Method for evaluating the minimum fuel ratio of a blast furnace ironmaking process

Abstract

The present application relates to a kind of evaluation methods of lowest fuel ratio of blast furnace iron-making process, the three-dimensional model of blast furnace body is constructed in the present application;The three-dimensional model of blast furnace body is gridded;According to the principle of computational fluid dynamics, the three-dimensional model of blast furnace body is used as input model, and blast furnace submodel is established, and blast furnace submodel includes: furnace top cloth model, heat transfer model, mass transfer model, chemical reaction model, injection model, gas-solid two-phase model and soft melting zone model;The simulation model is integrated into blast furnace submodel;Production data and simulation model are used to simulate blast furnace production process;Adjust and optimize simulation model, when iron-making process parameters meet one of the following three states: the dew point temperature of furnace top gas temperature, the position of soft melting zone reaches blast furnace dead coke zone, and the temperature of molten iron is lower than the freezing point, the fuel ratio of blast furnace at this time is the lowest fuel ratio of blast furnace iron-making process;During the process, by changing parameters to observe its influence on fuel ratio, to more accurately determine the evaluation of lowest fuel ratio.

Description

Technical Field

[0001] This invention relates to the field of blast furnace ironmaking simulation analysis technology, and in particular to a method for evaluating the minimum fuel ratio in a blast furnace ironmaking process. Background Technology

[0002] Blast furnace ironmaking, as a crucial link in the steel production process, aims to provide molten iron that meets both quality requirements and economic viability for subsequent processes. "Qualified" refers to the quality of the molten iron, while "economical" emphasizes achieving the smelting process at a relatively low cost.

[0003] In the entire blast furnace ironmaking process, fuel cost is undoubtedly one of the most critical cost factors. The fuel-to-fuel ratio is a core indicator for measuring the economic efficiency of blast furnace ironmaking. Currently, the steel industry is in a challenging development stage. How to reduce production costs and improve production efficiency while ensuring the stability of blast furnace operation, and continuously reduce the blast furnace fuel-to-fuel ratio, thereby ensuring the efficient, smooth, low-energy, and stable progress of the ironmaking process, has become a major problem that steel companies urgently need to solve.

[0004] Currently, the main methods for reducing the fuel ratio in steel production are mostly through optimizing blast furnace operation procedures, which heavily rely on the practical experience of production technicians. However, this traditional approach has significant limitations, namely, it cannot accurately determine whether the blast furnace ironmaking process has reached the minimum fuel ratio. Therefore, developing a method for assessing the minimum fuel ratio in blast furnace ironmaking based on computational fluid dynamics algorithms and simulation technology has significant and far-reaching practical implications. Summary of the Invention

[0005] In order to solve the above-mentioned technical problems, or at least partially solve the above-mentioned technical problems, the present invention provides a method for evaluating the minimum fuel ratio in a blast furnace ironmaking process.

[0006] In a first aspect, the present invention provides a method for evaluating the minimum fuel ratio in a blast furnace ironmaking process, comprising: Collect various parameter data of blast furnace equipment and production data during the blast furnace equipment production process; Based on 3D modeling software, a 3D model of the blast furnace body is constructed using blast furnace equipment parameter data such as blast furnace volume, blast furnace height, and blast furnace inner diameter. The 3D model of the blast furnace body is meshed according to the set configuration; Based on the principles of computational fluid dynamics, a 3D model of the blast furnace body is used as the input model to establish a blast furnace sub-model. The blast furnace sub-model includes: a furnace top charging model, a heat transfer model, a mass transfer model, a chemical reaction model, a blowing model, a gas-solid two-phase model, and a softening zone model. The various blast furnace models established above are integrated to form a complete simulation model that simulates the blast furnace ironmaking process. Simulation of blast furnace production process using production data and simulation models; The simulation model is adjusted and optimized. When the ironmaking process parameters meet one of the following three conditions, the furnace top gas temperature is at the dew point temperature, the soft melting zone reaches the dead coke zone of the blast furnace, and the molten iron temperature is below the solidification point, the blast furnace fuel ratio at this time is the minimum fuel ratio for the blast furnace ironmaking process. During the process, the parameters are changed to observe their impact on the fuel ratio in order to more accurately determine the minimum fuel ratio.

[0007] Furthermore, the configuration for mesh generation of the blast furnace body 3D model includes: Based on the dimensions of the 3D model of the blast furnace body, the maximum and minimum mesh sizes are set, and the mesh growth rate is set to 1.2 to generate a surface mesh. The boundary layer is set according to the specific location of the blast furnace body three-dimensional model structure. The number of boundary layers is set between 5 and 7, the growth rate is kept at 1.2, and the transition ratio is set at 0.272. The volume mesh is set to a hexahedral mesh, and the growth rate is also 1.2, thus generating the final required volume mesh.

[0008] Furthermore, the furnace top feeding model uses the discrete element method to simulate the packing angle and porosity distribution of the particles under the feeding: Define the inclination angle θ of the feeding chute, the radius of rotation R, and the diameter of the blast furnace throat D; construct a three-dimensional annular feeding domain and divide the boundary between the particle falling area and the accumulation area; configure the chute rotation speed and define the inlet particle flow rate by mass flow rate or volume flow rate. The falling particles of smelting materials follow parabolic kinematics. The contact mechanics model is used to provide the contact forces that affect the packing angle and porosity in the discrete element method simulation; Calculate the rolling friction torque between particles in smelting materials: ; in, The coefficient of rolling friction is This is the unit vector of relative angular velocity between particles; At predetermined time steps, the motion of each particle is described using Newton's and Euler's equations, based on contact force and rolling friction torque: ; in, Let p be the mass of the particle; It is the particle linear velocity; The contact force between particle p and particle q is the resultant of the tangential and normal contact forces; g is the acceleration due to gravity. Let p be the moment of inertia of the particle. Let p be the angular velocity of particle p; The torques are the rolling friction torque and the tangential contact torque between particle p and particle q. The particle state is updated using the velocity-Verlet algorithm at set time steps. Based on the particle collision energy and momentum transfer data recorded within each time step, the simulation continues until stability is achieved. Stability is determined using the particle collision energy and momentum transfer data. Measurements of the angle of repose and porosity distribution were performed on a simulated stockpile.

