A two-way forward-backward calculation method for initial parameters of underwater high-pressure bubble and explosive equivalent based on Matlab

Abstract

The application provides a two-way positive and negative deduction calculation method for initial parameters of underwater high-pressure bubbles and explosive equivalent based on Matlab, and belongs to the field of underwater explosion dynamics and numerical simulation of ocean engineering. The method establishes a two-way positive and negative deduction calculation process in the Matlab environment, uniformly couples Cole empirical formula, Rayleigh-Plesset equation and initial pressure empirical formula, and solves the coupled nonlinear equation by using Newton-Raphson iteration method; the maximum bubble radius, initial bubble radius and initial bubble pressure are calculated by the charge mass and water depth during positive deduction, and the equivalent TNT charge equivalent is deduced by the known bubble parameters during negative deduction. The application realizes the integrated processing of positive parameter calculation and negative explosive equivalent deduction, can provide consistent initial conditions for numerical simulation such as SPH, can also be used for engineering test design and equivalent load evaluation, and improves the calculation efficiency, repeatability and engineering operability.

Description

Technical Field

[0001] This invention relates to the fields of underwater explosion dynamics, bubble dynamics, marine engineering numerical simulation, and explosion impact safety assessment. More specifically, it relates to a method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. Background Technology

[0002] During an underwater explosion, the detonation products of the explosive form high-pressure bubbles in the water. The initial parameters of these bubbles (including the initial radius) are... Initial pressure and maximum radius Initial parameters (TNT) are core physical quantities describing the dynamic behavior of bubbles, such as pulsation, migration, and collapse. In underwater explosion numerical simulations using methods like SPH, finite volume method, and finite element-fluid-structure interaction, these initial parameters, as boundary and initial conditions, directly affect the simulation accuracy of bubble pulsation period, maximum radius, and peak pressure. Furthermore, in engineering test design and equivalent load assessment, it is often necessary to back-estimate the corresponding equivalent TNT charge based on known bubble parameters to assist in underwater explosion similarity tests, surface / ingress load analysis of vehicles, blast resistance assessment of ships and marine structures, and the design of low-yield alternative test schemes.

[0003] Currently, the main methods for obtaining initial parameters of high-pressure bubbles or assessing explosive equivalent include: physical underwater explosion tests, manual calculation using empirical formulas, separate bubble dynamics equation solving programs, and directly setting the initial radius and initial pressure of the high-pressure bubble empirically in numerical software such as SPH. Specifically, in engineering, the initial parameters of the high-pressure bubble are often determined first based on the Cole empirical formula and the TNT charge mass. and water depth Estimate the maximum radius of the bubble Rm Then, by combining the GH model, the unified bubble equation, or the Rayleigh-Plesset equation, the bubble motion parameters are calculated; for the initial pressure This is often achieved by adjusting the initial bubble volume. or initial radius Related empirical calculations. If it is necessary to deduce the explosive equivalent from the bubble parameters, it is usually necessary to manually reorganize the formula, perform multiple trial calculations, or write a special program.

[0004] However, the aforementioned existing technologies have the following shortcomings: First, physical underwater explosion tests are costly and dangerous, with high requirements for the test water area, measurement equipment, and safety conditions, making them unsuitable for frequent parameter estimation; second, single empirical formulas are mostly used for forward estimation, making it difficult to simultaneously perform bidirectional calculations from charge mass to bubble parameters and from bubble parameters to equivalent charge quantity; third... , , , and There is a strong coupling relationship between them, especially Iterative solutions combining the Rayleigh-Plesset equations and boundary conditions are necessary; manual calculations or decentralized programs are prone to issues such as inconsistent units, inconsistent convergence judgments, and poor result repeatability. Fourth, in existing numerical simulations, the initial bubble radius... As equivalent parameters used in numerical calculations, the lack of a unified solution process can easily lead to arbitrary selection of initial conditions, which in turn affects the simulation accuracy of bubble pulsation period, maximum radius, and pressure peak.

