A Method for Constructing a Model of the Detonation-Driven Velocity of a Composite Charge Metal Plate

Abstract

The present invention relates to a method for constructing a model of the detonation-driven velocity of a composite charge, belonging to the technical field of composite charge overpressure detonation, and solves the problem in the prior art that the driving law of the composite charge structure is incomplete due to the lack of theoretical calculation and analysis of the parameters for driving the metal plate by the composite charge. The method includes determining each movement time period of the metal plate based on each detonation process stage during the detonation process of the composite charge and the initial parameters of the composite charge; obtaining the internal flow field parameters and detonation incident angle of the composite charge during each movement time period based on the detonation process stage in which the metal plate is located during each movement time period; obtaining the velocity of the metal plate during each movement time period based on the internal flow field parameters of the composite charge during each movement time period, the initial parameters of the composite charge, and the detonation incident angle, and completing the construction of the model of the metal plate velocity. The determination of the detonation-driven velocity of the metal plate by the composite charge overpressure is realized, providing technical support for the research and development of the design of composite high-energy charge structures, the enhancement of detonation wave superposition driving, etc.

Description

Technical Field

[0001] The present invention relates to the technical field of overpressure detonation of composite charges, and particularly to a method for constructing a model of the velocity of a metal plate driven by overpressure detonation of a composite charge. Background Art

[0002] In recent years, under the guidance of the concept of asymmetric warfare, in urban warfare or peacekeeping operations, it is not desirable for the main charge of the warhead to undergo complete detonation. One reason is to reduce collateral damage, and the other is to avoid the escalation of conflicts. Therefore, a damage-power controllable composite warhead that can improve combat adaptability and flexibility while reducing the logistical burden has become one of the current research hotspots. The composite charge warhead can select the damage effect of the weapon according to different target types, thereby improving the battlefield flexibility of the weapon and realizing the energy output of the composite charge in the controllable warhead. With the wide application of new composite structure warheads, how to accurately describe the dynamic evolution of the internal flow field symmetric collision zone of the composite charge and related issues such as the work capacity of the composite charge have become the difficulties and hotspots in the field of engineering applications.

[0003] Currently, in terms of calculating the flow field parameters after the detonation collisions inside the composite charge, the domestic and foreign research focuses on two aspects: experiments and simulations. Among them, the theoretical research is mainly based on the isentropic theory of explosives under ideal conditions to characterize the dynamic mechanical and physical parameters of the products in the detonation reaction collision zone of the explosives. However, due to the strong shock effects such as different charge structures and initiation methods of the explosives, the convergence and superposition of detonation waves are caused, resulting in the explosives exceeding their detonation critical conditions, causing the state of the detonation products to deviate from the main isentropic line, and the flow field parameters such as pressure and velocity are much higher than the normal CJ detonation state, thus generating the overpressure detonation phenomenon, making the equation of state used to describe the state of ideal explosive detonation products no longer applicable. And there is very little theoretical research on explosives under overpressure detonation conditions, especially the lack of theoretical calculation and analysis of the parameters for driving a metal plate (also called a flyer plate) by a new composite charge. The driving law of the composite charge structure is not comprehensive enough to further analyze the axial driving and work capacity of the composite charge. Summary of the Invention

[0004] In view of the above analysis, the embodiments of the present invention aim to provide a theoretical calculation method for the velocity of a metal plate driven by overpressure detonation of a composite charge to solve the problem that the driving law of the composite charge structure is not comprehensive enough due to the lack of theoretical calculation and analysis of the parameters for driving a metal plate by a composite charge in the prior art.

[0005] The embodiments of the present invention provide a method for constructing a model of the velocity of a metal plate driven by overpressure detonation of a composite charge, including the following steps:

[0006] Determine the motion time periods of the metal plate based on the stages of the detonation process in the composite charge and the initial parameters of the composite charge; wherein, taking the detonation initiation moment of the composite charge as the initial moment, the initial parameters include the length of the composite charge, the diameters of the inner and outer charges, and the detonation velocities of the inner and outer charges.

[0007] Based on the stages of the detonation process in which the metal plate is in each motion time period, obtain the internal flow field parameters and the detonation incident angle of the composite charge in each motion time period.

[0008] Based on the internal flow field parameters of the composite charge in each motion time period, the initial parameters of the composite charge, and the detonation incident angle, obtain the velocity expression of the metal plate in each motion time period, and complete the model construction of the metal plate velocity.

[0009] Compared with the prior art, the present invention can at least achieve one of the following beneficial effects:

[0010] A method for constructing a model of the velocity of a metal plate driven by overpressure detonation of a composite charge provided by the present invention

[0011] 1. Construct the motion characteristic law of the metal plate at any moment in the overpressure detonation of the composite charge, and the velocity of the metal plate at any moment can be obtained. By describing the driving law of the composite charge structure through the motion of the metal plate, the work performance of the composite charge can be effectively evaluated, which can provide technical support for the in-depth study of the energy release rate of the composite charge and the structural optimization design, and can also provide technical support for the research and development of composite high-energy charge structure design technology, detonation wave superposition driving enhancement technology, new generation directional fragmentation warhead, etc.;

[0012] 2. Considering the interaction between the oblique shock wave and the rarefaction wave generated inside the composite charge during the detonation process, a theoretical calculation method for the internal flow field parameters of the composite charge is established. By partitioning and deriving the spatio-temporal relationship of physical parameters such as pressure inside the detonation products of the composite charge over time, the internal parameters after the overpressure detonation of the explosive can be accurately analyzed, and the theoretical closure of the interaction parameters of the detonation waves of the condensed explosive is realized. This method has wide applicability, high accuracy, and strong stability, and can be used to characterize the theoretical calculation model of the explosive under overpressure detonation, laying a foundation for studying the internal detonation reaction mechanism, driving damage model, and energy output response law of the composite charge.

[0013] In the present invention, the above technical solutions can also be combined with each other to achieve more preferred combination schemes. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can be made obvious from the description, or understood by implementing the present invention. The objectives and other advantages of the present invention can be realized and obtained through the content specifically pointed out in the description and the drawings. Description of the Drawings

[0014] The accompanying drawings are only for the purpose of showing specific embodiments and are not considered to be a limitation of the present invention. Throughout the drawings, the same reference signs denote the same components;

[0015] Figure 1 It is a schematic flow diagram of a method for constructing a model of the detonation-driven metal plate velocity of a composite charge provided by an embodiment of the present invention;

[0016] Figure 2 It is a schematic diagram of the detonation wave process of a composite charge provided by an embodiment of the present invention;

[0017] Figure 3 It is a schematic diagram of the detonation wave structure of a composite charge provided by an embodiment of the present invention;

[0018] Figure 4 It is a schematic diagram of the flow near the collision point of a regular reflection detonation wave provided by an embodiment of the present invention;

[0019] Figure 5 It is a schematic diagram of the flow of the medium before and after an oblique shock wave provided by an embodiment of the present invention;

[0020] Figure 6 It is a schematic diagram of the polar curve of pressure and turning angle provided by an embodiment of the present invention;

[0021] Figure 7 It is a schematic diagram for solving the polar curve of a shock wave regular oblique collision provided by an embodiment of the present invention;

[0022] Figure 8 It is the polar curve of pressure and turning angle of the reflected wave at different incident angles provided by an embodiment of the present invention;

[0023] Figure 9 It is a schematic diagram of the distribution of flow field parameters near the collision point of an irregular oblique reflection detonation wave provided by an embodiment of the present invention;

[0024] Figure 10 It is a schematic diagram of the wave system development within a certain time interval after the collision of an irregular oblique reflection detonation wave provided by an embodiment of the present invention. Specific Embodiments

[0025] The following will specifically describe the preferred embodiments of the present invention with reference to the accompanying drawings. The accompanying drawings form a part of this application and are used together with the embodiments of the present invention to explain the principles of the present invention, and are not used to limit the scope of the present invention.

