Table establishing method for simulating turbulent heat diffusion unstable hydrogen combustion

Abstract

The invention discloses a table establishing method for simulating turbulent flow heat diffusion unstable hydrogen combustion, and belongs to the field of hydrogen turbulent flow combustion numerical simulation calculation. On the basis of a multi-component space model (CSM), a small flame model containing a difference diffusion effect, curvature and a strain rate is established, an original solution of the small flame model is mapped into a component space to establish a small flame table, and the influence of the curvature and the strain rate on turbulent flow thermal diffusion unstable hydrogen combustion characteristics is considered at the same time. According to the method, the thermochemical variables in the small flame table are directly extracted according to the space components, and direct calculation in numerical simulation is avoided, so that the calculation cost is reduced. The method has certain guiding significance in researching the application of low-propagation-speed turbulent heat diffusion unstable premixed hydrogen flame combustion.

Description

Technical Field

[0001] This invention belongs to the field of numerical simulation calculation of hydrogen turbulent combustion, specifically involving a table construction method for simulating unstable hydrogen combustion in turbulent thermal diffusion. Background Technology

[0002] Hydrogen, as a clean and renewable energy source, has become a research hotspot in the field of combustion, and premixed lean hydrogen combustion offers advantages such as low emissions and high efficiency. The biggest challenge for premixed lean hydrogen combustion is its thermal diffusion instability, which significantly alters flame dynamics and heat release rates, leading to safety issues such as combustion instability, backfire, and blowout. Turbulence itself also contributes to the hydrodynamic instability of the premixed hydrogen flame, posing a challenge to the numerical calculation of turbulent thermal diffusion instability in premixed hydrogen combustion. While direct data simulation can capture the combustion process in detail, it is costly and not suitable for practical engineering applications. Previous studies have focused more on thermal diffusion instability under laminar flame conditions; whether current table construction methods are applicable to the calculation of thermal diffusion instability under turbulent conditions remains unknown. Summary of the Invention

[0003] In response to the problems mentioned in the background art, the present invention provides a table-building method for simulating unstable hydrogen combustion in turbulent thermal diffusion.

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

[0005] The table-building method for simulating turbulent thermal diffusion-unstable hydrogen combustion includes the following steps:

[0006] Step 1: Establish a multi-component spatial model and a generalized small flame model, including component equations, temperature equations, and gradient equations for reaction progress variables; for premixed unburned hydrogen under different equivalence ratios, curvature and strain rate are used as independent parameters, and the small flame model is solved numerically by changing the values ​​of the two parameters to obtain the original solutions of the small flame model under different equivalence ratios, curvatures, and strain rates.

[0007] Step 2: Map the original solution of the small flame model to the multi-component space model, map the stoichiometry of unburned gas to the Bilger mixing fraction space, map the curvature and strain rate to the corresponding component space, select H radicals as trajectory variables for curvature and strain rate, and obtain the small flame table;

[0008] Step 3: Perform prior analysis based on the small flame table to verify its rationality. The trajectory variables in the small flame table are calculated based on direct numerical simulation data. The calculated trajectory variables are used as input parameters to extract the thermochemical variables in the small flame table and compared with the direct numerical simulation data to evaluate the rationality and accuracy of the small flame table.

[0009] Beneficial effects:

[0010] 1. It can be used to address the effects of differential diffusion on turbulent premixed hydrogen flames and takes into account the characteristic effects of curvature and strain rate on combustion. This method provides accurate values ​​of thermochemical variables for numerical equations in numerical simulations, which helps to improve the accuracy and efficiency of numerical simulations and enables more effective development of stable burners.

[0011] 2. This method has high scalability and can cover a wider range of unburned premixed hydrogen flames with different equivalence ratios. It can also solve small flame models with different curvatures and strain rates to build tables, which can meet the numerical simulation configuration under different working conditions. In addition, this method can also be extended to more complex multi-component gas premixed combustion, not limited to hydrogen / air mixing. Attached Figure Description

[0012] Figure 1 This is a flowchart of the table-building method for simulating unstable hydrogen combustion under turbulent thermal diffusion according to the present invention;

[0013] Figure 2 This is a comparison chart (a) of the table lookup values ​​and DNS under conditional averaging in this invention.

