Non-temperature-balance aluminum-containing explosive detonation parameter calculation method

Abstract

The invention relates to a non-temperature-balanced aluminum-containing explosive detonation parameter calculation method, belongs to the technical field of detonation parameter calculation, and solves the problems of complexity and inaccurate result of a calculation method in the prior art. The method comprises the following steps: supposing detonation pressure, and calculating the aluminum powder temperature based on the supposed detonation pressure; supposing the detonation temperature, and calculating the internal energy variation of the detonation product based on the supposed detonation pressure, the supposed detonation temperature and the aluminum powder temperature; based on the assumed detonation pressure, the assumed detonation temperature and the detonation product internal energy variable quantity, judging whether the assumed detonation pressure and the assumed detonation temperature meet the detonation Rayleigh-Newton relationship or not, and if not, returning to the step of calculating the detonation product internal energy variable quantity based on the assumed detonation pressure, the assumed detonation temperature and the aluminum powder temperature; if not, the detonation velocity is calculated based on the assumed detonation pressure, if the detonation velocity converges, the current assumed detonation pressure, the assumed detonation temperature and the detonation velocity are determined detonation parameters, and if not, the step of calculating the aluminum powder temperature based on the assumed detonation pressure is executed again. And rapid and accurate detonation parameter determination of the aluminum-containing explosive is realized.

Description

Technical Field

[0001] The invention relates to the technical field of detonation parameter calculation, and in particular to a method for calculating detonation parameters of non-temperature-equilibrium aluminum-containing explosives. Background Art

[0002] Detonation parameters are important performance indicators of explosives, among which detonation velocity, detonation pressure and other parameters can be easily measured through relevant experiments. However, in order to further study the detonation performance of explosives, it is necessary to further obtain information such as the composition and detonation temperature of the detonation products of explosives, but this information is difficult to obtain through experiments. In addition, the cost of testing the detonation performance of explosives is high, the experimental process is complicated, and the information obtained is limited.

[0003] CJ theory refers to the one-dimensional fluid dynamics theory of detonation waves proposed by Chapman and Jouget in the early 20th century. The physical quantities used in the state equation: pressure, temperature, volume, are all in the system of cm-g-μs-k. Considering numerical stability, energy is calculated in joules. CJ theory provides an effective way to quickly examine the detonation performance of explosives. It regards the detonation of explosives as a one-dimensional problem, combines the conservation of mass, conservation of momentum, conservation of energy and the principle of minimum free energy, and uses the state equation to solve the detonation parameters of explosives. Once the state equation is determined, it is only necessary to give the atomic composition, density and standard formation enthalpy of the explosive to calculate the parameters of the explosive such as detonation pressure, detonation velocity and detonation temperature. At present, state equations such as BKW, LJD and VLW have been widely used in engineering. They can not only obtain information that is difficult to measure experimentally, such as detonation temperature and detonation product composition, but also make predictions and guidance on experimental results, which have important practical application value.

[0004] The thermodynamic calculation program for the detonation parameters of ideal explosives is already very complete, but the thermodynamic calculation program for aluminum-containing explosives is not yet mature enough. At present, the prediction of the detonation parameters of aluminum-containing explosives depends on the introduction of reactivity into the thermodynamic program, which is unreasonable for most high-energy explosives. In addition, the reactivity required for different state equations to reproduce the detonation parameters of aluminum-containing explosives is also different. The method of introducing reactivity into the thermodynamic program cannot guide the formulation design of aluminum-containing explosives. The existing calculation methods for the detonation performance parameters of aluminum-containing explosives are complex and the results are inaccurate. Summary of the invention

[0005] In view of the above analysis, an embodiment of the present invention aims to provide a non-temperature equilibrium method for calculating the detonation parameters of aluminum-containing explosives, so as to solve the problem that the existing methods for calculating the detonation parameters of aluminum-containing explosives are complicated and the results are inaccurate.

[0006] On the one hand, an embodiment of the present invention provides a method for calculating detonation parameters of aluminum-containing explosives in a non-temperature equilibrium manner, comprising the following steps: Assuming explosion pressure, calculate the aluminum powder temperature based on the assumed explosion pressure; Assuming explosion temperature, calculating the change in internal energy of the detonation product based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature; Based on the assumed explosion pressure, assumed explosion temperature and the change in internal energy of the detonation products, determine whether the assumed explosion pressure and the assumed explosion temperature satisfy the detonation Hugonius relationship; if not, return to the assumed explosion temperature, and calculate the change in internal energy of the detonation products based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature; otherwise, calculate the detonation velocity based on the assumed explosion pressure; if the detonation velocity converges, the current assumed explosion pressure, assumed explosion temperature and detonation velocity are determined detonation parameters; otherwise, return to the assumed explosion pressure, and calculate the aluminum powder temperature based on the assumed explosion pressure.

