CN109916586A - A kind of calculation method of propellant tank bomb fragments initial velocity - Google Patents
A kind of calculation method of propellant tank bomb fragments initial velocity Download PDFInfo
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Abstract
The invention belongs to dynamics of detonation fields, are related to the calculation method of propellant tank bomb fragments initial velocity；After estimating propellant tank accidental explosion, the size of bomb fragments initial velocity.The calculation method of a kind of propellant tank bomb fragments initial velocity proposed, firstly, proposing basic assumption；Then, propellant explosion release gross energy, the expression formula that energy, detonation product kinetic energy, bomb fragments kinetic energy, tank Shell destruction energy, tank case swells do work in detonation product are established respectively；Secondly, determining the calculation formula of bomb fragments initial velocity；Finally, it is verified that the accuracy of bomb fragments initial velocity calculation formula.It is an advantage of the invention that having fully considered the factors such as case material characteristic and ambient air medium, it can predict that the initial velocity of explosion time bomb fragments occurs in different height for the tank of different housings material.
Description
Technical field
The invention belongs to dynamics of detonation fields, and after being related to propellant tank generation accidental explosion, bomb fragments are initially fast
The calculation method of degree.
Background technique
Propellant explosion generates the detonation product of high temperature and pressure, and detonation product forces tank shell to expand outward, is expanded into
When to a certain degree, shell is cracked, and crackle is broken into bomb fragments after being mutually communicated.Impact of the bomb fragments in detonation product
Lower setting in motion is acted on, the speed of fragment is known as initial velocity at this time.The initial velocity of bomb fragments be measure fragment cast away from
From and its to target Damage effect important parameter, it not only influences the range of dispersing of fragment, has an effect on fragment to peripheral facilities
The degree of injury of equipment and personnel.Therefore, it is very necessary for carrying out estimation to propellant tank bomb fragments initial velocity.
Following documents has also related to the research of bomb fragments initial velocity calculation method.
1, Northeastern University Pan Ke et al. " rocketing fragment initial velocity is predicted in storage tank explosion accident ", Northeastern University's journal,
In July, 2014.Paper is in theory analysis, it is assumed that the probability density function of the energy conversion efficiency factor obeys gamma distribution, builds
The method that storage tank explosion gross energy determines fragment kinetic energy multiplied by the energy conversion efficiency factor has been found, it is broken based on fragment Kinetic Energy Calculation
Piece initial velocity.But different explosion accidents have different primary condition and boundary condition, and the energy conversion efficiency factor has
Very big randomness and otherness, therefore, the method that fragment kinetic energy is calculated in text have certain limitation.
2, institute Wang Weijie et al. " research of explosion of liquid rocket fragment model ", Shanghai space flight, in December, 2013 are equipped.By
Text explodes for liquid rocket core level-one tank, has derived the calculation formula of bomb fragments initial velocity, but neglects in derivation process
It has omited the energy of rupture of tank shell and has passed to the energy of air dielectric, it is broken in the explosion of different height explosion time that tank can not be calculated
The initial velocity of piece.
3, the Baker W E in the U.S. et al. " Workbook for predicting pressure wave and
Fragment effects of exploding propellant tanks and gas storage vessels ", NASA
Report, 1977.NASA report, which proposes, consults the side that chart solves cylindricality and spherical high-pressure container explosion fragment initial velocity
Method, but this method has certain requirement to the detonation pressure in container, and the scope of application is restricted.
4, Zhang Shouzhong " explosion basic principle ", National Defense Industry Press, 1988.The book proposes based on Explosive Heat
The semiempirical formula of shelled explosive bomb fragments initial velocity is calculated, but the formula is for single chmical compound explosive bomb fragments initial velocity
Computational accuracy is preferable, and it is larger to calculate error for the bomb fragments initial velocity of composite explosives.
Although above-mentioned document is related to the calculation method of storage tank, tank and high-pressure bottle bomb fragments initial velocity, but neglect
It has omited tank housing distortion and tank and has externally expanded consumed energy, also do not accounted for atmospheric density and explosion in modeling process
The influence of height, the scope of application are restricted.
Summary of the invention
Aiming at the problem that present invention estimates bomb fragments initial velocity after propellant tank accidental explosion, it is based on the conservation of energy
Law proposes a kind of method for calculating propellant tank bomb fragments initial velocity.
