Numerical Simulation of the Operating Conditions for the Reduction of Iron Ore Powder in a Fluidized Bed Based on the CPFD Method

: In this work, the computational particle ﬂuid dynamics (CPFD) method is used to simulate the high-pressure visual ﬂuidized bed experimental equipment independently designed and developed by the experimentation of the ﬂuidized reduction process of iron ore powder. A numerical model for reducing iron ore ﬁnes in a three-dimensional ﬂuidized bed is established, and the model is veriﬁed by combining numerical simulation and experimental testing. Moreover, the inﬂuences of different reducing factors on the reduction effect in the process of the ﬂuidized reduction of iron ore ﬁnes are simulated in detail. Via the CPFD simulation of the ﬂuidized reduction of iron ore ﬁnes, the optimal reduction pressure is found to be 0.2 MPa, and the optimal reducing gas is found to be H 2 . Moreover, the optimal gas velocity is 0.6 m/s, and the optimal reduction temperature is 923 K. This conclusion is consistent with the experimental measurements, so the simulation results can be used to verify the reliability of the optimal operating conditions.


Introduction
The fluidized direct reduction process has the advantages of a large gas-solid contact area, a uniform temperature and concentration, good heat and mass transfer conditions, and high operating efficiency [1][2][3]. However, due to the complex multiphase flow system, particles will be entrained by the airflow to cause material loss, and the particles will cause wear and tear to the equipment [4][5][6]; consequently, the scale-up of industrial-scale fluidized beds faces huge challenges. Experimental research and numerical simulation are the main ways to study gas-solid two-phase flow, and experimental measurement data are the basis of theoretical analysis. At present, relevant scholars have carried out large amounts of experimental measurements and research on the internal flow mechanism of the fluidized bed, such as the minimum fluidization velocity, bed height, and local particle aggregation [7][8][9]. However, due to the limitation of the experimental conditions and the complexity and uncertainty of gas-solid two-phase flow, it is difficult to obtain specific information at the micro-level, such as the particle motion state and gas distribution [10][11][12], and experimental measurement has the disadvantages of a large amount of engineering, a high cost, a long cycle, and limited measurement methods. With the continuous development of computer technology, numerical simulation has become an important means by which to study dense gas-solid two-phase flow, and plays an increasingly important role in supplementary experimental research [13][14][15][16][17]. Numerical simulation can be used to accurately calculate, predict, and study gas-solid two-phase flow, and to more intuitively obtain the process and details of the gas-solid flow on the particle and grid scales, which are difficult to measure in an experiment. Moreover, this method is not limited by the measurement means, and can yield rich micro-information about the core factors [18][19][20]. Furthermore, numerical simulation can be used to directly calculate equipment of any scale, and can provide prediction results for the development of new reaction equipment to aid in the

Experimental Steps and Protocols
The reduced iron ore powder used in this experiment was Newman ore from Australia, the shielding gas was N 2 , and the reducing gases were H 2 , CO, and a mixture of H 2 and CO. The main device was a pressurized visible fluidized bed ( Figure 1) with double stainlesssteel tubes as the reactor, and the inner tube was a fluidized bed. First, N 2 was introduced into the fluidized bed to discharge all the air and raise the pressure to 0.5-0.6 MPa to check the air tightness of the device. After heating the fluidized bed to the set temperature, the N 2 valve was closed, and the reducing gas was introduced. The gas was regulated by a flowmeter and gas mass flow controller to allow the gas to enter the bed to reach the required linear speed and control the inlet flow of the gas. The experiment was initiated after the pressure stabilized to the set pressure value. A quantitative amount of fine mineral powder particles (500 g) was placed into the fluidized bed and reacted with the reducing gas for the set time, and then the experiment was stopped. After cooling to room Processes 2022, 10, 1870 3 of 18 temperature, the mineral powder in the fluidized bed was removed, and the samples were analyzed by the potassium dichromate volumetric method and the ferric chloride titration method to determine the contents of metallic iron (M Fe ) and total iron (T Fe ) and calculate the metallization rate η. The higher the metallization rate, the better the quality of the reduced mineral powder. To reduce the experimental error, the measurement was repeated twice, and the average value was taken as the final experimental result. The experimental scheme is shown in Table 1.  The metallization rate is calculated as follows: where η is the metallization rate, M Fe is metallic iron (g), and T Fe is total iron (g).

