A numerical calculation method for soot generation during pulverized coal combustion based on orthogonal moment method

Abstract

The present invention discloses a numerical calculation method for soot generation during coal powder combustion based on the orthogonal moment method, which belongs to the technical field of soot simulation. This method solves the problem that traditional methods cannot accurately describe the multimodal distribution of soot and lack numerical stability by coupling an improved splitting-based extended orthogonal moment method (S‑EQMOM) with a small flame model and combining it with a detailed chemical reaction mechanism. The specific steps include: establishing a gas-particle two-phase control equation, splitting the number density function through S‑EQMOM and solving the population equilibrium equation; discretizing the model and coupling the pressure-velocity field; and analyzing the physicochemical behaviors such as pyrolysis, nucleation, and coagulation during the soot generation process. The present invention significantly improves the calculation stability by decomposing complex dynamic processes and reducing the accumulation of numerical errors. It can accurately predict properties such as soot volume fraction and particle size distribution, providing theoretical support for the design of coal powder burners.

Description

Technical Field

[0001] The invention belongs to the field of numerical simulation calculation of soot generation, and specifically relates to a numerical calculation method for soot generation during pulverized coal combustion based on an orthogonal moment method. Background Art

[0002] Numerical calculation methods for soot generation from pulverized coal combustion can accurately describe soot generation processes, such as pulverized coal pyrolysis and gaseous hydrocarbon polymerization, by considering multi-physics coupling and establishing various numerical models. However, many traditional numerical calculation methods, such as those based on empirical formulas, can only estimate the overall average particle size of soot particles and cannot accurately describe the distribution of individual particle sizes. Furthermore, some simplified single-parameter models cannot simultaneously consider the concentration and mass distribution of soot particles. Compared to these traditional and simplified methods, moment methods not only reduce the computational dimensionality but also effectively reflect the overall particle characteristics by solving moments of different orders. For example, the extended orthogonal moment method (EQMOM) provides a continuous number density function (NDF) reconstruction based on a set of transport moments, representing the unknown NDF as a sum of weighted continuous kernel density functions (KDFs). However, the NDF reconstructed by the EQMOM can deviate from the original NDF and may exhibit oscillations. Moreover, the EQMOM-predicted NDF is highly dependent on the selected KDF shape. The Split-based Extended Quadrature Method of Moments (S-EQMOM) incorporates detailed physical and chemical processes and uses a splitting algorithm to decompose complex particle dynamics into multiple simple subprocesses. Each subprocess is then solved independently, effectively avoiding the complexity of dealing with multiple coupled processes simultaneously, reducing the accumulation of numerical errors and maintaining good numerical stability. Furthermore, the S-EQMOM method can be well integrated into existing numerical solvers. Summary of the Invention

[0003] To address the shortcomings of existing technologies, the present invention provides a technical solution: a numerical calculation method for soot generation from pulverized coal combustion based on the orthogonal moment method. This method expands upon the splitting-based extended orthogonal moment method and combines a flamelet model with detailed chemical reaction mechanisms to simulate the soot generation process in pulverized coal flames.

[0004] The technical solution of the present invention is as follows:

[0005] A numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method comprises the following steps:

[0006] Step one involves establishing the relevant mathematical models, primarily encompassing density, pressure, velocity, composition, and energy equations for the gas phase; the particle phase is primarily solved using moment equations. The results from the mass, momentum, and energy equations for the pulverized coal particles, as well as the moment equations for the soot particles, are also required as inputs to these two-phase equations to provide a detailed analysis of the soot generation mechanism and process during pulverized coal combustion.

[0007] Step 2: Combine the boundary conditions, initial conditions and grid division to numerically discretize the mathematical model in step 1 to obtain the corresponding algebraic equations of velocity, pressure, density, composition and energy. Then, perform nonlinear processing on each algebraic equation and iteratively solve each nonlinear equation in each time step.

[0008] In step three, the PIMPLE algorithm is used to couple the velocity and pressure, and the velocity and pressure fields are continuously and iteratively corrected to ensure convergence. Through the above three steps, the numerical calculation of the soot generation process during coal powder combustion can be realized.

[0009] Furthermore, the moment equation method for solving the particle phase in step 1 is based on the split extended orthogonal moment method, and the specific steps are as follows:

[0010] Step (1) defines the coal dust soot generation process, thereby determining the number density function, and splitting the number density function of the entire soot particle into multiple overlapping and coupled sub-number density functions.

