CN109460562B - Method for evaluating distribution characteristics of fragments disintegrated by satellite explosion - Google Patents
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Abstract
The invention provides a method for evaluating distribution characteristics of fragments disintegrated by satellite explosion, which comprises the following steps: the method comprises the following steps: performing satellite equivalent calculation, wherein the satellite equivalent calculation comprises satellite shape equivalence, structural strength equivalence and residual propellant equivalence; step two: and according to the equivalent calculation result of the satellite, carrying out explosive disintegration fragment distribution characteristic evaluation, wherein the evaluation content comprises the total explosive disintegration fragment number prediction, fragment mass distribution, surface-to-mass ratio distribution and velocity increment distribution relation. According to the invention, through satellite modeling analysis and numerical operation of disintegration behaviors, the distribution characteristics of disintegration fragments when the orbit satellite is subjected to accidental explosion disintegration can be rapidly evaluated, and the damage of the disintegration fragments to the normally operating satellite and orbit resources can be scientifically analyzed, so that effective countermeasures can be taken.
Description
Technical Field
The invention mainly relates to the field of impact dynamics technology and space protection of aerospace vehicles, in particular to an evaluation method for distribution characteristics of fragments disintegrated by satellite explosion.
Background
With the increasing frequency of human aerospace launching activities, the space debris environment is increasingly deteriorated, and the space debris environment poses a serious threat to the on-orbit safe operation of a spacecraft.
The space debris mainly comes from the last rocket body of the carrier rocket, the on-orbit disintegration debris of the spacecraft, the mission-related debris (also called operation debris), the failure spacecraft and the like, and the proportion of each part is changed along with the time. According to the statistics of the number of objects cataloged by the US SS, after 2007, the rising trend of the disintegrated fragments caused by the burst satellite disintegration event is very obvious, and even the burst satellite disintegration event becomes the most main source of the burst newly-added space fragments. The causes of satellite disintegration events are often accidental collisions, residual propellant explosions and deliberate events, batteries, etc., of which the residual propellant explosions and deliberate events account for the most part. Therefore, how to scientifically evaluate the accidental explosion disintegration of the in-orbit satellite, analyze the possible harm and adverse effect of the disintegrated fragments on the normally-operated satellite and orbit resources, and take effective counter measures is a major research subject in the field of the current space fragments.
The explosion intensity level, the disintegration mode, the mass of the disintegrated fragments generated by the explosion intensity level and the disintegration mode, the velocity increment, the space density and other distribution characteristics of the orbit satellite (or spacecraft) are mainly determined by two factors, namely the residual propellant amount carried by the satellite and self constraint conditions such as the shape, the material and the structure of the satellite.
The on-orbit satellite (or spacecraft) has various forms and structures and complex disintegration behaviors and modes, and both on-orbit or ground simulation experiments and theoretical analysis have considerable difficulty, so that the development of research work is restricted to a great extent, and particularly, the disintegration model with higher application value is yet to be further deeply researched and established.
Disclosure of Invention
In order to solve the defects and problems in the prior art, the invention provides an evaluation method for the distribution characteristics of explosion disintegration fragments of a satellite (or a spacecraft) by combining the distribution rule of explosion disintegration fragments of a cased charge.
The technical scheme of the invention is as follows:
a satellite explosion disintegration fragment distribution characteristic evaluation method comprises two main modules, namely a satellite equivalent module, wherein the satellite equivalent module mainly comprises three aspects of satellite shape equivalence, structural strength equivalence and residual propellant equivalence; and secondly, the explosion disintegration fragment distribution characteristic evaluation module mainly comprises the relations of total explosion disintegration fragment number prediction, fragment mass distribution, surface-to-mass ratio distribution, velocity increment distribution and the like.
According to the overall evaluation framework, the detailed steps of the evaluation method for the distribution characteristics of the fragments disintegrated by the satellite explosion are as follows:
firstly, the equivalence of the shape of the satellite is carried out, and considering that the geometric shapes of the shell are various, such as spherical, prismatic, cylindrical and various irregular polyhedrons, etc., besides the shape maintenance, the shell also meets the requirements of surface area, internal volume of the satellite, heat control, space radiation protection, various surface openings, etc. To facilitate the problem analysis and the ground simulation test, the satellite shape is equivalent to a simple geometric body, such as a sphere, a cylinder, a cube and the like.
