Computational Fluid Dynamics Analysis of Radiation Characteristics in Gas–Iron Ore Particle Reactive Flow Processes at an Industrial-Scale in a Hydrogen-Based Flash Smelting Furnace

Abstract

Iron smelting is one of the primary sources of carbon emissions. The development of low-carbon ironmaking technologies is essential for the iron and steel industry to realize the “dual carbon” ambition. Hydrogen-based flash ironmaking technology eliminates traditional pretreatment steps such as sintering, pelletizing, and coking while using hydrogen as a reducing agent, significantly reducing carbon emissions. In the present work, a computational fluid dynamics approach is employed to conduct an in-depth analysis of the radiative properties inside the reaction shaft of a flash smelting furnace. The results illustrate that the lowest gas absorption coefficient and volumetric absorption radiation along the radial direction appear at y = 2.84 m, with the values of 0.085 m⁻¹ and 89,364.6 W/m³, respectively, whereas the largest values for these two variables in the axial direction can be obtained at h = 6.14 m with values of 0.128 m⁻¹ and 132,841.11 W/m³. The reduced incident radiation intensity under case 1’s condition led to distinct differences in the radiative temperature compared to the other four cases. The spatial distributions of the particle absorption and scattering coefficients exhibit excellent consistency. The thermal conductivities of all investigated cases depict similar trends along both the axial and radial directions. Volumetric emissive radiation presents a non-linear trend of first increasing and then decreasing, followed by the rise as the height decreases. This study highlights the critical role of hydrogen-based flash ironmaking technology in reducing carbon emissions and provides valuable insights into the radiative characteristics of its reaction shaft under different operating conditions.

1. Introduction

Iron smelting technology is primarily categorized into blast furnace ironmaking and non-blast furnace ironmaking, the former of which is the most commonly employed technology at present, offering advantages comprising technological maturity, high energy efficiency, scalability, and high production efficiency. Nevertheless, as the smelting process emits gases that increase the extent of atmospheric pollution, problems related to the blast furnace ironmaking process have become increasingly prominent, and its extremely high carbon emissions have become a critical constraint on progress toward achieving “net-zero emissions” targets [1].

To reduce carbon emissions during the blast furnace ironmaking process, ironmaking technologies have been optimized and innovated, such as blast furnace top gas recycling technology [2], oxygen enrichment and pulverized coal injection (PCI) [3], coke oven gas (COG) injection technology [4], enhanced sintering technology [5], hydrogen-rich blast furnace technology [6], and other blast furnace ironmaking technologies. In addition, Midrex [7], HYL/Energiron [8], coal-based direct reduction [9], flash ironmaking [10], Corex [11], Finex [12], HIsmelt [13], Hlsarna [14], and other non-blast furnace ironmaking technologies have been developed. Among them, the flash smelting ironmaking process, proposed by Sohn [15], employs a “suspension ironmaking” method to decrease iron oxides in concentrate into ferrum (Fe). As a pivotal technology for modern intensified smelting in non-blast furnace ironmaking, the flash smelting ironmaking process eliminates the sintering, pelletizing, and coking steps traditionally required in blast furnaces, offering excellent performance in terms of its low energy consumption, low emissions (especially CO₂), and short process [16].

The flash ironmaking process incorporates a complex multiphase heat and mass transfer process. The reactor used in the flash smelting process is mainly composed of a nozzle, reaction tower, settler, upward shaft, etc. The powder is generally injected into the reaction tower at high speed by the nozzle positioned at the top. The charge supply rate is 1~7 kg/h, with natural gas and oxygen flow rates of 25 m³/h and 20 m³/h, respectively.

As the material drops down, the temperatures of the reaction tower and the upward shaft increase to 1573 K, which is lower than that of the settler (1973 K). The high-temperature particles move in a downward motion in the reaction tower for 5~10 s and then fall into the settler for slag–iron separation and discharge. Simultaneously, the high-temperature flue gas is recycled after waste heat utilization, purification, condensation, and dehydration [17]. To investigate the thermodynamic and kinetic properties of iron ore particles during this process, numerous experiments have been carried out over the past few years. Chen et al. [18] examined the reduction kinetics of hematite concentrate particles (average particle size: 21 μm) with different partial pressures, within a temperature range of 1473 K to 1623 K. The results reveal that the reduction in hematite concentrate particles exceeds 90% in a pure carbon monoxide environment. Although the reduction rate is slower than that of hydrogen, it still suggests that carbon monoxide plays a role in the reduction in the hematite concentrate during the flash evaporation process. In addition, an experimental rate equation was obtained to predict the kinetics of carbon monoxide reduction in hematite concentrate particles. A theoretical basis was provided for the design of a new flash ironmaking reactor. Yang et al. [19] investigated the reduction kinetics of FeO utilizing H₂-CO mixtures of varying compositions at temperatures of 873 K, 973 K, and 1173 K. The results indicate that at low temperatures, carbon deposition reactions disrupt the kinetic profiles, whereas reduction curves exhibit regularity as the H₂ content increases at 1173 K. Moreover, the reaction rate of CO is linearly correlated with its concentration. The increase in reaction temperature leads to a significant expansion of pores in the reduction products. At this temperature, the iron phase develops and grows adequately, and the sintering phenomenon becomes more pronounced. However, conventional experimental methods typically have limitations, such as high cost, and difficulty in predicting the thermodynamic behavior under high-temperature conditions.