Governing Equations
In Barracuda Virtual Reactor 17.4.0 software, large eddy simulation (LES) was used for the turbulence model of the gas field, the MP-PIC method was used for particles in the solid phase, the normal stress of particle collision and the gas-solid heterogeneous reaction were calculated based on the Euler grid, and the properties of discrete particles were interpolated to the Euler grid. The solution was then interpolated back to the particles, and this process was realized by the interpolation operator. In order to make the grid size of the fluid phase larger than that of the particle phase, the total number of grids was finally determined to be 69,584 by grid-independence analysis when dividing the fluidized bed grid model, and the grid size was 3.1579 × 3.1707 × 3.1098, which had the least effect on the pressure and temperature variations in the simulation. The drag force between the gas and solid was calculated by the Wen-Yu model, and the "calculated particles" with the same properties were packaged. Chemical reactions were combined with the complex hydrodynamics calculations of gas-solid fluidized beds. The setting of an "equivalent particle size" was adopted for the method based on CPFD, and small particles clustered to form large particles, which were replaced by equivalent particles when solving the drag force. The calculation method and fluidization phenomenon of large particles were revealed, and the thermal conductivity effect brought by agglomeration was simultaneously simulated. The fluidized bed model in the simulation was established and simplified according to the reaction principle presented in Figure 1. The main part was a cylinder with a height of 0.78 m and a diameter of 0.30 m. The system grid is presented in Figure 2. The main air intake was located at the bottom of the entire system. The origin was set at the center of the bottom of the riser, and the z-axis was opposite to the direction of gravity. An overview of the main governing equations is provided in Table 2.   [35][36][37][38].

Equation Equation Expression
Continuity equation ∇ ρ g a g u g + ∂ ∂t ρ g a g = δ . m s , − f dm s dt dT s du s dm s = δ . m

Momentum equation
−a∇p + ∇τ g + ρ s a g u g g + F = ∇ ρ s a g u g u g + ∂ ∂t ρ g a g u g Component transport equation δ . m g,i + δ . m s,i + ∇ ρ g a g D g Y g,i = ∇ ρ g a g Y g,i u g + ∂ ∂t ρ g a g Y g,i Energy conservation equation ∂ ∂t a g ρ g h g + ∇ a g ρ g h g u g = a g ∂p ∂t + u g ∇p + ϕ − ∇ a g q + Volume fraction of particles in unit grid f V p dρ s dV p du s = ε s Local fluid wall heat transfer coefficient

Chemical Reactions
All elemental reactions and reaction rates can be determined for the many chemical reactions present in a fluidized bed. However, the large number of coupled reactions in large-scale industrial reactors cannot be calculated within hundreds of seconds of simulation time [39][40][41]. The reduction reaction system between the particles and gas phase considered in this study is similar to that considered by Parisi et al. [36]. The reduction process of Fe 2 O 3 actually includes Fe 2 O 3 →Fe 3 O 4 →FeO→Fe [36]. In the simulation, the intermediate process was omitted, and the chemical reaction was directly reduced from Fe 2 O 3 to Fe. Because the water-gas shift reaction (WGSR) = reaction (3) − reaction (2), the water-gas reaction is not linearly independent and implicit in the system, and its reaction rate is not listed. The reaction of the reduction of ore powder is as follows: To incorporate this chemistry in CPFD, cell mean chemistry calculations were used. The homogeneous reaction rate was obtained by the Arrhenius equation, which is written as k = Ae −Ea/RT [42]. The average properties of particle phases in the chemical rate equation were calculated by interpolating the discrete calculated particle properties into the grid [43][44][45]. The reaction rates in each grid cell were calculated by solving a set of ordinary differential equations of the above form. In the implicit solution, the mass of the solid phase involved was contained in the mass of the gas phase.For reactions (1) and (2), the consumption rates of H 2 and CO per unit volume are [46], respectively, as follows: RTs . The generation or consumption rate of other substances in the reaction system was obtained by using the stoichiometric coefficients of reaction (Equations (2) and (3)).

