CN118070716A - Modeling method for restraining internal reaction pressure of charging system - Google Patents
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Abstract
The invention relates to a modeling method for internal reaction pressure of a constraint charging system, and belongs to the field of insensitive ammunition design and evaluation. Comprising the following steps: dividing a shell of a constraint charging system into small deformation, large deformation and inertia effect stages, and constructing a function of the total surface area of an explosive combustion crack network in the system and the pressure in the shell; and bringing the mass of the gas product, the volume of the small deformation stage system, the volume of the large deformation stage system and the volume of the inertia effect stage system into an ideal gas state equation to obtain models of the internal reaction pressure and the shell expansion speed of the small deformation stage, the large deformation stage and the inertia effect stage system relative to time t respectively. According to the method, a model of the reaction pressure of the system is obtained through an ideal gas state equation, the increasing speed of the gas product mass and the increasing volume of a restraint loading system, and the problem that the reaction intensity quantitative evaluation method lacks theoretical basis due to the fact that the internal pressure of the system cannot be directly measured in the restraint loading reaction evolution process is solved.
Description
Technical Field
The invention relates to the field of insensitive ammunition design and evaluation, in particular to a modeling method for restraining internal reaction pressure of a charging system.
Background
The ammunition is often subjected to unexpected stimulus such as falling, impact, friction and the like in the whole life cycle, so that mechanical, chemical and thermal responses are generated in an ammunition structure, uncontrolled chemical reactions and energy release occur, and ammunition charge is triggered to ignite, burn until explosion is even converted into typical accidents such as detonation.
Aiming at the typical accidents, the reaction evolution process after the ignition of a constraint charging system is quite complex, and gas products generated after the ignition of the charging lead to deformation and local fracture of pores of a charging matrix under the high-temperature and high-pressure state, so that the specific combustion area is increased rapidly, and a combustion mechanism is converted into 'dismantling combustion'; under the action of continuously-increased internal pressure, the deformation of the shell of the system is subjected to the stages of elasticity, elastoplasticity, plasticity and yield, and when the shell reaches a full yield state, the bearing capacity is lost, and after the failure strain is reached, the shell is destroyed and disintegrated to form fragments; the gas product drives the fragments to continuously accelerate, so that the volume of the system is increased continuously to cause pressure relief of the system, and the gas product generated by continuous reaction of the internal charge causes pressure boost of the system, and the coupling effect of the gas product and the gas product is a core factor for determining the expansion speed of the shell and the change of the internal reaction pressure. At present, the research on explosive ignition reaction evolution is less, the difference between the established reaction evolution model and the actual explosive charge ignition reaction evolution process is larger, and the internal reaction pressure of the system cannot be truly reflected.
Therefore, how to build a reaction evolution model for restraining the internal reaction pressure of the charging system becomes a problem to be solved.
Disclosure of Invention
In view of the above analysis, the invention aims to provide a modeling method for the internal reaction pressure of a constrained charging system, which is used for solving the problem that the existing constrained charging reaction evolution process cannot directly measure the internal pressure of the system, so that a reaction intensity quantitative evaluation method lacks theoretical basis.
The invention provides a modeling method for restraining reaction pressure in a charging system, which comprises the following steps:
Dividing a shell of a constraint charging system into small deformation, large deformation and inertia effect stages, setting thresholds of the small deformation and the large deformation stages, and constructing a function of the total surface area of an explosive combustion crack network in the system and the pressure in the shell;
Obtaining the gas product quality of the explosive explosion in the small deformation stage and the large deformation stage based on the function of the total surface area of the combustion crack network and the pressure in the shell and Vielle law; bringing the volume and the gas product mass of the small deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the small deformation stage system relative to time t, and bringing the volume and the gas product mass of the large deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the large deformation stage system relative to time t;
Obtaining the volume of the inertial effect stage system based on the volume of the large deformation stage system and the generalized equivalent inertial constraint stiffness; obtaining the leakage speed of the gas product based on the enthalpy inside the shell and the enthalpy at the pressure release position of the shell crack; and obtaining the mass of the gas product in the inertia effect stage based on the function of the total surface area of the combustion crack network and the pressure in the shell, vielle law, the pressure release area of the shell crack and the leakage speed of the gas product, and taking the volume of the inertia effect stage system and the mass of the gas product in the inertia effect stage into an ideal gas state equation to obtain a model of the internal reaction pressure of the inertia effect stage system and the expansion speed of the shell relative to time t.
