Method for Correcting Initial Conditions of Explosives in Numerical Simulation of Underwater Explosions

Abstract

The present invention discloses a method for correcting explosive initial conditions for numerical simulation of underwater explosions. The explosive is approximated as a sphere, and a computational model for a free-field spherically symmetric underwater explosion is established. Initial parameters of the explosive, including initial density and initial internal energy per unit mass of the explosive, are input into the JWL equation of state to obtain preliminary pressure-time curves at different spatial positions. The peak value of the shock wave pressure is extracted and compared with the results of an experiment or empirical formula. If the error does not exceed 5%, the initial internal energy per unit mass of the explosive is maintained unchanged; otherwise, the initial internal energy per unit mass of the explosive is adjusted until the error does not exceed 5%. The bubble pulsation period is determined and compared with the results of an experiment or empirical formula. If the error does not exceed 5%, the initial density of the explosive is maintained unchanged; otherwise, the initial density of the explosive is adjusted until the error does not exceed 5%. The present invention can accurately predict the peak value of the shock wave pressure and the bubble pulsation period, has the advantages of low cost and high efficiency, and can provide more accurate load input for the calculation of three-dimensional underwater explosion models.

Description

Technical Field

[0001] The present invention relates to the technical field of underwater explosion numerical calculation, and in particular to a method for correcting explosive initial conditions for underwater explosion numerical simulation. Background Art

[0002] Ships are vulnerable to various weapons when conducting maritime combat missions. Underwater explosion damage caused by underwater weapons such as torpedoes, mines, and depth charges is a major threat to a ship's viability. Shock waves and bubble pulsations are the primary load forms during underwater explosions. Predicting underwater explosion loads is fundamental to ship blast and shock resistance design and the control of explosive power. Due to the incompressible nature of water, the impulse generated by an explosion is also greater. Existing research on underwater explosions focuses primarily on ship shock resistance and protection. However, obtaining accurate and objective ship blast and shock resistance performance requires precise underwater explosion load input. Therefore, conducting high-precision numerical simulations of underwater explosion shock waves and bubble pulsations is of great significance for studying ship underwater explosion resistance and evaluating explosive power.

[0003] As a complex physical phenomenon, underwater explosions often rely on numerical calculation methods for the initial design and evaluation of structural damage and protection. Although numerical calculations have the advantages of high efficiency, convenience, and economy, the accurate prediction of underwater explosion loads remains a huge challenge. Shock waves and bubble pulsations are the main forms of loads during underwater explosions. At present, the main initial condition assignment method for numerical calculations of underwater explosions is to directly give the actual explosive size and density, or to establish a high-pressure bubble with a bubble radius equal to the explosive radius and a bubble initial pressure equal to the initial internal energy per unit mass of the bubble substituted into the JWL state equation. Calculated pressure. However, due to the inaccuracy of the JWL state equation parameters, the calculation results using conventional state equation parameters often deviate greatly from the test results. Carrying out a series of tests to calibrate the state equation parameters is expensive and is usually not suitable for some problems where the damage effect is verified only through a small number of tests. If the simulation results are inaccurate, the design of underwater weapons and underwater structures may not meet actual requirements, thereby affecting the evaluation of the damage power of underwater weapons and the safety and reliability of the structure. Design errors may also lead to excessive or insufficient reinforcement of the structure, increasing construction and maintenance costs. Therefore, there is an urgent need to propose a simple and efficient method to achieve accurate prediction of underwater explosion loads. Summary of the Invention

[0004] The main purpose of the present invention is to address the problem that the state equation parameters of the commonly used explosives mentioned above are inaccurate in predicting underwater explosion shock waves and bubble pulsations, which seriously affects the accuracy of underwater explosion numerical calculations. Carrying out underwater explosion tests to calibrate the state equation parameters often consumes a lot of time, manpower and material resources. Therefore, a method for correcting the initial conditions of explosives for underwater explosion numerical simulation is proposed. This method achieves accurate prediction of the shock wave pressure peak and bubble pulsation period by simply adjusting the initial density and initial internal energy per unit mass of the explosive, thereby improving the accuracy of numerical calculations of underwater explosion loads. Applying the explosive parameters obtained by the method of the present invention to a three-dimensional calculation model can reduce the research cost of underwater explosion numerical simulations, save calculation time, and provide support for underwater structure protection design and explosive power evaluation.