Simulated Experimental Conditions
According to the experimental conditions, in the simulation, the gas phase was N 2 , CO, and H 2 , and the solid phase was iron ore powder and silica sand. The particle size distribution of the ore powder is shown in Figure 3. The initial setup was the same as the experimental setup, as presented in Figure 4. Particles were filled above the inlet boundary with a volume fraction of 0.56, and the other input parameters are listed in Table 3. First, the temperature of the fluidized bed reactor was heated to the set value, after which N 2 was introduced and the mineral powder was added, and the reducing gas was finally introduced to reduce the mineral powder. The gas in the experiment was introduced from the bottom of the fluidized bed to fluidize the particles and reduce the mineral powder under high-temperature conditions. The solid phase was not allowed to be discharged from the reactor, and atmospheric pressure boundary conditions were specified at the outlet. The simulation time required 2500 s to eliminate the initial oscillation and achieve complete mass dynamic balance and the mineral powder composition reaction.   To study the effects of the reduction temper duction pressure, and the linear velocity of the re iron ore fines, experiments, and simulations wer These four factors are, respectively, represented duction temperature, and A1, A2, and A3 are 923 represents the type of reducing gas, and B1, B2, and an H2:CO mixed gas with a ratio of 0.6:0.4. C rep C2, and C3 represent the atmospheric pressures of tively. Finally, D represents the linear velocity of respectively, 0.4 m/s, 0.6 m/s, and 0.8 m/s (see Ta effect was analyzed by measuring the metallizati mal experimental operating conditions of the flu optimization analysis. Table 3. Input parameters in the CPFD simulation.

Parameters
Gravitational acceleration To study the effects of the reduction temperature, the type of reducing gas, the reduction pressure, and the linear velocity of the reducing gas on the fluidized reduction of iron ore fines, experiments, and simulations were combined to investigate these factors. These four factors are, respectively, represented by A, B, C, and D. A represents the reduction temperature, and A 1 , A 2 , and A 3 are 923 K, 1023 K, and 1123 K, respectively. B represents the type of reducing gas, and B 1 , B 2 , and B3, respectively, represent H 2 , CO, and an H 2 :CO mixed gas with a ratio of 0.6:0.4. C represents the reduction pressure, and C 1 , C 2 , and C 3 represent the atmospheric pressures of 0.1 MPa, 0.2 MPa, and 0.4 MPa, respectively. Finally, D represents the linear velocity of the reducing gas, and D 1 , D 2 , and D 3 are, respectively, 0.4 m/s, 0.6 m/s, and 0.8 m/s (see Table 4). In the experiment, the reduction effect was analyzed by measuring the metallization rate of the ore powder, and the optimal experimental operating conditions of the fluidized bed reduction were obtained via optimization analysis.

