3D numerical modeling analysis method for municipal solid waste incineration oriented to particulate matter generation

CN116579039BActive Publication Date: 2026-10-16BEIJING UNIV OF TECH
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Patent Information

Application Number
CN202310620061.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2023-05-29
Publication Date
2026-10-16
Estimated Expiration
2043-05-29

AI Technical Summary

Technical Problem

[0004]针对3D模型的仿真模拟主要是分析焚烧炉内燃烧情况或某一参数对MSWI过程整体的影响,缺少针对颗粒物的数值建模与分析,未深入研究影响颗粒物浓度特性的因素

Benefits of technology

[0071] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation provided by the present invention first obtains incineration plant information from actual design drawings and then constructs a 3D model of the incinerator and waste heat boiler. Combining mechanism and experience, the key factors affecting particulate matter generation are determined to be solid MSW combustion temperature, wall particle collision mode, and second baffle length. Then, the solution method of the 3D model is described. Then, the key factors are analyzed based on the 3D model as single factors. Finally, the influence of the key factors on the particulate matter concentration at the outlet is analyzed based on orthogonal experiments to obtain the optimal parameter combination. This can provide data support for reducing particulate matter concentration from the perspective of process improvement and optimization control, and can provide support for accumulating experience in the simulation of particulate matter in MSWI process and obtaining the theoretical upper and lower limits of particulate matter emission concentration.

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Abstract

The application provides a kind of city solid waste incineration 3D numerical modeling analysis method for particulate matter generation, the method is first from actual design drawing obtains the information of incineration plant, and then constructs the 3D model of incinerator and waste heat boiler, the key factors for influencing particulate matter generation are determined by combining mechanism and experience, solid MSW combustion temperature, wall particle collision mode and second baffle length, then the solving method of 3D model is described, then the key factors are analyzed based on 3D model, finally, the influence of the key factors on the concentration of particulate matter at the outlet is analyzed based on orthogonal experiment, and the best parameter combination is obtained. The city solid waste incineration 3D numerical modeling analysis method for particulate matter generation provided by the application can realize the construction of city solid waste combustion 3D model, can carry out numerical modeling analysis on particulate matter, and then study the factors influencing the concentration characteristics of particulate matter.
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Description

Technical Field

[0001] This invention relates to the field of urban solid waste treatment technology, and in particular to a 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation. Background Technology

[0002] Municipal solid waste (MSW) refers to items and materials generated during production, daily life, and other activities that have lost their original value or have not lost their utilization value but are discarded. The increasing amount of MSW has had varying degrees of negative impact on residents' daily lives and socio-economic development, even leading to environmental problems such as "garbage siege." MSW incineration technology has significant advantages such as high volume reduction rate, fast processing speed, and on-site incineration capability, making it one of the effective methods for solving these environmental problems. Grate-type incinerators are widely used due to their reliable technology, large capacity, strong adaptability, and convenient operation and maintenance.

[0003] Despite its numerous advantages, MSWI technology also generates a variety of air pollutants, including particulate matter (PM2.5 and PM10), acid gases (NOx, SO2, and HCl, etc.), heavy metals and their compounds, and trace organic compounds (dioxins, furans, etc.). Fine particulate matter is the main component of fly ash produced by the MSWI process and is one of the main sources of PM2.5 in the atmosphere. Studies have shown that fine particulate matter fly ash has strong adsorption properties, and the content of heavy metals within it increases with decreasing fly ash particle size. These heavy metals are non-degradable and possess toxicity and bioavailability, which can lead to various diseases and even death in humans. Therefore, it is essential to conduct 3D simulations of particulate matter concentration and diffusion levels during the MSWI process to provide feasible suggestions for controlling particulate matter generation concentration and improving particulate matter capture equipment, thereby reducing particulate matter content.

[0004] Simulations using 3D models primarily analyze combustion conditions within the incinerator or the impact of a specific parameter on the overall MSWI process, lacking numerical modeling and analysis specifically for particulate matter, and failing to delve into the factors influencing particulate matter concentration characteristics. Therefore, current research lacks studies on numerical modeling and analysis of particulate matter within the incinerator using 3D models that include both solid waste combustion and waste heat exchange sections. Thus, designing a 3D numerical modeling and analysis method for urban solid waste incineration, specifically addressing particulate matter generation, is essential. Summary of the Invention

[0005] The purpose of this invention is to provide a 3D numerical modeling and analysis method for urban solid waste incineration that addresses particulate matter generation. This method enables the construction of a 3D model for urban solid waste incineration, allows for numerical modeling and analysis of particulate matter, and further studies the factors affecting particulate matter concentration characteristics.

[0006] To achieve the above objectives, the present invention provides the following solution:

[0007] A 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation includes the following steps:

[0008] Step 1: Construct a 3D model of the incinerator and waste heat boiler based on the actual design drawings. Combine the MSWI process flow and the particulate matter generation mechanism to determine the key factors affecting the outlet particulate matter concentration. According to the on-site operation requirements, obtain the baseline operating condition adjustment and conduct the baseline experiment. Based on the baseline experiment, simulate and study the impact of the key factors on the outlet particulate matter concentration.

[0009] Step 2: Describe the solution method for the 3D model of the incinerator and waste heat boiler;

[0010] Step 3: Conduct single-factor analysis on the key factors affecting the outlet particle concentration;

[0011] Step 4: Conduct orthogonal experimental analysis on the key factors affecting the outlet particle concentration.

[0012] Optionally, in step 1, a 3D model of the incinerator and waste heat boiler is constructed based on the actual design drawings. Combining the MSWI process flow and the particulate matter formation mechanism, the key factors affecting the outlet particulate matter concentration are determined. According to on-site operational requirements, baseline operating parameters are obtained, and baseline experiments are conducted. Based on the baseline experiments, the impact of key factors on the outlet particulate matter concentration is simulated and studied. Specifically:

[0013] Based on the actual design drawings, a 3D model of the incinerator and waste heat boiler was constructed. Combining the MSWI process flow and the particulate matter generation mechanism, the key factors affecting the outlet particulate matter concentration were determined. According to the on-site operation requirements, the benchmark operating parameters were obtained and benchmark experiments were conducted. Based on the benchmark experiments, the influence of key factors on the outlet particulate matter concentration was simulated and studied. Among them, the key factors affecting the outlet particulate matter concentration include the solid MSW combustion temperature, the wall particle collision mode, and the length of the second baffle.