[0014] Figure 3 This is a comparison chart (II) of the table lookup values ​​and DNS under conditional averaging in this invention.

[0015] Figure 4 This is a comparison chart (III) of the table lookup values ​​and DNS under conditional averaging of the present invention.

[0016] Figure 5 This is a comparison chart (IV) of the table lookup values ​​and DNS under conditional averaging of the present invention.

[0017] Figure 6 Figure 5 shows a comparison of the table lookup values ​​and DNS values ​​under conditional averaging in this invention.

[0018] Figure 7 Figure 6 shows a comparison of the table lookup values ​​and DNS values ​​under conditional averaging in this invention.

[0019] Figure 8 This is a comparison diagram (a) of the lookup table value and DNS at the flame front in this invention;

[0020] Figure 9 This is a comparison diagram (II) of the table lookup value and DNS at the flame front in this invention;

[0021] Figure 10 This is a comparison diagram (III) of the table lookup value and DNS at the flame front in this invention;

[0022] Figure 11 This is a comparison diagram (IV) of the table lookup value and DNS at the flame front in this invention;

[0023] Figure 12 This is a comparison diagram (V) of the table lookup value and DNS at the flame front in this invention;

[0024] Figure 13 This is a comparison diagram (VI) of the table lookup value and DNS at the flame front in this invention. Detailed Implementation

[0025] 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.

[0026] The present invention will now be described in detail with reference to the accompanying drawings and specific a priori examples. However, the following embodiments are limited to verifying the practicality of the invention through a priori analysis using Direct Numerical Simulation (DNS) data. The scope of protection of the present invention should include all the contents of the claims, and those skilled in the art can fully implement all the contents of the claims of the present invention through the following description of the embodiments. The present invention, running in the OpenFOAM environment, considers the effects of differential diffusion, curvature, and strain rate on turbulent premixed hydrogen flames, achieving high-precision prediction of thermochemical variables. This method can be applied to numerical simulation processes to achieve high-precision calculations.

[0027] like Figure 1 As shown, the present invention provides a method for creating tables to simulate unstable hydrogen combustion in turbulent thermal diffusion, which specifically includes the following steps:

[0028] Step 1: A generalized small flame model was established, and the component equation, temperature equation, and gradient equation for the reaction progress variable were determined, for different equivalence ratios. Unburned gas under operating conditions, curvature and strain rate By changing the numerical values ​​of both parameters, the original solutions of the small flame model under different curvature and strain rate values ​​are obtained by solving the small flame model as independent parameters.

[0029] Step 2: The original solution of the small flame model is mapped to the component space. Suitable components are selected as trajectory variables to obtain the final small flame table. This process mainly involves converting the equivalence ratio... Mapping to Bilger Mixed Score In space, the curvature and strain rate Mapping to a suitable component space, H free radicals are generally chosen as trajectory variables for curvature and strain rate;

[0030] Step 3: Based on the small flame table established in Step 2, perform prior analysis to verify the rationality of the small flame table establishment. The trajectory variables in the small flame table are calculated based on DNS data. The calculated trajectory variables are used as input parameters to extract the thermochemical variables in the small flame table and are compared with the DNS data to evaluate the rationality of the small flame table dimensions and the accuracy of the calculation.

[0031] Through the above three steps, the table of turbulent thermal diffusion unstable premixed hydrogen flames was established, providing a more efficient and convenient method for subsequent numerical simulation calculations.

[0032] Specifically, such as Figure 1 As shown, a generalized premixed hydrogen small flame model was established in step 1. This model considers the effects of differential diffusion, curvature, and strain rate in the progress variable space, and mainly includes the following equations:

[0033] (a) Component equation: The component equation describes the transport characteristics of each component in the reaction progress variable space during the combustion of hydrogen.