Computational fluid dynamics (CFD) has emerged as a powerful tool to predict gas–solid multi-physical field properties in flash ironmaking furnaces because of its efficiency and cost-effectiveness. Tan et al. [20] developed a numerical simulation platform to explore the effects of ore-feeding methods and reduced gas composition on reaction efficiency in a pilot-scale hydrogen-based flash smelting furnace. The results illustrate that the feeding of gas and pellets from the same lance results in a strong exchange of momentum and energy, which leads to a rapid decrease in the velocity and temperature of the pellets and significantly affects the residence time of the pellets in the furnace. Increasing the hydrogen concentration is effective in reducing the residence time, but even at the highest hydrogen concentration, the minimum residence time exceeds 2.2 s. When the hydrogen concentration is increased from 50 Vol% to 100 Vol%, the ore processing capacity can be increased from 0.60 kg/s to 0.80 kg/s. Under these conditions, the reduction degree exceeds 90% and the overall utilization rate of the reducing gas reaches 24.10%. This indicates that increasing the hydrogen concentration in the reducing gas can significantly improve the efficiency of the flash furnace. Yang et al. [21] proposed a novel counter-current descending reactor design to optimize the flash ironmaking process and predict gas–particle reaction flows by means of the CFD approach. This novel design exhibits higher degrees of reduction compared to co-current systems. At a gas flow velocity of 0.333 m/s, the counter-current reactor shows the highest gas utilization rate (35.7%) and reduction degree (74.5%). The high airflow rate results in a decrease in metal yield from 89.3% to 27.5%, but the reduction of fugitive particles increases. Cheng et al. [22] simulated a flash ironmaking process using pulverized coal and iron concentrate as raw materials, revealing the flow regime, temperature, gas composition distribution, and particle trajectories inside the reaction shaft. Both the flow and temperature fields present symmetrical distributions, where the oxygen in the central region diffuses rapidly to form a bell-shaped distribution, while the temperature is distributed in a wing-like pattern inside the reactor tower, reaching a maximum value of 2615 K at 5 m below the top of the tower. At 6 m below the top of the tower, the oxygen concentration is almost zero, while the carbon monoxide concentration peaks. In addition, more than 95 % of the iron particles are formed between 1.2 and 7.7 s. Abdelghany et al. [23,24] modeled a large-scale bench reactor (LSBR) for flash ironmaking based on the partial combustion of iron concentrate and natural gas and studied the effects of oxygen/natural gas ratios, gas flow rates, and powder inlet positions on product gas composition, temperature, and magnetite concentrate reduction rates. The results demonstarte that the highest reduction rate of magnetite concentrate occurs at an oxygen-to-natural gas ratio of 0.8. Increasing the total gas flow rate raises the reactor temperature but reduces particle residence times. The percentage heat loss from the walls is minimized when the total gas flow is set at 1810 SLPM (nominal residence time of 4 s). At this point, the reactor achieves 99.9% metallization at 2/3 of its length. The results of the above studies have clarified the relevant mechanisms of flash ironmaking, thereby laying a theoretical foundation for the involvement of flash furnaces and the optimization of the smelting process. Nevertheless, in industrial applications, flash ironmaking technology involves a gas–particle two-phase high-temperature reaction flow, which implies that radiative heat transfer plays an important role in the reaction inside the reaction shaft. Among the CFD approaches, several radiation models, comprising the DO model [25,26], P-1 model [27,28], DTRM model [29], etc., have been proposed and are commonly utilized. Among them, the DTRM model cannot be employed to predict the gas–particle systems. Moreover, the P-1 radiation model can be easily applied to complex geometries with curved coordinates and is easy to solve compared with the DO model with a low CPU requirement. Considering the computational cost, the P-1 radiation model was chosen for this study.

To fill this research gap, an industrial-scale hydrogen-based flash ironmaking reactor tower is taken into account to investigate the radiation characteristics of the gas–particle reaction process by means of the CFD technique. The reactions between the gas and particles inside the furnace are considered, together with a discussion of the influence of the spatial distribution of incident radiation, thermal conductivity, volume-absorbed radiation, etc., under different operating conditions.

2. Mathematical Model

The reduction process of iron powder particles in the flash smelting furnace involves momentum, mass, and heat transfer between gas–gas and gas–particle phases. The governing equations for the gas phase are constructed based on the Eulerian frame, treating the gas as a continuous medium. The flow characteristics of the gas are analyzed by solving the momentum conservation equations. The discrete phase model, based on the Lagrangian frame, is adopted to track the motion behaviors of individual particles. The standard k-ε turbulence model is employed to predict the turbulence characteristics of the fluid in the furnace due to its high convergence rate, low memory requirement, and favorable stability. Since the flash furnace smelting process is in a high-temperature operating atmosphere, the effect of radiative heat transfer on the heat field in the furnace is dramatic. The P1 radiation model, which can be applied to optical thicknesses larger than 1, is used due to its excellent computational efficiency, applicability, and flexibility.

2.1. Gas-Phase Governing Equations

The gas-phase governing equations include the mass conservation equation, momentum conservation equation, and energy conservation equation, which can be generally expressed as follows [30,31,32,33]:

$${\displaystyle \frac{\partial \rho }{\partial t}}+\mathrm{\Delta }\cdot (\rho {\mathit{u}}_g)=S_m$$

(1)

$${\displaystyle \frac{\partial }{\partial t}}(\rho {\mathit{u}}_g)+\mathrm{\Delta }\cdot (\rho {\mathit{u}}_g{\mathit{u}}_g)=-\mathrm{\Delta }p+\rho \mathit{g}+{\mathit{F}}_p$$

(2)

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho E\right)+\mathrm{\Delta }\cdot \left({\mathit{u}}_g\left(\rho E+P\right)\right)=-\mathrm{\Delta }\cdot \left(\sum _j{h}_j{J}_j\right)+S_h$$

