Numerical Simulation of Vanadium–Titanium Blast Furnace under Different Smelting Intensities

Abstract

The blast furnace smelting of vanadium–titanium ore plays a crucial role in the efficient utilization of vanadium-titanium resources. In this research, a detailed numerical simulation study of the temperature, velocity, and concentration fields during the smelting process in a vanadium–titanium blast furnace was conducted. The actual production data from a 1750 m³ vanadium–titanium blast furnace was utilized, combined with softening and dripping parameters and material balance calculations, to develop a two-dimensional blast furnace model. This model was employed to analyze the effects of varying smelting intensities on the internal operating conditions of the furnace. The study found that as smelting intensity increased, significant changes occurred in the temperature fields and CO concentration fields within the furnace, thereby affecting the reduction efficiency of the burdens. Additionally, this research also shows that increasing the proportion of Baima pellets in the furnace will lead to the expansion of the soft melting zone and the upward movement of the soft melting zone. This investigation not only revealed the variations in the internal physical fields of the blast furnace under different operating conditions but also provided theoretical foundations and references for optimizing the design and operation of vanadium–titanium blast furnaces. By comparing the velocity field under different smelting intensities, it was found that the difference was small, which was mainly related to the expansion behavior of the pellets. These findings provide an important scientific basis for further improving the efficiency of blast furnace smelting and reducing costs.

1. Introduction

Vanadium–titanium magnetite, as a strategic resource, is stored in China with reserves of 135 million tons, accounting for 37% of the world’s total [1]. Extensive research has been conducted by predecessors, and processes for the efficient utilization of vanadium–titanium ore have been developed and perfected, providing a large quantity of high-quality vanadium–titanium products to the world annually. Compared to corresponding products without vanadium–titanium, the addition of vanadium–titanium can significantly improve the mechanical properties of the materials. For instance, the addition of an appropriate amount of vanadium to steel can enhance its wear resistance, strength, and hardness; titanium alloys, known for their high hardness and corrosion resistance, are widely used in fields such as aerospace and medicine [2,3]. These vanadium–titanium-containing products exhibit strong competitiveness compared to traditional products, so production units in the industry have more distinctive industrial characteristics. The expanded application of vanadium–titanium products will help promote the industrial development and upgrading of various countries. Among these resource utilization methods of vanadium–titanium magnetite, the blast furnace smelting process, in conjunction with the situation in China and many developing countries, enables the large-scale production of vanadium–titanium hot metal and slag, producing high value-added products while ensuring infrastructure construction.

Due to the titanium element being combined with carbon or nitrogen during the smelting process to form high-melting-point titanium carbide or carbonitride, the viscosity of the furnace slag is increased, making the separation of slag and iron difficult and reducing the desulfurization capacity, which significantly impacts the smooth operation of blast furnace smelting [4,5,6,7,8]. Therefore, research on the blast furnace smelting of vanadium–titanium ore has been predominantly focused on vanadium–titanium slag over the past several decades. The effects of TiO₂ content on the melting and viscosity properties of vanadium–titanium slag have been investigated by Jing et al. [9] and Pang et al. [10]. The distribution behavior of Ti in slag and hot metal has been studied by Jiao et al. [11], who found that a reduction in the operating temperature and carbon content in the hot metal can assist in decreasing the distribution of Ti into the hot metal. In order to improve the mobility of vanadium–titanium slag in blast furnace, Wang et al. [12] and Lin et al. [13] studied the effect of MgO and B₂O₃ content on vanadium–titanium slag and obtained their optimum ratio. The high-melting-point material in vanadium–titanium blast furnace slag is more sensitive to temperature, and compared with ordinary blast furnace slag, its existence plays a better role in protecting blast furnace lining. Typically, when the liquid slag and iron of a blast furnace pass through the cooling stave with low temperature in the furnace, the slag or molten iron can be solidified on the top to form a protective layer, thus reducing the erosion of the gas flow and the burden on the lining and enhancing the lifetime of the furnace lining [14,15]. With the increase in market demand for high-quality vanadium–titanium products, the smelting intensity of vanadium–titanium blast furnaces is increased to obtain more vanadium–titanium molten iron and vanadium–titanium slag. The smelting intensity of a blast furnace refers to the comprehensive dry coke amount or dry coke amount that can be burned in a day with an average effective volume per cubic meter of a blast furnace. It is an index of smelting speed. The improvement of blast furnace smelting intensity has an important influence on the change in multi-physical field in the furnace, which further tests the rationality of a blast furnace cooling system.

