A method for constructing differential diffusion flamelet model for buoyancy-driven plumes

Abstract

This paper proposes a method for constructing a differential diffusion flamelet model for buoyancy-driven plumes and extends its application to pool fire combustion processes in the field of fire safety. This method uses the flamelet model to solve the buoyancy-driven plume. Through coordinate transformation and dimensionality reduction, the number of component equations to be solved for the buoyancy plume is significantly reduced, enabling the reproduction of the key characteristics of the buoyancy plume with high accuracy and faster computational speed. This method achieves high-precision numerical solution of buoyancy plumes and is applicable to pool fire combustion of gaseous fuels, liquid fuels, and all other buoyancy-driven plume numerical solutions.

Description

Technical Field

[0001] The present invention belongs to the field of fire safety, and in particular relates to a method for constructing a differential diffusion small flame model for a buoyancy-driven plume. Background Art

[0002] Currently, in the field of fire safety, the numerical modeling of buoyancy plumes typically relies on large eddy simulation (LES) methods from computational fluid dynamics (CFD). The combustion model uses an infinitely rapid chemical reaction model, but this model fails to consider the interaction between flame structure and turbulence, namely the influence of finite chemical reaction rates. Traditional finite chemical reaction rate models require a large number of component equations to solve, consuming significant computational resources. However, the flamelet model, through dimensionality reduction through coordinate transformation, significantly reduces the number of equations to solve during plume numerical modeling, shortening computational time and reducing computational resource consumption. Furthermore, the differential diffusion flamelet model, compared to conventional flamelet models, considers the influence of differential diffusion on the distribution of material components, improving the precision and accuracy of buoyancy plume calculations. Therefore, the differential diffusion flamelet model offers advantages such as accuracy, high efficiency, and resource savings, and can effectively reproduce the key characteristics of buoyancy plumes. However, the current application of flamelet models is primarily concentrated in the fields of energy and combustion engineering, with very little application in the field of fire safety. Therefore, a method for constructing a differential diffusion flamelet model for buoyancy-driven plumes is urgently needed. Summary of the Invention

[0003] To overcome the shortcomings of existing technologies, the present invention proposes a method for constructing a differential diffusion flamelet model for buoyancy-driven plumes and extends its application to pool fire combustion processes in the field of fire safety. This method uses a flamelet model to solve buoyancy-driven plumes. Through coordinate transformation and dimensionality reduction, the number of component equations to be solved for the buoyancy plume is significantly reduced, enabling the reproduction of the key characteristics of the buoyancy plume with high accuracy and faster computational speed. This method achieves high-precision numerical solutions for buoyancy plumes and is applicable to pool fires involving gaseous and liquid fuels, as well as all buoyancy-driven plume numerical solutions.

[0004] In order to achieve the above object, the technical solution adopted by the present invention is:

[0005] A method for constructing a differential diffusion flamelet model for a buoyancy-driven plume includes the following steps:

[0006] Step 1: Establish an unsteady, viscous, multi-dimensional plume mathematical model, design the computational domain, and divide the grid;

[0007] Step 2: Based on the grid division of step 1, the multi-dimensional plume mathematical model established in step 1 is physically discretized to obtain a system of equations including the mixture fraction equation, process variable equation, density equation, velocity equation, enthalpy equation, and pressure equation. The differential diffusion term is coupled to the flamelet model, that is, the differential diffusion term is considered when solving the system of equations for the control parameters enthalpy, process variable, mixture fraction, and second-order moment of the mixture fraction.

[0008] In step three, the initial and boundary conditions are first set, and then the mixture fraction equation, process variable equation, density equation, velocity equation, enthalpy equation, and pressure equation mentioned in step two are solved. After solving the control parameter equations, the calculation results are input into the pre-calculated small flame library, and the components, temperature, chemical reaction source terms, and differential diffusion terms are obtained by looking up the table; then, the pressure equation is solved within the estimation and correction iteration, and pressure correction is performed.

[0009] Through the above three steps, the construction process of the differential diffusion flamelet model for buoyancy-driven plumes was established.

[0010] Furthermore, in the step 1, a small flame model is used to model the plume;

[0011] Furthermore, in the step 1, the calculation domain is designed and the grid is divided with reference to the diameter and height of the combustion chamber of the experimental facility and other necessary facilities, such as fuel nozzles;

[0012] Furthermore, in the step 2, the finite volume method is used, and according to the grid division situation, the mixed fraction transport equation, process variable transport equation, density transport equation, process variable second-order moment transport equation, velocity transport equation, enthalpy transport equation, process variable transport equation, and pressure transport equation established in step 1 are volume integrated within the grid, and time integrated within the time step. Finally, the space and time discrete formats are introduced to obtain the algebraic equation defined at the center point of the grid.