[0026] A specific embodiment of the present invention discloses a method for constructing a model of the detonation-driven metal plate velocity of a composite charge, as Figure 1 shown, including the following steps:

[0027] S1. Determine the movement time periods of the metal plate based on the stages of the detonation propagation process of the composite charge and the initial parameters of the composite charge; wherein, taking the detonation initiation moment of the composite charge as the initial moment, the initial parameters include the length of the composite charge, the diameters of the inner and outer charges, and the detonation velocities of the inner and outer charges.

[0028] Specifically, as Figure 2 shown in the detonation wave process of the composite charge, in this embodiment, first determine the conditions for the composite charge explosive to undergo overpressure detonation, that is, determine the detonation incident angle when Mach reflection occurs. According to the interaction relationship between the reflection angle and the incident angle, divide the reaction process of the composite charge into regular oblique reflection and irregular oblique reflection. Thus, the stages of the detonation process include the regular oblique reflection process and the irregular oblique reflection process. When the detonation of the composite charge develops to a certain stage, the detonation waves will not collide on the axis of the charge, and the detonation waves propagate as stable plane waves. At this time, the detonation process stage is in the stable detonation propagation process, and at this time the metal plate follows the one-dimensional detonation driving theory. Thus, the movement process of the metal plate is divided.

[0029] During implementation, the stages of the detonation process include the regular oblique reflection process, the irregular oblique reflection process, and the stable detonation propagation process; wherein,

[0030] The movement time period of the metal plate corresponding to the regular oblique reflection process is ;

[0031] The movement time period of the metal plate corresponding to the irregular oblique reflection process is ;

[0032] The movement time period of the metal plate corresponding to the stable detonation propagation process is ;

[0033] Wherein, represents the moment of the metal plate movement, represents the moment of the metal plate movement corresponding to when the detonation incident angle is the Mach critical angle, represents the moment of the metal plate movement corresponding to when the detonation products of the composite charge enter the stable plane wave propagation.

[0034] During specific implementation, the moment of the metal plate movement corresponding to when the detonation incident angle is the Mach critical angle is expressed as:

[0035] ,

[0036] The moment of the metal plate movement corresponding to when the detonation products of the composite charge enter the stable plane wave propagation is expressed as:

[0037] ,

[0038] Among them, ;

[0039] In the formula, and respectively represent the diameters of the outer charge and the inner charge of the composite charge, and respectively represent the detonation velocities of the outer charge and the inner charge of the composite charge, represents the length of the composite charge.

[0040] It should be noted that when the detonation incident angle satisfies , the detonation process of the composite charge belongs to the regular oblique reflection process; when the detonation incident angle satisfies , the detonation process of the composite charge belongs to the non - regular oblique reflection process; among them, represents the Mach critical angle. The detonation incident angle of means that the detonation wave is perpendicular to the interface. In this case, there is no reflection, but the detonation wave directly passes through the interface and continues to propagate along the original path; the detonation incident angle of means that the detonation wave is parallel to the interface. In this case, the detonation wave does not enter the other medium of the interface, but propagates along the surface of the interface. Therefore, in this embodiment, for the composite charge structure, there is a difference in detonation velocity between the inner and outer layers. is the moment when the composite charge just starts to detonate, and the detonation wave has not yet propagated to the metal plate, that is, the velocity of the metal plate is 0 at this time.

[0041] S2. Based on the detonation process stages of each movement time period of the metal plate, obtain the internal flow field parameters and detonation incident angles of the composite charge in each movement time period;

[0042] Specifically, based on the physical parameter expressions of the composite charge in each partition, obtain the variation relationship of each physical parameter with the incident angle during the process from the start of detonation to the convergence of the detonation wave of the composite charge; among them, based on the state equation, theoretically calculate the flow field parameters in the regular oblique reflection process of the composite charge, and then invert and calibrate the slow - varying coefficient based on the Whitham method to obtain the functional relationship between the Mach reflection pressure and the Mach reflection critical angle, and conduct the theoretical calculation of the pressure when non - regular oblique reflection occurs inside the composite charge model. In the regular oblique reflection process and the non - regular oblique reflection process, the calculation of the flow field parameters is closely related to the detonation incident angle. Combining the characteristics of the composite charge itself, the detonation incident angles at each moment in the regular oblique reflection process and the non - regular oblique reflection process are given as follows:

[0043] During implementation, when , the detonation incident angle satisfies the following formula:

[0044] ,

[0045] In the formula, represents the detonation incident angle at time .

[0046] It can be understood that when , there is no superposition of detonation waves, and the inner and outer charges of the composite charge drive the metal plate at the same detonation velocity. At this time, the metal plate follows the one-dimensional detonation drive theory.

[0047] S3. Based on the internal flow field parameters of the composite charge, the initial parameters of the composite charge, and the detonation incident angle in each motion time period, the velocity expression of the metal plate in each motion time period is obtained, and the model construction of the metal plate velocity is completed.

[0048] Specifically, by using the instantaneous detonation theory and the one-dimensional scattering theory, a model based on the instantaneous driving velocity of the metal plate by the composite charge is established, that is, the motion characteristic law of the metal flat plate at any time is constructed, and the driving work performance of the composite charge can be evaluated.

[0049] During implementation, when the motion time of the metal plate is , the internal detonation process stage of the composite charge is in the regular oblique reflection process. The regular oblique reflection process includes the undetonated explosive area, the detonation product area, and the post-reflected shock wave state area. In this motion time period, the metal plate moves at a velocity . The velocity of the metal plate is expressed as:

[0050] ,

[0051] In the formula, represents the detonation product pressure in the post-reflected shock wave state area at time , is the cross-sectional area of the metal plate, represents the mass of the metal plate.

[0052] During specific implementation, the detonation product pressure in the post-reflected shock wave state area is expressed as:

[0053] ,

[0054] In the formula, represents the specific volume of the detonation products in the CJ state of the explosive, represents the detonation pressure in the CJ state of the explosive, represents the flow group velocity in the detonation product area, , respectively represent the density and specific volume of the detonation products in the post-reflected shock wave state area, Denotes the flow mass deflection angle in the post-shock state region of the reflected shock wave.

[0055] Specifically, the flow mass velocity in the detonation product region Is expressed as:

[0056] ,

[0057] In the formula, Denotes the detonation velocity of the detonation products in the CJ state of the explosive, Denotes the detonation incident angle, Denotes the cotangent function.

