A numerical analysis method for quantifying differential diffusion in coal / ammonia hybrid combustion

Abstract

This invention discloses a numerical analysis method for quantifying differential diffusion in coal / ammonia co-combustion, belonging to the field of numerical simulation technology for coal / ammonia co-combustion. The steps include: establishing gas-solid two-phase governing equations and a general transport equation for the total mixture fraction based on element conservation; defining specific differential diffusion quantification parameters; calculating mass diffusion using a non-unity constant Lewis number; discretizing the model using the PIMPLE algorithm and coupling it with a velocity-pressure field; obtaining combustion characteristic data through CP-DNS solution; and comparing and analyzing the influence of differential diffusion on component distribution and temperature field. This invention solves the problem of incomplete physical process characterization caused by traditional models neglecting differential diffusion, and can systematically quantify the diffusion differences of heavy / light components and their effects on the combustion process, providing a reliable numerical tool for the optimized design of coal / ammonia co-combustion systems.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation technology for coal / ammonia co-combustion, specifically relating to a numerical analysis method for quantifying differential diffusion in coal / ammonia co-combustion. Background Technology

[0002] Coal / ammonia co-combustion is an important technology for low-carbon emissions. In actual combustion, the diffusion rates of heavy molecules in volatiles differ significantly from those of smaller molecules such as ammonia and hydrogen. This differential diffusion phenomenon inevitably exists and alters flame structure, component mixing, and combustion characteristics. Existing numerical simulation methods are mostly based on the Unity Lewis number assumption, neglecting the differences in diffusion rates between different components. This results in an incomplete physical characterization of the combustion process and an inability to accurately reflect the impact of differential diffusion.

[0003] Phase-direct numerical simulation (CP-DNS) can resolve all spatiotemporal scales of turbulence and chemistry, enabling independent analysis of specific physical processes. By comparing CP-DNS results based on and without the unity Lewis number assumption, the impact of differential diffusion can be assessed independently. However, existing CP-DNS studies have not established a dedicated quantitative system for differential diffusion in coal / ammonia blended combustion, lacking universal governing equations based on element conservation and explicit quantitative parameters, making it difficult to systematically characterize the intensity, dominant components, and influencing mechanisms of differential diffusion. Therefore, developing a numerical analysis method capable of accurately quantifying differential diffusion in coal / ammonia blended combustion is of great significance for improving the numerical simulation of co-combustion processes and optimizing system design. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion. By constructing a complete system of governing equations and specific quantification parameters, combined with CP-DNS, the differential diffusion effect can be systematically quantified.

[0005] The technical solution of the present invention is as follows:

[0006] A numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion includes the following steps:

[0007] Step 1: Establish a mathematical model, including the gas-phase governing equations and scalar transport equations. The scalar transport equations include the volatile matter mixing fraction. Coke exhaust gas mixture fraction ammonia flow mixing fraction The total enthalpy equation is derived based on element conservation, and a general control equation for the total mixing fraction containing differential diffusion terms is defined. The differential diffusion quantification parameter is defined.

[0008] Step 2: Combining the boundary conditions, initial conditions, and mesh generation of coal / ammonia blended combustion, the mathematical model is numerically discretized to generate a system of algebraic equations and then solved nonlinearly through iteration.

[0009] Step 3: Solve the discrete equations using the direct numerical simulation framework of the carrier phase, calculate the mass diffusion coefficient using a non-unity constant Lewis number, and couple the velocity field and pressure field using the PIMPLE algorithm to obtain combustion characteristic data including differential diffusion effects; CP-DNS represents direct numerical simulation of the carrier phase; PIMPLE represents direct numerical simulation.

[0010] Step 4: Compare the component distribution and temperature field under differential diffusion and unity Lewis number, and quantify the influence law through conditional analysis of physical space and component space.

[0011] Compared with the prior art, the present invention has the following advantages:

[0012] 1. A complete system of governing equations was established. Based on the general scalar transport equation, specific equations for components and energy were flexibly derived. For the first time, a general governing equation with differential diffusion terms specific to coal / ammonia blended combustion was derived, achieving a precise mathematical characterization of diffusion differences.