Then, the equivalent of the satellite structure strength is carried out, in the design of the satellite structure, the most common honeycomb sandwich plate structure is used, which accounts for almost 90% of the weight of the whole satellite structure, and the honeycomb sandwich structure becomes a main bearing structure. The honeycomb sandwich plate consists of an upper panel, a lower panel and a honeycomb core layer, and is equivalent to an isotropic equivalent target plate with the same strength as the original sandwich plate in order to facilitate problem analysis. Assuming that the stresses of the honeycomb sandwich panel and the equivalent housing are uniformly distributed along the thickness, the following relationship exists between the stresses
N＝δ 0 σ 0 +(δ 1 +δ 2 )σ＝σ eq δ eq (1)
The thickness of the equivalent plate, i.e. the equivalent formula of the satellite structural strength, can then be derived as
Wherein N is a plane stress; delta 0 Is the thickness of the sandwich layer; delta 1 Is the thickness of the upper panel; delta. For the preparation of a coating 2 Lower panel thickness; delta eq Is the equivalent plate thickness; sigma 0 The strength of the sandwich layer; sigma is the strength of the upper and lower templates; sigma eq Equivalent plate strength.
Next, an equivalence of the remaining propellant is made, considering that the propellant carried at the time of satellite launch generally has 4 uses: propellant for speed control, propellant for attitude control, reserve and residual amounts. The reserve propellant amount is 9% to 20% of the total propellant amount, and the remaining amount is 1% to 2% of the total propellant amount, and accordingly, the remaining propellant amount when an explosion occurs during the operation of the satellite can be considered as 1% to 20% of the total propellant amount.
When the residual propellant is equivalent, the invention utilizes common high explosive (such as TNT, B explosive and the like) to replace the propellant for explosion based on the principle of equivalent working capacity in the explosion process, and the mass of the propellant is equivalent to the mass of TNT with the same explosion power according to the concept of equivalent explosive quantity of TNT, namely the mass of the TNT is equivalent to the mass of the TNT with the same explosion power
m T ＝Y×m 0 (3)
In the formula, m 0 For the total mass of propellant (including fuel and oxidizer), kg; m is a unit of T Is equal to m 0 The propellant has a mass of TNT equivalent to the explosive power of the TNT, kg; y is the TNT equivalent explosion coefficient of the propellant, and the TNT equivalent explosion coefficient of the common liquid propellant is shown in the table 1.
After the quality of equivalent TNT is obtained by using the formula (3), equivalent replacement between TNT and other high explosives is carried out according to the equivalent principle of work-doing capacity, the work-doing capacity is calculated by adopting a characteristic product method, and the result of mortar method measurement of Johnson (C.H.Johansson) can be used for obtaining the result
A＝3.65×10 -4 Q v v g (4)
Wherein A is the work-doing ability, kJ.g -1 ；Q v As explosive heat, kJ · g -1 ；v g Volume, cm, of gaseous explosive 3 ·g -1 ；A T Is the working capacity of TNT; a. The B The working capacity of a certain equivalent explosive; m is B Is the mass of the equivalent explosive; m is T Is the quality of TNT. Wherein the explosion heat and the volume of the gas explosion products are determined according to experiments, and the explosion heat of a plurality of common explosives is shown in a table 2.
The mass of the propellant can be equivalent to the mass of any high explosive with the same explosion power through the formulas (3) to (5), so that the propellant can be replaced by the explosive in a ground simulation test, the ground simulation test of satellite explosion disintegration is carried out, and the basic data of satellite explosion disintegration is obtained.
TABLE 1 explosive TNT equivalent coefficient of liquid propellant
TABLE 2 several explosive heats of detonation and volume values of explosive products
The equivalent of the satellite can be completed through the steps, and on the basis, the equivalent enters a satellite explosion disintegration fragment distribution characteristic evaluation module. Firstly, aiming at the satellite equivalent model, a warhead fragment total number prediction formula is introduced to estimate the total number of the fragments disassembled from the satellite explosion, and the specific expression is
In the formula, N 0 The total number of fragments generated for an explosion; a is a constant related to the explosive (the value of A for conventional explosives is shown in Table 3), (g.mm) -3 ) 1/2 (ii) a M is the mass of the satellite model, g; d is the satellite equivalent diameter, mm; delta is the equivalent wall thickness of the satellite in mm; c is equivalent loading, g.
