Numerical method for calculating swirl hydrogen turbulent combustion heat loss and differential diffusion

Abstract

The application discloses a numerical calculation method of hot loss and differential diffusion of swirl hydrogen turbulent combustion, and belongs to the field of numerical calculation of swirl hydrogen turbulent combustion. The method establishes a swirl model containing a mixing fraction, a progress variable, a normalized enthalpy and a second-order control equation of the mixing fraction; simulates the heat loss / gain based on the reactant temperature adjustment of a counterflow flame device, constructs a small flame table in combination with a non-unit Lewis number assumption; maps parameters to a four-dimensional space to generate a small flame library; obtains thermochemical quantities by looking up a table after solving the control equation, and adopts a PIMPLE algorithm for iterative convergence. The application can accurately predict the double-swirl hydrogen flame velocity field and temperature distribution by comprehensively representing the heat loss and differential diffusion effect through the four-dimensional parameter space, and provides an efficient simulation tool for the optimization of a swirl burner.

Description

Technical Field

[0001] This invention belongs to the field of numerical calculation of swirling hydrogen turbulent combustion, specifically relating to a numerical calculation method for heat loss and differential diffusion in swirling hydrogen turbulent combustion. Background Technology

[0002] Hydrogen, as a zero-carbon fuel, is an ideal choice for mitigating the greenhouse effect and environmental pollution due to its clean properties. However, the associated risks of backfire and nitrogen oxide emissions are pressing issues that need to be addressed in the use of hydrogen energy. Swirl structures are currently the most commonly used solution, as they allow for uniform mixing of fuel and oxidizer before combustion and delay the injection of hydrogen, effectively preventing backfire. However, the introduction of swirl structures significantly increases the difficulty of simulations, such as complex turbulent-chemical interactions and multiple combustion modes. In previous work, many models used by researchers, such as the Dynamically Thickened Flame Model (DTFLES), are not suitable for simulating the diffusion flame portion. They often compensated for this deficiency by locally refining the mesh in the flame front region, but this method is computationally expensive and fails to consider detailed chemical reaction mechanisms. Furthermore, there are still many gaps in the calculation of heat loss and differential diffusion in swirling hydrogen turbulent flames. Summary of the Invention

[0003] To address the problems raised in the background art, this invention provides a numerical calculation method for heat loss and differential diffusion in swirling hydrogen turbulent combustion. This method combines a small flame model with large eddy simulation, and can be used to simulate and calculate heat loss and differential diffusion in multi-swirling hydrogen turbulent combustion.

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

[0005] A numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas includes the following steps:

[0006] Step 1: Establish the governing equations, which include mixed fractional transport equations, progress variable transport equations, normalized enthalpy equations, and mixed fractional second-order transport equations.

[0007] Step 2: Based on the counter-flame apparatus, adjust the reactant temperature to simulate heat loss and heat gain, set a non-unit Lewis number to account for differential diffusion, and construct a small flame table.

[0008] Step 3: Map the parameters of the miniflame table to the second-order four-dimensional control parameter space of the mixing fraction, progress variable, normalized enthalpy, and mixing fraction to generate the miniflame library;

[0009] Step 4: Solve the governing equations. Input the mixture fraction, progress variable, normalized enthalpy, and second-order mixture fraction into the small flame library to obtain the temperature, composition, chemical reaction source term, and diffusion coefficient.

[0010] Step 5: Iteratively update the flow field until convergence.

[0011] The beneficial effects of this invention compared to the prior art are as follows:

[0012] This invention proposes a method for simulating heat loss and differential diffusion in swirling hydrogen combustion. Based on a small flame model, it is applicable to the simulation of hydrogen turbulent combustion in complex multi-swirling structures. It considers differential diffusion effects and heat loss and gain during flame-wall contact, thus improving calculation accuracy and precision. Furthermore, coordinate transformation and dimensionality reduction significantly reduce the number of equations to be solved during the calculation, thereby lowering computational resource consumption. Attached Figure Description

[0013] Figure 1 This is a flowchart of the numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to the present invention;

[0014] Figure 2 This is a diagram of the device used for small flame database construction in an embodiment of the present invention;

[0015] Figure 3 This is a comparison chart (I) of the simulated and experimental speeds obtained in this embodiment of the invention;

[0016] Figure 4 This is a comparison chart (II) of the speeds obtained from simulation and experiments in this embodiment of the invention;

[0017] Figure 5 This is a comparison chart (III) of the speeds obtained from simulation and experiments in this embodiment of the invention;

[0018] Figure 6 This is a comparison chart (IV) of the speeds obtained from simulation and experiments in this embodiment of the invention;

[0019] Figure 7 This is a comparison chart of experimental and simulated temperatures in an embodiment of the present invention. Detailed Implementation

[0020] 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.