(3)

where ρ, u_g, and P stand for the density, velocity, and pressure of the gas phase, respectively, while t and g denote instant time and gravity acceleration, respectively. S_m and F_p represent the source terms for mass and momentum exchange between the phases, respectively. E represents the total energy (including internal, kinetic, and potential energy). The heat source term, represented by the symbol S_h, signifies all non-conductive and non-convective heat effects such as chemical reactions and radiation. For the standard k-ε turbulence model, the turbulent kinetic energy k and dissipation rate ϵ are computed as [34,35]:

$${\displaystyle \frac{\partial }{\partial t}}\left(\rho k\right)+{\displaystyle \frac{\partial }{\partial x_i}}\left(\rho k{\mathit{u}}_i\right)={\displaystyle \frac{\partial }{\partial x_j}}\left[\left[\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_k}}\right]{\displaystyle \frac{\partial k}{\partial x_j}}\right]+G_k+G_b-\rho \epsilon -Y_M+S_k$$

(4)

$$\left.{\displaystyle \frac{\partial }{\partial t}}(\rho \epsilon )+{\displaystyle \frac{\partial }{\partial x_i}}(\rho \epsilon {\mathit{u}}_i)={\displaystyle \frac{\partial }{\partial x_j}}[\left[\begin{array}{c}\mu +{\displaystyle \frac{{\mu }_t}{{\sigma }_{\epsilon }}}\end{array}\right.\right]{\displaystyle \frac{\partial \epsilon }{\partial x_j}}]+C_{1\epsilon }{\displaystyle \frac{\epsilon }{k}}(G_k+C_{3\epsilon }{G}_b)-C_{2\epsilon }\rho {\displaystyle \frac{{\epsilon }^2}{k}}+S_{\epsilon }$$

(5)

where G_k and G_b represent the turbulent kinetic energy generation due to the mean velocity gradients and buoyancy, respectively. Y_M indicates the contribution of fluctuating expansion to the total dissipation rate in compressible turbulence. ${\sigma }_k$ and ${\sigma }_{\epsilon }$ are turbulent Prandtl numbers for k and ε. The density of the gas mixture is determined based on the volume-weighted mixing law, the specific heat capacity is calculated according to the mixing law, the thermal conductivity is set as a constant value of 0.0454 W/m·K. The viscosity of the mixture is evaluated using the mass-weighted mixing law. The details of the gas parameters are shown in

Table 1. Parameters for gas types.

Names of Gases	Density (kg·m−3)	Thermal Conductivity (W/m·K)	Absorption Coefficient (m−1)	Standard State Entropy (J·kgmol·K)	Standard State Enthalpy (J·kgmol)
H2	0.08189	0.1672	0	130,579.1	0
H2O	0.5542	0.0261	0.54	188,696.4	−2.418 × 109
O2	1.2999	0.0246	0	205,026.9	0

.

2.2. Governing Equations for the Solid Phase

The motion of iron ore particles is calculated using the Lagrangian discrete phase model, with the governing equation expressed as [36]:

$$m_p{\displaystyle \frac{d{\mathit{v}}_p}{dt}}=m_p{\displaystyle \frac{\mathit{g}({\rho }_p-\rho )}{{\rho }_p}}+{\mathit{F}}_{d,i}+{\mathit{F}}_{vm,i}+{\mathit{F}}_{pg}+{\mathit{F}}_{saff,i}$$

(6)

where m_p, v_p and ρ_p stand for the mass, velocity and density of the particles, respectively. F_d,i represents the drag force between the gas and particles. F_vm,i, F_pg,i, and F_Saff,i are the virtual mass, pressure gradient and Saffman list forces, respectively. Heat transfer between gases and particles entails reactive heat transfer, convective heat transfer, and radiative heat transfer, which can be calculated as follows [36,37]:

$$m_p{\displaystyle \frac{d(C_P{T}_P)}{dt}}=Q_r+Q_c+Q_{rad}$$

(7)

$$Q_C=\pi d_p\mathsf{\lambda }(2.0+0.6\mathrm{R}{\mathrm{e}}^{{\displaystyle \frac{1}{2}}}{(\mathsf{\mu }{C}_P/\mathsf{\lambda })}^{{\displaystyle \frac{1}{3}}})(T_g-T_p)$$

(8)

$$Q_{rad}={\epsilon }_p^{\prime }\sigma ({\epsilon }_g{T}_g^4-a_g{T}_p^4)$$

(9)

where C_p and T_p signify the specific heat and temperature of the particles, respectively. Q_r, Q_c, and Q_rad denote the heat flux generated by the reaction and the convective and thermal radiation between the gas and solid phases, respectively. d_p, $\mathsf{\lambda }$, and ${\epsilon }_p^{\prime }$ are the diameter, conductive heat transfer coefficient, and emissivity of the particles, respectively, while T_g, a_g, and ${\epsilon }_g$ denote the temperature, absorptivity, and emissivity of the fluid, respectively. $\sigma$ is the Stefan–Boltzmann constant. The parameters for the discrete phase are shown in

Table 2. Partial physical parameters of particles.

Chemical Formula	Density (kg·m−3)	Molar Mass	Standard State Entropy (J·kgmol·K)	Standard State Enthalpy (J·kgmol)
Fe2O3	5240	159.70	87,404	−8.24 × 108
Fe3O4	5180	231.55	146,147	−1.12 × 109
FeO	5700	71.85	60,752	−2.27 × 108
Fe	7870	55.85	27,280	0
CaO	3300	56.00	38,074	−6.35 × 108
Al2O3	3790	129.00	50,950	−1.68 × 108
SiO2	2634	60.68	41,463	−9.11 × 108

.

