Modeling method for energy conversion and acting of launcher in launching channel

Abstract

The invention relates to a modeling method for energy conversion and acting of a launcher in a launching channel, and belongs to the field of insensitive charge design and evaluation. Comprising the following steps: establishing a function for constraining the internal energy of a charging gas product in the charging system, a function for constraining the external work of the charging system and a function for constraining the mass increase rate of the gas product; establishing an energy and work function in the launching channel, and obtaining an energy conversion and work model and a charge reactivity model in the launching channel based on the function of the internal energy of the charge gas product, the function of constraining the external work of the charge system, the function of the mass increase rate of the gas product and the energy and work function in the launching channel. According to the method, a function of internal energy of a charging gas product, a function of constraining external work of a charging system and a function of mass increase rate of the gas product are substituted into an energy and work function in a launching channel to obtain an energy conversion and work model in the launching channel; the problem that at present, a modeling method for an energy conversion and external work applying model in a launching channel is lacked is solved.

Description

Technical Field

[0001] The invention relates to the field of insensitive constrained charge design and evaluation, and in particular to a modeling method for energy conversion and work done by a projectile in a launch channel. Background Art

[0002] The initial velocity of a projectile is one of the important parameters for measuring the performance of a launch system, and it directly affects the range, accuracy, and penetration of the projectile. At present, the initial velocity of a projectile is mainly changed by manually adjusting the amount of charge. In order to maintain high pressure after launch, the initial velocity of the projectile is usually increased by increasing the amount of charge, but this will produce high chamber pressure, which will cause damage to the structure of the charge device and may even cause accidents that threaten the safety of the operator. With the rapid development of constrained charge launch technology in recent years, it is particularly important to optimize the initial velocity of the projectile by studying the charge combustion process.

[0003] During constrained charge launch, the launch path effect has an important influence on improving the initial velocity, range, power and accuracy of the projectile. However, the current disclosure of the motion behavior and characteristics of the projectile in the launch path is still insufficient, especially the formation mechanism and influence of energy conversion and external work in the launch path are not clear, and there is a lack of a method to model the mechanism of energy conversion and external work in the launch path.

[0004] Therefore, it becomes an urgent problem to study the energy conversion and work done by the projectile in the launch path, so as to provide a reference basis for optimizing the initial velocity control of the projectile. Summary of the invention

[0005] In view of the above analysis, the present invention aims to provide a modeling method for energy conversion and work done by a projectile in a launch channel, so as to solve the problem of the current lack of a modeling method for energy conversion and external work done in a launch channel.

[0006] The present invention provides a modeling method for energy conversion and work done by a projectile in a launch path, the method comprising the following steps:

[0007] Based on the laws of thermodynamics and the ideal gas state equation, a function constraining the internal energy of the charge gas product in the charge system is established;

[0008] Based on fluid mechanics and Lagrangian method, a function of kinetic energy of charge gas products is established. Based on the function of projectile kinetic energy and gas product kinetic energy, a function of constraining the charge system to do external work is established. Based on Vielle's law, a function of the rate of increase of gas product mass is obtained.

[0009] Based on the law of conservation of energy and interior ballistics, the energy and work functions in the launch channel are established, and the function of the internal energy of the charge gas product, the function of constraining the external work of the charge system and the function of the gas product mass increase rate are brought into the energy and work function in the launch channel to obtain a model of energy conversion and work in the launch channel; based on the function of the gas product mass increase rate, a charge reactivity model is obtained.

[0010] Furthermore, the process of energy conversion and work performance of the projectile in the launch channel is divided into a first process and a second process. The starting time of the first process is the ignition time of the ignition device, and the ending time is the time when the charge reaction is completed; the starting time of the second process is the time when the charge reaction is completed, and the ending time is the time when the projectile reaches the exit of the launch channel.

