A numerical calculation method for calculating lean hydrogen turbulent flow combustion

Abstract

The application discloses a numerical calculation method for calculating lean hydrogen turbulent combustion, and belongs to the field of hydrogen turbulent combustion numerical calculation. The method establishes an unsteady model containing a mixing fraction Z, a reaction progress variable C and a hydrogen mass fraction control equation, wherein the equation maps the influence of curvature; the control equation is solved, a pre-built small flame library is input to obtain components, temperature, chemical reaction source terms and diffusion coefficients; and a PIMPLE algorithm is used to couple pressure correction cycle iteration to update the flow field. Through dynamic characterization of the curvature effect and combination of the difference diffusion influence, the lean hydrogen flame local superadiabatic state can be efficiently captured, and a high-precision numerical tool is provided for laboratory scale turbulent hydrogen burner optimization.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation of hydrogen turbulent combustion, specifically a numerical calculation method for calculating lean hydrogen turbulent combustion. Background Technology

[0002] Hydrogen, as an ideal carrier of renewable energy, has become a core alternative fuel for power equipment such as gas turbines and hydrogen engines due to its advantages of zero carbon emissions, high energy density, and high combustion efficiency. However, hydrogen combustion inevitably produces nitrogen oxide emissions. To further reduce nitrogen oxide emissions, lean hydrogen combustion has become a major combustion form, with thermal diffusion instability being a key area of ​​research. At low turbulence levels, thermal diffusion instability and turbulence-chemical interactions cause the flame surface to become more wrinkled, leading to localized hydrogen accumulation and thus enhancing combustion efficiency. This locally intense combustion mode generally occurs in regions of positive curvature. However, many researchers have failed to consider the influence of curvature in their simulations. Even when the influence of curvature is considered, the simulations are limited to non-realistic flames obtained through direct numerical simulation (DNS). These non-realistic flames are greatly affected by human interference and cannot reflect the true state of flame combustion. In contrast, simulating lean hydrogen turbulent combustion flames at the laboratory scale has more practical application value and is beneficial for developing efficient hydrogen burners and numerical models. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a numerical calculation method for calculating lean hydrogen turbulent combustion. This method is based on a small flame model, considers the influence of differential diffusion, maps curvature to the mass fraction of a component, and uses this mass fraction as a control variable. During the simulation, the equation for this component's mass fraction is dynamically solved, effectively reflecting the morphological changes in the hydrogen flame. Furthermore, it can be applied to realistic laboratory-scale simulations of lean hydrogen combustion. This method can consider detailed chemical reaction mechanisms at a relatively low computational cost and can be applied to the study of hydrogen turbulent thermal diffusion instabilities in real gas turbine and internal combustion engine combustion systems.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A numerical calculation method for calculating lean hydrogen turbulent combustion includes the following steps:

[0006] Step 1: Establish a variable including density, rate, mixture fraction Z, reaction progress C, and hydrogen mass fraction. An unsteady gas-phase turbulent combustion model with governing equations;

[0007] Step 2: Determine the hydrogen mass fraction. The governing equations incorporate the effects of mapped curvature on the mixture fraction Z, reaction progress variable C, and hydrogen mass fraction. Input the pre-built small flame library to look up the table and obtain the components, temperature, chemical reaction source terms and diffusion coefficient;

[0008] Step 3: The coupling pressure is cyclically corrected, and the velocity field and density field are iteratively updated until convergence.

[0009] Beneficial effects:

[0010] 1. It can be used to simulate the flame morphology changes during the turbulent combustion process of lean hydrogen, taking into account the effects of differential diffusion and curvature. It can effectively predict the local intense combustion mode of lean hydrogen turbulent combustion, so as to develop more efficient hydrogen burners.

