Explosive initial condition correction method for underwater explosion numerical simulation

Abstract

The invention discloses an explosive initial condition correction method for underwater explosion numerical simulation, which comprises the following steps of: performing spherical approximation on an explosive, establishing a calculation model of free field spherical symmetry underwater explosion, and inputting initial parameters of the explosive by a JWL state equation, wherein the initial parameters comprise initial density and initial internal energy of the explosive per unit mass; preliminary pressure time travel curves at different spatial positions are obtained; extracting a shock wave pressure peak value, comparing the shock wave pressure peak value with a test or empirical formula result, and if an error does not exceed 5%, keeping the initial internal energy of unit mass explosive unchanged; otherwise, adjusting the initial internal energy of the explosive per unit mass until the error does not exceed 5%; determining a bubble pulsation period, comparing the bubble pulsation period with a test or empirical formula result, and if an error does not exceed 5%, keeping the initial density of the explosive unchanged; otherwise, adjusting the initial density of the explosive until the error does not exceed 5%. The method can accurately forecast the shock wave pressure peak value and the bubble pulsation period, has the advantages of low cost and high efficiency, and can provide more accurate load input for three-dimensional underwater explosion model calculation.

Description

Technical Field

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

[0002] When performing maritime combat missions, ships are vulnerable to attacks from various weapons. Underwater explosion damage caused by underwater weapons such as torpedoes, mines and depth charges is one of the main threats to the vitality of ships. Shock waves and bubble pulsations are the main forms of loads during underwater explosions. The prediction of underwater explosion loads is the basis for the design of ship anti-explosion and anti-shock and the regulation of explosive power. Since water is incompressible, the impulse generated by the explosion will be greater. The existing research on underwater explosions mainly focuses on the field of ship anti-impact and protection. Whether the correct and objective anti-explosion and anti-shock performance of ships can be obtained, higher requirements are placed on the accurate input of underwater explosion loads. Therefore, carrying out high-precision numerical simulation of underwater explosion shock waves and bubble pulsations is of great significance for studying the ship's anti-underwater explosion performance and evaluating the power of explosives.

[0003] As a complex physical phenomenon, the initial design and evaluation of structural damage and protection of underwater explosions often rely on numerical calculation methods. 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. It is expensive to conduct a series of tests to calibrate the state equation parameters, and it is usually not suitable for some problems that only verify the damage effect 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, it is urgent 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 solve the problem that the state equation parameters of the above-mentioned commonly used explosives are inaccurate in predicting the underwater explosion shock wave and bubble pulsation, which seriously affects the accuracy of the numerical calculation of underwater explosions. The calibration of the state equation parameters for underwater explosion tests often takes a lot of time, manpower and material resources. A method for correcting the initial conditions of explosives for numerical simulation of underwater explosions is proposed. The method achieves accurate prediction of the shock wave pressure peak and the bubble pulsation period by simply adjusting the initial density of the explosives and the initial internal energy per unit mass, thereby improving the accuracy of the numerical calculation 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 simulation, save calculation time, and provide support for underwater structure protection design and explosive power evaluation.

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

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

[0007] S1. The explosive is approximated as a sphere, and a computational model of free-field spherically symmetric underwater explosion is established. The initial parameters of the explosive input into the JWL state equation 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 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 shock wave pressure peak error does not exceed 5%, the initial internal energy per unit mass of the explosive is kept unchanged; if the shock wave pressure peak error exceeds 5% and is less than the test or empirical formula results, 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 results, 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 the shock wave stage has a comparison error of no more than 5% with the test or empirical formula results.

[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, 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 between the explosion center and the observation point and the horizontal line; ΔH is the floating distance of the bubble; T is the bubble pulsation period.

[0024] S3. Determine the bubble pulsation period according to the time when the secondary shock wave pressure peak appears in the pressure time history 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%, the initial density of the explosive is kept unchanged; if the bubble pulsation period error exceeds 5% and is less than the test or empirical formula results, 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 results, 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; then recalculate and update the pressure time history curve until the bubble pulsation period is compared with the test or empirical formula results. The error does not exceed 5%.

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

[0026] The present invention can realize accurate prediction of shock wave pressure peak and bubble pulsation period by simply adjusting the initial density of explosives and the initial internal energy per unit mass, so as to carry out high-precision numerical simulation of underwater explosion shock waves and bubble pulsation, and has the advantages of low cost and high efficiency, and can provide more accurate load input for three-dimensional underwater explosion model calculation, improve the accuracy and calculation efficiency of numerical simulation research, and provide more accurate guidance for underwater structure design and explosive power evaluation. Therefore, the proposal of the present invention has important engineering value and application significance in the field of underwater explosion. 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 briefly introduces 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 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 is a comparison diagram of the pressure peak value in the shock wave stage extracted after the pressure time history curve is updated in step S2 of embodiment 1 of the present invention and the test result;

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

[0031] Figure 4 This is a comparison diagram between 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 solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with 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 used to limit the present invention.

[0033] It should be noted that the illustrations provided in the embodiments of the present invention are only used to illustrate the basic concept of the present invention in a schematic manner. Therefore, the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout type may also be more complicated.

