Numerical Calculation Method and System for Hydrogen-Ammonia Blended Combustion Considering Flame Curvature

Abstract

This invention discloses a numerical calculation method and system for hydrogen-ammonia co-combustion considering flame curvature, belonging to the field of energy and combustion engineering. Addressing the problem that traditional models struggle to capture strong curvature effects, this method constructs a Composite Space Flame Model (CSM), explicitly introduces curvature parameters into the progress variable space, and solves self-contained equations; it combines a one-dimensional free-propagating flame (FPP) database to form a lookup table database; and it uses direct numerical simulation (DNS) to generate a validation dataset and performs NO... x Reaction path analysis; mapping the database to a four-dimensional parameter space of mixing fraction, reaction process variables, normalized enthalpy, and hydrogen radicals; outputting field variables by table lookup and comparing with DNS data for verification; this method innovatively uses hydrogen radicals to characterize curvature effect, significantly improving the prediction accuracy of unstable combustion modes and pollutant generation in hydrogen-ammonia blended flames.

Description

Technical Field

[0001] This invention belongs to the field of energy and combustion engineering, specifically relating to a numerical calculation method and system for hydrogen-ammonia co-combustion considering flame curvature. Background Technology

[0002] With the energy structure shifting towards low-carbon development, hydrogen and ammonia-hydrogen blends, due to their zero-carbon or low-carbon emission characteristics, show promising application prospects in power plants such as gas turbines. However, when hydrogen-ammonia blends are burned under lean-burn premixed conditions, the high diffusivity of hydrogen easily leads to significant thermal diffusion instability. This instability can even be exacerbated under high-pressure operating environments, further intensifying the coupling effect between hydrodynamic instability and thermal diffusion instability. This results in a strong folded and cellular structure on the flame surface, with significant changes in flame curvature. Curvature not only affects the local flame propagation speed, heat release distribution, and flame stability, but also significantly influences nitrogen oxides (NOx) by altering the transport and reaction pathways of free radicals. x The generation and consumption mechanism of ).

[0003] In existing numerical simulation methods for combustion, traditional small-flame models are typically based on the assumption of a one-dimensional steady-state flame, making it difficult to accurately capture the multi-physics coupling effects such as strong curvature, differential diffusion, and wall heat loss. For scenarios involving strong curvature changes and wall quenching coupling caused by thermal diffusion instability in hydrogen-ammonia mixed fuels under high pressure, existing models still lack a systematic modeling method. Therefore, developing a numerical calculation method for hydrogen-ammonia combustion that can consider flame curvature effects is crucial for improving NO₂ levels in gas turbine combustors. x Accurate emission prediction is of great significance for guiding low-NOx combustion design. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a numerical calculation method and system for hydrogen-ammonia co-combustion considering flame curvature. By coupling curvature parameters with reaction progress variables, a flame lookup table database reflecting local flame structure changes is constructed, and a dataset for direct numerical simulation is calculated to analyze pollutant NO. x The reaction path analysis enables high-precision and high-efficiency numerical simulation of unstable hydrogen-ammonia flames.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature includes the following steps:

[0007] Step 1: Construct a composite space flame model (CSM) with curvature parameters, solve the parameterized small flame equation in the reaction process variable space, explicitly introduce curvature as a control variable, and solve the gradient equation of the progress variable.

[0008] Step 2: Construct a one-dimensional free-propagating flame (FPP) database and integrate it with the model data of the composite space flame model (CSM) to form a small flame lookup table database;

[0009] Step 3: Solve the governing equations for hydrogen-ammonia blended combustion using direct numerical simulation, generating a high-precision direct numerical simulation dataset. Based on this dataset, perform reaction pathway analysis to quantify NO. x Generation mechanism;

[0010] Step 4: Map the small flame lookup table database to the four-dimensional control parameter space of mixture fraction, reaction process variables, normalized enthalpy and hydrogen radicals to generate a small flame lookup table;

[0011] Step 5: Solve the control parameter equations, output components, and temperature field by looking up tables, and verify the model accuracy by comparing it with the direct numerical simulation dataset.

[0012] This invention also provides a numerical calculation system for hydrogen-ammonia co-combustion considering flame curvature, comprising:

[0013] The CSM / FPP library building module, where CSM is model data and FPP is a one-dimensional free-propagating flame, is used to generate a small flame database containing curvature parameters;

[0014] The DNS solver module, which uses direct numerical simulation, is used to generate a high-precision validation dataset.

[0015] The lookup table solver outputs combustion field variables based on the four-dimensional control parameters in the numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature.

