A method of calculating the distribution of aluminum powder with detonation products

Abstract

The application discloses a method for calculating diffusion distribution of aluminum powder along with detonation products. Firstly, the detonation products and water are grid-divided by selecting a proper space step; secondly, the grid nodes are valued after calculating the flow field pressure of the detonation products by the Taylor wave theory, and then the state equation of the detonation products and the water medium is selected; finally, the control equation of the flow field is discretized, and a calculation format of the finite difference method is constructed for calculation. Thus, a kinetic model for calculating the diffusion of the aluminum powder along with the detonation products is established, and the distribution of the aluminum powder in the underwater explosion bubble is obtained. The calculation process of the application is simple and easy to understand, the calculation speed is fast, and the application is easy to use in engineering practice.

Description

Technical field:

[0001] The present invention relates to the field of new energy exploration, and specifically establishes a kinetic model to describe the diffusion of aluminum powder with detonation products in aluminum-containing explosives, thereby obtaining a method for optimizing explosive formula and improving the working capacity of explosives. Background technology:

[0002] Aluminized explosives are a type of explosive made by adding aluminum metal powder to a single explosive. During the detonation process, the aluminum powder reacts with the gaseous detonation products under high temperature and pressure, releasing a large amount of heat, significantly increasing the explosive heat and resulting in a higher work capacity. For example, in the military, when loading anti-aircraft ammunition, aluminized explosives can increase fragment temperature and shock wave impulse, enhancing the lethality and destructive effect on enemy targets. When loading underwater ammunition, aluminized explosives maintain their energy output for a longer period of time, significantly increasing bubble energy and significantly enhancing their damage capability against ships. In civilian applications, during mining blasting operations, aluminized explosives can increase the diameter and depth of blast craters, reduce the number of blasts, and improve operational safety. In automotive airbag design, a smaller charge can be used to deploy the airbag compared to conventional explosives, providing room for optimized structural design. Therefore, the use of aluminized explosives not only saves explosives but also improves blasting efficiency. Therefore, aluminized explosives remain one of the most widely used general-purpose mixed explosives for both military and civilian use.

[0003] Current research on aluminized explosives focuses primarily on the microscopic reaction mechanisms and energy output structures of aluminum powder, such as the double-shell collapse hotspot model and the influence of aluminum powder on shock wave and bubble energy. However, limited research has examined the diffusion and distribution of aluminum powder with detonation products. Furthermore, the high temperatures and pressures associated with explosive detonation significantly complicate the study of detonation and product expansion in aluminized explosives. Overall, a comprehensive understanding of the diffusion mechanisms of aluminum powder during detonation remains insufficient. With the development of modern energy extraction, aluminized explosives are becoming a common explosive in blasting operations. The diffusion reaction of aluminum powder during detonation is crucial for understanding the interaction between aluminum powder and detonation products and for designing the formulation of aluminized explosives. Furthermore, understanding the diffusion reaction mechanisms of aluminum powder during aluminized explosive detonation can further improve the performance of explosives, thus possessing considerable research value. Summary of the invention:

[0004] The present invention aims to provide a method for calculating the diffusion and distribution characteristics of aluminum powder in aluminized explosives during the expansion of detonation products. This method, based on underwater explosions of aluminized explosives, uses computational fluid dynamics to develop a dynamic model describing the diffusion of aluminum powder with detonation products. The method has dual military and civilian applications.

[0005] The technical solution to achieve the present invention is: a method for calculating the diffusion distribution of aluminum powder with detonation products, the steps are as follows:

[0006] Step 1: Select an appropriate spatial step size to mesh the detonation products and water area.

[0007] Step 2: Calculate the detonation product flow field pressure using Taylor wave theory, discretize the flow field pressure as the initial condition for calculation, and assign values ​​to the grid nodes to obtain the initial flow field distribution of the detonation products.

[0008] Step 3: Select the state equations of the detonation products and the water medium to calculate the pressure change at the grid node at the next moment.

[0009] Step 4: Discretize the flow field control equations and construct a finite difference method calculation format to obtain the diffusion distribution of aluminum powder along with the detonation products.

[0010] Compared with the prior art, the present invention has the following significant advantages:

[0011] (1) Due to the high temperature and high pressure characteristics of detonation products, current numerical simulation software has difficulty calculating the distribution of aluminum powder in the products. However, this method can quickly and accurately calculate the distribution of aluminum powder particles in detonation products.