[0007] Based on the further improvement of the above method, the aluminum powder temperature is calculated based on the assumed explosion pressure, including: Based on the impact Hugoniot relation of aluminum, the adiabatic temperature of aluminum under the assumed explosion pressure is calculated; A thermal conductivity model of aluminum is constructed based on the adiabatic temperature of aluminum; and the temperature of aluminum powder under assumed explosion pressure is calculated based on the thermal conductivity model of aluminum.

[0008] Based on the further improvement of the above method, a thermal conductivity model of aluminum is constructed based on the adiabatic temperature of aluminum; the temperature of aluminum powder under assumed explosion pressure is calculated based on the thermal conductivity model of aluminum, including: A one-dimensional spherically symmetric coordinate system is constructed with the center of the aluminum powder ball as the origin. A heat conduction equation is constructed based on the adiabatic temperature of aluminum to calculate the temperature of each node in the aluminum powder ball in the one-dimensional spherically symmetric coordinate system. The temperature of aluminum powder under assumed explosion pressure is calculated based on the temperature of each node.

[0009] Based on the further improvement of the above method, the heat conduction equation constructed is: ; Among them, T n represents the node temperature, t is the solution time, h is the radius of the sphere core, r represents the distance from the node to the origin, R Al Indicates the radius of aluminum powder, T m represents the melting point of aluminum under assumed explosion pressure, k Al represents the total thermal conductivity of aluminum under assumed explosion pressure, V Al represents the molar volume of aluminum under the assumed explosion pressure, C P represents the specific heat of aluminum under assumed explosion pressure, T Al represents the adiabatic temperature of aluminum under assumed explosion pressure.

[0010] Based on the further improvement of the above method, the following formula is used to calculate the aluminum powder temperature T under the assumed explosion pressure based on the temperature of each node: Al-S : ; Among them, TAl-S Indicates the temperature of aluminum powder, R melt represents the boundary position between liquid aluminum and solid aluminum, r is the distance from the node to the origin, Represents the temperature of the node corresponding to position r.

[0011] Based on the further improvement of the above method, the specific heat C of aluminum under assumed explosion pressure is calculated using the following formula: P : ; ; ; ; Among them, V Al represents the molar volume of aluminum under the assumed explosion pressure, represents the molar volume of aluminum at normal pressure, T Al represents the adiabatic temperature of aluminum, T0 represents the initial state temperature, represents the assumed explosion pressure P and temperature T Al The constant pressure specific heat of aluminum is the reference quantity, and β, n, and κ0 are the state equation parameters of aluminum.

[0012] Based on the further improvement of the above method, the following formula is used to calculate the radius of aluminum powder: ; Among them, R0 is the initial particle size of aluminum powder, V Al represents the molar volume of aluminum under the assumed explosion pressure, It represents the molar volume of aluminum at normal pressure.

[0013] Based on the further improvement of the above method, the boundary position between liquid aluminum and solid aluminum is obtained in the following way: If the difference between the node temperature and the melting point of aluminum under high pressure is less than the first threshold, the position of the current node is the boundary position between liquid aluminum and solid aluminum.

[0014] Based on the further improvement of the above method, the change in internal energy of the detonation product is calculated based on the assumed detonation pressure, assumed detonation temperature and aluminum powder temperature, including: Calculate the total internal energy change ΔE of aluminum according to the temperature of aluminum powder Al-T ; Calculation of the change in internal energy ΔE of gaseous detonation products based on assumed detonation pressure and assumed detonation temperature g and the change in internal energy of free carbon ΔE c ; Based on the formula Calculate the change in internal energy of the detonation products.

[0015] Based on the further improvement of the above method, judging whether the assumed explosion pressure and the assumed explosion temperature satisfy the detonation Hugoniot relationship based on the assumed explosion pressure, the assumed explosion temperature and the change in the internal energy of the detonation products includes: Determine whether the assumed explosion pressure and assumed heat preservation can make the equation If established, the assumed explosion pressure and the assumed explosion temperature satisfy the detonation rain-Gonio relationship. Otherwise, the assumed explosion pressure and the assumed explosion temperature do not satisfy the detonation rain-Gonio relationship. Wherein, P represents the assumed explosion pressure, M represents the molar mass of the explosive, V represents the total specific volume of the detonation products, V0 represents the molar volume of the explosive in the initial state, P0 represents the ambient pressure, Q represents the constant-pressure reaction heat of the explosive detonation, and E represents the change in the internal energy of the detonation products. According to the formula Calculate the total specific volume V,x of the detonation products c represents the number of moles of free carbon, x Al represents the number of moles of aluminum, represents the sum of the number of molecules of all gaseous detonation products, V Al-T represents the total molar volume of aluminum, Vc represents the molar volume of free carbon, V g Represents the molar volume of a gas.

