A modeling method for energy conversion and work done by a projectile in a launch path

Abstract

The present invention relates to a method for modeling the energy conversion and work performed by a projectile within a launch channel, and belongs to the field of insensitive charge design and evaluation. The method comprises: establishing a function constraining the internal energy of charge gas products in a charge system, a function constraining the external work performed by the charge system, and a function constraining the mass increase rate of the gas products; establishing an energy and work function within the launch channel, and obtaining a model for energy conversion and work performed within the launch channel and a charge reactivity model based on the function of the internal energy of charge gas products, the function constraining the external work performed by the charge system, the function of the mass increase rate of the gas products, and the energy and work function within the launch channel. This method substitutes the function of the internal energy of charge gas products, the function constraining the external work performed by the charge system, and the function of the mass increase rate of the gas products into the energy and work function within the launch channel to obtain a model for energy conversion and work performed within the launch channel, thus resolving the current problem of a lack of a modeling method for energy conversion and external work performed within the launch channel.

Description

Technical Field

[0001] The present 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] Projectile muzzle velocity is a key parameter in measuring launch system performance, directly affecting the projectile's range, accuracy, and penetration. Currently, varying projectile muzzle velocity primarily relies on manual adjustment of the charge quantity. To maintain high pressure after launch, increasing the charge quantity is often employed to increase the projectile's muzzle velocity. However, this generates high chamber pressure, which can damage the charge structure and even pose a risk to operator safety. With the rapid development of constrained charge launch technology in recent years, optimizing projectile muzzle velocity through studying the charge combustion process is becoming increasingly important.

[0003] During constrained charge launch, the launch path effect has a significant impact on improving the initial velocity, range, power, and accuracy of the projectile. However, the current understanding of the projectile's motion behavior and characteristics 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. There is a lack of a method to model the mechanism of energy conversion and external work in the launch path.

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

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

[0006] The present invention provides a method for modeling energy conversion and work performed 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 that constrains the internal energy of the charge gas products in the charge system is established.

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

[0009] Based on the law of conservation of energy and interior ballistics, the energy and work function in the launch channel is established. 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 substituted 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 and second processes are:

[0012]

[0013] 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 ​​solid charge column, t0 is the ignition time of ignition device, n is the burning rate pressure index, P(t) is the internal pressure of launch channel, E J is the energy absorbed by the charge from the outside, m is the mass of the gas product, V0 is the initial volume of the 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 constrained charge system and the outside world, t m is the time when the charge reaction is completed, t b The moment when the missile reaches the exit of the launch channel.

[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, t0 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 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.

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

[0018]

[0019] Where 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] Where V0 is the initial volume of space 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] Where E3 is the kinetic energy of the charge gas product, dE3 is the kinetic energy of the gas product at the current differential unit layer, 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.

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

[0027]

[0028] Where W(t) is the work done by the constrained charge system, V0 is the initial volume of the space between the charge and the projectile, V(t) is the volume of the space 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.

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

[0030]

[0031] in, is the rate of increase of the mass of the gaseous 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;

[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] Where E is the sum of the chemical energy generated by 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 restrained charge system and the outside world, and W(t) is the work done by the restrained charge system to the outside world.

[0038] E is represented by:

[0039]

[0040] 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.

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

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

[0043] 2. 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. Based on the difference in the mass of the gas products in the two processes, 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 energy conversion and external work done in the launch channel.

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

[0045] In the present invention, the above-mentioned technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of the present invention will be described in the following description, and some advantages will become apparent from the description or be learned through practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying 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 parts throughout the drawings.

[0047] Figure 1 Flowchart of a method for modeling energy conversion and work performed 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 will be 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, and 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 includes 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 products based on fluid mechanics and the Lagrangian method, establishing a function for constraining the charge system from doing external work based on the functions of the projectile kinetic energy and the kinetic energy of the gas products, 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, an energy and work function within the launch channel is established. The function of the internal energy of the charge gas product, the function constraining the external work of the charge system, and the function of the gas product mass increase rate are substituted into the energy and work function within the launch channel to obtain a model of energy conversion and work within the launch channel; and a charge reactivity model is obtained based on the gas product mass increase rate function.

