A method for predicting the state of detonation of a centrally symmetric TNT charge

Abstract

The application discloses a detonation state prediction method for a central symmetrical TNT charge, and relates to the technical field of detonation, which normalizes the distance between different positions and the detonation point of a charge into a normalized distance by using the distance between a detonation wave front and the detonation point, and provides a fitting function between normalized state parameters and the normalized distance under different TNT detonation working conditions, so that the normalized state parameters can be obtained by inputting the normalized distance at different positions into the fitting function, and then the detonation state parameters at different positions can be obtained by combining the normalized state parameters and the CJ state quantity of TNT. The method can realize fast and accurate prediction of the detonation state under the central symmetrical TNT charge scene, has better calculation accuracy, stability and engineering applicability, and can be used for near-field explosion prediction and far-field explosion prediction.

Description

Technical Field

[0001] This application relates to the field of detonation technology, and in particular to a method for predicting the detonation state of a centrosymmetric TNT charge. Background Technology

[0002] Explosions have wide applications in both military and civilian fields. Whether a charge containing explosives explodes in water or in the air, its chemical reaction process involves complex phenomena such as flame, deflagration, and detonation. The detonation process mainly includes two basic stages: initiation and propagation. When an explosive is subjected to external forces, it loses stability and explodes. This process from a stable state to an unstable state is called the initiation process of the explosive. The propagation of the detonation wave is caused by the impact and compression of the explosive by the shock wave. When the intensity of the shock wave exceeds a certain value, it will cause a chemical reaction of the explosive material behind the shock wave front. The energy released by the chemical reaction is used to support the continued propagation of the shock wave, thus forming the detonation process of the explosive.

[0003] In order to assess and predict the damage effects of an explosion, it is often necessary to predict the detonation state. There are currently two main methods: (1) Introducing a complex detonation calculation model, which can predict the detonation chemical reaction process from the initiation point in detail, mainly involving the generation and propagation process of the detonation wave. A common detonation calculation model is the "ignition-growth" reaction model proposed by Lee and Tarver. Using the detonation calculation model, a quantitative and refined prediction method for the detonation state can be realized. The calculation accuracy is high. Since it can describe the generation, development, and propagation process of the detonation wave, as well as the coupling effect between the detonation wave and the surrounding flow field, it can be applied to scenarios that consider the near-field effect of the explosion. However, the existing detonation calculation models are often very complex, require a lot of input parameters, and it is difficult to determine the specific values ​​of these parameters. The calculation complexity and amount of computation are large, and the time consumption is long. (2) Another method ignores the specific detonation process of the explosive, that is, it does not consider the details of the explosive detonation and simplifies the impact of the explosive on the surrounding environment to the effect of the expansion of a high-temperature gas. This method assumes that the explosive detonation is completed instantaneously, and the detonation product gas becomes a high-temperature, high-density, and high-pressure gas, thus constructing a simplified instantaneous detonation model. Compared with the first method, this method simplifies the calculation process and is easier to implement in engineering. However, since this method does not consider the details of the detonation process, it can only be used for qualitative engineering estimation in scenarios that consider the far-field effects of the explosion. When it is necessary to consider the near-field effects of the explosion or to make quantitative and high-precision predictions, this method is not applicable. It can be seen that the two existing commonly used detonation state prediction methods have their own shortcomings and cannot meet the needs of actual academic research and engineering application scenarios. Summary of the Invention

[0004] This application addresses the aforementioned problems and technical requirements by proposing a method for predicting the detonation state of a centrally symmetric TNT charge. The technical solution of this application is as follows:

[0005] A method for predicting the detonation state of a centrally symmetric TNT charge, comprising the following steps for any position Q at any time t:

[0006] Using the distance R0 = D × t between the detonation wave front and the detonation point at the current time t, the distance r between position Q and the detonation point of the explosive charge is normalized to obtain the normalized spacing between position Q and the detonation point. The explosive charge is filled with TNT. The explosive charge has a centrally symmetrical structure and the detonation point is located at the center of the explosive charge. D is the detonation velocity of TNT.

