Numerical method for simulating combustion of iron powder particle cloud considering differential diffusion

Abstract

The application discloses a numerical calculation method for simulating iron powder particle cloud combustion considering differential diffusion, and belongs to the field of iron powder combustion numerical simulation calculation. The application can numerically simulate 2D free propagation of a flame of an iron powder particle cloud under microgravity conditions considering differential diffusion. For the difference of thermal diffusion rates among gas phase components, the application considers the effects of surface reaction kinetics and diffusion control mechanism in the self-established iron powder particle combustion model, calculates a local Lewis number in real time, corrects a diffusion term in a gas phase component equation, quantitatively analyzes the effects of differential diffusion on the flame temperature and flame propagation speed of the iron powder particle cloud, and the effects of differential diffusion on the heat release rate of single particle combustion and the oxygen mass fraction of a particle surface, and further considers the effects of oxygen concentration and thermal expansion on the iron powder particle cloud combustion. The application has guiding significance for developing a lean fuel iron flame model with low flame propagation speed and other metal particle combustion models.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation calculation of iron powder combustion, specifically involving a numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion. Background Technology

[0002] As a highly reactive metal, iron holds immense potential in driving the transition to carbon-free energy. As a fuel, iron differs significantly from other solid fuels (such as coal and biomass), primarily in that its combustion follows a heterogeneous reaction pattern, meaning it does not release volatile substances or oxidation products into the gas phase. Measurement techniques and numerical models developed for carbonaceous fuels cannot be directly applied to iron combustion research. In recent years, progress has been made in studying the combustion characteristics of iron through both experimental and numerical simulation methods. For lean-burn iron flames with an average particle size greater than 20 µm, the laminar reaction front velocity is difficult to determine accurately due to particle settling phenomena and the measurement limits of observable flame velocities under natural convection conditions.

[0003] Differential diffusion is a key physical phenomenon in combustion, referring to the different diffusion rates of various chemical components in a multi-component gas mixture due to their varying molecular weights and thermal diffusivity during flow and reaction. Differential diffusion affects flame structure and the formation of combustion products and contaminants. For heterogeneous combustion systems like iron powder combustion, the impact of differential diffusion is particularly significant, as the oxygen diffusion rate directly affects the oxidant supply at the reaction interface.

[0004] Compared to terrestrial experiments, microgravity experiments offer unique value: by mitigating the particle dynamics effects driven by gravity and buoyancy, they create an ideal environment for detailed studies of flame propagation mechanisms. However, microgravity experiments are limited by high implementation costs and stringent technical requirements; in numerical simulations, the unit Lewis number assumption ignores differential diffusion effects, potentially failing to accurately predict local component distributions. Previous studies have not considered numerical simulations of iron flames under microgravity, and research on the impact of differential diffusion on combustion characteristics remains limited. In combustion numerical simulations, properly considering differential diffusion effects is crucial for accurately predicting flame characteristics and stability. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion. This calculation method is applicable to the combustion of single iron powder particles, as well as the combustion of iron powder particle clouds at various particle concentrations. Furthermore, for different oxygen environments, the influence of differential diffusion on combustion characteristics can be considered.

[0006] The technical solution of the present invention is as follows:

[0007] A numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion includes the following steps:

[0008] Step 1: Based on the iron powder size, oxygen environment and surface reaction kinetics, the particle combustion rate and temperature are calculated using a non-unit Lewis number. Combustion heat release and oxygen consumption are taken as gas phase source terms, thereby establishing a multiphase combustion mathematical model.

[0009] Step 2: The control equations are discretized numerically using the finite volume method. Spatial discretization uses the second-order central difference method, and time discretization uses the implicit Euler scheme.

[0010] Step 3: Coupled solution is achieved by updating the particle state step by step, calculating the interphase source term, iteratively solving the gas phase equation and the pressure-corrected velocity field. The interphase source term includes the momentum source term calculated by the particle drag force model, and the velocity vector of the particle motion is calculated based on the momentum source term.

[0011] Beneficial effects:

[0012] 1. The influence of gas-phase differential diffusion on the combustion of iron powder particles was considered, and the reason why differential diffusion affects combustion characteristics can be explained from the perspective of single-particle combustion. At the same time, the influence of gas expansion and flow on particle motion was considered, which effectively improved the accuracy of numerical simulation and reduced the cost compared with experimental research. The simulation results are meaningful for the development of iron powder particle combustion models.