[0016] The present invention also provides a computer-readable storage medium storing program instructions, which, when executed by a processor, implement the above-described numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention employs direct numerical simulation (DNS) based on detailed chemical reaction mechanisms and precise transport models to generate highly accurate data. This not only provides a reliable validation benchmark for flame lookup table models but also supports the analysis of NO. x A thorough reaction flux analysis is conducted on key generation and consumption pathways. Furthermore, this method innovatively incorporates curvature effects, differential diffusion, detailed chemical reaction kinetics, and wall heat loss. The constructed lookup table database, using mixing fraction, reaction progress variables, enthalpy, and curvature as multidimensional control parameters, significantly enhances the numerical characterization capability of unstable combustion modes in hydrogen-ammonia lean premixed flames. Attached Figure Description

[0019] Figure 1A flowchart illustrating the numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature in this invention;

[0020] Figure 2 This is an instantaneous distribution diagram of NO in an embodiment of the present invention;

[0021] Figure 3 This is an instantaneous distribution diagram of NO2 in an embodiment of the present invention;

[0022] Figure 4 The key component comparison diagram-T in the prior analysis of this invention embodiment is shown. DC is the data from direct numerical simulation used to refer to and compare the table lookup results of the CSM model and the FPP model.

[0023] Figure 5 A comparison diagram of key components in the prior analysis of this invention. DC is the data from direct numerical simulation used to compare the lookup results of the CSM model and the FPP model.

[0024] Figure 6 A comparison diagram of key components in the prior analysis of this invention. DC is the data from direct numerical simulation used to compare the lookup results of the CSM model and the FPP model.

[0025] Figure 7 A comparison diagram of key components in the prior analysis of this invention. DC is the data from direct numerical simulation used to compare the lookup results of the CSM model and the FPP model.

[0026] Figure 8 This is a reaction path diagram in an embodiment of the present invention. Detailed Implementation

[0027] 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.

[0028] Example:

[0029] This embodiment takes hydrogen-ammonia co-combustion as the research object and details the implementation process of this method (e.g. Figure 1 (as shown)

[0030] Step 1. Construct a composite space flame model (CSM) with curvature parameters, solve the parameterized small flame equation in the reaction process variable space, explicitly introduce curvature as a control variable, and solve the gradient equation of the progress variable.

[0031] Using the general-purpose laminar flame solver ULF software, the complete set of governing equations describing a one-dimensional steady-state, adiabatic, free-propagating premixed flame (FPP) was solved in physical space coordinates. This set of equations includes: a continuity equation, an energy equation, and a component mass conservation equation (using a detailed chemical reaction mechanism). The solutions were performed for different initial temperatures and equivalence ratios for various fuels. The calculation results (including component mass fraction Y) are presented. i Temperature (T), density (ρ), and heat release rate (Qdot) constitute the baseline flame database under unstretched conditions. Using ULF software, a composite space flame model (CSM) database based on the progress variable space is constructed, involving the following steps:

[0032] 1) Coordinate system and equation transformation:

[0033] Using a self-contained scalar space method, the governing equations are derived from physical space. Transform to a reaction progress variable Define the schedule variable in scalar space with spatial coordinates. A linear combination of the quality scores of key species: ,in, As weighting coefficients, ensure The changes within the flame are strictly monotonous.

[0034] Physical space gradient The modulus is defined as the gradient of the progress variable: This quantity is the key mapping factor connecting physical space and scalar space.

[0035] 2) Derive the self-contained flame equation in the schedule variable space. middle( For the flame time), the conservation equations of physical space are rewritten as the following coupled equations using the coordinate transformation rule (chain rule):

[0036] Component equation:

[0037] ,

[0038] in, It's density. Let be the species dispersal rate in the progress variable space. Let be the species dispersal rate in the progress variable space. For curvature, , This is the source term for a chemical reaction.

[0039] Temperature equation:

[0040] ,

[0041] in, It is specific heat capacity. It is thermal conductivity. It is the specific heat capacity of species k. It is the source term of the chemical reaction at temperature.

[0042] Key equation - gradient equation of schedule variable:

[0043] ,

[0044] The equations explicitly include the flame curvature. and strain (Introduced via related terms) as source terms or parameters. This makes the model "self-contained," meaning it no longer requires an externally provided gradient or scalar dissipation rate model, but instead directly specifies the physical flame stretching parameters. To close the system of equations.

[0045] 3) Define the parameter space and boundary conditions:

[0046] Parameter range: Curvature As a core input parameter (lookup table dimension), temperature is also included. Equivalent ratio (or by mixed fractions) (Represented by...) Boundary conditions: at both ends of the progress variable space (corresponding to fresh reactants and equilibrium / combustion products). Corresponding to fresh reactants, Dirichlet boundary conditions are applied to the equilibrium state / combustion products.

