Post - combustion effect simulation method for introducing chemical reaction analysis

Abstract

The present invention discloses a simulation method for post-combustion effect introducing chemical reaction analysis, including: obtaining detonation energy, detonation products, mass fraction, and relevant thermodynamic parameters according to the detonation process of explosives; obtaining energy release parameters including chemical reaction source terms; establishing a post-combustion analysis calculation model for enclosed space explosion introducing chemical reaction source terms; solving the initial temperature and initial pressure of the equivalent gas mass of explosives; inputting relevant parameters into the post-combustion analysis calculation model for enclosed space explosion introducing chemical reaction to solve and obtain the energy release rate; calculating the specific heat energy of the post-combustion effect, modifying the JWL equation of state, and simulating the internal explosion response in the enclosed space considering the post-combustion effect. The beneficial effects of the present invention are: introducing a calculation model including chemical reaction source terms can accurately and effectively simulate the explosive initiation process, obtain the start and end times of the post-combustion reaction and the energy release rate, and the simulation results are accurate.

Description

Technical Field

[0001] The present invention relates to the technical field of post - combustion effect evaluation, and particularly to a simulation method for post - combustion effect introducing chemical reaction analysis. Background Art

[0002] When an explosive detonates in a closed space, a high - temperature and high - pressure environment will be formed in the confined space. The combustible detonation products will continue to burn and release energy after mixing with oxygen, which is called the post - combustion effect. When there is sufficient oxygen in the closed space, the detonation products of oxygen - rich explosives will completely react. At this time, the post - combustion effect is more significant, and there is an obvious enhancement effect on the quasi - static pressure load in the closed space, thereby increasing the degree of structural deformation under the action of the explosion.

[0003] During the mission execution, a ship may face threats from many extreme loads such as anti - ship missiles and suffer scenarios of explosion in a closed space. Therefore, accurately evaluating the damage situation and vulnerability level of a ship after encountering extreme loads has become an inevitable requirement for taking effective measures to deal with the strike. However, due to many problems such as the economic cost of current test evaluations and the guarantee of military capabilities, it is difficult to carry out damage tests on actual ships. Therefore, using simulation software to carry out finite - element calculation and simulation is a currently widely accepted solution, and considering the post - combustion effect in finite - element calculations has become a prerequisite for accurately evaluating the explosive effect.

[0004] In current mainstream finite - element software (Autodyn, Abaqus, and Ls - Dyna), the method for considering the post - combustion effect is based on the JWL equation of state, and an additional energy is added at a specific energy release rate during the time period set by the user. Therefore, the start and end times of the action of the post - combustion effect (that is, the start and end times of the aforementioned time period) and the energy release rate have become key factors for accurately describing the post - combustion effect. However, there is no relevant theory in the existing method to guide users on how to correctly calculate and select the start and end times and the energy release rate. Only the start and end times of the post - combustion effect and the two simulation parameters of the energy release rate can be inferred in reverse from the chamber pressure change in the test. Therefore, the main defect of the existing mainstream method lies in its dependence on specific test results. Specifically, this method cannot obtain the simulation parameters of the post - combustion effect outside the test conditions of the test, the simulation results are not accurate enough, and thus it cannot reasonably characterize the post - combustion effect of different explosive types and different closed - space sizes included in the research and design space, and does not have the generality required by professionals. Summary of the Invention

[0005] The purpose of the present invention is to provide a simulation method for post - combustion effect introducing chemical reaction analysis to improve the accuracy of simulation results in view of the deficiencies of the existing technology.

[0006] The technical solution adopted by the present invention is as follows: A method for simulating the afterburning effect by introducing chemical reaction analysis, comprising the following steps:

[0007] According to the detonation process of the explosive, the detonation energy and detonation products are obtained, as well as the mass fractions and related thermodynamic parameters of each detonation product;

[0008] Based on the composition of the detonation products, the chemical reactions that further occur during the afterburning process of the explosive are clarified, and the energy release parameters including the chemical reaction source term are obtained;

[0009] Calculate the source term including chemical reactions, and establish an afterburning analysis calculation model for closed-space explosion by introducing the chemical reaction source term;

[0010] Divide the explosion process in the closed space into three stages: detonation stage, adiabatic expansion stage, and afterburning reaction stage;

[0011] Based on the characteristics of the detonation stage, solve the initial temperature and initial pressure of the equivalent gas mass of the explosive;

[0012] Input the relevant parameters obtained by calculation into the afterburning analysis calculation model for closed-space explosion by introducing chemical reactions, solve the diffusion velocity, energy release amount, and pressure of each detonation product in the adiabatic expansion stage and afterburning reaction stage as a function of explosion time, then determine the start and end times of afterburning, calculate the energy release amount, and obtain the energy release rate;

[0013] Calculate the specific heat energy of the afterburning effect using the start and end times and energy release rate of the afterburning effect, modify the JWL equation of state, and solve it through the Euler-Lagrange coupling solver to simulate the explosion response in the closed space considering the afterburning effect.