[0011] Furthermore, the models of energy conversion and work done in the emission channel corresponding to the first process and the second process are:

[0012]

[0013] Where ΔH is the energy released per unit mass of charge, a is the burning rate coefficient, and ρ 0 is the density of solid charge, A 0 is the cross-sectional area of ​​the solid charge column, t 0 is the ignition time of the ignition device, n is the burning rate pressure index, P(t) is the internal pressure of the launch channel, E J is the energy absorbed by the charge from the outside, m is the mass of the gas product, V 0 is the initial space volume between the charge and the projectile, M is the mass of the projectile, v(t) is the velocity of the projectile, A is the cross-sectional area of ​​the launch path, γ is the adiabatic index, Q(t) is the heat exchanged between the constrained charge system and the outside world, t m is the time when the charge reaction is completed, t b It is the moment when the missile reaches the exit of the launch track.

[0014] Furthermore, the charge reactivity model corresponding to the first process and the second process is:

[0015]

[0016] Among them, λ(t) is the reactivity of the charge, t 0 is the ignition time of the ignition device, t is the time variable, t m The moment when the charge reaction is completed. is the derivative of λ(t), m is the mass of the gas product, is the rate of increase of gas product mass, a is the burning rate coefficient, ρ 0 is the density of solid charge, A 0is the cross-sectional area of ​​the solid charge column, and P(t) is the internal pressure of the launch channel.

[0017] Furthermore, the function of the internal energy of the charge gas product is:

[0018]

[0019] Among them, ΔU(t) is the internal energy of the charge gas product, P(t) is the internal pressure of the launch channel, V(t) is the volume of the space between the charge and the projectile, and γ is the adiabatic index.

[0020] Furthermore, V(t) is expressed by the following formula:

[0021]

[0022] Among them, V 0 is the initial space volume between the charge and the projectile, v(t) is the velocity of the projectile, and A is the cross-sectional area of ​​the launch path.

[0023] Furthermore, the function of the kinetic energy of the charge gas product is:

[0024]

[0025] Among them, E 3 is the kinetic energy of the charge gas product, dE 3 is the kinetic energy of the current differential unit layer of the gas product, L is the distance between the bottom of the launch object and the bottom of the launch channel at the current moment, v d is the velocity of the projectile at the current moment, x is the distance between the differential unit layer of the gas product at the current moment and the bottom of the launch channel, μ is the mass of the gas product at the current moment, dx is the differential unit layer of the gas product at the current moment, m is the mass of the gas product, and v(t) is the velocity of the projectile.

[0026] Furthermore, the function of the work done by the constrained charge system is:

[0027]

[0028] Where W(t) is the work done by the constrained charge system, V 0 is the initial volume of space between the charge and the projectile, V(t) is the volume of space between the charge and the projectile, P(t) is the internal pressure of the launch channel, and E 1 is the kinetic energy of the missile, M is the mass of the missile, v(t) is the velocity of the missile, E 3 is the kinetic energy of the charge gas product, and m is the mass of the gas product.

[0029] Further, the function of the gas product mass increase rate is:

[0030]

[0031] in, is the rate of increase of gas product mass, ρ 0 is the density of solid charge, A 0 is the cross-sectional area of ​​the solid charge column, r(t) is the burning rate of the charge, i.e., the combustion velocity;

[0032] r(t) is expressed as:

[0033] r(t)=a·P n (t),

[0034] Where a is the burning rate coefficient, n is the burning rate pressure exponent, and P(t) is the internal pressure of the launch channel.

[0035] Furthermore, the energy and work function in the emission channel is:

[0036] E-ΔU(t)=Q(t)+W(t),

[0037] Among them, E is the sum of the chemical energy generated by the charge combustion and the energy absorbed by the charge from the outside world, ΔU(t) is the internal energy of the charge gas product, Q(t) is the heat exchanged between the constrained charge system and the outside world, and W(t) is the work done by the constrained charge system to the outside world;

[0038] E is represented by:

[0039]

[0040] Where ΔH is the energy released per unit mass of charge, t 0 is the ignition timing of the ignition device, is the rate of increase of gas product mass, E J To absorb the energy input from the outside world for the charge.