Further, the generalized equivalent inertial confinement stiffness of the system is:
，
wherein, For generalized equivalent inertial confinement stiffness of the system,/>For the generalized equivalent inertial confinement stiffness of the shell,/>Is the bulk modulus of the explosive,/>For the volume of the explosive at the end of large deformation,/>The system volume is the end time of the large deformation.
Further, the generalized equivalent inertial confinement stiffness of the housing is:
，
wherein, To constrain the pressure of the charge system,/>To constrain the bulk strain of the inertial effect phase of the charge system.
Further, the bulk strain of the inertial effect phase of the confined charge system is obtained by the following method:
，
wherein, For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>For the shell height at the end of the large deformation phase,/>Is the end time of the large deformation phase.
Further, the volume of the inertial effect phase system increase is obtained by the following method:
，
wherein, For the volume of the system growth in the shell inertia effect phase,/>For the pressure inside the shell at the end of the large deformation phase,/>For the system volume at the end of large deformation,/>For generalized equivalent inertial confinement stiffness of the system,/>To constrain the pressure of the charge system,/>。
Further, the rate of mass increase of the gas product during the inertial effect phase is obtained by:
，
wherein, Is the combustion coefficient of explosive,/>Is the combustion index of explosive/(Is the burning rate of the explosive,/>Initial surface area of combustion crack for ignition time,/>Is the initial density of the explosive/>Is the initial volume of explosive,/>Saturation specific surface area for combustion cracking,/>For initial pressure in the housing at ignition time,/>For combustion crack reference pressure,/>Is a positive integer,/>As a function of total surface area of the explosive combustion crack network and internal pressure of the shell,/>Is the mass of the gas product in the system,/>Is the mass leakage rate of the gas product,/>To constrain the pressure of the charge system,/>，/>。
Further, the pressure release area of the shell crack is:
，
wherein, Is the pressure relief area of the shell crack,/>For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>For the shell height at the end of the large deformation phase,/>Is the end time of the large deformation phase.
Further, the rate of leakage of the gaseous product is obtained by the following method:
，
wherein, Is the rate of leakage of gaseous products,/>Is a multiparty index of gas products,/>Is the pressure at the leak of the gaseous product,/>To constrain the pressure of the charge system,/>Is the total volume of the inertial effect phase system.
Further, the gas product mass leakage rate is:
，
wherein, Is of atmospheric density,/>Is the pressure relief area of the shell crack,/>Is molar mass,/>Is a universal gas constant,/>Is the gas product temperature,/>Is the gas product mass leak rate.
Further, bringing the volume of the inertial effect stage system and the mass of the inertial effect stage gas product into an ideal gas state equation yields the following equation:
，
wherein, Is the mass of the gas product in the system,/>For the initial volume of the void,/>For the pressure inside the shell at the end of the small deformation phase,/>For the initial volume of the system,/>Is the generalized equivalent stiffness of the system,/>For the pressure inside the shell at the end of the large deformation phase,/>For small deformation end time system volume,/>For a generalized deformation equivalent stiffness of the system,For the volume of the system growth in the shell inertia effect phase,/>For the end time of the large deformation phase,/>，/>；
The model of the internal reaction pressure and the shell expansion speed in the inertia effect stage relative to the time t is obtained by deriving and integrating the formula:
，
wherein, ，/>For the system volume at the end of large deformation,/>For the volume of the explosive at the end of large deformation,/>Is an integral variable,/>Is a time variable,/>Is the bulk modulus of the explosive,/>Is the combustion coefficient of explosive,/>Is the combustion index of explosive/(As a function of total surface area of the explosive combustion crack network and internal pressure of the shell,/>For the speed of radial movement of the housing,For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>Is the shell height at the end of the large deformation phase.
Compared with the prior art, the invention has at least one of the following beneficial effects:
1. According to the invention, the model of the internal reaction pressure and the shell expansion speed of the system is obtained through an ideal gas state equation and the speed of increasing the mass of a gas product and the volume of a constrained explosive loading system, so that the problem that the quantitative evaluation method of the reaction intensity lacks theoretical basis due to the fact that the internal pressure of the system cannot be directly measured in the constrained explosive loading reaction evolution process is solved.