[0007] When the normalized spacing between position Q and detonation point At that time, each normalized state parameter at position Q is determined to be a platform constant corresponding to the current TNT detonation condition type; when the normalized spacing between position Q and the detonation point... At that time, the normalized spacing between position Q and the detonation point is... Substituting the values ​​into the fitting formulas for each normalized state parameter yields the normalized state parameters for position Q. The functional form of the fitting formula for each normalized state parameter is... Among them, the current TNT detonation condition type corresponds to the charge structure of the explosive package; the boundary distance r0 of the detonation stationary zone, the plateau constant corresponding to the detonation condition type, and the values ​​of parameters b0, b1, b2, b3, and b4 in the fitting formula of each normalized state parameter are all related to the detonation characteristics under the current TNT detonation condition type; the obtained normalized state parameters at position Q include the normalized density. Normalized speed Normalization pressure and normalized internal energy

[0008] The detonation state parameters at location Q include density. speed pressure Internal energy Where, ρ CJ =2228kg / m 3 u CJ =1859m / s, p CJ =21GPa, e CJ =6.02×10 6 J / kg are the CJ state quantities of TNT.

[0009] The further technical solution is that when the charge structure of the explosive package is a one-dimensional planar charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition.

[0010] The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional planar detonation condition of TNT is 0.5;

[0011] Normalized density corresponding to TNT one-dimensional planar detonation The platform constant is 0.656, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.269, and the normalized internal energy is... The platform constant is 0.552.

[0012] A further technical solution is that when the explosive charge structure is a one-dimensional planar explosive charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition; the fitting formulas for the various normalized state parameters corresponding to the one-dimensional planar TNT detonation condition are:

[0013]

[0014] The further technical solution is that when the charge structure of the explosive package is a two-dimensional circular charge structure, the current TNT detonation condition type is a one-dimensional cylindrical TNT detonation condition.

[0015] The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional cylindrical detonation condition of TNT is 0.485.

[0016] Normalized density corresponding to TNT one-dimensional cylindrical detonation The platform constant is 0.622, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.225, and the normalized internal energy is... The platform constant is 0.521.

[0017] A further technical solution is that when the charge structure is a two-dimensional circular charge structure, the current TNT detonation condition is a one-dimensional cylindrical TNT detonation condition; the fitting formulas for the normalized state parameters corresponding to the one-dimensional cylindrical TNT detonation condition are as follows:

[0018]

[0019] The further technical solution is that when the charge structure of the explosive package is a three-dimensional spherical charge structure, the current TNT detonation condition is a one-dimensional spherical TNT detonation condition.

[0020] The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional spherical detonation condition of TNT is 0.47.

[0021] Normalized density corresponding to the one-dimensional spherical detonation of TNT The platform constant is 0.602, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.201, and the normalized internal energy is... The platform constant is 0.502.

[0022] A further technical solution is that when the charge structure is a three-dimensional spherical charge structure, the current TNT detonation condition is a one-dimensional spherical detonation condition; the fitting formulas for the normalized state parameters corresponding to the one-dimensional spherical detonation condition are as follows:

[0023]

[0024] The further technical solution is that the detonation velocity of TNT is D = 6950m / s.

[0025] The beneficial technical effects of this application are:

[0026] This application discloses a detonation state prediction method for centrosymmetric TNT charges. This method targets classic explosion scenarios using TNT, a common explosive type, with a centrosymmetric charge structure. By analyzing the propagation characteristics of the detonation wave after the detonation of the centrosymmetric TNT charge, it finds that the detonation wave exhibits good similarity within the charge. Therefore, a high-precision instantaneous detonation model for this explosion scenario is provided through the constructed normalized variables. The normalized state parameters at different locations can be directly and quickly calculated using the fitting formula provided in this application. Then, by combining the CJ state variables of the TNT, the detonation state parameters at different locations can be obtained. The fitting function provided in this application is established considering the details of the detonation process, thus achieving high prediction accuracy. Furthermore, the simple form of the fitting function results in low computational load and short computation time. This makes the prediction method of this application perform well in both prediction accuracy and speed. It can be used for both near-field and far-field explosion prediction, exhibiting superior computational accuracy, stability, and engineering applicability. It has significant meaning and value in both academic research and engineering applications.