Conclusion and Analysis
For different indicators, the degrees of influence of different factors are different, and the comprehensive optimal solution can be obtained via the comprehensive analysis of the four factors. Via the comprehensive analysis of the metallization rate and bonding ratio in the experiment, the optimal experimental operating conditions were determined to be a temperature of 923 K, a pressure of 0.2 MPa, a linear velocity of the reducing gas of 0.6 m/s, and the use of pure H 2 as the reducing gas. For the specific research process and conclusion of the experiment, please refer to the paper published by the research group [47]. Figure 5 presents the initial fluidization process of the iron ore powder. The ore powder was reduced to iron to a certain extent, and the composition remained unchanged. ratio in the experiment, the optimal experimental operating conditions were determined to be a temperature of 923 K, a pressure of 0.2 MPa, a linear velocity of the reducing gas of 0.6 m/s, and the use of pure H2 as the reducing gas. For the specific research process and conclusion of the experiment, please refer to the paper published by the research group [47]. Figure 5 presents the initial fluidization process of the iron ore powder. The ore powder was reduced to iron to a certain extent, and the composition remained unchanged.
T=0 s T=10 s T=50 s T=100 s T=500 s T=1000 s T=2000 s T=2500 s Figure 5. The initial fluidization process of simulated bed. Figure 6 exhibits the changing trends of the metallization rates of the three groups of I, II, and III. Figure 6a is the simulation result of the metallization rate, and Figure 6b is the experimental measurement value of the metallization rate. By comparing the simulation data with the experimental data, it can be seen that the simulation results of the CPFD method can adequately verify the variation trend of the metallization rate observed in the experiment. Within 1800 s, the metallization rate increased with time, and after 1800 s, the metallization rate exhibited an almost stable trend and no longer changed. Since the chemical reaction rate set by the simulation is in a more ideal state, while the real experiment requires a heated reaction time to reduce the iron ore powder, the simulated value of the metallization rate in the first 600 s is in the ideal state of linear growth, while the real experimental measured value has a lower growth rate than the simulated result. Moreover, the reaction time is long enough for the powder to be mostly reduced under the simulated experiment, which leads to the metallization rate under the simulated result being larger than the metallization rate in the experimental result.  Figure 6 exhibits the changing trends of the metallization rates of the three groups of I, II, and III. Figure 6a is the simulation result of the metallization rate, and Figure 6b is the experimental measurement value of the metallization rate. By comparing the simulation data with the experimental data, it can be seen that the simulation results of the CPFD method can adequately verify the variation trend of the metallization rate observed in the experiment. Within 1800 s, the metallization rate increased with time, and after 1800 s, the metallization rate exhibited an almost stable trend and no longer changed. Since the chemical reaction rate set by the simulation is in a more ideal state, while the real experiment requires a heated reaction time to reduce the iron ore powder, the simulated value of the metallization rate in the first 600 s is in the ideal state of linear growth, while the real experimental measured value has a lower growth rate than the simulated result. Moreover, the reaction time is long enough for the powder to be mostly reduced under the simulated experiment, which leads to the metallization rate under the simulated result being larger than the metallization rate in the experimental result. The experimentally measured value of the metallization rate at 1200 s was compared with the simulated calculated value, as shown in Table 5. The comprehensive analysis shows that under the same conditions, the simulated values of the metallization rate were in good agreement with the change trend of the experimentally measured values. Therefore, the simulated metallization rate can provide reference values for the optimization of the experimental operating conditions, and can be used to verify the accuracy of the experimental results. However, there was an error in the simulation result, and the calculated value was higher than the experimental value. The reason for this is that the simulation result was in an ideal state, which ignored the fact that some particles were blown away and the energy loss in the experiment. Moreover, the setting of the chemical reaction rate could not completely reflect the real situation. As the particle composition in the ideal state was without impurities, most of the mineral powder could be reduced over a sufficiently long amount of time, which caused the metal content in the simulation result to be greater than the experimentally measured value. When the metallization rate in the simulation tended to be stable, the particles under the simulation were mostly reduced, resulting in a higher metallization rate.

Reduction Temperature
Factor A (reduction temperature): The initial temperatures of the gas and solid phases, the inlet temperature, and the wall heating temperature were simulated according to the experimental conditions, and the fluidization effect was judged by the time required for the reaction to reach equilibrium. Table 6 shows the simulation experimental scheme and results to study the reduction temperature. Figure 7 presents the fluid temperature distribution of simulation experiments 1, 2, and 3, and the cross-section temperature field distribution of simulation experiments 2. The superimposition on the right is the change of the average temperature of simulation experiments 1, 2, and 3 over time. Figure 8 shows the changes in the compositions of the three groups of experimental gases with time, which reveals that the time required for the ore powder to be completely reduced to iron to reach the equilibrium state in these experiments was approximately 1215 s, 990 s, and 1240 s. When gases of different compositions are blown into the fluidized bed from the inlet, the mineral powder is continuously reduced to Fe by the reducing gas, and when the mineral powder is completely reduced, no chemical reaction occurs in the fluidized bed, and the gas in the fluidized bed is detected as the composition set by the initial conditions. When the temperature exceeded a certain value, the higher the temperature, the poorer the reduction effect of the ore powder as compared to that at a low temperature. According to the simulation results, the shortest time required to reach the equilibrium occurred when the reduction temperature was 1023 K. When the mineral powder with a lower temperature was added to the bed, it took a period of time to increase the temperature, and the reduction effect of the mineral powder gradually increased with the reduction reaction. When the temperature reached a certain level, the reduction effect was optimal. The higher the energy of iron whiskers produced by reduction on the particle surface, the greater the physical adsorption, and the more likely the agglomeration between high-energy iron whiskers, resulting in bonding/loss of flow and a decrease in the metallization rate [47]. Therefore, the best choice for the reduction temperature was determined to be 1023 K. The simulation conclusion is consistent with the experimental conclusion, so this method can simulate the effect of the reduction temperature on fluidized ironmaking. face, the greater the physical adsorption, and the more likely the aggl high-energy iron whiskers, resulting in bonding/loss of flow and a de lization rate [47]. Therefore, the best choice for the reduction temperatu to be 1023 K. The simulation conclusion is consistent with the experim this method can simulate the effect of the reduction temperature on flu