The blast furnace has been recognized as a large “black box” which complicates direct observations of the gas–solid flows within. Therefore, in the past, for a long time, the majority of researchers used experience to summarize the blast furnace smelting process. However, with the rapid advancement of computer technologies, the utilization of simulation and modeling to study substance flowing and multi-physics field changes within blast furnaces has become increasingly sophisticated. A two-dimensional full furnace model was established by Chu et al. [16], which examined the effects of operational conditions on the internal state of the furnace. Numerical simulations of gas flow redistribution in the lump zone of a blast furnace shaft were conducted by Zhu et al. [17]. To date, there have been few multi-physical field studies related to vanadium–titanium blast furnaces. This research focused on the temperature fields, velocity differences, and concentration fields in a vanadium–titanium blast furnace, revealing the internal working state of the furnace under various smelting intensities. This study is based on actual production data from a 1750 m³ vanadium–titanium blast furnace, combined with experimentally measured parameters of softening and dripping and material balance calculations. A two-dimensional blast furnace model was developed using FLUENT to conduct numerical simulations of this furnace. This research provided a detailed description of the model’s formulation, solution methods, computational principles, and their application. The effects of high (1.40 t/(m³·d)), medium (1.25 t/(m³·d)), and low (0.80 t/(m³·d)) smelting intensities on the internal state of the vanadium–titanium blast furnace were resolved, offering a theoretical basis for engineering applications. Low smelting intensity represents abnormal furnace conditions, while medium and high smelting intensities correspond to moderate and higher production efficiency, as well as the operational load of the blast furnace. The specific smelting intensity values were derived from a summary of historical data from the production site at Xichang Steel Vanadium of Pangang Group.

2. Model Development

A 2D model of the blast furnace was established based on the 2# blast furnace, which smelts vanadium–titanium magnetite, from Pangang Group Xichang Steel & Vanadium Co. Ltd. in China, as shown in Figure 1. A two-dimensional structure grid is developed and is shown in Figure 1b. The research object is the gas–solid reaction above the soft melt zone of vanadium–titanium blast furnace. Therefore, the two-phase flow is mainly considered in the mathematical model.

The model includes the flow, heat and mass transfer between gasses and solids, so the basic mathematical equations in the model include the conservation equations of mass, momentum, energy and chemical component transport, which can be described by Equation (1) under a steady state.

$${\displaystyle \frac{\partial }{\partial \mathsf{\tau }}}\left({\mathsf{\epsilon }}_{\mathrm{i}}{\mathsf{\rho }}_{\mathrm{i}}{\mathsf{\varphi }}_{\mathrm{i}}\right)+{\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left({\mathsf{\epsilon }}_{\mathrm{i}}{\mathsf{\rho }}_{\mathrm{i}}{{\mathrm{u}}_{\mathrm{i}}\mathsf{\varphi }}_{\mathrm{i}}\right)+{\displaystyle \frac{1}{\mathrm{r}}}{\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left(\mathrm{r}{\mathsf{\epsilon }}_{\mathrm{i}}{\mathsf{\rho }}_{\mathrm{i}}{{\mathrm{u}}_{\mathrm{i}}\mathsf{\varphi }}_{\mathrm{i}}\right)={\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left({\mathsf{\Gamma }}_{{\mathsf{\varphi }}_{\mathrm{i}}}{\displaystyle \frac{\partial {\mathsf{\varphi }}_{\mathrm{i}}}{\partial \mathrm{x}}}\right)+{\displaystyle \frac{1}{\mathrm{r}}}{\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left({\mathrm{r}\mathsf{\Gamma }}_{{\mathsf{\varphi }}_{\mathrm{i}}}{\displaystyle \frac{\partial {\mathsf{\varphi }}_{\mathrm{i}}}{\partial \mathrm{x}}}\right)+{\mathrm{S}}_{{\mathsf{\varphi }}_{\mathrm{i}}}{\sum }_{\mathrm{j}}{\mathrm{F}}_{\mathsf{\varphi }}\dots$$

