A simplified chemical reaction kinetics model construction method based on evolutionary algorithm

Abstract

This invention discloses a method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm, which relates to the field of computational fluid dynamics. The method includes: obtaining target flame and detonation characteristics such as laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width from experimental data or detailed chemical reaction mechanisms; establishing a set of governing equations to describe the one-dimensional laminar flame and detonation development process and using the solution error as the target optimization function of the evolutionary algorithm; solving the governing equations and using the evolutionary algorithm to iteratively optimize simplified chemical reaction kinetic parameters in the equations, such as activation energy, specific heat capacity ratio, calorific value of combustion, pre-exponential factor, thermal diffusivity, and relative molecular mass, until the solution can reproduce the target flame and detonation characteristics. This method can quickly and reliably develop simplified chemical reaction kinetics parameters, ensuring the reproduction of flame and detonation characteristics in computational fluid dynamics analysis and reducing calculation time.

Description

Technical Field

[0001] The present invention belongs to the field of computational fluid dynamics (CFD), and in particular relates to a method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm. Background Art

[0002] With the rapid development of industry and the growing demand for economic construction, clean gas energy will usher in rapid development. Combustible gases such as hydrogen and natural gas (methane) have the advantages of large reserves and high conversion efficiency. In the wave of energy transformation, this type of clean gas energy will play an important "bridge" role. However, if improperly operated or used, it may cause accidental fire and explosion risks. Especially in confined areas (such as pipelines or tunnels), when combustible gases accumulate and mix with air to ignite, the temperature and pressure rise rapidly, which may cause detonation and cause serious consequences, such as damage to surrounding facilities and buildings and casualties. Explosion accidents of combustible gases or flammable liquid vapor clouds occur frequently, so it is crucial to carry out relevant research to improve safety in practical applications.

[0003] In recent years, with the development of high-performance computing and computational fluid dynamics (CFD) technologies, numerical simulation has become an important research method for studying the combustion and explosion laws of combustible gases. The combination of numerical calculations, experiments, and theoretical analysis is a good way to solve flow combustion problems. Many scientific decisions regarding the design of industrial gas pipelines and fire protection plans have already used the results of numerical combustion simulations as an important reference. In the CFD solution process, an appropriate chemical reaction model is required to describe the deflagration, detonation, and deflagration-to-detonation processes of combustible gases or flammable liquid vapor clouds. Currently, commonly used chemical reaction models can be roughly divided into two categories: single-step chemical reaction models and detailed chemical reaction mechanism models. Among them, the single-step chemical reaction model is the most basic and widely used chemical reaction model. It has high computational efficiency, but compared with experimental data, the validity of the simulation results and the accuracy of the data still have major problems. The detailed chemical reaction mechanism model has high computational accuracy and can describe the distribution of chemical reaction intermediates, but its control equations have obvious rigidity problems during the computational fluid dynamics solution process. To ensure the stability of the calculation process and the accuracy of the calculation results, it is often necessary to use an extremely small solution time step, which results in a large amount of time and computing resources being consumed in the solution process. In addition, the development of the above two chemical reaction kinetics models also has a series of problems, such as long development cycle, cumbersome process, narrow scope of application, and difficulty in balancing deflagration and detonation. Summary of the Invention

[0004] To address the above technical issues, the present invention provides a method for constructing a simplified chemical reaction kinetic model based on an evolutionary algorithm. Based on experimental data or target flame and detonation characteristics (laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width) derived from detailed chemical reaction mechanisms, the method employs techniques such as the evolutionary algorithm and the simplex method to determine the optimal reaction kinetic parameters (activation energy, specific heat ratio, heat of combustion, pre-exponential factor, thermal diffusivity, and relative molecular mass) of the simplified reaction model that can reproduce the target flame and detonation characteristics. This method boasts high model accuracy, high development efficiency, and a wide range of applicability. It can be used for computational fluid dynamics simulation and theoretical analysis of phenomena such as deflagration, detonation, and deflagration-to-detonation transitions, as well as for simulation calculations of diffusion flames.