[0009] Furthermore, at predetermined time steps, the particle state is updated using the velocity-Verlet algorithm, including: Update particle half-step linear velocity: ; in, Let be the net force acting on particle p at time t. Let be the linear velocities of particle p at times t+Δt / 2 and t, respectively; Update position using half-step linear velocity: ; in, Let be the positions of particle p at times t+Δt and t, respectively; Update the forces after updating the position: ; Update the complete linear velocity using the updated forces: .

[0010] Furthermore, a contact mechanics model is used to provide the contact forces affecting the packing angle and porosity for the discrete element method simulation. The process includes: Define the particle properties of materials used in smelting, including: particle type, density, elastic modulus, shear modulus, Poisson's ratio, coefficient of friction between particles, and coefficient of friction between particle walls; Calculation of normal contact force between particles in smelting materials using the Hertz-Mindlin contact mechanics model Contact force with tangential direction : ; in, For the equivalent elastic modulus, , Poisson's ratio is the ratio of two materials in contact. The elastic modulus of the two materials; The equivalent contact radius is determined based on the average diameter of the two material particle types. , It is the average diameter; The normal penetration depth of the two materials; The tangential stiffness coefficient is... , Equivalent shear modulus , The shear modulus of the two materials; The tangential overlap between the two materials; The tangential damping coefficient is... The tangential relative velocity.

[0011] Furthermore, the measurement of the angle of repose and porosity distribution is based on the simulated stockpile: When measuring the angle of repose, the three-dimensional surface of the material pile is reconstructed, the contour of the material surface is extracted by Voronoi subdivision, multiple radial profiles are taken along the circumference, and the average angle of repose of the selected radial profiles is taken as the measured angle of repose. When measuring porosity distribution, the accumulation area of ​​the material pile is divided into a pile network. The porosity within each pile network is calculated using the ratio of the total volume of particles within the pile network to the volume of the pile network itself. , in, Let p be the volume of particle. The particle p is confined within the material pile grid cell. The volume of the material pile grid cell; Statistically analyze the radial or axial porosity gradient curves of all material pile grids.

[0012] Furthermore, the heat transfer model comprehensively considers three heat transfer mechanisms: heat conduction, heat convection, and heat radiation. For heat conduction, it is calculated using Fourier's law based on the thermal conductivity physical parameters of different materials in the furnace. For heat convection, it is simulated using Newton's law of cooling, taking into account the flow characteristics of the gas in the furnace and the temperature gradient in different areas. For heat radiation, it is described using the radiation transfer equation based on the radiative heat transfer characteristics under the high-temperature environment in the furnace.

[0013] Furthermore, the mass transfer model incorporates a pore-corrected diffusion coefficient and, combined with the velocity and concentration fields of the gas flow, accurately calculates the gas diffusion flux using the Fick model. The Fick model for porosity correction is as follows: ; in, The mass flux of gaseous component i represents the amount of moles of substance passing through a unit area per unit time; The free diffusion coefficient; Porosity; The concentration of gas component i, The apparent velocity of the gas is calculated using the flow equations for porous media. Porous media flow equation formula: ; For pressure drop, The height of the material pile, For gas dynamic viscosity, The density of the gas; The coupling with chemical reactions is established through Sherwood number correlations, as shown in the formula: ; in, The mass transfer coefficient (m / s) is used to calculate the rate at which a component reaches the particle surface, and is therefore related to the reduction reaction rate. Where A is the specific surface area of ​​the particles. Particle surface concentration of gas component i.

[0014] Furthermore, the chemical reaction model covers the processes of coke combustion, iron ore reduction, and slag formation: for the coke combustion reaction, the combustion rate and the generation of combustion products are accurately described by kinetic equations based on the composition and particle size of the coke and the oxygen supply in the furnace. For the reduction reaction of iron ore, considering the characteristics of different reduction stages and the influence of temperature and gas composition conditions, accurate simulation is carried out using the corresponding chemical reaction equilibrium constants and kinetic parameters. For the slag-forming reaction, based on the composition of the furnace charge and the temperature and pH conditions inside the furnace, a phase diagram model is used to model the relationship between the liquidus temperature of the slag and its various components: ; in, The liquidus temperature and alkalinity of the slag; The mass fractions of calcium oxide, silicon dioxide, and aluminum oxide in slag are determined by adding CaO to increase basicity and lower melting point, and adding aluminum oxide to increase melting point.

[0015] Furthermore, the blowing model is configured with the physical properties of the blowing material, including: particle size distribution, density, and volatile matter content; Configure the parameters of the blowing equipment, including: blowing pressure and blowing speed; A model for the motion and combustion of injected material is constructed, in which the dynamics of the injected material particles in the blast furnace tuyeres are described by Newton's second law: ; in, , The mass velocity of the sprayed material particles. For aerodynamic drag, For gravity; For thermophoretic force; For Saffman lift; , The drag coefficient, For jet density, The projected area of ​​the sprayed material particles. The jet velocity and the velocity of the propellant particles; , Diameter of the sprayed material particles; ; In the combustion model, the kinetics of volatile matter combustion reaction are as follows: ; Kinetic equations for combustion of fixed carbon: ; Thermochemical coupling was constructed using the thermal equilibrium equation and the Boudouard chemical equilibrium equation.

[0016] Secondly, the present invention provides an apparatus for evaluating the minimum fuel ratio in a blast furnace ironmaking process, comprising: at least one processing unit, the processing unit being connected to a storage unit via a bus unit, the storage unit storing a computer program, and the processing unit implementing the method for evaluating the minimum fuel ratio in a blast furnace ironmaking process by running the computer program stored in the storage unit.

[0017] Thirdly, the present invention provides a computer-readable storage medium storing a computer program, which, when executed, implements the method for evaluating the minimum fuel ratio in the blast furnace ironmaking process.