2. According to the invention, in the constrained explosive reaction evolution process, the shell of the system is divided into the small deformation, large deformation and inertia effect stages, and the models of the internal reaction pressure and the shell expansion speed of the constrained explosive system corresponding to the three stages are respectively obtained according to the different reaction evolution characteristics of the three stages, so that the accuracy of obtaining the internal reaction pressure of the system according to the models is improved.
3. According to the invention, a model of the internal reaction pressure of the constrained charging system based on the expansion speed of the shell is established, so that a theoretical basis is provided for insensitive ammunition reaction intensity evaluation.
In the invention, the technical schemes can be mutually combined to realize more preferable combination schemes. Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and drawings.
Drawings
The drawings are only for purposes of illustrating particular embodiments and are not to be construed as limiting the invention, like reference numerals being used to designate like parts throughout the drawings;
FIG. 1 is a flow chart of a modeling method of constraining reaction pressure within a charge system in accordance with an embodiment of the present invention;
FIG. 2 is a schematic illustration of a constrained charge combustion crack propagation in accordance with an embodiment of the present invention;
FIG. 3 is a diagram showing the force analysis of the wall of a cylindrical shell according to an embodiment of the present invention;
FIG. 4 is a schematic view of the movement of a cylindrical housing according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of gas product crack leakage according to an embodiment of the present invention.
Detailed Description
The following detailed description of preferred embodiments of the application is made in connection with the accompanying drawings, which form a part hereof, and together with the description of the embodiments of the application, are used to explain the principles of the application and are not intended to limit the scope of the application.
The invention discloses a modeling method for restraining reaction pressure in a charging system. As shown in fig. 1, the method comprises the steps of:
S1, dividing a shell of a constraint charging system into small deformation, large deformation and inertia effect stages, setting thresholds of the small deformation and the large deformation stages, and constructing a function of the total surface area of an explosive combustion crack network in the system and the pressure in the shell;
S2, obtaining the gas product mass of the explosive explosion in a small deformation stage and a large deformation stage based on the function of the total surface area of the combustion crack network and the pressure in the shell and Vielle law; bringing the volume and the gas product mass of the small deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the small deformation stage system relative to time t, and bringing the volume and the gas product mass of the large deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the large deformation stage system relative to time t;
S3, obtaining the volume of the inertial effect stage system based on the volume of the large deformation stage system and generalized equivalent inertial constraint stiffness; obtaining the leakage speed of the gas product based on the enthalpy inside the shell and the enthalpy at the pressure release position of the shell crack; and obtaining the mass of the gas product in the inertia effect stage based on the function of the total surface area of the combustion crack network and the pressure in the shell, vielle law, the pressure release area of the shell crack and the leakage speed of the gas product, and taking the volume of the inertia effect stage system and the mass of the gas product in the inertia effect stage into an ideal gas state equation to obtain a model of the internal reaction pressure of the inertia effect stage system and the expansion speed of the shell relative to time t.
Specifically, in step S1, the restraining charge system is composed of a charge (explosive) and a casing, and the casing is spherical, cylindrical or other three-dimensional regular geometric body.
It will be appreciated that the charge, after ignition, produces a localized crack in which combustion propagates and causes the pressure within the system to build up. Under the action of continuous increase of internal pressure, namely in the reaction evolution process of the restraining charge system, the deformation of the shell is subjected to the stages of elasticity, elastoplasticity, plasticity and yield, and the shell loses bearing capacity after reaching a full yield state, but cannot instantaneously break, and breaks to form fragments after continuing to expand to a certain degree. The internal restraint charge continuously reacts to cause the system to be in a pressurized state to drive the shell to expand, and the shell expands to expand the volume of the system to enable the system to be in a pressure release state, so that energy release generated by combustion and external work generated by gas products exist simultaneously, and the coupling effect of the energy release and the external work generated by gas products is a core factor for determining the expansion speed of the shell and the pressure change in the system.