[0047] 4) Numerical solution and mesh adaptation, using numerical methods (damped Newton's method) in Discretize the space and solve the above system of equations. The mesh is automatically refined in high-gradient regions (such as near reaction fronts) to accurately capture rapidly changing chemical and transport processes. Adaptive criteria are typically based on the second derivative of the source terms of temperature or progress variables.

[0048] Step 2. Construct a one-dimensional free-propagating flame (FPP) database and integrate it with the model data of the composite space flame (CSM) model to form a small flame lookup table database.

[0049] In a pre-defined multidimensional parameter space The system performs a parameter scan. For each parameter combination, a complete set of flame solutions, i.e., a "small flame," is obtained. Each solution includes: along... Coordinate distribution: And key global quantities, such as laminar flame velocity and peak heat release rate. Based on these solutions, chemical reaction source terms were also calculated to determine the forward and reverse reaction rates of pollutants, such as NO and NO2. Finally, all solutions were integrated and interpolated to construct a structured multidimensional lookup table database, providing data support for subsequent lookup table solvers (e.g., Figure 2 and Figure 3 (As shown).

[0050] Step 3. The governing equations for hydrogen-ammonia co-combustion are solved using direct numerical simulation to generate a high-precision dataset, and reaction pathway analysis is performed based on this dataset to quantify the NOx formation mechanism.

[0051] Direct numerical simulations were performed using the EBIdnsFOAM solver in OpenFOAM, employing a mixture-average diffusion model. The computational domain was initially constructed with flame thicknesses of 100 (x-direction) and 150 (y-direction), generating a high-resolution grid of 2000 (x-direction) × 3000 (y-direction), totaling six million grids. Initial simulation conditions were set as an unburned hydrogen-ammonia / air premixed gas at a temperature of 298 K, a pressure of 8 atm, and an equivalence ratio of 0.6, with a molar ratio of H2 to NH3 of 0.44:0.56. A detailed chemical reaction mechanism supporting the combustion of hydrogen-ammonia co-combustion, comprising 31 components and 203 reactions, was defined, using a mixture-average diffusion model. A wall boundary condition was set at y=0, with an isothermal wall at a fixed temperature of 298 K, a no-slip velocity condition, and a zero-gradient diffusion condition for species mass fraction. A set of governing equations was established, including the total mass conservation equation, momentum equation, species mass transport equation, and energy equation. The partial differential equations are physically discretized using the finite volume method, transforming them into a system of nonlinear algebraic equations concerning density, velocity, pressure, component mass fraction, and enthalpy.

[0052] Then, numerical solutions were performed: the fully compressible Navier-Stokes equations were solved, including coupled detailed chemical reaction kinetics. The operator splitting method was used to handle rigid chemical source terms, and a second-order low-dissipation scheme was used for spatial discretization. Calculations were executed under dynamic time step control to ensure that the CFL and Fourier number met stability requirements. Key physical quantities were monitored in real time, and data output and analysis were performed after the simulation time was reached: complete field data were output, and reaction pathway analysis was conducted for key regions, quantifying NO... x The generation mechanism (such as) Figure 4 , Figure 5 , Figure 6 and Figure 7 (As shown).

[0053] Furthermore, the steps to continue solving for the chemical reaction rate are as follows:

[0054] 1) Initialize the reaction thermodynamic model of OpenFOAM and extract the mass fraction data of all components in the flow field from the model to provide the basic input for chemical rate calculation.

[0055] 2) Load the chemical mechanism file (containing reaction kinetic parameters and species thermodynamic data) from the specified path and create an ideal gas mixture model. Find the index of the target species, such as NO and NO2, in the Cantera mechanistic species list.

[0056] 3) Calculate point by point in the grid cell, extract the mass fraction of all components in the current grid cell. If the mass fraction of a component is too small (below the minimum threshold), it is corrected to the threshold to avoid numerical calculation errors.

[0057] It is also necessary to extract the temperature and pressure data of the current unit and complete the thermodynamic state initialization of the unit (matching the actual working conditions of the flow field).

[0058] 4) Calculate the "molar generation rate," "molar consumption rate," and "net molar generation rate" for all species under this state to obtain basic chemical kinetic data. Then, multiply the "molar rate" by the molecular weight of the corresponding species to convert it into a "mass rate," ensuring that the units are consistent with the output field variables. Finally, write the data into the species rate field corresponding to the current unit to complete the calculation for a single unit.