[0013] 2. The simulation can automatically set the oxygen concentration and iron powder particle concentration, and can carry out numerical simulation calculations on the combustion of iron powder particles under various working conditions, which helps to develop more stable metal particle burners. Attached Figure Description

[0014] Figure 1 This invention relates to a simulation calculation method for the combustion of iron powder particle clouds.

[0015] Figure 2 The evolution of O2 mass fraction and heat release rate on the surface of a single burning particle over time, and the evolution curve of unburned iron powder particle mass fraction of the corresponding particle (I).

[0016] Figure 3 The evolution of O2 mass fraction and heat release rate on the surface of a single burning particle over time, and the evolution curve of unburned iron powder particle mass fraction of the corresponding particle (II).

[0017] Figure 4 The average oxygen mass fraction at time t = 1.5 s, calculated using both unitless and unit Lewis numbers in this embodiment of the invention. Distribution curve of gas temperature T (I).

[0018] Figure 5The average oxygen mass fraction at time t = 1.5 s, calculated using both unitless and unit Lewis numbers in this embodiment of the invention. Distribution curve of gas temperature T (II).

[0019] Figure 6 The average oxygen mass fraction at time t = 1.5 s, calculated using both unitless and unit Lewis numbers in this embodiment of the invention. Distribution curve of gas temperature T (III).

[0020] Figure 7 The average oxygen mass fraction at time t = 1.5 s, calculated using both unitless and unit Lewis numbers in this embodiment of the invention. Distribution curve of gas temperature T (IV).

[0021] Figure 8 The image shows the particle trajectory at equal time intervals in an embodiment of the present invention.

[0022] Figure 9 The comparison results of various parameters in the embodiments of the present invention, considering and ignoring particle motion, are as follows: average velocity of gas and particles.

[0023] Figure 10 The comparison results of various parameters in the embodiments of the present invention, considering and ignoring particle motion, are as follows: gas temperature distribution.

[0024] Figure 11 The comparison results of various parameters in the embodiments of the present invention considering and ignoring particle motion are as follows: flame velocity normalized to gas velocity.

[0025] Figure 12 The comparison results of various parameters in the embodiments of the present invention, considering and ignoring particle motion, are as follows: equivalent iron concentration distribution.

[0026] Figure 13 For the purpose of predicting flame velocity s in this embodiment of the invention L Comparison with experimental measurements.

[0027] Figure 14 This is a comparison between the predicted flame temperature and experimental data in an embodiment of the present invention. Detailed Implementation

[0028] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. However, the following embodiments are only for explaining the present invention, and the scope of protection of the present invention should include all the contents of the claims. Moreover, through the description of the following embodiments, those skilled in the art can fully realize all the contents of the claims of the present invention. Under the framework of the finite volume method, the present invention simultaneously solves the gas phase control equation and the self-constructed iron powder particle combustion model through a pressure-velocity coupling algorithm (such as PISO / SIMPLE), realizing a multiphase reactive flow numerical simulation system considering heterogeneous reaction, heat and mass transfer, and differential diffusion effects. It is suitable for numerical calculation of iron powder particle group combustion considering differential diffusion under microgravity conditions.

[0029] Example:

[0030] This invention, by considering the difference in diffusion rates of oxygen and other components in the iron powder particle combustion model and gas phase component transport equation, and calculating the Lewis number of oxygen based on local gas temperature and oxygen mass fraction, can handle the numerical simulation of the iron powder particle cloud combustion process under different oxygen environments and particle concentrations considering differential diffusion in microgravity.

[0031] like Figure 1 As shown, the specific implementation steps of the numerical calculation method for iron powder particle cloud combustion considering differential diffusion under microgravity according to the present invention are as follows:

[0032] Step 1: Establish a multiphase combustion mathematical model. Based on the size and distribution of iron powder, oxygen environment, initial temperature, and surface reaction rate model, considering surface reaction kinetics and diffusion control mechanisms, and using a non-unit Lewis number, calculate the combustion rate, iron oxide formation rate, and particle temperature of the iron powder particles while considering differential diffusion. Use the calculated iron powder combustion heat release rate and oxygen consumption as source terms in the gas phase equation. Simultaneously, consider the difference in transport rates between components when solving the component equation to further calculate the state of each component in the gas phase. Finally, obtain the particle velocity by solving the drag force on the iron powder particles in the flow field, thus realizing the establishment and solution of the solid-gas phase coupled system.