Types of Reducing Gases
Factor B (type of reducing gas): Different components of the reducing gas have a great influence on the reduction effect. Table 7 shows the simulation experimental scheme and results of studying the components of the reducing gas, and Figure 9 presents the changes in the simulation results of the gas components in simulation experiments 7, 8, and 9 over time. In the three experiments, the time required for the ore particles to be completely reduced to the equilibrium state was roughly 1375 s, 1675 s, and 1580 s, respectively. The simulation results show that the higher the H 2 , the shorter the equilibrium time, and the better the fluidization reduction effect. Therefore, pure H 2 was determined to be the best reducing gas. When pure H 2 was used as the reducing gas in the experiment, the reduction effect was good and the metallization rate was high. According to the preceding analysis, when the temperature exceeds a certain value, the lower the temperature, the more conducive the reaction. The CO reduction of iron ore is an exothermic reaction, while the H 2 reduction of iron ore is an endothermic reaction. When a certain temperature is reached, the high temperature is conducive to particle bonding/loss of flow, and CO will precipitate carbon powder and adsorb around the ore powder, thus affecting the reaction. The chemical reaction rate settings in the simulation were consistent with the real experimental results. This method can simulate the effect of the reducing gas on fluidized smelting.

Reduction Pressure
Factor C (reduction pressure): Table 8 shows the experimental plan and results of the reduction pressure study, and Figure 10 presents the fluid temperature and particle temperature distributions of simulation experiments 13, 14, and 15. The overlay on the right shows the average temperatures of the three groups of experiments. Figure 11 exhibits the simulation results of gas changes in the three groups of experiments. It can be seen from the figure that the time required for the three groups of reactions to reach equilibrium was roughly 1625 s, 1115 s, and 1050 s, respectively. According to the experimental analysis, it can be seen that when the pressure was higher, the gas density in the bed was higher, and the contact between the gas and the solid was more sufficient, which accelerated the reduction rate of the solid. However, the higher the pressure, the higher the gas velocity. Before the set heating temperature was reached, the gas flowed out from the gas outlet, thereby reducing both the fluid temperature and the particle temperature in the fluidized bed. The higher the outlet pressure, the lower the temperature, and the better the reduction effect. However, when the pressure was 0.2 MPa and 0.4 MPa, the time required for the balance of the ore powder was very similar. Considering the cost and the reduction effect, the best reduction pressure was selected as 0.2 MPa. This method can simulate the effect of the reduction pressure on fluidized ironmaking.

Linear Gas Velocity
Factor D (linear gas velocity): Table 9 shows the experimental plan and results of the Linear Gas Velocity study, and Figure 12 shows the distributions of the fluid temperature and particle temperature in simulation experiments 19, 20, and 21, as well as the crosssectional distribution of the fluid temperature in simulation experiment 20. Figure 13 presents the variations of the gas composition in the three groups of experimental beds. It can be seen from Figures 12 and 13 that when the gas velocity was 0.4 m/s, the ore powder was not completely reduced, and the gas velocity was 0.6 m/s and 0.8 m/s. When the gas velocity was 0.6 m/s, the ore powder was completely reduced and the reaction reached the equilibrium state after 1580 s, whereas when the gas velocity was 0.8 m/s, the reaction required 1875 s. Therefore, the best gas velocity was determined to be 0.6 m/s. With the increase of the linear gas velocity, the upward drag force of the gas on the particles also increases, the load of the particles decreases, the spacing of the particles increases, the tightness of the particles in the bed decreases, the porosity increases, the gas and particles fully contact and react, and adhesion/loss of flow does not easily occur. Furthermore, with the increase of the linear gas velocity, the temperature of normal-temperature gas decreases, the particle temperature and cell fluid temperature decrease, and the effective