[0012] (2) Compared with the finite volume method commonly used in numerical simulation software, the finite difference method used in the present invention is simpler in form and more convenient for engineers to learn and apply.

[0013] (3) Compared with the existing technology, this method can calculate the reactivity of single or whole aluminum powder, which is difficult to achieve with conventional numerical simulation software. Description of the drawings:

[0014] Figure 1 Schematic diagram of grid division of the present invention.

[0015] Figure 2 Schematic diagram of the ZND model of the present invention.

[0016] Figure 3 This is a schematic diagram of the node calculation format of the present invention.

[0017] Figure 4 Schematic diagram of the calculation process of the present invention.

[0018] Figure 5 This is a curve showing the change of the aluminum powder position over time according to the present invention.

[0019] Figure 6 Schematic diagram of aluminum powder distribution of the present invention. Specific implementation method:

[0020] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0021] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in this field can implement it. When the combination of technical solutions is mutually contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0022] The following will further introduce the specific implementation methods, as well as the technical difficulties and inventive points of this invention in combination with this design example.

[0023] The method described in the present invention is based on the principles of fluid mechanics, establishes a correlation between the diffusion motion of aluminum powder and the flow field of detonation products, and solves it through numerical calculation methods to obtain the distribution of aluminum powder in detonation products and explain the interaction process between aluminum powder and detonation products.

[0024] Combine Figures 1 to 4 The method for calculating the diffusion distribution of aluminum powder with detonation products according to the present invention comprises the following steps:

[0025] Step 1: Select an appropriate spatial step size to mesh the detonation products and water area.

[0026] like Figure 1 As shown in the figure, after the explosive detonation is completed, the length of the detonation product area at the initial moment is L1. According to the selected spatial step length h, the total number of grids in the detonation product area J1 can be obtained, that is,

[0027] J1=L1 / h (1)

[0028] In order to obtain better calculation results, 20 to 50 times the length of the detonation product region is usually selected as the water medium region L2, that is,

[0029] L2=(20~50)×L1 (2)

[0030] Similarly, the total number of grids in the water medium area J2 can be obtained, that is,

[0031] J2=L2 / h (3)

[0032] The total number of grids in the two regions is J = J1 + J2, with a total of J + 1 grid nodes. The position of the jth grid node is r j, j = 1, 2, 3, ..., J + 1. After the grid division is completed, an aluminum powder particle aggregate is set in each detonation product grid, and the total mass of all aluminum powder aggregates is equal to the total mass of aluminum powder added to the explosive.

[0033] Step 2: Calculate the detonation product flow field pressure using Taylor wave theory, discretize the flow field pressure as the initial condition for calculation, and assign values ​​to the grid nodes to obtain the initial flow field distribution of the detonation products.

[0034] like Figure 2 The following is a schematic diagram of the ZND model. It can be seen that the closer to the reaction zone, the higher the detonation product pressure. Conversely, the pressure gradually decreases farther away from the reaction zone until it reaches a stable pressure. Therefore, it is also necessary to obtain the detonation product pressure distribution at the initial moment to obtain the pressure at each grid node. This invention uses Taylor wave theory to calculate the detonation product pressure distribution. The governing equation for a known one-dimensional spherically symmetric flow is as follows:

[0035]

[0036]

[0037]

[0038] Where: t is time; r is a one-dimensional coordinate; u, ρ, and p correspond to particle velocity, density, and pressure, respectively; N is 2 for one-dimensional spherically symmetric flow; c is the speed of sound, () s represents isentropic.

[0039] Let the intermediate variable x = r / t, then equations (4) and (5) become

[0040]

[0041]

[0042] Combined with formula (6), it can be rewritten as dp / dx=c 2 dρ / dx, eliminating dρ / dx in equations (7) and (8), we get

[0043]

[0044] Let variable ξ = u / x and variable Z = log e x, variable η = ξ 2 / ψ 2 , variable ψ=u / c, variable Equations (7) and (9) can be transformed into dimensionless forms:

[0045]

[0046]

[0047] From the CJ condition and the Rankine-Hugoniot relationship, it can be obtained that the detonation velocity D and the particle velocity u satisfy u / D=1-1 / μ.