[0016] Compared with the prior art, the present invention considers the thermodynamic state of aluminum powder separately, calculates the corresponding aluminum powder temperature according to the assumed explosion pressure, calculates the change in internal energy of the detonation product according to the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature, and judges whether the assumed explosion pressure and assumed explosion temperature are reasonable according to the detonation Hugonius relationship. If they are unreasonable, the explosion temperature can be re-assumed until the assumed explosion temperature corresponding to the current assumed explosion pressure is determined; at the same time, the corresponding detonation velocity can be calculated according to the assumed explosion pressure, and the assumed explosion pressure and assumed explosion temperature corresponding to the minimum explosion velocity are the detonation performance parameters of aluminum-containing explosives. The method of the present invention is based on non-temperature equilibrium, which not only does not require the introduction of aluminum powder reactivity, but also can more accurately predict the detonation parameters of aluminum-containing explosives, and when the explosion temperature is re-assumed, it is not necessary to recalculate the aluminum powder temperature, and the calculation is simple. It can guide the formulation design of aluminum-containing explosives, and the present invention has positive significance for the formulation design of aluminum-containing explosives.

[0017] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components; Figure 1It is a flow chart of a method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to an embodiment of the present invention; Figure 2 Schematic diagram of the calculation results of the detonation velocity of aluminum-containing explosives according to an embodiment of the present invention. DETAILED DESCRIPTION

[0019] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0020] A specific embodiment of the present invention discloses a method for calculating the detonation parameters of aluminum-containing explosives without temperature equilibrium, such as Figure 1 As shown, the following steps are included: S1, assumed explosion pressure, calculate the aluminum powder temperature based on the assumed explosion pressure; S2, assuming explosion temperature, calculating the change in internal energy of the detonation product based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature; S3. Based on the assumed explosion pressure, assumed explosion temperature and the change in internal energy of the detonation products, determine whether the assumed explosion pressure and the assumed explosion temperature satisfy the detonation Hugonius relationship. If not, return to the assumed explosion temperature and calculate the change in internal energy of the detonation products based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature. Otherwise, calculate the detonation velocity based on the assumed explosion pressure. If the detonation velocity converges, the current assumed explosion pressure, assumed explosion temperature and detonation velocity are determined detonation parameters. Otherwise, return to the assumed explosion pressure and calculate the aluminum powder temperature based on the assumed explosion pressure.

[0021] Compared with the prior art, the present invention considers the thermodynamic state of aluminum powder separately, calculates the corresponding aluminum powder temperature according to the assumed explosion pressure, calculates the change in internal energy of the detonation product according to the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature, and judges whether the assumed explosion pressure and assumed explosion temperature are reasonable according to the detonation Hugonius relationship. If they are unreasonable, the explosion temperature can be re-assumed until the assumed explosion temperature corresponding to the current assumed explosion pressure is determined; at the same time, the corresponding detonation velocity can be calculated according to the assumed explosion pressure, and the assumed explosion pressure and assumed explosion temperature corresponding to the minimum explosion velocity are the detonation performance parameters of aluminum-containing explosives. The method of the present invention is based on non-temperature equilibrium, which not only does not require the introduction of aluminum powder reactivity, but also can more accurately predict the detonation parameters of aluminum-containing explosives, and when the explosion temperature is re-assumed, it is not necessary to recalculate the aluminum powder temperature, and the calculation is simple. It can guide the formulation design of aluminum-containing explosives, and the present invention has positive significance for the formulation design of aluminum-containing explosives.

[0022] During implementation, step S1 first assumes a pressure value.

[0023] In practice, in order to realize the thermodynamic calculation of the detonation parameters of aluminum-containing explosives, a thermodynamic database, gas state equation parameters and solid state equation parameters are required. In order to make the calculation results objective and accurate, the thermodynamic database adopts the internationally public and widely used NASAGleen thermodynamic database, which is based on the constant pressure specific heat of segmented fitting and describes the reference thermodynamic state of the material under a certain temperature with 9 parameters, as shown in equations (1)-(3).

[0024] ; ; ; ; In the formula, a0~a8 are fitting parameters, R represents the universal gas constant, T represents the temperature, is the reference quantity of specific heat at constant pressure, H 0 is the enthalpy reference quantity, S 0 is the entropy reference, G 0 is the Gibbs free energy reference quantity.

[0025] Specifically, step S1 calculates the temperature of aluminum powder based on the assumed explosion pressure, including: S11. Based on the impact Hugoniot relation of aluminum, the adiabatic temperature of aluminum under the assumed explosion pressure is calculated; S12. Construct a thermal conduction model of aluminum based on the adiabatic temperature of aluminum; and calculate the temperature of aluminum powder under an assumed explosion pressure based on the thermal conduction model of aluminum.

[0026] During implementation, the present invention adopts a modified Murnaghan state equation for the detonation product aluminum, and the state equation of aluminum is shown in equation (5).

[0027] ; ; Among them, V Al represents the molar volume of aluminum, represents the molar volume of aluminum at normal pressure, T Al represents the temperature of aluminum, T0 represents the initial state temperature, β, n, and κ0 are the state equation parameters of aluminum, and P represents the detonation pressure. In implementation, T0 is taken as 298.15K.

[0028] To solve the detonation-Hugoniot relation and the principle of minimum free energy, it is necessary to solve the chemical potential and internal energy change of the substance.