[0041] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0042] 1. The present invention brings the function of the internal energy of the charge gas product, the function of the external work done by the charge system and the function of the gas product mass increase rate into the energy and work function in the launch channel to obtain a model of energy conversion and work in the launch channel, which solves the current problem of unclear formation mechanism and influence of energy conversion and external work in the launch channel.

[0043] 2. The present invention divides the process of energy conversion and work done by the launch object in the launch channel into a first process and a second process. According to the difference in the mass of the gas products in the two processes, the models of energy conversion and work done in the launch channel corresponding to the first process and the second process are obtained, thereby improving the accuracy of obtaining the energy conversion in the launch channel and the external work done.

[0044] 3. The present invention provides a theoretical basis for evaluating the loss of energy conversion of a projectile in a launch channel by establishing a model of energy conversion and work done in a launch channel and a charge reactivity model.

[0045] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0047] Figure 1 The figure is a flow chart of a modeling method for energy conversion and work done by a projectile in a launch path according to an embodiment of the present invention. DETAILED DESCRIPTION

[0048] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0049] A specific embodiment of the present invention discloses a modeling method for energy conversion and work done by a projectile in a launch path. Figure 1 As shown, the method comprises the following steps:

[0050] Step S1, establishing a function constraining the internal energy of the charge gas product in the charge system based on the laws of thermodynamics and the ideal gas state equation;

[0051] Step S2, establishing a function of the kinetic energy of the charge gas product based on fluid mechanics and the Lagrangian method, establishing a function of constraining the charge system to do external work based on the function of the projectile kinetic energy and the gas product kinetic energy; and obtaining a function of the rate of increase of the gas product mass based on Vielle's law;

[0052] Step S3, based on the law of conservation of energy and interior ballistics, establish the energy and work function in the launch channel, bring the function of the internal energy of the charge gas product, the function of constraining the external work of the charge system and the function of the gas product mass increase rate into the energy and work function in the launch channel to obtain the model of energy conversion and work in the launch channel; obtain the charge reactivity model based on the function of the gas product mass increase rate.

[0053] Specifically, in step S1, the constrained charge system is composed of a projectile, a charge, a launch track and an ignition device. The charge begins to burn after being ignited by the ignition device, and continuously produces gas products in the launch track, thereby converting the chemical energy of the charge into the internal energy of the gas products. As the combustion continues, the gas products continue to increase, thereby causing the pressure in the launch track to continue to increase. Under the action of the continuous increase in the internal pressure of the launch track, the high-temperature and high-pressure gas products expand and do work, converting the internal energy of the gas products into the kinetic energy of the projectile and the gas products. It can be seen that the above process is a process in which the chemical energy of the charge in the launch track is continuously converted into the internal energy of the gas products, and finally converted into the kinetic energy of the projectile and the gas products, and the external work is performed.

[0054] It should be noted that this application studies the formation mechanism of energy conversion and work of the projectile in the launch channel. Therefore, the starting time of the study is the ignition time of the ignition device, and the ending time is the time when the projectile reaches the exit of the launch channel. The detonation method of the charge in this application is to ignite it through the ignition device to make it burn, rather than detonate, to avoid the destruction and deformation of the restrained charge system caused by detonation; and, in this application, the charge produces a large amount of gas products relatively slowly during the combustion reaction, rather than exploding instantly, to avoid the destruction and deformation of the restrained charge system caused by explosion.

[0055] Furthermore, assuming that the gas product expands isentropically, the laws of thermodynamics yield:

[0056]

[0057] Where ΔU(t) is the internal energy of the charge gas product, C p is the molar heat capacity at constant pressure, N(t) is the number of moles, T(t) is the absolute temperature of the gas product, P(t) is the internal pressure of the launch channel, V(t) is the volume of space between the charge and the projectile, t 0 is the ignition time of the ignition device, and t is the time variable.

[0058] Furthermore, based on the ideal gas state equation, we can obtain:

[0059]

[0060] Where R is the ideal gas constant.

[0061] Specifically, from the ideal gas state equation we know:

[0062] P(t)V(t)=N(t)RT(t), (3)

[0063] therefore,

[0064] Substituting (4) into (1), we can obtain equation (2).