[0048] Let R be the location of the detonation wave, then R = Dt. Combined with x = r / t, we can get

[0049]

[0050] Therefore

[0051]

[0052]

[0053]

[0054]

[0055] According to the CJ condition, u+c=D, we can get

[0056]

[0057] Where: μ is the ratio of the density of the detonation products at r = R to the density of the explosive; D is the detonation velocity.

[0058] By combining equations (10) to (17), the initial flow field distribution of the detonation products can be calculated. However, the detonation product pressure calculated by this method is a continuous curve, and it should also be calculated based on the node position r j Find the corresponding pressure value p j Assign the grid nodes as initial values ​​for the calculation. For the water medium region, since the detonation products have not initially expanded, the pressure at the grid nodes in the water medium region is calculated based on the hydrostatic pressure. Additionally, the detonation product pressure to the left of the water-air interface is calculated based on the explosion pressure, while the water medium pressure to the right is calculated based on the hydrostatic pressure.

[0059] Step 3: Select the state equations of the detonation products and the water medium to calculate the pressure change at the grid node at the next moment.

[0060] In order to obtain the pressure of each grid node at the next moment (i.e., moment n+1) The equation of state for the detonation products and the water medium also needs to be determined. The detonation of aluminum-containing explosives involves multiple complex non-equilibrium physical and chemical processes, mainly including: the thermal effect of the aluminum powder combustion reaction, the interaction between the aluminum powder and the detonation products, such as the oxygen transport process on the aluminum powder surface, the two-phase flow of aluminum powder and detonation products, and the resulting bath vortex evolution, turbulent transition, mass and heat transport, etc. Therefore, the equation of state used in the simulation often needs to be simplified to some extent for certain key points in order to be usable. Therefore, the JWL equation with Miller expansion terms is selected to simulate the state changes of the detonation products, and its form is as follows:

[0061]

[0062] in

[0063]

[0064]

[0065] Where: A, B, R1, R2, ω are constant terms; p represents pressure; E is mainly related to the energy released by the ideal components in the explosive. In addition, for aluminized explosives, the combustion energy released by a small amount of aluminum powder also contributes to E; Q is the specific internal energy released by the combustion of aluminum powder; V is the specific energy; λ is the reactivity of aluminum powder; η1 is the mass fraction of aluminum powder; ρ0 is the initial density of the aluminized explosive; M is the molar mass; ΔH is the heat released by aluminum powder; t is the reaction time, and m, g, and a are all constants related to the characteristics of aluminum powder.

[0066] Generally, the heat released by aluminum powder, ΔH, is related to the oxygen balance of the explosive. When the explosive is in a positive oxygen balance, the aluminum powder mainly reacts with the detonation products as follows:

[0067] Al(s)+0.75O2→0.5Al2O3(s),ΔH=-834.9kJ / mol

[0068] Al(s)+1.5CO2→0.5Al2O3(s)+1.5CO,ΔH=-410.4kJ / mol

[0069] When the explosive is in zero oxygen or negative oxygen balance, the aluminum powder mainly reacts with the detonation products as follows:

[0070] Al(s)+1.5H2O(g)→0.5Al2O3(s)+1.5H2, ΔH=-472.2kJ / mol

[0071] Al(s)+1.5CO→0.5Al2O3(s)+1.5C(s), ΔH=-669.2kJ / mol

[0072] It can be seen that when one mole of aluminum reacts, the ideal maximum heat release is 834.9 kJ and the minimum is 410.4 kJ, but in reality the heat release should be somewhere in between. To minimize the differences in heat release between different types of aluminum-containing explosives, the average value of 622.65 kJ is used as the value of ΔH for the heat release of aluminum powder.

[0073] During an underwater explosion, the high-temperature and high-pressure detonation products will expand violently, causing the water to be in a highly compressed state. The following state equation is usually used to describe the thermodynamic state of such substances:

[0074]

[0075] Where: f1, f2, f3, f4 are state variables, which are all polynomial functions of internal energy E obtained by fitting experimental data; p is pressure; v is specific volume.

[0076] Step 4: Discretize the flow field control equations and construct a finite difference method calculation format to obtain the diffusion distribution of aluminum powder along with the detonation products.