[0014] Optionally, in step 2, the solution method for the 3D model of the incinerator and waste heat boiler is described, specifically as follows:

[0015] A third-order discrete scheme was used for data modeling. Fluent was used to simulate the gas-phase heat and mass transfer processes above the bed in an incinerator and waste heat boiler. A discrete phase model was used to solve the particle diffusion process, and a coupled algorithm was used to solve the steady-state control equations. The simulation process was brought to convergence by increasing the number of iterations and reducing the relaxation factor. The gas-phase conservation equations, turbulence model, and discrete phase model were calculated respectively. The gas-phase conservation equations include the continuity equation, momentum equation, and energy equation, which are as follows:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, ρ g U is the gas density. g and V g For velocities in the X and Y directions, the source term S sg p is the rate at which MSW is converted into gas. g For gas pressure, F(U) g ) and F(V g H represents the resistance of the bed to gas flow, calculated using the Ergun equation. g For gas enthalpy, λ g Q is the thermal diffusivity, which is composed of diffusion and turbulence. h The heat gained by the gas phase due to combustion;

[0021] The turbulence model is as follows: the K-Omega SST model is used to calculate turbulent motion, and the k-equations and omega equations are used for the rest, specifically:

[0022]

[0023]

[0024] In the formula, U i For the i-th component of velocity, U j Let x be the j-th component of the velocity. i ρ is a Cartesian coordinate system; ρ is the fluid density, μ is the viscosity, and σ is the viscosity. k β * σ ω γ, β and σ ω2 Here are the model coefficients, F1 is the mixing function, and k and ω are the turbulent kinetic energy and specific turbulent dissipation rate, respectively, as shown below:

[0025]

[0026]

[0027] In the formula, u avg Let I be the average velocity, I be the turbulence intensity, and C be the turbulence intensity. μ τ is the empirical constant of the K-Omega model, taken as 0.09, l is the characteristic length of the obstacle, and τ ij For Reynolds stress, it is:

[0028]

[0029] In the formula, δ ijLet ν be the Kronecker function. T =μ T / ρ represents dynamic eddy viscosity, μ T It exhibits eddy viscosity;

[0030] The discrete phase model involves solving the Navier-Stokes equations for the continuous phase fluid within an Euler framework. Before starting the continuous phase calculations, the discrete phase model is configured. Once the initial values ​​of the continuous phase calculations are obtained, particles are injected into the flow field, i.e., sprayed into the flow field in the form of a surface. The discrete phase model calculates the particle trajectory equations within a Lagrange framework. Simultaneously, the particle mass load also affects the gas phase flow field. When the calculation converges again, the results are obtained in terms of particle trajectories. The particle motion equations are established based on Newton's second law. By applying the equilibrium equations of the external forces acting on the particles, the following motion trajectory equations are obtained:

[0031]

[0032]

[0033] In the formula, U is the fluid phase velocity, with units of m / s. p F represents the velocity of particulate matter, measured in m / s. The subscript p indicates the particle size. p For Saffman lift and virtual mass force, ρ p For particle density, d p Where μ is the particle size, μ is the viscosity coefficient, and C is the particle size. d As a correction factor, the concentration distribution of particulate matter was obtained using the log-normal distribution method, and the distribution of the random variable x is as follows:

[0034]

[0035]

[0036]

[0037] In the formula, θ and σ are parameters, and m g and S g These are the geometric mean and standard deviation, respectively, x i Here, n represents the particulate matter concentration value, and n is the number of concentration values. The formula for calculating the percentage concentration of particulate matter is:

[0038]

[0039] In the formula, q i For percentiles, z i The deviation of the percentile from the median is used. Since particles will rebound on the wall surface, the rebound recovery coefficients in the normal and tangential directions of fly ash, proposed by Grant & Tabakoff, are used. The calculation formula is as follows:

[0040] e n =0.993-1.76θ+1.56θ 2 -0.49θ 3

[0041] e τ =0.998 - 1.16θ + 2.11θ 2 -0.67θ 3 (14)

[0042] In the formula, e n It is the normal rebound coefficient, e τ The tangential rebound coefficient;

[0043] Force analysis of particulate matter inside the furnace: In the discrete phase model settings, the particles are defined as ash-soiled and spherical in shape. The inertial force of the particles in motion is expressed as follows:

[0044]

[0045] The pressure gradient force is the force exerted on particles by the pressure gradient in the gas phase flow field, and is expressed as:

[0046]

[0047] In the formula, V P For the solid phase velocity, the spurious mass force generated by the apparent mass effect is expressed as:

[0048]

[0049] Magnus lift is the lift force generated by the rotation of particles, and it is generally on the same order of magnitude as gravity, expressed as:

[0050]

[0051] In the formula, ω p Let be the particle's spin angular velocity. In the discrete phase model, the equilibrium equations of the forces acting on the particle are as follows:

[0052]

[0053]

[0054] In the formula, F D (uu p Let be the drag force per unit mass of the particle, and Re be the relative Reynolds number, defined as:

[0055]

[0056] Traction coefficient C D The expression is:

[0057]

[0058] For a spherical particle, within a certain Reynolds number range, α1, α2, and α3 are all constants, and the gravitational force acting on the particle is as follows:

[0059]

[0060] In the formula, m p is the particle mass, and g is the acceleration due to gravity.

[0061] Optionally, in step 3, a single-factor analysis is performed on the key factors affecting the outlet particle concentration, specifically:

[0062] Single-factor analysis was performed on three factors: solid MSW combustion temperature, particle collision mode at the wall, and length of the second baffle. Let y represent the particle concentration at the incinerator outlet, and its relationship with the above three factors is expressed as follows:

[0063] y = f model (x T ,x W ,x G ) (twenty four)

[0064] In the formula, x T x W and x G These represent the values ​​of solid MSW combustion temperature, wall particle collision mode, and second baffle length, respectively.