(1)

where i is the phase, the symbol “ϕ” represents the variable to be solved, and “Γ” and S denote the effective diffusion and source term for each variable, respectively. The term F characterizes the interactions between different phases, primarily including the gaseous phase (g) and solid phase (s). Based on a coordinate system (u and v), temperature (T), and mass fractions of chemical components (m), variables such as velocity components are calculated by solving conservation equations. The pressures of the gas and solid phases are computed through the continuity equation, which is derived by substituting the single variable “ϕ” into a unified formula, represented as Equation (1). The heat exchange between the gas and solid phases is incorporated into the source term S. In the mass conservation equations, the reaction rates of chemical components during phase changes are considered within the term F. The governing equations are shown in

Table 1. Parameters in Equation (1) [18].

Items	$\mathsf{\varphi }$	$\mathsf{\Gamma }$	S
continuity	1	0	${\displaystyle {\mathrm{M}}_{\mathrm{O}}·\sum _{\mathrm{n}=1}^{\mathrm{N}}{\mathrm{R}}_{\mathrm{n}}}$
			${\displaystyle {-\mathrm{M}}_{\mathrm{O}}·\sum _{\mathrm{n}=1}^{\mathrm{N}}{\mathrm{R}}_{\mathrm{n}}}$
momentum	$\overrightarrow{{\mathsf{\nu }}_{\mathrm{g}}}$	0	$\nabla ·{\stackrel{\mathrm{̿}}{\mathsf{\tau }}}_{\mathrm{g}}+{\mathsf{\epsilon }}_{\mathrm{g}}\left(-\nabla \mathrm{P}+{\mathsf{\rho }}_{\mathrm{g}}·\overrightarrow{\mathrm{g}}\right)+{\overrightarrow{\mathrm{F}}}_{\mathrm{gs}}$
	$\overrightarrow{{\mathsf{\nu }}_{\mathrm{s}}}$		$\nabla ·{\stackrel{\mathrm{̿}}{\mathsf{\tau }}}_{\mathrm{g}}+{\mathsf{\epsilon }}_{\mathrm{g}}\left(-\nabla \mathrm{P}+{\mathsf{\rho }}_{\mathrm{g}}·\overrightarrow{\mathrm{g}}\right)$
energy	${\mathrm{H}}_{\mathrm{g}}$	${\mathrm{K}}_{\mathrm{g}}/{\mathrm{C}}_{\mathrm{P},\mathrm{g}}$	${\displaystyle {\mathrm{E}}_{\mathrm{gs}}+{\mathrm{M}}_{\mathrm{O}}·\sum _{\mathrm{n}=1}^{\mathrm{N}}\left({\mathrm{R}}_{\mathrm{n}}·∆{\mathrm{H}}_{\mathrm{n}}^{\mathrm{T}}\right)}$
	${\mathrm{H}}_{\mathrm{s}}$	${\mathrm{K}}_s/{\mathrm{C}}_{\mathrm{P},\mathrm{s}}$	${\displaystyle {\mathrm{E}}_{\mathrm{gs}}+{\mathrm{M}}_{\mathrm{O}}·\sum _{\mathrm{n}=1}^{\mathrm{N}}\left({\mathrm{R}}_{\mathrm{n}}·∆{\mathrm{H}}_{\mathrm{n}}^{\mathrm{T}}\right)}$

[18].