[0013] 2. Defined the differential diffusion quantification parameters. By extracting thermochemical quantity data from the central xy plane of the 3D computational domain and statistically averaging nine xy planes, the spatial distribution characteristics and quantitative laws of differential diffusion are fully revealed.

[0014] 3. By combining CP-DNS solution with multi-dimensional condition analysis, the influence of differential diffusion can be independently separated, and its effect on component reconstruction and temperature field can be systematically quantified, providing direct data support for the optimization of coal / ammonia co-combustion systems. Attached Figure Description

[0015] Figure 1 is a flowchart of a numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to the present invention;

[0016] Figure 2 is a schematic diagram of the CP-DNS calculation domain setting and grid distribution for coal / ammonia blended combustion of the present invention;

[0017] Figure 3 shows the instantaneous two-dimensional spatial distribution of thermochemical quantities in the xy plane under the consideration of differential diffusion (DD) and unity Lewis number (Le1) in this invention - temperature distribution;

[0018] Figure 4 shows the instantaneous two-dimensional spatial distribution of thermochemical quantities in the xy plane considering differential diffusion (DD) and unity Lewis number (Le1) in this invention - distribution of heavy component (C6H6O2);

[0019] Figure 5 shows the instantaneous two-dimensional spatial distribution of thermochemical quantities in the xy plane considering differential diffusion (DD) and unity Lewis number (Le1) in this invention - distribution of light components (H radicals);

[0020] Figure 6 shows the instantaneous two-dimensional spatial distribution of thermochemical quantities in the xy plane considering differential diffusion (DD) and unity Lewis number (Le1) in this invention - distribution of reaction products (H2O);

[0021] Figure 7 shows the differential diffusion quantization parameters of the present invention. Distribution of conditional average values ​​along the y-direction;

[0022] Figure 8 shows the differential diffusion quantization parameters of the present invention. Distribution of conditional average values ​​for decomposition by heavy / light components. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. However, the following embodiments are only for explaining the present invention, and the scope of protection of the present invention should include all the contents of the claims. Moreover, through the description of the following embodiments, those skilled in the art can fully implement all the contents of the claims of the present invention.

[0024] Example:

[0025] This embodiment takes stable coal / ammonia co-combustion in a turbulent mixing layer as the research object, and details the implementation process of this method (see...). Figure 1 ):

[0026] Step 1: Establish the relevant mathematical model:

[0027] 1. General scalar transport equation:

[0028] Establish a mathematical model, including gas-phase governing equations (density, pressure, velocity, composition, and energy equations) and scalar transport equations (volatile matter mixing fraction). Coke exhaust gas mixture fraction ammonia flow mixing fraction (Total enthalpy equation), based on element conservation, derives a general governing equation for the total mixing fraction containing differential diffusion terms, and defines differential diffusion quantification parameters; the general form of the gas-phase governing equation is a scalar transport equation, specifically expressed as:

[0029] ,

[0030] in, It is a general scalar quantity that can represent the mass fraction of a component. Total enthalpy Volatile matter mixture fraction Coke exhaust gas mixture fraction Mixing fraction with ammonia gas flow ; The density is the gas phase density. Euler time, for directional fluid velocity, The index of three-dimensional spatial coordinates representing the Cartesian coordinate system ( Corresponding to direction), Represents the divergence sign. For the diffusion flux corresponding to the scalar, The chemical reaction rate corresponds to a scalar value, with only the component mass fraction. This rate exists in the corresponding scalar equation. For gas-solid two-phase coupling source terms; scalar It can be used to determine the component mass fraction, total enthalpy, and mixture fraction according to the requirements, providing a unified basis for the derivation of specific equations.

[0031] 2. Gas-phase component equation: Based on the generalized scalar transport equation, when At that time, the governing equations for the gas phase components are:

[0032] ,

[0033] in, Components The mass fraction, Components The mass diffusion coefficient, To correct for velocity, used to ensure that the net diffusion flux is zero. Components The chemical reaction rate was calculated from a detailed mechanism involving 129 components and 1664 elementary reactions. The source term is a gas-solid two-phase coupled term, originating from volatile matter release and coke surface reactions. The diffusion flux includes the mass diffusion coefficient and a corrected rate to ensure a net diffusion flux of zero. The chemical reaction mechanism covers key pathways such as ammonia oxidation and volatile matter combustion, and the reaction rate is calculated using finite-rate chemistry.