[0053] Specifically, in step S1, the constrained charge system consists of a projectile, a charge, a launch track, and an ignition device. After the charge is ignited by the ignition device, it begins to burn, continuously producing gaseous products within the launch track, thereby converting the chemical energy of the charge into the internal energy of the gaseous products. As combustion continues, the gaseous products continue to increase, causing the pressure within the launch track to continue to rise. Under the influence of the continuously increasing pressure within the launch track, the high-temperature and high-pressure gaseous products expand and perform work, converting the internal energy of the gaseous products into the kinetic energy of the projectile and the gaseous products. It can be seen that the above process is a process in which the chemical energy of the charge within the launch track is continuously converted into the internal energy of the gaseous products, and ultimately into the kinetic energy of the projectile and the gaseous products, as well as external work.

[0054] It should be noted that this application studies the energy conversion and work generation mechanisms of projectiles within the launch path. Therefore, the study begins at the ignition of the ignition device and ends at the moment the projectile reaches the launch path exit. The charge in this application is detonated by ignition via the ignition device, resulting in combustion, rather than detonation, thus avoiding detonation-induced damage and deformation of the confined charge system. Furthermore, the charge in this application produces a large amount of gaseous products relatively slowly during the combustion reaction, rather than exploding instantly, thus avoiding detonation-induced damage and deformation of the confined charge system.

[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 the space between the charge and the projectile, t0 is the ignition moment 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 formula (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] Where V0 is the initial volume of space 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, and therefore the charge is also cylindrical before ignition and combustion. It is separated from the projectile by a certain distance, creating a certain initial volume of space between them. The gaseous products produced by the charge ignition and combustion fill this initial volume, then begin to expand outward, performing work and propelling the projectile, causing the volume of the space between them to continuously increase.

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

[0079]

[0080] Where 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 confined charge system on the environment. After the charge is ignited, gas products are continuously produced, causing the pressure inside the confined charge system to continuously increase. While pushing the projectile to accelerate, the high-pressure gas expands in the launch channel, generating expansion work. In addition, the chemical reaction evolution of the charge is also ongoing. Therefore, the energy release generated by combustion and the external work generated by the confined charge system exist simultaneously. The coupling effect of the two results in the energy conversion and work done by the projectile in the launch channel.

[0082] Specifically, the external work done by the constrained charge system includes: work done on the projectile, work done by the projectile to overcome friction, work done by the movement of gas products, work done by the recoil of the constrained 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., the application of 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 equation:

[0084]

[0085] Where E1 is the kinetic energy of the missile and M is the mass of the missile.

[0086] Furthermore, while the gas products propel the projectile to move, their own expansion also possesses kinetic energy. Therefore, the work done by the movement of the gas products is represented by the kinetic energy of the gas products.

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

[0088]

[0089] Where 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 time-dependent changes in the fluid. The differential unit layer of the gas product described above represents the product gas uniformly distributed in the emission channel being divided vertically along the emission channel into individual microelements.

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

[0095]

[0096] Wherein, dE3 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] Where E3 is the kinetic energy of the charge gas product, and m is the mass of the gas product.

[0102] Specifically, dE3 is integrated from the bottom of the emission channel to the bottom of the projectile. Therefore, the lower limit of the integration is x = 0, and the upper limit of the integration is x = L. At this time, μ = m.

[0103] It should be noted that, since work performed by the projectile overcoming friction is undesirable in practical applications, the projectile and the inner wall of the launch chute are designed to be very smooth, minimizing friction. Historical experimental data shows that the work performed by the projectile overcoming friction typically accounts for less than 3% of the external work performed by the confined charge system and can be ignored. Since recoil work is also undesirable in practical applications, confined charge systems are typically heavy, and combustion releases energy more slowly than detonation, minimizing recoil. Historical experimental data shows that recoil work typically accounts for less than 2% of the external work performed by the confined charge system and can be ignored. Since the launch chute is very short in practical applications, the air column formed between the top of the projectile and the launch chute exit is also very short, minimizing the work performed by the projectile overcoming air column resistance. Historical experimental data shows that the work performed by the projectile overcoming air column resistance typically accounts for less than 1% of the external work performed by the confined charge system and can be ignored.

[0104] In summary, the function of the 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 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, 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 channel 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 the energy input from the outside. For example, if a laser is used for ignition, the laser will generate the 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 constrained charge system, i.e., equations (17) and (21), into the energy and work functions within 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, while in the second process, only physical work exists.