[0059] Furthermore, reaction pathway analysis is performed to assess the contribution of different chemical reaction pathways to the transfer of specific elements (such as nitrogen). The detailed implementation steps are as follows:

[0060] 1) System definition and reaction mechanism import: The reaction mechanism file is imported using the chemical kinetics software Cantera. This file contains all reaction equations, species information, thermodynamic data, and kinetic parameters. The system automatically identifies the total number of species N. s and the total number of reactions. For those with N s For a reaction system of substances, the formula for reaction j can be written in a general form:

[0061] ,

[0062] in, and It is the stoichiometric coefficient of species i in reaction j.

[0063] 2) Calculate the average reaction rate for each reaction. For each spatial location (grid point) in the computational domain, set the temperature, pressure, and mass fraction of all species as the thermodynamic state. For each reaction j, calculate its net reaction rate. Calculated according to the formula:

[0064] ,

[0065] Among them, the forward and reverse rate coefficients and The mechanism of introduction is provided by the Arrhenius equation, and the molar concentrations of each species are given. The rate is calculated from the mass fraction, molecular weight, and mixture density. The forward, reverse, and net reaction rates for each reaction are accumulated by iterating through all grid points, and finally the average reaction rate over the entire computational domain is obtained.

[0066] 3) Calculate the net species formation rate and the basic elemental flux, based on the average net reaction rate. The net mass production rate of each species i in each reaction j is calculated by the following formula:

[0067] ,

[0068] Among them, the Department of Purification Measurement For subsequent element-based flux analysis, it is necessary to pre-calculate the characteristic value of each species containing the target element N, which is the number of atoms of the target element in the species multiplied by the molar mass of the element.

[0069] 4) Element-based reaction flux analysis: Select nitrogen (N) and the species pair of interest (e.g., starting species A and ending species C). Iterate through all reactions, selecting those involving species A, C, and the target element N. For each such reaction j, calculate the flux of element N transferred from species C to species A using the following formula:

[0070] ,

[0071] The parameters required for the calculation include: the number of N atoms in species A and C. and The total number of N atoms on either side in reaction j molar mass of N The stoichiometric coefficient of species A in the reaction and the average net rate of the reaction. . The symbol indicates the direction of element flow (positive: flowing to A; negative: flowing out of A).

[0072] 5) Integrate and normalize net fluxes: For a selected species A, calculate its elemental fluxes across all relevant reactions. The data is summarized by reaction. To facilitate comparison of the importance of different species or pathways, normalization is usually required. This involves identifying the species with the largest sum of absolute element flux values ​​among all species, using its sum as the normalization benchmark, and converting all flux values ​​into percentages relative to this benchmark. This visually demonstrates the relative contribution of each reaction pathway, ultimately yielding a reaction pathway map.

[0073] Step 4. Map the small flame database to a four-dimensional control parameter space of mixture fraction, reaction process variables, normalized enthalpy, and hydrogen radicals to generate a small flame lookup table.

[0074] In the lookup table solver, instead of directly solving detailed species transport equations, it solves transport equations for mixture fraction, reaction process variables, normalized enthalpy, and curvature. When solving these equations, the differential diffusion term introduced by the mixture-average diffusion model is explicitly considered. At each grid cell and each time step, the solved instantaneous (mixture fraction) transport equations are... , reaction progress variable Normalized enthalpy Hydrogen radicals (H) are used as input, where , and They are total enthalpy The maximum and minimum values.

[0075] Step 5. Solve the control parameter equations by looking up tables, output the composition and temperature field, and verify the model accuracy by comparing it with the direct numerical simulation dataset.

[0076] The temperature, mass fractions of all components, and chemical reaction source terms for a given point are directly obtained by searching the generated three-dimensional small flame table. It should be noted that curvature is an instantaneous and highly refined physical quantity. On the one hand, it is difficult to characterize the cumulative changes in curvature effects caused by flow, diffusion, and reaction processes; on the other hand, the curvature parameter is closely coupled with process variables, requiring consideration of the distribution of trajectory variables in conjunction with probability density functions, which undoubtedly increases the difficulty of practical implementation. After testing, H free radicals can better reflect the curvature change law; therefore, H free radicals are selected as the control parameter characterizing the curvature effect.

[0077] The lookup results of the above small flame model (based on FPP and CSM flames) are compared with the high-precision DNS dataset obtained in step 1 (e.g.) Figure 8 As shown, red arrows indicate the dominant NO generation pathway, and blue arrows indicate the dominant NO consumption pathway; the arrow width is proportional to the contribution rate of the reaction flux. By comparing the flame structure, quenching distance, and near-wall NO levels in the wall-side case, we can better understand the process. xBy analyzing key parameters such as the concentration distribution of hydrogen and ammonia, the predictive ability of this method for the interaction between the flame and the wall in hydrogen-ammonia co-combustion was quantitatively evaluated. The results show that the flame model incorporating curvature can significantly improve the prediction and capture of the chemical state in the near-wall region.

