquids, iron and slag, was undertaken in this study.

2. Methodology

In order to intensively focus on the effect of physical properties of the melts on the separation behaviour of two immiscible liquids, molten slag and melted Fe–C, a numerical simulation was performed for different cases corresponding to the experimentally observed iron-slag separation conditions in a previous work.²⁴⁾ The melting process including the iron carburization reaction was ignored in this report, although the influence of the coexisting solid phases was implied in the previous work.²⁴⁾

2.1. Iron-slag Separation Conditions for Numerical Analysis

In the previous work,²⁴⁾ an in-situ observation of the iron-slag separation during heating was performed with the help of a confocal laser-scanning microscope combined with an infrared image-heating furnace.²⁷⁾

The iron-slag separation process of a self-reducing pellet consists of the following steps. In the first stage, a reduction reaction occurs due to the direct and/or indirect contact of iron and coal during heating. In the second stage after slag formation, a smelting reduction of the iron oxide in the formed slag occurs due to coal. In the final stage, including the iron melting step due to the carburization by coal, slag and metal separate out into their individual phases. Thus, reduced iron, formed slag, and residual carbon exist in the composite in the final stage.

In order to simulate the final stage of the iron-slag separation process, electrolytic iron powder, carbon powder, and synthetic slag were chosen to imitate reduced iron, residual carbon, and slag, respectively. They were mixed well according to the mass ratios decided from the composition of the self-reducing pellet as shown in Table 1.²⁴⁾ The mixing ratios of these powders were decided based on the following concepts: (1) Three kinds of mixing ratios of carbon to iron powder (2, 3 or 4 mass%) were used; (2) The mixing ratio of slag to iron powder was fixed at 13.1 mass%, as derived from a practical self-reducing pellet;²⁸⁾ and (3) Four kinds of slags were prepared by completely melting and rapidly quenching of the mixtures of reagent grade oxide powders in Pt crucible under Ar atmosphere. The slag’s compositions were shown in Table 2²⁴⁾ and a ternary phase diagram of CaO–SiO₂–Al₂O₃ shown in Fig. 1.²⁹⁾ Slag A and B were designed based on a typical slag component in a blast furnace. Slag C and D were prepared to investigate the effect of slag viscosity.³⁰⁾ The slag’s melting behaviours are confirmed with the hot thermocouple method measurement as shown in previous report.²⁴⁾ Their liquidus temperature were almost same trends with Factsage calculation results as shown in Table 2.

Table 1. Basic mixing ratio of Fe powder, carbon powder, and synthesized slag for preparation of experimental tablets.²⁴⁾

Fe (mass%)	Carbon (mass%)	Slag (mass%)
86.8	1.8	11.4
86	2.7	11.3
85.2	3.6	11.2

Table 2. Slag compositions for experimental tablet.²⁴⁾

	Content (mass%)				Liquidus temperature (°C)
	Al2O3	CaO	SiO2	CaO/SiO2	Measured	Calculated
Slag A	20.5	37.9	41.6	0.91	1295	1312
Slag B	30	36.8	33.3	1.17	1475	1471
Slag C	21	25.6	53.4	0.48	1400	1444
Slag D	21	22.1	56.9	0.39	1400	1449

Fig. 1.

Experimental slag compositions in CaO–SiO₂–Al₂O₃ ternary phase diagram.²⁹⁾ (Online version in color.)

The grain size of the iron powder was 150 μm and the purity was 99.9%. The particle size of the carbon powder was 25–32 μm and the purity was 99.99%. The synthetic slag powder was prepared to the same particle size as that of carbon. The mixtures were pressed into tablets of a diameter of 5 mm using dies. A tablet was placed in the sample chamber of the infrared image heating furnace of the laser microscope. The inside of the chamber was kept at an inert gas atmosphere by purging with highly pure Ar gas (flow rate of 200 ml/min) during this experiment. The sample was heated up to 1100°C rapidly at the heating rate of 1000°C/min to prevent carburization at low temperatures. After the sample temperature reached 1100°C, the sample was continuously heated at 100°C/min until the tablet crumbled and changed into a sphere. Then, the sample was quenched immediately after confirmation of the changed shape. Phenomena on the surface of the sample during this heating experiment were directly observed and were recorded as a PC-based movie data. The iron part of the tablet was cut and polished after this experiment, and an average carbon concentration in this part was analysed with the help of a wavelength dispersion type electron probe micro analyser, EPMA.

