A method for calculating and measuring the critical explosion distance between natural fragments and shock waves

Abstract

The present invention provides a method for calculating the critical explosion distance between natural fragments and shock waves. Based on a prediction model of the fragment field and shock wave overpressure field distribution, the method theoretically analyzes the interaction between fragment flight patterns and shock wave propagation patterns at different ranges. This method then deduces a formula for calculating the post-explosion encounter position between fragments and shock waves, thereby resolving the technical challenge of accurately and quickly determining the critical explosion distance between the sequential action of shock waves and fragments under warhead explosions. Furthermore, by comparing experimental measurements with the theoretical calculation formula, the method demonstrates a low error of 2.75%, demonstrating the rationality and feasibility of the proposed formula for calculating the post-explosion encounter position between fragments and shock waves.

Description

Technical Field

[0001] The present invention relates to the technical field of research on formation characteristics and propagation laws of damage elements in natural fragment warhead air explosions, and in particular to a method for calculating and measuring the critical explosion distance between natural fragments and shock waves. Background Art

[0002] The airborne detonation of a fragmentation warhead produces both a shock wave and high-speed fragments. The fragment cluster and shock wave are the two primary damaging elements of a blast warhead. The propagation velocity of the shock wave generated by the warhead after detonation differs significantly from the initial velocity of the high-speed fragments. The initial shock wave velocity after detonation is much greater than the initial velocity of the fragments, and the shock wave travels ahead of the fragments. Due to the significant difference in the velocity attenuation of the two in air, especially the rapid attenuation of the shock wave, the fragments tend to catch up with the shock wave. Consequently, the shock wave and fragments may encounter each other during their propagation. This encounter point is the critical detonation distance at which the shock wave and high-speed fragments act sequentially.

[0003] For warhead designers, accurately understanding the critical explosion distance of a warhead provides valuable guidance for further enhancing its destructive power. In the field of defense, determining the critical explosion distance of a warhead against a target provides valuable insights into the design of protective structures that minimize the destructive effects of the warhead explosion. Therefore, accurately and quickly determining the critical explosion distance, which determines the sequential effects of shock waves and fragments upon a warhead explosion, has become a prerequisite and key to in-depth research in the fields of damage and defense. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating and measuring the critical explosion distance between natural fragments and shock waves. Based on the prediction model of the distribution law of the fragment field and the shock wave overpressure field, the mutual disturbance effect mechanism between the fragment flight law and the shock wave propagation law at different action distance domain scales is theoretically analyzed, and a calculation formula for the meeting position of the fragment and the shock wave after the explosion is deduced, thereby solving the technical problem of accurately and quickly obtaining the critical explosion distance value of the successive action of the shock wave and fragments under the warhead explosion.

[0005] The present invention provides a method for calculating the critical explosion distance between natural fragments and shock waves, which specifically includes the following steps:

[0006] S1. Obtain the peak overpressure value ΔP when the warhead airblast shock wave propagates in the air m ;

[0007] S2. Get the propagation speed of the shock wave in the air V s ;

[0008] S3. According to the obtained shock wave propagation speed value V in the air s, and the propagation distance R of the airburst shock wave front is obtained s ;

[0009] S4. Obtain the distance R that the natural fragments fly in the air after the warhead explodes. f ;

[0010] S5. Based on the distance R of the fragments flying in the air f Propagation distance R from the shock wave front s , and obtain the critical explosion distance between fragments and shock waves.

[0011] 8. At the same time, the present invention also provides a method for measuring the critical explosion distance of natural fragments and shock waves, which specifically includes the steps of:

[0012] S1. Design the detailed structure of the warhead;

[0013] S2. Obtain the peak overpressure of the free-field air shock wave at different locations driven by the explosion;

[0014] S3. Observe the fragment velocity and shock wave evolution during the explosion drive process;

[0015] S4. Analysis and verification of measurement results.

[0016] Specifically, the warhead includes a detonator, a detonator seat, a shell, explosives, a steel ball, and epoxy resin; the explosive charge is a passivated RDX pressure charge, 133 mm long, 70 mm in diameter, and a density of 1.71 g / cm 3 , detonation velocity 8425m / s; the shell material is 45# steel, density 7.85g / cm 3 The inner lining layer has a wall thickness of 2mm, the outer lining layer has a wall thickness of 1.5mm, and the inner and outer lining layers are connected to the upper and lower end covers by threaded connections; the diameter of a single steel ball is 5mm and the mass is 0.51g. The prefabricated fragments are evenly arranged from top to bottom and then fixed by pouring epoxy resin.