[0078] This invention also provides a numerical calculation system for hydrogen-ammonia co-combustion considering flame curvature, comprising:

[0079] The CSM / FPP library building module, where CSM is model data and FPP is a one-dimensional free-propagating flame, is used to generate a small flame database containing curvature parameters;

[0080] The DNS solver module, which uses direct numerical simulation, is used to generate a high-precision validation dataset.

[0081] The lookup table solver outputs combustion field variables based on the four-dimensional control parameters in the numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature.

[0082] The present invention also provides a computer-readable storage medium storing program instructions, which, when executed by a processor, implement the above-described numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature.

[0083] 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 calculation method for hydrogen-ammonia co-combustion considering flame curvature, characterized in that, include: Step 1: Construct a composite space flame model (CSM) including curvature parameters, solve the parameterized small flame equation in the reaction process variable space, explicitly introduce curvature as a control variable, and solve the progress variable gradient equation; the composite space flame model (CSM) realizes the mapping between the physical space and the progress variable space through a self-contained scalar space method, and the progress variable gradient equation explicitly includes flame curvature as a source term; the parameter space includes curvature, unburned gas temperature, and equivalence ratio; Step 2: Construct a one-dimensional free-propagating flame (FPP) database and integrate it with the model data of the composite space flame model (CSM) to form a small flame lookup table database. The one-dimensional free-propagating flame (FPP) database is obtained by solving the one-dimensional steady-state premixed flame control equations, covering different equivalence ratios and unburned gas temperature conditions. The lookup table database stores components, temperature, chemical reaction source terms, and NO. x Generate rate data; Step 3: Solve the governing equations for hydrogen-ammonia blended combustion using direct numerical simulation, generating a high-precision direct numerical simulation dataset. Based on this dataset, perform reaction pathway analysis to quantify NO. x Generation mechanism; Step 4: Map the small flame lookup table database to the four-dimensional control parameter space of mixture fraction, reaction process variables, normalized enthalpy and hydrogen radicals to generate a small flame lookup table; Step 5: Solve the control parameter equations, output components, and temperature field by looking up tables, and verify the model accuracy by comparing it with the direct numerical simulation dataset.

2. The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature according to claim 1, characterized in that, In step 2: The computational domain size for direct numerical simulation is 100 x × 150 y times the flame thickness, and the mesh resolution is 2000 × 3000. The wall boundary conditions are set as follows: no slip velocity field, isothermal cooling temperature field at 298 K, and zero gradient diffusion of species mass fraction.

3. The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature according to claim 1, characterized in that, Calculate the mixed fraction in step 3. , reaction process variables Hydrogen radical H and normalized enthalpy Mixed fractions Calculations were performed using the Bilger equation applicable to the combustion of hydrogen and ammonia; reaction progress variables. Defined as a linear combination of the quality scores of key species; Normalized enthalpy , For total enthalpy, This is the maximum enthalpy. This is the minimum enthalpy value; The hydrogen radical H characterizes the flame curvature effect.

4. The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature according to claim 1, characterized in that, Step 3, reaction pathway analysis, includes: Calculate the net reaction rate and element transfer flux of nitrogen-containing species; A NOx reaction pathway contribution rate distribution map was generated by normalization.

5. The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature according to claim 1, characterized in that, In step 4: The four-dimensional control parameter equation set includes equations for mixture fraction, reaction process variables, enthalpy, and hydrogen radical transport.

6. The numerical calculation method for hydrogen-ammonia co-combustion considering flame curvature according to claim 1, characterized in that, The small flame lookup table contains two types of data: data based on the Composite Space Flame Model (CSM) and data based on the One-Dimensional Free-Propagating Flame (FPP) model.

7. A numerical calculation system for hydrogen-ammonia co-combustion considering flame curvature, characterized in that, include: The CSM / FPP library building module, where CSM stands for Composite Space Flame Model and FPP stands for One-Dimensional Free Propagation Flame, is used to generate a small flame database containing curvature parameters. The DNS solver module, which uses direct numerical simulation, is used to generate a high-precision validation dataset. The lookup table solver outputs combustion field variables based on the four-dimensional control parameters in the numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature as described in any one of claims 1-6.

8. A computer-readable storage medium storing program instructions, characterized in that, When the program instructions are executed by the processor, they implement the numerical calculation method for hydrogen-ammonia blended combustion considering flame curvature as described in any one of claims 1-6.

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