Figure 2 shows sequential photographs obtained from the in-situ observation of iron-slag separation during the heating experiment. In the beginning, the shape of the sample changed due to the primary melt formation of Fe–C. Next, the primary slag liquid seeped onto the surface. Then, the liquid slag became spherical with the completion of the melting of slag. Finally, iron-slag separation was observed with the completion of the melting of iron. The iron- slag separation temperature was determined as the temperature at which the shape of the molten iron completely changed to spherical.

Fig. 2.

Laser micrographs of melting behavior of samples during heating experiment. (Online version in color.)

The relationship between the carbon concentration and the iron-slag separation temperatures is shown in Fig. 3. The concentrations of carbon in the tablets after heating were lower than the corresponding carbon mixing ratios, indicating that all the carbon powder in the tablet was not used for carburization, similar to the results in a previous report.²³⁾ This may be due to the elimination of a part of the carbon powder from the metal agglomerate during the iron-slag separation. Further, several iron-slag separation temperatures are observed to lie below the liquidus line of Fe–C, indicating that a complete melting of iron is not necessary to cause the iron-slag separation.

Fig. 3.

Relationship between the metal-slag separation temperature and carbon concentration in the iron part after the metal-slag separation. (Online version in color.)

Liquid slag phase ratios of each condition are given in Table 3. These values were calculated with the help of FactSage from the liquid phase composition at the separation temperature and the initial slag compositions. As implied in our previous work,²⁴⁾ all slags, except for Slag A, showed the possibility of separation even if they included solid phases. These cases are shown as open marks in Fig. 3. Slag A has a eutectic composition and melts at a temperature lower than both the separation temperatures. The residual solid phase in the slag might affect the slag physical properties. Haruki et al.³¹⁾ reported that the presence of dispersed solids in melts increased their viscosity. In this study, the separation of two immiscible liquids was used for an SPH simulation of the iron-slag separation, and the effect of the solid phase was excluded to simplify the complex phenomena.

Table 3. Slag compositions at the separation temperatures with physical properties and liquid phase ratios.

	Separation Temp. (°C)	Carbon content in iron (mass%)	Liquid iron phase ratio (mass%)	Liquid slag composition (mass%)			Liquid slag phase ratio (mass%)	Viscosity (Pa.s)	Density (kg/m3)	Surface tension (mN/m)	Iron-slag interfacial tension (mN/m)
				Al2O3	CaO	SiO2
Slag A	1376	1.67	66.2	20.5	37.9	41.6	100	3.23	2750	444	1210
	1317	3.22	100	20.5	37.9	41.6	100	5.91	2750	443	1260
Slag B	1527	1.39	100	30	36.8	33.2	100	0.88	2790	475	1220
	1421	2.09	100	28.6	36.0	35.4	83.4	2.55	2780	466	1230
Slag C	1444	1.6	100	21	25.6	53.4	100	12.1	2670	407	1186
	1353	2.89	100	17.3	26.9	55.8	80.6	34.9	2650	398	1236
Slag D	1453	1.51	100	21	22.1	56.9	100	19.3	2640	397	1175
	1351	2.02	74.2	17.2	22.6	60.2	80.5	65.8	2610	385	1192

Physical properties of liquid slags at the separation temperatures were estimated as described subsequently. Viscosities were estimated using an interpolation of reported values of Machin et al.,³²⁾ where the influence of the solid phase precipitation on the composition and viscosity was ignored. Densities were calculated using the estimation model by Mills et al.³³⁾ where the temperature dependence of the molar volume is adopted as a constant value of 0.01%/K. Surface tensions were calculated using the estimation model given by M. Nakamoto et al.³⁴⁾ Bretonnet et al., reported the interfacial tension between the CaO–SiO₂–Al₂O₃ slag at a constant CaO/Al₂O₃ mass ratio (c.a., 1) against Fe–C melt with a variation in the concentration of SiO₂ (0–42 mass%) in the slag and carbon (C: 1–4 mass%) in Fe–C melts at 1873 K. They concluded that the interfacial tension decreased with increasing SiO₂ concentration for the Fe–C melts with the lower carbon concentration (e.g., 1 mass% C) while this tendency was less pronounced as the carbon concentration in Fe–C melts increased. Interfacial tensions were estimated from an interpolation of the reported values of Bretonnet et al.,³⁵⁾ with the assumption that interfacial tension is governed by concentrations of carbon in molten iron and the silica in slag whereas temperature dependence of the interfacial tension is neglectable. The values are shown in Table 3. In order to simplify the simulation, physical properties of liquid Fe–C within the separation temperatures around 1400°C and a carbon concentration from 1.5 to 3.2 mass% were assumed to have the following values: ρ_m = 6800 kg/m³, μ_m = 0.01 Pa s, and σ_m = 1.25 N/m.³⁶⁾ The typical values of surface tension in ironmaking process comes from assumption that sufficient oxygen is adsorbed on the surface due to contact of molten iron with molten slag. These estimated values of slag and metal physical property were used in the SPH numerical simulation.