[0005] The technical solution adopted in the present invention is:

[0006] A method for correcting explosive initial conditions for underwater explosion numerical simulation comprises the following steps:

[0007] S1. The explosive is approximated as a sphere, and a computational model of a free-field spherically symmetric underwater explosion is established. The initial parameters of the explosive input into the JWL equation of state include the initial density and the initial internal energy per unit mass of the explosive. The Euler domain is spatially discretized using the difference method, finite volume method, or discontinuous Galerkin method, and the time domain is discretized using the Runge-Kutta method to obtain preliminary pressure-time history curves at different spatial positions.

[0008] The JWL state equation is:

[0009]

[0010] Where: P represents the pressure of the detonation products, A, B, R1, R2 and ω are material parameters, ρ0 is the initial density of the explosive, ρ is the density of the detonation products, and e is the internal energy per unit mass of the explosive.

[0011] The parameters of the JWL state equation are selected based on the literature (BM Dobratz, 1972. Properties of Chemical Explosives And Explosive Simulants, California University, Livermore (USA)): the initial density of the explosive ρ0 is 1630 kg / m 3 The initial internal energy e0 of unit mass of explosive is 3.681MJ / kg, and the constants A, B, R1, R2 and ω are 373.8GPa, 3.747GPa, 4.15, 0.9 and 0.35 respectively.

[0012] S2. Extract the shock wave pressure peak value in the pressure-time history curve obtained in S1, and compare it with the test or empirical formula results. According to the comparison results, if the error of the shock wave pressure peak value does not exceed 5%, the initial internal energy per unit mass of the explosive is maintained unchanged; if the error of the shock wave pressure peak value exceeds 5% and is less than the test or empirical formula result, the initial internal energy per unit mass of the explosive is increased; if the error of the shock wave pressure peak value exceeds 5% and is greater than the test or empirical formula result, the initial internal energy per unit mass of the explosive is reduced; then recalculate and update the pressure-time history curve until the pressure peak value in its shock wave stage has an error of no more than 5% compared with the test or empirical formula result.

[0013] The empirical formulas used for underwater explosions include:

[0014] 1) Shock wave stage:

[0015] p(t)=P m e -t / θ ,t<θ (2)

[0016]

[0017] Formula (2) is the pressure waveform in the exponential decay stage, formula (3) is the pressure waveform in the reciprocal decay stage, formula (4) is the pressure waveform in the latter part of the reciprocal decay stage, and formula (5) is the pressure waveform in the bubble expansion and contraction stage, where:

[0018]

[0019] 2) Bubble pulsation stage:

[0020]

[0021] in:

[0022]

[0023] Where p is the free field pressure in water; t is the time; Q is the mass of TNT; θ is the shock wave attenuation coefficient; R is the explosion distance; P m is the peak pressure of the shock wave; H0 is the depth of the explosive; r0 is the radius of the explosive; ρ w is the density of water; c is the speed of sound in water; P atm is atmospheric pressure; g is the acceleration due to gravity; P m1 is the peak value of the bubble pulsation load; θ1 is the bubble pulsation load attenuation coefficient; R bc is the distance from the measuring point to the center of the bubble; is the angle between the line connecting the explosion center and the observation point and the horizontal line; ΔH is the rising distance of the bubble; and T is the bubble pulsation period.

[0024] S3. Determine the bubble pulsation period based on the moment when the secondary shock wave pressure peak appears in the pressure-time curve obtained in S2, and compare it with the test or empirical formula results. According to the comparison results, if the bubble pulsation period error does not exceed 5%, keep the initial density of the explosive unchanged; if the bubble pulsation period error exceeds 5% and is less than the test or empirical formula results, reduce the initial density of the explosive; if the bubble pulsation period error exceeds 5% and is greater than the test or empirical formula results, increase the initial density of the explosive; the above-mentioned initial density adjustment is based on the law of conservation of mass to ensure that the product of the initial density and volume of the explosive remains unchanged; then recalculate and update the pressure-time curve until the bubble pulsation period has a comparison error of no more than 5% with the test or empirical formula results.