[0018] The technical solutions provided in the embodiments of the present invention have the following advantages compared with the prior art: Preferably, the blast furnace model includes at least: a top charging model, a heat transfer model, a mass transfer model, a chemical reaction model, a blowing model, a gas-solid dual-phase model, and a softening zone model. A rich and accurate blast furnace model can more meticulously depict the complex processes within the blast furnace, improving the scientific rigor and reliability of the entire evaluation method.

[0019] The present invention proposes a method for evaluating the minimum fuel ratio in a blast furnace ironmaking process based on computational fluid dynamics and simulation, which has the following significant advantages: This method, by combining a precise computational fluid dynamics model with comprehensive production data, can more accurately evaluate the minimum fuel ratio in the blast furnace ironmaking process, overcoming the current situation where existing methods for reducing the fuel ratio in blast furnace production mainly rely on operating procedures and personnel experience, and improving the accuracy of the evaluation results.

[0020] Utilizing advanced computational fluid dynamics algorithms and simulation technology, this method simulates and analyzes the blast furnace ironmaking process from a physicochemical perspective, making the evaluation method more scientific and providing a more reliable theoretical basis for optimizing blast furnace ironmaking. Through computer simulation, the blast furnace ironmaking process under different operating conditions and parameters can be quickly simulated and analyzed. Compared with traditional experimental and empirical methods, this significantly improves evaluation efficiency and helps enterprises optimize production processes and reduce costs more quickly. This evaluation method can be flexibly adjusted and applied according to the actual equipment parameters and production data of different blast furnaces, and has wide applicability. Whether for large, medium, or small blast furnaces, this method can effectively evaluate the minimum fuel ratio. Attached Figure Description

[0021] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0022] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating a method for determining the minimum fuel ratio in a blast furnace ironmaking process, provided as an embodiment of the present invention; Figure 2 This is a schematic diagram of an apparatus for evaluating the minimum fuel ratio in a blast furnace ironmaking process, provided in an embodiment of the present invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0026] Example 1 See Figure 1 As shown, the method for evaluating the minimum fuel ratio in the blast furnace ironmaking process provided in this application utilizes blast furnace production data and evaluates the minimum fuel ratio under blast furnace smelting conditions based on computational fluid dynamics algorithms combined with simulation, including: Step 1: Collect various parameter data of the blast furnace equipment and production data during the blast furnace production process. The blast furnace equipment parameter data and production data include: blast furnace volume, blast furnace height, blast furnace diameter, blast furnace throat diameter, exhaust temperature, utilization coefficient, daily output, hot blast temperature, top pressure, coke ratio, pulverized coal injection ratio, and slag-to-iron ratio.

[0027] Step Two: Using 3D modeling software, construct a 3D model of the blast furnace body using blast furnace equipment parameters such as blast furnace volume, height, and inner diameter. Suitable 3D modeling software includes SolidWorks, ANSYS, and FLUENT. During the modeling process, the blast furnace body must be drawn according to the actual shape characteristics of the blast furnace to ensure that the established 3D model accurately reflects the physical structure of the blast furnace, providing a reliable foundation model for subsequent simulations.

[0028] Step 3: Mesh the 3D model of the blast furnace body according to the set configuration.

[0029] The constructed 3D model of the blast furnace body is imported as input data into fluid simulation software, such as FluentMeshing. The mesh generation configuration in the fluid simulation software includes: Based on the dimensions of the 3D model of the blast furnace body, the maximum and minimum mesh sizes are set, and the mesh growth rate is set to 1.2 to generate a surface mesh. The boundary layer is set according to the specific location of the blast furnace body three-dimensional model structure. The number of boundary layers is set between 5 and 7, the growth rate is kept at 1.2, and the transition ratio is set at 0.272. The volume mesh is set to a hexahedral mesh, and the growth rate is also 1.2, thus generating the final required volume mesh.

[0030] Through the above meshing configuration, the meshed 3D model of the blast furnace body balances computational accuracy and efficiency, providing a good mesh foundation for subsequent fluid dynamics calculations and simulations.

[0031] Step 4: Based on the principles of computational fluid dynamics, the 3D model of the blast furnace body is used as the input model to establish the blast furnace sub-model. The blast furnace sub-model includes: furnace top charging model, heat transfer model, mass transfer model, chemical reaction model, injection model, gas-solid two-phase model, and softening zone model.

[0032] In the blast furnace ironmaking process, the uniformity and rationality of the top charging have a significant impact on the gas flow distribution and material reaction within the furnace. The top charging model is constructed based on the actual operating mechanism of the blast furnace charging equipment and the physical properties of the materials. It considers the falling trajectory and accumulation pattern of the charge particles within the furnace under different charging methods, as well as the resulting charge distribution state. Examples of charging methods include ring charging, spiral charging, and fixed-point charging. By combining mathematical and physical models, the model simulates the spatial distribution of the charge within the furnace under various charging operations, thereby accurately reflecting the impact of the charging process on the overall physicochemical environment within the furnace.

[0033] Taking the annular feeding furnace top feeding model as an example: the annular feeding system forms a concentric annular material layer by rotating the feeding chute, controlling the distribution of furnace materials of different particle sizes.

[0034] The discrete element method (DEM) was used to simulate the particle packing angle and porosity distribution under the annular fabric: The angle of repose is the slope angle formed after particles are packed together, influenced by friction and rolling resistance between particles. A higher coefficient of friction makes particles less prone to sliding during packing, resulting in a steeper angle of repose. Conversely, a lower coefficient of friction makes particles more likely to slide, leading to a smaller angle of repose. Porosity, on the other hand, is related to the density of particle packing and is influenced by particle shape, size distribution, and packing method. In discrete element method (DEM) simulations, the interaction forces between particles are defined through a contact mechanics model as factors affecting particle motion and packing processes, thus determining the final angle of repose and porosity distribution. The entire process includes: Define the inclination angle θ of the charging chute, the rotation radius R, and the blast furnace throat diameter D; construct a three-dimensional annular charging domain, dividing the particle falling area and the accumulation area boundary. Configure the chute rotation speed, and define the inlet particle flow rate through mass flow rate or volumetric flow rate; The falling particles of smelting feed follow parabolic kinematics. Considering the inclination angle θ of the feeding chute, the rotational speed ω, and the gravitational acceleration g, the following trajectory equation for the falling particles is established to give the initial contact position between the smelting feed particles and the feed pile during the change of the feed pile: .