The implementation of propellant tank bomb fragments initial velocity calculation method of the invention is as follows: proposing first basic
Assuming that；Then, establish that the gross energy of propellant explosion release, energy, detonation product kinetic energy, bomb fragments move in detonation product respectively
The expression formula of energy, tank Shell destruction energy and the acting of tank case swells；Secondly, it is public to determine that bomb fragments initial velocity calculates
Formula；Finally, it is verified that the accuracy of bomb fragments initial velocity calculation formula.
Propellant tank bomb fragments initial velocity calculation method of the invention is shown in that specific embodiment part describes.
The advantages of propellant tank bomb fragments initial velocity calculation method of the invention, is:
(1) present invention considers shear stress, yield stress and elasticity modulus of case material etc. to tank damaged deformation
Influence, the initial velocity of the tank explosion time fragment of different housings material can be calculated.
(2) present invention considers the influence that ambient air density and height of burst do work to case swells, can calculate storage
Initial velocity of the case in different height explosion time fragment.
(3) calculated result accurate and effective.Calculated result and three groups of shelled explosive explosive test data, Gurney of the invention
Formula coincide preferably, demonstrates the accuracy of bomb fragments initial velocity calculation formula.
Detailed description of the invention
The derivation of propellant tank bomb fragments initial velocity calculation method Fig. 1 of the invention and verifying flow chart；
The calculated result of Fig. 2 explosive test data, bomb fragments initial velocity calculation formula and Gurney formula.
Specific embodiment
It is done further in detail in conjunction with calculation method of the attached drawing to a kind of propellant tank bomb fragments initial velocity of the invention
Thin description.
Fig. 1 is the key step that the present invention is derived and verified.
Step 1: proposing basic assumption
Tank bomb fragments initial velocity computation model based on the assumption that do not consider detonation reaction process, will be chemical
Reaction zone regards a strong discontinuity surface as；Tank is regarded as to the cylindrical shell of equal wall thickness, only considers explosion product dispersing radially；
Propellant all participates in detonation reaction, and the size of bomb fragments initial velocity is identical.
Step 2: establish respectively propellant explosion release gross energy, energy, detonation product kinetic energy in detonation product, explode it is broken
The expression formula that piece kinetic energy, tank Shell destruction energy, tank case swells do work.
Analyze the energy conversion in propellant tank detonation process, the gross energy E of propellant explosion releasetIt is converted mainly into
Five part below:
Et=Ei+Ek+Edk+Ed+Ea (1)
In formula, EiFor the interior energy of detonation product；EkFor the kinetic energy of detonation product；EdkFor the kinetic energy of bomb fragments；EdFor tank
The energy of rupture of shell；EaFor the acting of tank case swells.
(1) the gross energy E of propellant explosion releaset
The gross energy E of Liquid Propellant Explosion releasetAre as follows:
Et=mpQp (2)
In formula, mpFor propellant mass；QpFor the quick-fried heat of propellant.
(2) the interior of detonation product can Ei
The specific internal energy e of unit mass detonation producti, quick-fried hot QpApproximation relation between explosion velocity D are as follows:
Then the interior of detonation product can EiAre as follows:
(3) the kinetic energy E of detonation productk
If propellant all participates in reaction, according to the conservation of mass, the quality of detonation product is equal to the quality of propellant, then quick-fried
Hong product kinetic energy Ek:
In formula, upFor the particle velocity of detonation product.
Detonation product particle velocity upRelationship between the explosion velocity D of propellant:
In formula, γ is the polytropic index of detonation product, γ=3.
Formula (6) are substituted into formula (5) to obtain
(4) the kinetic energy E of bomb fragmentsdk
If the number of tiles that explosion generates altogether is N, fragment initial velocity is v0, it is obtained by kinetic energy law:
In formula, miFor the quality of i-th of fragment；M is the quality of tank shell.
(5) the energy of rupture E of tank case materiald
Paper " the Deformation and Fragmentation Behavior of Exploded of Hiroe et al.
Metal Cylinders and the Effects of Wall Materials,Configuration,Explosive
Energy and Initiated Locations " (International Journal of Impact Engineering,
12nd phase in 2008), the paper " Dynamic Fracture of cylindrical steel shell under the conditions of inside-explosive loading " of Hu Yongle et al. it is (mechanical strong
Degree, the 1st phase in 2010), the paper " TA2 titanium alloy round tube expansion damage process under different blast loads " of Yu Xinlu et al. it is (quick-fried
Fried and impact, the 1st phase in 2018) it is had studied under the effect of internal explosion load respectively, the dynamic of aluminium, steel, titanium alloy cylindrical shell
Deformation and failure mode.The result shows that the cylindrical shell of different metal material occurs to move because being radially expanded under shock wave load
State plastic deformation, generates shear band, mainly shows shearing-type fracture characteristic.