2.2. Calculation of CLS-SPH

The basic idea of the SPH method is the introduction of a kernel function W for flow quantities, such that the fluid dynamics are represented by a set of particle evolution equations. A formulation for a kernel function is based on an interpolation scheme that allows the estimation of a function f at a position r in terms of the values at the discretization points.   

$$f(\mathbf{r})\cong \int f({\mathbf{r}}^{\prime })W(\mathbf{r},h)dV$$(1)

The summation of function f can be replaced with a summation over particles only within the cut-off distance h from r_i owing to the compactness; thus, W(r_ij, h) = 0 when |r_ij| > h. The kernel must possess a form symmetrical to |r_ij| = 0. The kernel has at least a continuous first derivative and must satisfy the normalization condition, as ∫ W(r_ij, h) dr = 1. Within the h → 0 limit, the kernel is required to reduce to a Dirac delta function δ(r_ij). We chose the Wendland’s kernel to prevent having various kernel artifacts in a multiphase system:³⁷⁾   

$$W({\mathbf{r}}_{ij},\mathrm{\hspace{0.17em} }h)=\frac{21}{16\pi h^3}\{\begin{array}{l}{\left(1-\frac{q}{2}\right)}^4(2q+1),\mathrm{\hspace{0.17em} }q<2\\ 0,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}q\ge 2\end{array}$$(2)

where |r_ij|₀ is the interparticle distance corresponding to the initial conditions q = |r_ij|/h, and it is assumed that h = 1.05|r_ij|₀.³⁸⁾ The gradient form of Eq. (1) can be represented as:   

$$\nabla f(\mathbf{r})\cong -\int f({\mathbf{r}}^{\prime })\nabla W(\mathbf{r},\mathrm{\hspace{0.17em} }h)dV$$(3)

The SPH formulation can be transformed into a particle-based format to express the mass- area-density consistency process. The density of the particles was expressed in terms of the sum of the kernel functions of the N particles present within the radius of influence as follows:   

$${\rho }_i=\sum _{j=1}^N{m}_{j}W({\mathbf{r}}_{ij},\mathrm{\hspace{0.17em} }h)$$(4)

Therefore, the kernel function around particle i can be discretized using the following equation, which is derived from Eqs. (1), (2), and (3).   

$$f_i(\mathbf{r})=\sum _{j=1}^N\frac{m_j}{{\rho }_j}f({\mathbf{r}}_j)W({\mathbf{r}}_{ij},\mathrm{\hspace{0.17em} }h)$$(5)

The gradient of f_i can be represented as expressed in Eq. (6).   

$$\nabla f_i(\mathbf{r})=-\sum _{j=1}^N\frac{m_j}{{\rho }_j}f({\mathbf{r}}_j)\nabla W({\mathbf{r}}_{ij},\mathrm{\hspace{0.17em} }h)$$(6)

To avoid non-physical pressure fluctuation of dispersed phase, the multidimensional moving least squares interplant with constraint condition (CLS) method is introduced in the SPH framework.³⁹⁾ CLS involves a first-order consistent gradient approximation, which allows pressure smoothing, and its first derivative values are obtained using the method for the homogenous bulk phase. The detailed procedure for determining the parameters has been described in a previous report.⁴⁰⁾

The governing equations for a weakly compressible viscous flow are based on the relationship between the velocity of sound and the flow density under adiabatic conditions, as well as on the Navier-Stokes equations:   

$${\left(\frac{Dp}{D\rho }\right)}_s=c^2$$(7)