[0025] The beneficial effects produced by the present invention are:

[0026] By simply adjusting the initial density and initial internal energy per unit mass of the explosive, the present invention can accurately predict the peak shock wave pressure and bubble pulsation period, enabling high-precision numerical simulation of underwater explosion shock waves and bubble pulsations. This method offers the advantages of low cost and high efficiency, providing more accurate load input for three-dimensional underwater explosion model calculations, improving the accuracy and computational efficiency of numerical simulation research, and providing more accurate guidance for underwater structure design and explosive power assessment. Therefore, the present invention has important engineering value and application significance in the field of underwater explosions. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following is a brief introduction to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 is a flow chart of the method for correcting the initial conditions of explosives of the present invention;

[0029] Figure 2 1. A comparison diagram of the pressure peak value extracted during the shock wave phase after the pressure time history curve is updated in step S2 of Example 1 of the present invention and the test results;

[0030] Figure 3 This is a comparison chart of the bubble pulsation period extracted after updating the pressure time history curve in step S3 of Example 1 of the present invention and the test results;

[0031] Figure 4 This is a comparison diagram of the bubble pulsation period extracted after the pressure time history curve is updated in step S3 of Example 2 of the present invention and the test results. DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0033] It should be noted that the illustrations provided in the embodiments of the present invention are only schematic illustrations of the basic concept of the present invention. Therefore, the drawings only show components related to the present invention and are not drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component can be changed at will, and the component layout type may also be more complicated.

[0034] Example 1:

[0035] Based on the experimental results in the literature (Swift Jr., E., Decius, JC, 1950. Measurement of Bubble Pulse Phenomena, III. Radius and Period Studies. Technical Report. Office of Naval Research (ONR).), the feasibility of the method for correcting the initial conditions of explosives in underwater explosion numerical simulation is verified by comparison. The experiment used for verification is described as follows: 0.227kg equivalent TNT was used, and the charging depths were 182.88m and 91.44m respectively. Two free-field power tests were carried out. The underwater free-field pressure sensor was placed in the water area 0.69m away from the center of the starting bubble. According to the measured pressure time history curve at the charging depth of 182.88m, and the bubble radius time history curve at the charging depths of 182.88m and 91.44m, the method proposed in this invention was used to correct the initial conditions of the explosives during the numerical calculation, so that the numerical simulation results were consistent with the experimental results. The specific steps are as follows:

[0036] Step 1: The explosive is approximated as a sphere, and a free-field spherically symmetric underwater explosion calculation model is established. The parameters of the JWL state equation are based on the literature (BM Dobratz, 1972. Properties of Chemical Explosives And Explosive Simulants, University of California, Livermore (USA)): the initial density of TNT is ρ0 1630 kg / m 3The initial internal energy per unit mass of explosive, e0, is 3.681 MJ / kg, and the constants A, B, R1, R2, and ω are 373.8 GPa, 3.747 GPa, 4.15, 0.9, and 0.35, respectively. The Euler domain is spatially discretized using the discontinuous Galerkin method, and the time domain is discretized using the third-order Runge-Kutta method, obtaining preliminary pressure-time history curves at different spatial locations.

[0037] Step 2: Under the working condition of charging depth of 182.88m, the peak pressure of shock wave extracted from the pressure-time curve obtained in step 1 is 45.2MPa, which has an error of 7.0% compared with the experimental shock wave pressure peak of 48.6MPa. Therefore, the initial internal energy per unit mass of explosive is increased to 1.2 times, that is, e0 = 4.4172MJ / kg. The pressure-time curve is recalculated and updated, and the peak pressure of shock wave extracted is 47.3MPa, which has an error of 2.7% compared with the experimental result (see Figure 2 ).

[0038] Step 3: The bubble pulsation period determined from the pressure-time curve obtained in step 2, which is 14.6ms, is 8.2% lower than the experimental bubble pulsation period of 15.9ms. Therefore, the density of the explosive is reduced to 1580kg / m 3 , increasing the volume of explosives, thereby increasing the bubble period. Recalculating and updating the pressure time history curve, the bubble pulsation period extracted is 15.6ms, which is 1.9% less than the test result (see Figure 3 ).