[0014] According to the above scheme, the afterburning analysis calculation model for closed-space explosion by introducing the chemical reaction source term includes a modified reaction fluid control equation, a modified component mass fraction conservation equation, and a modified chemical kinetic energy and reaction component transport model. All three modified equations are obtained by introducing the corresponding chemical reaction source term into the original initial equations;

[0015] (1), Introduce a specified source term including chemical reactions into the initial continuity equation S u , and the obtained modified continuity equation is:

[0016] ;

[0017] Among them, t is time, with the unit s; V is volume, with the unit m 3 ; a is the area vector, with the unit m 2 ; ρis the density, with the unit of kg / m 3 ; v is the velocity, with the unit of m / s; S u is the specified source term related to mass, and its value is 0;

[0018] (2) Introduce the specified source term including chemical reaction into the initial momentum equation S u , and the obtained corrected momentum equation is:

[0019] ;

[0020] Among them, p is the pressure, with the unit of MPa; T is the viscous stress tensor, with the unit of MPa; f b is the resultant body force, with the unit of N; I is the impulse, N·s; S u is the specified source term related to mass, and its value is 0;

[0021] (3) Introduce the energy source term including chemical reaction into the initial energy equation S E , and the obtained corrected energy equation is:

[0022] ;

[0023] Among them, E is the total energy per unit mass, with the unit of J; σ is the hydrodynamic stress, with the unit of MPa; q is the heat flux, with the unit of J; S E is the energy source term including chemical reaction, which is the total combustion heat of each detonation product;

[0024] (4) Introduce the mass fraction source term including chemical reaction into the initial component mass fraction conservation equation S Yi , and the obtained corrected component mass fraction conservation equation is:

[0025] ;

[0026] Among them, i is the component serial number; Y i is the mass fraction of component i : ρ is the density, with the unit of kg / m 3 ; U is the total internal energy, with the unit of J; J i is the molecular diffusion flux, with the unit of mol / (m²·s); μ tis the turbulent dynamic viscosity, with the unit of Pa·s; σ t is the turbulent Schmidt number, which is a dimensionless number; S Yi is the mass fraction source term from chemical reactions, and the specific value is the mass fraction of each mixed gas.

[0027] According to the above scheme, S E the solution method of is: S E is the sum of the combustion heats of all detonation products, but it changes with the progress of the reaction; while the combustion heat of a single detonation product is the product of the combustion heat per unit molar mass of the detonation product and the number of moles of the detonation product during the reaction. Since the chemical reaction is a process of incomplete reaction, the number of moles of the reaction detonation product can be obtained according to the reaction rate;

[0028] The overall reaction rate constant k is usually determined using the Arrhenius equation, and the specific formula is:

[0029] ;

[0030] Among them, R is the universal gas constant, with the unit of J / (kg·K); A is the pre-exponential factor; T is the temperature, with the unit of K; β is the temperature exponent; E a is the activation energy, with the unit of J / mol;

[0031] The sum of the combustion heats per unit molar mass of the detonation products considering the reaction rate is calculated according to the following formula :

[0032] ;

[0033] Among them, is the formation enthalpy of the corresponding component, that is, the combustion heat per unit molar mass of the detonation product, with the unit of KJ / mol;

[0034] The sum of the combustion heats per unit molar mass of a certain detonation product considering the reaction rate is , after multiplying by the amount of substance of the detonation product, the combustion heat of the detonation product can be obtained; then, by summing up the combustion heats of all detonation products, S E can be obtained, that is, the sum of the combustion heats of all detonation products.

[0035] According to the above scheme, the modified JWL equation of state is:

[0036] ;

[0037] In the formula, λQ is the specific heat energy of the afterburning effect, with the unit of J / (kg·K), which is the product of the afterburning energy release rate and the duration; P is the pressure, with the unit of MPa; R 1. R 2. A , B , ω are all constants related to the explosive material; V is the volume of the closed space, with the unit of m 3 , E is the specific heat energy, with the unit of J / (kg·K).

[0038] According to the above scheme, the specific method for dividing the explosion process in the closed space into three stages is as follows:

[0039] The detonation stage is simplified according to the instantaneous detonation hypothesis, that is, it is assumed that the explosive detonation process is completed instantaneously, and all the explosives are converted into detonation products at the moment of initiation, and the size of the gas mass is the same as the initial size of the charge; during the adiabatic expansion stage, the mixing of air and detonation products is insufficient, that is, in a restricted mixing state, and the energy released by the detonation products is very limited. It is assumed that no chemical reaction occurs during this process until the restricted mixing state ends; in the afterburning reaction stage, the reflected shock wave enhances the mixing degree of the detonation products and oxygen, and the restricted mixing state ends. In the calculation, the time when the shock wave first touches the near wall surface of the closed space is taken as the starting time of the afterburning reaction stage.