[0011] Step (2) defines each split kernel density function, reconstructs the number density function equation, establishes the population balance equation (PBE) based on the number density function equation, transforms the population balance equation into a moment equation, and then approximates the population balance equation by solving the moment of the distribution.

[0012] Step (3) integrates and calculates the initial moments, and determines the variances and means based on the known low-order moments, usually by solving a system of nonlinear equations, such as solving the roots of orthogonal polynomials.

[0013] Step (4) solves the source terms corresponding to the multiple physical and chemical processes involved in the soot generation and evolution process to update the value of the high-order moments.

[0014] Step (5) Select an appropriate explicit, implicit, or semi-implicit method to advance time. Within each time step, the source terms and moment values ​​corresponding to each physicochemical process of soot formation are solved sequentially. At the same time, since there may be coupling relationships between the various physicochemical processes, an iterative solution is required until the change in each moment is less than a preset value, that is, the convergence condition is met.

[0015] Step (6) Solve each sub-number density function and group balance equation through the above steps, and couple the final results to obtain the overall number density function.

[0016] Furthermore, the moment method in step 1 introduces more nodes, variances, and means, thereby being able to more accurately approximate the multimodal distribution.

[0017] Furthermore, in the above step 2, the finite volume method is used to discretize the calculation area into several control volumes, and the physical quantities are integrated over each control volume, and the partial differential equations are converted into a system of algebraic equations, and then the physical quantities at the discrete points are solved.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] This method is based on an improved orthogonal moment method, namely the splitting-based extended orthogonal moment method, combined with a small flame model. Using the results of solving detailed chemical reactions as a reference, it can simulate and analyze the detailed physical and chemical processes of soot formation. Compared with the traditional orthogonal moment method, this method effectively avoids the complexity of dealing with multiple coupled processes simultaneously, thereby reducing numerical errors and improving the stability of numerical calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 This is a flow chart of a numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method of the present invention;

[0021] Figure 2 Schematic diagram of S-EQMOM of bimodal number density function in an embodiment of the present invention;

[0022] Figure 3 The hypothetical pathways for primary and secondary pyrolysis of pulverized coal particles and soot generation in the embodiments of the present invention are as follows;

[0023] Figure 4 Schematic diagram of calculation settings for convective pulverized coal flame in an embodiment of the present invention;

[0024] Figure 5 This is a comparison chart of the soot property simulation results using the detailed chemical reaction mechanism method in an embodiment of the present invention and the coupled calculation results of the small flame model and the S-EQMOM model. DETAILED DESCRIPTION

[0025] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. However, the following embodiments are intended only to explain the present invention, and the scope of protection of the present invention should include the entire contents of the claims. Moreover, through the description of the following embodiments, those skilled in the art can fully implement the entire contents of the claims of the present invention.

[0026] Example

[0027] The present invention is based on an improved moment method, which can efficiently and accurately simulate the dynamic behavior in the particle system and accurately capture the multimodal characteristics of the particle size distribution. It can handle the numerical simulation of the generation and evolution of tiny particles during the combustion process.

[0028] like Figure 1 As shown, the specific implementation steps of the numerical calculation method of soot generation during pulverized coal combustion based on the orthogonal moment method of the present invention are as follows:

[0029] Step 1: Establish a relevant mathematical model. The mass equation, momentum equation, and governing equations for the mass fractions of components in the chemical reaction, as well as the energy equation in this embodiment, are solved in a detailed chemical reaction mechanism method, and the resulting values ​​are used as a reference. The governing equations for the components and energy of the gas phase are in the form of:

[0030] Component equation: ,

[0031] Energy equation: ,

[0032] in, : gas phase density; : Component The mass fraction of; t: Euler time; : Gas phase velocity at the first Components in each direction; : No. Cartesian coordinates of directions; : mass diffusion coefficient; : Component The chemical reaction rate is calculated by the Arrhenius equation; : The coupled source term for soot particles and gas phases is calculated based on the soot generation model of chemical surface growth and oxidation. For other uncoupled components, ; : Due to the reaction between volatile analysis and coke surface, there is a bidirectional coupling energy source term between the pulverized coal particle phase and the gas phase. ,in, : the volume of the grid cell where the pulverized coal particles are located; : the index of all coal powder particles in the circulating local grid; : the total number of pulverized coal particles in the local grid; and They represent the volatile analysis rate and the coke surface reaction rate respectively. α: thermal diffusivity; : The gas-soot-coal coupled energy source term can be calculated as follows:

[0033] ;

[0034] in, : surface area of ​​pulverized coal particles; : Nusselt number, calculated by the Ranz-Marshall model; : gas phase thermal conductivity; : diameter of pulverized coal particles; : pulverized coal particle temperature; : Index of circulating all volatiles; :Components in volatile matter enthalpy; : enthalpy change due to mass transfer in the reaction on the coke surface; : Radiative heat transfer between the gas phase and the solid phase (coal pulverized and soot). The mass transfer processes in this example primarily involve coal volatilization and surface chemical reactions, as well as soot nucleation and surface oxidation reactions. To simplify the calculations, heat and mass transfer between coal pulverized and soot particles is not considered in this example.