Here, Rn refers to different reactions; MO, represents the molecular weight of O, kg/kmol; $\overrightarrow{{\mathsf{\nu }}_{\mathrm{g}}}$ and $\overrightarrow{{\mathsf{\nu }}_{\mathrm{s}}}$ represent the physical velocity of gasses and solids, respectively, m/s; ${\mathrm{H}}_{\mathrm{g}}$ and ${\mathrm{H}}_s$ represent the specific enthalpy of gasses and solids, respectively, J/kg; ${\mathrm{K}}_{\mathrm{g}}$ and ${\mathrm{K}}_s$ represent the equilibrium constant of gasses and solids, respectively; ${\mathrm{C}}_{\mathrm{P},\mathrm{g}}$ and ${\mathrm{C}}_{\mathrm{P},\mathrm{s}}$ represent the specific heat capacity of gasses and solids, respectively, J/kg/K; ${\stackrel{\mathrm{̿}}{\mathsf{\tau }}}_{\mathrm{g}}$ represents the stress tensor of gas, Pa; ${\mathsf{\epsilon }}_{\mathrm{g}}$ represents volume fraction of gas; P represents pressure, Pa; ${\mathsf{\rho }}_{\mathrm{g}}$ represents the density of the gas phase, kg/m³; $\overrightarrow{\mathrm{g}}$ represents gravitational acceleration, m/s²; ${\mathrm{E}}_{\mathrm{gs}}$ represents volumetric heat flux, J/m³; and ${\mathrm{H}}_n$ represents the specific enthalpy of reaction n, J/Kg.

The reactions included in the model are listed in

Table 2. Reactions.

No.	Reactions	Chemical Reaction Rate
1	${\mathrm{Fe}}_{\mathrm{w}}\mathrm{O}\left(\mathrm{s}\right)+\mathrm{CO}\left(\mathrm{g}\right)$ $\to \mathrm{wFe}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$	$\mathrm{R}=\left({\displaystyle \frac{6{\mathsf{\epsilon }}_{\mathrm{ore}}{\mathrm{F}}_{\mathrm{ore}}}{{\mathsf{\Phi }}_{\mathrm{ore}}{\mathrm{D}}_{\mathrm{p}}}}\right){\displaystyle \frac{3\left({\mathrm{C}}_{\mathrm{CO}}-{\mathrm{C}}_{{\mathrm{CO}}_2}/{\mathrm{K}}_{1.1}\right)}{\frac{{\mathrm{D}}_{\mathrm{p}}}{2{\mathrm{k}}_{\mathrm{m}}}+\frac{{\mathrm{r}}_0^2}{{\mathrm{D}}_{\mathrm{eff}1.1}}\left[{\left(1-\mathrm{f}\right)}^{\frac{1}{3}}-1\right]+\frac{{\mathrm{D}}_{\mathrm{p}}{\mathrm{K}}_{1.1}}{2{\mathrm{k}}_{1.1\left(1+{\mathrm{K}}_{1.1}\right)}}{\left(1-\mathrm{f}\right)}^{\frac{2}{3}}}}$
2	${\mathrm{Fe}}_{\mathrm{w}}\mathrm{O}\left(\mathrm{s}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$ $\to \mathrm{wFe}\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$	$\mathrm{R}=\left({\displaystyle \frac{6{\mathsf{\epsilon }}_{\mathrm{ore}}{\mathrm{F}}_{\mathrm{ore}}}{{\mathsf{\Phi }}_{\mathrm{ore}}{\mathrm{D}}_{\mathrm{p}}}}\right){\displaystyle \frac{3\left({\mathrm{C}}_{{\mathrm{H}}_2}-{\mathrm{C}}_{{\mathrm{H}}_2\mathrm{O}}/{\mathrm{K}}_{2.1}\right)}{\frac{{\mathrm{D}}_{\mathrm{p}}}{2{\mathrm{k}}_{\mathrm{m}}}+\frac{{\mathrm{r}}_0^2}{{\mathrm{D}}_{\mathrm{eff}2.1}}\left[{\left(1-\mathrm{f}\right)}^{\frac{1}{3}}-1\right]+\frac{{\mathrm{D}}_{\mathrm{p}}{\mathrm{K}}_{1.1}}{2{\mathrm{k}}_{2.1\left(1+{\mathrm{K}}_{2.1}\right)}}{\left(1-\mathrm{f}\right)}^{\frac{2}{3}}}}$
3	$\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{CO}}_2\left(\mathrm{g}\right)$ $\to 2\mathrm{CO}\left(\mathrm{g}\right)$	$\mathrm{R}={\displaystyle \frac{{\mathrm{k}}_{3.1}{\mathrm{P}}_{{\mathrm{CO}}_2}{\mathsf{\omega }}_{\mathrm{C},\mathrm{s}}{\mathsf{\rho }}_{\mathrm{s}}{\mathsf{\epsilon }}_{\mathrm{s}}}{1+{\mathrm{k}}_{3.2}{\mathrm{P}}_{\mathrm{CO}}+{\mathrm{k}}_{3.3}{\mathrm{P}}_{{\mathrm{CO}}_2}}}$
4	$\mathrm{C}\left(\mathrm{s}\right)+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$ $\to \mathrm{CO}\left(\mathrm{g}\right)+{\mathrm{H}}_2\left(\mathrm{g}\right)$	$\mathrm{R}={\displaystyle \frac{{\mathrm{k}}_{4.1}{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}{\mathsf{\omega }}_{\mathrm{C},\mathrm{s}}{\mathsf{\rho }}_{\mathrm{s}}{\mathsf{\epsilon }}_{\mathrm{s}}}{1+{\mathrm{k}}_{3.2}{\mathrm{P}}_{\mathrm{CO}}+{\mathrm{k}}_{3.3}{\mathrm{P}}_{{\mathrm{CO}}_2}+{\mathrm{k}}_{4.2}{\mathrm{P}}_{{\mathrm{H}}_2\mathrm{O}}}}$