[0040] According to the above scheme, the calculation method for the initial temperature of the equivalent gas mass of the explosive is as follows:

[0041] Use the thermodynamic polynomial data to define the properties of the detonation products involved in the detonation process, and fit the specific heat C p of each detonation product with a polynomial of 5 coefficients;

[0042] ;

[0043] In the formula are all fitting coefficients; C p is the specific heat capacity, with the unit of J / (kg·K); R is the universal gas constant, taking 8.314 J / (mol·K);

[0044] Convert the fitted specific heat C p of each detonation product into the specific heat at constant volume C V :

[0045] ;

[0046] The specific heat at constant volume of the mixed gas is obtained by mass-weighting each detonation product component. C vm :

[0047] ;

[0048] Among them, C vm represents the specific heat at constant volume of the mixed gas, with the unit of J / (kg·K); i is the type of detonation products in the mixed gas; y i represents the detonation products in the mixed gas i 's mass fraction; C v ( i ) represents the specific heat at constant volume of the detonation products in the mixed gas, with the unit of J / (kg·K); i represents the total number of components of the mixed gas; N The temperature of the mixed gas in the gas mass is obtained through thermodynamic relations

[0049] : T m :

[0050] ;

[0051] In the formula, W is the charge mass, with the unit of g; Q is the detonation energy of the fuel-rich explosive, with the unit of MJ / kg; n is the amount of substance of the mixed gas, in mol; T 0 is the room temperature, with the unit of K; T m is the initial temperature of the detonation products to be solved, with the unit of K;

[0052] By integrating the change curve of the mixed specific heat at constant volume, the initial temperature of the detonation products is finally obtained T m .

[0053] According to the above scheme, the initial pressure p 0 of the equivalent gas mass of the explosive is calculated by the following formula:

[0054] ;

[0055] In the formula, n is the amount of substance of the gas mass, with the unit of mol; R is the universal gas constant; V TNTis the volume of the air mass, with the unit of m 3 .

[0056] The beneficial effects of the present invention are as follows:

[0057] 1. By introducing a computational model including a chemical reaction source term in the afterburning effect, the present invention can accurately and effectively simulate the explosive detonation process, and obtain the start and end times of the afterburning reaction and the energy release rate, solving the defect that the mainstream solution methods rely on experimental results and cannot reasonably obtain the action time and energy release rate of the afterburning effect; compared with the prior art, the simulation results of the afterburning effect obtained based on the present invention are more accurate, can simulate the afterburning effect of different explosive types and different closed space sizes, have strong versatility, and can provide support for accurately evaluating the damage effect of explosives.

[0058] 2. The present invention divides the process of internal explosion in a closed space based on the physical characteristics at different stages. This model provides a theoretical basis and support for the simulation of the afterburning effect, and improves the defect that the existing mainstream solution methods completely rely on experimental data and cannot predict the afterburning effect under non-experimental conditions.

[0059] 3. The simulation of the explosive detonation process of the present invention is completely determined by the thermodynamic properties of the explosive detonation products, does not completely depend on specific explosive characteristics, and the solution analysis of the afterburning effect is applicable to all explosion problems with known detonation products and detonation energy, has extremely high versatility and a very wide application range, and has great engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is a schematic flow chart of the present invention.

[0061] Figure 2 is a schematic diagram of the grid division of the closed space in this embodiment.

[0062] Figure 3 is a schematic diagram of the energy release change process of the detonation products in the closed space in this embodiment.

[0063] Figure 4 is a schematic diagram of the change process of the amount of substance of each detonation product in the closed space in this embodiment.

[0064] Figure 5 is a schematic diagram of the comparison of the test and numerical calculation pressure histories in this embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0065] In order to have a clearer understanding of the technical features, objectives, and effects of the present invention, the specific implementation manners of the present invention will now be described in detail with reference to the accompanying drawings.

[0066] As Figure 1A post-combustion effect simulation method introducing chemical reaction analysis is as follows:

[0067] S1. According to the detonation process of the explosive, obtain the detonation energy, detonation products, mass fractions of each detonation product, and related thermodynamic parameters, including the pre-exponential factor and activation energy.

[0068] In the present invention, both the pre-exponential factor and the activation energy Ea can be obtained by existing methods.

[0069] S2. Based on the composition of the detonation products, clarify the chemical reactions further occurring during the post-combustion process of the explosive, and obtain the energy release parameters including the chemical reaction source term. The energy release parameters include the reaction temperature, the amount of substance of the detonation products released by the combustion of unit TNT chemical reaction, and the heat of combustion of the detonation products per unit molar mass.

[0070] The reaction temperature, the amount of substance of the detonation products released by the combustion of unit TNT chemical reaction, and the heat of combustion of the detonation products per unit molar mass can all be obtained by existing technologies.

[0071] S3. Calculate and obtain the source term including chemical reactions according to the relevant energy release parameters, and establish a post-combustion analysis calculation model for the explosion in a closed space introducing the chemical reaction source term.

[0072] In the present invention, the closed space refers to the physical space where the explosion occurs; the post-combustion analysis calculation model for the explosion in a closed space introducing the chemical reaction source term includes the modified reaction fluid control equation, the modified component mass fraction conservation equation, and the modified chemical kinetic energy and reaction component transport model. The three modified equations are all obtained by introducing the corresponding chemical reaction source term into the original initial equations.