[0033] In calculating interphase mass transfer, it is assumed that iron combustion is a completely heterogeneous reaction process: the oxidant is transported to the particle surface through the boundary layer, and the chemical reaction occurs at the particle surface. The chemical reaction equation is: Fe + 1 / 2O₂ = FeO. Based on this mechanism, the interphase mass transfer rate is jointly determined by the oxidant diffusion rate and the surface reaction rate, expressed as:

[0034] ,

[0035] In the formula, A d This represents the total surface area of ​​the particles. The density of the mainstream gas, A represents the mass fraction of oxygen. r Let be the effective reactive surface area of ​​the particle. The diffusion coefficient D0 characterizes the ability of oxygen to diffuse from the mainstream gas to the particle surface, and its expression is: Sh represents the Wood number, and dp is the particle diameter calculated based on the mass and density of pure iron and iron oxide. The oxygen diffusion coefficient at the particle film layer is also mentioned. Calculations using non-unit Lewis numbers:

[0036] ,

[0037] In the formula, C is the thermal conductivity of the film. p,g,s This refers to the isobaric specific heat capacity of the gas phase at the film layer. The gas density at the membrane layer, Let be the local oxygen Lewis number in the membrane layer. Based on the mixed-average diffusion model under the studied oxidizing environment, the Lewis number Le is obtained by fitting data calculated by Cantera. In Cantera, the Lewis number of oxygen is calculated, which is mainly determined by the mass fraction of oxygen and temperature. The Lewis number for the entire range is calculated, and the expression for the oxygen Lewis number is obtained by fitting:

[0038]

[0039] Where p is the fitting coefficient obtained from the fitting process. T and T represent the mass fraction of oxygen and temperature, respectively.

[0040] The fitting variance reached 0.99. In each iteration, the Lewis number was recalculated based on the local gas phase temperature and oxygen mass fraction. The surface reaction rate R... k Described using the single-step first-order Arrhenius equation:

[0041] R k = R0·exp[-Ea / (R·Tp)],

[0042] Where R0 is the pre-exponential factor, Ea is the activation energy, R is the universal gas constant, and Tp is the particle temperature. Iron oxidizes to FeO, and the surface reaction rate parameter determined from this is R0 = 7.5 × 10⁻⁶. 6 m / s, Ea = 1.2×10 8 J / kmol. Considering the effect of differential diffusion on single-particle combustion, as follows: Figure 2 As shown, considering the differential diffusion effect, the peak heat release rate increases significantly, and the combustion rate of iron powder particles is significantly faster than the calculation results based on the unit Lewis number assumption. Furthermore, the oxidant concentration on the particle surface is low in the initial stage of combustion, but its concentration is higher as the iron powder particles approach complete combustion. Figure 2 and Figure 3The mass fraction curve of unburned iron powder particles shows that the particle combustion process is significantly accelerated when differential diffusion is considered.

[0043] Furthermore, based on the interphase mass transfer rate calculated above, which is also the combustion rate of Fe, the heat transfer between iron powder particles and the surrounding gas is achieved through convective heat transfer, particle reaction heat release, and mass transfer-related thermal effects. The instantaneous temperature of the particles can be solved by the following energy equation:

[0044] ,

[0045] In the formula, is the specific heat capacity of the particulate phase; For particle mass; The Nusselt number is calculated using the Ranz-Marshall model. For particle temperature, Specific heat capacity of the gas near the particle; Prandtl number Set to 0.6. The relaxation time of the particles is determined by... The calculation yielded that, Particle density, The gas phase dynamic viscosity, Particle diameter. Enthalpy of combustion. Based on previous experimental data, the stoichiometric ratio was set to 4844 kJ / kg. The ratio of the change in mass of unburned particles to the change in mass of burned particles, the last item. Due to the energy change caused by interphase mass transfer, the total enthalpy of oxygen can be calculated as follows: ,in This is the specific heat capacity of oxygen. For reference temperature, This is the enthalpy of oxygen formation at the reference temperature.

[0046] In particulate combustion models, to measure the relative importance of oxidant diffusion rate and surface reaction rate, a normalized Damköhler number is defined for quantification, expressed as:

[0047] ,

[0048] When the dimensionless Darmque number (Da) approaches 1, the overall reaction rate is limited by the oxygen diffusion rate, corresponding to the diffusion-controlled region; when the Da value approaches 0, the overall reaction rate is limited by the surface reaction kinetics, corresponding to the kinetic-controlled region.