2.3. Reaction Modeling

In the hydrogen-based flash ironmaking process, chemical reactions primarily comprise hydrogen combustion and iron oxide reduction. The reaction processes of iron- particles at temperatures above 843 K are demonstrated in Figure 1. Reaction rates were calculated by utilizing Arrhenius equations, which are listed in

Table 3. Chemical reactions, pre-exponential factor, and activation energy.

Reaction Formula	Reaction Rate Equation	Activation Energy
${2\mathrm{H}}_2+{\mathrm{O}}_2{=2\mathrm{H}}_2\mathrm{O}$	R1 = 4.15 × 10−11 exp(−35,482.32/T) [H2]2[O2]	−462,801.26 + 108.52 T
${3\mathrm{Fe}}_2{\mathrm{O}}_3+{\mathrm{H}}_2{=2\mathrm{Fe}}_3{\mathrm{O}}_4+{\mathrm{H}}_2\mathrm{O}$	R2 = 1.307 exp(2331.01/T) [H2]	−27,482.75 − 91.12 T
${\mathrm{Fe}}_3{\mathrm{O}}_4+{\mathrm{H}}_2=3\mathrm{FeO}+{\mathrm{H}}_2\mathrm{O}$	R3 = 68.58 exp(4538.13/T) [H2]	42,289.27 − 54.52 T
$\mathrm{FeO}+{\mathrm{H}}_2=\mathrm{Fe}+{\mathrm{H}}_2\mathrm{O}$	R4 = 6.071 exp(3608.37/T) [H2]	15,275.68 − 11.17 T

[38].

3. Physical Model

The flash furnace studied in the current work primarily consists of four components, i.e., the nozzle, reaction shaft, settler, and upward shaft. The intricate nozzle structure includes a process gas inlet, dispersion air inlet, central hydrogen inlet, and iron ore particle inlet. The process gas inlet, located at the top of the reaction shaft, delivers the highest flow rate, enhancing axial and radial turbulent mixing of the gas–solid phases while providing an oxidizing atmosphere for the hydrogen-based flash smelting process. Iron ore particles are injected with high velocity from the particle inlet located below the process gas inlet. Hydrogen, serving as both a heat source and reducing agent, enters vertically downward through the central hydrogen inlet, concentrating primarily in the core region of the shaft. The high-speed jet introduced radially from the inlet of the dispersed air enhances the radial entrapment of the particles with the gas phase, increasing the particle expansion angle, dispersion intensity, and contact efficiency between the particles and the reducing gas. It also causes an “explosive” reaction kinetic condition, enabling the reduction reaction to complete within 3 to 6 s [17]. Subsequently, a portion of the particles proceed downwards into the bath consisting of the slag and metal phases, while the other particles enter the upward shaft from the gas region above the slag.

Given the high computational demands of simulating gas–particle reactive flows and the inherent symmetry of flash bath furnaces, half of an industrial-scale furnace is modeled, which optimizes computational resources while preserving simulation accuracy. Moreover, the present employment focuses on the thermal radiation characteristics of iron ore particles during the reduction reaction in the reaction tower, thereby omitting the upward shaft and the molten in the settler. Figure 2 presents a schematic of the hydrogen-based flash ironmaking apparatus, where the reaction shaft is 6 m in height and 4.3 m in diameter. The length, width, and height of the settler are 18.5 m, 2.75 m, and 1 m, respectively. The distribution of iron ore particles inside the reaction shaft is also illustrated in the figure, where different colors represent particles with varying temperatures. Specifically, particles colored dark blue, light blue, green, yellow, and red denote ambient-temperature particles, relatively low-temperature particles, heated particles, relatively high-temperature particles, and extremely high-temperature particles, respectively. For descriptive purposes, the reaction shaft is further divided into the core region and the diffusion region. In current employment, the reduction in particle size during solid combustion reactions is neglected due to the small effect of the change in particle size on the reaction process in a very short period of time. Moreover, to simplify the calculation process, the particle size distribution and the activation energy of different reduction steps were set as constants.

In the simulation of hydrogen-based flash ironmaking, the gas is assumed to be an incompressible ideal gas. Based on this assumption, a pressure-based solver is employed, with an implicit scheme selected for the solution. Such a choice is intended to enhance the stability of computational convergence, thereby obtaining a more stable solution. The discretization of the system of partial differential equations is carried out using the least squares cell-based method. Moreover, in the spatial discretization, the second-order upwind method is utilized.

Table 4. Boundary conditions and gas flow rate.

Serial Number	Boundary Name	Type	Value (kg/h)
1	Process gas inlet	Mass flow inlet	7920
2	Dispersion air inlet	Mass flow inlet	1008
3	Central hydrogen inlet	Mass flow inlet	792
4	Iron ore particle inlet	Mass flow inlet	792
5	Outlet	Pressure outlet	Atmospheric

shows the setting of each boundary condition.

In the present study, the structured hexahedral mesh is utilized, with a total of 239,574 elements, as depicted in Figure 3. Localized mesh refinement is applied to the nozzle due to the small size of the configuration and to the core region of the reaction shaft as a result of the high intensity of momentum, heat, and mass transfer between gas and solid phases. Grid independence is verified in this study by using the volume-averaged temperature and the exit temperature, as shown in Figure 4. The fluctuation in the exit temperature is within 10 K, while the maximum relative error of the volume-averaged temperature is only 1.96%. Thus, the number of 239,574 grids was chosen for the calculation in this study. The flash furnace processes 36 tons of iron ore per hour. The mass percentage composition of specific components is detailed in

Table 5. Particle composition and mass fraction of iron ore powder under different operating conditions (wt.%).