[0034] Embodiment 1:

[0035] Based on the comparison of 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 numerical simulation of underwater explosions is verified. The experiment used for verification is introduced as follows: 0.227kg equivalent of TNT was used, and the charging depths were 182.88m and 91.44m respectively. Two free-field power tests were carried out, and the underwater free-field pressure sensor was arranged in the waters 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 the present invention is used to correct the initial conditions of the explosives during numerical calculation, so that the numerical simulation results are 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, where the JWL state equation parameters are based on the literature (BM Dobratz, 1972. Properties of Chemical Explosives And Explosive Simulants, California University, Livermore (USA)): The initial density ρ0 of TNT is 1630 kg / m 3The initial internal energy of unit mass explosive e0 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. The discontinuous Galerkin method is used to discretize the Euler domain in space, and the third-order Runge-Kutta method is used to discretize the time domain to obtain preliminary pressure-time curves at different spatial positions.

[0037] Step 2: Under the condition of charging depth of 182.88m, the peak pressure of the shock wave extracted from the pressure-time curve obtained in step 1 is 45.2MPa, which is 7.0% compared with the peak pressure of the shock wave of 48.6MPa in the test. 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 the shock wave extracted is 47.3MPa, which is 2.7% compared with the test result (see Figure 2 ).

[0038] 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 14.6ms, which has an error of 8.2% compared with the experimental bubble pulsation period of 15.9ms. Therefore, the density of the explosive is reduced and adjusted to 1580kg / m 3 , increasing the volume of the explosive, thereby increasing the bubble period. Recalculating and updating the pressure time history curve, the bubble pulsation period extracted is 15.6ms, and the error compared with the test result is 1.9% (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. According to 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 the explosive density is adjusted to 1390kg / m 3 , increasing the volume of the explosive, thereby 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] Embodiment 2:

[0041] The feasibility of the method for correcting the initial conditions of explosives in underwater explosion numerical simulation is verified by comparing the results calculated based on the empirical formula. The verification conditions are: using 1kg equivalent TNT, the charging depth is 100m, and the explosion distance is 1m. The method proposed in the present invention is used to correct the initial conditions of explosives in numerical calculation, so that the numerical simulation results are consistent with the empirical formula results. 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, where the JWL state equation parameters are based on the literature (BM Dobratz, 1972. Properties of Chemical Explosives And Explosive Simulants, California University, Livermore (USA)): The initial density ρ0 of TNT is 1630 kg / m 3 The initial internal energy of unit mass explosive e0 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. The discontinuous Galerkin method is used to discretize the Euler domain in space, and the third-order Runge-Kutta method is used to discretize the time domain to obtain preliminary pressure-time curves at different spatial positions.

[0043] Step 2: Extract the shock wave pressure peak value from the pressure-time 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 explosive is kept unchanged, and there is no need to update the pressure-time 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, which has an error of 11.3% compared with the bubble pulsation period of 42.4ms in the empirical formula. Therefore, the density of the explosive is reduced to 1400kg / m 3 , increasing the volume of the explosive, thereby increasing the bubble period. Recalculate and update the pressure time history curve. According to the time when the bubble pulsation peak occurs, the bubble pulsation period is extracted to be 42.1ms, which is 0.7% error compared with the empirical formula result (see Figure 4 ).

[0045] The embodiments of the present invention show that in the field of underwater explosion numerical calculation research, the present invention can solve the problem that the state equation parameters of commonly used explosives are inaccurate in predicting the underwater explosion shock wave pressure peak and bubble pulsation period, and provide strong support for realizing high-precision numerical simulation of underwater explosions. At the same time, the present invention reduces the dependence on complex computing resources, while maintaining high accuracy, reducing the cost of research and application, and also has the advantages of simplicity and efficiency, and is suitable for a wide range of application scenarios, including ship resistance to underwater explosion shock design, underwater structure safety assessment, and explosive power assessment.

[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, and 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 order of execution of each step in the above embodiment does not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiment 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 these improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A method for correcting the initial conditions of explosives 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 of free-field spherically symmetric underwater explosion is established. The initial parameters of the explosive input into the JWL state equation include the initial density and the initial internal energy per unit mass of the explosive. The Euler domain is spatially discretized, and the time domain is discretized to obtain preliminary pressure-time curves at different spatial positions. S2, extracting the peak value of the shock wave pressure in the pressure-time curve obtained in S1, and comparing it with the test or empirical formula result. According to the comparison result, 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 kept 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 explosives shall be 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 explosives shall be reduced; Then recalculate and update the pressure time history curve until the pressure peak value 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 according to the time when the secondary shock wave pressure peak appears in the pressure time history curve obtained in S2, and comparing it with the test or empirical formula results. According to the comparison results, if the bubble pulsation period error does not exceed 5%, the initial density of the explosive is kept 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; then recalculate and update the pressure time history curve until the error between the bubble pulsation period and the test or empirical formula result does not exceed 5%.

2. The method for correcting the initial conditions of explosives 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 the initial conditions of explosives 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 the initial conditions of explosives 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 the initial conditions of explosives 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 the initial conditions of explosives 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, 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 between the explosion center and the observation point and the horizontal line; ΔH is the floating distance of the bubble; T is the bubble pulsation period.

Images