[0005] Therefore, existing technologies lack a systematic calculation method that can be implemented in Matlab, which can uniformly couple empirical formulas and bubble dynamics equations, and simultaneously perform forward parameter calculations and reverse explosive equivalent extrapolation. Summary of the Invention

[0006] To address the technical problems in existing technologies, such as the separation of forward calculation and backward deduction, lack of a unified solution process, arbitrary selection of initial conditions, and poor repeatability of calculation results, this invention provides a two-way forward and backward deduction calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. This invention primarily utilizes the unified coupling of Cole's empirical formula, Rayleigh-Plesset equation, and empirical formula for initial pressure within the Matlab environment, and employs the Newton-Raphson iterative method to solve the coupled nonlinear equations. Through a unified calculation process and graphical interface, it achieves bidirectional calculation of forward parameters and backward deduction of explosive equivalent, thereby reducing manual conversion and repetitive modeling errors. It provides well-defined and consistent initial parameters for high-pressure bubbles in underwater explosion numerical simulation, and supports rapid back-calculation of equivalent TNT charge from target bubble parameters, improving computational efficiency, repeatability, and engineering operability.

[0007] The technical means employed in this invention are as follows: A method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, including: S1. Establish a two-way forward and backward inference calculation process in the Matlab environment, obtain common basic parameters and determine the calculation mode. The common basic parameters include water depth and gas specific heat ratio, and the calculation modes include forward inference mode and backward inference mode. S2. Obtain the charge mass and determine the maximum bubble radius; S3. Calculate the ambient hydrostatic pressure based on the water depth; S4. Based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio, the Rayleigh-Plesset equation and the empirical formula for initial pressure are combined to construct a nonlinear equation for the initial bubble radius. S5. Solve the nonlinear equations using the Newton-Raphson iterative method to obtain the initial bubble radius; S6. Calculate the initial bubble volume based on the initial bubble radius, and calculate the initial bubble pressure based on the initial bubble volume, charge mass, and gas specific heat ratio. Output the forward derivation result including the maximum bubble radius, initial bubble radius, and initial bubble pressure. When in the reverse derivation mode, execute steps S7 to S9 sequentially. S7. Obtain known bubble parameters, including at least one of the maximum bubble radius, initial bubble radius, and initial bubble pressure; S8. Based on the known bubble parameters, water depth, and gas specific heat ratio, a nonlinear equation for the equivalent charge mass is constructed using the coupling relationship between the Cole empirical formula, the initial pressure empirical formula, and the Rayleigh-Plesset equation. The Newton-Raphson iterative method is then used to solve the equation and obtain the equivalent charge mass. S9. Output includes the inverse deduction results of the equivalent charge mass.

[0008] Further, in step S1, establishing a bidirectional forward and inverse deduction calculation process in the Matlab environment, obtaining common basic parameters, and determining the calculation mode includes: S11. Create a fixed-size graphics window in the Matlab environment and name the window "Bubble Initial Condition Calculator" to serve as the unified interface for the bidirectional forward and reverse inference calculation process. S12. A parameter input module including a water depth input unit and a specific heat ratio input unit is arranged in the upper and upper middle parts of the graphics window. The water depth is obtained through the water depth input unit and the specific heat ratio of the gas is obtained through the specific heat ratio input unit. S13. A calculation mode selection module, including a forward deduction mode selection unit and a reverse deduction mode selection unit, is arranged in the graphics window to receive the calculation mode selected by the user. S14. A maximum bubble radius acquisition method selection module, including an automatic calculation selection unit and a manual input selection unit, is arranged in the middle right position of the graphics window. When in forward deduction mode, the automatic calculation selection unit calls the Cole empirical formula to automatically calculate the maximum bubble radius based on the charge mass and water depth. The manual input selection unit allows users to directly input the maximum bubble radius value given by external calculation, experiment or literature. S15. A manual maximum bubble radius input module and a calculation trigger module are arranged in the lower center of the graphics window. The manual maximum bubble radius input module is connected to the maximum bubble radius acquisition method selection module. When the manual input selection unit is selected, the manual maximum bubble radius input module switches to an editable state. When the automatic calculation selection unit is selected, the manual maximum bubble radius input module remains in an uneditable state. The calculation trigger module is used to read the parameters in the current interface and start the subsequent calculation process. S16. A result display module is arranged at the bottom of the graphics window. The result display module is connected to the calculation trigger module and is used to output forward deduction results or backward deduction results. S17. Establish an exception prompt module. Connect the exception prompt module to the parameter input module, the calculation trigger module and the background calculation process through a try-catch structure. When the input parameters are unreasonable, the nonlinear equation has no roots, or the iterative solution fails, the exception prompt information will be output in the result display module.