  

$$\rho \frac{D\mathbf{v}}{Dt}=-\nabla p+\mu {\nabla }^2\mathbf{v}+{\mathbf{F}}_s$$(8)

where p is the pressure, c is the velocity of sound, v is the velocity and F_s is the interfacial tension. Subsequently, Eq. (8) can be formulated for each particle as follows:   

$$\begin{array}{l}{m}_i{\displaystyle \frac{D{\mathbf{v}}_i}{Dt}}=-\sum _{j=1}^N\left({⟨p⟩}_i{V}_i^2+{⟨p⟩}_j{V}_j^2+{\prod }_{ij}\right)\nabla W_{ij}\\ \hspace{1em}\hspace{1em}\hspace{1em}+\sum _{j=1}^N{\displaystyle \frac{2{\mu }_i{\mu }_j}{{\mu }_i+{\mu }_j}}\left(V_i^2+V_j^2\right){\displaystyle \frac{{\mathbf{r}}_{ij}}{{\left|{\mathbf{r}}_{ij}\right|}^2}}{\mathbf{v}}_{ij}\nabla W_{ij}+{⟨{\mathbf{F}}_s⟩}_i\end{array}$$(9)

where Π is the artificial viscosity term, which is usually added to the pressure gradient term to help in diffusing sharp variations in the flow and dissipate the energy of the high-frequency term.⁴¹⁾ To determine the time derivative of pressure from Eq. (7), Tait’s equation of state can generally be used:⁴²⁾   

$${⟨p⟩}_i=\frac{c^2{\rho }_0}{\gamma }\left\{{\left(\frac{{\rho }_i}{{\rho }_0}\right)}^{\gamma }-1\right\}$$(10)

Where the adiabatic exponent γ = 7, and ρ₀ is the reference density (actual value).

Considering the interfacial force F_s, the interparticle potential force is defined using the space derivative of potential E(|r_ij|). F_s is localized at the liquid interface by applying it to the liquid elements in the transition region of the interface. The force per unit area ⟨F_s⟩_i is then converted into force per unit volume using the expression:⁴³⁾   

$${⟨{\mathbf{F}}_s⟩}_i=-2{\sigma }_i{\left|{\mathbf{r}}_{ij}\right|}_0{}^2{\left(\sum _{j=1}^{N}E\left(\left|{\mathbf{r}}_{ij}\right|\right)\right)}^{-1}\cdot \sum _{j=1}^N\frac{\partial E\left(\left|{\mathbf{r}}_{ij}\right|\right)}{\partial \mathbf{r}}\frac{{\mathbf{r}}_{ij}}{\left|{\mathbf{r}}_{ij}\right|}$$(11)

Here, σ_i is the interfacial tension force, and this term can be simply expanded to calculate the multiphase interfacial force on the boundary. Fowkes hypothesis is considered in calculating the interfacial force on the multiphase boundary.⁴⁴⁾ This theory states that in a system in which two immiscible liquid phases (liquid iron and molten slag) are in contact, the elements present at the two-phase interface are subject to forces. At the interface between liquid iron and molten slag, liquid iron interface elements receive the attractive force σ_m equivalent to the “surface tension” of liquid iron and the dispersion force σ_D from molten slag. The force acting on the interface elements of the molten slag can be described similarly. Hence, σ_D is expressed as follows:   

$${\sigma }_{\mathrm{D}}=\frac{1}{2}\left({\sigma }_m+{\sigma }_s-{\sigma }_{ms}\right)$$(12)

This simple hypothesis indicates that the unknown dispersion force σ_D and interfacial tension can be calculated explicitly using the surface tension as the input and the interfacial tension of the two liquids in contact as the conditions.

2.3. Conditions of Calculations

The separation behaviours of two randomly distributed immiscible liquids in the spherical sample including voids were numerically analysed in this study. Although the initial shape of the experimental sample was cylindrical, a sphere of a diameter of 3 mm was adopted as the initial shape for the calculations to account for the possibility of a concentration of force at the edge (Fig. 4). In order to simplify the simulation, the spherical object was assumed to consist of identical cubes of slag and metal with an edge length of 150 μm. The initial porosity of the object was assumed to be 30 vol%. In this study, a particle diameter d_p of 30 μm was adopted as a constant value in all the calculations. The unit number of particles of iron and slag was 234729 and 118250, i.e., the volumes of iron and slag were 6.34 × 10⁻⁹ m³ and 3.19 × 10⁻⁹ m³, respectively. The time step of this analysis was set to 10⁻⁸ s, and analysis time is 5 × 10⁻³ s.

Fig. 4.

Schematic of the initial condition in three-dimensional view.