[0017] Specifically, obtaining the peak overpressure of the free-field air shock wave at different positions driven by the explosion is as follows: using a piezoelectric pressure sensor to measure the peak overpressure of the free-field air shock wave at different positions driven by the explosion.

[0018] Furthermore, there are three piezoelectric pressure sensors, which are placed along a measuring line and two pressure measuring lines are arranged. The predetermined distances for overpressure testing of the shock wave overpressure sensor are 2.3m, 3m, and 4m, respectively, with a total of three measuring points, and the sensor receiving end face is flush with the ground.

[0019] The method for calculating and measuring the critical explosion distance between natural fragments and shock waves provided by the present invention has the following beneficial effects compared with the prior art:

[0020] The present invention provides a calculation formula for the position where fragments and shock waves meet after an explosion, thereby solving the technical problem of accurately and quickly obtaining the critical explosion distance value of the successive action of shock waves and fragments under a warhead explosion. Moreover, by comparing and analyzing the results of measurement experiments with the theoretical calculation formula, the error value obtained is only 2.75%, indicating that the calculation formula for the position where fragments and shock waves meet after an explosion provided by the present invention is reasonable and feasible. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a schematic diagram of the warhead;

[0022] Figure 2 It is a schematic diagram of the measurement scheme layout;

[0023] Figure 3 It is the expansion process of the fireball and the evolution of the shock wave trajectory driven by the explosion recorded by high-speed photography;

[0024] Figure 4 This is the image 0.9ms after the charge exploded;

[0025] Figure 5 It is a curve showing the distance of fragments and shock waves changing with time. DETAILED DESCRIPTION

[0026] The following will be combined with the accompanying drawings provided by the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are all in a very simplified form and are not in exact proportions. They are only used to facilitate and clearly illustrate the purpose of the embodiments of the present invention.

[0027] Example 1: This example provides a method for calculating the critical explosion distance between natural fragments and shock waves, which specifically includes the following steps:

[0028] S1. Obtain the peak overpressure value ΔP when the warhead airblast shock wave propagates in the air m .

[0029] Specifically, when the warhead charge explodes in the air, an airblast shock wave is formed. As the airblast shock wave propagates in the air, the pressure continues to decay, and the peak overpressure ΔP m The relationship between the propagation distance and the transmission distance is:

[0030]

[0031] Where, is the proportional explosion distance, R is the distance from the explosion center (m), and ω is the equivalent TNT charge of the warhead (kg).

[0032] S2. Get the propagation speed of the shock wave in the air Vs .

[0033] Specifically, the propagation speed of the shock wave in the air is related to its overpressure. According to the basic relationship of shock waves, the propagation speed of the airburst shock wave front V s (m / s) and peak overpressure ΔP m The approximate relationship between (MPa) is:

[0034]

[0035] The propagation velocity of the airburst shock wave front obtained by power function fitting

[0036] Substituting the expression of proportional explosion distance into the above formula, we can get the propagation velocity V of the airburst shock wave front: s and propagation distance R s The relationship is:

[0037] V s =1195.07ω 0.25 R s -0.76

[0038] S3. According to the obtained shock wave propagation speed value V in the air s , and the propagation distance R of the airburst shock wave front is obtained s .

[0039] Specifically, for V s Integrate and sort out the propagation distance R of the airburst shock wave front s With time t s Relationship:

[0040] R s =(2103.32ω 0.25 t s ) 1 / 1.76

[0041] S4. Obtain the distance R that the natural fragments fly in the air after the warhead explodes. f .

[0042] Specifically, according to the theory that high-speed fragments are formed by the explosion of natural fragment warheads, the initial velocity of high-speed fragments is calculated, and according to the principle of conservation of impulse and Newton's second law, the distance R that the fragments fly in the air is derived from the resistance formula. f and the time required t f The relationship is:

[0043]

[0044] Where mf is the mass of the fragment, c f is the windward drag coefficient related to the fragment shape, ρ0 is the mass density of air, is the average frontal area of ​​the fragments.

[0045] S5. Based on the distance R of the fragments flying in the air f Propagation distance R from the shock wave front s , and obtain the critical explosion distance between fragments and shock waves.

[0046] Specifically, when a warhead explodes in mid-air, the initial shock wave velocity is much greater than the initial velocity of the fragments, and the shock wave moves ahead of the fragments. However, since the shock wave's velocity decays quickly, the fragments will catch up with the shock wave, resulting in a problem of where the fragments and shock wave meet.

[0047] When R f =R s And t f =t s When , it is the meeting position of the fragments and the shock wave after the explosion:

[0048]

[0049] Solving the above formula can give the time t when the fragments catch up with the shock wave front, and then substituting it into the above distance calculation formula to get the distance R when the fragments catch up with the shock wave front, that is, the critical explosion distance between the fragments and the shock wave.