[0034] (ii) Temperature equation: describes the changes in heat and temperature in the reaction progress variable space during the combustion of premixed hydrogen, and is used to predict the temperature distribution of hydrogen in the reaction zone;

[0035] (iii) Gradient equation for reaction progress variable: Since there are unclosed terms in the component equation and temperature equation, the gradient equation for reaction progress variable is introduced to close them.

[0036] like Figure 1 As shown, in step 2, spatial components are used as trajectory variables to map the solution of the original small flame model to the component space. The mapping steps are as follows:

[0037] Step 2.1, with other trajectory variables remaining constant, the equivalent ratio As parameters of the original small flame model solution, the Bilger mixing fraction is used. Spatial mapping is required; note that the Bilger mixture fraction needs to be calculated based on the mass fractions of each component calculated using the small flame model before mapping. ,get .

[0038] Step 2.2: Subsequently, with other trajectory variables remaining constant, the mass fraction of the H radical... Replace curvature ,get .

[0039] Step 2.3, final mass fraction of H free radicals Replacement strain rate Other transformed trajectory variables remain unchanged, resulting in the final small flame table. , As a variable representing the progress of the response, The mass fraction function of H free radicals after curvature mapping. This is the H radical mass fraction function after strain rate mapping.

[0040] After the above steps, the final small flame table can be obtained for subsequent prior analysis.

[0041] like Figure 1 As shown, step 3 performed a priori analysis on the small flame model, comparing the thermochemical variables extracted from the small flame lookup table with the DNS data to verify the rationality and accuracy of the small flame table. The priori analysis was performed in the OpenFOAM program, and the steps are as follows:

[0042] Step 3.1: Calculate trajectory variables based on DNS data. The calculation method for trajectory variables is consistent with that in the small flame model.

[0043] Step 3.2: Convert the calculated trajectory variables into a field file of the case using a program, and use it as the input parameters for extracting the small flame table.

[0044] Step 3.3: Perform a one-step solution using the solver, update the extracted thermochemical variables, compare them with the DNS data, and evaluate the rationality of the small flame table dimension and the accuracy of the calculation.

[0045] Example:

[0046] Taking DNS data of a turbulent thermally diffusing unstable premixed hydrogen flame as an example, this invention provides a detailed and comprehensive description. The embodiments of this invention mainly consist of the following steps: Step 1, description of the small flame model and selection of relevant parameters; Step 2, determination of trajectory variables and mapping steps; Step 3, extraction of surface thermochemical variables of the small flame for prior analysis.

[0047] Step 1: First, describe the small flame model and select relevant parameters:

[0048] The small flame model is established in the reaction progress variable space, mainly including the temperature equation, component equation, and gradient equation for the mixed reaction progress variable. The component governing equation is as follows:

[0049] ;

[0050] The temperature control equation is in the following form:

[0051] ;

[0052] in, Represents gas phase density; Representative components The mass fraction; Represents temperature; Represents Lagrange time; Represents the reaction progress variable; represent gradient, ; Represents the components in the reaction progress variable space. The diffusion rate; Represents the flame curvature. ; Components Chemical reaction progress source term; Specific heat at constant pressure representing a gas mixture; The specific heat capacity at constant pressure represents component i; Represents the number of components; Represents thermal conductivity; This represents the heat release rate; the physical meaning of each term is indicated by a subscript. Represents instantaneous terms. Represents the positive diffusion term. Represents the convection term. Represents the curvature term. Represents the source term.

[0053] The temperature equation and the composition equation are not closed, so additional equations are needed to close the above three equations. The governing equations for the reaction progress gradient variable that need to be solved are as follows:

[0054] ;

[0055] In the formula, For strain rate, , For gas velocity The tangential component, . For nable operators; Let be the unit normal vector of the flame front, denoted as ,in Let H2 be the reaction progress variable, expressed as , To calculate the mass fraction of H2 in any reaction region within the domain, The unburned side after the oxidizer and fuel are mixed. The quality fraction. Curvature and strain rate These are independent external parameters, and the solution for a small flame is obtained by changing the values ​​of two parameters. For thermally diffusely unstable flames, the curvature term dominates the change in flame surface area, while the strain rate term is more than 20 times smaller than that of the flame surface. Therefore, the strain rate is set to 0 in the small flame model, ignoring its influence. Although only the influence of curvature is considered in the specific instance, the influence of strain rate can also be considered; this is simply to reduce the dimensionality of the table to verify its rationality.