[0029] The change in the internal energy of aluminum is shown in formula (7).

[0030] ; Among them, ΔG Alrepresents the aluminum Gibbs free energy offset calculated by the equation of state, which can be calculated by formula (8); ΔS Al represents the aluminum entropy offset calculated by the equation of state, which is calculated using formula (14).

[0031] ; ; ; ; ; ; ; Among them, P0 represents the ambient pressure, that is, the pressure in the initial state, ΔG Al represents the aluminum Gibbs free energy shift calculated by the equation of state, η Al represents the compression degree of aluminum under assumed explosion pressure, η Al０ Indicates the compression degree of aluminum in the initial state, ΔS Al Represents the aluminum entropy offset calculated by the equation of state.

[0032] The impact Hugoniot relation describes the effect of volume work on the internal energy of a substance under a very short adiabatic compression relationship. The impact Hugoniot relation of aluminum is shown in equations (15)-(16).

[0033] ; ; Among them, ΔE Al The change in the internal energy of aluminum is represented by represents the enthalpy of aluminum calculated by equation (2), P0 is 1 bar, For aluminum at P0 and T Al The volume below Indicates temperature as T Al The change in internal energy when the pressure changes from P0 to P can be calculated by formula (7).

[0034] Combining equations (15) and (16), we can calculate the adiabatic temperature T of aluminum under the assumed explosion pressure P. Al , which is the temperature reached by the aluminum powder before heat conduction begins.

[0035] The particle sizes of aluminum powder in aluminum-containing explosives often vary, and the spatial scale of nano-scale aluminum powder matches the temporal width of the detonation reaction zone of aluminum-containing explosives, and can absorb more heat. In order to consider the influence of the aluminum powder particle size, the present invention establishes a heat conduction model under high pressure to describe the temperature rise of aluminum powder in the detonation reaction zone.

[0036] Specifically, a thermal conductivity model of aluminum is constructed based on the adiabatic temperature of aluminum; and the temperature of aluminum powder under assumed explosion pressure is calculated based on the thermal conductivity model of aluminum, including: S121. A one-dimensional spherically symmetric coordinate system is constructed with the center of the aluminum powder ball as the origin, a heat conduction equation is constructed based on the adiabatic temperature of aluminum, and the temperature of each node in the aluminum powder ball in the one-dimensional spherically symmetric coordinate system is calculated; S122. Calculate the temperature of the aluminum powder under the assumed explosion pressure based on the temperature of each node.

[0037] Assuming that the aluminum powders do not interfere with each other during the detonation of aluminum-containing explosives, the pressure in the detonation reaction zone is constant at the detonation pressure, and the surface of the aluminum powder instantly reaches the melting point of aluminum, the overall temperature of the aluminum powder can be obtained by calculating the heat conduction of a single aluminum powder. If the aluminum powder is always spherical and the state of each part of the detonation reaction zone is the same, the heat transfer of the aluminum powder can be calculated by a one-dimensional spherically symmetric coordinate system with the center of the aluminum powder as the origin. Therefore, a one-dimensional spherically symmetric coordinate system is constructed with the center of the aluminum powder as the origin. In this coordinate system, the heat conduction equation derived by applying the above assumptions and Fourier's heat transfer law is expressed as: ; Among them, T n represents the node temperature, t is the solution time, h is the radius of the sphere core, r represents the distance from the node to the origin, R Al Indicates the radius of aluminum powder, T m represents the melting point of aluminum under assumed explosion pressure, k Al represents the total thermal conductivity of aluminum under assumed explosion pressure, V Al represents the molar volume of aluminum under the assumed explosion pressure, C P represents the specific heat of aluminum under assumed explosion pressure, T Al represents the adiabatic temperature of aluminum under assumed explosion pressure.

[0038] Under high pressure, the thermal conductivity of aluminum powder is greater than that under normal pressure, and its variation law is shown in equations (18)-(20).

[0039] ; ; ; In the formula, k ele is the electronic thermal conductivity, k ph is the phonon thermal conductivity, k Al is the total thermal conductivity, the unit of thermal conductivity is W / mK, and the unit of pressure is Mbar.

[0040] The specific heat of aluminum will also change significantly under high pressure. The constant-pressure specific heat of aluminum under high pressure can be derived from the aluminum state equation and the thermodynamic database. The constant-pressure specific heat calculation method derived from the aluminum state equation (5) combined with the basic thermodynamic relationship is shown in formula (21).

[0041] ; ; ; ; Among them, V Al represents the molar volume of aluminum under the assumed explosion pressure, represents the molar volume of aluminum at normal pressure, T Al represents the temperature of aluminum, T0 represents the initial state temperature, represents the assumed explosion pressure P and temperature T Al The constant pressure specific heat of aluminum is calculated according to formula (1), where β, n, and κ0 are the state equation parameters of aluminum.