[0050] Example 2:

[0051] The present invention also provides a method for measuring the critical explosion distance between natural fragments and shock waves, which specifically includes the following steps:

[0052] S1. Design the specific structure of the warhead.

[0053] Specifically, such as Figure 1 As shown, the warhead includes a detonator, a detonator seat, a shell, explosives, a steel ball, and epoxy resin.

[0054] Furthermore, the explosive charge is a passivated RTX pressure charge with a length of 133 mm, a diameter of 70 mm, and a density of 1.71 g / cm 3 , the explosion speed is 8425m / s.

[0055] Furthermore, the shell material is made of 45# steel with a density of 7.85g / cm 3 The inner lining layer has a wall thickness of 2mm, the outer lining layer has a wall thickness of 1.5mm, and the inner and outer lining layers are connected to the upper and lower end covers by threaded connections. The diameter of a single steel ball (i.e., spherical prefabricated fragment) is 5mm and the mass is 0.51g. The prefabricated fragments are evenly arranged from top to bottom and then fixed by pouring epoxy resin.

[0056] In addition, since the warhead is detonated at one end, a detonator seat is installed at the detonating end to facilitate the installation and positioning of the detonator.

[0057] Furthermore, during the test, the charge device was placed on a wooden plank support at a height of 1.75 m from the ground.

[0058] S2. Obtain the peak overpressure of the free-field air shock wave at different locations driven by the explosion.

[0059] Specifically, in this embodiment, a 113B21 piezoelectric pressure sensor produced by PCB Corporation of the United States is used to measure the peak overpressure of the free-field air shock wave at different positions driven by the explosion.

[0060] Further, such as Figure 2 As shown, three pressure sensors are placed along a measuring line, and two pressure measuring lines are arranged. The overpressure test predetermined distances (from the explosion center) of the shock wave overpressure sensor are 2.3m, 3m, and 4m, respectively, with a total of three measuring points. The sensor receiving end surface is flush with the ground.

[0061] Furthermore, steel plates, aluminum plates, and foamed aluminum are placed on one side of the warhead. The steel plates are 1.57m×3.5m×3mm in size and are 5m away from the warhead horizontally. The aluminum plates and foamed aluminum are both 0.5m×0.5m×5mm in size and are arranged in an overlapping manner. The target stand is 1.8m high and is placed in sequence from 0.8m to 2.0m away from the warhead.

[0062] S3. Observe the fragment velocity and shock wave evolution during the explosion drive process.

[0063] Specifically, two high-speed photography systems were used to observe the target penetration speed of fragments, the development process of the charge's shock wave, the fireball expansion process, and the dispersion process of the explosion products.

[0064] Furthermore, the high-speed photography system is a FastcamnltimaAPX high-speed camera produced by Photron.

[0065] Furthermore, during the test, the shooting rates of the high-speed photography system were set to 13,000 frames / s and 9,439 frames / s respectively, and the horizontal distance between the warhead explosion drive device and the high-speed photography was 25m, in order to capture the instantaneous speed of fragments penetrating the target during the explosion drive process, the flame structure and the transient evolution of the shock wave.

[0066] Furthermore, to analyze the critical detonation distance for fragment shock wave coupling, the fireball radius and shock wave propagation distance were measured, using a 4m long and 2m wide background cloth as a reference. Furthermore, the aluminum sheet and aluminum foam composite material was bonded together and placed in a steel frame. After the test, the composite material was photographed and recovered for analysis of the coupling position.

[0067] Furthermore, in order to ensure the accuracy of the measurement, the number of repeatability tests in this embodiment is 3 times.

[0068] S4. Analysis and verification of measurement results.

[0069] Figure 3 The expansion process of the fireball and the evolution of the shock wave trajectory driven by the explosion were recorded by high-speed photography. The results show that after the explosion of the explosive, a clear flame was generated. As time went on, the flame first intensified and then gradually weakened. The time when the initial flame appeared was set to 0ms. The high-speed photography found that after the explosion, the shell flame lasted for 131ms. The flame generated by the explosion began to weaken after 1.5ms. At this time, the fireball and shock wave began to separate, and a large amount of black smoke was generated. The separation process of the fireball and shock wave and the analysis of the wavefront are shown in Figure 3 Furthermore, each high-speed photograph was scaled to the same scale, using the striped background cloth as a reference, allowing daily measurements of the fireball diameter at different times. At 0.6ms, 0.9ms, and 1.2ms, the shell fireball diameters were 3.3m, 2.13m, and 1.86m, respectively.