	Fe2O3	FeO	SiO2	Al2O3	CaO
Case 1	71.7	7.8	6.7	5.9	7.9
Case 2	80.0	1.4	6.6	1.8	10.2
Case 3	86.1	1.5	8.1	4.2	0.1
Case 4	89.2	1.6	6.4	2.7	0.1
Case 5	91.2	1.6	6.1	0.9	0.2

. In line with industrial production, the particle size of the iron ore is non-uniformly distributed, as shown in Figure 5.

4. Results and Discussion

In this section, the spatial distribution of radiative properties such as incident radiation, thermal conductivity, and volume-absorbed radiation within the reactor tower, as well as their variation trends along the axial and radial directions, is investigated. The data for the axial distribution diagrams are derived from the average values of the parameters at the same height, while the data for the radial distribution diagrams are obtained from the average values of the parameters at all heights at the same radial position.

Figure 6a–c present the spatial distribution of temperature, H₂O, and hydrogen, respectively. In the reaction tower, the distribution of temperature is high in the core region and low in the diffusion region. This is due to the high concentration of H₂ in the central region, which releases a large amount of heat when reacting with oxygen, resulting in a significantly higher temperature in the central region than in the diffusion region, which is the reason why the spatial distribution of hydrogen and temperature in the central region shows good agreement. Although the reaction between hydrogen and oxygen in the core region is more sufficient, the content of H₂O generated in the core region is relatively low due to the high content of hydrogen in this region, which results in the spatial distribution of H₂O being low in the core region and high in the diffusion region. Figure 6d illustrates the axial distribution of the particle species under case 1. The figure clearly shows that the reduction process of iron oxides is quite thorough. Regarding Fe₂O₃, as the starting material of the reduction reaction, its content continues to decrease during the descent of the iron ore particles. The content of Fe₃O₄, as the intermediate product of the reduction process, shows a tendency to increase and then decrease with the height of the iron ore particles. When the height drops to 5.91 m, the content of Fe₃O₄ reaches the maximum value of 17.15%. The reason for this phenomenon can be explained that during the reduction of Fe₃O₄ to FeO, Fe₂O₃ is also concurrently continuously reduced to Fe₃O₄, and the rate of Fe₃O₄ consumption is higher than the rate of its production, resulting in a decrease in its content with the decrease in the height of the iron ore particles. FeO is one of the raw materials of the reaction as well as an intermediate product. Since both FeO and Fe₃O₄ play the role of intermediate products, their content changes in a similar trend: as the height of the iron ore particles decreases, the content of both shows a tendency to increase and then decrease. Since the raw material contains FeO initially, the change in its content is relatively small. When the height decreased from 6.6 m to 5.91 m, the content of FeO changed from 7.78% to 11.08%. In the range of the remaining height of the reaction tower, its content continued to decrease from 11.08% to 1.97%. Fe, as the final product of the entire process and the reduction reaction, gradually increased with the decrease in the height of the iron ore particles from the initial 0% to 70.12%.

Figure 7a illustrates the spatial distribution of the gas absorption coefficient inside the flash bath smelting furnace. The gas absorption coefficient is defined as a constant in this study and the exact values are shown in Table 1. The regimented configuration of the reactor results in an approximately symmetrical distribution of the gas absorption coefficient along the radial direction. Notably, the asymmetrical distribution in the lower region of the apparatus is primarily attributed to geometric variations in this region and the diffusion of syngas in the positive y-direction. The gas dispersion behavior and its compositional distribution cause a dramatic gradient in the absorption coefficient within the reactor. Specifically, the absorption coefficient in the radial central region is lower than in the diffusion zone due to the relatively low absorption coefficient of H₂ injected vertically downward through the central inlet of the furnace, while components with higher absorption coefficients (e.g., H₂O) are concentrated in the vicinity of the reactor walls. Figure 7b reveals the axial distribution of the absorption coefficient of the gas phase. As the height decreases from 6.77 m to 6.14 m, the absorption coefficient under case 1 increases from 0.107 m⁻¹ to 0.128 m⁻¹. This can be explained by the decrease in the concentration of low-absorption components (H₂) and the increase in high-absorption components (H₂O) during the hydrogen oxidation combustion reaction. As the syngas undergoes downward movement from 6.14 m to 2.06 m, the reduction reaction between hydrogen and the iron ore particles moderates the generation rate of H₂O, leading to the gas-phase absorption coefficient decreasing from 0.128 m⁻¹ to 0.097 m⁻¹. Below a height of 2.06 m, fluctuations in the gas composition result in a trend in the absorption coefficient that first increases and then decreases. The radial distribution of the absorption coefficient is depicted in Figure 7c, Under case 1, The absorption coefficient attained a trough value of 0.085 m⁻¹ at y = 2.84 m, attributed to the high concentration of H₂ in the core region of the furnace. Furthermore, the difference in the lower iron oxide content of the feedstock under case 1 conditions resulted in a relatively minor change in the absorption coefficient compared to the other cases.