[0035] The contact mechanics model is used to provide influencing factors for discrete element method (DEM) simulations, including: Define the particle properties of the smelting material, including: particle type, density, elastic modulus, shear modulus, Poisson's ratio, inter-particle friction coefficient, and inter-particle wall friction coefficient. Particle type is defined by diameter distribution; one example shows that the diameter distribution of the smelting material particles follows a Gaussian distribution. Calculation of normal contact force between particles in smelting materials using the Hertz-Mindlin contact mechanics model Contact force with tangential direction : ; in, For the equivalent elastic modulus, , Poisson's ratio is the ratio of two materials in contact. The elastic modulus of the two materials; The equivalent contact radius is determined based on the average diameter of the two material particle types. , It is the average diameter; The normal penetration depth of the two materials; The tangential stiffness coefficient is... , Equivalent shear modulus , The shear modulus of the two materials; The tangential overlap between the two materials; The tangential damping coefficient is... The tangential relative velocity.

[0036] Calculate the rolling friction torque between particles in smelting materials: ; in, The coefficient of rolling friction is This is the unit vector of relative angular velocity between particles.

[0037] At predetermined time steps, the motion of each particle is described using Newton's and Euler's equations, based on contact force and rolling friction torque: ; in, Let p be the mass of the particle; It is the particle linear velocity; The contact force between particle p and particle q is the resultant of the tangential and normal contact forces; g is the acceleration due to gravity. Let p be the moment of inertia of the particle. Let p be the angular velocity of particle p; The torques are the rolling friction torque and the tangential contact torque between particle p and particle q. The time step does not exceed the critical time step, whereby the critical time step is: ; This is the minimum particle mass.

[0038] The particle state is updated using the velocity-Verlet algorithm at predetermined time steps: Update particle half-step linear velocity: ; in, Let be the net force acting on particle p at time t. Let be the linear velocities of particle p at times t+Δt / 2 and t, respectively.

[0039] Update position using half-step linear velocity: ; in, Let be the positions of particle p at times t+Δt and t, respectively; Update the forces after updating the position: ; Update the complete linear velocity using the updated forces: .

[0040] The simulation is performed based on the particle collision energy and momentum transfer data recorded within each time step, taking into account the motion and forces acting on the particles. The simulation continues until stability is achieved. Stability is determined using the particle collision energy and momentum transfer data when the system's kinetic energy decays to less than 1% of its initial value or the material surface height change rate is less than 0.1 mm / s.

[0041] To improve computational speed, the three-dimensional annular cloth domain is decomposed into multiple sub-regions, and each sub-region is computed in parallel. Furthermore, during the computation process, the far-field particles are aggregated using a coarse-graining method to reduce the computational load.

[0042] Measurements of angle of repose and porosity distribution were performed based on a simulated stockpile. When measuring the angle of repose, the three-dimensional surface of the material pile is reconstructed, the contour of the material surface is extracted by Voronoi subdivision, multiple radial profiles are taken along the circumference, and the average angle of repose of the selected radial profiles is taken as the measured angle of repose.

[0043] When measuring porosity distribution, the accumulation area of ​​the material pile is divided into a pile network. The porosity within each pile network is calculated using the ratio of the total volume of particles within the pile network to the volume of the pile network itself. , in, Let p be the volume of particle. The particle p is confined within the material pile grid cell. The volume of the material pile grid cell; Statistically analyze the radial or axial porosity gradient curves of all material pile grids.

[0044] The model needs to fully consider the complex physicochemical processes within the blast furnace, accurately describe the various modes of heat transfer, including conduction, convection, and radiation, and model chemical reactions such as the reduction of iron ore and the combustion of coke. Therefore, heat transfer, mass transfer, and chemical reaction models are established.

[0045] The heat transfer process inside a blast furnace is complex, involving the coupling of multiple heat transfer mechanisms. The heat transfer model described herein comprehensively considers three heat transfer mechanisms: heat conduction, heat convection, and heat radiation.

[0046] For heat conduction, calculations are performed using Fourier's law based on the thermal conductivity physical parameters of different materials inside the furnace (such as furnace wall refractory materials, furnace charge, molten iron, etc.). , For heat conduction flux, For the thermal conductivity of the material, Temperature gradient; For thermal convection, the flow characteristics of the gas inside the furnace and the temperature gradient in different regions are combined to simulate it using Newton's law of cooling: , Convective heat transfer flux; The convective heat transfer coefficient is calculated based on the gas flow state. The temperature of the solid surface participating in convection. The temperature of the gas participating in convection.

[0047] For thermal radiation, the radiation heat transfer characteristics under the high-temperature environment inside the furnace are described using a radiation transfer equation. The example uses the discrete coordinate method (DO) for modeling. The DO method discretizes the spatial directions of the blast furnace and assigns weights to each direction, dividing the blast furnace space into a grid. For each direction of each grid, the radiation heat transfer process inside the blast furnace is described by solving the following radiation transfer equation: ; in, Indicates radiation intensity The change in the spatial direction s describes the propagation of radiated energy in space.

[0048] It represents the absorption of radiation by the medium and is proportional to the absorption coefficient κ.

[0049] This refers to the thermal radiation emitted by the medium due to its own temperature.

[0050] By organically integrating the three heat transfer methods, the heat transfer model can accurately simulate the temperature distribution and dynamic changes at different locations and times inside the furnace, providing important temperature field data support for the subsequent accurate analysis of other physicochemical processes inside the blast furnace.