[0073] (1). Introduce the specified source term including chemical reactions into the initial continuity equation S u , and the obtained modified continuity equation is:

[0074] (1);

[0075] In formula (1), t is time, with the unit of s; V is volume, with the unit of m 3 ; a is the area vector, with the unit of m 2 ; ρ is density, with the unit of kg / m 3 ; v is velocity, with the unit of m / s; S u is the specified source term related to mass, and its value is 0.

[0076] (2). Introduce the specified source term including chemical reactions into the initial momentum equationS u , the obtained corrected momentum equation is:

[0077] (2);

[0078] In formula (2), p is the pressure, with the unit of MPa; T is the viscous stress tensor, with the unit of MPa; f b is the resultant body force, with the unit of N; I is the impulse, N·s; S u is the specified source term related to mass, with a value of 0; t is the time, with the unit of s; V is the volume, with the unit of m 3 ; a is the area vector, with the unit of m 2 ; ρ is the density, with the unit of kg / m 3 ; v is the velocity, with the unit of m / s;

[0079] For formula (1) and formula (2), S u is the mass source term including chemical reactions. The explosion process occurs in a closed space without involving the inflow and outflow of substances, so S u takes a value of 0.

[0080] (3), Introduce the energy source term including chemical reactions into the initial energy equation S E , and the obtained corrected energy equation is:

[0081] (3);

[0082] In formula (3), E is the total energy per unit mass, with the unit of J; σ is the hydrodynamic stress, with the unit of MPa; q is the heat flux, with the unit of J; S E is the energy source term including chemical reactions, which is the total combustion heat of each detonation product in S2.

[0083] (4), Introduce the mass fraction source term including chemical reactions into the initial component mass fraction conservation equation S Yi , and the obtained corrected component mass fraction conservation equation is:

[0084] (4);

[0085] In formula (4), i is the component serial number; Y i is the component iMass fraction; ρ is the density, with the unit of kg / m 3 ; U is the total internal energy, with the unit of J; J i is the molecular diffusion flux, with the unit of mol / (m²·s); μ t is the turbulent dynamic viscosity, with the unit of Pa·s; σ t is the turbulent Schmidt number, which is a dimensionless number; S Yi is the mass fraction source term from chemical reactions, and the specific value is the mass fraction of each mixed gas (i.e., detonation products) in step S1.

[0086] Regarding the solution of S E in formula (3):

[0087] S E is the sum of the heats of combustion of all detonation products, but it changes with the progress of the reaction. The heat of combustion of a single detonation product is the product of the heat of combustion per unit molar mass of the detonation product and the number of moles of the detonation product during the reaction. Since the chemical reaction is an incomplete reaction process, the number of moles of the reaction detonation products can be obtained according to the reaction rate.

[0088] Chemical kinetic energy involves the reaction mechanism and reaction rate at the molecular level of chemical components. When modeling the transport of reaction components, the reaction rates of all reactions in the chemical mechanism need to be calculated to provide source terms for the transport equation. Any elementary chemical reaction can be represented by the following general equation:

[0089] (5);

[0090] In formula (5), υ represents the stoichiometric coefficient, A 、 B respectively represent the reactants, 、 are respectively the stoichiometric coefficients of the reactants A 、 B ; C 、 D respectively represent the products, 、 are respectively the stoichiometric coefficients of the products; k f is the forward reaction rate constant, k b is the reverse reaction rate constant.

[0091] According to the net stoichiometric coefficient υij Give the reaction j Total number of moles of components produced or consumed i :

[0092] (6);

[0093] In formula (6), j represents the reaction, i represents the component serial number; represents the stoichiometric coefficient of component i in the product, represents the component i in the reactant represents the reaction j of component i net stoichiometric coefficient, that is, the reaction j produces or consumes the component i total number of moles; k is the overall reaction rate constant.

[0094] The reaction can proceed forward or backward, k f is the forward reaction rate constant, k b is the reverse reaction rate constant. k is to consider both k f and k b overall reaction rate constant

[0095] (7);

[0096] Overall reaction rate constant k is usually determined using the Arrhenius equation, where the rate is non-linearly related to temperature, and the specific formula is:

[0097] (8);

[0098] In formula (8), R is the universal gas constant, with the unit J / (kg·K); A is the pre-exponential factor; T is the temperature, with the unit K; β is the temperature exponent; E a is the activation energy, with the unit J / mol.

[0099] Calculate the total combustion heat of the detonation products per unit molar mass considering the reaction rate according to the following formula (that is, the chemical heat release rate):

[0100] (9);

[0101] In formula (9), is the enthalpy of formation of the corresponding component (i.e., the heat of combustion of the detonation products per unit mole, which can be directly found), and the unit is KJ / mol.

[0102] The total heat of combustion per unit mole of the detonation products considering the reaction rate is calculated according to the above formula , and after multiplying by the amount of substance of the detonation products in step 2, the heat of combustion of the detonation products can be obtained; then, by summing up the heats of combustion of all detonation products, S E can be obtained, that is, the sum of the heats of combustion of all detonation products.