Specifically, the deformation of the shell is divided into small deformation, large deformation and inertia effect phases; the small deformation stage is from the ignition start of the restraint charging system until the shell reaches a full yield state (namely the shell loses bearing capacity) and a small deformation stage threshold value, and the deformation degree of the shell is small in the stage, so that the expansion speed of the shell can be ignored; the large deformation stage is from the ending time of the small deformation stage until the threshold value of the large deformation stage is reached, and the deformation degree of the shell is large in the stage, so that the expansion speed of the shell cannot be ignored; the inertia effect stage is from the end time of the large deformation stage to the time when the pressure acting on the shell fragments is reduced to atmospheric pressure, the gas product generated by the continuous reaction of the internal charge in the stage causes the pressurization of the system, and the gas product drives the shell fragments to continuously perform the acceleration motion so that the volume of the system is continuously increased to cause the pressure relief of the system, and the two are mutually coupled. Preferably, the small deformation stage threshold is set to 3% of the shell failure strain, and the large deformation stage threshold is set to 1.3 times of the shell inner radius. The shell failure strain refers to the process by which the shell material loses its original function or performance.
It can be appreciated that the gas products generated after ignition of the restraining charge system flow along the system gap to drive the combustion cracks to expand into a net shape, so that the specific combustion surface area is increased, and the reaction evolution is accelerated. The combustion specific surface area refers to the combustion surface area of unit mass or unit volume during combustion, and the larger the combustion specific surface area is, the higher the combustion efficiency of the fuel is, and the more complete the combustion process is. When the shell enters a large deformation stage, the increase rate of the internal pressure and the deformation degree of the shell are obviously increased compared with those of the shell in a small deformation stage, and the shell continues to expand under the action of the internal pressure and the tensile stress until the shell is completely disassembled. Then, the gas product in the high-pressure state is not completely released instantaneously, but the broken piece formed by the broken shell is driven to continuously perform acceleration movement outwards, so that the system is decompressed due to continuous increase of the system volume, the gas product generated by continuous reaction of the explosive causes the system to be pressurized, and the mutual coupling effect of the explosive energy release and the gas product on external acting is reflected.
Specifically, the total surface area of the explosive combustion crack network in the system is a function of the pressure in the shell:
，
wherein, Initial surface area of combustion crack for ignition time,/>Is the initial density of the explosive/>Is the initial volume of explosive,/>Saturation specific surface area for combustion cracking,/>For initial pressure in the housing at ignition time,/>For combustion crack reference pressure,/>To constrain the pressure of the charge system,/>，/>For the pressure inside the shell at the end of the large deformation phase,/>Is a positive integer.
It will be appreciated that the number of components,The relation to the ignition intensity can be calibrated by typical experiments,/>、/>、/>And/>Depending on the nature of the charge itself and the combustion conditions,/>、/>Is determined by the initial state of the system.
Specifically, in step S2, during the small deformation phase of the shell, the total volume of the containment charge system includes the charge volume, the initial void volume, and the volume that is systematically increased during the evolution of the reaction, the volume that is the sum of the combustion crack growth volume and the expansion volume of the shell, i.e.Wherein/>Constraining the total volume of the charge for this stage,/>For this stage charge volume,/>For this stage initial void volume,/>The volume that grows for this stage of the system.
Initial volume of the constrained charging system is satisfiedWherein/>Is the initial volume of the system. The two formulas above are combined:
。
It will be appreciated that the housing changes its internal volume during the small deformation phase, i.e. the system becomes physically strained The volume strain of the explosive at this stage becomes/>。
Specifically, the generalized equivalent stiffness of the shell is:
，
wherein, Is the generalized equivalent stiffness of the shell.
Assume that the bulk modulus of the explosive at this stage satisfies:
，
wherein, Is the bulk modulus of the explosive.
Further, the generalized equivalent stiffness of the system is:
。
wherein, Is the generalized equivalent stiffness of the system.
Further, the volume of the system increase in the small deformation phase is obtained by the following method:
，
wherein, The volume of the system grows for the small deformation phase.
As shown in fig. 2, the shell is cylindrical, the center of the charging system is restrained to generate ignition with certain intensity, high-temperature and high-pressure gas generated by combustion initiates the surface combustion of the explosive matrix, the combustion leads to the increase of gas products, meanwhile, the explosive is promoted to generate more local cracks, more channels are provided for the combustion and the gas products, and the combustion and the gas products are mutually promoted to accelerate the reaction.