However, it should be noted that there is a substantial difference between the satellite blast demolition and the warhead blast demolition, and therefore, the parameters in equations (6) and (7) need to be obtained through ground simulation experiments, and the parameters related to the warhead blast demolition cannot be directly used. For a satellite which can be similar to a cylinder, a total fragment number prediction formula can be referred to as a reference [ Yuqing wave, xu kuei, wang Zhi and the like, the distribution characteristics of fragments exploded by satellite structure explosion are simulated, and the war industry science report ] and a specific expression is
In the formula (I), the compound is shown in the specification,
is the average mass of the chips (g); c is the residual fuel mass (g); m is satellite structure mass (g); delta is the satellite equivalent shell wall thickness (mm); d is the satellite equivalent structure diameter (mm); and Y is the TNT equivalent coefficient of explosion of the propellant.
TABLE 3A values of conventional explosives
After the total number of the fragments disintegrated by the explosion of the satellite is obtained, a low-intensity explosion disintegration fragment distribution model is introduced, and the distribution relation of the number of the fragments along with the mass of the fragments is obtained
In the formula, N f The number of fragments with mass larger than m; n is a radical of 0 Is the total number of fragments; m is the fragment mass;
to normalize the patch mass; b is the explosion intensity; c is a slope parameter; k is a calibration parameter, and the parameter is set as follows: c =0.55, k =8.7.
It should be noted that the value of the parameter B and N 0 Closely related, the relationship can be expressed as
In the formula, N f0max M is the maximum number of fragments that can be generated tr For a known trace mass, N ftr Is of mass greater than m tr The number of fragments of (a).
Then, under the condition that the relation between the number of fragments and the mass of the fragments is obtained, the relation between the number of fragments and the characteristic diameter is obtained according to the relation between the mass of the fragments and the characteristic diameter
In the formula (d) * 1cm for reference diameter; p is a power law parameter, p =1.13; rho * ＝ρ(d * )＝2700kg/m 3 ；ρ max ＝4700kg/m 3 (ii) a d is the fragment diameter, m; m is a unit of * For reference mass, 1.41372g; n is a radical of f Number of fragments with characteristic diameter greater than d; n is a radical of f0 Total number of fragments broken up by explosion; b is the explosion intensity; c is a slope parameter; k is a calibration parameter.
Moreover, taking into account the conversion relationship existing between the characteristic diameter and the surface-to-mass ratio is
On the basis, the combination formula (14) can obtain the relation between the number of fragments and the surface-to-quality ratio
In the formula, N f The number of fragments with a surface-to-mass ratio of less than A/m, f A And (3) each of the remaining physical quantities has the same meaning as in the formula (14).
Through equivalence between propellant and explosive, a warhead fragment initial velocity calculation formula is introduced to predict fragment initial velocity increment (namely maximum velocity increment) v of fragments generated by satellite explosive disintegration i I.e. by
Wherein beta is a filling coefficient; c is equivalent loading, kg; m is the satellite equivalent net mass (excluding propellant), kg;
in terms of Grignard constants, m/s, the Grignard constants for several explosives are shown in Table 4.
TABLE 4 Gernib constants of several explosives
Thus, a relationship between the velocity increment and the characteristic diameter can be obtained as
In the formula, b 0 、b 2 As fitting constant, b 0 ＝-0.125，b 2 = -0.0676; d is the chip diameter, m.
Considering that the mass of the chips has a relation with the characteristic diameter as
In the formula, ρ * ＝ρ(d * )＝2700kg/m 3 ；ρ max ＝4700kg/m 3 (ii) a d is the characteristic diameter, cm; p is a power law parameter, p =1.13；d * 1cm for reference diameter; d DEG is critical diameter, 0.47281cm; m is a unit of * 1.41372g for reference mass; m is the fragment mass, g; critical mass of m ° =2.60104 × 10 -4 kg，
Is a normalized critical mass, which is a dimensionless quantity.