[0065] Optionally, in step 4, an orthogonal experimental analysis is conducted on the key factors affecting the outlet particle concentration, specifically:

[0066] A multi-level comprehensive analysis was conducted on three factors: combustion temperature of solid MSW, particle collision mode on the wall, and length of the second baffle. For the orthogonal experiment, the output is as follows:

[0067]

[0068] In the formula, and They represent the values ​​of x respectively. T x W and x G The importance of each factor was analyzed using the range calculation formula for the level values ​​in the orthogonal experiment.

[0069]

[0070] In the formula, q represents the q-th factor in the orthogonal experiment, and v represents the v-th level of the q-th factor. This represents the r experimental data points at the v-th level of the q-th factor. The average value is r, which represents the number of times the level occurs in the experiment. Where q = 1, 2, 3 correspond to the solid MSW combustion temperature, the wall particle collision mode, and the second baffle length, respectively.

[0071] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation provided by the present invention first obtains incineration plant information from actual design drawings and then constructs a 3D model of the incinerator and waste heat boiler. Combining mechanism and experience, the key factors affecting particulate matter generation are determined to be solid MSW combustion temperature, wall particle collision mode, and second baffle length. Then, the solution method of the 3D model is described. Then, the key factors are analyzed based on the 3D model as single factors. Finally, the influence of the key factors on the particulate matter concentration at the outlet is analyzed based on orthogonal experiments to obtain the optimal parameter combination. This can provide data support for reducing particulate matter concentration from the perspective of process improvement and optimization control, and can provide support for accumulating experience in the simulation of particulate matter in MSWI process and obtaining the theoretical upper and lower limits of particulate matter emission concentration. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a process flow diagram of the MSWI power plant.

[0074] Figure 2 Scanning electron microscopy (SEM) images of incineration fly ash with different particle sizes;

[0075] Figure 3 This is a schematic diagram of the 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation, as described in an embodiment of the present invention.

[0076] Figure 4 A schematic diagram of the 3D model structure of the incinerator and waste heat boiler;

[0077] Figure 5 A schematic diagram of the 3D model mesh of the incinerator and waste heat boiler;

[0078] Figure 6a Velocity contour plots for the flow field of the incinerator and waste heat boiler;

[0079] Figure 6b Static pressure cloud diagrams of the flow field for incinerators and waste heat boilers;

[0080] Figure 7a Particle velocity cloud map for incinerators and waste heat boilers;

[0081] Figure 7b Particulate matter concentration cloud map for incinerators and waste heat boilers;

[0082] Figure 8 This is a schematic diagram showing the relationship between combustion temperature and particulate matter concentration for different solid MSWs under the rebound mode.

[0083] Figure 9 This is a schematic diagram showing the relationship between combustion temperature and particulate matter concentration of different solid MSWs under different capture methods.

[0084] Figure 10 This is a schematic diagram showing the relationship between the combustion temperature and particulate matter concentration of different solid MSWs under wall jetting conditions.

[0085] Figure 11a Particle concentration distribution at 850K for solid MSW combustion temperature during rebound mode;

[0086] Figure 11b Particle concentration distribution at a combustion temperature of 965K for solid MSW in the rebound mode;

[0087] Figure 12 This is a schematic diagram showing the relationship between the collision modes and concentrations of three wall-mounted particles at the same solid MSW combustion temperature.

[0088] Figure 13 This is a graph showing the changes in particle concentration under different baffle lengths. Detailed Implementation

[0089] The purpose of this invention is to provide a 3D numerical modeling and analysis method for urban solid waste incineration that addresses particulate matter generation. This method enables the construction of a 3D model for urban solid waste incineration, allows for numerical modeling and analysis of particulate matter, and further studies the factors affecting particulate matter concentration characteristics.

[0090] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0091] The process flow of a certain mechanical grate furnace MSWI process is as follows: Figure 1As shown. After undergoing fracture, high-temperature decomposition, and oxidation processes within the furnace, the complex composition of MSW (Metal-Oxide Flue Gas) gradually decreases in volume and particle size, eventually forming particles. Most of the non-combustible materials in the furnace are retained on the grate and discharged as slag. Some small, lightweight substances react with the high-temperature gases to form particulate-containing flue gas within the furnace, which is then discharged from the boiler tail end via the flue. The particles are mostly irregularly shaped aggregates, with spherical, rod-shaped, and flocculent aggregates being relatively less common. Field measurement data from an MSW plant in Beijing shows that the particle size of the flue gas exhibits a normal distribution, with 70% concentrated in the 38.5–75 μm range. Fly ash particles smaller than 38.5 μm and larger than 450 μm account for 6.3% and 2.9%, respectively. The microstructure of fly ash particles of different sizes is shown in the figure. Figure 2 As shown.

[0092] Depend on Figure 2 It is evident that the composition and structure of incineration fly ash exhibit significant differences, with numerous irregular agglomerates, uneven particle surfaces, and a divergent particle distribution. Studies show that smaller particle sizes correspond to smaller interparticle porosity and a more compact particle distribution. Research also indicates that the content and leaching toxicity of heavy metals vary across particles of different sizes, with the content relatively increasing as particle size decreases. Heavy metals in particulate matter possess non-degradable characteristics, toxicity, and bioavailability, posing a serious threat to human health. Therefore, 3D numerical modeling of particulate matter generation in the MSWI process is essential for achieving emission reduction control and optimization.

[0093] like Figure 3 As shown in the embodiment of the present invention, the 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation includes the following steps:

[0094] Step 1: Construct a 3D model of the incinerator and waste heat boiler based on the actual design drawings. Combine the MSWI process flow and the particulate matter generation mechanism to determine the key factors affecting the outlet particulate matter concentration. According to the on-site operation requirements, obtain the benchmark operating parameters and conduct benchmark experiments. Based on the benchmark experiments, simulate and study the impact of key factors on the outlet particulate matter concentration.

[0095] Step 2: Describe the solution method for the 3D model of the incinerator and waste heat boiler;

[0096] Step 2 provides a method for solving the 3D model constructed in Step 1, which is also the solution method used for particle simulation experiments and benchmark experiments for the three key factors in Step 3. It also provides the algorithm, model and control equations selected when using FLUENT software for simulation experiments. The simulation results provide data support for the visualization analysis in Steps 3 and 4.