[0051] The mass transfer process within a blast furnace is closely related to various factors, including gas diffusion and chemical reactions of materials. The proposed mass transfer model, based on the law of conservation of mass, simulates the mass transfer process of various substances within the furnace (such as oxygen, carbon monoxide, carbon dioxide, and various chemical components in the furnace charge). Considering the complex flow field environment within the furnace and the interactions between different substances, the model incorporates a pore-corrected diffusion coefficient and, combined with the velocity and concentration fields of the gas flow, accurately calculates the gas diffusion flux using the Fick model. Furthermore, the model also incorporates corresponding coupling treatments to address the impact of various chemical reactions occurring within the furnace on the mass transfer process, thereby realistically reflecting the concentration distribution of various substances within the furnace and their changes over time, providing crucial information for accurately understanding the chemical reaction process within the blast furnace.

[0052] The Fick model for porosity correction is as follows: ; in, The mass flux of gaseous component i represents the amount of moles of substance passing through a unit area per unit time; The free diffusion coefficient is... It depends on the type of gas and temperature, such as CO at 1500°C. It is 1.5 × 10−4 m2 / s; Porosity; The concentration of gas component i, The apparent velocity of the gas is calculated using the flow equations for porous media. Describes molecular diffusion of a gas caused by a concentration gradient. The characteristic decreases due to the tortuous diffusion path of the pores. Describes the transport of components carried by the overall flow of gas.

[0053] Porous media flow equation formula: ; For pressure drop, The height of the material pile, For gas dynamic viscosity, The density is the gas density.

[0054] The coupling with chemical reactions is established through Sherwood number correlations, as shown in the formula: ; in, The mass transfer coefficient (m / s) is used to calculate the rate at which a component reaches the particle surface, and is therefore related to the reduction reaction rate. Where A is the specific surface area of ​​the particles. Particle surface concentration of gas component i.

[0055] The blast furnace ironmaking process involves a series of complex and interrelated chemical reactions, which play a decisive role in the efficiency and quality of ironmaking. The chemical reaction model encompasses the processes of coke combustion, iron ore reduction, and slagging. For the coke combustion reaction, based on the coke's composition, particle size, and the oxygen supply in the furnace, a kinetic equation accurately describes its combustion rate and the formation of combustion products. The kinetic equation for the coke combustion reaction is as follows: ; in, It is the radius of the unreacted char nucleus, which gradually decreases as combustion progresses; The density of coke; This represents the oxygen concentration.

[0056] For the reduction reaction of iron ore, considering the characteristics of different reduction stages (such as indirect reduction and direct reduction) and the influence of temperature and gas composition conditions, accurate simulation is carried out using the corresponding chemical reaction equilibrium constants and kinetic parameters. The indirect reduction of iron ore involves the formation of carbon monoxide from coke. The carbon monoxide then reacts with ferric oxide, magnetite, and iron oxide. The kinetic equation is as follows: ; in, The degree of reduction indicates the proportion of iron oxide that is reduced. It is a pre-exponential factor that reflects the frequency of the reaction; It is the ideal constant of a gas. For activation energy, This represents the carbon monoxide concentration.

[0057] The direct reduction reaction, in which carbon reduces iron oxide, follows thermodynamic equilibrium constraints: ; in, The equilibrium constant determines the direction of the reaction; For the standard Gibbs free energy change, The pressures of carbon monoxide and carbon dioxide are used to determine the effect of the carbon monoxide to carbon dioxide ratio on the reaction. High CO partial pressure inhibits the direct reduction reaction.

[0058] For the slagging reaction, the formation and evolution of the slag phase are simulated based on the composition of the furnace charge and the temperature and pH conditions inside the furnace. By organically combining these chemical reaction processes and considering the mutual influence and constraints between the reactions (such as the influence of gases generated by the reduction reaction on the combustion reaction), the chemical reaction model can accurately simulate the overall chemical changes inside the blast furnace, providing important chemical process data for optimizing blast furnace operating parameters.

[0059] The slag-forming reaction is the reaction in which calcium oxide and silicon dioxide form calcium silicate. The slag-forming reaction is the core of blast furnace slag formation. The calcium silicate produced is the main component of slag and directly affects the melting characteristics and fluidity of slag.

[0060] Modeling the relationship between the liquidus temperature and the various components of slag using a phase diagram model: ; in, The liquidus temperature and alkalinity of the slag; The mass fractions of calcium oxide, silicon dioxide, and aluminum oxide in slag are determined by adding CaO to increase basicity and lower melting point, and adding aluminum oxide to increase melting point.

[0061] In modern blast furnace ironmaking, pulverized coal injection is a crucial process. This injection model is designed to model this process. It considers the physical properties of the injected material (taking pulverized coal as an example) (such as particle size distribution, density, and volatile matter content) and the operating parameters of the injection equipment (such as injection pressure and injection speed). By tracking the trajectory of the injected material within the furnace and combining this with the airflow and temperature fields, the model simulates its dispersion, combustion, and interaction with other substances. The injection model accurately reflects the distribution of the injected material within the furnace and its impact on the overall thermal and chemical balance, providing strong technical support for optimizing the injection process.

[0062] Configure the physical properties of the sprayed material, including: particle size distribution, density, and volatile matter content; Configure the parameters of the blowing equipment, including blowing pressure and blowing speed.

[0063] Constructing a model of the motion and combustion of injected material: The motion of injected material particles in the blast furnace tuyeres is influenced by multiple forces, which can be described by Newton's second law: ; in, , The mass velocity of the sprayed material particles. For aerodynamic drag, For gravity; For thermophoretic force; For Saffman lift.

[0064] , The drag coefficient, For jet density, The projected area of ​​the sprayed material particles. The jet velocity and the velocity of the propellant particles; , Diameter of the sprayed material particles; This causes lateral displacement of particles in high-speed shear flow.

[0065] In the combustion model, the kinetics of volatile matter combustion reaction are as follows: ; The kinetic equation for the combustion of fixed carbon is the same as that for the combustion reaction of coke: ; Thermochemical coupling is constructed using the thermal equilibrium equation and the Boudouard chemical equilibrium equation, where the thermal equilibrium equation is as follows: ; in, Let b be the mass flow rate of the corresponding component b of the injected material. The isobaric specific heat capacity of the corresponding component b of the injected material. For the rate of temperature change, The combustion efficiency of pulverized coal in the injected material, The mass flow rate of pulverized coal in the injected material. The lower heating value of pulverized coal, This represents the heat loss rate.