The combination of equations (19) and (20) yields a velocity increment versus chip mass of
Finally, the relationship between the speed increment and the surface-to-mass ratio obtained by the united type (15), (19) and (20) is
The invention has the beneficial effects that:
through satellite modeling analysis and disintegration behavior numerical operation, the distribution characteristics of disintegrated fragments when the orbit satellite is exploded by accidental explosion can be rapidly evaluated, and the damage of the disintegrated fragments to the normally operating satellite and orbit resources can be scientifically analyzed so as to take effective countermeasures.
Drawings
FIG. 1 is a framework for evaluating the distribution characteristics of fragments disintegrated by satellite explosion;
FIG. 2 is a flow chart of analysis of the distribution characteristics of explosion disintegration fragments;
FIG. 3 is a distribution of explosive fragmentation numbers in an embodiment of the present invention;
fig. 4 is a velocity increment profile for blast breakdown fragments in an embodiment of the invention.
Detailed Description
The invention is further described with reference to the accompanying drawings and the specific embodiments. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and these equivalents also fall within the scope of the present application.
Example (b): for the satellite to be evaluated, the total mass of the cylindrical satellite is 80kg, the used propellant is liquid oxygen + liquid hydrogen, the mass of the residual propellant is 80kg, the length after equivalence is 1.2m, the equivalent diameter is 0.8m, and the equivalent thickness is 2mm. The specific number of the explosion disintegration fragments in different interval ranges obtained by the method provided by the invention is shown in table 5, the distribution of the number of the explosion disintegration fragments is shown in fig. 3, and the velocity increment distribution of the explosion disintegration fragments is shown in fig. 4.
TABLE 5 fragmentation number distribution statistics
Claims (1)
1. A method for evaluating the distribution characteristics of fragments disintegrated by satellite explosion is characterized by comprising the following steps:
the method comprises the following steps: performing satellite equivalent calculation, wherein the satellite equivalent calculation comprises satellite shape equivalence, structural strength equivalence and residual propellant equivalence;
in the first step, firstly, the satellite shape is equivalent, and the satellite shell shape is equivalent to a simple geometric body;
then the structural strength of the satellite is equivalent, the structural strength is equivalent to an isotropic equivalent target plate with the same strength as the honeycomb sandwich plate of the satellite, the stress of the honeycomb sandwich plate and the equivalent shell is set to be uniformly distributed along the thickness, and the following relational expressions exist among the stresses
N＝δ 0 σ 0 +(δ 1 +δ 2 )σ＝σ eq δ eq (1)
The thickness of the equivalent plate can be derived through the above formula, namely the equivalent formula of the satellite strength structure is
Wherein N is a plane stress; delta 0 Is the thickness of the sandwich layer; delta. For the preparation of a coating 1 Is the thickness of the upper panel; delta. For the preparation of a coating 2 Is the lower panel thickness; delta. For the preparation of a coating eq Is the equivalent plate thickness; sigma 0 The strength of the sandwich layer; sigma is the strength of the upper and lower templates; sigma eq Equivalent plate strength;
and finally, performing equivalence on the residual propellant, and enabling the mass of the propellant to be equivalent to the mass of TNT with the same explosion power according to the concept of TNT explosion equivalent based on the working capacity equivalence principle in the explosion process, namely the mass of the TNT with the same explosion power
m T ＝Y×m 0 (3)
In the formula, m 0 Kg is the total mass of the propellant; m is a unit of T Is a is m 0 The mass of TNT with equivalent explosive power of the propellant, kg; y is the TNT explosion equivalent coefficient of the propellant;
after obtaining the equivalent TNT quality by using the formula (3), carrying out equivalent replacement of TNT according to the equivalent principle of the work capacity, and calculating the work capacity by adopting a characteristic product method, wherein the formula is as follows
A＝3.65×10 -4 Q v v g (4)
Wherein A is the work-doing ability, kJ.g -1 ；Q v For explosive heat, kJ. G -1 ；v g Volume, cm, of gaseous explosive 3 ·g -1 ；A T Is the working capacity of TNT; a. The B The working capacity of a certain equivalent explosive; m is a unit of B Mass of equivalent explosive; m is a unit of T Is the mass of TNT;