[0009] Further, in step S2, obtaining the charge mass and determining the maximum bubble radius includes: S21. Arrange the explosive mass input unit in the graphics window to receive the explosive mass input by the user; S22. Provides a function to select the maximum bubble radius acquisition method, and receives the user's selection instruction for the acquisition method; the acquisition method includes automatic calculation method and manual input method; S23. When the automatic calculation method is selected, based on the underwater explosion bubble dynamics described by the unified bubble equation theory, the maximum bubble radius is automatically calculated using the Cole empirical formula according to the obtained charge mass and water depth. Simultaneously, the manual maximum bubble radius input control is set to an uneditable state to avoid conflicts between user error input and the automatic calculation results; wherein: The bubble unification equation unifies the Rayleigh-Plesset equation, the Gilmore equation, and the Keller-Miksis equation. Its complete form is as follows:

[0010] in, Indicates the instantaneous radius of the bubble. Indicates the speed of the bubble wall movement. This represents the acceleration of the bubble wall. This represents the speed of sound in water. Indicates the bubble migration speed. This represents the potential energy term in the unified bubble theory. Indicates time; When environmental flow and bubble migration are not considered, the unified bubble equation simplifies to:

[0011] in, Represents the velocity potential function; The bubble radius variation curves with time for different charge masses at different water depths were solved using the unified bubble equation, yielding the maximum bubble radius as shown in the following formula:

[0012] in, Indicates the maximum bubble radius. Indicates the quality of the explosive charge. Indicates water depth; S24. When the manual input method is selected, the manual maximum bubble radius input control is set to an editable state, receiving the maximum bubble radius value given by external calculation, experiment or literature directly input by the user, and using this value as the maximum bubble radius.

[0013] Further, in step S3, the calculation of the environmental hydrostatic pressure based on the water depth includes: S31. Set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure; S32. Based on the set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure, and according to the water depth, the environmental hydrostatic pressure is calculated using the following formula:

[0014] in, Indicates the density of water; Indicates standard atmospheric pressure; It represents the acceleration due to gravity.

[0015] Further, in step S4, the construction of a nonlinear equation regarding the initial bubble radius, based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio, by simultaneously applying the Rayleigh-Plesset equation and the empirical formula for the initial pressure, includes: S41. Based on the relationship between the initial bubble volume and the initial bubble radius, and the empirical formula for the initial pressure, establish a functional relationship between the initial bubble pressure and the initial bubble radius; S42. Solve the Rayleigh-Plesset equations simultaneously, as follows:

[0016] in, Indicates the ambient hydrostatic pressure; Indicates the internal pressure of the bubble. ; S43. Set boundary conditions: The bubble at the initial moment... When the surface velocity is zero, the bubble expands to its maximum radius. The surface velocity is zero at that time; S44. Substituting the established functional relationship, the bubble internal pressure formula, and the boundary conditions into the Rayleigh-Plesset equation, and rearranging, we obtain the initial bubble radius... The coupled nonlinear equations are as follows:

[0017] in, This indicates the specific heat ratio of high-pressure gases.

[0018] Further, in step S5, the step of using the Newton-Raphson iterative method to solve the nonlinear equation to obtain the initial bubble radius includes: S51. Use half of the determined maximum bubble radius as the initial guess value; S52. Call the built-in fzero function in Matlab, set the iteration tolerance, maximum number of iterations and convergence criteria, and perform Newton-Raphson iterative numerical solution on the constructed coupled nonlinear equations. S53. Determine if the iteration converges. If the iteration does not converge or the equation has no feasible roots, output the solution failure information and reason through the exception prompt module so that the user can modify the input parameters and recalculate. If the iteration converges, the initial bubble radius is obtained. .