[0013] Furthermore, when solving the transport equations of the process variables, mixture fraction, enthalpy and second-order moment of the mixture fraction, i.e., the control parameter equations, the influence of the differential diffusion effect is considered and the differential diffusion term is coupled.

[0014] Furthermore, in step 2, when solving the pressure transport equation, pressure correction is taken into account, and the velocity field and density field are corrected.

[0015] Furthermore, the step three specifically includes the following steps:

[0016] Step (1), design initial conditions and boundary conditions according to the experimental facilities;

[0017] Step (2), determine the global time step and perform time advancement calculation;

[0018] Step (3), solve the density transport equation to obtain the density value;

[0019] Step (4), solve the velocity transport equation to obtain the velocity estimate;

[0020] Step (5), solving the process variable transport equation to obtain the estimated value of the process variable;

[0021] Step (6), solve the mixture fraction transport equation to obtain the estimated value of the mixture fraction;

[0022] Step (7), solve the mixed fractional second-order moment transport equation to obtain its estimated value;

[0023] Step (8), solve the enthalpy transport equation to obtain the estimated enthalpy;

[0024] Step (9), input the results of steps (5) to (8) into the pre-solved small flame library, and obtain the results of components, temperature, chemical reaction source terms and differential diffusion terms by looking up the table;

[0025] Step (10), solving the pressure transport equation, substituting the pressure calculation result into the velocity equation and solving it to obtain the velocity correction value;

[0026] Step (11), looping step (10), and continuously correcting the speed value until the specified number of cycles is reached;

[0027] Step (12), loop step (4) to step (11) until convergence or the maximum number of loops is reached;

[0028] Step (13), solve the ideal gas state equation and update the density value;

[0029] In step (14), it is determined whether the specified end time has been reached. Otherwise, the time step is advanced and steps (3) to (13) are repeated.

[0030] Furthermore, it is used to deal with unsteady terms, convection terms, diffusion terms and source terms.

[0031] The beneficial effects of the present invention compared with the prior art are:

[0032] The differential diffusion flamelet model proposed in the present invention is aimed at buoyancy-driven plumes, and takes into account the influence of the differential diffusion effect on the distribution of material components in the buoyancy-driven plume, thereby improving the precision and accuracy of the calculation. It also reduces the number of component control equations to be solved through coordinate transformation and dimensionality reduction processing, greatly improving the solution efficiency and reducing the consumption of computing resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 A flow chart of a method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to the present invention;

[0034] Figure 2 A schematic diagram showing the grid division and the design of initial and boundary conditions in an embodiment of the present invention;

[0035] Figure 3 1 is a comparison chart of the simulation results and experimental data of the three models in the embodiment of the present invention. The left figure is an axial velocity comparison chart, and the right figure is a radial velocity comparison chart. The points correspond to the experimental data results, the black solid line corresponds to the calculation results of the infinitely rapid chemical reaction model, the black dashed line corresponds to the calculation results of the model without considering the influence of the differential diffusion effect, and the gray dashed line corresponds to the calculation results of the model considering the influence of the differential diffusion effect;

[0036] Figure 4 : This figure compares the distribution of the calculated product carbon dioxide mass fraction in the laminar flow (left figure) and turbulent flow (right figure) regions in an embodiment of the present invention, where the dotted line corresponds to the model that does not consider the influence of the differential diffusion effect, and the solid line corresponds to the model that considers the influence of the differential diffusion effect. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other. In order to facilitate understanding of the present invention, the present invention will be described in more comprehensive and detailed manner with reference to the examples below, but the scope of protection of the present invention is not limited to the following specific examples.

[0038] The present invention realizes high-precision numerical solution of buoyancy plume under the framework of finite volume method, and can handle pool fire combustion of gas fuel and liquid fuel and all numerical solutions of plumes driven by buoyancy.

[0039] like Figure 1 As shown, the method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to the present invention includes the following steps:

[0040] Step 1: Establish an unsteady, viscous, multi-dimensional plume mathematical model, design the computational domain, and divide the grid;

[0041] Step 2: Based on the grid division of step 1, the multi-dimensional plume mathematical model established in step 1 is physically discretized to obtain a system of equations including the mixture fraction equation, process variable equation, density equation, velocity equation, enthalpy equation, and pressure equation. The differential diffusion term is coupled to the flamelet model, that is, the differential diffusion term is considered when solving the system of equations for the control parameters enthalpy, process variable, mixture fraction, and second-order moment of the mixture fraction.