It is understood that volume strain refers to the change in volume of an object when subjected to an external force, as a ratio of the amount of volume change to the initial volume. When the external force is smaller or the object is stiffer, the body strain is smaller. The bulk modulus of an explosive refers to the extent to which the volume of the explosive changes when subjected to pressure. The greater the bulk modulus of the explosive, the less its volume changes when subjected to pressure, i.e., the better the compression resistance.
Specifically, the explosive burn rate satisfies Vielle's law: wherein/> Is the combustion coefficient of explosive,/>Is the combustion index of explosive/(Is the burn rate of the explosive.
The rate of mass increase of the gaseous product during the small deformation phase of the shell is obtained by the following method:
，
wherein, As a function of total surface area of the explosive combustion crack network and internal pressure of the shell,/>Is the mass of the gas product in the system.
Describing a gas product by adopting an ideal gas state equation, wherein the ideal gas state equation is as follows: wherein/> Is the density of the gas product,/>Is a universal gas constant,/>Is the gas product temperature,/>Is molar mass.
Further, bringing the volume of the small deformation stage system and the mass of the gas product into the ideal gas state equation yields the following equation:
，
wherein, For the end time of the small deformation phase,/>For the pressure inside the shell at the end of the small deformation phase,，/>；
The model of the internal reaction pressure and the shell expansion speed in the small deformation stage relative to the time t is obtained by deriving and integrating the formula:
，
wherein, ，/>Is an integral variable.
In the large deformation stage of the shell, the shell is subjected to the same deformation behavior in the longitudinal direction and the transverse direction under the assumption that the gas pressure is dynamically and uniformly distributed, and the radial expansion of the cylinder body is influenced by stretching 'resistance'. Illustratively, according to Newton's second law, as shown in FIG. 3, the radial and axial force conditions of the cylindrical shell at this stage are:
，
wherein, Is the radial mass per unit area of the shell/(Is the mass per unit area of the shell axial direction,/>Is the thickness of the shell wall,/>For the thickness of the shell end cover,/>For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the small deformation phase,/>For the shell height at the end of the small deformation phase,/>The circumferential stress to which the shell is subjected resists outward expansion of the shell,/>For the end cap to be subjected to shear forces in the axial direction,/>For the density of the shell material,，/>。
Taking the end time of the small deformation stage of the shell as the start time of the large deformation stage of the shell, wherein the total volume of the system consists of the explosive volume and the void volume at the time: wherein/> For the total volume of the system at this time,/>For the volume of the explosive at this moment,/>For the void volume at that moment,/>。
The motion process of the large deformation stage of the shell meets the following conditions:
，
wherein, For the total volume of the large deformation stage system,/>For the volume of the explosive in the large deformation stage,/>The volume of the system grows for the large deformation phase.
The above formula can be found in parallel:
，
wherein, For the volume of the explosive at the end of the small deformation,/>For small deformation end time system volume.
It will be appreciated that the bulk strain of the shell mass deformation stage system becomesWherein/>Is the volume strain of the explosive at this stage.
Further, the bulk strain of the large deformation stage of the confined charge system is obtained by the following method:
。
further, the generalized deformation equivalent stiffness of the shell is:
，
wherein, Equivalent rigidity is realized for the generalized deformation of the shell.
Assume that the bulk modulus of the explosive at this stage satisfies:
。
further, the generalized deformation equivalent stiffness of the system is:
，
wherein, Equivalent stiffness is the generalized deformation of the system.
Further, the volume of the system increase in the large deformation phase is obtained by the following method:
，
wherein, 。
Further, bringing the volume of the large deformation stage system and the mass of the gas product into an ideal gas state equation yields the following formula:
，
wherein, For the end time of the large deformation phase,/>，/>；
The model of the internal reaction pressure and the shell expansion speed in the large deformation stage relative to the time t is obtained by deriving and integrating the formula:
。
It will be appreciated that the amount of increase in volume of the system over time reflects the rate of expansion of the housing, and therefore the present application models the internal reaction pressure of the system with the rate of expansion of the housing with respect to time t.