[0011] 2. Obtaining the components and temperature by looking up tables, as well as directly extracting the chemical reaction source terms and component diffusion coefficients, can effectively reduce computational costs and take into account detailed chemical reaction mechanisms. Attached Figure Description

[0012] Figure 1 This is a flowchart of the simulation calculation method for lean hydrogen turbulent combustion according to the present invention;

[0013] Figure 2 This is a schematic diagram of the computational domain in an embodiment of the present invention;

[0014] Figure 3 This is a diagram showing the temperature distribution along the flame radial direction at the axial position x=7D (D is the diameter of the fuel injection nozzle) obtained from different models obtained by looking up tables in this embodiment of the invention.

[0015] Figure 4 This is a distribution diagram of the hydrogen mole fraction obtained from different models based on table lookup priors in this embodiment of the invention, along the radial direction of the flame at the axial position x=7D (D is the diameter of the fuel injection nozzle).

[0016] Figure 5 This is a comparison of the velocities predicted by different models in this embodiment of the invention along the radial direction of the flame at the axial position x=7D (D is the diameter of the fuel injection nozzle);

[0017] Figure 6 The OH mole fraction obtained posteriorly from different models in the embodiments of the present invention ( ) and average OH mole fraction ( The results of the cloud map comparison. Detailed Implementation

[0018] 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.

[0019] This invention is based on a small flame model, which maps the effect of curvature on the flame during lean hydrogen combustion to the hydrogen mass fraction, and considers the effect of differential diffusion. It can efficiently and accurately simulate the flame morphology changes and related characteristics in lean hydrogen turbulent flames.

[0020] like Figure 1 As shown, the numerical calculation method of the present invention for calculating the turbulent combustion flame of lean hydrogen specifically includes the following steps:

[0021] Step 1: Establish a variable including density, rate, mixture fraction Z, reaction progress C, and hydrogen mass fraction. An unsteady gas-phase turbulent combustion model was developed, incorporating the governing equations. The size of the computational domain was determined based on experimental operating conditions, and geometric modeling and meshing were performed. The computational domain was defined as a cylinder with a diameter of 135 mm and a height of 200 mm. Figure 2 As shown; define the initial conditions of the computational domain, and set the initial conditions and boundary conditions based on the velocity, temperature and other data given in the experiment. The stable turbulent field is pre-generated by the pipe flow, and the velocity that develops into a stable state is used as the inlet velocity boundary condition.

[0022] Step 2: Determine the hydrogen mass fraction. The governing equations incorporate the effects of mapped curvature on the mixture fraction Z, reaction progress variable C, and hydrogen mass fraction. Input the pre-built small flame library to look up the table and obtain the components, temperature, chemical reaction source terms and diffusion coefficient;

[0023] Combining boundary conditions and initial conditions, the finite volume method is used to discretize the gas-phase turbulent combustion mathematical model established in step 1, transforming the continuity equation into a system of algebraic equations. In this embodiment, a backward difference scheme is used for time integration, and a second-order discretization scheme is used for spatial integration. Next, the system of equations in each time step is solved using the PIMPLE (hybrid pressure implicit operator segmentation and pressure coupled equation) algorithm coupled with the small flame model. The specific steps are as follows:

[0024] Step (1) Solve the density equation to obtain the density value.

[0025] Step (2) Solve for the equations for rate, mixture fraction, reaction progress variable, and hydrogen mass fraction. The equations for mixture fraction, reaction progress variable, and hydrogen mass fraction are in the following forms:

[0026] Mixed fractions:

[0027] ,

[0028] in, The fluid density is the spatial average, and t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients of the mixture fraction. The eddy diffusion coefficient is... The Favre average of the cross-diffusivity coefficient for the mixture fraction. The Favre average of the thermal diffusivity of the mixture fraction. This is a flame front detection position indicator used to locate the position of the flame front.

[0029] Variables related to reaction progress:

[0030] ,

[0031] in, The fluid density is the spatial average, and t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients for the reaction progress variable. This is a flame front detection location indicator used to pinpoint the location of the flame front in order to achieve localized thickening. The eddy diffusion coefficient is... The Favre average of the cross-diffusion coefficients of the reaction progress variable. This is the Favre average of the source terms of the reaction progress variable.