[0027] This application also provides specific parameter values ​​in the fitting functions of various normalized state parameters under different TNT detonation conditions, which improves the calculation accuracy and efficiency of charge detonation and can provide key technical support for shock wave and bubble movement and load propagation under near-field and far-field explosions of TNT charges in air and underwater environments. Attached Figure Description

[0028] Figure 1 This is a schematic flowchart of a detonation state prediction method according to an embodiment of this application.

[0029] Figure 2 These are different normalized spacings under three different TNT detonation conditions. Normalized density under The curve graph.

[0030] Figure 3 These are different normalized spacings under three different TNT detonation conditions. Normalized speed The curve graph.

[0031] Figure 4 These are different normalized spacings under three different TNT detonation conditions. Normalization pressure under The curve graph.

[0032] Figure 5 These are different normalized spacings under three different TNT detonation conditions. Normalized internal energy under The curve graph.

[0033] Figure 6 This is a distribution curve of detonation state parameters at different times and locations at different positions from the detonation point in a detonation example of a one-dimensional planar detonation of TNT.

[0034] Figure 7 This is a density distribution cloud map at different times at different locations from the initiation point in another TNT one-dimensional cylindrical detonation case.

[0035] Figure 8 yes Figure 7 In the detonation example, the distribution cloud map of the velocity components along the X direction at different times at different locations from the detonation point.

[0036] Figure 9 yes Figure 7 In the detonation example, the distribution contour map of the velocity components along the Y direction at different times at different locations from the detonation point.

[0037] Figure 10 yes Figure 7 In the detonation example, the pressure distribution cloud map at different locations and times at different initiation points.

[0038] Figure 11 yes Figure 7 In the detonation example, the internal energy distribution cloud map at different times and locations at different locations from the detonation point. Detailed Implementation

[0039] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0040] This application discloses a method for predicting the detonation state of a centrally symmetric TNT charge. Please refer to... Figure 1 The diagram shows a schematic of the method. This method is designed for applications involving centrally symmetric TNT charges and can be used to calculate and predict the detonation state of a centrally symmetric TNT-filled explosive charge after detonation. The explosive charge in this application has a centrally symmetric structure, is filled with TNT, and has its detonation point located at the center of the charge.

[0041] There are three main types of charge structures for TNT detonation packages with centrosymmetry, each corresponding to a different type of TNT detonation condition:

[0042] (1) When the charge structure of the explosive package is a one-dimensional planar charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition.

[0043] (2) When the charge structure of the explosive charge is a two-dimensional circular charge structure, the current TNT detonation condition type is a one-dimensional cylindrical TNT detonation condition.

[0044] (3) When the charge structure of the explosive package is a three-dimensional spherical charge structure, the current TNT detonation condition is a one-dimensional spherical TNT detonation condition.

[0045] When predicting the detonation state of a centrally symmetric TNT charge, it is necessary to obtain the detonation state parameters at any position Q and any time t after detonation. These parameters include density, velocity, pressure, and internal energy. Regardless of the centrally symmetric charge structure used, the detonation wave structure inside the charge after central detonation exhibits significant structural similarities at different times, thus allowing for normalization. Therefore, this application introduces a normalized spacing. And the normalized state parameters, for any position Q:

[0046] Using the distance R0 = D × t between the detonation wave front and the detonation point at the current time t, the distance r between position Q and the detonation point of the explosive charge is normalized to obtain the normalized spacing between position Q and the detonation point. Normalized Spacing It is a dimensionless parameter and D is the detonation velocity of TNT, and D = 6950 m / s.