[0035] The moment equation of the soot particle phase is transformed by the population balance equation. The population balance equation corresponding to the number density function of the soot in this embodiment is as follows:

[0036] ,

[0037] in, : particle volume; : physical space; : kinematic viscosity; T: gas phase temperature; : number density function; : The sum of soot source terms, mainly including particle nucleation, polycyclic aromatic hydrocarbon formation, particle agglomeration, chemical surface growth and oxidation and other physical and chemical processes. The group balance equation is converted into a moment equation of a univariate number density function:

[0038] ,

[0039] in, Indicates the Next, the moment equation is solved by the extended orthogonal moment method based on splitting.

[0040] Step (1) splits the number density function of the entire soot particle into multiple overlapping and coupled sub-number density functions. The number density function is solved as follows:

[0041]

[0042] Where, In this embodiment, the entire number density function is divided into two sub-number density functions, namely , see attached Figure 2 .

[0043] Step (2) defines each split kernel density function, reconstructs the number density function equation, establishes the population equilibrium equation based on the number density function equation, and transforms it into a moment equation. The sub-number density function is solved by the following formula:

[0044] ,

[0045] in, It is The particle number density function is considered to be independent of time and space to simplify the calculation. is the kernel density function located on the horizontal axis; is a non-negative weight; The coefficients determine the shape of the kernel density function for each subset of the density function.

[0046] Step (3) is to determine the variances ( ) and mean ( ), which is usually determined by solving a system of nonlinear equations, such as solving the roots of orthogonal polynomials. In this example, each sub-number density function is obtained by the first three transport moments. Inversion to obtain relevant parameters (particle size), 、 .

[0047] Step (4) solves the source terms corresponding to the multiple physical and chemical processes involved in the soot generation and evolution process to update the value of the high-order moment. The products and paths generated by the primary and secondary pyrolysis of coal powder in this embodiment are shown in the attached Figure 3 The physical and chemical processes considered in the example include pyrolysis to form polycyclic aromatic hydrocarbons, soot particle nucleation, coagulation, chemical surface growth and oxidation. The source terms of each process are solved during the simulation calculation.

[0048] Step (5) selects an appropriate explicit, implicit, or semi-implicit method to advance time. The source terms and moment values ​​corresponding to each physicochemical process of soot formation are solved sequentially within each time step. At the same time, since there may be coupling relationships between the various sub-processes, an iterative solution is required until the change in each moment is less than a preset value, i.e., the convergence condition is met. In this embodiment, the implicit Euler method is used to update the moment value within each time step.

[0049] Step (6) Solve each sub-number density function and group balance equation through the above steps, and couple the final results to obtain the overall number density function. At the same time, the obtained results are input into the equations of the gas phase and soot particle phase as their source terms.

[0050] Step 2: Combine the boundary conditions, initial conditions and grid division to numerically discretize the mathematical model in step 1 to obtain the corresponding algebraic equations. Then perform nonlinear processing on each algebraic equation and solve it iteratively in each time step. Figure 4 In this example, the computational domain has a grid of 300(x) × 300(y). The finite volume method is used to solve the governing gas equations for momentum, energy, mass fraction, volatile mixture fraction, coke mixture fraction, moment set, and gas-soot coupling mass fraction. The spatial derivatives in the governing gas equations are discretized using a second-order central difference scheme, while the temporal derivatives are discretized using an implicit scheme.

[0051] Step three: Use the PIMPLE algorithm to couple the velocity and pressure, and continuously iterate and correct the velocity and pressure fields until the specified number of iterations or time step is reached.

[0052] Step 4: Evaluate and analyze the soot properties during pulverized coal combustion calculated using the flamelet model coupled with the split-based extended orthogonal moment method.

[0053] like Figure 5 In this example, the soot properties obtained by the detailed chemistry simulation (DC) method were compared with the results directly extracted from the small flame model coupled with the orthogonal moment method (FLT-table) and obtained through the transport equation (FLT-trans). It was found that the results obtained by the DC method were highly consistent with those obtained by the DC method. Therefore, it can be considered that this method can accurately predict the type of tar and can well predict the soot properties such as soot volume fraction, particle diameter, soot particle density, and soot surface density.

