CN110289053A - Gun propellant combustion generates plasma law study method - Google Patents
Gun propellant combustion generates plasma law study method Download PDFInfo
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- CN110289053A CN110289053A CN201910559092.XA CN201910559092A CN110289053A CN 110289053 A CN110289053 A CN 110289053A CN 201910559092 A CN201910559092 A CN 201910559092A CN 110289053 A CN110289053 A CN 110289053A
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Abstract
The invention discloses gun propellant combustions to generate plasma law study method, comprising the following steps: S1: the calculating of gun propellant combustion generation plasma parameter；S2: the chemical analysis of combustion gas is calculated with equilibrium constant method；S3: equation group is programmed in MATLAB according to calculation method above, can calculate the relationship between plasma parameter by interpretation of result；S4: the Physical Process Analyses；S5: model construction；S6: model verifying is drawn a conclusion.Research method of the invention can be derived that electron density and degree of ionization all increase as the temperature increases；Pressure is bigger at identical temperature, electron density is bigger, degree of ionization is smaller, explosive payload and the different of chambervolume change fuel gas temperature rate of change, the rate of change of plasma electron density is affected accordingly, the difference of impetus changes combustion gas maximum temperature, changes the maximum value of plasma electron density accordingly.
Description
Technical field
The present invention relates to plasma field, specially gun propellant combustion generates plasma law study method.
Background technique
Plasma after decades of development, have been developed as comprising astrophysical plasma, nuclear fusion plasma,
The independent educational project of the branches such as low temperature plasma, plasma are also widely used for controlled nuclear fusion, magnetohydrodynamic generator, material
The fields such as Surface Engineering, however, only additional plasma is applied to the research of electrothermal chemical gun in terms of cannon, for
The research that the plasma that gun propellant combustion generates is used to improve cannon performance is also not directed to；Gun propellant combustion generates plasma
Rule, be research and utilization propellant powder generate plasma improve cannon performance basis.
Summary of the invention
The purpose of the present invention is to provide gun propellant combustions to generate plasma law study method, to solve above-mentioned background
The problem of being proposed in technology.
To achieve the above object, the invention provides the following technical scheme: gun propellant combustion generates plasma law study
Method, comprising the following steps:
S1: gun propellant combustion generates plasma law study method, and reactant A in chemical reaction and B are generated and produced
Object C and D, a, b, c, d are the amount of the substance of respective substance respectively；
Its positive and backward reaction speed is respectively as follows:
V1=K1[A]a[B]b,V2=K2[C]c[D]d 2
Wherein, [A], [B], [C], [D] respectively indicate the concentration of each substance, when reaction reaches equilibrium state, i.e. forward and reverse
The rate of reaction reaches equal, it may be assumed that
K1[A]a[B]b=K2[C]c[D]d 3
The chemical equilibrium constant K of the available reaction after derivation:
According to mass conservation law, the atom number at any element any moment in the reaction for participating in reaction is constant
's；
Chemical equilibrium constant method is to pass through each reaction of simultaneous based on chemical reaction equilibrium and mass conservation law
Equation forms equation group, solves each component, its advantage is the true shape that can intuitively reflect chemical reaction
State, another advantage are to facilitate adjusting, can change the differential responses in reaction system according to target needs；
S2: calculating the chemical analysis of combustion gas with equilibrium constant method, according to equilibrium constant method principle, makes several presupposition: combustion
Product is burnt to be uniformly mixed；Gas Components are under chemistry balance state；Combustion Gas Plasma obeys The Ideal-Gas Equation, is
Acquisition higher plasma density, is added potassium carbonate in propellant powder, in propellant powder and additive altogether containing C, H, O,
N, five kinds of elements of K can indicate the chemical reaction process of burning with following 15 equations:
Ki is the chemical equilibrium constant of each composition, K in above formula6K7K8K9K10K11Value can pass through following formula meter
It obtains；
The combustion gas composition that propellant combustion gas generates plasma considers altogether 21 kinds of compositions in calculating, respectively CO2,
CO, H2O, OH, O2, O, H2, H, N2, NO, N, N2O, NO2, K2CO3, K2O, KO, KOH, K, K+, OH-, e electronics, according to above
The corresponding molar fraction x of sequenceiFollowing table be followed successively by 1,2 ... 21；
According to four mass conservation laws, available following four equation:
M in formula aboveC MH MO MN MKFive kinds of Elements Cs, the quality of H, O, N, K in reactant are respectively indicated,
Their numerical value can be calculated by the ratio of additive in propellant powder, as being added to quality in x kilograms of propellant powder
Percentage is the seed of n, then
MC=12 × (25.5243+1000 × n/ ((1-x) × 138)) 31
MH=33.1277 32
MO=16 × (33.0757+3 × 1000 × n/ ((1-x) × 138)) 33
MN=14 × 9.3395 34
MK=78 × 1000 × n/ ((1-x) × 138) 35
According to Dalton's law (of partial pressures):
Due to xiIt is molar fraction, so having:
pi=xip 37
It can be obtained by formula 37:
In addition, for charged particle, due to electroneutral, it is assumed that the i-th component carried charge qi, then have:
In this way, obtaining 21 equations, the closure equation group that can solve 21 kinds of combustion product components is constituted, calculating is passed through
The parameter of related component can be solved；
Partial ionization, the calculation formula of electron density occur in combustion gas are as follows:
S3: interpretation of result programs equation group according to calculation method above in MATLAB, can calculate etc. from
Relationship between daughter parameter；
S4: the Physical Process Analyses, classical interior ballistics are to study each fire under high pressure conditions using thermodynamics as theoretical foundation
The theory of big gun interior ballistic parameters average value, the mathematical model of classical interior ballistics are One first-order ordinary differential equations, by propellant shape letter
Number equation, energy equation, combustion rate of powder equation, Projectile Motion rate equation and velocity of shot and five equations of stroke equation form
Equation group；
According to the characteristics of powder burning situation, being made under high pressure conditions it is assumed hereinafter that:
Assuming that no matter main charge or ignition charge all meet geometry combustion law；
Powder burning uses burning rate exponent formula, i.e.,
It is assumed that gun propellant combustion and Projectile Motion are carried out under average pressure；
Heat leakage is more complicated when shooting, and is difficult to describe, usually using the method for reducing impetus or increase specific heat
It is modified, actually reduces transmitting dose；
All secondary function coefficientsIt calculates, mainly and kinetic energy due to function secondary in shooting courseHave
It closes, all secondary function can use coefficientTo take in；
The condition that the pressure for getting into bearing band using bullet starts as bullet；
Combustion gas meets Nobel in thorax --- Abel's state equation；
Gas leak phenomenon is not present in bearing band good seal；
For certain specific gunpowder, its quick-fried temperature be it is certain, this is related with the property of gunpowder, be one often
Amount, therefore, the equation of gas state under constant volume state is as shown in Equation 41:
Wherein, VψIt for free volume, changes with pressure one, under the constant volume state indicated using impetus and loading density
The equation of gas state it is as shown in Equation 42:
As can be seen that pressure is gradually changed with powder burning percentage in formula, still, ignition temperature is always
It is the quick-fried temperature of gunpowder；
In order to increase the thermal ionization of combustion product, a small amount of potassium carbonate is added in propellant powder in the present invention, according to thermoelectricity
From theory, following hypothesis is made:
Potassium carbonate decomposes completely in the high temperature environment；
It is assumed that combustion product is uniform；
Not the case where not considering double ionization or the Multiple ionization that probability of occurrence is minimum during thermal ionization；
S5: model construction, propellant shape functional equation are as shown in Equation 43:
Wherein, the shape feature amount before χ, λ are gunpowder division；Zk is that gunpowder has fired thickness relatively at the end of burning；χs、
λsFor the shape feature amount after gunpowder division；
Burning velocity equation is as shown in Equation 44:
According to the basic assumption of powder burning inner trajectory, while considering the influence of secondary function, can be obtained by Newton's law:
According to law of conservation of energy, the energy equation for obtaining powder burning is as shown in Equation 47:
It is as shown in Equation 48 that interior trajectory equations under high pressure conditions are obtained according to above equation:
Since powder gas constantly pushes bullet to do work and off-energy, so fuel gas temperature constantly reduces, powder gases
The variation relation of temperature and volume is as shown in Equation 49:
p(Vψ+ Sl)=ω ψ RT 49
Usually indicated with bullet stroke:
Sp(l+lψ)=ω ψ RT 50
Temperature is to have fired the related function of percentage ψ with pressure p, bullet stroke l, gunpowder, these data can be by interior
External ballistic equations acquire；
By fuel gas temperature equation, the combustion temperature of powder gas can be obtained, due to generating plasma in powder gas
Mode is thermal ionization, it is possible to calculate electron density in combustion gas using Saha's equation；
It generates plasma density equation group under high pressure conditions to consist of three parts: interior trajectory equations, fuel gas temperature side
Journey and electron density equation, simulation process are divided into three steps, calculate gaseous-pressure, bullet stroke etc. according to interior ballistic equation first
Powder gas is gone out by fuel gas temperature equation calculation then according to the calculated result of inner trajectory with the relationship of powder burning quality
Temperature, finally further according to electron density in electron density equation calculation plasma；
S6: model verifying, the data and test data obtained by numerical simulation compare, in bullet quality m=
In the case where 0.39kg, explosive payload ω=0.136kg, chambervolume V0=1.32 × 10-4m3, acquires gun pressure maximum value and exist
374MPa, muzzle velocity 898m/s coincide substantially with test result, and image is substantially close, demonstrates the correctness of model built.
Preferably, parameter a in the S1ik ajkRespectively indicate the atom of certain element in 1mol gaseous substance and solid matter
Number, ngi nsjRespectively indicate the molal quantity of gaseous component and solid phase components in unit material, NkThen indicate the atom of certain element
Sum.
Preferably, K in the S21K2K3K4K5K12K13K14K15Numerical value be known constant.
Preferably, electron density and temperature are positively related relationship, as the temperature increases, electron density in the S3
Increasing, and when temperature is the same, pressure is bigger, and electron density is bigger, this is because as the temperature increases, electronics
The energy of acquisition is more, the easier constraint for shaking off atom of electronics and become free electron.
Preferably, S is bullet the maximum cross-section area in the S4；P is powder gas average pressure；M is the quality of bullet；
L is bullet stroke；V is velocity of shot；It is secondary work factor.
Preferably, l in the S4ψIt is that the free volume undergauge of coyote hole is long, ω is charging quality, and θ is gunpowder thermal parameter, ψ
It is that gunpowder has fired percentage, f is impetus, and Δ is loading density, ρpIt is gunpowder density, α is covolume.
Preferably, T is thermodynamic temperature in the S5, and Ei is the ionization potential of ion, goFor the statistical weight of atomic ground state
Weight, giFor the statistical weight of ion ground-state, me is electron mass, and ne is electron density, and ni is ion concentration, and n0 is that atom is close
Degree, for alkali metal,Value be about 1, other gases are generally 2.
Preferably, electron density in the plasma in the S5
Compared with prior art, the beneficial effects of the present invention are: electron density and degree of ionization all as the temperature increases and
Increase；Pressure is bigger at identical temperature, and electron density is bigger, and degree of ionization is smaller, and explosive payload and the different of chambervolume change combustion
Gas rate temperature change, affects the rate of change of plasma electron density accordingly, and the difference of impetus changes combustion gas
Maximum temperature changes the maximum value of plasma electron density accordingly.