[0005] In order to achieve the above technical objectives, the present invention adopts the following technical solutions:

[0006] A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm comprises the following steps:

[0007] Step 1: Obtaining target characteristic parameters of combustible flame and detonation based on experimental data or calculations from a detailed chemical reaction mechanism, wherein the target characteristic parameters of combustible flame and detonation include laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0008] Step 2: Establish a control equation group for describing the one-dimensional laminar flame and detonation development process, and solve the control equation group to obtain flame and detonation characteristic parameters, wherein the flame and detonation characteristic parameters include laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0009] Step 3: estimating upper and lower limits of the value range of simplified chemical reaction kinetic parameters and initial values ​​of iteration, wherein the simplified chemical reaction kinetic parameters include activation energy, specific heat ratio, heat of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass;

[0010] Step 4: Substitute the estimated iterative initial values ​​in step 3 into the evolutionary algorithm to solve and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equations constructed in step 2 and solve the flame and detonation characteristic parameters;

[0011] Step 5: Evaluate the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in Step 4 and the target characteristic parameters obtained in Step 1, and use the solution error as the target optimization function of the evolutionary algorithm; if the error is greater than a threshold, continue to iteratively optimize the simplified chemical reaction kinetic parameters using the evolutionary algorithm and perform error evaluation until the solution error of the control equations meets the predetermined requirements;

[0012] Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error in solving the control equation group is less than the set value; use the optimized simplified chemical reaction kinetic parameters in the computational fluid dynamics analysis to calculate and accurately reproduce the target characteristic parameters of the combustible flame and detonation.

[0013] Furthermore, step 1 includes: obtaining the characteristic parameters of the combustible flame and detonation target by conducting experimental measurements or using a detailed chemical reaction mechanism according to the type of combustible; wherein, the laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; the laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone; the adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; the constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; the CJ detonation velocity refers to the minimum detonation wave velocity calculated by the Chapman-Jouguet theory, which simplifies the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the shock wave surface in the detonation wave structure.

[0014] Furthermore, the step 2 includes:

[0015] The governing equations describing the heat conduction and energy release processes are established to solve the characteristic parameters of one-dimensional laminar flames:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] (4)

[0020] (5)

[0021] in, Indicates the horizontal direction, Indicates the calculation of the initial density, Represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, represents the thermal diffusivity, represents the chemical reaction source term, A represents the pre-exponential factor, represents activation energy, Y represents the mass fraction of unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, represents the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum value of the absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant;

[0022] Establish the governing equations for describing the detonation wave structure:

[0023] (6)

[0024] (7)

[0025] (8)

[0026] (9)

[0027] Where, t represents time, U represents the flow velocity of combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and They represent the x-coordinates corresponding to the mass fractions of unburned reactants of 1 and 0.5, respectively. The flame and detonation characteristic parameters are obtained by solving the two sets of equations.

[0028] Furthermore, the step 3 includes:

[0029] Each parameter uses a different value range, and the initial value of the iteration is the average of the upper and lower limits of the corresponding value range.

[0030] Furthermore, in step 4, a centroid-based evolutionary algorithm is adopted, and the centroid definition is used to create the evolutionary direction of individuals in the population. According to the target optimization function value, individuals with larger calculation errors in the population are moved to the area with smaller calculation errors in the value interval, thereby accelerating the convergence of the calculation error.

[0031] Furthermore, the evolutionary algorithm includes: determining the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N=2K×D; initialize the population containing N individuals according to the iterative initial value population , , the data dimension of each individual is D, and an empty set V is established to store the newly generated individuals; when the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a subpopulation , using subpopulation U s All individuals in the current mass center c are calculated according to formula (11) m ; In the interval Internal random value determines the evolution step length According to formula (10), from the subpopulation U s Randomly select individuals And use the centroid c m Generate new individuals ; If the calculated objective optimization function value > , then the individual Join set V; take The first N individuals with the largest target optimization function value in the population P are used to update the population P; the above iterative optimization process is repeated until the target optimization function value calculated by the individuals in the population P reaches the predetermined stopping standard, and the best individual in the population P is output as the target optimization result; the best individual is the individual when the target optimization function value is the largest;

[0032] (10)

[0033] (11)

[0034] in, represents the new individuals generated in the population, represents an individual in the population P, represents the step size, c m Indicates the use of subpopulation U s Calculate the center of mass, Represents the population U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, f represents an arbitrary function relationship; These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution results of the control equations of laminar flame and detonation development process and the target value.