[0097] Step 3: Conduct single-factor analysis on the key factors affecting the outlet particle concentration;

[0098] Step 4: Conduct orthogonal experimental analysis on the key factors affecting the outlet particle concentration.

[0099] In step 1, a 3D model of the incinerator and waste heat boiler is constructed based on the actual design drawings. Combining the MSWI process flow and the particulate matter formation mechanism, the key factors affecting the outlet particulate matter concentration are determined. According to on-site operational requirements, baseline operating parameters are obtained, and baseline experiments are conducted. Based on the baseline experiments, the impact of the key factors on the outlet particulate matter concentration is simulated and studied. Specifically:

[0100] Based on the actual design drawings, a 3D model of the incinerator and waste heat boiler was constructed. Combining the MSWI process flow and the particulate matter generation mechanism, the key factors affecting the outlet particulate matter concentration were determined. According to the on-site operation requirements, the benchmark operating parameters were obtained and benchmark experiments were conducted. Based on the benchmark experiments, the influence of key factors on the outlet particulate matter concentration was simulated and studied. Among them, the key factors affecting the outlet particulate matter concentration include solid MSW combustion temperature, wall particle collision mode and second baffle length.

[0101] The 3D model structure constructed by this invention is as follows: Figure 4 As shown, in Figure 4 In the incinerator, the widths of the grate and flue are 12.9m and 11.622m respectively. The grate is divided into three sections: a drying section, a combustion section, and a burnout section, with lengths of 2.81m, 5.57m, and 2.14m respectively. The lengths of the three flues of the incinerator from left to right are 4.68m, 2.423m, and 2.4m respectively. The height of the incinerator is 22.5m. The waste heat boiler has a length of 25.975m, a height of 6.795m, and a width of 7.1m.

[0102] Due to the complex structure of the incinerator, simplified aspects such as the economizer and waste heat boiler ash hopper were implemented during SpaceClaim modeling. When using ICEM CFD for mesh generation, the primary mesh type was Tetra / Mixed for unstructured meshing. The mesh in the furnace section was refined, resulting in an overall mesh count of 880,000. Figure 5 As shown;

[0103] Particulate matter generated by the combustion of solid MSW on the grate rises with the high-temperature gas flow. The combustion temperature of the solid MSW affects the initial concentration of particulate matter produced. As the particulate matter flows through the incinerator, it collides with the incinerator walls due to the turbulent gas flow. Different wall materials affect the collision patterns, such as bounce, adsorption, and wall jetting. Furthermore, the process design incorporates particulate trapping devices (second baffles) in the incinerator flue to reduce particulate concentration; therefore, the length of the second baffle directly impacts the particle trapping effect. Thus, the combustion temperature of the solid MSW, the wall particle collision pattern, and the length of the second baffle are crucial factors influencing the particulate matter concentration at the incinerator outlet.

[0104] Step 2 describes the solution method for the 3D model of the incinerator and waste heat boiler, specifically as follows:

[0105] A third-order discrete scheme was used for data modeling. Fluent was used to simulate the gas-phase heat and mass transfer processes above the bed in an incinerator and waste heat boiler. A discrete phase model was used to solve the particle diffusion process, and a coupled algorithm was used to solve the steady-state control equations. The simulation process was brought to convergence by increasing the number of iterations and reducing the relaxation factor. The gas-phase conservation equations, turbulence model, and discrete phase model were calculated respectively. The gas-phase conservation equations include the continuity equation, momentum equation, and energy equation, which are as follows:

[0106]

[0107]

[0108]

[0109]

[0110] In the formula, ρ g U is the gas density. g and V g For velocities in the X and Y directions, the source term S sg p is the rate at which MSW is converted into gas. g For gas pressure, F(U) g ) and F(V g H represents the resistance of the bed to gas flow, calculated using the Ergun equation. g For gas enthalpy, λ g Q is the thermal diffusivity, which is composed of diffusion and turbulence. h The heat gained by the gas phase due to combustion;

[0111] The turbulence model is as follows: The flow of turbulent gas in the incinerator is solved using the standard K-Omega model. This model is an empirical model based on the turbulence energy equation and diffusion rate equation, considering Reynolds number, compressibility, and shear flow propagation. It is suitable for numerical calculations at low Reynolds numbers. The K-Omega SST model is used to calculate turbulent motion, and the remaining equations are the k-equations and omega equations, specifically:

[0112]

[0113]

[0114] In the formula, U i For the i-th component of velocity, U j Let x be the j-th component of the velocity. i ρ is a Cartesian coordinate system; ρ is the fluid density, μ is the viscosity, and σ is the viscosity. k β * σ ω γ, β and σ ω2 Here are the model coefficients, F1 is the mixing function, and k and ω are the turbulent kinetic energy and specific turbulent dissipation rate, respectively, as shown below:

[0115]

[0116]

[0117] In the formula, u avg Let I be the average velocity, I be the turbulence intensity, and C be the turbulence intensity. μ τ is the empirical constant of the K-Omega model, taken as 0.09, l is the characteristic length of the obstacle, and τ ij For Reynolds stress, it is:

[0118]

[0119] In the formula, δ ij Let ν be the Kronecker function. T =μ T / ρ represents dynamic eddy viscosity, μ T It exhibits eddy viscosity;

[0120] The discrete phase model involves solving the Navier-Stokes equations for the continuous phase fluid within an Euler framework. Before starting the continuous phase calculations, the discrete phase model is configured. Once the initial values ​​of the continuous phase calculations are obtained, particles are injected into the flow field, i.e., sprayed into the flow field in the form of a surface. The discrete phase model calculates the particle trajectory equations within a Lagrange framework. Simultaneously, the particle mass load also affects the gas phase flow field. When the calculation converges again, the results are obtained in terms of particle trajectories. The particle motion equations are established based on Newton's second law. By applying the equilibrium equations of the external forces acting on the particles, the following motion trajectory equations are obtained:

[0121]

[0122]

[0123] In the formula, U is the fluid phase velocity, with units of m / s. p F represents the velocity of particulate matter, measured in m / s. The subscript p indicates the particle size. p For Saffman lift and virtual mass force, ρ p For particle density, d p Where μ is the particle size, μ is the viscosity coefficient, and C is the particle size. d As a correction factor, the concentration distribution of particulate matter was obtained using the log-normal distribution method, and the distribution of the random variable x is as follows:

[0124]

[0125]

[0126]

[0127] In the formula, θ and σ are parameters, and m g and S g These are the geometric mean and standard deviation, respectively, x i Here, n represents the particulate matter concentration value, and n is the number of concentration values. The formula for calculating the percentage concentration of particulate matter is:

[0128]

[0129] In the formula, q i For percentiles, z i The deviation of the percentile from the median is used. Since particles will rebound on the wall surface, the rebound recovery coefficients in the normal and tangential directions of fly ash, proposed by Grant & Tabakoff, are used. The calculation formula is as follows:

[0130] e n =0.993-1.76θ+1.56θ 2 -0.49θ 3

[0131] e τ =0.998 - 1.16θ + 2.11θ 2 -0.67θ 3 (14)

[0132] In the formula, e n It is the normal rebound coefficient, e τ The tangential rebound coefficient;

[0133] Force analysis of particulate matter inside the furnace: In the discrete phase model settings, the particles are defined as ash-soiled and spherical in shape. The inertial force of the particles in motion is expressed as follows:

[0134]

[0135] The pressure gradient force is the force exerted on particles by the pressure gradient in the gas phase flow field, and is expressed as:

[0136]

[0137] In the formula, V P For the solid phase velocity, the spurious mass force generated by the apparent mass effect is expressed as:

[0138]

[0139] Magnus lift is the lift force generated by the rotation of particles, and it is generally on the same order of magnitude as gravity, expressed as:

[0140]

[0141] In the formula, ω p Let be the particle's spin angular velocity. In the discrete phase model, the equilibrium equations of the forces acting on the particle are as follows:

[0142]

[0143]

[0144] In the formula, F D (uu p Let be the drag force per unit mass of the particle, and Re be the relative Reynolds number, defined as:

[0145]

[0146] Traction coefficient C D The expression is:

[0147]

[0148] For a spherical particle, within a certain Reynolds number range, α1, α2, and α3 are all constants, and the gravitational force acting on the particle is as follows:

[0149]

[0150] In the formula, m p is the particle mass, and g is the acceleration due to gravity.

[0151] In step 3, a single-factor analysis was conducted on the key factors affecting the outlet particle concentration, specifically:

[0152] Single-factor analysis was performed on three factors: solid MSW combustion temperature, particle collision mode at the wall, and length of the second baffle. Let y represent the particle concentration at the incinerator outlet, and its relationship with the above three factors is expressed as follows:

[0153] y = f model (x T ,x W ,x G ) (twenty four)

[0154] In the formula, x T x W and x G These represent the values ​​of solid MSW combustion temperature, wall particle collision mode, and second baffle length, respectively.

[0155] In step 4, an orthogonal experimental analysis was conducted on the key factors affecting the outlet particle concentration, specifically:

[0156] A multi-level comprehensive analysis was conducted on three factors: combustion temperature of solid MSW, particle collision mode on the wall, and length of the second baffle. For the orthogonal experiment, the output is as follows:

[0157]

[0158] In the formula, and They represent the values ​​of x respectively. T x W and x G The importance of each factor was analyzed using the range calculation formula for the level values ​​in the orthogonal experiment.

[0159]

[0160] In the formula, q represents the q-th factor in the orthogonal experiment, and v represents the v-th level of the q-th factor. This represents the r experimental data points at the v-th level of the q-th factor. The average value is r, which represents the number of times the level occurs in the experiment. When q = 1, 2, and 3, they correspond to the solid MSW combustion temperature, the wall particle collision mode, and the second baffle length, respectively.

[0161] One embodiment of the present invention is as follows: The data source is a field of an MSWI power plant in Beijing. Fluent is used to simulate the particulate flow in the incinerator. The continuous phase is calculated using the Coupled method. The velocities of the primary air inlet, secondary air inlet and outlet are set to 2.4 m / s, 0.4 m / s and 13.4 m / s, respectively. The discrete phase is calculated using a two-phase coupling method. The particulate matter is injected upward into the furnace from the primary air inlet at a velocity of 2.4 m / s. The number of iterations is 1000. The outlet velocity adopts the inlet boundary condition. The turbulence intensity at both the inlet and outlet is 5%, the turbulence viscosity ratio is 10, and the four walls are set to be adiabatic. The temperature settings of each wall are shown in Table 1. The discrete phase parameter settings are shown in Table 2. The point attributes and physical model settings are shown in Table 3.

[0162] Table 1 Wall Temperature Setting Table

[0163]

[0164] Table 3. Point Attributes and Physical Model Settings

[0165]

[0166]

[0167] This invention uses the particle concentration at the outlet of an industrial incinerator as the benchmark condition for verifying a 3D numerical model, and conducts experiments on particle concentration. Using FLUENT, particle simulations of the two stages of solid waste incineration and waste heat exchange in the incinerator were performed. The final confirmed numerical model, which matches the particle concentration at the incinerator outlet and can be used as the benchmark condition, is set as follows: discrete phase is calculated using a two-way coupling method; the particle injection velocity at the primary air inlet is set to 0.7 m / s; the particle diameter adopts the Rosin-rammler distribution; the average particle size is set to 45 mm; the solid combustion temperature is set to 1080 K; the particle collision mode on the wall is set to rebound; and the length of the second baffle is set to 11.2 m.

[0168] To clearly and intuitively observe the changes in the flow field within the incinerator, the velocity contour plot and dynamic pressure vector plot of the XY section are used as references, such as... Figure 6a and Figure 6b As shown.

[0169] Depend on Figure 6aIt can be seen that the fluid flow within the incinerator can be roughly divided into five stages: the furnace, the first flue, the second flue, the third flue, and the waste heat boiler. The fluid velocity increases significantly in both the second and third flues, reaching its maximum in the third flue. The main reason is that turbulence exists within the incinerator; the velocity of the flue gas increases as it enters the second flue from the first, and further increases as it enters the third. Figure 6b It can be seen that there is a strong correlation between the distribution of dynamic pressure and the distribution of velocity. During the complete process of fluid flowing from the furnace through the flue and through the waste heat boiler, the dynamic pressure shows a gradual decreasing trend. The main reason is that the pressure will decrease relatively when the fluid velocity in the furnace increases.