[0066] The gas-solid two-phase flow and the formation and evolution of the softening zone within the blast furnace have a significant impact on the smooth operation and production indicators of the blast furnace. The gas-solid two-phase model, based on the Euler-Euler two-fluid model or the Euler-Lagrange particle trajectory model, accurately simulates the flow state, mixing degree, and heat and mass transfer processes at the phase interface of the gas-solid two phases, taking into account the interaction characteristics of gas and solid particles (such as burden and coke) within the furnace, the forces acting on the particles (including gravity, buoyancy, and drag), and the flow characteristics of the gas. The softening zone model, based on the furnace temperature distribution and the softening and melting characteristics of the burden, simulates the formation location, shape, thickness, and dynamic changes of the softening zone over time, while also considering the influence of the softening zone on the gas flow distribution, pressure distribution, and material descent within the furnace.

[0067] In establishing the sub-models of each blast furnace, the solver in Fluent software is set to pressure basis, the gravitational acceleration is set to 9.8 m / s², the energy equation is enabled, the k-epsilon turbulence model is adopted, and the standard wall function is processed using wall functions. Various complex physicochemical processes within the blast furnace are accurately simulated by dividing the model into groups. Furthermore, appropriate boundary conditions are set based on the actual conditions of key locations such as the blast furnace roof, tuyeres, and tapholes. The SIMPLE algorithm is used to ensure the accuracy and stability of the calculations for each sub-model.

[0068] Step 5: Integrate the various blast furnace sub-models established above to form a complete simulation model that simulates the blast furnace ironmaking process. During the integration process, the interrelationships and coupling relationships between the various blast furnace sub-models are linked to ensure that each physicochemical process can be accurately and coordinately simulated in the simulation model, thereby truly reflecting the overall picture of the blast furnace ironmaking process.

[0069] Step Six: Simulate the blast furnace production process using production data and simulation models.

[0070] The actual parameters of the blast furnace production process are input into the simulation model of the complete blast furnace ironmaking process. These parameters include, but are not limited to: exhaust temperature, utilization coefficient, daily output, hot blast temperature, blast volume, top pressure, coke ratio, pulverized coal injection ratio, slag-to-iron ratio, furnace life, charging method, molten iron output, slag production, and average furnace temperature. During the simulation, reasonable boundary conditions and initial conditions should be set for the model based on actual production conditions to improve the realism and reliability of the simulation.

[0071] Step 7: Adjust the simulation model to determine the minimum fuel ratio.

[0072] The simulation model was adjusted and optimized. The minimum fuel ratio for the blast furnace ironmaking process was determined when the ironmaking process parameters met one of the following three conditions: the furnace top gas temperature was at the dew point, the softening zone reached the dead coke zone of the blast furnace, and the molten iron temperature was below the solidification point. During the model adjustment process, the effects of changing parameters on the fuel ratio were observed to more accurately determine the minimum fuel ratio.

[0073] The heat input and output in the furnace under different operating conditions are calculated using a heat transfer model. The relationship between the heat output items (hot blast temperature, heat source of coke combustion, heat dissipation from the furnace body, heat carried away by molten iron and slag) and the fuel ratio is analyzed. For example, the corresponding trend of fuel ratio change when the hot blast temperature increases by a certain degree, and the degree of influence of changes in coke combustion on the overall heat balance and fuel ratio are observed.

[0074] By simulating blast furnace operation under different slag and molten iron temperature settings, the correlation between slag and molten iron temperature and fuel ratio was analyzed. Changes in slag and molten iron temperature affect heat consumption, which in turn affects the amount of fuel input.

[0075] Based on chemical reaction models, the influence of the equilibrium state of iron ore reduction and slagging reactions on the fuel ratio is analyzed. For example, when the degree of iron ore reduction changes, the fuel ratio is observed to change accordingly, as well as the indirect effects of different slagging components and proportions on the fuel ratio.

[0076] By adjusting the injection rate and the composition parameters of the injected material, the effects on the fuel ratio are simulated and analyzed. The combustion and gasification reaction processes of the injected material (such as pulverized coal) in the furnace, as well as the influence of its substitution relationship with other fuels such as coke, on the fuel ratio are examined.

[0077] For parameters such as air volume, top pressure, coke ratio, and pulverized coal injection ratio, a single-factor sensitivity analysis method was used. With other parameters remaining constant, the value of each parameter was changed sequentially (e.g., air volume increased or decreased within a certain range in increments), and the simulation model was run, recording the fuel ratio values ​​obtained in each simulation. By plotting the relationship curves between the changes in key parameters and the changes in fuel ratio, the sensitivity of each key parameter to the fuel ratio was visually determined, identifying the parameter with the most significant impact on the fuel ratio.

[0078] Orthogonal experimental design was used to combine multiple parameter values ​​and conduct multiple simulations. Analysis of variance was then used to analyze the overall impact of the interactions between parameters on the fuel ratio, determining the weight of each parameter's influence on the fuel ratio under different combinations.

[0079] Through the above detailed and systematic steps, the minimum fuel ratio in the blast furnace ironmaking process can be effectively evaluated based on computational fluid dynamics and simulation technology, providing strong technical support for production optimization and energy conservation and emission reduction in the steel industry.