[0019] Further, in step S6, the calculation of the initial bubble volume based on the initial bubble radius, and the calculation of the initial bubble pressure based on the initial bubble volume, charge mass, and gas specific heat ratio, outputting a forward derivation result including the maximum bubble radius, initial bubble radius, and initial bubble pressure, includes: S61, based on the initial bubble radius Calculate the initial bubble volume The formula is as follows:

[0020] S62, Based on the initial bubble volume Calculate the initial bubble pressure The formula is as follows:

[0021] S63. Output the maximum bubble radius, the initial bubble radius, and the initial bubble pressure to the result display module in tabular form, wherein the initial bubble pressure is displayed in megapascals. S64. The output maximum bubble radius, initial bubble radius, and initial bubble pressure are used as the initial conditions for underwater high-pressure bubble numerical simulation, bubble boundary motion calculation, or explosive equivalent back-calculation.

[0022] Further, in steps S7 to S9, the reverse deduction includes: S71. Arrange the known bubble parameter input area in the graphics window, receive the known bubble parameters input by the user, and simultaneously obtain the water depth and gas specific heat ratio; S81. When the known bubble parameters include the maximum bubble radius and the initial bubble radius, the maximum bubble radius and the initial bubble radius in the known bubble parameters are taken as known quantities, the environmental hydrostatic pressure and the gas specific heat ratio are taken as known parameters, and the equivalent charge mass is taken as the only unknown quantity. These are substituted into the coupled nonlinear equation to establish a nonlinear equation with the equivalent charge mass as the unknown quantity. In this equation, the equivalent charge mass replaces the charge mass in the original equation, and the known maximum bubble radius and the initial bubble radius replace the corresponding parameters to be solved in the original equation. S82. Using the preset initial guess value as the initial value for iteration, call the built-in iterative solver of Matlab and use the Newton-Raphson iterative method to numerically solve the established nonlinear equation to obtain the equivalent charge mass. S83. If the iteration does not converge or the equation has no feasible roots, the solution failure information and the reason shall be output through the exception prompt module. S91. Output the equivalent charge mass in tabular form to the result display module; S92. The equivalent charge mass is used to assist in the design of underwater explosion similarity tests, analysis of the load of a vehicle emerging from or entering the water, assessment of the explosion resistance of ships and marine structures, estimation of the safe distance for near-field explosions, and design of small-yield alternative test schemes.

[0023] Compared with the prior art, the present invention has the following advantages: 1. This invention provides a two-way forward and inverse derivation calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. It unifies the Cole empirical formula, Rayleigh-Plesset equation, and initial pressure empirical formula into the same Matlab calculation process, so that the forward and inverse derivations use the same physical relationships, variable definitions, and convergence criteria. This realizes the two-way integrated processing of initial parameter calculation and explosive equivalent inversion for underwater high-pressure bubbles, which significantly reduces the errors caused by manual conversion and repeated modeling.

[0024] 2. This invention provides a two-way forward and inverse derivation calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. By starting from the charge mass and water depth, and combining the calculation of the maximum bubble radius, empirical formula for initial pressure, and boundary conditions of the Rayleigh-Plesset equation, the maximum bubble radius, initial bubble radius, and initial bubble pressure are obtained. This provides initial bubble parameters with clear origins, clear physical relationships, and consistency for numerical simulations such as SPH, effectively improving the reliability of numerical simulation.

[0025] 3. The present invention provides a two-way forward and backward deduction calculation method for initial parameters of underwater high-pressure bubbles and explosive equivalent based on Matlab. By back-calculating the equivalent TNT charge based on known or target bubble parameters, the explosive equivalent is rapidly deduced in reverse. This facilitates similar test design, load equivalence analysis and selection of small-yield alternative schemes, and significantly reduces the cost and risk of relying entirely on actual explosion tests for scheme exploration.

[0026] 4. The present invention provides a two-way forward and inverse derivation calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. By using the Newton-Raphson iterative method to solve the coupled nonlinear equations, and setting the initial value, tolerance, maximum number of iterations and convergence judgment criteria in Matlab, the method achieves rapid and stable acquisition of numerical solutions for the initial radius or equivalent, which significantly improves the calculation efficiency, repeatability and engineering operability.