[0065] Specifically, from the ideal gas state equation we know:

[0066] C p =C v +R, (5)

[0067] Among them, C v is the molar heat capacity at constant volume;

[0068]

[0069] Where γ is the adiabatic index;

[0070] From (5) and (6), we can get formula (7):

[0071]

[0072] Substituting equation (7) into equation (2), we get the function of the internal energy of the charge gas product:

[0073]

[0074] Specifically, V(t) is expressed by the following formula:

[0075]

[0076] Among them, V 0 is the initial space volume between the charge and the projectile, v(t) is the velocity of the projectile, and A is the cross-sectional area of ​​the launch path.

[0077] It should be noted that in the constrained charge system, the launch path is cylindrical, so the charge is also cylindrical before ignition and combustion, and is separated from the projectile by a certain distance, with a certain initial space volume between the two. The gas products generated after the charge ignites and burns will fill the initial space volume, and then begin to expand outward and do work, pushing the projectile to move, causing the space volume between the two to continue to increase.

[0078] Specifically, in step S2, the work done by the constrained charge system can be expressed as:

[0079]

[0080] Among them, W(t) is the work done by the constrained charge system.

[0081] It should be noted that the negative sign in the above formula represents the work done by the constrained charge system on the environment. After the charge is ignited, gas products are continuously generated, causing the pressure inside the constrained charge system to continue to increase. The high-pressure gas expands in the launch channel while pushing the projectile to accelerate, forming expansion work. In addition, the chemical reaction evolution of the charge is also ongoing. Therefore, the energy release generated by the combustion and the external work generated by the constrained charge system exist simultaneously. The coupling effect of the two forms the energy conversion and work of the projectile in the launch channel.

[0082] Specifically, the work done by the restrained charge system includes: work done on the projectile, work done by the projectile to overcome friction, work done by movement of gas products, work done by the recoil of the restrained charge system, and work done by the projectile to overcome the resistance of the air column.

[0083] Furthermore, the work done on the projectile, i.e., applying pressure to the projectile, gradually converts the internal energy of the charge into the kinetic energy of the projectile. Therefore, the work done on the projectile is expressed by the following formula:

[0084]

[0085] Among them, E 1 is the kinetic energy of the missile and M is the mass of the missile.

[0086] Furthermore, while the gaseous product propels the projectile, its own expansion also has kinetic energy. Therefore, the work done by the movement of the gaseous product is represented by the kinetic energy of the gaseous product.

[0087] Specifically, based on the assumption that the Lagrangian fluid mass is uniformly distributed, we can obtain:

[0088]

[0089] Wherein, L is the distance between the bottom of the launch object and the bottom of the launch channel at the current moment, μ is the mass of the gas product at the current moment, dx is the differential unit layer of the gas product at the current moment, and dμ is the mass of the fluid in the differential unit layer of the gas product at the current moment.

[0090] It should be noted that in fluid mechanics, the Lagrangian method uses material derivatives to represent the change of fluid over time. The differential unit layer of the above gas product represents the product gas uniformly distributed in the emission channel being divided vertically into microelements along the emission channel.

[0091] Specifically, assuming that the velocity of the gas product is linearly distributed, we can obtain:

[0092]

[0093] Among them, v w is the flow rate of the gas product at the current moment, that is, the speed of the gas product; v dis the velocity of the launch object at the current moment; x is the distance between the differential unit layer of the gas product and the bottom of the launch channel at the current moment.

[0094] Further, the kinetic energy of the differential unit layer of the gas product is expressed as:

[0095]

[0096] Among them, dE 3 is the kinetic energy of the current differential unit layer of the gas product.

[0097] Specifically, by substituting equations (12) and (13) into equation (14), we can obtain:

[0098]

[0099] Specifically, by integrating the above formula, we can get the function of the kinetic energy of the charge gas product as:

[0100]

[0101] Among them, E 3 is the kinetic energy of the charge gas product, and m is the mass of the gas product.