Detailed description of the invention
Fig. 1 is the flow chart of research method of the invention；
Table 1 is the formula composition of propellant powder of the present invention；
Fig. 2 is the relational graph of electron density and temperature of the invention；
Fig. 3 is internal ballistic tests curve and simulation curve comparison diagram of the invention；
Fig. 4 is gun pressure time plot of the invention；
Fig. 5 is velocity of shot time plot of the invention；
Fig. 6 is gun pressure displacement curve figure of the invention；
Fig. 7 is velocity of shot displacement curve of the invention.
Specific embodiment
The technical scheme in the embodiments of the invention will be clearly and completely described below, it is clear that described implementation
Example is only a part of the embodiment of the present invention, instead of all the embodiments.Based on the embodiments of the present invention, this field is common
Technical staff's every other embodiment obtained without making creative work belongs to the model that the present invention protects
It encloses.
Embodiment one
Fig. 1 is please referred to, the present invention provides a kind of technical solution: gun propellant combustion generates plasma law study method,
The following steps are included:
S1: as shown in table 1, gun propellant combustion generates plasma law study method, for reactant A in chemical reaction
Product C and D are generated with B, a, b, c, d are the amount of the substance of respective substance respectively；
Its positive and backward reaction speed is respectively as follows:
V1=K1[A]a[B]b,V2=K2[C]c[D]d 2
Wherein, [A], [B], [C], [D] respectively indicate the concentration of each substance, when reaction reaches equilibrium state, i.e. forward and reverse
The rate of reaction reaches equal, it may be assumed that
K1[A]a[B]b=K2[C]c[D]d 3
The chemical equilibrium constant K of the available reaction after derivation:
According to mass conservation law, the atom number at any element any moment in the reaction for participating in reaction is constant
's；
Chemical equilibrium constant method is to pass through each reaction of simultaneous based on chemical reaction equilibrium and mass conservation law
Equation forms equation group, solves each component, its advantage is the true shape that can intuitively reflect chemical reaction
State, another advantage are to facilitate adjusting, can change the differential responses in reaction system according to target needs；
Parameter aik ajkRespectively indicate the atom number of certain element in 1mol gaseous substance and solid matter, ngi nsjRespectively
Indicate the molal quantity of gaseous component and solid phase components in unit material, NkThen indicate the total atom number of certain element；
S2: it as in Figure 2-4, is made with the chemical analysis that equilibrium constant method calculates combustion gas according to equilibrium constant method principle
Several presupposition: combustion product is uniformly mixed；Gas Components are under chemistry balance state；Combustion Gas Plasma obeys perfect gas
Potassium carbonate is added in propellant powder, has altogether in propellant powder and additive in order to obtain higher plasma density for state equation
The chemical reaction process of burning can be indicated with following 15 equations containing five kinds of elements of C, H, O, N, K:
Ki is the chemical equilibrium constant of each composition, K in above formula2K3K4K5K12K13K1K14K15Numerical value be it is known often
Number, K6K7K8K9K10K11Value can be calculated by the following formula to obtain；
The combustion gas composition that propellant combustion gas generates plasma considers altogether 21 kinds of compositions in calculating, respectively CO2,
CO, H2O, OH, O2, O, H2, H, N2, NO, N, N2O, NO2, K2CO3, K2O, KO, KOH, K, K+, OH-, e electronics, according to above
The corresponding molar fraction x of sequenceiFollowing table be followed successively by 1,2 ... 21；
According to four mass conservation laws, available following four equation:
M in formula aboveC MH MO MN MKFive kinds of Elements Cs, the quality of H, O, N, K in reactant are respectively indicated,
Their numerical value can be calculated by the ratio of additive in propellant powder, as being added to quality in x kilograms of propellant powder
Percentage is the seed of n, then
MC=12 × (25.5243+1000 × n/ ((1-x) × 138)) 31
MH=33.1277 32
MO=16 × (33.0757+3 × 1000 × n/ ((1-x) × 138)) 33
MN=14 × 9.3395 34
MK=78 × 1000 × n/ ((1-x) × 138) 35
According to Dalton's law (of partial pressures):
Due to xiIt is molar fraction, so having:
pi=xip 37
It can be obtained by formula 37:
In addition, for charged particle, due to electroneutral, it is assumed that the i-th component carried charge qi, then have:
In this way, obtaining 21 equations, the closure equation group that can solve 21 kinds of combustion product components is constituted, calculating is passed through
The parameter of related component can be solved；
Partial ionization, the calculation formula of electron density occur in combustion gas are as follows:
S3: interpretation of result programs equation group according to calculation method above in MATLAB, can calculate etc. from
Relationship between daughter parameter, electron density and temperature are positively related relationships, and as the temperature increases, electron density is also increasing
Add, and when temperature is the same, pressure is bigger, and electron density is bigger, this is because as the temperature increases, electronics obtains
Energy it is more, the easier constraint for shaking off atom of electronics and become free electron；
S4: as shown in figure 5, the Physical Process Analyses, classical interior ballistics are to study high pressure shape using thermodynamics as theoretical foundation
The theory of each gun interior ballistics mean parameter, the mathematical model of classical interior ballistics are One first-order ordinary differential equations under state, by
Propellant shape functional equation, energy equation, combustion rate of powder equation, Projectile Motion rate equation and velocity of shot and stroke equation five
The equation group of a equation composition；
According to the characteristics of powder burning situation, being made under high pressure conditions it is assumed hereinafter that:
Assuming that no matter main charge or ignition charge all meet geometry combustion law；
Powder burning uses burning rate exponent formula, i.e.,
It is assumed that gun propellant combustion and Projectile Motion are carried out under average pressure；
Heat leakage is more complicated when shooting, and is difficult to describe, usually using the method for reducing impetus or increase specific heat
It is modified, actually reduces transmitting dose；
All secondary function coefficientsIt calculates, mainly and kinetic energy due to function secondary in shooting courseHave
It closes, all secondary function can use coefficientTo take in；
The condition that the pressure for getting into bearing band using bullet starts as bullet；
Combustion gas meets Nobel in thorax --- Abel's state equation；
Gas leak phenomenon is not present in bearing band good seal；
For certain specific gunpowder, its quick-fried temperature be it is certain, this is related with the property of gunpowder, be one often
Amount, therefore, the equation of gas state under constant volume state is as shown in Equation 41:
Wherein, VψIt for free volume, changes with pressure one, under the constant volume state indicated using impetus and loading density
The equation of gas state it is as shown in Equation 42:
As can be seen that pressure is gradually changed with powder burning percentage in formula, still, ignition temperature is always
It is the quick-fried temperature of gunpowder；
In order to increase the thermal ionization of combustion product, a small amount of potassium carbonate is added in propellant powder in the present invention, according to thermoelectricity
From theory, following hypothesis is made:
Potassium carbonate decomposes completely in the high temperature environment；
It is assumed that combustion product is uniform；
Not the case where not considering double ionization or the Multiple ionization that probability of occurrence is minimum during thermal ionization；
S is bullet the maximum cross-section area；P is powder gas average pressure；M is the quality of bullet；L is bullet stroke；V is
Velocity of shot；It is secondary work factor, lψIt is that the free volume undergauge of coyote hole is long, ω is charging quality, and θ is gunpowder thermal parameter, ψ
It is that gunpowder has fired percentage, f is impetus, and Δ is loading density, ρpIt is gunpowder density, α is covolume；
S5: as shown in fig. 6-7, model construction, propellant shape functional equation is as shown in Equation 43:
Wherein, the shape feature amount before χ, λ are gunpowder division；Zk is that gunpowder has fired thickness relatively at the end of burning；χs、
λsFor the shape feature amount after gunpowder division；
Burning velocity equation is as shown in Equation 44:
According to the basic assumption of powder burning inner trajectory, while considering the influence of secondary function, can be obtained by Newton's law:
According to law of conservation of energy, the energy equation for obtaining powder burning is as shown in Equation 47:
It is as shown in Equation 48 that interior trajectory equations under high pressure conditions are obtained according to above equation:
Since powder gas constantly pushes bullet to do work and off-energy, so fuel gas temperature constantly reduces, powder gases
The variation relation of temperature and volume is as shown in Equation 49:
p(Vψ+ Sl)=ω ψ RT 49
Usually indicated with bullet stroke:
Sp(l+lψ)=ω ψ RT 50
Temperature is to have fired the related function of percentage ψ with pressure p, bullet stroke l, gunpowder, these data can be by interior
External ballistic equations acquire；
By fuel gas temperature equation, the combustion temperature of powder gas can be obtained, due to generating plasma in powder gas
Mode is thermal ionization, it is possible to calculate electron density in combustion gas using Saha's equation；
It generates plasma density equation group under high pressure conditions to consist of three parts: interior trajectory equations, fuel gas temperature side
Journey and electron density equation, simulation process are divided into three steps, calculate gaseous-pressure, bullet stroke etc. according to interior ballistic equation first
Powder gas is gone out by fuel gas temperature equation calculation then according to the calculated result of inner trajectory with the relationship of powder burning quality
Temperature, finally further according to electron density in electron density equation calculation plasma, T is thermodynamic temperature, and Ei is ion
Ionization potential, goFor the statistical weight of atomic ground state, giFor the statistical weight of ion ground-state, me is electron mass, and ne is that electronics is close
Degree, ni is ion concentration, and n0 is atomic density, for alkali metal,Value be about 1, other gases are generally 2；
S6: model verifying, the data and test data obtained by numerical simulation compare, in bullet quality m=
In the case where 0.39kg, explosive payload ω=0.136kg, chambervolume V0=1.32 × 10-4m3, acquires gun pressure maximum value and exist
374MPa, muzzle velocity 898m/s coincide substantially with test result, and image is substantially close, demonstrate the correctness of model built,
Electron density is in plasma
By carrying out experimental study to above-described embodiment, research method of the present invention can be derived that electron density and degree of ionization all
Increase as the temperature increases；Pressure is bigger at identical temperature, and electron density is bigger, and degree of ionization is smaller, explosive payload and coyote hole
The different of volume change fuel gas temperature rate of change, affect the rate of change of plasma electron density, impetus accordingly
Difference change combustion gas maximum temperature, change the maximum value of plasma electron density accordingly.
It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with
A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding
And modification, the scope of the present invention is defined by the appended.
Claims (8)
1. gun propellant combustion generates plasma law study method, which comprises the following steps:
S1: gun propellant combustion generates the calculating of plasma parameter, generates product C and D for reactant A in chemical reaction and B,
A, b, c, d are the amount of the substance of respective substance respectively,
Its positive and backward reaction speed is respectively as follows:
V1=K1[A]a[B]b,V2=K2[C]c[D]d 2
Wherein, [A], [B], [C], [D] respectively indicate the concentration of each substance, when reaction reaches equilibrium state, i.e., positive back reaction
Rate reach equal, it may be assumed that
K1[A]a[B]b=K2[C]c[D]d 3
The chemical equilibrium constant K of the available reaction after derivation:
According to mass conservation law, the atom number at any element any moment in the reaction for participating in reaction be it is constant,
Chemical equilibrium constant method is to pass through the side of each reaction of simultaneous based on chemical reaction equilibrium and mass conservation law
Journey forms equation group, solves each component, its advantage is the time of day that can intuitively reflect chemical reaction,
Another advantage is to facilitate adjusting, can change the differential responses in reaction system according to target needs；
S2: calculating the chemical analysis of combustion gas with equilibrium constant method, and according to equilibrium constant method principle, make several presupposition: burning produces
Object is uniformly mixed；Gas Components are under chemistry balance state；Combustion Gas Plasma obeys The Ideal-Gas Equation, in order to obtain