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

[0124]

[0125] Among them, t m is the time when the charging reaction is completed, t b The moment when the missile reaches the exit of the launch channel.

[0126] It should be noted that in this application, the heat Q(t) exchanged between the constrained charge system and the outside world is very small and can be ignored. If necessary, Q(t) can be estimated by correction. In the first process, since the chemical reaction has not yet 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 is complete, the mass of the gas product is m.

[0127] As can be understood, the present invention incorporates a function of the internal energy of the charge gas products, a function constraining the external work performed by the charge system, and a function of the rate of increase in the mass of the gas products into the energy and work functions within the launch channel to produce a model of energy conversion and work performed within the launch channel. This solves the current problem of unclear understanding of the formation mechanism and impact of energy conversion and external work performed within the launch channel. The present invention divides the process of energy conversion and work performed by the projectile within the launch channel into a first process and a second process. Based on the difference in the mass of the gas products in the two processes, the present invention derives models of energy conversion and work performed within the launch channel corresponding to the first and second processes, thereby improving the accuracy of the energy conversion and external work performed within the launch channel.

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

[0129]

[0130] Where 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, that is, t m At this moment, the charge's reactivity is 100%. Based on the charge's reactivity, we can derive the theoretical amount of energy it can release. By comparing this 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, we can assess the energy loss of the projectile in the launch channel.

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

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

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

[0135] 2. 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. Based on the difference in the mass of the gas products in the two processes, 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 energy conversion and external work done in the launch channel.

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

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

[0138] The above description is only a preferred specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any technician familiar with this technical field within the technical scope disclosed by the present invention should be covered by the scope of protection 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 that constrains the internal energy of the charge gas products in the charge system is established. Based on fluid mechanics and the Lagrangian method, a function for the kinetic energy of the charge gas products is established. Based on the functions of the projectile kinetic energy and the kinetic energy of the gas products, a function for constraining the charge system to do external work is established. Based on Vielle's law, a function for the rate of increase of the gas product mass is obtained. Based on the law of conservation of energy and interior ballistics, an energy and work function within the launch channel is established. A function of the internal energy of the charge gas products, a function constraining the external work of the charge system, and a function of the mass increase rate of the gas products are substituted into the energy and work function within the launch channel to obtain a model of energy conversion and work within the launch channel. A charge reactivity model is obtained based on the function of the mass increase rate of the gas products. The process of energy conversion and work performed by the projectile in the launch channel is divided into a first process and a second process. The first process starts when the ignition device is ignited and ends when the charge reaction is completed. The second process starts when the charge reaction is completed and ends when the projectile reaches the exit of the launch channel. The models of energy conversion and work done in the emission channel corresponding to the first and second processes 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 ​​solid charge column, t0 is the ignition time of ignition device, n is the burning rate pressure index, P(t) is the internal pressure of launch channel, E J is the energy absorbed by the charge from the outside, m is the mass of the gas product, V0 is the initial volume of the 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 constrained charge system and the outside world, t m is the time when the charge reaction is completed, t b The moment when the missile reaches the exit of the launch track; The charge reactivity model corresponding to the first and second processes 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, 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.

2. The modeling method for energy conversion and work performed 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: Where 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.

3. The modeling method for energy conversion and work performed by a projectile in a launch path according to claim 2, characterized in that: V(t) is expressed by the following formula: Where V0 is the initial volume of space 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.

4. The modeling method for energy conversion and work performed by a projectile in a launch path according to claim 1, characterized in that: The function of the kinetic energy of the charge gas product is: Where E3 is the kinetic energy of the charge gas product, dE3 is the kinetic energy of the gas product at the current differential unit layer, 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.

5. The modeling method for energy conversion and work performed by a projectile in a launch path 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 volume of the space between the charge and the projectile, V(t) is the volume of the space 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.

6. The modeling method for energy conversion and work performed 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 gaseous 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.

7. The modeling method for energy conversion and work performed by a projectile in a launch path according to claim 1, characterized in that: The energy and work function in the emission channel are: E-ΔU(t)=Q(t)+W(t), Where E is the sum of the chemical energy generated by 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 restrained charge system and the outside world, and W(t) is the work done by the restrained 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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