Specifically, in step S3, in the shell inertia effect stage, due to the inertia constraint effect, the gas product drives the shell fragments to do acceleration motion, and the size of the fragments does not change in this stage, i.e. the total area of the internal pressure acting fragments is unchanged. Illustratively, according to Newton's second law, as shown in FIG. 4, the radial and axial force conditions of the cylindrical shell at this stage are:
，
wherein, For the inner radius of the shell at the end of the large deformation phase,/>For the shell height at the end of the large deformation phase,/>，/>。
Taking the end time of the shell large deformation stage as the starting time of the shell inertia effect stage, wherein the total volume of the system consists of the explosive volume and the void volume at the moment: wherein/> For the total volume of the system at this time,/>For the volume of the explosive at this moment,/>For the void volume at that moment,/>。
The motion process of the shell inertia effect phase is as follows:
，
wherein, For the total volume of the inertial effect phase system,/>Volume of explosive in inertial effect phase,/>Is the volume of the system growth in the inertia effect phase.
The above formula can be found in parallel:
，
wherein, For the volume of the explosive at the end of large deformation,/>The system volume is the end time of the large deformation.
It can be appreciated that the bulk strain of the shell inertia effect phase system isWherein/>Is the volume strain of the explosive at this stage.
Further, the bulk strain of the inertial effect phase of the confined charge system is obtained by the following method:
。
Further, the generalized equivalent inertial confinement stiffness of the housing is:
，
wherein, Equivalent rigidity is realized for the generalized deformation of the shell.
Assume that the bulk modulus of the explosive at this stage satisfies:
。
Further, the generalized equivalent inertial confinement stiffness of the system is:
，
wherein, Is the generalized equivalent inertial restraint stiffness of the system.
Further, the volume of the inertial confinement phase system increase is obtained by the following method:
，
wherein, 。
Further, the pressure release area of the shell crack is:
，
wherein, Is the pressure relief area of the shell crack.
Specifically, as shown in fig. 5, after the casing is broken, the crack is composed of a plurality of random micro cracks, and since the internal and external pressures of the system have a pressure difference, the gas product leaks outwards through the crack, i.e., a leakage phenomenon occurs, and the leakage effect is equivalent to that of the crack which increases as the radius of the casing increases.
Further, the rate of leakage of the gaseous product is obtained by the following method:
，
wherein, Is the rate of leakage of gaseous products,/>Is a multiparty index of gas products,/>Is the pressure at which the gaseous product leaks (i.e., atmospheric pressure). /(I)
Specifically, regardless of the heat dissipation flow, the gas moves along with the shell fragments to be approximately steady flow, and as known from the law of conservation of energy, any point in the system and any point at the leakage point exist:
，
wherein, Is the flow rate of the gas product in the system,/>Enthalpy at the leak of gas product,/>Is the enthalpy in the system,/>Is of atmospheric density,/>Is the density of the gaseous product.
Assuming isentropic expansion of the gas product, according to the multiparty equationThe rate of leakage of gaseous products can be obtained.
It is understood that enthalpy refers to the sum of the internal energy of the system and the external work. At constant pressure, the change in enthalpy is equal to the amount of heat absorbed or released by the system, and if the change in enthalpy is regular, the change in enthalpy is negative, the change in enthalpy is indicative of the system releasing heat. Thus, enthalpy can be used to describe the energy change of the system and the transfer and conversion of heat.
Further, the gas product mass leakage rate is:
，
wherein, Is molar mass,/>Is a universal gas constant,/>Is the gas product temperature,/>Is the gas product mass leak rate.
Further, the rate of mass increase of the gas product during the inertial effect phase is obtained by:
，
wherein, ，/>。
Further, bringing the volume of the inertial effect stage system and the mass of the inertial effect stage gas product into an ideal gas state equation yields the following equation:
，
wherein, ，/>；
The model of the internal reaction pressure and the shell expansion speed in the inertia effect stage relative to the time t is obtained by deriving and integrating the formula:
，
wherein, As a function of the total surface area of the network of explosive combustion cracks and the pressure within the enclosure.
Compared with the prior art, the modeling method for the internal reaction pressure of the constraint charging system has the following beneficial effects:
1. According to the invention, the model of the internal reaction pressure and the shell expansion speed of the system is obtained through an ideal gas state equation and the speed of increasing the mass of a gas product and the volume of a constrained explosive loading system, so that the problem that the quantitative evaluation method of the reaction intensity lacks theoretical basis due to the fact that the internal pressure of the system cannot be directly measured in the constrained explosive loading reaction evolution process is solved.