[0021] Example:

[0022] This embodiment selects a hydrogen flame with a dual-swirl structure. By adjusting parameters such as the inlet hydrogen and air velocities, two flame modes can be obtained: an anchored flame and a diffusion-dominated flame. The anchored flame is a diffusion-dominated flame, while the anchored flame is a partially premixed flame. Therefore, applying the method of this invention to this dual-swirl hydrogen flame is representative and persuasive.

[0023] like Figure 1 As shown, the specific implementation method of the numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to the present invention is as follows:

[0024] Step 1: Define the physical model, determine the simulation type and governing equations. In this embodiment, the mixed fractional transport equation, schedule variable transport equation, normalized enthalpy equation, and mixed fractional second-order transport equation take the following forms:

[0025] Mixed fractional transport equations:

[0026] ,

[0027] Schedule variable transport equations:

[0028] ,

[0029] Normalized enthalpy equation:

[0030] ,

[0031] Mixed fractional second-order transport equations:

[0032] ,

[0033] in, Density; For mixed fractions; Euler time; For speed in the first Components in each direction; For the first Cartesian coordinates in each direction; Thermal conductivity; is the specific heat capacity of the mixture; The molecular diffusion coefficient is... The subgrid eddy diffusion rate is calculated by solving the subgrid Schmidt number. For the reaction progress variable; For the reaction progress source term; Normalized enthalpy; The thermal diffusivity; The subgrid eddy diffusion coefficient; It is a mixed fractional second order; The grid length; , and These are the differential diffusion terms for mixing fraction, progress variable, and normalized enthalpy, respectively. This term is mainly used to consider the influence of differential diffusion on hydrogen turbulent flames. The superscript ~ represents the Favre average, and the superscript — represents the spatial average.

[0034] Then, proportional geometric modeling and meshing were performed according to the experimental settings. Locally refined meshes were used in the swirling part and the flame front to analyze complex flow field information. At the same time, the initial and boundary conditions of the computational domain were set according to the parameters provided by the experiment.

[0035] Step 2: Create a small flame table using FlameMaster software. In this embodiment, a counter-flame device is used for table creation. The specific device is as follows: Figure 2 As shown, fuel and oxidizer are introduced into the combustion chamber in opposite directions to form a stable planar flame. During this process, the temperature of the reactants at the time of introduction needs to be modified to account for enthalpy loss and gain. Furthermore, the scalar dissipation rate needs to be adjusted to regulate the mixing intensity of the reactants. The influence of differential diffusion is considered based on the "non-unity Lewis number assumption," ultimately yielding a small flame table containing information on thermophysical parameters, component concentrations, chemical reaction source terms, and diffusion coefficients.

[0036] Step 3: Dimensionally reduce the parameter information in the pre-generated miniflame table in Step 2, and map it onto the space of mixing fraction, progress variable, normalized enthalpy, and second moment of mixing fraction to generate a miniflame library for subsequent table lookup.

[0037] Step 4: Combining the boundary conditions, initial conditions, and mesh division set in Step 1, the finite volume method is adopted. Each mesh divided in Step 1 is treated as a control volume, and the conservation law is applied to each control volume to achieve the volume integral of the control equation within each control volume. Then, a first-order implicit scheme is used for time discretization, and a second-order scheme is used for spatial discretization to discretize the continuous equation into a system of algebraic equations.

[0038] Step 5: Iteratively update the flow field until convergence.

[0039] Furthermore, this embodiment employs an "iterative linearization and pressure-velocity coupling algorithm" to nonlinearize the discrete algebraic equations. Simultaneously, during the solution process, the obtained mixing fraction, progress variable, normalized enthalpy, and second-order mixing fraction values ​​are input into a small flame database to retrieve corresponding component and temperature information. The chemical reaction source terms and diffusion coefficients in the governing equations are directly extracted from the small flame database.