[0049] Furthermore, the calculated iron powder combustion heat release rate and oxygen consumption are used as source terms in the gas phase equation to further calculate the states of each component in the gas phase, thereby establishing and solving the solid-gas phase coupled system.

[0050] Component equation:

[0051] ,

[0052] Energy equation:

[0053] ,

[0054] Momentum equation:

[0055] ,

[0056] In the above system of equations, This represents the gas phase density, and u is the velocity vector. He represents the mass fraction of the gaseous component, p represents the enthalpy, and g represents the gravitational acceleration. It is the viscous stress tensor. and These represent the derivatives in time and space, respectively.

[0057] In the component equation, the effect of differential diffusion is considered by using a non-unit Lewis number. Figure 4 , Figure 5 , Figure 6 and Figure 7 Comparison using unit Lewis number ( = 1) and non-unit Lewis numbers ( ≠ 1) The calculated oxygen concentration and temperature distribution are based on the following: under iron powder particle concentrations of 1 g / L and 2 g / L, considering differential diffusion, the flame propagation speed is faster; while at a low mass concentration of 0.5 g / L, the difference in flame structure can be ignored. Due to the effect of gas thermal expansion flow on the particles, the drag force on the particles is calculated, and the particle velocity and trajectory are also calculated, where:

[0058] Velocity equation:

[0059] ,

[0060] In the formula, For the first Particle velocity in each direction, The drag coefficient is calculated based on the solid sphere assumption. For particle density, the calculation formula is: ,in, For particle mass, The magnitude of the relative velocity between the gas and the particles. No. Gravitational acceleration in each direction, It is the density of the gas. It is the first Gas velocity in each direction.

[0061] Step 2, Numerical Discretization: Combining the characteristics of the computational grid, initial conditions, and boundary conditions, the governing equations in the multiphase combustion mathematical model are numerically discretized. The finite volume method is used to spatially discretize the mass, momentum, composition, and energy equations. A suitable difference scheme is used to process the convection and diffusion terms, resulting in a set of nonlinear algebraic equations concerning velocity, density, composition, temperature, and pressure. The algebraic equations are then linearized to construct the coefficient matrix and source term vector.

[0062] This invention supports the autonomous setting of key parameters such as initial oxygen mass fraction, particle size distribution, and particle concentration. In the implementation example, the computational domain uses a two-dimensional rectangular region of 80mm × 30mm. A suspension system is constructed by randomly distributing iron powder particles of different mass concentrations, and the iron powder particles are numerically characterized based on the point source within a particle unit (PSI-CELL) model. In the initial state, both the iron powder particles and the gaseous medium remain stationary, thus ensuring uninterrupted observation of the flame propagation process within the stationary iron suspension system. By presetting the iron powder particles in the x < 1 mm region to a high temperature of 2000 K, fresh iron powder particles in the x > 1 mm region can be effectively ignited, thereby forming a self-sustaining flame structure propagating along the x direction.

[0063] Furthermore, the study employs a highly refined grid system, with ten grid nodes within each average particle spacing to ensure accurate analysis of the heat transfer mechanism between spatially discrete particles. The z-axis domain depth is set to match the grid size in the x and y directions. The component mass fractions and temperature in the governing equations are solved using the open-source platform OpenFOAM. For numerical discretization, the spatial derivative term is discretized using a second-order central difference scheme, while time progression is based on an implicit Euler scheme. All examples are uniformly set to a 1-second physics duration to ensure comparability of results.

[0064] Step 3, Time Progression and Coupled Solution: The solution process is progressively advanced using a time discretization method. Within each time step: first, the particle phase equation is solved, updating the particle temperature, composition, and reaction state; then, the mass, momentum, and energy exchange source terms between the particle phase and the gas phase are calculated. Although the iron powder particles and gas are initially at rest under the microgravity conditions involved in this embodiment, the thermal expansion effect of the gas will change the spatial distribution of the particles, thereby affecting the particle concentration distribution. Figure 8 It shows the trajectories of two independent particles moving within equal time intervals. Figure 9 , Figure 10 , Figure 11 and Figure 12The average velocities of gas and particles in the x-direction were compared when considering and neglecting the motion of iron powder particles. Ignoring the effect of gas expansion on particle motion resulted in a significant increase in gas velocity. Considering the coupling effect of gas expansion on particle motion, the gas temperature in the flame front and the already burned zone was lower, and when particle motion was considered, some iron powder particles would move out of the computational domain, leading to a decrease in iron concentration.