[0042] Assume that the radius of aluminum powder under explosion pressure P adopts the following formula: ; Among them, R0 is the initial particle size of aluminum powder, V Al represents the molar volume of aluminum at the assumed explosion pressure and adiabatic temperature, It represents the molar volume of aluminum at normal pressure.

[0043] Assuming that the melting point of aluminum under the explosion pressure P can be calculated according to the following Simon melting formula: ; Among them, T m0 Indicates the normal pressure melting point, A and B are parameters. When implemented, T m0 Take 978 K, A take 7.98 GPa, and B take 0.57.

[0044] In order to solve the problem of the heat conduction equation listed in equation (17), the present invention adopts a finite difference calculation method. The present invention adopts a second-order forward difference for the spatial flux at the center of the sphere and a central difference for the spatial flux outside the center of the sphere. The time difference adopts a prediction-correction method with second-order accuracy. In this way, a one-dimensional spherical coordinate heat conduction equation finite difference format with second-order accuracy in time and space is established. When implementing, the number of nodes n is set al , then the spatial step size in the finite difference calculation is R Al / (n al -1), the time step is 10 -3 ns, and the total calculation time is 300 ns.

[0045] After obtaining the temperature of each node, the following formula is used to calculate the aluminum powder temperature T under the assumed explosion pressure based on the temperature of each node: Al-S : ; Among them, T Al-SIndicates the temperature of aluminum powder, R melt represents the boundary position between liquid aluminum and solid aluminum, r is the distance from the node to the origin, Represents the temperature of the node corresponding to position r. T Al-S That is, the equivalent temperature of solid aluminum powder. The integral is calculated using the complex Simpson formula.

[0046] During implementation, the boundary position between liquid aluminum and solid aluminum is obtained in the following manner: If the difference between the node temperature and the melting point of aluminum under high pressure is less than the first threshold, the position of the current node is the boundary position between liquid aluminum and solid aluminum. During implementation, the first threshold can be set to 1K.

[0047] After the aluminum powder temperature is calculated, it is assumed that the temperature is kept at the current assumed explosion pressure, and the change in the internal energy of the detonation product is calculated based on the assumed explosion pressure, the assumed explosion temperature and the aluminum powder temperature. Specifically, step S2 includes: S21. Calculate the total internal energy change ΔE of aluminum based on the temperature of aluminum powder Al-T ; S22. Calculate the change in internal energy ΔE of the gaseous detonation products based on the assumed explosion pressure and assumed explosion temperature g and the change in internal energy of free carbon ΔE c ; S213, based on formula Calculate the change in internal energy of the detonation products.

[0048] Specifically, the melting point of aluminum powder can be obtained from the melting point, as shown in formula (28).

[0049] ; After obtaining the melting point of aluminum powder, the overall thermodynamic parameters of aluminum powder can be calculated by the mixing law.

[0050] ; ; In the formula, ΔE Al-T ΔE is the change in the total internal energy of aluminum, used to calculate the detonation rain-Goniotropospheric relationship. Al-S (P,T Al-S ) is the pressure P and temperature T Al-S The change in internal energy of solid aluminum calculated by equation (7) is: Al-L (P,T m ) is the pressure P and temperature T m The change in internal energy of liquid aluminum calculated by equation (7) is: Al-T is the total molar volume of aluminum, V Al-S (P,T Al-S ) is the pressure P and temperature T Al-S The molar volume of solid aluminum calculated by formula (5) is:Al-L (P,T m ) is the pressure P and temperature T m The molar volume of liquid aluminum is calculated by formula (5).

[0051] It is necessary to solve the detonation parameters of aluminum-containing explosives and obtain the components of explosive detonation products. According to the state equations and chemical potentials of the aforementioned gas, free carbon, and aluminum, the components of aluminum-containing explosives can be solved. During implementation, the present invention adopts the minimum free energy principle to iteratively solve the detonation products of aluminum-containing explosives, and its format is shown in equations (31)-(35).

[0052] ; ; ; ; ; In the formula, is the number of molecules of the i-th gaseous detonation product obtained in the s-th iteration, represents the number of molecules of the i-th gaseous detonation product obtained in the s-1th iteration, represents the sum of the number of molecules of the gaseous detonation products obtained in the sth iteration, , represents the sum of the number of molecules of the gaseous detonation products obtained in the s-1th iteration, , a ik represents the number of the kth element in the i-th gaseous product, a jk represents the number of the kth element in the jth solid detonation product, a lk represents the number of the kth element in the lth detonation product, x l represents the number of molecules of the lth detonation product, represents the chemical potential of the i-th gaseous detonation product, μ j represents the chemical potential of the jth solid detonation product, is the Lagrangian operator for finding the extreme value of free energy condition under the condition of mass conservation, n ele is the number of elements in the explosive, n t is the total number of detonation products, n g is the total amount of gas, b k Refers to the content of b per mole of explosive k The kth element of the mole.

[0053] During implementation, aluminum is considered inert and therefore does not participate in the above component calculations. The solid detonation product is free carbon. For the free carbon in the detonation product, the present invention adopts a modified Murnaghan state equation, and the free carbon state equation is shown in equations (36)-(38).