[0058] Specifically, the density of the detonation products in the post-shock state region of the reflected shock wave Is expressed as:

[0059] ,

[0060] Specifically, the flow mass deflection angle in the post-shock state region of the reflected shock wave Is expressed as:

[0061] ,

[0062] Specifically, the specific volume of the detonation products in the post-shock state region of the reflected shock wave Is obtained by simultaneously solving the following formula:

[0063] ,

[0064] In the formula, Denotes the charge density of the composite charge, , , , , , , Are respectively The constant coefficients of the equation of state, Denotes the polytropic exponent, Denotes the specific internal energy of the detonation products in the CJ state of the explosive.

[0065] More specifically, , where Denotes the initial specific volume of the composite charge.

[0066] More specifically, the polytropic exponent Is expressed as:

[0067] ,

[0068] Where

[0069] ,

[0070] In the formula, represents the total adiabatic index, represents the total number of components in the composite charge, represents the amount of substance of the th component in the composite charge, represents the mass fraction of the th component in the composite charge, represents the molar mass of the th component in the composite charge, represents the adiabatic index of the th component in the composite charge. It can be understood that the polytropic index obtained in this way is more accurate.

[0071] It should be noted that the velocity of the metal plate in this motion time period is obtained through the following analysis:

[0072] When the motion time of the metal plate is, due to the different degrees of shock compression of the high and low detonation waves in the inner and outer layers of the composite charge and the newly formed detonation wave, the pressure and particle velocity in the convergence area after the original two shock waves will not be the same as those in the overpressure detonation area after the newly formed shock wave. Therefore, a reflected wave will be generated to adjust the contradiction of unequal pressure and velocity between the two areas. At the same time, as Figure 2 shown, when the incident wave converges to the center, there is a phenomenon that the reacted area of the high-detonation-velocity explosive in the outer layer of the composite charge laterally initiates the unreacted area of the low-detonation-velocity explosive in the inner layer in the vertical direction. The detonation waves of the inner and outer layer charges are coupled to form an overall centripetal waveform. According to Newton's second law, the velocity of the metal plate in this time period can be obtained, where Newton's second law is expressed as:

[0073] ,

[0074] During implementation, when the motion time of the metal plate is , the detonation process stage of the composite charge is in an irregular oblique reflection process. The irregular oblique reflection process includes the unreacted explosive area, detonation product area, state area behind the reflected shock wave, and state area behind the Mach wave. The velocity of the metal plate in this motion time period is expressed as:

[0075] ,

[0076] In the formula, represents the Mach wave velocity in the state area behind the Mach wave, represents the sound velocity of the detonation products in the state area behind the Mach wave, represents the dynamic rigidity index of the metal plate material, represents the length of the post-Mach wave state region, represents the pressure of the detonation products in the post-Mach wave state region, represents the initial particle velocity of the Mach wave acting on the metal plate medium.

[0077] Specifically, the pressure of the detonation products in the post-Mach wave state region , is obtained by the following formula:

[0078] ,

[0079] wherein, represents the slow change coefficient, represents the detonation incident angle.

[0080] Specifically, the initial particle velocity of the Mach wave acting on the metal plate medium , is obtained by the following formula:

[0081] ,

[0082] In the formula, 、 respectively represent the first and second material compression coefficients, represents the pressure of the Mach wave acting on the metal plate medium, represents the polytropic exponent, represents the initial density of the metal plate material.

[0083] Specifically, the dynamic rigidity index of the material is expressed as:

[0084] ,

[0085] wherein,

[0086] ,

[0087] In the formula, represents the ratio of the shock wave impedance of the material and the explosive, represents the initial velocity of the explosion shock wave in the metal plate medium, 、 respectively represent the first medium coefficient and the second medium coefficient of the metal plate.

[0088] Preferably, the metal plate is a copper metal plate, , , .

[0089] Specifically, the sound velocity of the detonation products in the post-Mach wave state region is expressed as:

[0090] ,

[0091] Among them,

[0092] ,

[0093] In the formula, represents the internal energy per unit volume at the initial stage.

[0094] Specifically, at the moment the Mach wave speed is expressed as:

[0095] ,

[0096] Among them,

[0097] ,

[0098] In the formula, represents the three-wave growth angle.

[0099] Specifically, at the length of the post-Mach wave state region at a certain moment is the abscissa of the triple point corresponding to the triple-wave growth angle at the corresponding moment in the triple-point trajectory.

[0100] It should be noted that the velocity of the metal plate in this movement time period is obtained through the following analysis:

[0101] Using the initial and boundary conditions, that is, when at a certain distance and angle when the detonation wave propagates, the cancellation effect generated by the reflected shock wave is not sufficient to turn the flow field back, and reflection will occur when encountering the solid wall or interface, generating a relatively high pressure. The rapidly increasing pressure will generate a Mach reflection phenomenon in the axisymmetric internal contraction flow field. Based on the local isentropic hypothesis, in the micro-time domain the following relationship can be obtained:

[0102] ,

[0103] In the formula, represents the pressure acting on the metal plate wall.

[0104] Each wave in the right-propagating simple wave system behind the Mach wave propagates to the right at its own velocity. When it reaches the metal plate wall, the particle velocity of the detonation product immediately becomes the velocity of the metal plate wall. The sound velocity of the detonation product behind the Mach wave immediately becomes the sound velocity of the product at the wall, and the pressure Immediately becomes the pressure at the wall , and there is . Therefore, the variation law of the metal plate wall velocity is determined as follows:

[0105] ,

[0106] ,

[0107] In the formula, represents the displacement of the metal plate.

[0108] Among them,

[0109] ,

[0110] ,

[0111] In the formula, represents the initial internal energy per unit volume, represents the isentropic calculation.

[0112] The motion law of the product at the metal plate wall can be calculated by the following empirical formula:

[0113] ,

[0114] Among them, the length of the post-Mach wave state region is the abscissa of the triple point corresponding to the triple point growth angle in the triple wave point trajectory.

[0115] Among them, the initial particle velocity acted on by the Mach wave in the metal plate medium satisfies:

[0116] ,

[0117] ,

[0118] ,

[0119] By jointly solving equations (20), (21) and (22), we get:

[0120] ,

[0121] Then, according to the motion velocity of the metal plate wall being , from equation (22), we get:

[0122] ,

[0123] By changing and integrating equation (24), we get:

[0124] ,

[0125] Substituting Equation (25) into Equation (23), we get:

[0126] ,

[0127] Substituting Equation (26) into Equation (20) and integrating, the velocity of the metal plate during this motion period is expressed as:

[0128] ,

[0129] During implementation, the inner layer of the composite charge is aluminized explosive; when the motion time of the metal plate is , the detonation process stage of the composite charge is in the stable detonation propagation process, and the velocity of the metal plate during this motion period of the metal plate is expressed as:

[0130] ,

[0131] where

[0132] ,

[0133] In the formula, represents the content of aluminum powder in the inner-layer aluminized explosive of the composite charge; represents the specific heat capacity at constant volume of the gas, which is solved by the Kast average molar heat capacity at constant volume formula; represents the reaction rate of aluminum powder, represents the universal gas constant, represents the reaction heat of aluminum powder in the inner-layer aluminized explosive of the composite charge, represents the polytropic exponent, , represent the specific volume and density of the detonation products during the stable detonation propagation process.