2. According to the invention, in the constrained explosive reaction evolution process, the shell of the system is divided into the small deformation, large deformation and inertia effect stages, and the models of the internal reaction pressure and the shell expansion speed of the constrained explosive system corresponding to the three stages are respectively obtained according to the different reaction evolution characteristics of the three stages, so that the accuracy of obtaining the internal reaction pressure of the system according to the models is improved.
3. According to the invention, a model of the internal reaction pressure of the constrained charging system based on the expansion speed of the shell is established, so that a theoretical basis is provided for insensitive ammunition reaction intensity evaluation.
Those skilled in the art will appreciate that all or part of the flow of the methods of the embodiments described above may be accomplished by way of a computer program to instruct associated hardware, where the program may be stored on a computer readable storage medium. Wherein the computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory, etc.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention.
Claims (10)
1. A method of modeling a reaction pressure within a confined charge system, the method comprising the steps of:
Dividing a shell of a constraint charging system into small deformation, large deformation and inertia effect stages, setting thresholds of the small deformation and the large deformation stages, and constructing a function of the total surface area of an explosive combustion crack network in the system and the pressure in the shell;
Obtaining the gas product quality of the explosive explosion in the small deformation stage and the large deformation stage based on the function of the total surface area of the combustion crack network and the pressure in the shell and Vielle law; bringing the volume and the gas product mass of the small deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the small deformation stage system relative to time t, and bringing the volume and the gas product mass of the large deformation stage system into an ideal gas state equation to obtain a model of the internal reaction pressure and the shell expansion speed of the large deformation stage system relative to time t;
Obtaining the volume of the inertial effect stage system based on the volume of the large deformation stage system and the generalized equivalent inertial constraint stiffness; obtaining the leakage speed of the gas product based on the enthalpy inside the shell and the enthalpy at the pressure release position of the shell crack; and obtaining the mass of the gas product in the inertia effect stage based on the function of the total surface area of the combustion crack network and the pressure in the shell, vielle law, the pressure release area of the shell crack and the leakage speed of the gas product, and taking the volume of the inertia effect stage system and the mass of the gas product in the inertia effect stage into an ideal gas state equation to obtain a model of the internal reaction pressure of the inertia effect stage system and the expansion speed of the shell relative to time t.
2. A method of modelling in relation to the internal reaction pressure of a confined charge system according to claim 1 wherein the generalized equivalent inertial confinement stiffness of the system is:
，
wherein, For generalized equivalent inertial confinement stiffness of the system,/>For the generalized equivalent inertial confinement stiffness of the shell,/>Is the bulk modulus of the explosive,/>For the volume of the explosive at the end of large deformation,/>The system volume is the end time of the large deformation.
3. A method of modelling in terms of the internal reaction pressure of a confined charge system as claimed in claim 2 wherein the generalized equivalent inertial confinement stiffness of the housing is:
，
wherein, To constrain the pressure of the charge system,/>To constrain the bulk strain of the inertial effect phase of the charge system.
4. A method of modelling internal reaction pressure of a confined charge system as claimed in claim 3 wherein the bulk strain of the inertial effect phase of the confined charge system is obtained by:
，
wherein, For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>For the shell height at the end of the large deformation phase,/>Is the end time of the large deformation phase.
5. A method of modelling of the internal reaction pressure of a confined charge system according to claim 1 wherein the volume of system growth during the inertial effect phase is derived by:
，
wherein, For the volume of the system growth in the shell inertia effect phase,/>For the pressure inside the shell at the end of the large deformation phase,/>For the system volume at the end of large deformation,/>For generalized equivalent inertial confinement stiffness of the system,/>To constrain the pressure of the charge system,/>。
6. A method of modelling in relation to the internal reaction pressure of a confined charge system according to claim 1 wherein the rate of increase of the mass of the gas product during the inertial effect phase is obtained by:
，
wherein, Is the combustion coefficient of explosive,/>Is the combustion index of explosive/(Is the burning rate of the explosive,/>Initial surface area of combustion crack for ignition time,/>Is the initial density of the explosive/>Is the initial volume of explosive,/>Saturation specific surface area for combustion cracking,/>For initial pressure in the housing at ignition time,/>For combustion crack reference pressure,/>Is a positive integer,/>As a function of total surface area of the explosive combustion crack network and internal pressure of the shell,/>Is the mass of the gas product in the system,/>Is the mass leakage rate of the gas product,/>To constrain the pressure of the charge system,/>，/>。
7. A method of modeling internal reaction pressure of a confined charge system as claimed in claim 1 wherein the pressure relief area of the casing fracture is:
，
wherein, Is the pressure relief area of the shell crack,/>For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>For the shell height at the end of the large deformation phase,/>Is the end time of the large deformation phase.