Higher plasma density is obtained, potassium carbonate is added in propellant powder, contains C, H, O, N, K five altogether in propellant powder and additive
Kind element can indicate the chemical reaction process of burning with following 15 equations:
Ki is the chemical equilibrium constant of each composition, K in above formula6 K7 K8 K9 K10 K11Value can pass through following formula meter
It obtains；
The combustion gas composition that propellant combustion gas generates plasma considers altogether 21 kinds of compositions in calculating, respectively CO2, CO,
H2O, OH, O2, O, H2, H, N2, NO, N, N2O, NO2, K2CO3, K2O, KO, KOH, K, K+, OH-, e electronics, according to above suitable
The corresponding molar fraction x of sequenceiFollowing table be followed successively by 1,2 ... 21；
According to four mass conservation laws, available following four equation:
M in formula aboveC MH MO MN MKFive kinds of Elements Cs, the quality of H, O, N, K in reactant are respectively indicated, they
Numerical value can be calculated by the ratio of additive in propellant powder, as being added to quality percentage in x kilograms of propellant powder
Than the seed for n, then
MC=12 × (25.5243+1000 × n/ ((1-x) × 138)) 31
MH=33.1277 32
MO=16 × (33.0757+3 × 1000 × n/ ((1-x) × 138)) 33
MN=14 × 9.3395 34
MK=78 × 1000 × n/ ((1-x) × 138) 35
According to Dalton's law (of partial pressures):
Due to xiIt is molar fraction, so having:
pi=xip 37
It can be obtained by formula 37:
In addition, for charged particle, due to electroneutral, it is assumed that the i-th component carried charge qi, then have:
In this way, obtaining 21 equations, the closure equation group that can solve 21 kinds of combustion product components is constituted, it can be with by calculating
Solve the parameter of related component；
Partial ionization, the calculation formula of electron density occur in combustion gas are as follows:
；
S3: equation group is programmed in MATLAB according to calculation method above, can calculate plasma by interpretation of result
Relationship between parameter；
S4: the Physical Process Analyses, classical interior ballistics are studied under high pressure conditions in each cannon using thermodynamics as theoretical foundation
The theory of trajectory parameter average value, the mathematical model of classical interior ballistics are One first-order ordinary differential equations, by propellant shape function side
The side of journey, energy equation, combustion rate of powder equation, Projectile Motion rate equation and velocity of shot and five equations of stroke equation composition
Journey group；
According to the characteristics of powder burning situation, being made under high pressure conditions it is assumed hereinafter that:
Assuming that no matter main charge or ignition charge all meet geometry combustion law；
Powder burning uses burning rate exponent formula, i.e.,
It is assumed that gun propellant combustion and Projectile Motion are carried out under average pressure；
Heat leakage is more complicated when shooting, and is difficult to describe, and carries out usually using the method for reducing impetus or increase specific heat
Amendment actually reduces transmitting dose；
All secondary function coefficientsIt calculates, mainly and kinetic energy due to function secondary in shooting courseIt is related, institute
The secondary function having can use coefficientTo take in；
The condition that the pressure for getting into bearing band using bullet starts as bullet；
Combustion gas meets Nobel in thorax --- Abel's state equation；
Gas leak phenomenon is not present in bearing band good seal；
For certain specific gunpowder, its quick-fried temperature be it is certain, it is a constant that this is related with the property of gunpowder, because
This, the equation of gas state under constant volume state is as shown in Equation 41:
Wherein, VψFor free volume, change with pressure one, the gas under the constant volume state indicated using impetus and loading density
Body state equation is as shown in Equation 42:
As can be seen that pressure is gradually changed with powder burning percentage in formula, still, ignition temperature is always fire
The quick-fried temperature of medicine；
In order to increase the thermal ionization of combustion product, a small amount of potassium carbonate is added in propellant powder in the present invention, is managed according to thermal ionization
By making following hypothesis:
Potassium carbonate decomposes completely in the high temperature environment；
It is assumed that combustion product is uniform；