[0077] After determining the grid division, the initial value of the grid node pressure, and the state equation of the detonation products and the water medium, they can be substituted into the calculation format for solution. In order to solve the underwater explosion problem of aluminum-containing explosives, the q method is used for calculation. The q method is a type of finite difference method, and the meaning of q is the artificial viscosity term. The corresponding 4-node calculation unit of this method is as follows Figure 3 As shown in (4), where n = 1, 2, 3, ..., j = 1, 2, 3, ..., n represents the time index number, j represents the spatial index number, and represents the logical grid rather than the actual calculation grid. The governing equations for one-dimensional spherically symmetric flow are shown in Equations (4) to (6). After discretization, the calculation format is as follows:

[0078]

[0079]

[0080]

[0081] (ΔM) j+1 / 2 =M j+1 -M j (25)

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] However, in the past, when this method was used to study underwater explosions, it was used to deal with the explosion of ideal explosives (without aluminum powder added). This method is not applicable to underwater explosions of aluminum-containing explosives. Therefore, the present invention improves the calculation format of this method. First, in terms of the flow field pressure calculation P, the pressure p generated by the energy released by the aluminum powder is added to the pressure p generated by the detonation products. l , transforming formula (24) into the following form:

[0088]

[0089] Secondly, considering that aluminum powder will react in the detonation products, the mass of aluminum powder M l for:

[0090]

[0091] Finally, the aluminum powder particle velocity u is added to the calculation cycle l and displacement r l The solution is:

[0092]

[0093]

[0094]

[0095] Where: t is time, P is total pressure; p is the pressure generated by the detonation products; Δt is the time interval; M is mass, ΔM is the mass increment; A is the surface area, A(r) represents the surface area at coordinate r; λ is the reactivity of aluminum powder; u and r are the node velocity and coordinate; v is the specific volume; q is the artificial viscosity term; c max is the maximum sound speed in detonation products and water; K1, K2, and K3 are all artificial viscosity coefficients. Among them, K1 is 2.5 regardless of detonation products or water, while K2 is 0.3 in detonation products and 0.5 in water, and K3 is 1 in detonation products and (R0 / R) in water. 1 / 2 , R0 is the initial radius of detonation products.

[0096] By combining equations (22) to (35), we can calculate the diffusion distribution of aluminum powder along with the detonation products.

[0097] Example 1: Calculation of the diffusion distribution of aluminum powder in detonation products of aluminum-containing explosives:

[0098] The density of the aluminum explosive used in the calculation is 1.749 g / cm 3 , size is The sphere has an aluminum powder content of 30%. The calculation results are as follows: Figure 5 As shown in the figure, 100, 200, and 300 are the numbers of the aluminum powder particles, representing the number of aluminum powder particles. It can be seen that the aluminum powder particles gradually move toward the bubble boundary as the detonation products expand, and finally appear as shown in the figure. Figure 6 As shown in the phenomenon, aluminum powder will gather at the bubble boundary until it is completely burned. The energy generated is used to maintain the speed of the bubble wall and enhance the work capacity of the subsequent expansion process.

Claims

1. A method for calculating the diffusion distribution of aluminum powder with detonation products, characterized in that: Here are the steps: Step 1: Select an appropriate spatial step size and mesh the detonation products and water area as follows: When the explosive detonates, the length of the detonation product region at the initial moment is L1. According to the selected spatial step length h, the total number of grids in the detonation product region J1 is obtained, that is, J1=L1 / h (1) The water medium area L2 is: L2=(20~50)×L1 (2) Similarly, the total number of grids in the water medium area J2 is as follows: J2=L2 / h (3) The total number of grids in the two regions is J = J1 + J2, with a total of J + 1 grid nodes. The position of the jth grid node is r j ,j=1,2,3,…,J+1; After the grid division is completed, an aluminum powder particle aggregate is set in each detonation product grid, and the total mass of all aluminum powder aggregates is equal to the total mass of aluminum powder added to the explosive; Step 2: Calculate the detonation product flow field pressure using Taylor wave theory. Discretize the flow field pressure as the initial condition for calculation and assign values ​​to the grid nodes to obtain the initial flow field distribution of the detonation products. Step 3: Select the state equations of the detonation products and the water medium to calculate the pressure change at the grid node at the next moment; Step 4: Discretize the flow field control equations and construct a finite difference method calculation format to obtain the diffusion distribution of aluminum powder along with the detonation products.