[19]. In the study of the internal processes of a furnace, the indirect chemical reactions occurring within are modeled using the unreacted core model. In this model, due to the presence of rate-limiting steps in the unreacted cores, only the reduction reactions of wüstite are considered.

In Table 2, ε_ore is the ore volume fraction, %; F_ore is the volume fraction of ore in the solid phase, %; Φ_ore represents the average shape coefficient of the ore, 1. K_i.i and Deff_i.i represent the equilibrium constant and effective diffusion coefficient, respectively, which are taken from Takahashi et al.’s work [20]. ki.i is the reduction rate constant which was taken from other work [21,22].

The standard k − ϵ turbulence model was employed to model the turbulent flow. The model constants used were turbulent viscosity coefficient (Cμ) = 0.09, TKE prandtl number = 1, TDR prandtl number = 1.3, energy prandtl number = 0.85, wall prandtl number = 0.85, and turbulent schmidt number = 0.7, with standard wall function.

The governing equations were discretized using the finite volume method (FVM), and the pressure–velocity coupling was solved using the SIMPLE algorithm.

The gas composition from the soft melting zone into the indirect reduction zone is calculated by the material balance, and the original condition of the material is listed in

Table 3. Composition of coke and pulverized coal, %.

Item	C	Ash	Volatile	Moisture	CO	CO2	H2	N2	O2
Coke	85.01	13.02	1.11	0.13	0.17	0.26	0.34	0.16	-
Coal	76.77	12.55	11.48	0.84	-	-	-	2.40	1.76

. The calculation process refers to our previous research [23]. The initial gas composition calculated by material balance is as follows: ① (smelting intensity 0.80 t/(m³·d))40.19% CO, 1.39% H₂, 58.42% N₂; ② (smelting intensity 1.25 t/(m³·d))42.96% CO, 4.64% H₂, 52.40% N₂; and ③ (smelting intensity 1.40 t/(m₃·d))44.03% CO, 5.72% H₂, 50.25% N₂.