[0134] Preferably, , , .

[0135] It should be noted that the inner layer of the composite charge in this embodiment is aluminized explosive, and the velocity of the metal plate during this motion period is obtained through the following analysis:

[0136] When , the detonation waves will not collide on the axis of the charge, and the detonation waves propagate as stable plane waves, satisfying:

[0137] ,

[0138] In the formula, represents the total pressure of the detonation products of the composite charge during the stable detonation propagation process, is the cross-sectional area of the metal plate.

[0139] At this time, after the detonation of the composite charge, if the ideal component of the inner aluminized explosive detonates instantaneously, as the detonation products continue to expand and diffuse, the internal pressure and temperature of the detonation products will decrease accordingly. When the detonation products expand, it is assumed that the aluminum powder does not undergo a chemical reaction but only a physical reaction. Then, at this time, the internal pressure of the detonation products will decrease as the volume of the detonation products continues to increase. For the state equation of the expansion of the composite high-pressure gas at this stage, so there is:

[0140] ,

[0141] Among them,

[0142] ,

[0143] ,

[0144] In the formula, represents the pressure in the pressure decay equation of the detonation products, represents the initial specific volume of the composite charge.

[0145] The reaction rate of the non-ideal component of the inner aluminized explosive in the composite charge is the reaction rate of the aluminized explosive. The general equation of the aluminized explosive is a reaction rate equation related to pressure, and the expression is as follows:

[0146] ,

[0147] In the formula, represents the aluminum powder reaction degree, represents the detonation product pressure of the inner aluminized explosive in the composite charge, is the specific energy of non-ideal detonation when the non-ideal component of the explosive in the composite charge detonates,.

[0148] Among them, is the specific energy of non-ideal detonation when the non-ideal component of the explosive in the composite charge detonates. It can be seen that the non-ideal component of the explosive in the composite charge releases energy with a maximum value, and as the reaction proceeds, the speed of releasing energy becomes smaller and smaller. When the reaction degree is reached, the released energy reaches the maximum value (the maximum value), and the reaction speed is zero.

[0149] According to formula (31), the change of the heat release of aluminum powder with time during the non-ideal detonation of the explosive in the composite charge can be obtained. Taking the first and second derivatives of the time in the aluminum powder heat release formula (31) for the non-ideal detonation of the explosive in the composite charge, under constant volume conditions, considering the time change is When, according to the relationship between heat and heat capacity in the first law of thermodynamics and the gas state equation, the heat released by the reaction of aluminum powder is:

[0150] ,

[0151] In the formula, represents the detonation product temperature.

[0152] Combining formulas (31) and (32), and organizing and integrating under the conditions of constant volume and constant pressure, the pressure contribution equation of the heat release of aluminum powder after the non-ideal detonation of the explosive in the composite charge is obtained as:

[0153] ,

[0154] In the formula, represents the pressure contribution equation of the heat release of aluminum powder.

[0155] Through the analysis and research on the secondary reaction theory of the explosive in the composite charge, the total pressure of the detonation products of the composite charge is:

[0156] ,

[0157] According to formulas (30) and (33), the detonation pressure during the non-ideal detonation of the explosive in the composite charge is as:

[0158] ,

[0159] Substituting formula (35) into formula (29) and organizing using Newton's second law, it can be obtained that:

[0160] ,

[0161] Through formula (36), the relationship between the velocity and time of the detonation driving the metal plate in the composite charge can be obtained. By organizing formula (36), the velocity of the metal plate when the detonation of the composite charge drives the metal plate to move is:

[0162] ,

[0163] To sum up, the detonation of the composite charge driving the metal plate to move is solved in three stages, namely the detonation wave convergence stage, i.e., the regular oblique reflection process, the detonation wave overpressure detonation stage, i.e., the non-regular oblique reflection process, and the stage of the composite charge moving with a stable plane wave, i.e., the stable detonation propagation process. Combining formulas (4), (12), and (28), and organizing and solving, the model representing the velocity of the detonation of the composite charge driving the metal plate is:

[0164]

[0165] It should be noted that the flow field parameters of the detonation process of the composite charge in the regular oblique reflection process and the irregular oblique reflection process are obtained through the following derivation process. The internal division of the composite charge is as Figure 3 shown as follows:

[0166] Based on the evolution law of the detonation wave collision zone of the explosive during the overpressure process, the conditions for the explosive to undergo overpressure detonation are determined. The core problem is to determine the critical angle when Mach reflection occurs. According to the interaction relationship between the reflection angle and the incident angle, the reaction process of the explosive is divided into zones: regular oblique reflection and irregular oblique reflection. Based on the physical parameters of the explosive in each zone, the physical parameter expressions of the explosive in each sub-region are obtained, and the physical parameter expressions in each zone are integrated to construct a theoretical calculation method for the flow field parameters of the explosive under overpressure detonation.

[0167] When the detonation incident angle of the detonation wave of the composite charge satisfies , the collision in the composite charge belongs to a regular oblique collision.

[0168] The reaction zone during regular oblique collision is divided into regions, as Figure 4 shown. The regular oblique collision of two detonation waves with equal intensities can be regarded as the regular oblique reflection of one side of the detonation wave on a rigid wall. The detonation wave collides with the rigid wall at a certain detonation incident angle , generating an oblique shock wave. This process is an unsteady process. The coordinate origin is taken at the collision point T, and the incident detonation wave front TI and the reflected shock wave front TR are regarded as plane waves. The physical image near the detonation wave collision point is as Figure 4 shown.

[0169] Thus, the entire detonation region is divided into three zones by the plane where the incident wave front, the reflected wave front, and the symmetry plane are located: zone (0) is the unreacted explosive zone, zone (1) is the detonation product zone, and zone (2) is the region behind the reflected shock wave. In the coordinate system where point T is stationary, the flow becomes a steady flow. Zone 0 flows vertically into the detonation wave front TI at the detonation velocity , and the detonation products flow out of the detonation wave front TI vertically at the velocity into zone (1). Then the fluid mass passes through the reflected wave front TR vertically at another velocity . From the perspective parallel to the rigid wall, zone (0) flows towards the incident detonation wave front TI at a velocity parallel to the rigid wall , and then turns inward by an angle , and flows towards the reflected shock wave front TR at a velocity of . After passing through the reflected shock wave front, the flow direction turns by another angle . According to the conditions of the wall surface in zone (2), the flow velocity The direction is parallel to the rigid wall surface. At this time, the deflection angles of the fluid masses flowing out of the wave fronts TI and TR are equal, that is . Thus, the division of the detonation reaction zone of the explosive under the condition of regular reflection has been completed.

[0170] The flow field parameters in zone (0) are defined as follows: the charge density of the explosive is , the detonation velocity is , the pressure of the detonation products is , the internal energy per unit volume is , the particle velocity is , the sound velocity is ; the density in zone (1), which is the detonation product zone, is , the detonation velocity is , the pressure of the detonation products is , the internal energy per unit volume is , the particle velocity is , the sound velocity is ; the density in zone (2), which is the detonation product zone, is , the detonation velocity is , the pressure of the detonation products is , the internal energy per unit volume is , the particle velocity is , the sound velocity is ; among them, the flow field parameters in zone (0) are all known quantities.