2. The method for calculating the diffusion distribution of aluminum powder with detonation products according to claim 1, characterized in that: In step 2, the detonation product flow field pressure is calculated using Taylor wave theory. The flow field pressure is discretized as the initial condition for the calculation, and values ​​are assigned to the grid nodes to obtain the initial flow field distribution of the detonation products, as follows: Taylor wave theory is used to calculate the pressure distribution of detonation products. The governing equation of the one-dimensional spherically symmetric flow is as follows: Where: t is time; r is one-dimensional coordinate; u, ρ, and p correspond to particle velocity, density, and pressure, respectively; for one-dimensional spherically symmetric flow, N=2; c is the speed of sound, () s represents isentropic; Let the intermediate variable x = r / t, then equations (4) and (5) become Combined with formula (6), it can be rewritten as dp / dx=c 2 dρ / dx, eliminating dρ / dx in equations (7) and (8), we get Let variable ξ = u / x and variable Z = log e x, variable η = ξ 2 / ψ 2 , variable ψ=u / c, variable Equations (7) and (9) can be transformed into dimensionless forms: From the CJ condition and the Rankine-Hugoniot relationship, we can get the detonation velocity D and the particle velocity u satisfying u / D=1-1 / μ; Let R be the location of the detonation wave, then R = Dt; Combining x=r / t, we get Therefore According to the CJ condition, u+c=D, so we get Where: μ is the ratio of the density of the detonation products at r = R to the density of the explosive; D is the detonation velocity; By combining equations (10) to (17), the initial flow field distribution of detonation products is calculated.

3. The method for calculating the diffusion distribution of aluminum powder with detonation products according to claim 2, characterized in that: In step 3, the state equations of the detonation products and the water medium are selected to calculate the pressure change of the grid node at the next moment, as follows: The JWL equation with Miller expansion term is selected to simulate the state change of detonation products, which is as follows: in Where: A, B, R1, R2, ω are constant terms; p represents pressure; E is mainly related to the energy released by the ideal components in the explosive, Q is the specific internal energy released by the combustion of aluminum powder; V is the specific energy; λ is the reactivity of aluminum powder; η1 is the mass fraction of aluminum powder; ρ0 is the initial density of the aluminum-containing explosive; M is the molar mass; ΔH is the heat released by aluminum powder; t is the reaction time, and m, g, and a are all constants related to the characteristics of aluminum powder. During an underwater explosion, the high-temperature and high-pressure detonation products will expand violently, causing the water to be in a highly compressed state. The thermodynamic state of such substances is described using the following state equation: Where: f1, f2, f3, f4 are state variables, p is pressure; v is specific volume.

4. The method for calculating the diffusion distribution of aluminum powder with detonation products according to claim 3, characterized in that: In step 4, the flow field control equation is discretized and a finite difference method calculation format is constructed to calculate the diffusion distribution of aluminum powder along with the detonation products, as follows: In terms of flow field pressure calculation P, the pressure p generated by the energy released by the aluminum powder is added to the pressure p generated by the detonation products. l , transforming formula (24) into the following form: Secondly, considering that aluminum powder will react in the detonation products, the mass of aluminum powder M l for: Finally, the aluminum powder particle velocity u is added to the calculation cycle l and displacement r l The solution is: Where: t is time, P is total pressure; p is the pressure generated by the detonation products; Δt is the time interval; M is mass, ΔM is the mass increment; A is the surface area, A(r) represents the surface area at coordinate r; λ is the reactivity of aluminum powder; u and r are the node velocity and coordinate; v is the specific volume; q is the artificial viscosity term; c max is the maximum sound velocity of the detonation products and water; K1, K2, and K3 are all artificial viscosity coefficients; In order to solve the underwater explosion problem of aluminum-containing explosives, the q method is used to calculate the diffusion distribution of aluminum powder along with the detonation products.

5. The method for calculating the diffusion distribution of aluminum powder with detonation products according to claim 4, characterized in that: K1 is 2.5 in both detonation products and water, K2 is 0.3 in detonation products and 0.5 in water, and K3 is 1 in detonation products and (R0 / R) in water. 1 / 2 , R0 is the initial radius of detonation products.

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