[0042] In step three, initial and boundary conditions are set. The system of equations mentioned in step two, namely, the mixture fraction equation, the process variable equation, the density equation, the velocity equation, the enthalpy equation, and the pressure equation, is then solved. After solving the system of equations for the control parameters enthalpy, process variable, mixture fraction, and the second-order moment of the mixture fraction, the calculated results are input into a precalculated flamelet library. The table then retrieves the composition, temperature, chemical reaction source term, and differential diffusion term. The pressure equation is then solved within the prediction-correction iteration, and a pressure correction is applied. Through these three steps, a solution process for the differential diffusion flamelet model of a buoyancy-driven plume is established.

[0043] Specifically, in the step one, the multidimensional plume mathematical model established adopts the small flame mathematical model, including the pressure equation, density equation, mixture fraction equation, process variable equation, velocity equation, enthalpy equation, and mixture fraction second-order moment equation. Among them, the process variable equation, mixture fraction equation, enthalpy equation, and mixture fraction second-order moment equation are the control parameter equations to be solved in the small flame model. The process variable can reflect the progress of the chemical reaction. Different parameters can be set according to different cases. Generally, it is set to the sum of the mass fractions of the key product and the key reactant. The more reasonable the setting, the more efficient and accurate the calculation. The second-order moment of the mixture fraction, that is, the mixture fraction variance, can be solved to take into account the turbulent pulsation conditions at any position in space.

[0044] Specifically, in step 2, the finite volume method is used. Based on the grid division, the mixture fraction transport equation, process variable transport equation, density transport equation, process variable second-order moment transport equation, velocity transport equation, enthalpy transport equation, process variable transport equation, and pressure transport equation established in step 1 are volume-integrated within the grid and time-integrated within the time step. Finally, the spatial and temporal discretization formats are introduced to obtain the algebraic equation defined at the center point of the grid. The transport equations for the process variable, mixture fraction, enthalpy, and mixture fraction second-order moment, i.e., the control parameter equations, are solved by considering the influence of differential diffusion effects and coupling differential diffusion terms. When solving the pressure transport equation, pressure correction is considered, and corrections are made to the velocity field and density field. The order of solving each equation group will be explained in step 3.

[0045] like Figure 1 As shown, the step three specifically includes the following steps:

[0046] Step (1), design initial conditions and boundary conditions according to the experimental facilities;

[0047] Step (2), determine the global time step and perform time advancement calculation;

[0048] Step (3), solve the density transport equation to obtain the density value;

[0049] Step (4), solve the velocity transport equation to obtain the velocity estimate;

[0050] Step (5), solving the process variable transport equation to obtain the estimated value of the process variable;

[0051] Step (6), solve the mixture fraction transport equation to obtain the estimated value of the mixture fraction;

[0052] Step (7), solve the mixed fractional second-order moment transport equation to obtain its estimated value;

[0053] Step (8), solve the enthalpy transport equation to obtain the estimated enthalpy;

[0054] Step (9), input the results of steps (5) to (8) into the pre-solved small flame library, and obtain the results of components, temperature, chemical reaction source terms and differential diffusion terms by looking up the table;

[0055] Step (10), solving the pressure transport equation, substituting the pressure calculation result into the velocity equation and solving it to obtain the velocity correction value;

[0056] Step (11), looping step (10), and continuously correcting the speed value until the specified number of cycles is reached;

[0057] Step (12), loop step (4) to step (11) until convergence or the maximum number of loops is reached;

[0058] Step (13), solve the ideal gas state equation and update the density value;

[0059] In step (14), it is determined whether the specified end time has been reached. Otherwise, the time step is advanced and steps (3) to (13) are repeated.

[0060] The equations to be solved in steps (5) to (8) are:

[0061] ;

[0062] in, is the density; are the variables to be determined, including process variables, mixture fraction, second-order moment of mixture fraction, and enthalpy; is the mass diffusion coefficient, , where c p is the specific heat capacity at constant pressure, is the thermal conductivity; is the source item corresponding to the variable; refers to the gradient operator, where refers to the Cartesian coordinate of the jth direction; represents the velocity vector, Refers to the component of velocity in the j direction; Represents time, is the differential diffusion term, ,in .