[0035] Furthermore, the error in step 5 includes:

[0036] The flame and detonation characteristic parameters ( 、 、 、 、 、 ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as:

[0037] ;

[0038] Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( 、 、 、 、 、 ), each characteristic parameter in Represents the corresponding target characteristic parameter. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

[0039] Furthermore, the simplex method used in step 6 includes:

[0040] For n-dimensional optimization problems, we first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, and then analyze and compare the vertex function values. We construct new vertices and simplexes through reflection, diffusion, contraction and other operations until the convergence conditions are reached.

[0041] Beneficial effects:

[0042] The present invention can overcome a series of problems in the prior art such as long cycle, cumbersome process, narrow scope of application, and difficulty in taking into account both deflagration and detonation in the construction of reaction kinetic models. Based on evolutionary algorithm and simplex method, a method is proposed that can quickly determine the optimal reaction kinetic parameters of a simplified reaction model for reproducing the target characteristics of flame and detonation. Compared with the traditional method of solving the optimal reaction kinetic parameters of a simplified reaction model based on genetic algorithm or graphical method, the method greatly improves the parameter development speed and reduces the parameter calculation error. The present invention is suitable for the calculation of most combustion and explosion scenarios (including premixed and non-premixed combustion processes), and can be used for computational fluid dynamics simulation and theoretical analysis of phenomena such as deflagration, detonation, and deflagration to detonation. It has the characteristics of high accuracy, wide scope of application and high development efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flow chart of a method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to the present invention;

[0044] Figure 2 This is the flowchart of the centroid-based evolutionary algorithm;

[0045] Figure 3 Schematic diagram of the convergence acceleration principle of the centroid-based evolutionary algorithm;

[0046] Figure 4 This is the flow chart of the simplex method algorithm;

[0047] Figure 5a , Figure 5b is the error trend diagram in the optimization process; Figure 5a is the trend of solution error in the iterative optimization process of the centroid-based evolutionary algorithm, Figure 5b The error trend of the solution in the iterative optimization process of the simplex method;

[0048] Figure 6 The distribution of flame characteristic parameters calculated using the optimized simplified chemical reaction parameters; the line graph represents the theoretical calculation results, and the scattered points represent the numerical calculation results;

[0049] Figure 7 is the distribution of detonation wave characteristic parameters calculated using the optimized simplified chemical reaction parameters. DETAILED DESCRIPTION

[0050] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only intended to illustrate the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0051] like Figure 1 As shown, a simplified chemical reaction kinetics model construction method based on an evolutionary algorithm of the present invention includes the following steps:

[0052] Step 1: Obtain the laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ (Chapman-Jouguet) detonation velocity, half-reaction width and other combustible flame and detonation target characteristic parameters based on experimental data or detailed chemical reaction mechanism;

[0053] Step 2: Establish a control equation group to describe the one-dimensional laminar flame and detonation development process. Solving the control equation group can obtain flame and detonation characteristic parameters such as laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0054] Step 3: Estimate the upper and lower limits of the range of simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, relative molecular mass, and the initial value of iteration;

[0055] Step 4: Substitute the estimated iterative initial values ​​in step 3 into the evolutionary algorithm for solution, and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equations and solve the flame and detonation characteristic parameters;

[0056] Step 5: Evaluate the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and use the error as the target optimization function of the evolutionary algorithm; if the error is greater than the threshold, continue to use the evolutionary algorithm to iteratively optimize the simplified chemical reaction kinetic parameters and perform error evaluation until the solution error of the control equations meets the predetermined requirements; preferably, the threshold is 10 -3 .

[0057] Step 6: Use the simplex method to perform local optimization on the simplified chemical reaction kinetic parameters obtained in step 5 until the error in solving the control equations is less than the set value. At this point, the optimized simplified chemical reaction kinetic parameters can be used in the computational fluid dynamics analysis to accurately reproduce the target characteristic parameters of the combustible flame and detonation. Preferably, the set value is 10 -5 .