8. A method of modelling in relation to the internal reaction pressure of a confined charge system according to claim 1 wherein the rate of gas product leakage is derived by:
，
wherein, Is the rate of leakage of gaseous products,/>Is a multiparty index of gas products,/>Is the pressure at the leak of the gaseous product,/>To constrain the pressure of the charge system,/>Is the total volume of the inertial effect phase system.
9. A method of modeling internal reaction pressure of a confined charge system as claimed in claim 8 wherein the gas product mass leak rate is:
，
wherein, Is of atmospheric density,/>Is the pressure relief area of the shell crack,/>Is molar mass,/>Is a universal gas constant,/>Is the gas product temperature,/>Is the gas product mass leak rate.
10. A method of modelling in relation to the internal reaction pressure of a confined charge system according to claim 9 wherein bringing the volume of the inertial effect stage system and the mass of the inertial effect stage gas product into an ideal gas state equation yields the following equation:
，
wherein, Is the mass of the gas product in the system,/>For the initial volume of the void,/>For the pressure inside the shell at the end of the small deformation phase,/>For the initial volume of the system,/>Is the generalized equivalent stiffness of the system,/>For the pressure inside the shell at the end of the large deformation phase,/>For small deformation end time system volume,/>Equivalent stiffness for generalized deformation of the system,/>For the volume of the system growth in the shell inertia effect phase,/>For the end time of the large deformation phase,/>，/>；
The model of the internal reaction pressure and the shell expansion speed in the inertia effect stage relative to the time t is obtained by deriving and integrating the formula:
，
wherein, ，/>For the system volume at the end of large deformation,/>For the volume of the explosive at the end of large deformation,/>Is an integral variable,/>Is a time variable,/>Is the bulk modulus of the explosive,/>Is the combustion coefficient of explosive,/>Is the combustion index of the explosive,As a function of total surface area of the explosive combustion crack network and internal pressure of the shell,/>For the speed of radial movement of the housing,/>For the speed of the axial movement of the housing,/>For the inner radius of the shell at the end of the large deformation phase,/>Is the shell height at the end of the large deformation phase.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111898261A (en) * | 2020-07-22 | 2020-11-06 | 北京理工大学 | Ammunition reaction intensity quantitative evaluation method based on combustion network reaction evolution model |
| CN112800623A (en) * | 2020-07-22 | 2021-05-14 | 北京理工大学 | Reaction severity evaluation method of ammunition with pressure relief structure based on reaction evolution model |
| CN113591249A (en) * | 2021-08-09 | 2021-11-02 | 全球能源互联网研究院有限公司 | Simulation calculation method and system for explosion impact resistance of converter station plugging structure |
| GB2614352A (en) * | 2021-12-24 | 2023-07-05 | China Special Equipment Inspection & Res Inst | Hydraulic bulge testing method and system for material properties of HDPE |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111898261A (en) * | 2020-07-22 | 2020-11-06 | 北京理工大学 | Ammunition reaction intensity quantitative evaluation method based on combustion network reaction evolution model |
| CN112800623A (en) * | 2020-07-22 | 2021-05-14 | 北京理工大学 | Reaction severity evaluation method of ammunition with pressure relief structure based on reaction evolution model |
| CN113591249A (en) * | 2021-08-09 | 2021-11-02 | 全球能源互联网研究院有限公司 | Simulation calculation method and system for explosion impact resistance of converter station plugging structure |
| GB2614352A (en) * | 2021-12-24 | 2023-07-05 | China Special Equipment Inspection & Res Inst | Hydraulic bulge testing method and system for material properties of HDPE |
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