Volume absorption radiation, which refers to the portion of radiative energy absorbed and reduced while passing through a fluid medium due to the absorption effect of the medium, is visualized in Figure 8. As shown in Figure 8a, the distribution of volume absorption radiation within the reactor exhibits a pattern of low values in the central region but high values near the walls, attributed to the relatively small absorption coefficient in the core region. As a crucial indicator of the medium’s ability to absorb radiation, the absorption coefficient exhibits a high degree of coherence with the spatial distribution of volumetrically absorbed radiation, which can be calculated by using the following equation [39]:

$$Q_{abs}={\displaystyle \int \alpha IdV}$$

(10)

where Q_abs signifies the volume absorption radiation energy. α denotes the absorption coefficient of the fluid medium. I represents the radiation intensity. Additionally, α is the manual input value, while Q_abs and I are computationally calculated output values. Under the case 1 condition, as the height decreases from 6.77 m to 6.14 m, the increased steam concentration enhances the gas-phase absorption coefficient, leading to a significant augment in volume absorption radiation from 112,421.98 W/m³ to 132,841.11 W/m³ (Figure 8b). When the height further decreases to 2.06 m, the volume absorption radiation demonstrates a declining trend. This is because of the reduction reaction between H₂ and iron ore particles, which slows the generation of steam, thereby reducing both the absorption coefficient and volume absorption radiation. In the radial direction, the lowest volume absorption radiation for arbitrary operating conditions occurs in the core region. At y = 2.84 m, the minimum volume absorption radiation under the case 1 condition can be observed, with a value of 89,364.6 W/m³. This can be explained by the lower absorption coefficient in the core region compared to the diffusion region. The differences between the case 1 condition and the other four conditions are primarily due to variations in the raw material composition.

Incident radiation is defined as radiant energy incident from all directions on a specific point or control volume. The incident radiation can be calculated by Equation (11):

$$\nabla \cdot (\mathsf{\Gamma }\nabla G)-\alpha G+4\alpha n^2\sigma T^4=S_G$$

(11)

where $G$ is the incident radiation. $n$ is the refractive index of the medium. $\sigma$ is the Stefan–Boltzmann constant. $S_G$ is a user-defined radiation source. In this study, $S_G$ is defined as zero. $G$ is a computed output value, while $n$ and $\sigma$ are manual input values. Figure 9a illustrates the spatial distribution of incident radiation within the reactor. The highest incident radiation intensity appears in the central region of the furnace, followed by the near-wall region, while the lowest incident radiation intensity is symmetrically distributed on both sides of the nozzle along the axial centerline. This is attributed to the dense distribution of iron ore particles scattered around the central axis, which absorb significant heat during reduction reactions, resulting in local temperature drops that affect incident radiation. The low incident radiation near the nozzle is due to heat exchange between the freshly introduced low-temperature ore particles and the high-temperature gas phase. When the height decreases from 6.77 m to 4.77 m, the incident radiation intensity considerably increases from 1,019,068.78 W/m² to 1,090,361.81 W/m² (Figure 9b). The variation in the height interval 6.14 m ≤ h ≤ 6.77 m is ascribed to the increase in temperature, while the increase in the range of 4.77 m ≤ h ≤ 6.14 m is due to a decrease in the absorption coefficient. As the height further decreases, particularly in the range of 4.77 m to 2.4 m, the reduction reaction of iron ore absorbs heat, lowering the furnace temperature and gradually reducing the incident radiation intensity to 1,061,935.48 W/m². In the lower altitude range, the incident radiation intensity under the case 1 condition illustrates a distinctly different distribution pattern compared to the other four conditions. Specifically, in the height range of 0.25 m ≤ h ≤ 2.4 m, the incident radiation intensity under the case 1 condition continues to rise, reaching 1,086,711.31 W/m², whereas in the other four conditions, it increases and then decreases. The large difference in the trends is primarily due to the sufficiently reduction reactions of iron ore particles for case 1. Compared to cases 3, 4, and 5, the variations in case 2 are especially pronounced, mainly because of its higher concentrations of CaO, SiO₂, and Al₂O₃, which have lower absorption coefficients than iron ore. The radial distribution of incident radiation in the reactor for cases 2–5 exhibits a pattern of high- and low-intensity values in the core and diffusion regions, respectively, with the low values concentrated near the central axis, as shown in Figure 9c. This phenomenon is also related to the distribution of iron ore particles around the central axis and the temperature reduction caused by their reduction reactions. The differentiation of case 1 from the other cases in terms of raw materials results in lower values of incident radiation in the core region, leading to a different distribution from that of cases 2–5.

Figure 10a demonstrates the spatial distribution of radiation temperature in the apparatus. The central region along the radial direction has the largest temperature, while in the diffusion zone, the temperature initially decreases and then increases with increasing distance from the central axis. It is noted that the heat is absorbed by the high concentration of iron ore around the central axis during reduction reactions, thus reducing the incident radiation in the diffusion zone. Figure 10b illustrates the axial distribution of radiation temperature. As the height decreases from 6.77 m to 4.77 m, the enhanced incident radiation of the gas phase results in the radiation temperature increasing from 1447.9 K to 1479.59 K. In the range of the height of 4.77 m to 2.4 m, the persistent heat-absorbing reduction reaction of the iron ore powder particles reduces the radiation temperature to 1470.65 K. At the bottom of the reactor, the differences in radiation temperature between the case 1 condition and the other four conditions are primarily caused by variations in incident radiation. Figure 10c presents the radial distribution of radiation temperature. Except for case 1, the other four conditions exhibit symmetrical distribution patterns, where the largest radiation temperature appears in the core region of the furnace, whereas the radiation temperature in the vicinity of the reactor walls is slightly higher than in other regions. However, under case 1, the radiation temperature shows a unique distribution pattern, i.e., lower temperature in the core region and higher temperature at the sides. Specifically, the radiation temperature for case 1 drops to a minimum of 1458.91 K at the vertical position y = 2.6 m. This phenomenon can be explained by the fact that the iron ore powder particles can carry out the reduction reaction sufficiently under the condition of specific ore composition, while the incident radiation intensity in the core region is low, which together results in the above radiation temperature distribution characteristics.

Combining the distribution characteristics of incident radiation and radiation temperature, it is obvious that the areas with higher values of both are concentrated in the center. Accordingly, it can be reasonably deduced that reducing the diameter of the reactor tower will effectively improve the heating efficiency of iron ore particles, which is expected to increase the production output.