[0054] ; ; ; In the formula, Vc represents the molar volume of free carbon, T represents the temperature, T0 represents the initial state temperature, and P represents the pressure. represents the molar volume of carbon in the initial state, and n, α0, α1, κ0, and T' are the state equation parameters of free carbon.

[0055] Based on the state equation of free carbon, the chemical potential of free carbon is obtained as follows: ; ; ; Where, η is the compression degree of free carbon, η ０ is the compression degree of carbon in the initial state, is the reference enthalpy of free carbon calculated by equation (2), is the free carbon reference entropy calculated by equation (3), μ c is the chemical potential of free carbon.

[0056] In order to accurately reflect the thermodynamic state of gaseous detonation products, it is necessary to use the real gas state equation to calculate the thermodynamic state of various gaseous detonation products. The present invention uses the VLW state equation to describe the gaseous detonation products. The VLW state equation refers to the Virial-Wu state equation proposed by Wu Xiong in 1985. The VLW state equation used in this paper is the improved form of Long Xinping in 1999, and its form is shown in equations (42)-(47).

[0057] ; ; ; ; ; ; In the formula, x i represents the number of molecules of the i-th gaseous detonation product, V g is the gas molar volume, P is the pressure, is the dimensionless second virial coefficient, is the dimensionless temperature, ε, k and b0 are the Lennard-Jones 6-12 potential parameters.

[0058] Based on the basic thermodynamic relations, the chemical potential expressions of the VLW state equation are written as shown in Equations (48)-(51).

[0059] ; ; ; ; In the formula, μ i represents the chemical potential of the i-th gaseous detonation product, is the reference Gibbs free energy of the ith gaseous detonation product calculated by equation (4), and P0 is the ambient pressure.

[0060] Therefore, the chemical potential of each gaseous detonation product can be calculated by equation (48).

[0061] Equations (31)-(35) form a closed set of equations, which can be solved by a linear equation solver through iterative cycles until Less than a given small amount, the component composition with the minimum free energy can be obtained During implementation, the present invention adopts the full principal element method to solve the linear equations.

[0062] After solving for the components of the explosive detonation products, the expression for the change in the internal energy of the gas is shown in equations (52)-(53).

[0063] ; ; In the formula, ΔE g is the change in internal energy of the gas.

[0064] The change in internal energy of free carbon is calculated according to formula (58): ; ; ; ; ; Among them, ΔS c is the free carbon entropy offset calculated from the equation of state, ΔE c is the change in the internal energy of free carbon.

[0065] After obtaining the change in internal energy of the gas and the change in internal energy of free carbon, the total change in internal energy of the detonation products is calculated according to formula (59).

[0066] ; After the change in internal energy of the detonation products is obtained, judging whether the assumed detonation pressure and the assumed detonation temperature satisfy the detonation Hugoniot relationship based on the assumed detonation pressure, the assumed detonation temperature and the change in internal energy of the detonation products specifically includes: Determine whether the assumed explosion pressure and the assumed temperature insulation can make equation (60) valid; if so, the assumed explosion pressure and the assumed explosion temperature satisfy the detonation-rain-Gonio relationship; otherwise, the assumed explosion pressure and the assumed explosion temperature do not satisfy the detonation-rain-Gonio relationship; ; Among them, P represents the assumed explosion pressure, M represents the molar mass of the explosive, V represents the total specific volume of the detonation products, V0 represents the molar volume of the explosive in the initial state, Q represents the constant-pressure reaction heat of the detonation of the explosive; E represents the change in the internal energy of the detonation products.

[0067] According to formula (61), the total specific volume V,x of the detonation products is calculated: c represents the number of moles of free carbon, x Al represents the number of moles of aluminum, represents the sum of the number of molecules of all gaseous detonation products, V Al-T represents the total molar volume of aluminum, Vc represents the molar volume of free carbon, V g Represents the molar volume of a gas.

[0068] ; The heat Q of a constant-pressure chemical reaction can be derived from the enthalpy change. If T Al-S is greater than 933.610 k. Assuming that the thermodynamic reference quantity of liquid aluminum minus the melting enthalpy at normal pressure can represent the thermodynamic reference quantity of solid aluminum, the constant-pressure chemical reaction enthalpy change is as shown in Eq. (62). If T Al-S Below 933.610 K, the enthalpy change of the constant-pressure chemical reaction is as shown in equation (63).

[0069] ; ; Where ΔH is the enthalpy change of a chemical reaction at constant pressure, is the standard formation enthalpy of explosive, ΔH pc is the phase change enthalpy of aluminum, x i represents the number of moles of the i-th gas component, the subscript c represents free carbon, and x i is the number of moles of free carbon, x Al The subscript Al represents the number of moles of aluminum, and the superscript 0 represents the state when the pressure is one atmosphere. represents the enthalpy of the gas detonation product in the ith gas, represents the enthalpy of free carbon, which can be calculated by formula (2): represents the enthalpy of aluminum at a specified temperature calculated by equation (2).