[0171] Regarding the physical parameter problem of the detonation wave collision zone under the condition of oblique collision, the core problem is to solve the pressure-deflection angle relationship behind the oblique shock wave. In order to study the high-pressure flow of the medium caused by the detonation wave, a relative coordinate system in which the oblique shock wave is stationary is adopted. Suppose there is a Figure 5 steady oblique shock wave discontinuity surface S as shown. In practice, the curved and smooth wave front can always be regarded as planar near a point. Take the wave front flow direction as the x-axis. Suppose the flow velocity before the shock wave is , and the pressure before the wave front is ; the flow velocity after the shock wave is , and the pressure after the wave is . The flow before and after the oblique shock wave can be decomposed according to the normal and tangential directions of the shock wave front. , represent the normal and tangential components of the flow velocity before the wave front, , represent the normal and tangential components of the flow velocity after the wave front. In Figure 5 , , and , , ​Denote the density, isentropic sound speed, and specific internal energy before and after the wavefront. Since there is no flow velocity at the tangential discontinuity, the pressures on both sides of the discontinuity are equal. However, the entropy, density, and tangential velocity are discontinuous. There is a flow velocity across the normal discontinuity, but both the mass flow and energy flow across the normal discontinuity must be conserved. From the conservation of mass and the tangential component of momentum, the condition for the continuity of the tangential velocity can be derived. Combining with the interface conditions, the flow relationships before and after the wave can be obtained.

[0172] From the conservation of mass and the tangential component of momentum across the discontinuity surface, we know that:

[0173] ,

[0174] where, is the mass flow rate per unit time through a unit area of the discontinuity surface. From the condition of tangential velocity continuity, we know that . From the conservation of momentum, we get:

[0175] ,

[0176] From the conservation of energy across the discontinuity surface, we get:

[0177] ,

[0178] where, is the energy released per unit mass of the fluid when crossing the discontinuity surface, is the specific internal energy with the wavefront pressure being and the density before the wavefront being , is the specific internal energy with the wavefront pressure being and the density before the wavefront being .

[0179] From equations (38) and (39), we can solve for:

[0180] ,

[0181] Substitute this equation (41) into equation (40) to obtain the Hugoniot relation:

[0182] ,

[0183] According to Figure 5 and equation (41), we get:

[0184] ,

[0185] where, is the angle between the oblique shock wavefront S and the wavefront velocity .

[0186] The normal velocity difference across the strong discontinuity is calculated from Equation (41). as follows:

[0187] ,

[0188] To obtain the pressure-rotation polar curve, the direction of the x-axis is selected to be the same as the direction, and the y-axis is perpendicular to it to form a right-handed system. Let and be the unit vectors in the corresponding directions. Then, from Figure 5 we have:

[0189] ,

[0190] where and are the x- and y-axis components of the post-wave velocity respectively.

[0191] From the momentum conservation equation (41), the mass conservation equation (40), and the tangential velocity continuity equation , we obtain:

[0192] ,

[0193] Substituting Equation (45) into Equation (46), we have:

[0194] ,

[0195] From the tangential velocity continuity equation (45), we have:

[0196] ,

[0197] And from Equation (45), we have:

[0198] ,

[0199] Comparing Equation (48) and Equation (49), and considering Equation (47), we have:

[0200] ,

[0201] From Figure 5 it can be seen that the vector rotates by relative to the vector by an angle, and this value is:

[0202] ,

[0203] Substituting Equation (47) and Equation (50) into Equation (51), we obtain:

[0204] ,

[0205] By simultaneously eliminating according to Equation (52) and the Hugoniot relation of the shock wave (Equation (42)) , the relationship between the post-shock pressure and the turning angle can be obtained under the known wave-front parameters, that is the polar curve. It can be seen from Equation (52) that each set value corresponds to two values with opposite signs and equal magnitudes. Therefore, the polar curve is axisymmetric with respect to . When has two roots, one root is , and at this time the shock wave degenerates into a sound wave. The other root corresponds to , and at this time , the oblique shock wave becomes a direct collision of detonation waves; among them, is the maximum detonation product pressure.

[0206] Using the theoretical analysis method of the shock wave polar curve, similarly for the supersonic flow problem around a wedge with a given , where represents an arbitrary incident angle; draw a straight line of , which intersects the polar curve at , and points. Discard the solution behind the non-shock wave and the unstable solution , and the solvable point's weak branch solution can directly obtain the corresponding value on Figure 6 . For subsequent solving of the interaction problem of oblique shock waves, using the tangential discontinuity as the separation surface and the equal pressure and parallel velocities on both sides of the tangential discontinuity as the definite solution conditions. And the polar curve is particularly convenient in its solution. The shock wave polar curve diagram is shown in

[0207] . Curve 1 is the shock wave polar curve emitted from point Figure 7 point, and curve 2 is the shock wave polar curve emitted during . The two polar curves intersect at points A and B. Usually, the weak branch solution (point A) is the required one. When the shock wave collision angle during is not too large, the two shock wave polar curves intersect, belonging to the normal oblique collision range of shock waves. As the angle increases, angle increases, and ​The absolute value of increases, and the two polar curves move farther and farther apart. Eventually, the two polar curves change from intersecting to tangent, which is the limiting case of the normal oblique collision of the shock wave. When the limiting case is reached, When the angle increases further, the two polar curves move farther apart again and there will be no intersection point. At this time, it changes to the non-normal oblique collision of the shock wave.

[0208] To sum up, this paper mainly introduces how to solve the relationship between the pressure and turning angle behind the oblique shock wave, and then calculates the flow field parameters in the above three regions based on the equation of state. For Figure 4 the variation relationship between the parameters from region (0) to region (1), the parameters in region (0) are all known; assuming that the explosive reacts completely and within a very short time interval, the expansion of the detonation products is not considered, then for the detonation product pressure in region (1), based on the equation of state is in the form of:

[0209] ,

[0210] In the formula, , , , , , , are the constant coefficients of the equation of state respectively, represents the polytropic exponent, , are the specific volume and internal energy per unit volume of the detonation products in region (1) respectively.

[0211] Since the state of the detonation products in region (1) satisfies the CJ state and the state parameters of the detonation products in region (1) satisfy the isentropic condition, then:

[0212] ,

[0213] In the direction of the tangent line TI of the incident detonation wave, according to the constant tangential velocity, there is , so the flow velocity and Mach number in region (1) are:

[0214] ,

[0215] According to the geometric relationship before and after the incident detonation wave TI, there is:

[0216] ,

[0217] Applying the trigonometric function transformation formula, we get:

[0218] ,

[0219] Furthermore, considering the variation relationship between parameters from region (1) to region (2), region (2) is the region after the oblique reflection shock wave. According to the pressure-turn angle relationship formula (52) after the oblique shock wave, for the oblique reflection shock wave TR, there is:

[0220] ,

[0221] For the regular oblique collision of two detonation waves with equal intensity, it can be regarded as the regular oblique reflection of one side of the detonation wave on the rigid wall. The detonation wave collides with the rigid wall at a certain angle, and an oblique shock wave is generated during the collision. This process is an unsteady process. For the convenience of studying the problem, the coordinate origin is taken at the collision point, and the incident detonation wave and the reflected shock wave are regarded as plane waves. The physical image near the detonation wave collision point is as Figure 4 shown.