[0103] S4. Divide the explosion process in the closed space into three stages: the detonation stage, the adiabatic expansion stage, and the afterburning reaction stage.

[0104] The method of dividing the explosion process in the closed space is mainly based on the physical characteristics of each stage. The detonation stage can be simplified according to the instantaneous detonation hypothesis, that is, it is assumed that the detonation process of the explosive is completed instantaneously, and all the TNT explosives are converted into detonation products at the moment of initiation. The explosive can be equivalent to a gas mass at high temperature and high pressure (the temperature of the gas mass exceeds the reaction temperature of the detonation products), and the size of the gas mass is the same as the initial size of the charge. During the adiabatic expansion stage, the mixing of air and detonation products is not sufficient, that is, in a restricted mixing state, and the energy released by the detonation products is very limited. It is assumed that no chemical reaction occurs during this process until the restricted mixing state ends. In the afterburning reaction stage, the reflected shock wave enhances the mixing degree of the detonation products and oxygen, and the restricted mixing state ends. In the calculation, the time when the shock wave first contacts the near-wall surface of the closed space is taken as the starting time of the afterburning reaction stage.

[0105] S5. Based on the characteristics of the detonation stage, solve the initial temperature and initial pressure of the equivalent gas mass of the explosive.

[0106] Use the thermodynamic polynomial data to define the properties of the detonation products involved in the detonation process, and fit the specific heat of each detonation product C p with a polynomial of five coefficients; R is the universal gas constant, taking 8.314 J / (mol·K).

[0107] (10);

[0108] In formula (10), are all fitting coefficients; C p is the specific heat capacity, and the unit is J / (kg·K).

[0109] Furthermore, since the explosion in the test closed space is a constant-volume explosion, the specific heat of each detonation product obtained by fitting is converted into the specific heat at constant volume by the following formula C p (unit: J / (kg·K)): C V (unit: J / (kg·K)):

[0110] (11);

[0111] In formula (11), R is the universal gas constant.

[0112] Furthermore, the specific heat at constant volume of the mixed gas is obtained by mass-weighting the components of each detonation product C vm , as shown in the following formula:

[0113] (12);

[0114] In formula (12), C vm represents the specific heat at constant volume of the mixed gas, with the unit of J / (kg·K); i is the type of detonation product in the mixed gas; y i represents the detonation product in the mixed gas i 's mass fraction; C v ( i ) represents the specific heat at constant volume of the detonation product in the mixed gas, with the unit of J / (kg·K), i and N represents the total number of components of the mixed gas.

[0115] Furthermore, the temperature of the mixed gas in the air mass is obtained through thermodynamic relations T m , and the relevant expression is as follows:

[0116] (13);

[0117] In formula (13), W is the charge mass, with the unit of g; Q is the detonation energy of the fuel-rich explosive, with the unit of MJ / kg; n is the amount of substance of the mixed gas, in mol; T 0 is the room temperature (unit: K), T m is the initial temperature of the detonation product to be solved (unit: K), and by integrating the change curve of the mixed specific heat at constant volume, the initial temperature of the detonation product is finally obtained T m .

[0118] The initial pressure p0 of the air mass is calculated by the following formula,

[0119] (14);

[0120] In formula (14), n is the amount of substance of the air mass, with the unit of mol; R is the universal gas constant; V TNT is the volume of the air mass, with the unit of m 3 .

[0121] In the present invention, for explosives with a specific composition, the proportion of detonation products can be considered relatively stable, which means that the initial temperature and pressure parameters of the high-pressure air mass are also relatively fixed under any explosive charge explosion of a specific explosive.

[0122] S6. Input the calculated relevant parameters into the combustion analysis calculation model after explosion in a closed space introducing a chemical reaction, and use the Euler solver to solve the diffusion velocity, energy release amount, and pressure of each detonation product with the change of explosion time in the adiabatic expansion stage and the post-combustion reaction stage, then determine the start and end time of the post-combustion, and calculate the energy release amount to obtain the energy release rate.

[0123] In the present invention, the specific relevant parameters input include the structural dimensions of the closed space, the initial temperature and initial pressure of the environment, the initial temperature and initial pressure of the high-pressure air mass, the types and amounts of substances generated by detonation, which are obtained through the foregoing steps.

[0124] Place the modified continuity equation, momentum equation, and energy equation in the calculation model into the Euler solver. After inputting the relevant parameters, the diffusion velocity, energy release, and pressure with the change of explosion time can be solved. Then, determine the start and end time of the post-combustion according to the diffusion velocity and pressure change of the detonation products, and obtain the energy release amount through the energy change of the detonation products; energy release amount / time = energy release rate.

[0125] In the present invention, using the Euler solver to calculate the modified continuity equation, momentum equation, and energy equation to simulate the diffusion process of the high-pressure air mass in the closed space is a prior art, which will not be elaborated here.