[0065] The nonlinear equations of the gas-phase control equations are further solved iteratively, and finally the updated pressure field is used to correct the velocity field to satisfy mass conservation. Based on these steps, the combustion process of iron powder particles under laminar flow conditions can be numerically simulated.

[0066] Figure 13 Predicted flame speed s L The flame temperature was compared with measurements under different oxidant environments. When the differential diffusion effect (i.e.) was ignored... When =1), the flame velocity decreased under different iron concentration conditions. Figure 14 Comparing the predicted flame temperature with the experimental measurements, it can be seen that the predicted flame temperatures in 20% O2 and 40% O2 environments are 2526 K and 2983 K, respectively, which are close to the experimentally measured values ​​of 2504 K and 2897 K.

[0067] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion, characterized in that, Includes the following steps: Step 1: Based on the iron powder size, oxygen environment and surface reaction kinetics, the particle combustion rate and temperature are calculated using a non-unit Lewis number. Combustion heat release and oxygen consumption are taken as gas phase source terms, thereby establishing a multiphase combustion mathematical model. Step 2: The control equations are discretized numerically using the finite volume method. Spatial discretization uses the second-order central difference method, and time discretization uses the implicit Euler scheme. Step 3: Coupled solution is achieved by updating the particle state step by step, calculating the interphase source term, iteratively solving the gas phase equation and the pressure-corrected velocity field. The interphase source term includes the momentum source term calculated by the particle drag force model, and the velocity vector of the particle motion is calculated based on the momentum source term. The multiphase combustion mathematical model established in step 1 includes: The iron powder particle surface combustion model, within the Lagrange framework, assumes that iron combustion is a purely heterogeneous reaction process, with the chemical reaction occurring on the particle surface, and that the iron powder particle combustion rate is determined by the oxidant diffusion rate and the surface reaction rate. The calculation of the oxidant diffusion rate takes into account the non-unit Lewis number. The mass conservation equation, momentum conservation equation, component transport equation, and energy conservation equation are used as source terms to solve the conservation equations for gas phase components based on the calculation results of the particle surface combustion model. Non-unit Lewis numbers are used in the mass conservation equation, momentum conservation equation, component transport equation, and energy conservation equation. State equations coupled with pressure-velocity algorithm; Oxygen diffusion coefficient at the particulate membrane layer ; in, , and These represent the gas phase thermal conductivity, density, and specific heat capacity at the particle film layer, respectively; the Lewis number for oxygen is set to a unit Lewis number. =1 and non-unit Lewis number ≠ 1. Calculations are performed using two modes; Non-unit Lewis numbers ≠1 was obtained by fitting the results calculated by chemical kinetics and transport property calculation tools based on oxygen and xenon at different temperatures and volume fractions.

2. The numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion according to claim 1, characterized in that, In step 2, a numerical discretization strategy based on the finite volume method is adopted to discretize the computational domain into a control volume and integrate the control equations on the control volume; the transient terms are discretized using an implicit scheme to transform the partial differential equations into a system of nonlinear algebraic equations.

3. The numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion according to claim 1, characterized in that, The combustion process of iron powder particles includes particle convection heating, surface heterogeneous oxidation reaction, and oxide layer diffusion control.

4. The numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion according to claim 1, characterized in that, In multiphase combustion mathematical models, the reaction rate is determined by both the Arrhenius equation and the oxygen diffusion rate, and its general form is: ,in Let dt represent the interphase mass transfer rate, and let dt denote the derivative with respect to time. This represents the total surface area of ​​the particles. For the Damköhler number, and These represent the density of the gas phase and the mass fraction of oxygen, respectively.

5. The numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion according to claim 1, characterized in that, Solid-gas coupling is achieved through source terms, where the momentum source term is calculated by the particle drag force model, and the energy source term S... h Includes convective heat transfer and reaction heat, component source term S Y This corresponds to the consumption of oxygen and the formation of iron oxide products.

6. The numerical calculation method for simulating the combustion of iron powder particle clouds considering differential diffusion according to claim 1, characterized in that, In step 3, the drag force on the particle is calculated, and the velocity vector of the particle's motion is calculated based on the force.

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