[0039] Since the literature does not list the test pressure data for the working condition with a charge depth of 91.44m, only the bubble pulsation period is corrected for this working condition. In the working condition with a charge depth of 91.44m, the test bubble pulsation period is 26.7ms. Based on the initial parameters in step 1, the calculated bubble pulsation period is 24.1ms, which has an error of 9.7% compared with the test result. Therefore, the density of the explosive is reduced and adjusted to 1390kg / m 3 , the volume of the explosive is increased, thus increasing the bubble pulsation period. After recalculation, the bubble radius time history curve is obtained (see Figure 3 ), it can be seen that the bubble pulsation period is 26.9ms, and the error compared with the experimental result is 0.7%.

[0040] Example 2:

[0041] The feasibility of the method for correcting the initial explosive conditions for underwater explosion numerical simulations was verified by comparing the results calculated using the empirical formula. The verification conditions were: 1 kg equivalent of TNT, a charge depth of 100 m, and a blast distance of 1 m. The method proposed in this invention was used to correct the initial explosive conditions during numerical calculations, ensuring that the numerical simulation results matched those of the empirical formula. The specific steps are as follows:

[0042] Step 1: The explosive is approximated as a sphere, and a free-field spherically symmetric underwater explosion calculation model is established. The parameters of the JWL state equation are based on the literature (BM Dobratz, 1972. Properties of Chemical Explosives And Explosive Simulants, University of California, Livermore (USA)): the initial density of TNT is ρ0 1630 kg / m 3 The initial internal energy per unit mass of explosive, e0, is 3.681 MJ / kg, and the constants A, B, R1, R2, and ω are 373.8 GPa, 3.747 GPa, 4.15, 0.9, and 0.35, respectively. The Euler domain is spatially discretized using the discontinuous Galerkin method, and the time domain is discretized using the third-order Runge-Kutta method, obtaining preliminary pressure-time history curves at different spatial locations.

[0043] Step 2: Extract the shock wave pressure peak value from the pressure-time history curve obtained in step 1 to be 52.3 MPa. Compared with the shock wave pressure peak value of 53.4 MPa calculated by the empirical formula (taking into account the hydrostatic pressure at a water depth of 100 m), the error is 2.1%. Therefore, the initial internal energy per unit mass of explosives remains unchanged, and there is no need to update the pressure-time history curve.

[0044] Step 3: The bubble pulsation period determined from the pressure-time curve obtained in step 2 at the time of the secondary shock wave pressure peak is 37.6ms. Compared with the bubble pulsation period of 42.4ms in the empirical formula, the error is 11.3%. Therefore, the density of the explosive is reduced to 1400kg / m 3 , increasing the volume of explosives, thereby increasing the bubble period. Recalculate and update the pressure time curve. According to the time when the bubble pulsation peak appears, the bubble pulsation period is extracted to be 42.1ms. The error compared with the result of the empirical formula is 0.7% (see Figure 4 ).

[0045] The embodiments of this invention demonstrate that, in the field of underwater explosion numerical calculation research, this invention can address the inaccurate prediction of underwater explosion shock wave pressure peak and bubble pulsation period using state equation parameters of commonly used explosives, providing strong support for achieving high-precision numerical simulation of underwater explosions. Furthermore, this invention reduces reliance on complex computing resources, while maintaining high accuracy, lowering research and application costs. Its simplicity and efficiency make it suitable for a wide range of applications, including underwater explosion shock resistance design for ships, underwater structure safety assessment, and explosive power evaluation.

[0046] It should be pointed out that, according to the needs of implementation, the various steps / components described in this application can be split into more steps / components, or two or more steps / components or partial operations of steps / components can be combined into new steps / components to achieve the purpose of the present invention.