[0032] Hydrogen mass fraction:

[0033] ,

[0034] in, The fluid density is the spatial average, and t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients for hydrogen mass fraction is given. This is a flame front detection location indicator used to pinpoint the location of the flame front in order to achieve localized thickening. The eddy diffusion coefficient is... The Favre average of the thermal diffusivity of hydrogen is given. The Favre average of temperature, This is the Favre average of the hydrogen reaction rate source term.

[0035] ,

[0036] ,

[0037] in, , The cross-diffusion coefficient is the mixture fraction. It is a stoichiometric ratio. For the diffusion rate of fuel, The diffusion rate of the oxidant. The thermal diffusivity of the mixture fraction is . The thermal diffusivity of the fuel The thermal diffusivity of the oxidant is... The mass fraction of fuel on the fuel flow side. This represents the mass fraction of the oxidant on the air side. The stoichiometric coefficient of the oxidizing agent. The stoichiometric coefficient of the fuel. The molecular weight of the oxidant is... Let T be the molecular weight of the fuel, and T be the temperature.

[0038] The obtained values ​​of mixture fraction, reaction progress variable, and hydrogen mass fraction are then input into the small flame library to retrieve the corresponding components and temperatures. The chemical reaction source terms and diffusion coefficients required by the equation are directly extracted from the small flame library.

[0039] Step 3: The coupling pressure is cyclically corrected, and the velocity field and density field are iteratively updated until convergence.

[0040] Specifically, the pressure equation is solved based on the composition and temperature information obtained from a lookup table to obtain the pressure value, and the velocity field is corrected. The convergence of the residuals of the mass conservation equation is then checked; if not, pressure correction is performed until convergence. After the residuals of the mass conservation equation converge, it is still necessary to check whether the preset number of iterations and time have been reached. Otherwise, a pre-calculation correction iteration is performed, and the density field value is updated using the mass flux obtained from the pressure correction. The above process is repeated until the preset end time is reached.

[0041] The applicability and accuracy of the coupled small flame model, considering the effects of differential diffusion and curvature, were evaluated and analyzed for laboratory-scale simulation of lean hydrogen turbulent flames. Figure 3 This diagram shows the temperature distribution along the radial direction of the flame at the axial position x=7D (D is the diameter of the fuel injection nozzle) obtained by different models with lookup table priors in this embodiment of the invention. Here, Exp represents the experimental results of this embodiment; CSM-Cur-3D represents the results obtained by a model where the control variables are mixture fraction, reaction progress variable, and hydrogen mass fraction, and differential diffusion is considered; FPP-DD-2D represents the results obtained by a model where the control variables are mixture fraction, reaction progress variable, and differential diffusion is considered; FPP-Le1-2D represents the results obtained by a model where the control variables are mixture fraction and reaction progress variable, but differential diffusion is not considered; and FPP-Le1-1D represents the results obtained by a model where the control variable is only the reaction progress variable. Figure 4 The following is a diagram showing the distribution of hydrogen mole fraction along the flame radial direction at the axial position x=7D (D is the diameter of the fuel injection nozzle) obtained from different models obtained by looking up tables in embodiments of the present invention. Figure 3 and Figure 4 The comparison between the lookup prior and experimental data shows that considering differential diffusion and curvature can effectively and accurately predict the local intense combustion state of lean hydrogen flame, i.e., the superadiabatic state. However, for the case where only the reaction progress variable is considered, the local accumulation state of hydrogen cannot be predicted. Figure 5 This is a comparison of the velocities predicted by different models in this embodiment of the invention along the radial direction of the flame at the axial position x=7D (D is the diameter of the fuel injection nozzle); Figure 6 The OH mole fraction obtained posteriorly from different models in the embodiments of the present invention ( ) and average OH mole fraction ( The cloud map comparison results show that the position marked by the red line corresponds to the position where the above parameters are compared, i.e., the axial position x=7D (D is the diameter of the fuel injection nozzle). Figure 5 As shown, the speeds obtained by each model are all well compared with the experimental data. Figure 6 As shown, the mole fraction of OH obtained by different library construction methods is simulated. ) and average OH mole fraction ( Qualitative analysis reveals that the predicted flame height, considering both differential diffusion and curvature effects, is higher than the simulated flame height when only differential diffusion is considered or when differential diffusion is not considered.