[0102] Specifically, from the bottom of the emission channel, dE 3 Start integrating until the bottom of the missile, so the lower limit of the integration is x = 0 and the upper limit of the integration is x = L, at which point μ = m.

[0103] It should be noted that, since it is not desirable to generate work for the projectile to overcome friction in practical applications, the projectile and the inner wall of the launch channel are designed to be very smooth, so that the friction is very small. According to historical experimental data, the proportion of work done by the projectile to overcome friction in the external work of the constrained charge system is usually less than 3%, so it can be ignored. Since it is also not desirable to generate recoil work of the constrained charge system in practical applications, the constrained charge system is usually heavier, and the combustion is slower than the detonation energy release, so that the recoil of the constrained charge system is very small. According to historical experimental data, the proportion of recoil work of the constrained charge system to the external work of the constrained charge system is usually less than 2%, so it can be ignored. Since the launch channel is very short in practical applications, the air column formed between the top of the projectile and the exit of the launch channel is very short, so that the projectile does very little work to overcome the resistance of the air column. According to historical experimental data, the proportion of work done by the projectile to overcome the resistance of the air column in the external work of the constrained charge system is usually less than 1%, so it can be ignored.

[0104] In summary, the function of constrained charge system doing external work is established as:

[0105]

[0106] Furthermore, because the charge combustion satisfies Vielle's law, the function of the mass increase rate of the gas product per unit time based on Vielle's law is:

[0107]

[0108] in, is the rate of increase of gas product mass, ρ 0 is the density of solid charge, A 0 is the cross-sectional area of ​​the solid charge column, and r(t) is the burning rate of the charge, that is, the combustion rate.

[0109] Specifically, r(t) is expressed as:

[0110] r(t)=a·P n (t), (19)

[0111] Where a is the burning rate coefficient and n is the burning rate pressure exponent.

[0112] Specifically, in step S3, based on the law of conservation of energy and interior ballistics, the energy and work function in the launch path is established as:

[0113] E-ΔU(t)=Q(t)+W(t), (20)

[0114] Among them, E is the sum of the chemical energy generated by the combustion of the charge and the energy absorbed by the charge from the outside world, and Q(t) is the heat exchanged between the constrained charge system and the outside world.

[0115] Furthermore, E is expressed as:

[0116]

[0117] Where ΔH is the energy released per unit mass of charge, E J To absorb the energy input from the outside world for the charge.

[0118] It should be noted that when the ignition device ignites the charge, the charge will absorb external input energy. For example, when a laser is used for ignition, the laser will generate input energy. J Smaller.

[0119] Furthermore, by substituting the function of the internal energy of the charge gas product, i.e., equation (8), and the function of the external work performed by the charge system, i.e., equations (17) and (21), into the energy and work function in the launch channel, we can obtain:

[0120]

[0121] Furthermore, the process of energy conversion and work performance of the projectile in the launch channel is divided into a first process and a second process. The starting time of the first process is the ignition time of the ignition device, and the ending time is the time when the charge reaction is completed; the starting time of the second process is the time when the charge reaction is completed, and the ending time is the time when the projectile reaches the exit of the launch channel.

[0122] It should be noted that the process of energy conversion and work done by the projectile in the launch channel includes chemical reaction and physical work. In the first process, chemical reaction and physical work exist simultaneously, and in the second process, only physical work exists.

[0123] Furthermore, by substituting the functions of the gas product mass increase rate, i.e., equations (18), (9), and (19), into equation (22), the models of energy conversion and work done in the emission channel corresponding to the first process and the second process are obtained as follows:

[0124]

[0125] Among them, t m is the time when the charge reaction is completed, t b It is the moment when the missile reaches the exit of the launch track.

[0126] It should be noted that in the present application, the heat Q(t) exchanged between the constrained charge system and the outside world is very small and can be ignored. If actually needed, Q(t) can be estimated by correction. In the first process, since the chemical reaction has not been completed, the gas product is still increasing, so the mass of the gas product is obtained based on Vielle's law. In the second process, since the chemical reaction has been completed, the mass of the gas product is m.