[0034] 3. Gas-phase energy equation: Based on the generalized scalar transport equation, when At that time, the gas phase energy equation is:

[0035] ,

[0036] in, For total enthalpy, For gas phase thermal conductivity, The gas phase temperature, Components diffusion flux, Components enthalpy, For the gas-solid two-phase coupled energy source term, including radiative heat transfer and reaction enthalpy change, radiative heat transfer is calculated using the discrete coordinate method, and the absorption and emission coefficients are solved through a weighted sum model of the gray gas. Considering the enthalpy transport of heat conduction and component diffusion, as well as the energy exchange between the gas and solid phases, radiative heat transfer is calculated using the discrete coordinate method.

[0037] 4. Overall Mixed Fraction Equation: The general governing equation is derived based on the Bilger mixed fraction derivation, and its specific form is as follows:

[0038] ,

[0039] in, for Mixed fractions, and These are the weighted values ​​of the elemental mixing fractions on the fuel side and the oxidizer side, respectively. and They represent the elements in the combustion system. and components Quantity, For element weighting factors, specifically , , , , , These represent the molecular weights of the three elements C, H, and O, respectively. Components Middle elements The number of atoms, and elements respectively and components molecular weight, Components diffusion flux, To account for the diffusion term of differential diffusion, This is a gas-solid two-phase coupling source term. The elemental weighting factors are set according to the coal / ammonia co-combustion characteristics. The mixing characteristics of ammonia, volatile matter, and coke tail gas were reflected by calculation using a three-mixing-fraction small flame model.

[0040] 5. Quantization of Difference Diffusion: Parameters for Quantization of Difference Diffusion Defined as the difference between the diffusion term and the diffusion term under the Unity Lewis number assumption, considering the diffusion of differences:

[0041] ,

[0042] in, The diffusion term under the unity Lewis number assumption is expressed as follows: , The specific heat capacity of the gas; The refined expression based on the component mass fraction is:

[0043] ,

[0044] Among them, components coefficient Defined as:

[0045] ,

[0046] , , Components The number of carbon, hydrogen, and oxygen atoms in the sample can be directly correlated with the Lewis number and mass fraction distribution of each component through this expression, which can accurately quantify the contribution weight of different components to differential diffusion. Indicates light components ( Dominant difference diffusion, Indicates recombinant components ( (Leading) Through Parameter characterization, further divided into recombinants and light components Decompose and identify the dominant factors of diffusion differences, where DD represents diffusion differences and Le1 represents the unity Lewis number.

[0047] Step 2, Numerical Discretization and Iterative Solution:

[0048] 1. Mesh generation (see...) Figure 2 The computational domain was meshed using a cuboid format with dimensions of 59.7 mm × 59.7 mm × 14.9 mm in the flow (x), lateral (y), and spanwise (z) directions, a mesh resolution of 384 × 384 × 96, and a uniform mesh spacing of 155.5 μm. A cubic discretization scheme was used to handle the spatial derivative, while the temporal derivative was discretized using an implicit scheme. This cuboid computational domain and mesh resolution ensured that the multi-scale characteristics of the turbulent vortices and flame front were fully analyzed. The computational domain boundary was set as follows: coal particle diameter 25 μm, number density 6.1 × 10⁻⁶. 10 particles / m³, initial velocity and temperature consistent with the gas phase; the upper laminar flow is a coal / ammonia / air mixture, in which , , Speed ​​= 15 m / s, Temperature = 600 K , , These represent the mass fractions of NH3, O2, and N2, respectively. The lower laminar flow is hot air with a velocity of -15 m / s in the x-direction and a temperature of 1300 K; the x and z directions have periodic boundaries, and the y-direction has a zero-gradient boundary. The initial turbulent disturbance was generated using a digital filtering method, and its intensity... Length scale .

[0049] 2. Discretization and Solution: The spatial derivative is discretized using a cubic scheme, and the time integral is performed using an implicit scheme to ensure the stability of the solution.