[0042] 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 calculating lean hydrogen turbulent combustion, characterized in that, Includes the following steps: Step 1: Establish a variable including density, rate, mixture fraction Z, reaction progress C, and hydrogen mass fraction. An unsteady gas-phase turbulent combustion model with governing equations; Step 2: Determine the hydrogen mass fraction. The governing equations incorporate the effects of mapped curvature on the mixture fraction Z, reaction progress variable C, and hydrogen mass fraction. Input the pre-built small flame library to look up the table and obtain the components, temperature, chemical reaction source terms and diffusion coefficient; Step 3: The coupling pressure is cyclically corrected, and the velocity field and density field are iteratively updated until convergence.

2. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, In step 1, the mass fraction of hydrogen gas The governing equations are: ， in, For the spatial average of fluid density, The Favre average of the hydrogen mass fraction is given by t, where t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients for hydrogen mass fraction is given. The eddy diffusion coefficient is... The Favre average of the thermal diffusivity of hydrogen is given. The Favre average of temperature, The Favre average of the hydrogen reaction rate source term. It serves as a flame front detection position indicator, used to track the location of the flame front in order to achieve local thickening.

3. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, The governing equations for the mixing fraction Z and the reaction progress variable C in step 1 are as follows: The governing equation for the mixed fraction Z is: ， in, For the spatial average of fluid density, The Favre average of the mixed fractions, where t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients of the mixture fraction. This is a flame front detection position indicator used to track the position of the flame front in order to achieve localized thickening. The eddy diffusion coefficient is... The Favre average of the cross-diffusion coefficients of the mixture fraction. The Favre average of the thermal diffusivity of the mixture fraction. The Favre average of the reaction progress variable. The Favre average of the temperature; The governing equation for the reaction progress variable C is: ， in, The fluid density is the spatial average, and t is the Euler time. Let x be the Favre average of the component of the velocity vector in the j-th direction. j Let be the spatial coordinate of the j-th direction in the Cartesian coordinate system. As an efficiency factor, As a thickening factor, The Favre average of the molecular diffusion coefficients for the reaction progress variable. For flame front detection location indicators, The eddy diffusion coefficient is... The Favre average of the thermal diffusivity of the reaction progress variable. The Favre average of the source terms of the reaction progress variable. The Favre average of the reaction progress variable. This is the Favre average of the temperature.

4. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, In step 2, the small flame chamber is controlled by the mixing fraction Z, the reaction progress variable C, and the hydrogen mass fraction. These are the parameters for a three-dimensional lookup table.

5. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, In step 3, a hybrid algorithm combining pressure implicit operator segmentation and pressure coupling equations is used. The execution process includes: Solve the density equation; Solve for the rate of mixture fraction Z, the reaction progress variable C, and the hydrogen mass fraction. The governing equations and small flame library are used to look up and update thermochemical quantities; Solve the pressure equation and correct the velocity field; Cyclic pressure is corrected to convergence with mass conservation. Update the density field and advance the time step.

6. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, The method is applicable to equivalent ratios. A lean hydrogen flame between 0.3 and 0.

7.

7. The numerical calculation method for calculating lean hydrogen turbulent combustion according to claim 1, characterized in that, The accuracy of the flame morphology predicted by looking up the small flame database was verified by comparing it with experimental data.

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