[0170] Cloud maps of particulate matter from incinerators and waste heat boilers are shown below. Figure 7a and Figure 7b As shown.

[0171] Depend on Figure 7a It can be seen that the velocity distribution of particulate matter is similar to the velocity distribution of the fluid inside the incinerator. This is mainly because the particulate matter does not participate in the reaction of the internal gas, and its interaction with the fluid inside the furnace is very small or even negligible. The flow velocity of the particles only changes with the flow velocity of the fluid inside the furnace. Figure 7b It can be seen that the particulate matter concentration is relatively high at the top of the corner from the first flue to the second flue, and the particulate matter concentration in the waste heat boiler is slightly higher than that in the flue, with the maximum particulate matter concentration at the waste heat boiler hopper.

[0172] The results of the univariate analysis were as follows:

[0173] Analysis of the Influence of Solid MSW Combustion Temperature on Outlet Particle Concentration: The combustion temperature of solid MSW affects the distribution of outlet particulate matter concentration by influencing pressure changes. Through particulate matter simulation experiments at different solid MSW combustion temperatures, the close relationship between particle concentration and temperature at the incinerator outlet was analyzed. When the collision mode of particles on the wall is rebound, the particulate matter concentration change curves at different solid MSW combustion temperatures are shown below. Figure 8 As shown;

[0174] Depend on Figure 8 It is evident that when the collision mode of particles on the wall is rebound, changing the combustion temperature of the solid MSW and thus the temperature within the entire incinerator has a significant impact on the particle concentration. When the temperature is between 850K and 875K, the particle concentration decreases significantly; when the temperature is between 875K and 950K, the particle concentration remains almost constant at 1.5 g / m³. 3Near the vicinity; when the temperature is between 950K and 975K, the particulate matter concentration increases rapidly; when the temperature is between 975K and 1100K, the particulate matter concentration gradually increases with increasing temperature, but the growth trend is slow; with further increases in temperature, the particulate matter concentration reaches its minimum at 925K; when the temperature is between 850K and 975K, combustion is incomplete, and the corresponding amount of particulate matter produced is relatively small; after the temperature reaches 975K, the combustion of MSW is more complete, thus producing a large amount of particulate pollutants, the concentration of which remains at 3 g / m³. 3 Approximately. When the collision mode of particles with the wall is rebound, the particles will rebound after contacting the wall, causing the particulate matter concentration at the outlet to change accordingly with temperature. From the above data, it can be seen that, under the premise of ensuring stable combustion and not affecting normal operation, maintaining the combustion temperature of the solid MSW between 875K and 950K can effectively reduce particulate matter generation.

[0175] When the collision mode of particles at the wall is capture, the changes in particulate matter concentration at different solid MSW combustion temperatures are as follows: Figure 9 As shown.

[0176] Depend on Figure 9 It can be seen that when the collision mode of particles on the wall is capture, the combustion temperature of solid MSW is between 850K and 900K, and the particle concentration gradually decreases with increasing temperature. This is because the combustion of MSW is incomplete at this stage, and the particle concentration gradually decreases. Between 900K and 1025K, the particle concentration first increases and then decreases. Between 925K and 1000K, the particle concentration remains almost constant at 1.61 g / m³. 3 Between 1025K and 1100K, the particulate matter concentration gradually increases with increasing temperature. This is because the MSW combustion is complete at this temperature, generating a large amount of particulate matter. The particulate matter concentration at the economizer outlet shows a trend of first decreasing and then increasing with increasing internal incinerator temperature. Therefore, when the wall surface has a strong adsorption capacity for particulate matter, maintaining the solid MSW combustion temperature between 925K and 1000K can effectively reduce the particulate matter concentration, provided that MSW combustion meets process requirements.

[0177] When the collision mode of particles at the wall surface is wall jet, the changes in particulate concentration at different solid MSW combustion temperatures are as follows: Figure 10 As shown.

[0178] Depend on Figure 10It can be observed that: when the temperature is between 850K and 900K, the particulate matter concentration decreases significantly; between 900K and 950K, the particulate matter concentration gradually increases with increasing temperature; between 950K and 975K, the particulate matter concentration gradually decreases; and between 975K and 1100K, the particulate matter concentration shows a trend of first increasing and then decreasing. Overall, the particulate matter concentration exhibits a sawtooth-like change with increasing temperature, first decreasing and then increasing. Therefore, when the collision mode of particulate matter on the wall surface is similar to that of a wall jet, maintaining a constant temperature is beneficial for stable detection of particulate matter concentration.

[0179] When the wall particle boundary condition is rebound, and the solid MSW combustion temperatures are 850K and 965K, the particulate matter concentration distributions in the incinerator and waste heat boiler are as follows: Figure 11a and Figure 11b As shown.

[0180] Depend on Figure 11a and Figure 11b It can be seen that the particulate matter concentration distribution varies at different temperatures. Specifically, the distribution in the furnace and the first flue is almost the same; however, there is a difference between the hopper and the waste heat boiler. At a temperature of 965K, the particulate matter concentration distribution is more uniform, and the concentration at the outlet is lower.

[0181] Analysis of the impact of different wall particle collision modes on the outlet particle concentration: The following is a numerical simulation conducted at the same temperature, setting the wall particle collision modes to three modes: bounce, capture, and wall jet. The results are as follows. Figure 12 As shown;

[0182] Depend on Figure 12 It can be seen that, under the same solid MSW combustion temperature, the influence of wall particle collision mode on particulate matter concentration, from highest to lowest, is rebound, wall jet, and capture. When the temperature is between 875K and 950K, the particle concentration under the rebound collision mode is similar to that under the capture mode. When the incinerator temperature is between 975K and 1100K, the particle concentration under the wall jet collision mode is similar to that under the rebound collision mode. Under different wall particle collision modes, the overall trend of particulate matter concentration with temperature is first decreasing and then increasing, which verifies the accuracy of the experimental results. Based on the above analysis, it can be seen that the wall material can be changed according to the incinerator temperature to reduce the particle concentration. The solid MSW combustion temperature can be adjusted to reduce particulate matter concentration based on the on-site wall particle collision mode, while ensuring normal combustion.