[0080] Example 2 See Figure 2 As shown, this embodiment of the invention provides an apparatus for evaluating the minimum fuel ratio in a blast furnace ironmaking process, comprising: at least one processing unit, the processing unit being connected to a storage unit via a bus unit, the storage unit serving as a computer-readable storage medium for storing software programs, computer-executable programs, and modules, such as the software program, computer-executable program, and module corresponding to the method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to this embodiment of the invention. The processing unit implements the aforementioned method for evaluating the minimum fuel ratio in a blast furnace ironmaking process by running the software program, computer-executable program, and module stored in the storage unit, including: Collect various parameter data of blast furnace equipment and production data during the blast furnace equipment production process; Based on 3D modeling software, a 3D model of the blast furnace body is constructed using blast furnace equipment parameter data such as blast furnace volume, blast furnace height, and blast furnace inner diameter. The 3D model of the blast furnace body is meshed according to the set configuration; Based on the principles of computational fluid dynamics, a 3D model of the blast furnace body is used as the input model to establish a blast furnace sub-model. The blast furnace sub-model includes: a furnace top charging model, a heat transfer model, a mass transfer model, a chemical reaction model, a blowing model, a gas-solid two-phase model, and a softening zone model. The various blast furnace models established above are integrated to form a complete simulation model that simulates the blast furnace ironmaking process. Simulation of blast furnace production process using production data and simulation models; The simulation model is adjusted and optimized. When the ironmaking process parameters meet one of the following three conditions, the furnace top gas temperature is at the dew point temperature, the soft melting zone reaches the dead coke zone of the blast furnace, and the molten iron temperature is below the solidification point, the blast furnace fuel ratio at this time is the minimum fuel ratio for the blast furnace ironmaking process. During the process, the parameters are changed to observe their impact on the fuel ratio in order to more accurately determine the minimum fuel ratio.

[0081] Of course, the computer program stored in the storage unit of the blast furnace ironmaking process minimum fuel ratio evaluation device provided in the embodiments of the present invention is not limited to the method operation described above, and can also execute related operations in the blast furnace ironmaking process minimum fuel ratio evaluation method provided in any embodiment of the present invention.

[0082] Example 3 This invention provides a computer-readable storage medium storing a computer program. When executed, the computer program implements the method for evaluating the minimum fuel ratio in a blast furnace ironmaking process, comprising: Collect various parameter data of blast furnace equipment and production data during the blast furnace equipment production process; Based on 3D modeling software, a 3D model of the blast furnace body is constructed using blast furnace equipment parameter data such as blast furnace volume, blast furnace height, and blast furnace inner diameter. The 3D model of the blast furnace body is meshed according to the set configuration; Based on the principles of computational fluid dynamics, a 3D model of the blast furnace body is used as the input model to establish a blast furnace sub-model. The blast furnace sub-model includes: a furnace top charging model, a heat transfer model, a mass transfer model, a chemical reaction model, a blowing model, a gas-solid two-phase model, and a softening zone model. The various blast furnace models established above are integrated to form a complete simulation model that simulates the blast furnace ironmaking process. Simulation of blast furnace production process using production data and simulation models; The simulation model is adjusted and optimized. When the ironmaking process parameters meet one of the following three conditions, the furnace top gas temperature is at the dew point temperature, the soft melting zone reaches the dead coke zone of the blast furnace, and the molten iron temperature is below the solidification point, the blast furnace fuel ratio at this time is the minimum fuel ratio for the blast furnace ironmaking process. During the process, the parameters are changed to observe their impact on the fuel ratio in order to more accurately determine the minimum fuel ratio.

[0083] The computer-readable storage medium provided in the embodiments of the present invention stores a computer program that is not limited to the method operation described above, but can also execute related operations in the evaluation method for the minimum fuel ratio in a blast furnace ironmaking process provided in any embodiment of the present invention.

[0084] In the embodiments provided by this invention, it should be understood that the disclosed structures and methods can be implemented in other ways. For example, the structural embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces, structures, or units, and may be electrical, mechanical, or other forms.

[0085] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0086] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0087] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. 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 the invention. Therefore, the present invention 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 method for evaluating the minimum fuel ratio in a blast furnace ironmaking process, characterized in that, include: Collect various parameter data of blast furnace equipment and production data during the blast furnace equipment production process; Based on 3D modeling software, a 3D model of the blast furnace body is constructed using blast furnace equipment parameter data such as blast furnace volume, blast furnace height, and blast furnace inner diameter. The 3D model of the blast furnace body is meshed according to the set configuration; Based on the principles of computational fluid dynamics, a 3D model of the blast furnace body is used as the input model to establish a blast furnace sub-model. The blast furnace sub-model includes: a furnace top charging model, a heat transfer model, a mass transfer model, a chemical reaction model, a blowing model, a gas-solid two-phase model, and a softening zone model. The various blast furnace models established above are integrated to form a complete simulation model that simulates the blast furnace ironmaking process. Simulation of blast furnace production process using production data and simulation models; The simulation model is adjusted and optimized. When the ironmaking process parameters meet one of the following three conditions, the furnace top gas temperature is at the dew point temperature, the soft melting zone reaches the dead coke zone of the blast furnace, and the molten iron temperature is below the solidification point, the blast furnace fuel ratio at this time is the minimum fuel ratio for the blast furnace ironmaking process. During the process, the parameters are changed to observe their impact on the fuel ratio in order to more accurately determine the minimum fuel ratio.

2. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The configuration for mesh generation of the 3D model of the blast furnace body includes: Based on the dimensions of the 3D model of the blast furnace body, the maximum and minimum mesh sizes are set, and the mesh growth rate is set to 1.2 to generate a surface mesh. The boundary layer is set according to the specific location of the blast furnace body three-dimensional model structure. The number of boundary layers is set between 5 and 7, the growth rate is kept at 1.2, and the transition ratio is set at 0.

272. The volume mesh is set to a hexahedral mesh, and the growth rate is also 1.2, thus generating the final required volume mesh.

3. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The furnace top material distribution model uses the discrete element method to simulate the packing angle and porosity distribution of particles under the material distribution. Define the inclination angle θ of the feeding chute, the radius of rotation R, and the diameter of the blast furnace throat D; construct a three-dimensional annular feeding domain and divide the boundary between the particle falling area and the accumulation area; configure the chute rotation speed and define the inlet particle flow rate by mass flow rate or volume flow rate. The falling particles of smelting materials follow parabolic kinematics. The contact mechanics model is used to provide the contact forces that affect the angle of repose and porosity in the discrete element method simulation; Calculate the rolling friction torque between particles in smelting materials: ； in, The coefficient of rolling friction is This is the unit vector of relative angular velocities between particles; At predetermined time steps, the motion of each particle is described using Newton's and Euler's equations, based on contact force and rolling friction torque: ； in, Let p be the mass of the particle; It is the particle linear velocity; The contact force between particle p and particle q is the resultant of the tangential and normal contact forces; g is the acceleration due to gravity. Let p be the moment of inertia of the particle. Let p be the angular velocity of particle p; The torques are the rolling friction torque and the tangential contact torque between particle p and particle q. The particle state is updated using the velocity-Verlet algorithm at set time steps. Based on the particle collision energy and momentum transfer data recorded within each time step, the simulation continues until stability is achieved. Stability is determined using the particle collision energy and momentum transfer data. Measurements of the angle of repose and porosity distribution were performed on a simulated stockpile.

4. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 3, characterized in that, The particle state is updated using the velocity-Verlet algorithm at predetermined time steps, including: Update particle half-step linear velocity: ； in, Let be the net force acting on particle p at time t. Let be the linear velocities of particle p at times t+Δt / 2 and t, respectively; Update position using half-step linear velocity: ； in, Let be the positions of particle p at times t+Δt and t, respectively; Update the forces after updating the position: ； Update the complete linear velocity using the updated forces: 。 5. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 3, characterized in that, The contact forces affecting the angle of repose and porosity are provided for the discrete element method simulation using a contact mechanics model. The process includes: Define the particle properties of materials used in smelting, including: particle type, density, elastic modulus, shear modulus, Poisson's ratio, coefficient of friction between particles, and coefficient of friction between particle walls; Calculation of normal contact force between particles in smelting materials using the Hertz-Mindlin contact mechanics model tangential contact force : ； in, For the equivalent elastic modulus, , Poisson's ratio is the ratio of two materials in contact. The elastic modulus of the two materials; The equivalent contact radius is determined based on the average diameter of the two material particle types. , It is the average diameter; The normal penetration depth of the two materials; The tangential stiffness coefficient, , Equivalent shear modulus , The shear modulus of the two materials; The tangential overlap between the two materials; The tangential damping coefficient is... The tangential relative velocity.

6. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 3, characterized in that, The measurement of the angle of repose and porosity distribution based on the simulated stockpile is as follows: When measuring the angle of repose, the three-dimensional surface of the material pile is reconstructed, the contour of the material surface is extracted by Voronoi subdivision, multiple radial profiles are taken along the circumference, and the average angle of repose of the selected radial profiles is taken as the measured angle of repose. When measuring porosity distribution, the accumulation area of ​​the material pile is divided into a pile network. The porosity within each pile network is calculated using the ratio of the total volume of particles within the pile network to the volume of the pile network itself. ， in, Let p be the volume of particle. The particle p is confined within the material pile grid cell. This refers to the volume of the material pile grid cell. Statistically analyze the radial or axial porosity gradient curves of all material pile grids.

7. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The heat transfer model comprehensively considers three heat transfer mechanisms: heat conduction, heat convection, and heat radiation. For heat conduction, it is calculated using Fourier's law based on the thermal conductivity physical parameters of different materials in the furnace. For heat convection, it is simulated using Newton's law of cooling, taking into account the flow characteristics of the gas in the furnace and the temperature gradient in different areas. For heat radiation, it is described using the radiation transfer equation based on the radiative heat transfer characteristics under the high-temperature environment in the furnace.

8. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The mass transfer model incorporates a pore-corrected diffusion coefficient and, combined with the gas flow velocity and concentration fields, accurately calculates the gas diffusion flux using the Fick model. The Fick model for porosity correction is as follows: ； in, The mass flux of gaseous component i represents the amount of moles of substance passing through a unit area per unit time; The free diffusion coefficient; Porosity; The concentration of gas component i, The apparent velocity of the gas is calculated using the flow equations for porous media. Porous media flow equation formula: ； For pressure drop, The height of the material pile, For gas dynamic viscosity, The density of the gas; The coupling with chemical reactions is established through Sherwood number correlations, as shown in the formula: ； in, The mass transfer coefficient (m / s) is used to calculate the rate at which a component reaches the particle surface, and is therefore related to the reduction reaction rate. Where A is the specific surface area of ​​the particles. Particle surface concentration of gas component i.

9. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The chemical reaction model covers the processes of coke combustion, iron ore reduction, and slag formation: for the coke combustion reaction, the combustion rate and the generation of combustion products are accurately described by kinetic equations based on the composition and particle size of the coke and the oxygen supply in the furnace. For the reduction reaction of iron ore, considering the characteristics of different reduction stages and the influence of temperature and gas composition conditions, accurate simulation is carried out using the corresponding chemical reaction equilibrium constants and kinetic parameters. For the slag-forming reaction, based on the composition of the furnace charge and the temperature and pH conditions inside the furnace, a phase diagram model is used to model the relationship between the liquidus temperature of the slag and its various components: ； in, The liquidus temperature and alkalinity of the slag; The mass fractions of calcium oxide, silicon dioxide, and aluminum oxide in slag are determined by adding CaO to increase basicity and lower melting point, and adding aluminum oxide to increase melting point.

10. The method for evaluating the minimum fuel ratio in a blast furnace ironmaking process according to claim 1, characterized in that, The jetting model is configured with the physical properties of the jetting material, including: particle size distribution, density, and volatile matter content; Configure the parameters of the blowing equipment, including: blowing pressure and blowing speed; A model for the motion and combustion of injected material is constructed, in which the dynamics of the injected material particles in the blast furnace tuyeres are described by Newton's second law: ； in, , The mass velocity of the sprayed material particles. For aerodynamic drag, For gravity; For thermophoretic force; For Saffman lift; , The drag coefficient, For jet density, The projected area of ​​the sprayed material particles. The jet velocity and the velocity of the propellant particles; , Diameter of the sprayed material particles; ； In the combustion model, the kinetics of volatile matter combustion reaction are as follows: ； Kinetic equations for combustion of fixed carbon: ； Thermochemical coupling was constructed using the thermal equilibrium equation and the Boudouard chemical equilibrium equation.

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