[0222] Since the movement direction of the detonation products in region (1), i.e., the medium after the detonation wave, is no longer parallel to the x-axis but deflected by an angle in the direction of the x-axis, the wall will necessarily impede the flow of the detonation products, thereby generating a reflected shock wave on the wall. When the detonation products pass through the reflected shock wave, their flow deflects by another angle in the opposite direction and then flows along the wall. Region (2) satisfies the equation of state, then

[0223] ,

[0224] wherein, , are the specific volume and internal energy per unit volume of the detonation products in region (2).

[0225] From the Hugoniot relationship, we have:

[0226] ,

[0227] Furthermore, combining the Hugoniot relationship and the equation of state, we get:

[0228] ,

[0229] Simplifying equation (29) gives:

[0230] ,

[0231] After arrangement, we have:

[0232] ,

[0233] From the relative specific volume, we have:

[0234] ,

[0235] but

[0236] ,

[0237] Based on this, the physical parameters of the flow field when the detonation products are transformed from region (1) to region (2) can be solved according to formulas (59)-(64), which can be obtained according to The state equation iteration method is used to solve the pressure of regular oblique reflection collision.

[0238] In summary, when solving the flow field parameters of the regular oblique reflection collision zone, the known parameters include: the charge density of the explosive , dynamite State equation parameters , , , , , , , , the initial specific internal energy of the explosive , Specific volume of explosive CJ detonation products , , explosive detonation velocity .

[0239] The Mach critical angle is determined by: The flow velocity is calculated from equations (55) and (57): and the incident wave TI, the flow group deflection angle , then combine the Hugoniot relation (60) and The state equation (59) is , substitute (61) into (65) to obtain , then Substituting into (65), the pressure after the reflected wave is calculated by formula (65): and flow mass deflection angle The display solution of The point is Figure 7 The polar curve of the reflected shock wave TR is obtained ; Polar curve pay The axis is at points a and b. According to Von Neumann's detached shock wave criterion, they are both weak shock wave solutions. Obviously, point a is the stable solution of regular oblique reflection. Increase to hour, Figure 8 The two points a and b in the above equation coincide with each other. Axis tangent ( Figure 8 Middle Curve ). According to Von Neumann's detached shock wave criterion, That is the critical incident angle for the transition from regular oblique collision to Mach reflection.

[0240] The flow field parameters are calculated as follows: By simultaneously solving equations (53)-(58), the flow field parameters from the detonation product region (0) to region (1) can be obtained. Region (1) is the detonation product region with a density of , detonation velocity of , pressure of the detonation product , internal energy per unit volume of , particle velocity of , and sound velocity of . Based on this, according to formulas (59)-(64), the physical parameters of the flow field when the detonation product transforms from region (1) to region (2) can be obtained. Region (2) is the detonation product region with a density of , detonation velocity of , pressure of the detonation product , internal energy per unit volume of , particle velocity of , and sound velocity of .

[0241] When the incident angle of the detonation wave of the composite charge satisfies , the collision in the composite charge belongs to an irregular oblique collision.

[0242] The irregular oblique collision of two detonation waves with equal strength can be regarded as the irregular oblique reflection of one detonation wave on a rigid wall. For Figure 9 regular oblique reflection, when the angle between the incident detonation wave front TI and the rigid wall gradually increases, the flow deflection angle of the fluid mass passing through the incident detonation wave TI and the flow deflection angle of the fluid mass passing through the reflected shock wave TR both gradually increase. When the incident angle of the detonation wave increases to the critical incident angle of Mach reflection , the fluid mass velocity in region (2) behind the reflected shock wave can no longer be parallel to the rigid wall, resulting in the accumulation of matter, forcing the reflected shock wave to move upward and intersecting the incident detonation wave at a certain distance from the rigid wall, that is, the collision point S moves to point T, thus forming the Mach reflection as shown in Figure 9 . As the detonation wave propagates, the height of the Mach stem continuously increases, and its pressure and velocity rapidly decrease. When the pressure and detonation velocity on the Mach stem decrease to the CJ value, the Mach reflection disappears and normal detonation occurs.

[0243] For the convenience of research, a coordinate system with the origin at the collision point is still adopted to transform the flow into a steady flow. Figure 9At point S is the collision point, point T is the triple point, TI is the incident detonation wave front, TR is the reflected shock wave front, and TS is the Mach stem. The flow field near the triple point can be divided into four regions: region (0) in front of the incident detonation wave TI and the Mach stem wave TS, i.e., the undetonated region, region (1) behind the incident detonation wave TI and in front of the reflected shock wave TR, i.e., the detonation product region, region (2) between the reflected shock wave TR and the contact discontinuity TQ, i.e., the region of the state behind the reflected shock wave, and region (3) between the Mach stem TS and the contact discontinuity TQ, i.e., the region of the state behind the Mach wave.

[0244] The Mach stem is a highly compressed strong detonation wave. TS is a curved surface, and the angle between the tangent at each point on it and the rigid wall varies between and . At point S, the wave front is perpendicular to the rigid wall, and at point T, the angle between the wave front and the wall direction is . The fluid behind point T all comes from region (0) in front of the incident detonation wave and the Mach stem. Part of it passes through the Mach stem TS, and another part of the fluid first crosses the incident detonation wave TI and then passes through the reflected shock wave TR. From the fact that the entropy increase across a shock wave is of the third order of the pressure difference across the shock wave, starting from the same state, the entropy increase of part of the fluid mass after being compressed by a single shock wave is , while for another part of the fluid mass that undergoes two compressions, its entropy increase is , and , where , are the first and second entropy increases during Mach reflection. Therefore, the entropy increase of single compression is always greater than that of double compression, and thus the detonation product densities behind the reflected wave TR and behind the Mach stem TS are different. Thus, there is a tangential discontinuity, called the contact discontinuity or slip line, denoted by TQ, between the reflected wave and the Mach stem.