[0063] In the aforementioned solution process, since buoyancy plumes involve coupled heat and mass transfer and flow processes in the field of fire safety, the velocity and density equations are placed before the control parameter solution system. When solving the control parameter equations—namely, the process variable equation, the mixture fraction equation, the mixture fraction second-order moment equation, and the enthalpy equation—differential diffusion terms are added to couple the differential diffusion effect. The flamelet library is established by solving the one-dimensional flamelet equation. Therefore, during the solution process, only the control variable equations need to be solved, which are then input into the flamelet library to calculate parameters such as component temperature. This coordinate transformation and dimensionality reduction process significantly reduces the number of control equations to be solved, improving solution efficiency.

[0064] Example:

[0065] Taking the numerical calculation of three-dimensional methane / air counter-flow diffusion flame as an example, the present invention is described in full and in detail. This method is not limited to pool fire combustion scenarios, but is applicable to all buoyancy-driven plumes. In this embodiment, three different combustion models are used to model the methane / air combustion process respectively to compare the effects of finite chemical reaction rate and differential diffusion effect on the results. The infinitely rapid chemical reaction model uses the EDM model, the finite rapid chemical reaction model uses a small flame model (FPV_Le1) based on the uniform Lewis number assumption without considering the differential diffusion effect, and finally the differential diffusion effect small flame model (FPV_DD) is used to compare and analyze the influence of the differential diffusion effect.

[0066] The embodiment of the present invention is mainly divided into the following steps: step (1) description of the mathematical model; step (2) establishment and description of the calculation domain, initial conditions, and boundary conditions; step (3) grid division and calculation process description. Afterwards, flame characteristics such as temperature field and component field are analyzed based on the model.

[0067] Step (1) first describes the mathematical model, which is divided into three parts, including:

[0068] A mathematical model of an unsteady, viscous, multi-dimensional small flame is established, in which the continuity equation is established according to the law of conservation of mass, the momentum equation is established according to Newton's second law of motion, and the energy equation is established according to the law of conservation of energy, thereby forming the control equations that restrict fluid flow and heat and mass transfer.

[0069] The three models have the same governing equations for velocity and density, where the governing equation for density is:

[0070] ;

[0071] is the density; refers to the gradient operator, where refers to the Cartesian coordinate of the jth direction; represents the velocity vector, Refers to the component of velocity in the j direction; Represents time.

[0072] The governing equation for velocity is:

[0073] ;

[0074] in, For pressure, is the acceleration due to gravity, and is the viscous stress tensor.

[0075] When solving the components and enthalpy in the infinitely rapid chemical reaction model, the direct solution method is also used, where the component equation is:

[0076] ;

[0077] is the density; is the mass fraction of each component; is the mass diffusion coefficient, , where c p is the specific heat capacity at constant pressure, is the thermal conductivity; is the component source term;

[0078] Solving the enthalpy equation is:

[0079] ;

[0080] in, is the standard enthalpy, is the thermal diffusivity, For pressure, is the radiation source term, Refers to the heat release rate produced by combustion per unit volume.

[0081] In the two small flame models, enthalpy and components are not solved directly. The control parameters are solved first. The equations are in the form of:

[0082] ;

[0083] is the differential diffusion term, are the variables to be determined, including process variables, mixture fraction, second-order moment of mixture fraction, and enthalpy. , .

[0084] In the FPV_Le1 model with the uniform Lewis number assumption, the differential diffusion term on the right side of the equation is 0. However, when solving the differential diffusion flamelet model FPV_DD, the differential diffusion term on the right side of the equation is not 0.

[0085] Step (2) Establishment and description of computational domain, grid division, initial conditions, and boundary conditions:

[0086] In the first part, in this embodiment, the computational domain and boundary conditions of the methane / air diffusion flame are set with reference to the methane pool fire combustion experiment of Sandia Laboratory in the United States, such as Figure 2 The n shown here refers to the number of grid divisions, R1 refers to the half-price of the fuel inlet, R2 refers to the radius of the base-shaped plane, and R3 refers to the radius of the entire computational domain. The computational domain is a cylinder with a diameter of 4.6 m and a height of 4.56 m. The cylinder is divided into a three-dimensional orthogonal grid, of which 350 grids are evenly divided along the axial direction. A stretched grid is set along the radial direction. According to the stretching parameter 1.3, the computational domain is divided into 200 grids and 80 grids are evenly divided along the tangential direction. The total number of grids is 22.4 million.