[0056] Step 2, determine trajectory variables and mapping steps:

[0057] This step primarily involves selecting suitable components as trajectory variables and mapping the original solution of the small flame model to the trajectory variable space, ultimately obtaining the small flame table. (Bilger Mixture Fraction) It is the only variable that can identify the diffusion of differences, so It is a suitable trajectory variable to characterize fuel stratification caused by differential diffusion, but The solution was not found in the small flame model, so it needs to be solved first during the mapping process. The calculation formula is as follows:

[0058] ,

[0059] here, and These represent the local mixing fractions of hydrogen and oxygen elements, with subscripts 1 and 2 indicating pure fuel and pure air flows, respectively. This represents the relative molecular mass of element H. This represents the relative molecular mass of element O. Curvature itself is not a suitable trajectory variable because it is an instantaneous, small-scale quantity and cannot be directly used to describe changes in curvature caused by convection, diffusion, and reaction. Previous studies have verified that H radicals are suitable trajectory variables for characterizing curvature; therefore, H radicals are chosen here. The steps for mapping the original small flame solution to the component space are as follows:

[0060] (1) First, calculate according to the definition of Bilger mixed fractions. With other trajectory variables remaining constant, the equivalent ratio As parameters of the original small flame model solution, the Bilger mixing fraction is used. Spatial mapping, to obtain ;

[0061] (2) Subsequently, with other trajectory variables remaining constant, the mass fraction of the H radical Replace curvature ,get ;

[0062] (3) The three parameters of the small flame table , and Discretizing the grid with linear interpolation using 111, 101, and 101 grid points respectively, further increasing the grid density did not improve the prediction accuracy, thus verifying the grid independence.

[0063] Step 3: Extract the thermochemical variables from the small flame surface for prior analysis:

[0064] Extracting the thermochemical variables of the small flame table needs to be done in the OpenFOAM environment, using the trajectory variable values ​​of the small flame table as input parameters to extract the thermochemical variables in the table.

[0065] (1) Input parameters need to be calculated based on DNS data. , and The three input parameters are calculated in the same way as those in the small flame model.

[0066] (2) The prior calculation grid is consistent with the DNS configuration, with 359 and 625 uniform grids set in the x and y directions, respectively.

[0067] (3) The calculated , and Based on the field file of the transformation case according to the grid sorting, in the prior process, there is a corresponding [file] in each grid. , and The parameters are derived from the thermochemical variables of the small flame table, and the final output is a thermochemical variable field file.

[0068] (4) Extract the data from the thermochemical variable field file and compare it with the DNS data to evaluate the rationality of the small flame table dimension and the accuracy of the calculation.

[0069] The values ​​obtained by looking up the table using the method of this invention are basically consistent with the results of the DNS data. A comparison chart of the conditional averages of the main components, free radicals, and chemical reaction source terms is shown below. Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 As can be seen from the figure, the predicted values ​​obtained by the table construction method are basically consistent with the DNS data. Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 and Figure 13 This involves predicting the components, free radicals, and chemical reaction source terms along the flame front path. Figure 8 For the curvature fluctuations along the path, where For process variables, The local arc length is represented by the ordinate, and the ordinate represents the equivalence ratio and curvature. It can be seen that the predicted peak values ​​for the components, free radicals, and chemical reaction source terms corresponding to the positive / negative curvature peaks are close to those of the DNS. Based on the prediction results, it can be considered that this invention, combined with numerical simulation methods, provides good prediction results for the combustion of turbulent thermally diffusively unstable premixed hydrogen. CSM represents the multi-component spatial model.