If only considering shear fracture of the tank shell under Explosion Loading, the energy of rupture E of tank shelldEqual to cutting
Shear deformation energy:
It is obtained by shearing Hooke's law:
τ=G η (10)
Wushu (10) substitutes into formula (9) and obtains:
In formula, τ is shear stress；η is shearing strain, dimensionless；G is the coefficient of rigidity；VcFor the volume of tank shell.
(6) tank case swells acting Ea
Instant of detonation, the shock front pressure P formed in aira
In formula, k is the constant entropy adiabatic exponent of air, for strong shock wave, k=1.2；ρaFor the sky for the wave disturbance that is not hit
Air tightness；vaFor the air particle velocity of wave surface.
The initial velocity D of air-shock waveaClose to the detonation rate D of propellant, and vaWith DaRelational expression are as follows:
Formula (13) are substituted into (12) to obtain:
Local atmospheric density ρaThe general expression changed with sea level altitude y are as follows:
ρa=ρ0H(y) (15)
In formula, ρ0For the atmospheric density on sea level, ρ0=1.293kgm-3。
H (y) is air density correction:
If detonation instantaneously acts on the air-impingement wave pressure P on tank shellaIt remains unchanged, then tank shell equipressure is swollen
Air-impingement wave pressure work done E is overcome when swollena:
In formula, V0For the initial volume of tank；V1Volume after being expanded completely for tank.
According to shear fracture criterion, shell expand completely after radius rfWith initial radium r0Relational expression are as follows:
In formula, PeFor the pressure of detonation product；σ is the yield stress of tank material；N is correction factor, for cylinder
Shell, n=2；For spherical shell, n=3.
The pressure P of detonation producteWith the relationship between explosion velocity D:
In formula, ρpFor the density of propellant.
Formula (14), (15), (18), (19) are substituted into (17) and can obtained:
Step 3: determining bomb fragments initial velocity calculation formula.
According to law of conservation of energy, the gross energy of propellant explosion release be equal to energy in detonation product, detonation product kinetic energy,
The sum of bomb fragments kinetic energy, tank Shell destruction energy and the acting of tank case swells.By formula (2), (4), (7), (8), (11),
(20) formula (1) is substituted into, obtains bomb fragments initial velocity v0Calculation formula:
Step 4: the accuracy of verifying bomb fragments initial velocity calculation formula.
(1) explosive test one
Wuhan University of Technology Kong Xiangshao et al. paper " cylindrical warhead explosion fragment characteristic research " (engineering mechanics,
1st phase in 2014) in carried out the explosive test of TNT explosive in Q235 mild steel cylindrical shell, housing inner diameter 110mm, height
160mm, thickness 6mm, explosive payload 1.9kg.For TNT explosive, ρp=1630kgm-3, D=6900ms-1。
(2) explosive test two
Paper " the Relation of Fragment with Air Shock Wave of Beijing Institute of Technology Zhang Qi et al.
Intensity for Explosion in a Shell”(International Journal of Impact
Engineering, the 10th phase in 2003) in carried out the explosive test of T-H-Al explosive in steel cylinder shell, filled out in shell
Full explosive, housing inner diameter 120mm, thickness 3.5mm.For T-H-Al explosive, ρp=1752kgm-3, D=7054ms-1。
(3) explosive test three
Lao Lunsi-livermore laboratory is in report " Calculations of Fragment Velocities From
Comp in copper cylindrical shell is carried out in Naturally Fragmenting Munitions " (ADB007377,1979)
The explosive test of B explosive fills up explosive, housing inner diameter 25.4mm, thickness 2.6mm in shell.For Comp B explosive, ρp=
1720kg·m-3, D=7980ms-1。
Gurney is in report " The Initial Velocities of Fragments From Bombs, Shells
The experience public affairs of prediction explosion fragment initial velocity are proposed for warhead of different shapes in and Grenades " (nineteen forty-three)
Formula --- Gurney formula, the formula are the most extensive in Fragment Velocities calculating field application.
For cylindrical housings:
In formula,Referred to as Gurney constant, Gurney are obtained by testIt is linear with explosion velocity D,β=m/M indicates the ratio of quality of explosive and shell quality.