[0058] Specifically, the step 1 includes:

[0059] The laminar combustion velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, half-reaction width and other characteristic parameters of the combustible flame and detonation target are obtained by conducting experimental measurements or calculating using detailed chemical reaction mechanisms. Among them, laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone. In the present invention, the laminar flame thickness is defined based on the temperature distribution, that is, it is characterized by the ratio of the combustion temperature rise to the maximum temperature gradient; adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; CJ detonation velocity refers to the Chapman-Jouguet (CJ) theory, which simplifies the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate, combines the continuity equation and the momentum equation to obtain the Rayleigh line, and further considers the energy equation and uses the gas state equation to eliminate the temperature to obtain the Hugoniot curve. The point where the upper branch of the Rayleigh line is tangent to the Hugoniot curve corresponds to the minimum possible detonation velocity, which is the CJ detonation velocity; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the shock wave surface in the detonation wave structure.

[0060] Specifically, the step 2 includes:

[0061] The governing equations describing the heat conduction and energy release processes are established to solve the characteristic parameters of one-dimensional laminar flames:

[0062] (1)

[0063] (2)

[0064] (3)

[0065] (4)

[0066] (5)

[0067] in, Indicates the horizontal direction, Indicates the calculation of the initial density, Represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, represents the thermal diffusivity, represents the chemical reaction source term, A represents the pre-exponential factor, represents activation energy, Y represents the mass fraction of unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, represents the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant.

[0068] Establish the governing equations for describing the detonation wave structure:

[0069] (6)

[0070] (7)

[0071] (8)

[0072] (9)

[0073] Where, t represents time, U represents the flow velocity of combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and represent the x-coordinates corresponding to the points where the mass fraction of unburned reactants is 1 and 0.5 respectively. Solving the above two sets of equations can obtain the flame and detonation characteristic parameters.

[0074] Furthermore, the step 3 includes:

[0075] Estimate the upper and lower limits of the value ranges for simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, calorific value, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass, as well as the initial value for the iteration. The value range will limit the subsequent optimization search range of the evolutionary algorithm and affect the convergence speed of the optimization results. When the value range is too large, the evolutionary algorithm parameter search range may be too wide, thereby increasing the time required for convergence of the optimization results. Conversely, when the value range is too small, it may be impossible to search for the simplified chemical reaction parameters required to meet the solution error, which will lead to the failure of the iterative optimization. In addition, the value range of the simplified chemical reaction parameters can be set differently for each parameter depending on the type of combustible material; the initial value for the iteration can be set as the average of the upper and lower limits of the corresponding value range.

[0076] Specifically, step 4 includes:

[0077] The present invention adopts the centroid-based evolutionary algorithm, and the mathematical description of the evolutionary algorithm is as follows: Determine the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N=2K D; initialize N individuals according to the iterative initial value population , i represents the individual number, the data dimension of each individual is D, and an empty set V is established to store newly generated individuals. When the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a subpopulation , using subpopulation U s All individuals in the current mass center c are calculated according to formula (11) m In the interval Internal random value determines the evolution step length According to formula (10), from the subpopulation U s Randomly select individuals And use the centroid c m Generate new individuals If the calculated objective optimization function value > , then the individual Join set V. Take The first N individuals with the largest value of the objective optimization function update the population P, Represents the union. Repeat the above iterative optimization process until the target optimization function value calculated by the individuals in the population P reaches the predetermined stopping standard, and output the best individual in the population P (the individual with the maximum target optimization function value) as the target optimization result. The algorithm flow chart is as follows Figure 2 shown.

[0078] (10)

[0079] (11)

[0080] in, represents the new individuals generated in the population, represents an individual in the population P, represents the step size, c m Indicates the use of subpopulation U s Calculate the center of mass, Represents the population U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, and f represents an arbitrary function relationship. In the present invention, the population individual These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution results of the control equations of laminar flame and detonation development process and the target value.