[0050] Step 3, CP-DNS (Planet Phase Direct Numerical Simulation) Solution and Data Acquisition:

[0051] 1. Numerical solution: The low Mach number finite volume solver based on OpenFOAM is used, coupled with OpenSMOKE++ to solve the detailed chemical reaction mechanism; two sets of simulations are performed, considering differential diffusion (DD) and unity Lewis number (Le1), while keeping other parameters consistent.

[0052] 2. Convergence judgment: Iterative correction until the numerical calculation convergence criterion is met. The total physical time for each simulation calculation is 3.84 ms, ensuring the statistical validity of the data.

[0053] Step 4, Quantitative analysis of the impact of differential diffusion:

[0054] 1. Instantaneous distribution analysis: Instantaneous data were extracted from the central xy plane of the 3D computational domain, and significant differences were observed in the distribution of thermochemical quantities under DD and Le1 conditions (see...). Figure 3 , Figure 4 , Figure 5 and Figure 6 The overall temperature distribution is similar, but there are differences in local areas. The heavy component (C6H6O2) is more concentrated in the high-concentration area under DD conditions, while the light component (H free radical) has a larger peak under Le1 conditions. The main reaction product H2O only has different distributions in the upper fuel mixing layer, clearly showing the influence of differential diffusion on the spatial reconstruction of thermochemical quantities.

[0055] 2. Quantitative Analysis: Nine xy-plane data points were extracted and statistically averaged to compare the temperature field, heavy component, and light component distribution under DD and Le1 conditions. Parameter changes (see) Figure 7 The study found that the spatial distribution differences of recombinant components were dominated by difference diffusion. Significant changes were observed in the high-temperature region (y = 20-37 mm), and the decomposition was based on the heavy components. With the whole The trend of change is consistent (see) Figure 8 This indicates differential diffusion in the combustion of coal / ammonia, which is dominated by recombinant components.

[0056] This embodiment demonstrates that, through a complete system of governing equations and CP-DNS solutions, combined with multi-dimensional data extraction and statistical analysis, this method can accurately quantify the intensity, dominant components, and influence patterns of differential diffusion in coal / ammonia blended combustion, providing reliable numerical support for the optimized design of co-combustion systems.

[0057] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion, characterized in that, Includes the following steps: Step 1: Establish a mathematical model, including the gas-phase governing equations and scalar transport equations. The scalar transport equations include the volatile matter mixing fraction. Coke exhaust gas mixture fraction ammonia flow mixing fraction The total enthalpy equation is derived based on element conservation, and a general control equation for the total mixing fraction containing differential diffusion terms is defined. The differential diffusion quantification parameter is defined. Step 2: Combining the boundary conditions, initial conditions, and mesh generation of coal / ammonia blended combustion, the mathematical model is numerically discretized to generate a system of algebraic equations and then solved nonlinearly through iteration. Step 3: Solve the discrete equations using the direct numerical simulation framework of the carrier phase, calculate the mass diffusion coefficient using a non-unity constant Lewis number, and obtain combustion characteristic data containing differential diffusion effects by coupling the velocity field and pressure field using the PIMPLE algorithm; CP-DNS represents direct numerical simulation of the carrier phase; PIMPLE represents pressure-velocity coupled iterative correction. Step 4: Compare the component distribution and temperature field under differential diffusion and unity Lewis number, and quantify the influence law through conditional analysis of physical space and component space; When the scalar in step one Indicates the mass fraction of the component At that time, the governing equations for the gas phase components are: ， in, For gas phase density, Components mass fraction, Euler time, for directional fluid velocity, Represents the three-dimensional spatial coordinate index of the Cartesian coordinate system. Corresponding to direction, Represents the divergence sign. Represents the gradient sign. Components The mass diffusion coefficient, To correct the speed, Components The chemical reaction rate, It is a gas-solid two-phase coupled source term, originating from volatile matter and coke surface reaction.

2. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, When the scalar in step one Indicates total enthalpy At that time, the gas phase energy equation is: ， in, For gas phase density, For total enthalpy, Euler time, for directional fluid velocity, Represents the three-dimensional spatial coordinate index of the Cartesian coordinate system. Represents the divergence sign. Represents the gradient sign. For gas phase thermal conductivity, The gas phase temperature, Components diffusion flux, Components enthalpy, It is a gas-solid two-phase coupled energy source term, including radiation heat transfer and reaction enthalpy change.

3. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, The general governing equation for the total mixture fraction in step one is based on the Bilger mixture fraction derivation, and its specific form is as follows: ， in, For gas phase density, for Mixed fractions, Euler time, for directional fluid velocity, Represents the three-dimensional spatial coordinate index of the Cartesian coordinate system. Corresponding to direction, and These are the weighted values ​​of the elemental mixing fractions on the fuel side and the oxidant side, respectively. and They represent the elements in the combustion system. and components Quantity, For element weighting factors, , , , Represents the molecular weight of element O. Components Middle elements The number of atoms, and elements respectively and components molecular weight, Represents the divergence sign. Components diffusion flux, To account for the diffusion term of differential diffusion, It is a gas-solid two-phase coupling source term.

4. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, Differential diffusion quantization parameters in step one Defined as the difference between the diffusion term and the diffusion term under the Unity Lewis number assumption, considering the diffusion of differences: ， in, The Bilger mixture fraction represents the mixing state of fuel and oxidizer in the combustion system. For the diffusion term under the assumption of a constant Lewis number without unity, The diffusion term under the unity Lewis number assumption is expressed as follows: , Represents the divergence sign. Represents the gradient sign. For gas phase thermal conductivity, The specific heat capacity of the gas; The refined expression based on the component mass fraction is: ， Among them, components coefficient Defined as: ， in, , , Components The number of carbon, hydrogen, and oxygen atoms in the medium can be directly correlated with the Lewis number and mass fraction distribution of each component through this expression, which can accurately quantify the contribution weight of different components to differential diffusion. Representative components in the combustion system Quantity, Representative components Lewis number, Representative components mass fraction, Representative components molecular weight, and These are the element mixing fraction weights for the fuel side and the oxidant side, respectively; DD represents differential diffusion; and Le1 represents the unity Lewis number. Indicates light components Dominant Difference Diffusion Indicates reorganization leading.

5. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, The mass diffusion coefficient in step one The calculation is as follows: ， in, For gas phase thermal conductivity, Components Non-unity constant Lewis number For gas phase density, This represents the specific heat capacity of the gas phase; its value is determined based on the characteristics of the coal / ammonia co-combustion components and provided in the model input parameters.

6. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, The boundary conditions in step two are set as follows: coal particle diameter 25 μm, number density 6.1 × 10⁻⁶. 10 particles / m³, initial velocity and temperature consistent with the gas phase; the upper laminar flow is a coal / ammonia / air mixture, in which , , Speed ​​15 m / s, temperature 600 K , , These represent the mass fractions of NH3, O2, and N2, respectively; the lower laminar flow is hot air with a velocity of -15 m / s and a temperature of 1300 K; the x and z directions are periodic boundaries, and the y direction is a zero gradient boundary.

7. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, In step two, the mesh generation adopts a cuboid computational domain with flow, transverse, and spanwise dimensions of 59.7 mm × 59.7 mm × 14.9 mm, a mesh resolution of 384 × 384 × 96, and a uniform mesh spacing of 155.5 μm.

8. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, In step two, the spatial derivative is processed using a cubic discretization scheme, while the temporal derivative is discretized using an implicit scheme.

9. The numerical analysis method for quantifying differential diffusion in coal / ammonia blended combustion according to claim 1, characterized in that, The conditional analysis in step four includes physical space analysis and component space analysis. Physical space analysis involves extracting two-dimensional instantaneous data of temperature, heavy components, light components, and products from the central xy plane of the 3D computational domain, and comparing thermochemical quantities in differential diffusion (DD) with the non-unity constant Lewis number of the first component. The study examined the two-dimensional spatial distribution differences under various conditions, including thermochemical quantities such as temperature, heavy component C6H6O2, light component H radicals, and reaction product H2O, covering high-concentration areas and local aggregation characteristics. Spatial analysis of the components involved extracting data from nine xy-planes and performing statistical averaging to obtain parameters for temperature, heavy components, light components, and differential diffusion quantification. The conditional average value was used to clarify the dominant role of heavy / light components in differential diffusion and their spatial distribution patterns.

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