[0047] The size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0048] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A method for correcting explosive initial conditions for underwater explosion numerical simulation, characterized in that: The following steps are involved: S1. The explosive is approximated as a sphere, and a computational model for a free-field spherically symmetric underwater explosion is established. The initial parameters of the explosive, including the initial density and the initial internal energy per unit mass of the explosive, are input into the JWL equation of state. The Euler domain is spatially discretized, and the time domain is discretized to obtain preliminary pressure-time history curves at different spatial positions. S2. Extract the peak value of the shock wave pressure from the pressure-time curve obtained in S1 and compare it with the experimental or empirical formula results. If the error of the peak value of the shock wave pressure does not exceed 5%, the initial internal energy per unit mass of the explosive is maintained unchanged. If the shock wave pressure peak error exceeds 5% and is less than the test or empirical formula result, the initial internal energy per unit mass of the explosive is increased; if the shock wave pressure peak error exceeds 5% and is greater than the test or empirical formula result, the initial internal energy per unit mass of the explosive is reduced; Then recalculate and update the pressure time history curve until the pressure peak in the shock wave stage has an error of no more than 5% compared with the result of the test or empirical formula; S3, determining the bubble pulsation period based on the time when the secondary shock wave pressure peak appears in the pressure-time curve obtained in S2, and comparing it with the experimental or empirical formula results. If the bubble pulsation period error does not exceed 5% based on the comparison results, then the initial density of the explosive is maintained unchanged; If the bubble pulsation period error exceeds 5% and is less than the test or empirical formula result, the initial density of the explosive is reduced. If the bubble pulsation period error exceeds 5% and is greater than the test or empirical formula result, the initial density of the explosive is increased. The above initial density adjustment is based on the law of conservation of mass to ensure that the product of the initial density and volume of the explosive remains unchanged. The pressure time history curve is then recalculated and updated until the error between the bubble pulsation period and the test or empirical formula result does not exceed 5%.

2. The method for correcting explosive initial conditions for underwater explosion numerical simulation according to claim 1, characterized in that: In step S1, the JWL state equation is: Where: P represents the pressure of the detonation products, A, B, R1, R2 and ω are material parameters, ρ0 is the initial density of the explosive, ρ is the density of the detonation products, and e is the internal energy per unit mass of the explosive.

3. The method for correcting explosive initial conditions for underwater explosion numerical simulation according to claim 2, characterized in that: The parameters of the JWL state equation are selected based on existing literature: the initial density of the explosive ρ0 is 1630 kg / m 3 The initial internal energy e0 of unit mass of explosive is 3.681MJ / kg, and the constants A, B, R1, R2 and ω are 373.8GPa, 3.747GPa, 4.15, 0.9 and 0.35 respectively.

4. The method for correcting explosive initial conditions for underwater explosion numerical simulation according to claim 1, characterized in that: In step S1, the Euler domain is spatially discretized using a difference method, a finite volume method, or a discontinuous Galerkin method.

5. The method for correcting explosive initial conditions for underwater explosion numerical simulation according to claim 1, characterized in that: In step S1, the time domain is discretized using the Runge-Kutta method.

6. The method for correcting explosive initial conditions for underwater explosion numerical simulation according to claim 1, characterized in that: In steps S2 and S3, the underwater explosion empirical formula used includes: 1) Shock wave stage: p(t)=P m e -t / θ ,t<θ (2) Formula (2) is the pressure waveform in the exponential decay stage, formula (3) is the pressure waveform in the reciprocal decay stage, formula (4) is the pressure waveform in the latter part of the reciprocal decay stage, and formula (5) is the pressure waveform in the bubble expansion and contraction stage, where: 2) Bubble pulsation stage: in: Where p is the free field pressure in water; t is the time; Q is the mass of TNT; θ is the shock wave attenuation coefficient; R is the explosion distance; P m is the peak pressure of the shock wave; H0 is the depth of the explosive; r0 is the radius of the explosive; ρ w is the density of water; c is the speed of sound in water; P atm is atmospheric pressure; g is the acceleration due to gravity; P m1 is the peak value of the bubble pulsation load; θ1 is the bubble pulsation load attenuation coefficient; R bc is the distance from the measuring point to the center of the bubble; is the angle between the line connecting the explosion center and the observation point and the horizontal line; ΔH is the rising distance of the bubble; T is the bubble pulsation period.

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