At the inlet, a uniform velocity profile of gas was imposed, with velocities of 8.95 m/s, 9.00 m/s, and 9.05 m/s corresponding to low, medium, and high smelting intensities, respectively. The inlet temperatures of the gas under different smelting intensities were obtained from the softening–smelting experiment results (see Section 3.1 for details). The no-slip boundary condition was applied on all solid walls, assuming zero velocity at the wall surface.

The temperature of the cohesive zone corresponding to different smelting intensities is obtained from the softening droplet experiment. The sample composition and experimental scheme are listed in

Table 4. Chemical composition of furnace burden.

Item	Concentration, %
	TFe	FeO	CaO	SiO2	MgO	Al2O3	V2O5	TiO2
Sinter	49.68	8.39	12.76	6.57	2.51	3.12	0.30	4.53
Baima pellet	53.64	2.57	0.61	4.87	3.13	3.45	0.67	9.63
Self-produced pellet	54.73	1.18	0.44	3.94	3.11	3.40	0.70	9.62

and

Table 5. Softening droplet experimental scheme.

Item	Smelting Intensity, t/(m3·d)
	0.8	1.25	1.4
Sinter, %	75.00	66.03	61.78
Baima pellet, %	25.00	33.97	1.45
Self-produced pellet, %	-	-	36.77

, respectively. The experimental steps and instruments refer to our previous research [24]. The results of the initial gas composition and softening temperature were then loaded in the simulation with a consideration of all the transfers and reactions. The conservation equations were solved numerically by the finite volume method with commercial software ANSYS FLUENT (release 2023 R1) [25]. The simulation was considered to have converged when the residuals for each variable were less than 10⁻⁵.

The assumptions for this model were as follows: (1) the powder phase was not considered; (2) other chemical reactions such as reduction of carbonate decomposition and reduction of non-ferrous compounds were ignored; (3) the initial gas temperature was 100 K higher than the temperature of the soft melting zone; and (4) the melting of solids was ignored.

3. Results and Discussion

3.1. Results of Measurements on Softening–Smelting Properties and Model Validation

The results of the softening–dripping test experiments are illustrated in Figure 2. It can be observed from the figure that there is a significant range for the dripping zones corresponding to the three types of furnace burdens, with all exhibiting relatively high dripping temperatures (Td). This was attributed to the presence of high concentrations of difficult-to-reduce materials, the oxides of vanadium and titanium, which required higher reduction temperatures. Further observations from Figure 2 reveal that as the proportion of Baima pellets increases, the cohesive zone of the mixed burdens become wider, with both the onset of softening and the beginning dripping temperatures decreasing. When a substantial amount of Baima pellets were replaced by the self-produced pellets, an improvement in the softening–melting indices of the mixed burdens was noted, specifically seen as a decrease in the position of the s cohesive zone and a thinning of its thickness. The material analysis in Table 4 reveals a noticeable difference in the FeO content between the two types of pellets; the FeO content in Baima pellets is more than double that of the self-produced pellets. FeO easily forms a hard-to-reduce fayalite phase with SiO₂, which hinders the reduction process [26]. Consequently, Baima pellets with higher FeO content are more difficult to reduce than self-produced pellets. The self-produced pellets, having better reducibility, can rapidly reduce to form metallic iron phases, thus raising the overall melting point of the furnace burdens and causing a lowering of the softening band.

The main composition and temperature of the top gas obtained by bringing the above drop temperature into the numerical simulation are listed in

Table 6. Comparison of top gas parameters.