[0183] Analysis of the impact of the second baffle length on the outlet particle concentration: Particle concentration variations under different second baffle lengths are as follows: Figure 13 As shown;

[0184] Depend on Figure 13It can be seen that the second baffle between the second and third flues can capture particles, meaning that increasing the length of the second baffle can significantly reduce the particulate matter concentration. When the particle size distribution is Rosin-rammler, as the baffle length increases from 11.2m to 12.45m, the particulate matter concentration first decreases and then increases, reaching a minimum at a baffle length of 11.7m. When the length of the second baffle is between 11.7m and 12.45m, it does not significantly reduce the particulate matter concentration. When the baffle length is between 12.45m and 12.95m, the particulate matter concentration decreases significantly. Simulation results show that increasing the length of the second baffle can reduce the particulate matter concentration at the economizer outlet, providing data support for the process design of particulate matter capture equipment.

[0185] Orthogonal Experiment Results: An orthogonal experiment was conducted to analyze the effects of solid MSW combustion temperature (A), wall collision mode (B), and second baffle length (C) on particle concentration at the incinerator outlet. The number of factor levels for the above three factors is shown in Table 4, and the orthogonal experimental scheme and results are shown in Table 5.

[0186] Table 4. Hybrid Orthogonal Array

[0187]

[0188] Table 5. Orthogonal experimental design and results

[0189]

[0190]

[0191] The results of the orthogonal experiment were analyzed by range analysis and are shown in Table 6.

[0192] Table 6. Range Analysis Results

[0193]

[0194] Table 6 shows that: (1) Factor A has the greatest impact on the particle concentration at the outlet. As particulate matter flows through the flue and waste heat boiler in the furnace with the high-temperature flue gas to the outlet, it collides with the wall due to the turbulence of the high-temperature flue gas in the furnace. The wall material determines the collision mode of the particles on the wall, which in turn directly determines whether the particles continue to flow, and thus has a great impact on the particle concentration at the outlet of the incinerator; (2) Secondly, factors C and B have the second and third largest impacts on the particle concentration at the outlet, respectively. Among them, the impact of factor C is much greater than that of factor B. This is because the second baffle acts as a particle collection device, which blocks the flowing particles at the second and third flue to collect the particles into the ash hopper, that is, it reduces the particle concentration at the outlet under physical action; (3) Factor B has the least impact on the particle concentration at the outlet. It can be seen that although the combustion temperature of solid MSW affects the initial concentration of particulate matter generated by MSW combustion, the particle flow is greatly affected by the collision mode of the wall and the length of the second baffle during the process of the particulate matter flowing through the flue and waste heat boiler, and is least affected by the temperature. In practice, the first step should be a reasonable process design, using wall materials that allow particle collision effects to approximate wall jet flow. Secondly, the length of the second baffle should be maximized without affecting flue gas flow. Finally, the combustion temperature of the solid MSW should be increased as much as possible to further reduce the particulate concentration at the outlet. From the above, it can be seen that the optimal combination in this orthogonal experiment is A2B6C6, corresponding to the values ​​(wall jet, 1000, 12.95), and the corresponding particle concentration is 1.214 g / m³. 3 .

[0195] The meanings of the symbols involved in this invention are as follows.

[0196] ρ g U is the gas density. g V is the velocity in the X direction. g Let S be the velocity in the Y direction. sg p is the rate at which MSW is converted into gas. g For gas pressure, F(U) g F(V) represents the resistance of the bed to gas flow. g H represents the resistance of the bed to gas flow. g For gas enthalpy, λ g Q is the thermal diffusivity. h The heat gained by the gas phase for combustion, U i For the i-th component of velocity, U j Let x be the j-th component of the velocity. i Let ρ be the Cartesian coordinates, μ be the fluid density, and σ be the viscosity. k For model coefficients, β * For model coefficients, σ ω Here, γ is the model coefficient, β is the model coefficient, and σ is the model coefficient. ω2Here are the model coefficients, F1 is the mixing function, k is the turbulent kinetic energy, ω is the specific turbulent dissipation rate, and u is the model coefficient. avg Let I be the average velocity, I be the turbulence intensity, and C be the turbulence intensity. μ τ is the empirical constant of the K-Omega model, l is the characteristic length of the obstacle, and τ is the constant of the K-Omega model. ij For Reynolds stress, δ ij Let ν be the Kronecker function. T For dynamic eddy viscosity, μ T Given eddy viscosity, U is the fluid phase velocity, U p Let F be the particle velocity, Re be the Reynolds number, p be the particle size, and F be the particle velocity. p For Saffman lift and virtual mass force, ρ p For particle density, d p Where μ is the particle size, μ is the viscosity coefficient, and C is the particle size. d Here, θ is a correction factor, σ is a parameter, and m is a parameter. g S is the geometric mean. g x is the standard deviation. i Here, n represents the particulate matter concentration value, and q represents the number of concentration values. i For percentiles, z i e is the deviation of the percentile from the median. n e is the normal bounce coefficient. τ F is the tangential rebound coefficient. i For inertial force, F pre For pressure gradient force, F vm For false mass force, V P For the solid phase velocity, F Mag For Magnus lift, ω p C is the angular velocity of particle spin. D Here, α1 is a constant, α2 is a constant, α3 is a constant, and m is a constant. p Let g be the particle mass, y be the particle concentration at the incinerator outlet, and x be the particle mass. T x is the combustion temperature of solid MSW. W For wall particle collision mode, x G y is the length of the second baffle. design These are the particle concentration values ​​from the orthogonal experiment. For orthogonal experiments x T Design values, For orthogonal experiments x W Design values, For orthogonal experiments x G Design value, R i Let q be the range, q be the q-th factor in the orthogonal experiment, and v be the v-th level of the q-th factor. For the q-th factor at the v-th level, there are r experimental data. The average value is r, where r is the number of times that level occurred in the experiment.

[0197] This invention provides a 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation. The method first obtains incineration plant information from actual design drawings and then constructs a 3D model of the incinerator and waste heat boiler. Combining mechanism and experience, it identifies the key factors affecting particulate matter generation as solid MSW combustion temperature, wall particle collision mode, and second baffle length. Next, it describes the solution method for the 3D model, then performs single-factor analysis on the key factors based on the 3D model, and finally analyzes the impact of the key factors on the particulate matter concentration at the outlet based on orthogonal experiments to obtain the optimal parameter combination. This provides data support for reducing particulate concentration from the perspective of process improvement and optimized control, and can accumulate experience for the simulation of particulate matter in the MSWI process, as well as provide support for obtaining the theoretical upper and lower limits of particulate emission concentration.