[0047] Using the CJ state variables of TNT, the detonation state parameters at position Q are normalized to construct the normalized state parameters at position Q. The normalized state parameters at position Q include the normalized density. Normalized speed Normalization pressure and normalized internal energy and: The detonation state parameters at position Q include density ρ(r), velocity u(r), pressure p(r), and internal energy e(r). The CJ state variables of TNT include ρ... CJ =2228kg / m 3 u CJ =1859m / s, p CJ =21GPa, e CJ =6.02×10 6 J / kg.

[0048] This application studies the detonation characteristics under different TNT detonation conditions, dividing the detonation region into a static detonation zone near the detonation point and a sparse detonation zone far from the detonation point. Normalized state parameters of the static and sparse zones are directly fitted to normalized intervals, allowing the normalized state parameters to be obtained directly by substituting the normalized intervals into the calculations, thus yielding the detonation state parameters. This applies to all TNT detonation conditions under the aforementioned charge structures.

[0049] When the normalized spacing between position Q and detonation point At that time, that is, for position Q located in the detonation static zone, each normalized state parameter of position Q is determined to be the platform constant corresponding to the current TNT detonation condition type.

[0050] When the normalized spacing between position Q and detonation point At that time, that is, for a position Q located within the detonation sparse region, the normalized distance between position Q and the detonation point is... Substituting the values ​​into the fitting formulas for each normalized state parameter yields the normalized state parameters for position Q. The functional form of the fitting formula for each normalized state parameter is...

[0051] Among them, the current TNT detonation condition type corresponds to the charge structure of the explosive package, the boundary distance r0 of the detonation stationary zone, the plateau constant corresponding to the detonation condition type, and the values ​​of parameters b0, b1, b2, b3, and b4 in the fitting formula of each normalized state parameter are all related to the detonation characteristics under the current TNT detonation condition type.

[0052] The three types of propellant loading structures are described below:

[0053] (1) When the explosive charge structure is a one-dimensional planar explosive charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition. At this time:

[0054] The boundary distance r0 = 0.5 for the detonation stationary zone corresponding to the one-dimensional planar detonation condition of TNT.

[0055] Normalized density corresponding to TNT one-dimensional planar detonation The platform constant is 0.656, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.269, and the normalized internal energy is... The platform constant is 0.552.

[0056] The fitting formulas for the normalized state parameters corresponding to the one-dimensional planar detonation condition of TNT are as follows:

[0057]

[0058] The normalized state parameters at different locations under the one-dimensional planar detonation scenario of TNT are shown in Table 1 below:

[0059] Table 1. Normalized state parameters under one-dimensional planar detonation of TNT

[0060]

[0061] (2) When the explosive charge structure is a two-dimensional circular charge structure, the current TNT detonation condition is a one-dimensional cylindrical TNT detonation condition. At this time:

[0062] The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional cylindrical detonation condition of TNT is 0.485.

[0063] Normalized density corresponding to TNT one-dimensional cylindrical detonation The platform constant is 0.622, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.225, and the normalized internal energy is... The platform constant is 0.521.

[0064] The fitting formulas for the normalized state parameters corresponding to the one-dimensional cylindrical detonation condition of TNT are as follows:

[0065]

[0066] The normalized state parameters at different locations under the one-dimensional cylindrical TNT detonation scenario are shown in Table 2 below:

[0067] Table 2. Normalized state parameters under one-dimensional cylindrical TNT detonation.

[0068]

[0069]

[0070] (3) When the explosive charge structure is a three-dimensional spherical explosive charge structure, the current TNT detonation condition is a one-dimensional spherical TNT detonation condition. At this time:

[0071] The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional spherical detonation condition of TNT is 0.47.

[0072] Normalized density corresponding to the one-dimensional spherical detonation of TNT The platform constant is 0.602, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.201, and the normalized internal energy is... The platform constant is 0.502.