Item		Simulated Values	Actual Value	Error
Smelting Intensity	Gas Parameters
0.80 t/(m3·d)	CO, %	23.40	24.22	3.38%
	N2, %	57.89	58.78	1.51%
	Temperature, K	428.75	428.00	0.18%
1.25 t/(m3·d)	CO, %	24.91	25.55	2.50%
	N2, %	51.96	53.04	2.03%
	Temperature, K	493.30	494.00	0.14%
1.40 t/(m3·d)	CO, %	24.34	25.01	2.68%
	N2, %	51.41	52.67	2.39%
	Temperature, K	481.60	482.00	0.08%

and compared with the actual blast furnace gas composition and temperature. It can be observed from Table 6 that the simulation results of the two main gas components are slightly lower than the actual blast furnace value, while the gas temperature is very close to the actual value. These simulation results agree with the actual BF in-furnace state, and the error between the top gas parameters and the actual value is less than 5%, suggesting that the developed model is reliable.

3.2. The Effect of Different Smelting Intensities on Multi-Physics Field of Blast Furnace

The simulation results of the multi-physics fields in the vanadium–titanium blast furnace are displayed in Figure 3, Figure 4 and Figure 5. Figure 3 illustrated the variation in the temperature field with different smelting intensities. Based on the characteristics of the temperature changes shown in the figure, the temperature field can be divided into three regions: (1) low-temperature areas, entailing temperatures below 831 K; (2) medium-temperature areas, entailing temperatures between 831 and 1313 K; and (3) high-temperature areas, entailing temperatures above 1313 K. From Figure 3, it is observed that at a smelting intensity of 0.80 t/(m³·d), the medium and high temperature intervals are narrower, while the low temperature interval is larger. When the smelting intensity is increased to 1.25 t/(m³·d), the medium and high temperature intervals noticeably widen, with an increase of approximately 23%. At the smelting intensity of 1.40 t/(m³·d), the high temperature interval slightly declines compared to previous levels, with a reduction of less than 5%, and the lowest temperature reached in the low-temperature area is also lower. The darker spots on the upper part of the left and right sides indicate the dynamic nature of the process. These spots on the left and right side at the upper part reflect changes over time, and the simulation uses a time-dependent model with a time step of 1 s to capture these variations.

At the same time, a similar pattern was displayed in the CO concentration field, as shown in Figure 4. As the smelting intensity progressively increases, the concentration of CO in the height of the blast furnace gradually rises. In conjunction with the analysis of the previously mentioned softening–dripping behavior, at the lower smelting intensity (0.80 t/(m³·d)), the burden predominantly consists of sinter, which is relatively easy to reduce; thus, a lower concentration of CO was sufficient to ensure the continuation of indirect reduction in the high-temperature areas near the softening zone. As the proportion of harder-to-reduce pellets gradually increased in the mixed burdens, a higher reduction potential within the blast furnace was required, necessitating an expansion of the CO concentration interval. Additionally, increasing the temperature was beneficial for promoting the reduction of iron ore by CO, thereby necessitating the expansion of the medium- and high-temperature areas, as demonstrated in the temperature fields at medium and high smelting intensities. In Figure 4, the concentration fields at medium and high smelting intensities appear similar, but when combined with previous material balance calculations, it can be noted that the initial CO concentration at high smelting intensity is higher. This indicates that, compared to medium smelting intensity, CO was consumed more rapidly at high intensity. This rapid consumption was attributed to the higher proportion of easily reducible self-produced pellets replacing Baima pellets at high smelting intensity. Indeed, due to the use of more difficult-to-reduce Baima pellets, the medium and high temperature intervals at medium smelting intensity are somewhat larger than those at high smelting intensity.