[0126] S7. Calculate the specific heat energy of the post-combustion effect using the start and end time and energy release rate of the post-combustion effect, modify the JWL equation of state, and solve it through the Euler-Lagrange coupling solver to simulate the internal explosion response in the closed space considering the post-combustion effect.

[0127] Modify the JWL equation of state using parameters such as the start and end times and energy release rate of the obtained afterburning effect, and combine the geometric characteristics and material properties of the explosive. Through the Euler-Lagrange coupling solver, accurately simulate the implosion response process in a closed space considering the afterburning effect.

[0128] The difference between the modified JWL equation of state and the original JWL equation of state is that the former introduces the specific heat energy of the afterburning effect λQ. The modified JWL equation of state is:

[0129] (15);

[0130] In Equation (15), λQ is the specific heat energy of the afterburning effect, with the unit of J / (kg·K), which is the energy release rate of the afterburning Q and the duration λ product. P is the pressure, with the unit of MPa; R 1 、R 2 、 A, B, ω is a constant related to the explosive material (which can be obtained by fitting experimental data); V is the volume of the closed space, with the unit of m 3 ; E is the specific heat energy, with the unit of J / (kg·K).

[0131] In the present invention, calculating the JWL equation of state using the Euler-Lagrange coupling solver and simulating the implosion response process in a closed space are prior arts and will not be elaborated here.

[0132] Embodiment

[0133] Taking a cylindrical TNT explosive with a height of 36 mm, a diameter of 25.2 mm, and a mass of 28 g as an example, illustrate the detonation process of the explosive.

[0134] S1. According to the detonation process of the explosive, obtain the detonation energy and detonation products, as well as the mass fractions and relevant thermodynamic parameters of each detonation product, including the pre-exponential factor and activation energy.

[0135] The chemical reaction occurring during the detonation process of TNT is shown in Formula 1. The types of detonation products generated during the detonation process and their corresponding mass fractions are shown in Table 1. After calculation, the total amount of substances generated by detonation is 1.2895 mol. When T 0 = 298 K (room temperature), the detonation energy per unit mass is 4.495 MJ / kg. The pre-exponential factor and activation energy Ea of the detonation products are both shown in Table 2. The pre-exponential factor and activation energy Ea can both be obtained by existing methods.

[0136] C7H5N3O6 → 2.2CO + 1.6H2O + 1.5N2 + 1.1CO2 + 0.36H2 + 0.27CH4 + 3.43C(1).

[0137] Table 1 Mass fractions of detonation products in the detonation product mixture gas

[0138]

[0139] Table 2 Thermodynamic parameters of detonation products

[0140]

[0141] S2. Based on the composition of detonation products, clarify the further chemical reactions occurring during the afterburning process of the explosive, and obtain the energy release parameters including the chemical reaction source term, including the reaction temperature, the amount of substance of detonation products released by the chemical reaction combustion of unit TNT, and the heat of combustion of detonation products per unit molar mass.

[0142] In this embodiment, as can be seen from formula (1) in S1, the components of detonation products mainly include C, CO, H2O, N2, CO2, H2, and CH4. Among them, CO, H2, CH4, and C are all combustible products, and will further release energy after being mixed with sufficient oxygen in a high-temperature environment. The specific chemical reactions occurring during the further afterburning process of detonation products and the combustion energy release parameters are shown in Table 3. The reaction temperature, the amount of substance of detonation products released by the chemical reaction combustion of unit TNT, and the heat of combustion of detonation products per unit molar mass can all be obtained through existing technologies.

[0143] Table 3 Energy parameters released by the chemical reaction combustion of detonation products

[0144]

[0145] S3. According to the energy release parameters including the chemical reaction source term obtained in S2, establish an afterburning analysis and calculation model for the explosion in a closed space by introducing the chemical reaction source term; S u is the mass source term including chemical reactions. Since the explosion process is in a closed space and there is no inflow or outflow of substances, so S u takes a value of 0; S E is the energy source term including chemical reactions, which is the total heat of combustion of each detonation product in S2; S Yi is the mass fraction source term from chemical reactions, and the specific value is the mass fraction of each mixed gas in Table 1 in step S1.

[0146] S4. Divide the explosion process in the closed space into three stages: the detonation stage, the adiabatic expansion stage, and the afterburning reaction stage.

[0147] S5. Based on the characteristics of the detonation stage, solve for the initial temperature and initial pressure of the equivalent gas mass of the explosive.

[0148] W is the charge mass, with a value of 28 g; Q is the detonation energy of the fuel-rich explosive, with a value of 4.495 MJ / kg; T m is the initial temperature of the detonation products to be solved (in K), calculated as 3366 K; the initial pressure of the high-pressure gas mass p 0 is 2016 Mpa.

[0149] S6. Input the relevant parameters obtained from the calculation into the afterburning analysis calculation model of the closed-space explosion introducing chemical reactions, use the Euler solver to solve the diffusion velocity, energy release, and pressure changes of each detonation product with the explosion time in the adiabatic expansion stage and the afterburning reaction stage, then determine the start and end times of afterburning and calculate the energy release amount to obtain the energy release rate.