[0081] This method uses the centroid definition to create the evolution direction of individuals in the population, so that according to the target optimization function value, individuals with large calculation errors in the population are moved to the area with smaller calculation errors in the value interval, thereby achieving the purpose of accelerating the convergence of calculation errors. The schematic diagram of the algorithm's accelerated convergence principle is shown in the figure below. Figure 3 As shown in the figure, the subpopulation U s Individual u in r With the center of mass c m Determine the population evolution direction, and then use this evolution direction to transform the individuals in the population P Move to a new instance , so that the individuals in the population are closer to the global minimum point and the purpose of accelerating the convergence of calculation errors is achieved.

[0082] Specifically, step 5 includes:

[0083] The flame and detonation characteristic parameters ( 、 、 、 、 、 ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as:

[0084] (12)

[0085] Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( 、 、 、 、 、 ), each characteristic parameter in Represents the corresponding target characteristic parameter. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

[0086] Specifically, step 6 includes:

[0087] The simplex method is an optimization scheme for multivariable minimization problems based on heuristic rules. It was first proposed by John Nelder and Roger Mead in 1965, so it is also called the Nelder-Mead method. This method constructs an iterative optimization strategy for solutions based on the concept of simplex and does not rely on the derivative information of the function. It is suitable for function optimization problems where analytical expressions are difficult or impossible to obtain. For n-dimensional optimization problems, first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, then analyze and compare the vertex function values, and construct new vertices and simplexes through reflection, diffusion, contraction and other operations until the convergence condition is reached. For n-dimensional minimization problems, this method is used to search for the function to be optimized. The minimum process is as follows Figure 4 As shown:

[0088] (1) Initialize n+1 points 、 、……、 , as the vertices of the simplex; initialize the reflection coefficient, expansion coefficient, contraction coefficient and retraction coefficient as: a=1, b=2, c=0.5, d=0.5;

[0089] (2) According to The values ​​of are sorted from small to large, assuming: ,in, It is called the optimal point. It's called the worst point. It is called the second difference point, which checks whether the convergence condition is met;

[0090] (3) Abandon the worst point , calculate the average of the first n points , calculate the reflection point ;

[0091] (4) If Better than But worse than , then use replace Construct a new simplex and continue with step (2);

[0092] (5) If Better than , then calculate the extension point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, use replace Construct a new simplex and continue with step (2);

[0093] (6) If Better than But worse than , then calculate the external contraction point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, proceed to step (7);

[0094] (7) If Worse than , then calculate the inner contraction point ,if Better than , then use replace Construct a new simplex and continue with step (2); otherwise, proceed to step (8);

[0095] (8) Use all points except the current optimal point Replace, where , then continue with step (2).

[0096] This method is sensitive to the initial estimated value and can only search for a local optimal solution near the initial value rather than a global optimal solution. Therefore, in the present invention, the global optimization of simplified chemical reaction parameters is first performed by an evolutionary algorithm until the solution error is less than 10 -3 To narrow the search range, the optimization result of the evolutionary algorithm is then used as the initial estimate of the simplex method to perform local optimization until the solution error is less than 10 -5 The steps of using the simplex method to optimize and simplify chemical reaction parameters in the present invention are as follows:

[0097] (1) Use the optimized parameters obtained by the evolutionary algorithm as the initial estimate for the simplex method, and create a simplex around the initial estimate. In this model, there are six reaction parameters (activation energy, specific heat ratio, heat release rate, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass), so there are seven edges. The first vertex is defined by the initial estimate, which is the result of the evolutionary algorithm; each of the other vertices is created by adding 5% to the value of one of the variables while keeping the other variables unchanged;

[0098] (2) Sort each “individual” and calculate the error between each “individual” and the target characteristic according to formula (12);

[0099] (3) Generate a new vertex by reflecting the worst point, and then re-divide the simplex through the four basic processes of reflection, expansion, contraction, and retreat to self-improve and approach the optimality.