3. Results

Figure 5 presents the temporal changes in three-dimensional distributions of liquid iron (grey colour) and molten slag (black colour) as a result of the model calculations. These results show that iron aggregates into a unitary sphere, and slag aggregates and gets discharged onto the iron surface. This trend suitably corroborates the results of the in-situ observation. A movie comparing the direct observation movie and the simulation animation of the separation behaviour of Slag D at 1351°C has been presented in the Supplementary information. In the animation, the liquid iron and molten slag are depicted as white and red particles, respectively. It was confirmed from the comparison, that the separation behaviour varied for each condition. In this study, the following method was used to quantitatively evaluate the separation behaviour.

Fig. 5.

Temporal changes in three-dimensional distributions of the liquid iron (grey colour) and molten slag (black colour) as per the model calculation.

As our primary focus is on the effect of the physical properties of the slag on the iron-slag separation behaviour, the interfacial area for each phase should be estimated. The main advantage of the SPH method is its rapid prediction of the interface area A from its initial condition A₀ and the interface-judged particle number n.   

$$\frac{A(t)}{A_0}\cong \frac{n(t)}{n_0}$$(13)

The counting procedure of n is based on following concept. Figure 6 shows a schematic of the influence region, including the interface between two phases. The n is counted as the number of particles belonging to each kind of interface within the influence radius h. The term n₀ is geometrically determined from the initial conditions. In this study, the number of the free surface particles of liquid iron and slag is 76890 and 18868, respectively, and the number of the initial iron-slag interface particles is 84386.

Fig. 6.

Region of influence, including the interface boundary. (Online version in color.)

Figure 7 shows the number of particles n the influence region at each time step of the separation of Slag C at 1444°C. The legends depict the reference particles on the left and the target particles on the right. Horizontal axis indicates the number of contacting object particles counted from each reference particles. A greater number of the contacting particle means that the reference particle is surrounded by object particles. The vertical axis indicated the number of reference particles which have the contact number of horizontal axis value.

Fig. 7.

Number of particles in the influence region at each time step of Slag C separation at 1444°C. (Online version in color.)

In the initial state, the numbers of free surfaces and interface were randomly distributed. They further formed two large peaks and valleys with respect to time. The interface and bulk regions were defined based on these two peaks. For example, for an iron surface, the peak of the greater number (~60 in case of the iron-iron interface in Fig. 7(c)), indicates that the reference particle is located in the bulk region. Meanwhile, a shorter peak of the iron-iron interface with a number of around 40, means that the reference particle is located in the interface or the free surface region. One valley appears between these 2 peaks at a value of around 47. In this study, this value was defined as the threshold of free surface and bulk region. This value was also applied to the slag-slag interface. In case of the iron-slag interface, a larger peak was located around 15, indicating an iron-slag interface, and the threshold value was around 8 in the valley. The variation of the summation of the number of particles, related to each object with time, was used to derive the temporal variation of the interfacial area normalized by the number of iron particles, as shown in Fig. 8. Normalized areas of free surface of liquid iron and iron-slag interface decreased with time, although the area of liquid slag free surface increased. A reduction in the free surface of iron and iron-slag interface implies an agglomeration of dispersed iron particles and progress of the iron-slag separation, respectively. Meanwhile, increase in the free surface of the slag indicates that the iron-slag separation leads to decrease in the contact positions with iron and increase in the free surface of new slag. Cross sectional observation of the numerical simulation gives reasonable information about iron agglomeration and slag dispersion as shown in Fig. 9.

Fig. 8.

Interfacial area temporal variation normalized by the number of iron particle of Slag C separation at 1444°C.

Fig. 9.

Temporal changes in the cross-sectional distributions of the liquid iron (grey colour) and molten slag (black colour) of Slag C separation behaviour at 1444°C.

4. Discussions

Comparison of the normalized interfacial area value at 5 ms, as a quasi-equilibrium state, was carried out for each case as shown in Fig. 10, to analyse the influence of the physical properties of the melts on the iron-slag separation.

Fig. 10.

Comparison of normalized interfacial area values at 5 ms in for physical properties in each melt. (Online version in color.)

The variations in the iron-slag interface values were especially focused upon as the separation behaviour indices in this comparison. The slag viscosity has a positive correlation to the free surface area of the slag and the iron-slag interface area, and a negative correlation to the free surface area of iron. This result indicates that highly viscous slag prevents iron-slag separation. In other words, a highly mobile slag may decrease the negative effect on the separation, because the dispersed slag may behave as a disturber for iron agglomeration. Surface tension and density of the slag has a negative correlation to its free surface area and the iron- slag interface area, and a positive correlation to the free surface area of iron. A high slag surface tension enables the agglomeration of the slag particles and decreases the number of disturbers for iron agglomeration. A slag with a higher density has a strong influence on the variation of interface due to a greater momentum.