[0150] This embodiment is the TNT explosion environment in a closed space. The structural characteristics of the closed space include the length, width, height dimensions, wall thickness, material properties, etc. of the closed space; the structural dimensions of the closed space are 900 mm × 400 mm × 400 mm, the initial temperature is 298 K (room temperature), and the initial pressure is 0.101 MPa (atmospheric pressure). Model the TNT explosion environment in the test closed space, and the initial fluid domain mesh division is as Figure 2 shown; the energy release change process of the detonation products obtained by solving through the Euler solver Star-CCM is as Figure 3 shown, and the amount-of-substance change process of each detonation product is as Figure 4 shown. According to step S6, the start time of the afterburning effect is 0.1 ms, the duration is 2 ms, the stable time is 2.1 ms, the energy release amount is 6.5 MJ / kg, and the calculated energy release rate is 3.25 MJ / (kg•ms).

[0151] S7. Calculate the specific heat energy of the afterburning effect using the start and end times and the energy release rate of the afterburning effect, modify the JWL equation of state, and simulate the explosion response in the closed space considering the afterburning effect through the Euler-Lagrange coupling solver.

[0152] Based on the above parameters, solve for the combustion of detonation products for a 28 g charge through the Euler-Lagrange coupling solver Autodyn. The comparison result between the pressure change history at the measurement point obtained from the numerical calculation and the test measurement data is as Figure 5As shown, it can be found that the pressure change process during the combustion process considering the detonation products is in good agreement with the test results. In particular, good correlations are demonstrated in the capture of the initial pressure peak and the oscillatory changes. This indicates that the established simulation method for the afterburning effect incorporating chemical reaction analysis can well reflect the test pressure changes and can be used for the analysis of explosion load characteristics in a closed space.

[0153] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above specific embodiments. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit and scope protected by the claims of the present invention. All of these are within the protection scope of the present invention.

Claims

1. A post-combustion effect simulation method introducing chemical reaction analysis, characterized in that, It includes the following steps: According to the detonation process of the explosive, obtain the detonation energy and detonation products, as well as the mass fractions and relevant thermodynamic parameters of each detonation product; Based on the composition of the detonation products, clarify the further chemical reactions occurring during the afterburning process of the explosive, and obtain the energy release parameters including the chemical reaction source term; Calculate and obtain the source term including chemical reactions, and establish an analytical calculation model for the afterburning of an explosion in a closed space with the introduction of the chemical reaction source term; Divide the explosion process in the closed space into three stages: the detonation stage, the adiabatic expansion stage, and the afterburning reaction stage; Based on the characteristics of the detonation stage, solve for the initial temperature and initial pressure of the equivalent gas mass of the explosive; Input the relevant parameters obtained by calculation into the analytical calculation model for the afterburning of an explosion in a closed space with the introduction of the chemical reaction source term, solve for the diffusion velocity, energy release amount, and pressure of each detonation product in the adiabatic expansion stage and the afterburning reaction stage as a function of the explosion time, then determine the start and end times of the afterburning, calculate the energy release amount, and obtain the energy release rate; Calculate the specific heat energy of the afterburning effect, modify the JWL equation of state and solve it to simulate the explosion response in a closed space considering the afterburning effect; The energy release parameters include the reaction temperature, the amount of substance of the detonation products released by the chemical reaction combustion per unit of TNT, and the heat of combustion of the detonation products per unit molar mass; The analytical calculation model for the afterburning of an explosion in a closed space with the introduction of the chemical reaction source term includes the modified reaction fluid control equation, the modified component mass fraction conservation equation, and the modified chemical kinetic energy and reaction component transport model. The three modified equations are obtained by introducing the corresponding chemical reaction source terms into the original initial equations; (1) Introduce a specified source term including chemical reactions into the initial continuity equation S u , and the obtained modified continuity equation is: ； wherein, t is time, with the unit of s; V is volume, with the unit of m 3 ; a is the area vector, with the unit of m 2 ; ρ is density, with the unit of kg / m 3 ; v is velocity, with the unit of m / s; S u is the specified source term related to mass, and its value is 0; (2) Introduce a specified source term S including chemical reactions into the initial momentum equation u , and the obtained corrected momentum equation is: ； wherein, p is the pressure, unit MPa; T is the viscous stress tensor, unit MPa; f b is the resultant body force, unit N; I is the impulse, N·s; S u is the specified source term related to mass, with a value of 0; (3) Introduce an energy source term including chemical reactions into the initial energy equation S E , and the modified energy equation is obtained as follows: ； wherein, E is the total energy per unit mass, with the unit of J; σ is the hydrodynamic stress, with the unit of MPa; q is the heat flux, with the unit of J; S E is the energy source term including chemical reactions, which is the total combustion heat of each detonation product; (4) Introduce a mass fraction source term including chemical reactions into the initial component mass fraction conservation equation S Yi , and the corrected component mass fraction conservation equation is obtained as follows: ； Among them, i is the component serial number; Y i is the component i mass fraction: ρ is the density, unit kg / m 3 ; U is the total internal energy, unit J; J i is the molecular diffusion flux, unit mol / (m²·s); μ t is the turbulent dynamic viscosity, unit Pa·s; σ t is the turbulent Schmidt number, which is a dimensionless number; S Yi is the mass fraction source term from chemical reactions, and the specific value is the mass fraction of each detonation product.