Linear Gas Velocity
Factor D (linear gas velocity): Table 9 shows the experimental plan and results of the Linear Gas Velocity study, and Figure 12 shows the distributions of the fluid temperature and particle temperature in simulation experiments 19, 20, and 21, as well as the crosssectional distribution of the fluid temperature in simulation experiment 20. Figure 13 presents the variations of the gas composition in the three groups of experimental beds. It can be seen from Figures 12 and 13 that when the gas velocity was 0.4 m/s, the ore powder was not completely reduced, and the gas velocity was 0.6 m/s and 0.8 m/s. When the gas velocity was 0.6 m/s, the ore powder was completely reduced and the reaction reached the equilibrium state after 1580 s, whereas when the gas velocity was 0.8 m/s, the reaction required 1875 s. Therefore, the best gas velocity was determined to be 0.6 m/s. With the increase of the linear gas velocity, the upward drag force of the gas on the particles also increases, the load of the particles decreases, the spacing of the particles increases, the tightness of the particles in the bed decreases, the porosity increases, the gas and particles fully contact and react, and adhesion/loss of flow does not easily occur. Furthermore, with the increase of the linear gas velocity, the temperature of normal-temperature gas decreases, the particle temperature and cell fluid temperature decrease, and the effective gas-solid reduction temperature and reduction effect decrease. A large temperature decrease in a fluidized bed is not conducive to the reduction of ore powder. Considering the optimal reduction linear velocity of 0.6 m/s, it can be concluded that the method can simulate the influence of the linear gas velocity on fluidized smelting. gas-solid reduction temperature and reduction effect decrease. A large temperature decrease in a fluidized bed is not conducive to the reduction of ore powder. Considering the optimal reduction linear velocity of 0.6 m/s, it can be concluded that the method can simulate the influence of the linear gas velocity on fluidized smelting.

Conclusions
In this study, a combination of numerical simulation and experimental testing was used to carry out numerical simulation research on the thermal state of reduced iron ore powder in a pressurized fluidized bed with the help of Barracuda software. Coupling the characteristics of gas-solid flow and the reaction kinetics, a numerical model of the reduction of iron ore fines in a pressurized circulating fluidized bed was established to reveal the flow and reaction characteristics of the fluidized reduction of iron ore fines. The effects

Conclusions
In this study, a combination of numerical simulation and experimental testing was used to carry out numerical simulation research on the thermal state of reduced iron ore powder in a pressurized fluidized bed with the help of Barracuda software. Coupling the characteristics of gas-solid flow and the reaction kinetics, a numerical model of the reduction of iron ore fines in a pressurized circulating fluidized bed was established to reveal the flow and reaction characteristics of the fluidized reduction of iron ore fines. The effects of the operating parameters, namely the reduction pressure, reduction temperature, reducing gas type, and linear gas velocity, on the gasification results were explored. The simulation results reveal the following: (1) The change trends of the metallization rate in the fluidized reduction of iron ore powder simulated by the CPFD method were consistent with the experimental values; (2) The CPFD method simulated the effects of the reduction temperature, linear gas velocity, gas composition, and reduction pressure on the results of the fluidized reduction of iron powder, which were consistent with the experimental results. This indicates that the model selection was reasonable, and lays a foundation for further numerical simulation work; (3) Based on the CPFD method, the optimal operating parameters were determined to be a reduction temperature of 1023 K, a reduction pressure of 0.2 MPa, H 2 as the reducing gas, and a gas velocity of 0.6 m/s. The optimal operating parameters in the experimental test were a reduction temperature of 1023 K, a reduction pressure of 0.2 MPa, H 2 as the reducing gas, and a gas velocity of 0.6 m/s. The simulation conclusion is consistent with the experimental test conclusion, which verifies the reliability of the experimental data.