Not the case where not considering double ionization or the Multiple ionization that probability of occurrence is minimum during thermal ionization；
S5: model construction, propellant shape functional equation are as shown in Equation 43:
Wherein, the shape feature amount before χ, λ are gunpowder division；Zk is that gunpowder has fired thickness relatively at the end of burning；χs、λsFor
Shape feature amount after gunpowder division；
Burning velocity equation is as shown in Equation 44:
According to the basic assumption of powder burning inner trajectory, while considering the influence of secondary function, can be obtained by Newton's law:
According to law of conservation of energy, the energy equation for obtaining powder burning is as shown in Equation 47:
It is as shown in Equation 48 that interior trajectory equations under high pressure conditions are obtained according to above equation:
Since powder gas constantly pushes bullet to do work and off-energy, so fuel gas temperature constantly reduces, powder gases temperature
It is as shown in Equation 49 with the variation relation of volume:
p(Vψ+ Sl)=ω ψ RT 49
Usually indicated with bullet stroke:
Sp(l+lψ)=ω ψ RT 50
Temperature is to have fired the related function of percentage ψ with pressure p, bullet stroke l, gunpowder, these data can pass through inner trajectory
Equation group acquires；
By fuel gas temperature equation, the combustion temperature of powder gas can be obtained, due to generating the mode of plasma in powder gas
It is thermal ionization, it is possible to calculate electron density in combustion gas using Saha's equation；
Under high pressure conditions generate plasma density equation group consist of three parts: interior trajectory equations, fuel gas temperature equation and
Electron density equation, simulation process are divided into three steps, calculate gaseous-pressure, bullet stroke etc. and fire according to interior ballistic equation first
The relationship of medicine burning quality goes out the temperature of powder gas by fuel gas temperature equation calculation then according to the calculated result of inner trajectory
Degree, finally further according to electron density in electron density equation calculation plasma；
S6: model verifying, the data and test data obtained by numerical simulation compare, in bullet quality m=0.39kg, dress
In the case where dose ω=0.136kg, chambervolume V0=1.32 × 10-4m3, gun pressure maximum value is acquired in 374MPa, bullet
Initial velocity 898m/s coincide substantially with test result, and image is substantially close, demonstrates the correctness of model built.
2. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
Parameter a in S1ik ajkRespectively indicate the atom number of certain element in 1mol gaseous substance and solid matter, ngi nsjIt respectively indicates
The molal quantity of gaseous component and solid phase components, N in unit materialkThen indicate the total atom number of certain element.
3. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
K in S21 K2 K3 K4 K5 K12 K13K14 K15Numerical value be known constant.
4. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
Electron density and temperature are positively related relationships in S3, and as the temperature increases, electron density is also increasing, and work as temperature one
When sample, pressure is bigger, and electron density is bigger, this is because as the temperature increases, the energy that electronics obtains is more, electronics
The easier constraint for shaking off atom and become free electron.
5. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
S is bullet the maximum cross-section area in S4；P is powder gas average pressure；M is the quality of bullet；L is bullet stroke；V is bullet
Speed；It is secondary work factor.
6. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
L in S4ψIt is that the free volume undergauge of coyote hole is long, ω is charging quality, and θ is gunpowder thermal parameter, and ψ is that gunpowder has fired percentage, and f is
Impetus, Δ are loading density, ρpIt is gunpowder density, α is covolume.
7. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
T is thermodynamic temperature in S5, and Ei is the ionization potential of ion, goFor the statistical weight of atomic ground state, giFor the statistics of ion ground-state
Weight, me are electron mass, and ne is electron density, and ni is ion concentration, and n0 is atomic density, for alkali metal,
Value be about 1, other gases are generally 2.
8. generating plasma law study method according to gun propellant combustion as described in claim 1, it is characterised in that: described
Electron density in plasma in S5
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