[0087] In the second part, methane fuel enters the computational domain at an initial velocity of 0.097 m / s through an inlet with a half-diameter of 0.5 m. The fuel inlet is surrounded by a 1-meter-long pedestal plane, which is surrounded by air with an initial velocity of 0.327 m / s. In this example, the initial temperature of the fuel and oxidant is 300 K, the pressure is set to a constant 81.1 kPa, the fuel mixture fraction Z at the inlet is set to 1, and the oxidant mixture fraction Z at the inlet is set to 0. All other variables are set to zero gradient.

[0088] Step (3) The calculation process of the three-dimensional methane / air pool fire combustion diffusion flame is as follows:

[0089] First, the grid is divided according to the parameters mentioned in step (2). The process variable equation, enthalpy equation, mixed fraction equation, and mixed fraction second-order moment equation are numerically discretized on all grids using the PIMPLE algorithm with the help of the finite volume method. The time integral is integrated using the first-order Euler implicit method, that is, the convection term and the diffusion term are both included in the unknown time layer. The spatial integral is integrated using the second-order total variation non-increasing format.

[0090] Then, the equations are solved sequentially based on the coupled plume model of the flamelet model and the differential diffusion effect. The specific steps are as follows:

[0091] Step 1: Design initial conditions and boundary conditions according to the experimental facilities;

[0092] Step 2: Determine the global time step and perform time advancement calculation;

[0093] Step 3, solve the density transport equation to obtain the density value;

[0094] Step 4, solve the velocity transport equation to obtain the velocity estimate;

[0095] Step 5, solving the process variable transport equation to obtain the estimated value of the process variable;

[0096] Step 6, solve the mixture fraction transport equation to obtain an estimated value of the mixture fraction;

[0097] Step 7, solving the mixed fractional second-order moment transport equation to obtain its estimated value;

[0098] Step 8, solving the enthalpy transport equation to obtain the estimated enthalpy;

[0099] Step 9: Input the results of steps 4 to 7 into the pre-solved flamelet library, and look up the table to obtain the results of components, temperature, chemical reaction source terms, and differential diffusion terms;

[0100] Step 10, solving the pressure transport equation, substituting the pressure calculation result into the velocity equation and solving it to obtain the velocity correction value;

[0101] Step 11, looping step 10, continuously correcting the speed value until the specified number of cycles is reached;

[0102] Step 12: Repeat steps 3 to 11 until convergence or the maximum number of cycles is reached;

[0103] Step 13, solving the ideal gas state equation and updating the density value;

[0104] Step 14: Determine whether the specified end time has been reached. Otherwise, advance the time step and repeat steps 1 to 13.

[0105] According to the above steps, the variable value defined at each grid center point is obtained, and the numerical solution of the methane / air pool fire combustion diffusion flame using the differential diffusion flamelet model is realized.

[0106] Afterwards, the velocity field and material distribution characteristics of the three-dimensional methane / air pool fire diffusion flame are analyzed:

[0107] The calculated results are compared with the experimental data to analyze the accuracy of the model prediction. Based on the velocity field calculated by the present invention and after time averaging, as shown in FIG. Figure 3 As shown in the figure, the data point is a point on the circular section 0.9 m away from the bottom of the calculation domain, r is the distance from the data point on the selected circular section to the center of the circle, u is z Refers to the axial speed, u r Refers to the radial velocity, the points correspond to the experimental data, and the three lines correspond to three models: EDM model, the flamelet model FPV_Le1 based on the uniform Lewis number assumption, and the differential diffusion flamelet model FPV_DD, as shown in Figure 3 As shown, the data of the flame neck were selected. It can be seen that the three models are in good agreement with the experimental data, and the data of the two small flame models are in better agreement with the experimental data than the EDM model. However, the results of the FPV_DD model and the FPV_Le1 model considering the differential diffusion effect are not much different. Therefore, the present invention can conclude that the finite chemical reaction rate has an impact on the velocity field distribution, while the differential diffusion effect has little effect on the accuracy of the velocity field calculation results. Figure 3 In the figure, the left figure is the axial velocity comparison diagram, and the right figure is the radial velocity comparison diagram. The points correspond to the experimental data results, the black solid line corresponds to the calculation results of the infinitely fast chemical reaction model, the black dashed line corresponds to the model calculation results without considering the influence of the differential diffusion effect, and the gray dashed line corresponds to the model calculation results considering the influence of the differential diffusion effect.