[0127] It can be understood that the present invention brings the function of the internal energy of the charge gas product, the function of the external work done by the constrained charge system, and the function of the gas product mass increase rate into the energy and work function in the launch channel to obtain the model of energy conversion and work done in the launch channel, which solves the current problem of unclear formation mechanism and influence of energy conversion and external work done in the launch channel. The present invention divides the process of energy conversion and work done by the projectile in the launch channel into a first process and a second process, and obtains the model of energy conversion and work done in the launch channel corresponding to the first process and the second process according to the difference in the mass of the gas product in the two processes, thereby improving the accuracy of obtaining energy conversion and external work done in the launch channel.

[0128] Furthermore, the charge reactivity model is obtained by the following formula:

[0129]

[0130] Among them, λ(t) is the reactivity of the charge.

[0131] It should be noted that the reactivity of the charge represents the degree of chemical reaction and energy release of the charge, which is the mass of the reacted charge divided by the total mass of the charge. In the combustion reaction mode, at the moment when the charge reaction is completed, i.e., t m At this moment, the charge reactivity is 100%. Based on the charge reactivity, the amount of energy that the charge can theoretically release can be obtained. By comparing it with the sum of the internal energy of the gas products in the launch channel, the kinetic energy of the projectile, and the kinetic energy of the gas products, the energy conversion loss of the projectile in the launch channel can be evaluated.

[0132] It can be understood that the present invention provides a theoretical basis for evaluating the loss of energy conversion of a projectile in a launch channel by establishing a model of energy conversion and work done in a launch channel and a charge reactivity model.

[0133] Compared with the prior art, the modeling method for energy conversion and work done by a projectile in a launch channel provided by the present invention has the following beneficial effects:

[0134] 1. The present invention brings the function of the internal energy of the charge gas product, the function of the external work done by the charge system and the function of the gas product mass increase rate into the energy and work function in the launch channel to obtain a model of energy conversion and work in the launch channel, which solves the current problem of unclear formation mechanism and influence of energy conversion and external work in the launch channel.

[0135] 2. The present invention divides the process of energy conversion and work done by the launch object in the launch channel into a first process and a second process. According to the difference in the mass of the gas products in the two processes, the models of energy conversion and work done in the launch channel corresponding to the first process and the second process are obtained, thereby improving the accuracy of obtaining the energy conversion in the launch channel and the external work done.

[0136] 3. The present invention provides a theoretical basis for evaluating the loss of energy conversion of a projectile in a launch channel by establishing a model of energy conversion and work done in a launch channel and a charge reactivity model.

[0137] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0138] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A modeling method for energy conversion and work done by a projectile in a launch path, characterized in that: The method comprises the following steps: Based on the laws of thermodynamics and the ideal gas state equation, a function constraining the internal energy of the charge gas product in the charge system is established; Based on fluid mechanics and Lagrangian method, a function of kinetic energy of charge gas products is established. Based on the function of projectile kinetic energy and gas product kinetic energy, a function of constraining the charge system to do external work is established. Based on Vielle's law, a function of the rate of increase of gas product mass is obtained. Based on the law of conservation of energy and interior ballistics, the energy and work functions in the launch channel are established, and the function of the internal energy of the charge gas product, the function of constraining the external work of the charge system and the function of the gas product mass increase rate are brought into the energy and work function in the launch channel to obtain a model of energy conversion and work in the launch channel; based on the function of the gas product mass increase rate, a charge reactivity model is obtained.

2. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 1, characterized in that: The process of energy conversion and work performance of the projectile in the launch channel is divided into a first process and a second process. The starting time of the first process is the ignition time of the ignition device, and the ending time is the time when the charge reaction is completed; the starting time of the second process is the time when the charge reaction is completed, and the ending time is the time when the projectile reaches the exit of the launch channel.

3. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 2, characterized in that: The models of energy conversion and work done in the emission channel corresponding to the first process and the second process are: Where ΔH is the energy released per unit mass of charge, a is the burning rate coefficient, ρ0 is the density of solid charge, A0 is the cross-sectional area of ​​the solid charge column, t0 is the ignition time of the ignition device, n is the burning rate pressure index, P(t) is the internal pressure of the launch channel, and E J is the energy absorbed by the charge, m is the mass of the gas product, V0 is the initial space between the charge and the projectile, M is the mass of the projectile, v(t) is the velocity of the projectile, A is the cross-sectional area of ​​the launch path, γ is the adiabatic index, Q(t) is the heat exchanged between the charge system and the outside world, t m is the time when the charge reaction is completed, t b It is the moment when the missile reaches the exit of the launch track.

4. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 2, characterized in that: The charge reactivity model corresponding to the first process and the second process is: Among them, λ(t) is the reactivity of the charge, t0 is the ignition time of the ignition device, t is the time variable, and t m The moment when the charge reaction is completed. is the derivative of λ(t), m is the mass of the gas product, is the rate of increase of the mass of the gas product, a is the burning rate coefficient, ρ0 is the density of the solid charge, A0 is the cross-sectional area of ​​the solid charge column, and P(t) is the internal pressure of the launch channel.

5. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 1, characterized in that: The function of the internal energy of the charge gas product is: Among them, ΔU(t) is the internal energy of the charge gas product, P(t) is the internal pressure of the launch channel, V(t) is the volume of the space between the charge and the projectile, and γ is the adiabatic index.

6. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 5, characterized in that: V(t) is expressed by the following formula: Among them, V0 is the initial space volume between the charge and the projectile, v(t) is the speed of the projectile, and A is the cross-sectional area of ​​the launch path.

7. The modeling method for energy conversion and work done by a projectile in a launch channel according to claim 1, characterized in that: The function of the kinetic energy of the charge gas product is: Among them, E3 is the kinetic energy of the charge gas product, dE3 is the kinetic energy of the current differential unit layer of the gas product, L is the distance between the bottom of the projectile and the bottom of the launch channel at the current moment, v d is the velocity of the projectile at the current moment, x is the distance between the differential unit layer of the gas product at the current moment and the bottom of the launch channel, μ is the mass of the gas product at the current moment, dx is the differential unit layer of the gas product at the current moment, m is the mass of the gas product, and v(t) is the velocity of the projectile.

8. The modeling method for energy conversion and work done by a projectile in a launch channel according to claim 1, characterized in that: The function of the external work done by the constrained charge system is: Where W(t) is the work done by the constrained charge system, V0 is the initial space volume between the charge and the projectile, V(t) is the space volume between the charge and the projectile, P(t) is the internal pressure of the launch channel, E1 is the kinetic energy of the projectile, M is the mass of the projectile, v(t) is the velocity of the projectile, E3 is the kinetic energy of the charge gas product, and m is the mass of the gas product.

9. The modeling method for energy conversion and work done by a projectile in a launch path according to claim 1, characterized in that: The function of the gas product mass increase rate is: in, is the rate of increase of the mass of the gas product, ρ0 is the density of the solid charge, A0 is the cross-sectional area of ​​the solid charge column, and r(t) is the burning rate of the charge, i.e., the combustion rate; r(t) is expressed as: r(t)=a·P n (t), Where a is the burning rate coefficient, n is the burning rate pressure exponent, and P(t) is the internal pressure of the launch channel.

10. The modeling method for energy conversion and work done by a projectile in a launch channel according to claim 1, characterized in that: The energy and work function in the emission channel are: E-ΔU(t)=Q(t)+W(t), Among them, E is the sum of the chemical energy generated by the charge combustion and the energy absorbed by the charge from the outside world, ΔU(t) is the internal energy of the charge gas product, Q(t) is the heat exchanged between the constrained charge system and the outside world, and W(t) is the work done by the constrained charge system to the outside world; E is represented by: Among them, ΔH is the energy released per unit mass of charge, t0 is the ignition time of the ignition device, is the rate of increase of gas product mass, E J To absorb the energy input from the outside world for the charge.

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