Thermal conductivity, which is a fundamental physical property of matter, characterizes the extent to which a material is capable of conducting heat through a unit area per unit temperature gradient and per unit time. The spatial distribution of gas phase thermal conductivity exhibits a prominent high-center and low-sides pattern, as shown in Figure 11a. This distribution characteristic correlates with the high-central and low-side temperature gradient observed along the radial direction inside the furnace. Figure 11b illustrates the variation in gas phase thermal conductivity at different heights. As the height decreases from 6.77 m to 5.44 m, the thermal conductivity of the gas phase increases significantly from 15.55 W/m·K to 118.21 W/m·K. This is primarily owed to the high-temperature distribution in the upper regions of the reactor, which intensifies molecular thermal motion and enhances heat transfer efficiency. However, as the height further decreases from 5.44 m to 0.625 m, the gas phase thermal conductivity decreases gradually from 118.21 W/m·K to 52.79 W/m·K, resulting from the phase transformation of iron ore particles during the reaction process. In the lower region of the furnace, the gas phase thermal conductivity exhibits an anomalous rising trend. Specifically, as the height decreases from 0.625 m to 0.25 m, the increasing syngas temperature leads to the gas phase thermal conductivity increasing from 52.79 W/m·K to 83.66 W/m·K. Figure 11c depicts the radial distribution of gas phase thermal conductivity inside the furnace. In the radial direction, the high and low gas phase thermal conductivity of the gas phase can be observed in the core region and in the vicinity of the furnace wall, respectively. Notably, In particular, the gas phase thermal conductivity peaks at y = 2.84 m (150.5 W/m·K), which is attributed to the high-temperature distribution in this region.

Volumetric emission radiation, defined as the radiative energy emitted from within a medium due to thermal radiation effects, is introduced in this section to characterize the complex gas–particle multiphase reaction flow in the apparatus. This variation can be described utilizing the Stefan–Boltzmann law [40], as shown in Equation (12):

$$Q_{em}=ϵ\sigma T^4$$

(12)

Here, Q_em represents the volumetric emission radiation energy. σ denotes the Stefan–Boltzmann constant. ϵ and T are the emissivity and absolute temperature of the medium, respectively. Additionally, σ and ϵ are the manual input values, while Q_em and T are computationally calculated output values. In the vicinity of the nozzle, the ambient temperature iron ore particles injected as feed material reduce the volumetric radiation of the gas phase (Figure 12a). As the height decreases, the reactor temperature gradually increases, particularly in the core region. This temperature variation causes variation in the absorption coefficient, thereby influencing volumetric radiation. Figure 12b depicts the axial distribution of the volumetric radiation. When the height decreases from 6.77 m to 5.44 m, volumetric radiation increases gradually from 116,005.97 W/m³ to 167,951.86 W/m³, attributed to the limited heat exchange process between the low-temperature feed material and the high-temperature syngas. As the height further decreases to 3.72 m, volumetric radiation increases drastically to 561,612.73 W/m³ due to significant increases in temperature and absorption coefficient. Within the range of 1.68 m ≤ h ≤ 3.72 m, volumetric radiation decreases from 561,612.73 W/m³ to 325,640.67 W/m³ with decreasing height. This decline is a result of the heat absorption by reduction reactions, which reduce the gas-phase temperature and thereby affect both the absorption coefficient and volumetric emission radiation. When the height decreases further to 0.25 m, volumetric radiation gradually rises, reaching 548,746.74 W/m³. This can be explained that the iron ore particles have almost completed the heat-absorbing reduction reaction to iron while the hydrogen still continues to react with oxygen to release heat, raising the temperature in the furnace. The radial distribution of volumetric radiation exhibits a high-center, low-sides pattern, as shown in Figure 12c. Owing to the high-temperature atmosphere in the core region, a peak of the volume emitted radiation with a value of 395,017.72 W/m³ can be observed at y = 2.84 m, while the low-temperature distribution on both sides results in a distribution of low-volume emitted radiation. Among the five operating conditions, case 1 has a significantly lower peak due to the efficient absorption of heat during the sufficient reduction reaction between the iron ore particles and the hydrogen.

Figure 13a presents the spatial distribution of the particle absorption coefficient within the furnace. The absorption coefficient in the vicinity of the nozzle is appreciably higher than in other regions, while this variable in the core region is lower than that near the wall, indicating that the particles are primarily distributed in the region adjacent to the central axis. Moreover, in the region where the reactor shaft intersects with the settler, a noticeable gradient variation in the particle absorption coefficient can be observed, attributed to the dispersive behavior of the particles entrained by the high-velocity jet. Figure 13b illustrates the distribution of the particle absorption coefficient with respect to the height in the reactor. In the upper region of the reactor (6.77 m ≤ h ≤ 6.14 m), the particle absorption coefficient significantly decreases from 8.13 m⁻¹ to 1.44 m⁻¹. This is due to the dispersive behavior of the particles entering the reaction shaft reducing the concentration of particles per unit volume, suppressing the gas-phase fluid and particle radiation intensity, which is manifested as a reduction in the absorption coefficient on a macroscopic scale. As the particles continued to descend (6.14 m ≤ h ≤ 2.06 m), the particle absorption coefficient increased from 1.44 m⁻¹ to 6.1 m⁻¹, which is ascribed to the variation in the primary phase composition of the particles as a result of the reduction reaction of the iron ore particles in this region. Conversely, in the lower part of the reactor (0 m ≤ h ≤ 2.06 m), the particle absorption coefficient decreases from 6.1 m⁻¹ to 2.56 m⁻¹, which can be explained by the reduced particle concentration after entering the settler. Notably, the variation in the particle absorption coefficients for the five conditions in the region h ≥ 2.4 m exhibits a high degree of consistency. In other regions (h < 2.4 m), the performance of case 1 appeared dramatically dissimilar to that of the other four cases, because of the lower Fe₂O₃ and higher FeO content in the former compared to the latter. Figure 13c plots the radial distribution of the particle absorption coefficient. The particle absorption coefficient gives an oscillatory trend of increasing and then decreasing with increasing y-axis coordinate values, followed by increasing yet again. For case 1, at y = 2.83 m, the particle absorption coefficient reaches its peak value of 8.54 m⁻¹. Further examination of the 3.79 m ≤ y ≤ 4.74 m region reveals that the particle absorption coefficients for case 1 are essentially stabilized, and the increasing trend is by no means significant. However, for the other four conditions, the particle absorption coefficient exhibits a noticeable increase in the same region. This discrepancy is due to the insufficient reduction reaction of the iron oxides, leading to an increase in the particle absorption coefficient as the y-axis coordinate increases in the 3.79 m ≤ y ≤ 4.74 m region.