[0245] Based on the Whitham method, the Mach stem is regarded as the result of the incident detonation wave propagating in a converging variable cross-section flow tube and the Mach wave is simplified to a plane wave perpendicular to the rigid wall. In two dimensions, the position of the detonation wave and the position of the ray perpendicular to it. Figure 10 In and is a variable cross-section pipe between the two lines; where represents the incident angle, represents the reflection angle. OR is the position of the incident detonation wave at time , and is the Mach stem formed from the incident detonation wave OR at time . When Mach reflection occurs, a curved surface reflected shock wave and a Mach wave are formed. The Mach wave OM is perpendicular to the rigid wall (as shown in Figure 10 ), is the incident angle of the detonation wave, It is the growth angle of three wave points . During the time, the three wave point O moves to . Above the "three wave points" , the motions of the incident wave and the reflected wave are independent. During this process, the intersection of the incident wave and the reflected wave occurs, that is, the reflected wave catches up with the incident wave, generating a combined wave, namely the Mach wave. For a medium with normal compressibility, this view is reasonable. In the figure, points L and Y are the intersections of the extension lines of the incident and reflected waves with the parallel lines of the rigid wall respectively

[0246] Accordingly, from Figure 10 the geometric relationship, we can obtain

[0247] ,

[0248] wherein is the incident wave velocity is the reflected wave velocity represents the reflection angle

[0249] Since , that is

[0250] ,

[0251] so

[0252] ,

[0253] wherein is the Mach wave size change rate

[0254] From Figure 10 we get

[0255] ,

[0256] we can obtain the Mach wave velocity :

[0257] ,

[0258] It can be seen that for Mach reflection with different incident wave velocities and detonation incident angles , the Mach wave velocity will have different values

[0259] From equations (68) and (70), the growth angle of the "three wave points" or the slope of the trace line satisfies the following relationship

[0260] ,

[0261] or

[0262] ,

[0263] It can be seen from equations (68), (71), and (72) that

[0264] If then:

[0265] ,

[0266] If , then:

[0267] ,

[0268] Obviously, during the development of the Mach wave, the velocity of the reflected wave direction and the Mach wave velocity are greater than the velocity in the direction of the detonation incident wave, and the growth angle of the "triple point" is greater than zero. If the Mach wave reaches a steady state, then these three velocities are equal, equal to zero. From equation (72), we get:

[0269] ,

[0270] Substituting equation (75) into equation (70), we have

[0271] ,

[0272] It can be seen from equations (75) and (76) that the velocities of the incident wave, the reflected wave, and the Mach wave are equal along the trajectory direction of the "triple point". From the Figure 9 geometric relationship in, we can obtain:

[0273] ,

[0274] ,

[0275] where and are the areas of the pipeline at sections and respectively, and are the velocities of the incident detonation wave and the Mach wave respectively, and represents the height of the Mach stem.

[0276] Combining equations (77) and (78), we get:

[0277] ,

[0278] Furthermore, based on the relationship between the improved Whitham method and the area function , the Mach reflection pressure is solved:

[0279] ,

[0280] In the formula, , and are the pressures in the region after the Mach wave and the incident detonation wave, respectively. It represents the slow-varying coefficient, which is generally a constant and is usually obtained by fitting experimental data.

[0281] For the pressure in the Mach reflection (3) region The solution can be obtained according to formula (80). By combining formula (77), formula (78), and formula (80), and substituting them into formula (79), the Mach reflection pressure under different state equations can be calculated. However, it is worth noting that the slow-varying coefficient in the formula is an unknown quantity, which brings inconvenience to the theoretical calculation of Mach reflection detonation parameters. The theoretical calculations are derived.

[0282] According to Whitham's rules:

[0283] ,

[0284] Assume that the shock wave passes through the cross section When the wave speed is , then integrate the above formula to get:

[0285] ,

[0286] Similarly,

[0287] ,

[0288] In the formula, is the detonation wave velocity, and are the moving speed of the medium behind the detonation wave front and the local sound speed, is the density of the detonation products.

[0289] Taking the natural logarithm of both sides of equation (80) and equation (83), we can obtain:

[0290] ,

[0291] According to the definition of the speed of sound equation, we have:

[0292] ,

[0293] According to the laws of conservation of mass and momentum, the pressure in the rear area of ​​the detonation wave front can be calculated: and the moving speed of the medium , taking the differential of both sides, we get:

[0294] ,

[0295] In the formula, .

[0296] From equation (86), we can solve to obtain equations 、 .

[0297] Furthermore, based on equations (85) and (86), we can obtain

[0298] ,

[0299] ,

[0300] Let , then:

[0301] ,

[0302] where

[0303] ,

[0304] Determine the area function relationship according to the law of conservation of mass and the laws of conservation of momentum and energy. According to the equation of state and the Hugoniot relationship, this relationship can be used to calculate the pressure behind the detonation wave front and the moving velocity of the medium, as follows:

[0305] ,

[0306] According to the equation of state and the Hugoniot relationship, the detonation wave pressure can be calculated as:

[0307] ,

[0308] Using formula (84) and formula (85), the following expressions can be obtained:

[0309] ,

[0310] Furthermore, for the pressure solution in the Mach reflection (3) region, it can be solved according to formula (80).

[0311] Furthermore, by combining equations (90) and (92), we jointly obtain and relationship, substituting into equations (84)-(89), substituting , the slow change coefficient can be calculated. Since The value changes little, and the average value is taken.

[0312] Further, the slow - varying coefficient is substituted into Equation (93), and the Mach reflection pressure under different equations of state can be calculated:

[0313] ,

[0314] Generally speaking, for non - regular oblique reflection (Mach reflection), the core is to solve the pressure in region (3) after Mach reflection. The following parameters need to be known during the solution process: the charge density of the explosive , the explosive parameters of the equation of state , , , , , , , , the initial specific internal energy of the explosive , the specific volume of the CJ detonation products of the explosive , , the detonation velocity of the explosive .

[0315] The flow - field parameters are determined in the following way: First, based on the improved Whitham method, the Mach reflection pressure formula (80) is derived from Equations (66) - (79). The core problem in Equation (80) is to solve the slow - varying coefficient , and the detailed solution process for how to solve the slow - varying coefficient is carried out in Equations (81) - (92). Specifically, by combining Equation (90) and Equation (92), the relationship between and is obtained and substituted into Equations (84) - (89). With , the slow - varying coefficient can be calculated. Since the value of changes little, the average value is taken. Further, the slow - varying coefficient is substituted into Equation (93). Thus, the Mach reflection pressure under different equations of state can be calculated.

[0316] The triple - wave point trajectory is obtained in the following way:

[0317] a. Based on the composite charge radius and the Mach reflection critical angle, determine the intersection coordinates of the x - axis in the coordinate system and use them as the initial trajectory point coordinates of the triple - wave point; among them, in the coordinate system, the origin is the detonation position, the x - axis represents the propagation distance of the detonation wave along the flow direction, and the y - axis represents the propagation distance of the detonation wave perpendicular to the flow direction.

[0318] Specifically, the initial trajectory point coordinates are expressed as ;

[0319] wherein, , ;

[0320] In the formula, represents the radius of the composite charge, represents the critical angle of Mach reflection.

[0321] It should be noted that the radius of the composite charge is the sum of the inner charge radius and the outer charge radius.

[0322] b. Based on the initial trajectory point coordinates, the detonation wave reflection pressure calculation model, the set step size, and the number of trajectory points, the coordinates of each trajectory point are obtained in sequence.

[0323] Specifically, when implementing, the trajectory point coordinates are obtained through the following method:

[0324] b1. Based on the current trajectory point coordinates, the current detonation wave incident angle is obtained, and then the current triple point growth angle is obtained.

[0325] Specifically, the triple point growth angle is expressed as:

[0326] ,

[0327] wherein, ;

[0328] In the formula, represents the triple point growth angle corresponding to the coordinates of the th trajectory point, represents the detonation incident angle corresponding to the coordinates of the th trajectory point, represents the Mach reflection pressure when the detonation incident angle is , represents the coordinates of the th trajectory point, represents the detonation wave pressure in the CJ state.