By the relevant parameter of above three groups of explosive tests substitute into respectively bomb fragments initial velocity calculation formula (21) and
Gurney formula (22), by bomb fragments initial velocity calculation formula, the calculated result of Gurney formula and three groups of explosive tests
Data compare, and calculate separately relative error ε between the twoi(i=1,2,3), as shown in Figure 2.
As shown in Figure 2, relative error between the bomb fragments initial velocity that formula (21) calculates and three groups of explosive test results
Respectively less than 15%, in allowable range of error；Formula (21) and the calculated result of Gurney formula are also coincide preferably, and explosion is demonstrated
The accuracy of fragment initial velocity calculation formula.
Claims (1)
1. a kind of calculation method of propellant tank bomb fragments initial velocity, comprising:
Step 1: proposing basic assumption；
Step 2: establishing respectively, propellant explosion release gross energy, energy, detonation product kinetic energy, bomb fragments are moved in detonation product
The expression formula that energy, tank Shell destruction energy, tank case swells do work；
Step 3: determining bomb fragments initial velocity calculation formula；
Step 4: the accuracy of verifying bomb fragments initial velocity calculation formula.
It is characterized by:
Step 1: proposing basic assumption.
The process for not considering detonation reaction, regards chemical reaction zone as a strong discontinuity surface；Tank is regarded as to the cylinder of equal wall thickness
Shell only considers explosion product dispersing radially；Propellant all participates in detonation reaction, the size of bomb fragments initial velocity
It is identical.
Step 2: establishing respectively, propellant explosion release gross energy, energy, detonation product kinetic energy, bomb fragments are moved in detonation product
The expression formula that energy, tank Shell destruction energy, tank case swells do work.
Analyze the energy conversion in propellant tank detonation process, the gross energy E that propellant explosion in tank is dischargedtIt is divided into quick-fried
It can E in Hong producti, detonation product kinetic energy Ek, bomb fragments kinetic energy Edk, tank Shell destruction energy EdAnd tank case swells are done
Function EaFive parts.
Et=Ei+Ek+Edk+Ed+Ea (1)
(1) gross energy of propellant explosion release
The gross energy E of Liquid Propellant Explosion releasetAre as follows:
Et=mpQp (2)
In formula, mpFor propellant mass；QpFor the quick-fried heat of propellant.
(2) energy in detonation product
In formula, D is propellant explosion velocity.
(3) detonation product kinetic energy
(4) bomb fragments kinetic energy
If the number of tiles that explosion generates altogether is N, fragment initial velocity is v0, it is obtained by kinetic energy law:
In formula, miFor the quality of i-th of fragment；M is the quality of tank shell.
(5) tank Shell destruction energy
In formula, τ is shear stress；G is the coefficient of rigidity；VcFor the volume of tank shell.
(6) tank case swells do work
In formula, ρ0For the atmospheric density on sea level；H (y) is air density correction；V0For the initial volume of tank；ρpTo push away
Into the density of agent；σ is the yield stress of tank material.
Step 3: determining bomb fragments initial velocity calculation formula.
Formula (2)~(7) are substituted into formula (1), obtain bomb fragments initial velocity v0Calculation formula:
Step 4: the accuracy of verifying bomb fragments initial velocity calculation formula.
Wuhan University of Technology Kong Xiangshao et al. has carried out TNT explosive in the intracorporal explosive test of Q235 mild steel cylindrical shell, shell
Internal diameter 110mm, height 160mm, thickness 6mm, explosive payload 1.9kg.For TNT explosive, ρp=1630kgm-3, D=
6900m·s-1。
Beijing Institute of Technology Zhang Qi et al. has carried out T-H-Al explosive and has filled up in the intracorporal explosive test of steel cylinder shell, shell
Explosive, housing inner diameter 120mm, thickness 3.5mm.For T-H-Al explosive, ρp=1752kgm-3, D=7054ms-1。
Lao Lunsi-livermore laboratory has been carried out Comp B explosive and has been filled out in the intracorporal explosive test of copper cylindrical shell, shell
Full explosive, housing inner diameter 25.4mm, thickness 2.6mm.For Comp B explosive, ρp=1720kgm-3, D=7980ms-1。
Based on the explosive test of three groups of shelled explosives, bomb fragments initial velocity calculation formula and Gurney formula meter is respectively adopted
The initial velocity of bomb fragments is calculated, the result of bomb fragments initial velocity calculation formula and Gurney formula, shelled explosive is quick-fried
Fried test data compares, and verifies the accuracy of bomb fragments initial velocity calculation formula.
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Application publication date: 20190621 |