[0108] By comparing the distribution of carbon dioxide mass fraction in laminar and turbulent regions, the influence of differential diffusion effect is analyzed, such as Figure 4 As shown ( Figure 4 The figure shows the distribution comparison of laminar (left) and turbulent (right) regions, where the dotted line corresponds to the model without considering the influence of differential diffusion effect, and the solid line corresponds to the model with considering the influence of differential diffusion effect). Z is the mixing fraction, is the mass fraction of CO2, Lam refers to the laminar flow region, and Tur refers to the turbulent flow region. It can be seen from the figure that the mass fraction of CO2 in the laminar and turbulent regions, the prediction results of FPV_DD are higher than those predicted by the FPV_Le1 model. This is because the differential diffusion effect is affected by the relative molecular mass of the substance, which shows that the differential diffusion effect has an impact on the distribution of components, so both the finite rapid chemical reaction rate and the differential diffusion effect need to be considered.

[0109] It will be easily understood by those skilled in the art that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for constructing a differential diffusion flamelet model for buoyancy-driven plumes, characterized in that: The steps include: Step 1: Establish an unsteady, viscous, multi-dimensional plume mathematical model, design the computational domain, and divide the grid; Step 2: Based on the grid division of step 1, the multi-dimensional plume mathematical model established in step 1 is physically discretized to obtain a system of equations including the mixture fraction equation, process variable equation, density equation, velocity equation, enthalpy equation, and pressure equation. The differential diffusion term is coupled to the flamelet model, that is, the differential diffusion term is considered when solving the system of equations for the control parameters enthalpy, process variable, mixture fraction, and second-order moment of the mixture fraction. Step 3: First, set the initial conditions and boundary conditions, then solve the system of equations mentioned in step 2: the mixture fraction equation, process variable equation, density equation, velocity equation, enthalpy equation, and pressure equation. After solving the control parameter equation system, the calculated results are input into the pre-calculated flamelet library, and the components, temperature, chemical reaction source terms, and differential diffusion terms are obtained by table lookup. The pressure equation is then solved within the prediction-correction iteration and the pressure correction is performed.

2. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: In the step 1, a small flame model is used to model the plume.

3. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: In the first step, the calculation domain is designed and the grid is divided with reference to the combustion chamber diameter and height of the experimental facility.

4. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: In the step 2, the finite volume method is used to perform volume integration of the mixture fraction transport equation, process variable transport equation, density transport equation, process variable second-order moment transport equation, velocity transport equation, enthalpy transport equation, process variable transport equation, and pressure transport equation established in the step 1 within the grid according to the grid division situation, and time integration within the time step.

5. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 4, characterized in that: By introducing the spatial and temporal discretization format, we obtain the algebraic equations defined at the center points of the grid.

6. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 5, characterized in that: The transport equations of the process variables, mixture fraction, enthalpy and second-order moment of the mixture fraction, i.e., the control parameter equations, are solved by considering the influence of the differential diffusion effect and coupling the differential diffusion terms.

7. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: In the second step, when solving the pressure transport equation, the pressure correction is taken into account, and the velocity field and the density field are corrected.

8. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: The step three includes the following steps: Step (1), design initial conditions and boundary conditions according to the experimental facilities; Step (2), determine the global time step and perform time advancement calculation; Step (3), solve the density transport equation to obtain the density value; Step (4), solve the velocity transport equation to obtain the velocity estimate; Step (5), solving the process variable transport equation to obtain the estimated value of the process variable; Step (6), solve the mixture fraction transport equation to obtain the estimated value of the mixture fraction; Step (7), solve the mixed fractional second-order moment transport equation to obtain its estimated value; Step (8): Solve the enthalpy transport equation to obtain the estimated enthalpy.

9. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 8, characterized in that: The step three also includes: Step (9), input the results of steps (5) to (8) into the pre-solved small flame library, and obtain the results of components, temperature, chemical reaction source terms and differential diffusion terms by looking up the table; Step (10), solving the pressure transport equation, substituting the pressure calculation result into the velocity equation and solving it to obtain the velocity correction value; Step (11), looping step (10), and continuously correcting the speed value until the specified number of cycles is reached; Step (12), loop step (4) to step (11) until convergence or the maximum number of loops is reached; Step (13), solve the ideal gas state equation and update the density value; In step (14), it is determined whether the specified end time has been reached. Otherwise, the time step is advanced and steps (3) to (13) are repeated.

10. The method for constructing a differential diffusion flamelet model for a buoyancy-driven plume according to claim 1, characterized in that: Used to handle unsteady terms, convection terms, diffusion terms, and source terms.

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