[0070] Further results show that the fireball formation and shock wave trajectory evolution driven by the explosion of the prefabricated fragmentation warhead shell can be divided into three processes: (a) The initial oxygen-free explosion reaction, in which oxygen in the air does not participate in the reaction, is mainly a reaction of the molecular compounds of the HTX explosive charge. This reaction lasts less than 1 μs, and the fireball grows rapidly and then shrinks, forming an air particle image. Subsequently, the radius of the actual explosion fireball reaches 60%-70% of the maximum fireball radius in a short period of time. During this stage, the accompanying explosion shock wave and the fireball develop almost simultaneously. Due to the obstruction of the explosion light, the edge of the shock wave cannot be seen in high-speed photography. (b) After the explosion fireball and shock wave simultaneously expand to a certain radius, the explosion shock wave separates from the fireball boundary and then continues to move outward at a speed greater than the fireball growth rate. (c) The shock wave and fragments formed by the air explosion move outward simultaneously. Due to the rapid attenuation of the shock wave velocity, the prefabricated fragments gradually continue to move outward at a speed greater than the shock wave growth rate, resulting in a coupling critical position. Due to the obstruction of the ground, the incident wave and the ground reflection wave interact to form an irregular reflection wave with a spreading structure.

[0071] Further, Figure 4 The image 0.9ms after the charge explosion is shown. In order to clearly show the shock wave expansion trace, the image is pre-processed. It can be found that the shock wave front is approximately hemispherical with an ellipticity of 0.95 and a shock wave radius R s , the distance from the detonation point to the wavefront, the position of the shock wavefront, R sThe measurement was carried out at an angle of 60° relative to the ground, because by comparing the consecutive high-speed photography frames, it was found that 60° provided the best contrast image. The image of 0.95ms was displayed. The fireball cloud had now expanded to a radius of 2.1m. The maximum radius of the fireball was R f , defines the maximum range from the detonation point to the edge of the fireball.

[0072] Furthermore, by analyzing the motion of the shock wave and prefabricated fragments driven by the explosion, we can obtain an average velocity head of 1660m / s for the fragments. Based on the time it takes for the shock wave to reach different distances, a power function is used to fit the change in the shock wave propagation distance over time. The curve of the change in the distance of the fragments and shock wave over time is shown in the figure below. Figure 5 As shown in the figure, the fragments and shock wave meet at 660 μs, with the meeting point 1.09 m (approximately 15.57 times the charge diameter) from the warhead explosion center. The meeting distance calculated using the formula in Example 1 is 1.12 m, which is 2.75% less than the measured meeting distance (1.09 m). This further verifies that the distance calculation formula in Example 1 is reasonable and reliable.

[0073] Those skilled in the art should understand that the present invention can be implemented in many other specific forms without departing from the spirit and scope of the present invention. Based on the embodiments of the present invention, any changes and modifications made by ordinary technicians in the field of the present invention in accordance with the above disclosure are within the scope of protection of the claims.

Claims

1. A method for calculating the critical explosion distance of natural fragments and shock waves, characterized in that: Including steps: S1. Obtain the peak overpressure value of the warhead airblast shock wave when it propagates in the air ; S2. Get the propagation speed of the shock wave in the air ; S3. Based on the obtained shock wave propagation speed in the air , and the propagation distance of the airburst shock wave front is obtained ; S4. Obtain the distance that natural fragments fly in the air after the warhead explodes ; S5. Based on the distance the fragments travel in the air Propagation distance from the shock wave front , get the critical explosion distance between fragments and shock waves; The propagation distance of the S3 explosion shock wave front Specifically: ； The distance that the fragments in S4 fly in the air for: ； Where, is the mass of the fragments, is the headwind drag coefficient related to the fragment shape, is the mass density of air, is the average frontal area of ​​the fragments, The time that fragments fly in the air; The specific calculation process of the critical explosion distance between fragments and shock waves in S5 is: S51. When When , the encounter position of the fragments and the shock wave after the explosion is: ； S52. Solving the above equation yields the time t it takes for the fragments to catch up with the shock wave front. Substituting this into the distance calculation formula yields the distance R it takes for the fragments to catch up with the shock wave front, i.e., the critical explosion distance between the fragments and the shock wave.

2. The calculation method according to claim 1, characterized in that The peak overpressure in S1 Specifically: ； Where, , is the proportional explosion distance, R is the distance from the explosion center (m), and ω is the equivalent TNT charge of the warhead (kg).

3. The calculation method according to claim 2, characterized in that The propagation speed of the shock wave in the air in S2 Specifically: 。

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