[0054] The foregoing is merely a list of specific embodiments of the present application, intended to enable those skilled in the art to understand or implement the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application is not limited to the embodiments shown herein, but is intended to conform to the broadest scope consistent with the principles and novel features of the present application.

Claims

1. A numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method, characterized in that: The following steps are involved: Step 1: Establish a mathematical model, including the governing equations of the gas phase and the moment equations of the particle phase, wherein the moment equations are solved by the extended orthogonal moment method based on splitting; The gas phase control equation includes: Component equation: , Energy equation: , in, : gas phase density; : Component The mass fraction of; t: Euler time; : Gas phase velocity at the first Components in each direction; : No. Cartesian coordinates of directions; : mass diffusion coefficient; : Component The chemical reaction rate is calculated by the Arrhenius formula; : The coupled source term for soot particles and gas phases is calculated based on the soot generation model of chemical surface growth and oxidation. For other uncoupled components, ; : Due to the reaction between volatile decomposition and coke surface, there is a bidirectional coupling source term between the pulverized coal particle phase and the gas phase. ,in, : the volume of the grid cell where the pulverized coal particles are located; : the index of all coal powder particles in the circulating local grid; : the total number of pulverized coal particles in the local grid; and They represent the volatile analysis rate and the coke surface reaction rate respectively; α: thermal diffusivity; : The gas-soot-coal coupled energy source term can be calculated as follows: ； in, : surface area of ​​pulverized coal particles; : Nusselt number, calculated by the Ranz-Marshall model; : gas phase thermal conductivity; : diameter of pulverized coal particles; : pulverized coal particle temperature; : Index of circulating all volatiles; :Components in volatile matter enthalpy; : enthalpy change due to mass transfer in the reaction on the coke surface; : Radiative heat transfer between gas and solid phases; Step 2: Combine boundary conditions, initial conditions, and grid division to numerically discretize the mathematical model, generate algebraic equations, perform nonlinear processing, and iteratively solve each nonlinear equation in each time step; Step 3: The velocity field and pressure field are coupled by the PIMPLE algorithm, and the correction is iterated until convergence to complete the numerical calculation of the soot generation process; Step 4: Couple the small flame model with S-EQMOM and combine it with the detailed chemical reaction mechanism to analyze the physical and chemical behavior of the soot generation process.

2. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1 is characterized in that: The moment equation of the particle phase in step 1 is solved by the following sub-steps: (1) Splitting the number density function into multiple coupled sub-number density functions; (2) Reconstruct the sub-number density function through the kernel density function and transform it into the population equilibrium equation and moment equation; (3) Using the initial moments to invert the variance and mean, solve the nonlinear equations to determine the kernel density function parameters; (4) Calculate the source term of the soot generation process to update the high-order moments; (5) Using explicit, implicit or semi-implicit time-marching methods to iteratively solve the various physical and chemical processes of soot formation; (6) Couple the sub-number density function results and output the overall number density function.

3. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1 is characterized in that: In the second step, the control equation is discretized using the finite volume method, the spatial derivative is discretized using a second-order central difference format, and the time derivative is discretized using an explicit or implicit format.

4. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1 is characterized in that: When the velocity and pressure fields are iteratively corrected by the PIMPLE algorithm in step 3, preset convergence conditions must be met, including the threshold values ​​of each moment change and the maximum number of iterations.

5. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1 is characterized in that: The soot generation process includes coal powder pyrolysis, polycyclic aromatic hydrocarbon formation, soot nucleation, agglomeration, chemical surface growth and oxidation.

6. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 2 is characterized in that: In step (3), the nonlinear equations are solved by the orthogonal polynomial root method to invert the variance of the kernel density function. and mean .

7. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 2 is characterized in that: The subnumber density function is solved by the following formula: ， in, It is The particle number density function is considered to be independent of time and space to simplify the calculation. is the kernel density function located on the horizontal axis; is a non-negative weight; The coefficients determine the shape of the kernel density function for each subset of the density function.

8. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1 is characterized in that: The flamelet model predicts coal tar species and soot properties, including volume fraction, particle diameter, and surface density, by coupling detailed chemical reaction mechanisms.

9. The numerical calculation method for soot generation during pulverized coal combustion based on the orthogonal moment method according to claim 1, characterized in that: The grid division adopts a 300×300 Cartesian grid, and a bidirectional iterative solution is performed on the gas phase-particle phase coupling source term based on the finite volume method.

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