[0070] 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 method for constructing tables to simulate unstable hydrogen combustion in turbulent thermal diffusion, characterized in that, Includes the following steps: Step 1: Establish a multi-component spatial model and a generalized small flame model, including component equations, temperature equations, and gradient equations for reaction progress variables; for premixed unburned hydrogen under different equivalence ratios, curvature and strain rate are used as independent parameters, and the small flame model is solved numerically by changing the values ​​of the two parameters to obtain the original solutions of the small flame model under different equivalence ratios, curvatures, and strain rates. Step 2: Map the original solution of the small flame model to the multi-component space model, map the stoichiometry of unburned gas to the Bilger mixing fraction space, map the curvature and strain rate to the corresponding component space, select H radicals as trajectory variables for curvature and strain rate, and obtain the small flame table; Step 3: Perform prior analysis based on the small flame table to verify its rationality. The trajectory variables in the small flame table are calculated based on direct numerical simulation data. The calculated trajectory variables are used as input parameters to extract the thermochemical variables in the small flame table and compared with the direct numerical simulation data to evaluate the rationality and accuracy of the small flame table.

2. The table-building method for simulating unstable hydrogen combustion in turbulent thermal diffusion according to claim 1, characterized in that, The small flame model in step 1 is a premixed hydrogen small flame model, wherein: The component equation is used to describe the transport characteristics of each component in the reaction progress variable space during the combustion of hydrogen; The temperature equation is used to describe the changes in heat and temperature in the reaction progress variable space during the combustion of premixed hydrogen, and is used to predict the temperature distribution of hydrogen in the small flame reaction zone. Since the gradient equations for the reaction progress variable, the component equations, and the temperature equations are not closed, a gradient equation for the reaction progress variable is introduced to close them.

3. The table-building method for simulating turbulent thermal diffusion unstable hydrogen combustion according to claim 2, characterized in that, Step 2 includes: Step 2.1: With curvature and strain rate remaining constant as original parameters, the equivalent ratio As parameters of the original solution of the small flame model, the Bilger mixing fraction is used. Spatial mapping involves calculating the Bilger mixture fraction based on the mass fractions of each component calculated using the small flame model before mapping. To obtain the intermediate function .

4. The table-building method for simulating turbulent thermal diffusion unstable hydrogen combustion according to claim 3, characterized in that, Step 2 also includes: Step 2.2: Mass fraction of H radicals, with curvature and strain rate remaining constant as original parameters. Replace curvature To obtain the intermediate function .

5. The table-building method for simulating turbulent thermal diffusion unstable hydrogen combustion according to claim 4, characterized in that, Step 2 also includes: Step 2.3: The mass fraction of H free radicals Replacement strain rate The transformed trajectory variables remain unchanged, resulting in the final small flame table. .

6. The table-building method for simulating turbulent thermal diffusion unstable hydrogen combustion according to claim 5, characterized in that, Step 3 includes: Step 3.1: Calculate the trajectory variables based on the direct numerical simulation data. The calculation method for the trajectory variables is consistent with that in the small flame model.

7. The table-building method for simulating turbulent thermally diffuse unstable hydrogen combustion according to claim 6, characterized in that, Step 3 also includes: Step 3.2: Convert the calculated trajectory variables into a field file for the case, and use it as the input parameters for extracting the small flame table.

8. The table-building method for simulating turbulent thermally diffuse unstable hydrogen combustion according to claim 7, characterized in that, Step 3 also includes: Step 3.3: Perform a one-step solution using the solver, update the thermochemical variables, extract them, and compare them with the direct numerical simulation data.

9. The table-building method for simulating turbulent thermally diffuse unstable hydrogen combustion according to claim 1, characterized in that, The chemical reaction mechanism of the small flame model in step 1 is the same as that of the direct numerical simulation data.

10. The table-building method for simulating turbulent thermal diffusion unstable hydrogen combustion according to claim 1, characterized in that, The trajectory variables in step 2 are all solved by the governing equations in the turbulence numerical simulation. The solved trajectory variables are used to extract the thermochemical variables in the small flame table.

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