the propellant quality can be equivalent to any high explosive quality with the same explosion power through the formulas (3) to (5), so that the propellant can be replaced by the explosive in the ground simulation test, the ground simulation test of satellite explosion disintegration is carried out, and the basic data of satellite explosion disintegration is obtained;
step two: according to the equivalent calculation result of the satellite, carrying out explosive disintegration fragment distribution characteristic evaluation, wherein the evaluation content comprises total explosive disintegration fragment number prediction, fragment mass distribution, surface-to-mass ratio distribution and velocity increment distribution relation;
in the second step, firstly, aiming at the satellite equivalent model, a warhead fragment total number prediction formula is introduced to estimate the total number of the fragments disassembled from the satellite explosion, and the specific expression is
In the formula, N 0 The total number of fragments generated for an explosion; a is a constant related to the explosive, (g.mm) -3 ) 1/2 (ii) a M is the mass of the satellite model, g; d is the satellite equivalent diameter, mm; delta is the equivalent wall thickness of the satellite in mm; c is equivalent loading, g;
for a satellite which can be approximated to be a cylinder-like body, the total fragment number prediction concrete expression is
In the formula (I), the compound is shown in the specification,
is the average mass of the chips (g); c is the residual fuel mass (g); m is satellite structure mass (g); delta is the satellite equivalent shell wall thickness (mm); d is the satellite equivalent structure diameter (mm); y is the TNT explosion equivalent coefficient of the propellant;
after the total number of the fragments decomposed by the satellite explosion is obtained, a low-intensity explosion fragment distribution model is introduced, and the distribution relation of the number of the fragments along with the mass of the fragments is obtained
In the formula, N f1 The number of fragments with mass larger than m; n is a radical of 0 Is the total number of fragments; m is the mass of the fragments;
to normalize the patch mass; b is the explosion intensity; c is a slope parameter; k is a calibration parameter, and the parameter is set as follows: c =0.55, k =8.7;
value of parameter B and N 0 Closely related, the relationship can be expressed as
In the formula, N f0max M is the maximum number of fragments that can be generated tr For a known trace mass, N ftr Is of mass greater than m tr The number of fragments of (c);
then, under the condition that the relation between the number of fragments and the mass of the fragments is obtained, the relation between the number of fragments and the characteristic diameter is obtained according to the relation between the mass of the fragments and the characteristic diameter
In the formula (d) * 1cm for a reference diameter; p is a power law parameter, p =1.13; rho * ＝ρ(d * )＝2700kg/m 3 ；ρ max ＝4700kg/m 3 (ii) a d is the fragment diameter, m; m is a unit of * 1.41372g for reference mass; n is a radical of hydrogen f2 The number of fragments with a characteristic diameter larger than d; n is a radical of hydrogen f0 Total number of fragments broken up by explosion; b is the explosion intensity; c is a slope parameter; k is a calibration parameter;
considering the conversion relationship existing between the characteristic diameter and the surface-to-mass ratio as
On the basis, the combination formula (14) can obtain the relation between the number of fragments and the surface-to-quality ratio
In the formula, N f3 The number of fragments with a surface-to-mass ratio of less than A/m, f A = pi/4, and the meaning of the remaining physical quantities is the same as in formula (14);
through equivalence between propellant and explosive, a warhead fragment initial velocity calculation formula is introduced to predict fragment initial velocity increment v of fragments generated by satellite explosive disintegration i I.e. by
Wherein beta is a filling coefficient; c is equivalent loading, kg; m is the equivalent net mass of the satellite, kg;
is a gurney constant, m/s;
thus, a relationship between the velocity increment and the characteristic diameter can be obtained as
In the formula, b 0 、b 2 As fitting constant, b 0 ＝-0.125，b 2 = 0.0676; d is the fragment diameter, m;
considering that the fragment mass has a relation with the characteristic diameter
In the formula, ρ * ＝ρ(d * )＝2700kg/m 3 ；ρ max ＝4700kg/m 3 (ii) a d is the characteristic diameter, cm; p is a power law parameter, p =1.13; d * 1cm for a reference diameter; d DEG is critical diameter, 0.47281cm; m is * For reference mass, 1.41372g; m is the fragment mass, g; critical mass of m ° =2.60104 × 10 -4 kg，
Is a normalized critical mass, which is a dimensionless quantity;
the combination of equations (19) and (20) yields a velocity increment versus chip mass of
Finally, the relationship between the speed increment and the surface-to-mass ratio obtained by the united type (15), (19) and (20) is
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