[0198] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation, characterized in that, Includes the following steps: Step 1: Construct a 3D model of the incinerator and waste heat boiler based on the actual design drawings. Combine the MSWI process flow and the particulate matter generation mechanism to determine the key factors affecting the outlet particulate matter concentration. According to the on-site operation requirements, obtain the baseline operating conditions for adjustment and conduct baseline experiments. Based on the baseline experiments, simulate and study the impact of key factors on the outlet particulate matter concentration. Among them, the key factors affecting the outlet particulate matter concentration include solid MSW combustion temperature, wall particle collision mode and second baffle length. Step 2: The following solution method is used to solve the 3D model of the incinerator and waste heat boiler: a third-order discrete scheme is used for data modeling research, Fluent is used to simulate the gas phase heat and mass transfer process above the bed of the incinerator and waste heat boiler, a discrete phase model is used to solve the particle diffusion process, a coupled algorithm is used to solve the steady-state control equation, and the simulation process is made to converge by increasing the number of iterations and reducing the relaxation factor. The gas phase conservation equation, turbulence model and discrete phase model are calculated respectively. Step 3: Perform single-factor analysis on three factors: solid MSW combustion temperature, wall particle collision mode, and second baffle length. Let y represent the particle concentration at the incinerator outlet. The expression for its relationship with the above three factors is as follows: In the formula, , and These represent the values ​​of solid MSW combustion temperature, wall particle collision mode, and second baffle length, respectively. Step 4: A multi-level comprehensive analysis was conducted on three factors: solid MSW combustion temperature, wall particle collision mode, and second baffle length. For the orthogonal experiment, the output was: In the formula, , and They represent respectively to , and The importance of each factor was analyzed using the range calculation formula for the level values ​​in the orthogonal experiment. In the formula, In an orthogonal experiment, the first... One factor, Indicates the first The first factor A level, Indicates the first The first factor At each level Experimental data The average value, This indicates the number of times that level occurred in the experiment, where, The times correspond to the solid MSW combustion temperature, the wall particle collision mode, and the length of the second baffle, respectively.

2. The 3D numerical modeling and analysis method for urban solid waste incineration oriented towards particulate matter generation as described in claim 1, characterized in that, The gas phase conservation equations include the continuity equation, the momentum equation, and the energy equation, which are as follows: (1) (2) (3) (4) In the formula, For gas density, and for and velocity in direction, source term The rate at which MSW is converted into gas. For gas pressure, and The resistance of the bed to gas flow is calculated using the Ergun equation. For gas enthalpy, The thermal diffusivity is composed of diffusion and turbulence. The heat gained by the gas phase due to combustion; The turbulence model is as follows: the K-Omega SST model is used to calculate turbulent motion, and the k-equations and omega equations are used for the rest, specifically: (5) In the formula, For the speed of the first One portion, For the speed of the first One portion, Cartesian coordinates; For fluid density, For viscosity, , , , , and These are the model coefficients. It is a mixed function. and The turbulent kinetic energy and specific turbulent dissipation rate are shown below: (6) In the formula, For average speed, For turbulence intensity, is the empirical constant of the K-Omega model, taken as 0.

09. The characteristic length of the obstacle. For Reynolds stress, it is: (7) In the formula, For the Kronecker function, For dynamic eddy viscosity, It exhibits eddy viscosity; The discrete phase model involves solving the Navier-Stokes equations for the continuous phase fluid within an Euler framework. Before starting the continuous phase calculations, the discrete phase model is configured. Once the initial values ​​of the continuous phase calculations are obtained, particles are injected into the flow field, i.e., sprayed into the flow field in the form of a surface. The discrete phase model calculates the particle trajectory equations within a Lagrange framework. Simultaneously, the particle mass load also affects the gas phase flow field. When the calculation converges again, the results are obtained in terms of particle trajectories. The particle motion equations are established based on Newton's second law. By applying the equilibrium equations of the external forces acting on the particles, the following motion trajectory equations are obtained: (8) (9) In the formula, The fluid phase velocity is expressed in m / s. The velocity of particulate matter is expressed in m / s, with subscripts. Indicates particles, For Saffman lift and virtual mass force, Particle density, Particle size, For viscosity, For correction factor, For gravitational acceleration, the concentration distribution of particulate matter was obtained using the log-normal distribution method, and the random variable was... The distribution is as follows: (10) (11) (12) In the formula, and For parameters, and These are the geometric mean and standard deviation, respectively. This represents the particulate matter concentration value. The formula for calculating the percentage concentration of particulate matter, where the number of concentration values ​​is given, is: (13) In the formula, Percentiles The deviation of the percentile from the median is used. Since particles will rebound on the wall surface, the rebound recovery coefficients in the normal and tangential directions of fly ash, proposed by Grant & Tabakoff, are used. The calculation formula is as follows: (14) In the formula, It is the normal rebound coefficient. The tangential rebound coefficient; Force analysis of particulate matter inside the furnace: In the discrete phase model settings, the particles are defined as ash-soiled and spherical in shape. The inertial force of the particles in motion is expressed as follows: (15) The pressure gradient force is the force exerted on particles by the pressure gradient in the gas phase flow field, and is expressed as: (16) In the formula, For the solid phase velocity, the spurious mass force generated by the apparent mass effect is expressed as: (17) Magnus lift is the lift force generated by the rotation of particles, and it is generally on the same order of magnitude as gravity, expressed as: (18) In the formula, Let be the particle's spin angular velocity. In the discrete phase model, the equilibrium equations of the forces acting on the particle are as follows: (19) (20) In the formula, The drag force per unit mass of the particle. It is the relative Reynolds number, defined as: (21) Traction coefficient The expression is: (22) For spherical particles, within a certain Reynolds number range, , and All values ​​are constants, and the gravitational force acting on the particle is given by the following formula: (23) In the formula, It is particle mass. It is gravitational acceleration.

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