Although the interfacial tension did not show any obvious effect on the separation in the range of above-mentioned comparison, the interfacial tension could result from the interfacial reaction.⁴⁵⁾ In case of a slag coexisting with FeO, the interfacial tension can drastically change, as reported by Popel et al.⁴⁶⁾ and Ogino et al.,⁴⁷⁾ mainly because oxygen can act as an active element at the interface, as explained by Tanaka et al.⁴⁸⁾ This condition obviously decreases the interfacial tension. Hence, additional numerical simulations were carried out by changing the value of the interfacial tension of slag B to 75% and 50%, to simulate ideal conditions. The simulation results are shown in Fig. 11, and a comparison of the normalized interfacial areas at 5 ms are shown in Fig. 12. It was seen that a high interfacial tension is favourable for the separation. In other words, a variation in the interfacial tension in this range has a clear effect on the separation. Here, the decrease in the interfacial tension due to the interface reaction was not taken into count. A combination of an FeO-containing molten slag and a carbon-containing Fe- C melt is expected to promote the smelting reduction reaction at their interface. As is well known, the interface reaction decreases the interfacial energy.⁴⁶⁾ The interfacial reaction thus may hinder the iron-slag separation. However, this kind of smelting reduction may form CO gas at the interface, which may influence the separation. Hence, such complex effects of the interfacial reaction need further investigation.

Fig. 11.

Effect of interfacial tension on normalized interfacial area temporal variation of Slag B separation at 1527°C.

Fig. 12.

Comparison of normalized interfacial area values at 5 ms for different interfacial tensions. (Online version in color.)

Although the physical properties of the iron melts were assumed to be constant in this study, the effect of oxygen in the Fe–C melt on the surface tension of iron itself was reported. Morohoshi et al.⁴⁹⁾ concluded that carbon by itself has no influence on the surface tension.

However, it reduces the oxygen activity in the melt, which increases the surface tension. Although this trend was reported within a lower carbon concentration region in their report, the effect of carbon and oxygen in iron requires a deeper investigation in future.

5. Conclusions

In conclusion, a combination of in-situ observation and a numerical simulation was used to investigate the influence of the physical properties of the melts on the iron-slag separation. The numerical approach involved adoption of the CLS- SPH method.

This CLS-SPH method was able to reproduce the iron-slag separation, with the iron aggregation forming a unitary sphere and the slag discharging onto the iron surface. Here, the major assumption was the absence of a solid phase and an interface reaction. Further, a slag with a low viscosity may promote the separation, because a dispersed slag could behave as a disturber for iron agglomeration. Moreover, a slag with a high surface tension enables the agglomeration of the slag particles and decreases the number of disturbers for iron agglomeration. Meanwhile, a dense slag has a strong influence on variation of the interface due to its greater momentum. Although the interfacial tension shows no obvious effect on the separation in the range of experimental values, the FeO-containing slag may inhibit the separation.

Supporting Information

A movie comparing the direct observation movie and the simulation animation of the separation behaviour of Slag D at 1351°C.

This material is available on the Website at https://doi.org/10.2355/isijinternational.ISIJINT-2020-218.

Acknowledgements

This study was funded by the Steel Foundation for Environmental Protection Technology (SEPT), Japan, grant number C-41-52, and partially supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI, grant numbers 15H04168 and 20H02491.

Nomenclature

Symbols

c: the velocity of sound, m s⁻¹

F: the force, kg m s⁻²

h: the radius of influence, m

m: the mass, kg

p: the pressure, kg m⁻¹ s⁻²

r: the arbitrary coordinates, m

r′: the particle positions, m

v: the fluid velocity, m s⁻¹

V: the volume, m³

W: smoothing kernel function, m³

Greek letters

γ: the adiabatic exponent (= 7.0)

ρ: the local density around the particle, kg m⁻³

ρ₀: the true density value of the material, kg m⁻³

μ: the viscosity, kg m⁻¹ s⁻¹

Π: the artificial viscosity, kg m⁻¹ s⁻¹

σ: the interfacial tension, kg s⁻²

Subscripts

i: particle index

j: the index of the neighboring particle around i.

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