[0040] The above steps yield physical quantities defined at the center point of the grid, enabling numerical calculations of enthalpy loss and differential diffusion in turbulent combustion of swirling hydrogen.

[0041] Next, the velocity and temperature characteristics obtained from the simulated dual-swirling hydrogen turbulent combustion will be analyzed:

[0042] To verify the applicability and predictive accuracy of the method of this invention, the simulated axial velocity, radial velocity, and corresponding root mean square velocity were quantitatively compared with the experimental values, such as... Figure 3 , Figure 4 , Figure 5 and Figure 6 As shown, the comparison position corresponds to the middle of the flame, where Fl-A represents the anchored flame and Fl-L represents the rising flame. The red line represents the simulated velocity data of the anchored flame, and the blue line represents the data corresponding to the rising flame. The comparison results show that for both the rising and anchored flames, the axial velocity, radial velocity, and corresponding root-mean-square velocity are accurately predicted, both in terms of peak value and position. Therefore, the method proposed in this invention, which considers the effects of differential diffusion and enthalpy loss in numerical calculation, can effectively capture the turbulent flow field information of dual-swirling hydrogen gas.

[0043] like Figure 7 As shown, sim represents the temperature value obtained from the simulation calculation, and exp represents the temperature value obtained from the experiment. By comparing the temperature obtained from the simulation using this invention with the experimentally measured temperature, it can be found that the simulation underestimated the temperature at this point. This point is located in the outer circulation region. This is mainly due to the short simulation calculation time, because the circulation region requires a long calculation time to reach a stable state.

[0044] 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 in this invention 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 in this invention.

Claims

1. A numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas, characterized in that, Includes the following steps: Step 1: Establish the governing equations, which include mixed fractional transport equations, progress variable transport equations, normalized enthalpy equations, and mixed fractional second-order transport equations. Mixed fractional transport equations: ， Schedule variable transport equations: ， Normalized enthalpy equation: ， Mixed fractional second-order transport equations: ， in, Density; For mixed fractions; Euler time; For speed in the first Components in each direction; For the first Cartesian coordinates in each direction; Thermal conductivity; is the specific heat capacity of the mixture; The molecular diffusion coefficient is... The subgrid eddy diffusion rate is calculated by solving the subgrid Schmidt number. For the reaction progress variable; For the reaction progress source term; Normalized enthalpy; The thermal diffusivity; The subgrid eddy diffusion coefficient; It is a mixed fractional second order; This is the grid length; , and These are the differential diffusion terms for mixing fraction, progress variable, and normalized enthalpy, respectively. This term is mainly used to consider the influence of differential diffusion on hydrogen turbulent flame. The superscript ~ indicates Favre average, and the superscript — indicates spatial average. Step 2: Based on the counter-flame device, adjust the reactant temperature to simulate heat loss and heat gain, set a non-unit Lewis number to account for differential diffusion, and construct a small flame table. Step 3: Map the parameters of the miniflame table to the second-order four-dimensional control parameter space of the mixing fraction, progress variable, normalized enthalpy, and mixing fraction to generate the miniflame library; Step 4: Solve the governing equations. Input the mixture fraction, progress variable, normalized enthalpy, and second-order mixture fraction into the small flame library to obtain the temperature, composition, chemical reaction source term, and diffusion coefficient. Step 5: Iteratively update the flow field until convergence.

2. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Step 2 includes: quantifying the turbulent mixing intensity by changing the scalar dissipation rate.

3. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Step 4 includes: spatial discretization using the finite volume method, and time integration using a first-order implicit scheme.

4. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Step 1 includes implementing local mesh refinement in the swirling region and the flame front.

5. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Step 3 includes controlling the parameter dimensions, including: Mixed fractions: 0-1; Progress variable: 0-1; Normalized enthalpy: 0-1; Mixed fractional second order: 0-0.

25.

6. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Anchored flame Fl-A and rising flame Fl-L morphology simulation applicable to dual-swirling hydrogen flames.

7. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, Step 4 involves comparing the temperature prediction results from the lookup table with the experimental results to verify the accuracy of the heat loss simulation.

8. The numerical calculation method for heat loss and differential diffusion in turbulent combustion of swirling hydrogen gas according to claim 1, characterized in that, In step 5, the root mean square error of the axial and radial velocities in the velocity field prediction results is ≤5%.

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