[0329] Specifically, the number of trajectory points is set according to actual needs.

[0330] b2. Based on the current trajectory point coordinates, the triple point growth angle, and the set step size, the coordinates of the next trajectory point are obtained.

[0331] Specifically, the coordinates of the next trajectory point are expressed as ; wherein,

[0332] ,

[0333] ,

[0334] In the formula, represents the set step size.

[0335] Preferably, the step size is set to 0.1.

[0336] c. Connect the initial trajectory point coordinates and the coordinates of each trajectory point to obtain the trajectory of the triple point of the detonation wave of the composite charge.

[0337] It should be noted that in the (0) region in front of the incident detonation wave TI and the Mach stem wave TS, in the (1) region behind the incident detonation wave TI and in front of the reflected shock wave TR, that is, the detonation product region, and in the (2) region between the reflected shock wave TR and the contact discontinuity TQ, that is, the region of the state behind the reflected shock wave, the flow field parameters in each region are the same as the solution process in the regular oblique reflection process, which will not be elaborated here.

[0338] Compared with the prior art, a method for constructing a model of the velocity of a metal plate driven by the detonation of a composite charge provided in this embodiment constructs the law of the motion characteristics of the metal plate at any time during the overpressure detonation of the composite charge, can obtain the velocity of the metal plate at any time, describes the driving law of the composite charge structure through the movement of the metal plate, can effectively evaluate the work performance of the composite charge, and can provide technical support for the in-depth study of the energy release rate of the composite charge and the structural optimization design. It can also provide technical support for the research and development of composite high-energy charge structure design technology, detonation wave superposition driving enhancement technology, new-generation directional fragmentation warheads, etc.; considering the interaction between the oblique shock wave and the rarefaction wave generated inside the composite charge during the detonation process, a theoretical calculation method for the internal flow field parameters of the composite charge is established. By partitioning and deriving the spatio-temporal relationship of physical parameters such as the pressure acting inside the detonation products of the composite charge over time, the internal parameters after the overpressure detonation of the explosive can be accurately analyzed, realizing the theoretical closure of the interaction parameters of the detonation waves of condensed explosives. And this method has wide applicability, high precision and strong stability, can be used to characterize the theoretical calculation model of the explosive under overpressure detonation, and lays a foundation for studying the internal detonation reaction mechanism, driving damage model and energy output response law of the composite charge.

[0339] Those skilled in the art can understand that to implement all or part of the processes of the above embodiment methods, it can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.

[0340] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for constructing a model of the velocity of a metal plate driven by a composite charge detonation, characterized in that: The following steps are involved: Determine each movement time period of the metal plate based on each detonation process stage and initial parameters of the composite charge during the detonation process of the composite charge; wherein the composite charge detonation time is taken as the initial time, and the initial parameters include the length of the composite charge, the diameters of the inner and outer layers of the charge, and the detonation velocities of the inner and outer layers of the charge; Based on the detonation process stage of each moving time period of the metal plate, the internal flow field parameters and detonation incident angle of the composite charge in each moving time period are obtained; Based on the internal flow field parameters of the composite charge in each motion time period, the initial parameters of the composite charge and the detonation incident angle, the velocity expression of the metal plate in each motion time period is obtained, and the model construction of the metal plate velocity is completed; The detonation process stages include regular oblique reflection process, irregular oblique reflection process and stable detonation propagation process; wherein, The movement time period of the metal plate corresponding to the regular oblique reflection process is ; The movement time period of the metal plate corresponding to the irregular oblique reflection process is ; The motion time period of the metal plate corresponding to the stable detonation propagation process is ; in, represents the moment of motion of the metal plate, It represents the motion moment of the metal plate when the detonation incident angle is the Mach critical angle, It represents the metal plate motion moment corresponding to the composite charge detonation product entering the stable plane wave propagation; The metal plate movement moment corresponding to the composite charge detonation product entering the stable plane wave propagation It is expressed as: ， in, ， In the formula, Indicates the length of the composite charge; , They represent the detonation velocities of the outer and inner layers of the composite charge respectively; when When , the detonation incident angle satisfies the following formula: ， In the formula, Indicates at time Detonation incident angle at ; when When the detonation waves are superimposed, there is no phenomenon of superposition, and the inner and outer charges of the composite charge drive the metal plate at the same detonation speed.

2. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 1, characterized in that: The metal plate motion moment corresponding to the detonation incident angle being the Mach critical angle It is expressed as: ， In the formula, , They respectively represent the diameters of the outer and inner charges of the composite charge.

3. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 1, characterized in that: When the metal plate moves for When the composite charge is in the detonation process stage, it is in the regular oblique reflection process, which includes the undetonated area of ​​the explosive, the detonation product area and the post-reflection shock wave state area. During this motion period, the metal plate moves at a speed of Movement, speed of the metal plate It is expressed as: ， In the formula, Indicates at time The detonation product pressure in the state area after the reflected shock wave is is the cross-sectional area of ​​the metal plate, Indicates the mass of the metal sheet.

4. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 1, characterized in that: When the metal plate moves for The composite charge detonation process is in the irregular oblique reflection process, which includes the undetonated area of ​​explosives, the detonation product area, the post-reflection shock wave state area and the post-Mach wave state area. The speed of the metal plate in this motion period is It is expressed as: ， In the formula, represents the Mach wave velocity in the post-Mach wave state region, represents the speed of sound of the detonation products in the post-Mach wave state, Represents the dynamic rigidity index of the metal sheet material, represents the length of the post-Mach wave state region, represents the pressure of the detonation products in the post-Mach wave state region, represents the initial particle velocity of the Mach wave acting on the metal plate medium.

5. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 1, characterized in that: The inner layer of the composite charge is aluminum explosive; when the metal plate moves for The composite charge detonation process is in a stable detonation propagation process. The metal plate speed in the metal plate movement period is It is expressed as: ， in, ， In the formula, Indicates the content of aluminum powder in the inner layer of aluminum-containing explosive in composite charge. represents the specific heat of gas at constant volume, represents the reaction rate of aluminum powder, represents the universal gas constant, It indicates the reaction heat of aluminum powder in the inner layer of aluminum explosive in the composite charge. represents the multi-party index, , represents the specific volume and density of the detonation products during the stable detonation propagation process, Indicates the mass of the metal sheet, is the cross-sectional area of ​​the metal plate, Represents the initial specific volume of the composite charge.

6. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 3, characterized in that: The detonation product pressure in the state area after the reflected shock wave It is expressed as: ， In the formula, It represents the specific volume of the detonation products of explosives in the CJ state, Indicates the explosion pressure of explosives in CJ state, represents the velocity of the flow mass in the detonation product zone, , represent the density and specific volume of the detonation products in the state after the reflected shock wave, It represents the deflection angle of the flow mass in the state area after the reflected shock wave.

7. The method for constructing a model of the speed of a metal plate driven by composite charge detonation according to claim 4, characterized in that: The pressure of the detonation products in the post-Mach wave state region , obtained by the following formula: ， in, represents the slow-varying coefficient, represents the detonation incident angle.

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