[0073] The fitting formulas for the normalized state parameters corresponding to the one-dimensional spherical detonation of TNT are as follows:

[0074]

[0075] The normalized state parameters at different locations under the one-dimensional spherical detonation scenario of TNT are shown in Table 2 below:

[0076] Table 3. Normalized state parameters under one-dimensional spherical detonation of TNT

[0077]

[0078] Normalized density under the above three different TNT detonation conditions Normalized spacing with position The curve is as follows Figure 2 As shown. Normalized velocity under the above three different TNT detonation conditions. Normalized spacing with position The curve is as follows Figure 3 As shown. Normalized pressure under the above three different TNT detonation conditions. Normalized spacing with position The curve is as follows Figure 4 As shown. Normalized internal energy under the above three different TNT detonation conditions. Normalized spacing with position The curve is as follows Figure 5 As shown.

[0079] Using the functional relationship obtained by fitting the above-mentioned application, after determining the type of TNT detonation condition, the normalized spacing at each location is used to... The normalized state parameters at each location can be obtained directly. Then, by combining the CJ state variables, the detonation state parameters at any location Q, including density, can be further obtained. speed pressure Internal energy

[0080] For example, in one instance, the explosive charge structure is a one-dimensional planar charge structure. The detonation velocity of TNT is D = 6950 m / s. Therefore, the distance R0 between the detonation wave front and the detonation point at time t = 1 μs after detonation is 6.95 mm; at time t = 3 μs, it is 20.85 mm; at time t = 5 μs, it is 34.75 mm; at time t = 7 μs, it is 48.65 mm; and at time t = 9 μs, it is 62.55 mm. This is combined with the CJ state variable ρ of TNT. CJ =2228kg / m 3 u CJ =1859m / s, p CJ =21GPa, e CJ =6.02×10 6 J / kg. Based on the fitting function in Table 1, directly substituting it into the calculation, we can obtain the detonation state parameters at different times and locations within a distance r of 0.1m from the detonation point, as shown below. Figure 6 As shown in (a), (b), (c), and (d), the results are basically consistent with the prediction results obtained from existing detonation calculation models, indicating that the prediction method of this application has high prediction accuracy. Moreover, after verification in different instances, the prediction method of this application has good prediction accuracy under various TNT detonation conditions.

[0081] For example, in another instance, the explosive charge is a two-dimensional circular charge structure, with the detonation point located at the origin of the coordinate system, and the computational domain is [-0.15, 0.15] × [-0.15, 0.15] m. 2 A uniform grid was used. Given that the detonation velocity of TNT is D = 6950 m / s, the distance R0 between the detonation wave front and the detonation point at t = 5 μs after detonation is 34.75 mm; at t = 10 μs, it is 69.5 mm; at t = 15 μs, it is 104.25 mm; and at t = 20 μs, it is 139 mm. Substituting the fitting function from Table 1 directly into the calculation, the density distribution cloud maps at different locations within the computational domain at different times can be obtained as follows: Figure 7 As shown in the figure. The distribution contour plots of the velocity components along the X-direction at different locations within the computational domain at different times are shown in the figure. Figure 8As shown, the distribution contour plots of the velocity components along the Y direction at different locations within the computational domain at different times are as follows. Figure 9 As shown in the figure. The pressure distribution contour maps at different locations within the computational domain at different times are as follows. Figure 10 As shown, the distribution contour maps of internal energy at different locations within the computational domain at different times are as follows: Figure 11 As shown.

[0082] Based on the detonation characteristics of centrosymmetric TNT charges, this application directly provides quantitative calculation formulas for detonation state parameters under different TNT detonation conditions, enabling rapid prediction of the detonation process through substitution and solving. Furthermore, the quantitative calculation formulas for the detonation state parameters obtained by fitting have high prediction accuracy.

[0083] The above descriptions are merely preferred embodiments of this application, and this application is not limited to the above embodiments. It is understood that other improvements and variations that can be directly derived or conceived by those skilled in the art without departing from the spirit and concept of this application should be considered to be included within the protection scope of this application.