2. The post-combustion effect simulation method introducing chemical reaction analysis according to claim 1, characterized in that, S E The solution method is as follows: S E is the sum of the combustion heats of all detonation products, but it changes with the progress of the reaction; while the combustion heat of a single detonation product is the product of the combustion heat of the detonation product per unit molar mass and the number of moles of the detonation product in the reaction process. Since the chemical reaction is an incomplete reaction process, the number of moles of the reaction detonation products can be obtained according to the reaction rate; Overall reaction rate constant k It is usually determined using the Arrhenius equation, and the specific formula is: ； wherein, R is the universal gas constant, with the unit of J / (kg·K); A is the pre-exponential factor; T is the temperature, with the unit of K; β is the temperature exponent; E a is the activation energy, with the unit of J / mol; The total combustion heat of the detonation products per unit molar mass considering the reaction rate is calculated according to the following formula :[[]]END]] ； Among them, is the enthalpy of formation of the corresponding component, that is, the combustion heat of the detonation products per unit molar mass, with the unit of KJ / mol; Calculate the sum of the molar combustion heats of detonation products considering the reaction rate , after multiplying by the amount of substance of the detonation products, the combustion heat of the detonation products can be obtained; then summing up the combustion heats of all detonation products, S E , that is, the sum of the combustion heats of all detonation products.

3. The post-combustion effect simulation method for introducing chemical reaction analysis according to claim 1 or 2, characterized in that The modified JWL equation of state is: ； In the formula, λQ is the specific heat energy of the afterburning effect, with the unit of J / (kg·K), which is the product of the afterburning energy release rate and the duration; P is the pressure, with the unit of MPa; R 1, R 2, A , B , ω are all constants related to the explosive material; V is the volume of the closed space, with the unit of m 3 , E is the specific heat energy, with the unit of J / (kg·K).

4. The post-combustion effect simulation method introducing chemical reaction analysis according to claim 3, characterized in that The specific method for dividing the explosion process in the closed space into three stages is: The detonation stage is simplified according to the instantaneous detonation hypothesis, that is, it is assumed that the detonation process of the explosive is completed instantaneously, and all the explosive is converted into detonation products at the moment of initiation, and the size of the equivalent gas mass of the explosive is the same as the initial size of the charge; during the adiabatic expansion stage, the mixing of air and detonation products is insufficient, that is, in a restricted mixing state, and the energy released by the detonation products is very limited. It is assumed that no chemical reaction occurs during this process until the restricted mixing state ends; during the afterburning reaction stage, the reflected shock wave enhances the mixing degree of the detonation products and oxygen, and the restricted mixing state ends. In the calculation, the time when the shock wave first touches the near wall surface of the closed space is taken as the start time of the afterburning reaction stage.

5. The post-combustion effect simulation method for introducing chemical reaction analysis according to claim 3, characterized in that The calculation method for the initial temperature of the equivalent gas mass of the explosive is: Define the properties of detonation products involved in the detonation process using thermodynamic polynomial data, and fit the specific heat of each detonation product C p with a polynomial of five coefficients; ； In the formula are all fitting coefficients; C p is the specific heat capacity, with the unit of J / (kg·K); R is the universal gas constant, taking 8.314 J / (mol·K); Convert the specific heat of each detonation product obtained by fitting C p to the specific heat at constant volume C V : ； The specific heat at constant volume of the mixed gas is obtained by mass-weighting each detonation product component. C vm : ； Among them, C vm represents the specific heat at constant volume of the mixed gas, with the unit of J / (kg·K); i is the type of detonation products in the mixed gas; y i represents the detonation products in the mixed gas i mass fraction; C v ( i ) represents the detonation products in the mixed gas i the specific heat at constant volume has the unit of J / (kg·K); N represents the total number of components of the mixed gas; Obtain the temperature of the mixed gas in the air mass through thermodynamic relations T m : ； In the formula, W is the charge mass, with the unit of g; Q is the detonation energy of the fuel-rich explosive, with the unit of MJ / kg; n is the amount of substance of the mixed gas in mol; T 0 is the room temperature, with the unit of K; T m is the initial temperature of the detonation products to be solved, with the unit of K; By integrating the variation curve of the mixed constant-volume specific heat, the initial temperature of the detonation products is finally obtained T m 。 6. The post-combustion effect simulation method introducing chemical reaction analysis according to claim 3, characterized in that Initial pressure of explosive equivalent gas mass p 0 is calculated by the following formula: ； In the formula, n is the amount of substance of the air mass, with the unit of mol; R is the universal gas constant; V TNT is the volume of the air mass, with the unit of m 3 .

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