[0070] Under normal pressure, assuming that the ideal gas state equation holds, the constant-pressure chemical reaction heat and constant-pressure chemical reaction enthalpy change can be converted through equation (64): ; In the formula, Q is the heat of chemical reaction at constant pressure. It is different from the general sign that represents the energy change of chemical reactions. It is positive when releasing heat and negative when absorbing heat, so a minus sign is needed to maintain the correct meaning. i Originally meant to be the number of molecular changes of gas component i, but in the detonation chemical reaction of condensed explosives, the reactants have no gas component, so x i The meaning is the number of moles of the i-th gas component generated by the detonation of one mole of explosive, that is, the number of molecules of the i-th gaseous detonation product obtained according to formulas (31)-(35).

[0071] If the assumed explosion pressure and the assumed explosion temperature do not satisfy the detonation-rain-Gonio relationship, then return to step S2 to re-guess the explosion temperature, that is, to give the assumed explosion pressure again. At this time, the assumed explosion pressure remains unchanged, so the aluminum powder temperature remains unchanged. If the assumed explosion pressure and the assumed explosion temperature satisfy the detonation-rain-Gonio relationship, the corresponding detonation velocity can be calculated based on the assumed explosion pressure.

[0072] Specifically, the corresponding detonation velocity under the assumed detonation pressure P is calculated according to formula (65).

[0073] ; If the currently obtained detonation velocity converges, the currently assumed detonation pressure, assumed detonation temperature and detonation velocity are determined detonation parameters. Otherwise, return to step S1 to re-assume the detonation pressure, calculate the aluminum powder temperature based on the assumed detonation pressure, and perform iterative calculation.

[0074] During implementation, the minimum detonation velocity, i.e., the convergent detonation velocity, is solved by quadratic function interpolation iteration.

[0075] Specifically, the following method is used to determine whether the detonation velocity converges: The first three groups of hypothetical explosion pressure and explosion velocity data recorded are expressed as (P1, D1), (P2, D2), and (P3, D3); For each set of assumed explosion pressure and explosion velocity data obtained later, that is, the current assumed explosion pressure and explosion velocity (P, D), if max|D i -D|, (i=1,2,3) is less than the preset threshold, the detonation velocity converges; otherwise, the detonation velocity does not converge, and the set of detonation pressure and detonation velocity values ​​with the largest detonation velocity among (P1, D1), (P2, D2), and (P3, D3) are replaced by the current assumed detonation pressure and detonation velocity values.

[0076] Through continuous iteration until the detonation velocity converges. According to the CJ theory, the CJ detonation velocity is the minimum detonation velocity for the explosive to undergo stable detonation. Therefore, when the detonation velocity is the minimum, the corresponding detonation velocity can be considered to be the CJ detonation velocity, the pressure is the CJ detonation pressure, and the temperature is the CJ detonation temperature. That is, when the detonation velocity converges, the detonation parameters of aluminum-containing explosives, detonation pressure, detonation temperature and detonation velocity are obtained.

[0077] Through the above method, under the premise that aluminum is inert, the CJ detonation velocity can be iteratively obtained through the minimum free energy principle and the momentum conservation relationship of the detonation wave front, and the predicted value of the detonation parameters of aluminum-containing explosives can be obtained.

[0078] Figure 2 The present invention compares the calculation results of detonation velocity of RDX-based aluminum-containing explosives with different aluminum contents between the existing detonation parameter prediction program EXPLO5 and the present invention. By considering the thermodynamic state of aluminum powder in detail, the calculation results obtained by the present invention are not only more consistent with the experiment in terms of numerical value, but also can more accurately describe the influence of aluminum content on the detonation velocity of aluminum-containing explosives. The traditional detonation parameter prediction program needs to introduce reactivity to predict aluminum-containing explosives, and the reactivity needs to be calibrated through experiments, and cannot guide the formulation design of aluminum-containing explosives. The present invention considers the thermodynamic state of aluminum powder separately, based on non-temperature equilibrium, not only does not need to introduce aluminum powder reactivity, but also can more accurately predict the detonation parameters of aluminum-containing explosives, and can guide the formulation design of aluminum-containing explosives. The present invention has positive significance for the formulation design of aluminum-containing explosives.

[0079] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0080] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium, characterized in that: The following steps are involved: Assuming explosion pressure, calculate the aluminum powder temperature based on the assumed explosion pressure; Assuming explosion temperature, calculating the change in internal energy of the detonation product based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature; Based on the assumed explosion pressure, assumed explosion temperature and the change in internal energy of the detonation products, determine whether the assumed explosion pressure and the assumed explosion temperature satisfy the detonation Hugonius relationship; if not, return to the assumed explosion temperature, and calculate the change in internal energy of the detonation products based on the assumed explosion pressure, assumed explosion temperature and aluminum powder temperature; otherwise, calculate the detonation velocity based on the assumed explosion pressure; if the detonation velocity converges, the current assumed explosion pressure, assumed explosion temperature and detonation velocity are determined detonation parameters; otherwise, return to the assumed explosion pressure, and calculate the aluminum powder temperature based on the assumed explosion pressure.

2. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 1, characterized in that: Calculate the aluminum powder temperature based on the assumed explosion pressure, including: Based on the impact Hugoniot relation of aluminum, the adiabatic temperature of aluminum under the assumed explosion pressure is calculated; A thermal conductivity model of aluminum is constructed based on the adiabatic temperature of aluminum; and the temperature of aluminum powder under assumed explosion pressure is calculated based on the thermal conductivity model of aluminum.

3. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 2, characterized in that: Construct a heat conduction model for aluminum based on its adiabatic temperature; The aluminum powder temperature under assumed explosion pressure is calculated based on the aluminum heat conduction model, including: A one-dimensional spherically symmetric coordinate system is constructed with the center of the aluminum powder ball as the origin. A heat conduction equation is constructed based on the adiabatic temperature of aluminum to calculate the temperature of each node in the aluminum powder ball in the one-dimensional spherically symmetric coordinate system. The temperature of aluminum powder under assumed explosion pressure is calculated based on the temperature of each node.

4. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 3, characterized in that: The heat conduction equation constructed is: ； Among them, T n represents the node temperature, t is the solution time, h is the radius of the sphere core, r represents the distance from the node to the origin, R Al Indicates the radius of aluminum powder, T m represents the melting point of aluminum under assumed explosion pressure, k Al represents the total thermal conductivity of aluminum under assumed explosion pressure, V Al represents the molar volume of aluminum under the assumed explosion pressure, C P represents the specific heat of aluminum under assumed explosion pressure, T Al represents the adiabatic temperature of aluminum under assumed explosion pressure.

5. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 3, characterized in that: The aluminum powder temperature T under the assumed explosion pressure is calculated based on the temperature of each node using the following formula: Al-S : ； Among them, T Al-S Indicates the temperature of aluminum powder, R melt represents the boundary position between liquid aluminum and solid aluminum, r is the distance from the node to the origin, Represents the temperature of the node corresponding to position r.

6. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 4, characterized in that: The specific heat C of aluminum under assumed explosion pressure is calculated using the following formula: P : ； ； ； ； Among them, V Al represents the molar volume of aluminum under the assumed explosion pressure, represents the molar volume of aluminum at normal pressure, T Al represents the temperature of aluminum, T0 represents the initial state temperature, represents the assumed explosion pressure P and temperature T Al The constant pressure specific heat of aluminum is the reference quantity, and β, n, and κ0 are the state equation parameters of aluminum.

7. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 4, characterized in that: The radius of aluminum powder is calculated using the following formula: ； Among them, R0 is the initial particle size of aluminum powder, V Al represents the molar volume of aluminum under the assumed explosion pressure, It represents the molar volume of aluminum at normal pressure.

8. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 5, characterized in that: The boundary position between liquid aluminum and solid aluminum is obtained in the following way: If the difference between the node temperature and the melting point of aluminum under high pressure is less than the first threshold, the position of the current node is the boundary position between liquid aluminum and solid aluminum.

9. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 1, characterized in that: The change in internal energy of the detonation product is calculated based on the assumed detonation pressure, assumed detonation temperature and aluminum powder temperature, including: Calculate the total internal energy change ΔE of aluminum according to the temperature of aluminum powder Al-T ; Calculation of the change in internal energy ΔE of gaseous detonation products based on assumed detonation pressure and assumed detonation temperature g and the change in internal energy of free carbon ΔE c ; Based on the formula Calculate the change in internal energy of the detonation products.

10. The method for calculating detonation parameters of aluminum-containing explosives without temperature equilibrium according to claim 1, characterized in that: Judging whether the assumed explosion pressure and the assumed explosion temperature satisfy the detonation Hugoniot relationship based on the assumed explosion pressure, the assumed explosion temperature and the change in the internal energy of the detonation products comprises: Determine whether the assumed explosion pressure and assumed heat preservation can make the equation If established, the assumed explosion pressure and the assumed explosion temperature satisfy the detonation rain-Gonio relationship. Otherwise, the assumed explosion pressure and the assumed explosion temperature do not satisfy the detonation rain-Gonio relationship. Wherein, P represents the assumed explosion pressure, M represents the molar mass of the explosive, V represents the total specific volume of the detonation products, V0 represents the molar volume of the explosive in the initial state, P0 represents the ambient pressure, Q represents the constant-pressure reaction heat of the explosive detonation, and E represents the change in the internal energy of the detonation products. According to the formula Calculate the total specific volume V,x of the detonation products c represents the number of moles of free carbon, x Al represents the number of moles of aluminum, represents the sum of the number of molecules of all gaseous detonation products, V Al-T represents the total molar volume of aluminum, Vc represents the molar volume of free carbon, V g Represents the molar volume of a gas.

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