The particle scattering coefficient is a vital parameter in radiation models, describing the scattering capacity of particles to radiation. Figure 14a visually presents the spatial distribution of the particle scattering coefficient in the furnace, which exhibits a pattern similar to that of the particle absorption coefficient, attributed to the shared dependence of both coefficients on the intrinsic properties of the material. Moreover, the values of the scattering coefficient are consistently lower than those of the absorption coefficient, proving the quantitative difference between the two variables. The axial distribution of the particle scattering coefficient is demonstrated in Figure 14b. Within the height range of 6.77 m ≤ h ≤ 6.14 m, the particle scattering coefficient decreases dramatically from 0.09 m⁻¹ to 0.016 m⁻¹. While the particles continue descending to 2.06 m, the scattering coefficient increases from 0.016 m⁻¹ to 0.068 m⁻¹. In the lower region of the furnace (0 m ≤ h ≤ 2.06 m), the scattering coefficient decreases from 0.068 m⁻¹ to 0.028 m⁻¹. This segmented variation along the axis reveals the complex behavior of the scattering coefficient at different heights. The radial distribution of the particle scattering coefficient inside the furnace is similar to that of the particle absorption coefficient, as shown in Figure 14c. The peaks of both variables are observable at y = 2.83 m, where the peak of the particle scattering coefficient is 0.095 m⁻¹. This further confirms the intrinsic connection between the spatial distribution of particle scattering and absorption characteristics, as well as their law of being driven by co-factors.

5. Conclusions

In the current work, we focused on the comprehensive exploration of hydrogen-based flash ironmaking technology using hydrogen as both the heat source and reducing agent. The process is capable of achieving near-zero carbon emissions, which is vital for the green transformation of the steel industry. The spatial distribution patterns of incident radiation, thermal conductivity, and volumetric absorption radiation under various operating conditions are systematically analyzed by means of computational fluid dynamics technology. The main conclusions are summarized as follows:

(1) Both the gas absorption coefficient and volumetric absorption radiation exhibit lower distributions at the core region of the reaction shaft, with the lowest values of 0.085 m⁻¹ and 89,364.6 W/m³ at y = 2.84 m, respectively. During the downward movement of the syngas, both of them demonstrated an identical trend due to the influence of the intrinsic properties of the fluid. The largest values of these two variables along the axial direction can be observed at h = 6.14 m, with values of 0.128 m⁻¹ and 132,841.11 W/m³, respectively.

(2) The spatial distribution of the incident radiation and radiant temperature and corresponding profiles along the height exhibits a remarkable consistency. In the core region of the reactor shaft, the radial distribution of radiant temperatures in case 1 differs considerably compared to the other cases due to the lower incident radiation of the former. When the radiant temperatures of the remaining cases gradually increase and attain the largest value, the radiant temperature of case 1 attests to the lowest value of 1458.91 K at y = 2.6 m. In addition, it is evident that higher radiation values are concentrated in the core region. Based on this observation, it can be deduced that reducing the diameter of the reactor tower is likely to improve the heating efficiency of the iron ore pellets. Such an improvement is expected to facilitate an increase in production volume, thus contributing to higher operational productivity.

(3) The absorption and scattering coefficients of the particles are intimately related to the content of iron oxides at different reduction extents and the thermal properties of the ore concentrates. The dispersion behaviors of the particles result in a decrease in the concentration of the solid phase inside the reaction shaft, which further reduces the absorption and scattering coefficients of the particles, accompanied by noticeable fluctuations. In the region of h < 2.4 m and 3.79 m ≤ y ≤ 4.74 m, cases 2–4 demonstrate superior coherence, with the discrepancies in case 1 being explained by the fact that it possesses lower iron oxide content.

(4) The thermal conductivity for all cases exhibits consistent trends along the axial and radial directions. The highest thermal conductivities of 118.21 W/m·K and 150.5 W/m·K can be observed at h = 2.4 m and y = 2.84 m, respectively. When the height decreases, the volumetric emission radiation initially increases, then decreases, and later rises again. The largest volumetric emission radiation along the radial direction appears at y = 2.84 m for case 1, which is dramatically different from the remaining cases due to the lower iron oxide content of the former.

In the present study, we undertook an in-depth investigation into the radiative heat transfer aspect of the hydrogen-based flash ironmaking process, thereby providing a theoretical foundation for the study of radiative phenomena within the overall heat transfer process of this technology. Notwithstanding this, the current methodology is encumbered by the high cost of hydrogen production and the complexities associated with its storage. Future research endeavors will predominantly focus on ascertaining the specific impacts of radiation and gas injection rates on production efficiency, as well as devising strategies to enhance the safety of the process.