[0100] Example:

[0101] The present invention provides a simplified chemical reaction kinetics model construction method based on an evolutionary algorithm, which specifically comprises the following steps:

[0102] Step 1: Obtain the target characteristic parameters of the combustible flame and detonation, such as laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width, based on experimental data or detailed chemical reaction mechanism:

[0103] In this example, simplified chemical reaction kinetic parameters were developed to describe the combustion process of a hydrogen-air mixture with an equivalence ratio of 1 at an initial temperature of 298 K and an initial pressure of 101325 Pa. The flame and detonation characteristic parameters formed under these conditions can be calculated using a detailed chemical reaction mechanism. The specific parameter values ​​are shown in Table 1.

[0104] Table 1 Flame and detonation target characteristic parameters

[0105]

[0106] Step 2: Establish a control equation group to describe the one-dimensional laminar flame and detonation development process. Solving the control equation group can obtain flame and detonation characteristic parameters such as laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width;

[0107] Step 3: Estimate the upper and lower limits of the value ranges and the initial values ​​of iterations of simplified chemical reaction kinetic parameters such as activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass. In this embodiment, the value ranges and initial values ​​of iterations corresponding to each simplified chemical reaction parameter are shown in Table 2:

[0108] Table 2 Simplified chemical reaction parameters corresponding to the value range and iterative initial value

[0109]

[0110] Step 4: Substitute the estimated iterative initial values ​​in step 3 into the evolutionary algorithm to obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equations and solve the flame and detonation characteristic parameters;

[0111] Step 5: Evaluate the error between the flame and detonation characteristic parameters obtained by solving the control equations in step 4 and the target characteristic parameters obtained in step 1, and use the error as the target optimization function of the evolutionary algorithm; if the error is greater than 10 -3 Then, the simplified chemical reaction kinetic parameters are iteratively optimized and error evaluated using the evolutionary algorithm until the error in solving the control equations meets the predetermined requirements.

[0112] In this embodiment, the maximum evolution step size of the centroid-based evolutionary algorithm is set to , the number of subpopulation individuals K = 7, the data dimension D = 6, and the population size N = 2K × D = 84 are determined; after 202 rounds of iterative optimization, the error of the flame and detonation characteristic parameters is 9.83675 × 10 -4 The stopping criteria are reached, and the error decreases with the number of iterations during the optimization process. Figure 5a The simplified chemical reaction parameter values ​​calculated at this time are shown in Table 3, where R represents the universal gas constant, R = 8.314 J / (mol·K). The iterative optimization method used in this study consumed 134.2 s of CPU time, while the traditional genetic algorithm optimization method consumed 18,040 s of CPU time to achieve the same solution error, demonstrating the efficiency of the current algorithm in developing reaction parameters.

[0113] Table 3 Simplified chemical reaction parameter values ​​obtained by evolutionary algorithm optimization

[0114]

[0115] Step 6: Use the simplex method to perform local optimization on the simplified chemical reaction kinetic parameters obtained in step 5 until the error in solving the governing equations is less than 10 -5 At this point, the optimized simplified chemical reaction kinetic parameters can be used in computational fluid dynamics analysis to accurately reproduce the characteristic parameters of combustible flames and detonation targets. In this embodiment, the parameters optimized in step 5 are used as the iterative initial values ​​of the simplex method, and the reflection coefficient, expansion coefficient, contraction coefficient, and retraction coefficient in the simplex method are initialized as follows: a=1, b=2, c=0.5, d=0.5. After 346 rounds of iteration, the calculated characteristic parameter solution error is 9.7508×10 -6 , meeting the requirements for stopping iterative optimization, the error decreases with the number of iterations during the optimization process as shown in Figure 5b The simplified chemical reaction parameter values ​​calculated at this time are shown in Table 4. The comparison between the flame and detonation characteristic parameters calculated using the optimized simplified chemical reaction parameter values ​​and the target characteristic parameters is shown in Table 5:

[0116] Table 4 Simplified chemical reaction parameter values ​​obtained by simplex method optimization

[0117]

[0118] Table 5 Comparison of flame and detonation characteristic parameters calculated by optimizing chemical reaction parameter values ​​with target characteristic parameters

[0119]