The velocity fields within the blast furnace at different smelting intensities are displayed in Figure 5. It can be observed that the trajectories of the gas flow at high, medium, and low smelting intensities show only minor differences, with noticeable inflection points marked by red and blue dashed rectangular boxes. These subtle differences in inflection points were speculated to be associated with the behavior of pellet ore within the furnace. When interacting with reducing gasses inside the blast furnace, the reduction reaction of pellets occurs step by step according to the following steps: Fe₂O₃→Fe₃O₄→FeO→Fe at temperatures above 843 K, accompanied by expansion due to lattice changes, carbon deposition, and iron whisker formation, followed by shrinkage due to the sintering action of the Fe phase [27]. The volume expansion of the pellets depends on their inherent properties, and it is generally required that the expansion rate be below 20%. The specific degree of expansion over time varies with changes in temperature and atmosphere. The substantial amount of pellet ore used in this blast furnace made their expansion a significant factor influencing the trajectory of gas flow. Upon leaving the softening zone, the gas stream encounters furnace burdens at various states of reduction. If the burden is more easily reduced, the contraction of pellets can decrease porosity at that location, hindering the movement of gas and causing it to divert, as observed at a smelting intensity of 1.4; sinter maintains a more stable particle size, resulting in smaller changes in gas flow near the cohesive zone at lower pellet ratios (e.g., at the smelting intensity of 0.8). For pellets with slightly poorer reducibility, still near complete reduction, the higher porosity allows the gas to pass smoothly (as seen at the smelting intensity of 1.25). As the gas continues to rise, burdens with uniform change in temperature and reducing atmosphere were encountered. The streamlines alter minimally until the gas reaches the top of the furnace, where increased proportions of smaller pellets again cause a directional change in the gas flow, as demonstrated by the velocity fields at medium and high smelting intensities.

3.3. Limitations of the Current Model

This study focuses on investigating the distribution and comparison of multi-physical fields within a vanadium–titanium blast furnace under varying smelting intensities. While validation against practical data has confirmed the model’s ability to effectively capture the overall behavior of the furnace, several important limitations remain.

A primary limitation lies in the simplified grid structure used in the model, which was implemented to balance computational efficiency with accuracy. Although this approach is adequate for simulating the macroscopic distribution of temperature fields, carbon monoxide concentration, and flow velocity within the furnace, it does not provide the resolution needed to describe more intricate internal behaviors. For example, the current model is limited in its ability to accurately simulate gas flow dynamics near the furnace walls, particularly in the peripheral zones where complex interactions occur. These flow characteristics can significantly influence the overall efficiency of the furnace, especially in terms of heat transfer and material movement. Moreover, the model lacks the precision needed to pinpoint critical micro-scale phenomena, such as the exact initiation point of the Boudouard reactions. These localized processes are key to understanding the furnace’s overall performance and efficiency but require a much finer computational grid to capture them with sufficient detail. As a result, while the model serves as a useful tool for understanding general trends and patterns within the furnace, the model’s ability to describe micro-scale phenomena needs improvement.

Future work will focus on addressing these issues by exploring methods to optimize the model with a more refined grid. This will not only enhance the accuracy of the simulations but also improve the model’s applicability to complex real-world scenarios. By doing so, we aim to provide a more robust tool for researchers and practitioners in the field, facilitating better decision making and efficiency in blast furnace operations.

4. Conclusions

In this study, a 1750 m³ blast furnace for smelting vanadium–titanium ore was taken as the object. Combined with a material balance calculation and softening–dripping experiment, a 2D model from the top of the furnace to the cohesive zone was established to simulate the temperature field, concentration field and velocity field of the blast furnace under high, medium and low smelting intensity. The following conclusions were drawn:

(1)

The reduction capability of Baima pellets, in comparison to self-produced pellets, was found to be inferior. This led to an expansion of the softening–smelting interval and an upward shift of the cohesive zone when the proportion of Baima pellets in the furnace charge was high.

(2)

With the increase in smelting intensity, the medium- and high-temperature zones within the blast furnace temperature field noticeably expanded, with an increase of approximately 23%. However, a slight decrease (less than 5%) in the high-temperature area was observed when the more reducible self-produced pellets replaced the Baima pellets.

(3)

As smelting intensity gradually increases, the concentration of CO in the upper regions of the blast furnace also rises, thus ensuring the smooth progression of the reduction in charge.

(4)

The differences between the velocity fields corresponding to different smelting intensities were minor, and the slight changes in trajectories were associated with the expansion behavior of pellets within the furnace.