Claims

1. A method for predicting the detonation state of a centrally symmetric TNT charge, characterized in that, The detonation state prediction method includes any position Q at any time t: Using the distance R0 = D × t between the detonation wave front and the detonation point at the current time t, the distance r between position Q and the detonation point of the explosive charge is normalized to obtain the normalized spacing between position Q and the detonation point. The explosive charge is filled with TNT, and the explosive charge structure is centrally symmetrical with the detonation point located at the center of the explosive charge. D is the detonation velocity of TNT. When the normalized spacing between position Q and detonation point At that time, each normalized state parameter at position Q is determined to be a platform constant corresponding to the current TNT detonation condition type; when the normalized spacing between position Q and the detonation point... At that time, the normalized spacing between position Q and the detonation point is... Substituting the values ​​into the fitting formulas for each normalized state parameter yields the normalized state parameters for position Q. The functional form of the fitting formula for each normalized state parameter is... The current TNT detonation condition type corresponds to the charge structure of the explosive package. The boundary distance r0 of the detonation stationary zone, the plateau constant corresponding to the detonation condition type, and the values ​​of parameters b0, b1, b2, b3, and b4 in the fitting formula of each normalized state parameter are all related to the detonation characteristics under the current TNT detonation condition type. The normalized state parameters at position Q include the normalized density. Normalized speed Normalization pressure and normalized internal energy The detonation state parameters at location Q include density. speed pressure Internal energy Where, ρ CJ =2228kg / m 3 u CJ =1859m / s, p CJ =21GPa, e CJ =6.02×10 6 J / kg are the CJ state quantities of TNT.

2. The detonation state prediction method according to claim 1, characterized in that, When the charge structure of the explosive package is a one-dimensional planar charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition. The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional planar detonation condition of TNT is 0.5; Normalized density corresponding to TNT one-dimensional planar detonation The platform constant is 0.656, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.269, and the normalized internal energy is... The platform constant is 0.

552.

3. The detonation state prediction method according to claim 1, characterized in that, When the explosive charge structure is a one-dimensional planar explosive charge structure, the current TNT detonation condition type is a one-dimensional planar TNT detonation condition; the fitting formulas for the normalized state parameters corresponding to the one-dimensional planar TNT detonation condition are as follows:

4. The detonation state prediction method according to claim 1, characterized in that, When the charge structure of the explosive package is a two-dimensional circular charge structure, the current TNT detonation condition type is a one-dimensional cylindrical TNT detonation condition. The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional cylindrical detonation condition of TNT is 0.

485. Normalized density corresponding to TNT one-dimensional cylindrical detonation The platform constant is 0.622, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.225, and the normalized internal energy is... The platform constant is 0.

521.

5. The detonation state prediction method according to claim 1, characterized in that, When the explosive charge structure is a two-dimensional circular charge structure, the current TNT detonation condition type is a one-dimensional cylindrical TNT detonation condition; the fitting formulas for the normalized state parameters corresponding to the one-dimensional cylindrical TNT detonation condition are as follows:

6. The detonation state prediction method according to claim 1, characterized in that, When the charge structure of the explosive package is a three-dimensional spherical charge structure, the current TNT detonation condition type is a one-dimensional spherical TNT detonation condition. The boundary distance r0 of the detonation stationary zone corresponding to the one-dimensional spherical detonation condition of TNT is 0.

47. Normalized density corresponding to the one-dimensional spherical detonation of TNT The platform constant is 0.602, and the normalized velocity is... The platform constant is 0, and the normalized pressure is 0. The corresponding plateau constant is 0.201, and the normalized internal energy is... The platform constant is 0.

502.

7. The detonation state prediction method according to claim 1, characterized in that, When the explosive charge structure is a three-dimensional spherical explosive charge structure, the current TNT detonation condition type is a one-dimensional spherical TNT detonation condition; the fitting formulas for the normalized state parameters corresponding to the one-dimensional spherical TNT detonation condition are as follows:

8. The detonation state prediction method according to claim 1, characterized in that, The explosion speed of TNT is D=6950m / s.

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