[0120] The simplified chemical reaction kinetic parameters obtained by the current algorithm optimization are substituted into the computational fluid dynamics control equations and numerically solved. The distribution of one-dimensional laminar flame characteristic parameters obtained by numerical calculation is compared with the theoretical values ​​to verify the accuracy of the current simplified chemical reaction kinetic parameters. The comparison results are as follows: Figure 6 As shown in the figure, it can be seen that the numerical simulation results are in good agreement with the theoretical solution results, and the spatial distribution of each flame characteristic parameter is accurately predicted. The distribution of components, velocity, reaction rate, and pressure near the detonation wave obtained by using the optimized simplified chemical reaction kinetic parameters is shown in the figure. Figure 7 The results show that the CJ detonation velocity and half-reaction width calculated using the optimized parameters It is in good agreement with the theoretical value.

[0121] Although the above describes the illustrative specific embodiments of the present invention to facilitate understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concepts of the present invention are protected.

Claims

1. A method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm, characterized in that: The steps include: Step 1: Obtaining target characteristic parameters of combustible flame and detonation based on experimental data or calculations from a detailed chemical reaction mechanism, wherein the target characteristic parameters of combustible flame and detonation include laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width; Step 2: Establish a control equation group for describing the one-dimensional laminar flame and detonation development process, and solve the control equation group to obtain flame and detonation characteristic parameters, wherein the flame and detonation characteristic parameters include laminar burning velocity, laminar flame thickness, adiabatic flame temperature, constant volume flame temperature, CJ detonation velocity, and half-reaction width; Step 3: estimating upper and lower limits of the value range of simplified chemical reaction kinetic parameters and initial values ​​of iteration, wherein the simplified chemical reaction kinetic parameters include activation energy, specific heat ratio, heat of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass; Step 4: Substitute the estimated iterative initial values ​​in step 3 into the evolutionary algorithm to solve and obtain a set of optimized simplified chemical reaction kinetic parameters within the value range; substitute the optimized simplified chemical reaction kinetic parameters into the control equations constructed in step 2 and solve the flame and detonation characteristic parameters; Step 5: Evaluate the solution error between the flame and detonation characteristic parameters obtained by solving the control equations in Step 4 and the target characteristic parameters obtained in Step 1, and use the solution error as the target optimization function of the evolutionary algorithm; If the error is greater than the threshold, the simplified chemical reaction kinetic parameters are iteratively optimized using the evolutionary algorithm and the error is evaluated until the error in solving the control equations meets the predetermined requirements. Step 6: Use the simplex method to locally optimize the simplified chemical reaction kinetic parameters obtained in step 5 until the error in solving the control equation group is less than the set value; use the optimized simplified chemical reaction kinetic parameters in the computational fluid dynamics analysis to calculate and accurately reproduce the target characteristic parameters of the combustible flame and detonation.

2. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The step 1 comprises: obtaining the characteristic parameters of the combustible flame and detonation target by conducting experimental measurements or solving the problem using a detailed chemical reaction mechanism according to the type of combustible; wherein, the laminar flame speed refers to the propagation speed of the flame surface relative to the unburned gas; the laminar flame thickness refers to the sum of the widths of the preheating zone and the chemical reaction zone; the adiabatic flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under adiabatic conditions; the constant volume flame temperature refers to the temperature that the combustion products can reach when the combustible gas is completely burned under constant volume conditions; the CJ detonation velocity refers to the minimum detonation wave velocity calculated by the Chapman-Jouguet theory, which simplifies the detonation wave into a one-dimensional discontinuous surface with infinite reaction rate; the half-reaction width refers to the distance between the position where the fuel mass fraction Y = 0.5 and the shock wave surface in the detonation wave structure.

3. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 2, characterized in that: The step 2 includes: The governing equations describing the heat conduction and energy release processes are established to solve the characteristic parameters of one-dimensional laminar flames: （1） （2） （3） （4） （5） in, Indicates the horizontal direction, Indicates the calculation of the initial density, Represents the current density, T0 represents the initial temperature of calculation, T represents the current temperature, represents the specific heat at constant volume, represents the specific heat capacity at constant pressure, represents the thermal diffusivity, represents the chemical reaction source term, A represents the pre-exponential factor, represents activation energy, Y represents the mass fraction of unburned reactants, q represents the calorific value of combustion, represents the laminar flame speed, represents the adiabatic flame temperature, represents the constant volume flame temperature, represents the laminar flame thickness, represents the maximum value of the absolute value of the temperature gradient, exp represents the exponential function, and R represents the universal gas constant; Establish the governing equations for describing the detonation wave structure: （6） （7） （8） （9） Where, t represents time, U represents the flow velocity of combustibles, represents the speed of sound under initial conditions, E represents the specific total energy, c represents the current speed of sound, represents the initial pressure, p represents the current pressure, represents the specific heat ratio, represents the CJ detonation velocity, represents the half-reaction width, and They represent the x-coordinates corresponding to the mass fractions of unburned reactants of 1 and 0.5, respectively. The flame and detonation characteristic parameters are obtained by solving the two sets of equations.

4. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 3, characterized in that: The step 3 includes: Each parameter uses a different value range, and the initial value of the iteration is the average of the upper and lower limits of the corresponding value range.

5. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 4, characterized in that: In step 4, an evolutionary algorithm based on centroid is adopted, and the evolutionary direction of individuals in the population is created using the centroid definition. According to the target optimization function value, individuals with larger calculation errors in the population are moved to the area with smaller calculation errors in the value interval, thereby accelerating the convergence of the calculation error.

6. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 5, characterized in that: The evolutionary algorithm includes: determining the maximum evolutionary step length of the centroid-based evolutionary algorithm , the number of subpopulation individuals K, the data dimension D, determine the population size N=2K×D; initialize the population containing N individuals according to the iterative initial value population , , the data dimension of each individual is D, and an empty set V is established to store the newly generated individuals; when the calculated target optimization function value does not reach the stopping condition, K individuals are selected from the population P to form a subpopulation , using subpopulation U s All individuals in the current mass center c are calculated according to formula (11) m ; In the interval Internal random value determines the evolution step length According to formula (10), from the subpopulation U s Randomly select individuals And use the centroid c m Generate new individuals ; If the calculated objective optimization function value > , then the individual Join set V; take The first N individuals with the largest target optimization function value in the population P are used to update the population P; the above iterative optimization process is repeated until the target optimization function value calculated by the individuals in the population P reaches the predetermined stopping standard, and the best individual in the population P is output as the target optimization result; the best individual is the individual when the target optimization function value is the largest; （10） （11） in, represents the new individuals generated in the population, represents an individual in the population P, represents the step size, c m Indicates the use of subpopulation U s Calculate the center of mass, Represents the population U s The individuals selected from represents the subpopulation U s Any individual in the population, W represents the total mass of individuals in the population, f represents an arbitrary function relationship; These are the simplified chemical reaction kinetic parameters to be optimized. The data dimension D=6, which represent activation energy, specific heat ratio, calorific value of combustion, pre-exponential factor, thermal diffusion coefficient, and relative molecular mass respectively. The function relationship f is the error relationship between the solution results of the control equations of laminar flame and detonation development process and the target value.

7. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 6, characterized in that: The solution errors in step 5 include: The flame and detonation characteristic parameters ( 、 、 、 、 、 ) is compared with the target characteristic parameters in step 1 and the solution error is quantified. The solution error is defined as: ； Among them, error represents the solution error, i represents the flame and detonation characteristic parameter index, Represent the flame and detonation characteristic parameters respectively ( 、 、 、 、 、 ), each characteristic parameter in Represents the corresponding target characteristic parameters. The evolutionary algorithm will minimize the solution error by optimizing and simplifying the chemical reaction kinetic parameters, that is, the solution error of the control equation group is used as the target optimization function of the evolutionary algorithm.

8. The method for constructing a simplified chemical reaction kinetics model based on an evolutionary algorithm according to claim 1, characterized in that: The simplex method used in step 6 includes: For n-dimensional optimization problems, we first construct an n+1-dimensional simplex, calculate the function values ​​of the simplex vertices, and then analyze and compare the vertex function values. We construct new vertices and simplexes through reflection, diffusion, and contraction operations until the convergence condition is reached.

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