[0027] 5. The present invention provides a two-way forward and inverse derivation calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab. By implementing the formula calculation, iterative solution, parameter verification and result output in a programmatic manner, it realizes the batch calculation of results under different water depths, different charge amounts or different target bubble parameters, and can generate tabular data for subsequent numerical simulation, experimental scheme design and patent / paper data organization, which greatly improves the convenience of engineering applications.

[0028] In summary, by applying the technical solution of this invention, the shortcomings of existing technologies, such as the separation of forward calculation and backward deduction, lack of a unified solution process, arbitrary selection of initial conditions, poor repeatability of calculation results, and high cost and risk due to complete reliance on live-fire tests, are addressed. This is achieved by constructing a unified bidirectional forward and backward deduction calculation process, coupling empirical formulas with bubble dynamics equations, and implementing programmed solutions in the Matlab environment. This integrates forward parameter calculation and backward explosive equivalence deduction. Therefore, the technical solution of this invention solves the problem of the lack of a systematic calculation method in existing technologies that is oriented towards Matlab, unifies empirical formulas and bubble dynamics equations, and can simultaneously perform forward parameter calculation and backward explosive equivalence deduction.

[0029] Based on the above reasons, this invention can be widely applied in fields such as underwater explosion dynamics, bubble dynamics, marine engineering numerical simulation, explosion impact safety assessment, SPH and other numerical simulation preprocessing, underwater explosion similarity test design, ship and marine structure explosion resistance assessment, and small yield alternative test scheme design. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of the method of the present invention.

[0032] Figure 2 This is the initial interface provided for embodiments of the present invention.

[0033] Figure 3 This is the interface after the calculation is completed, as provided in the embodiments of the present invention. Detailed Implementation

[0034] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0035] It should be noted that the terms "comprising" and "having" and any variations thereof in the specification, claims and accompanying drawings of this invention are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product or device.

[0036] like Figure 1 As shown, this invention provides a two-way forward and inverse extrapolation calculation method for initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, including: S1. Establish a two-way forward and backward inference calculation process in the Matlab environment, obtain common basic parameters and determine the calculation mode. The common basic parameters include water depth and gas specific heat ratio, and the calculation modes include forward inference mode and backward inference mode. S2. Obtain the charge mass and determine the maximum bubble radius; S3. Calculate the ambient hydrostatic pressure based on the water depth; S4. Based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio, the Rayleigh-Plesset equation and the empirical formula for initial pressure are combined to construct a nonlinear equation for the initial bubble radius. S5. Solve the nonlinear equations using the Newton-Raphson iterative method to obtain the initial bubble radius; S6. Calculate the initial bubble volume based on the initial bubble radius, and calculate the initial bubble pressure based on the initial bubble volume, charge mass, and gas specific heat ratio. Output the forward derivation result including the maximum bubble radius, initial bubble radius, and initial bubble pressure. When in the reverse derivation mode, execute steps S7 to S9 sequentially. S7. Obtain known bubble parameters, including at least one of the maximum bubble radius, initial bubble radius, and initial bubble pressure; S8. Based on the known bubble parameters, water depth, and gas specific heat ratio, a nonlinear equation for the equivalent charge mass is constructed using the coupling relationship between the Cole empirical formula, the initial pressure empirical formula, and the Rayleigh-Plesset equation. The Newton-Raphson iterative method is then used to solve the equation and obtain the equivalent charge mass. S9. Output includes the inverse deduction results of the equivalent charge mass.

[0037] In a specific implementation, as a preferred embodiment of the present invention, step S1, which involves establishing a bidirectional forward and inverse deduction calculation process in the Matlab environment, obtaining common basic parameters, and determining the calculation mode, includes: S11, such as Figure 2 As shown, a fixed-size graphics window is created in the Matlab environment and named "Bubble Initial Condition Calculator" to serve as the unified interface for the bidirectional forward and inverse inference calculation process. S12. A parameter input module including a water depth input unit and a specific heat ratio input unit is arranged in the upper and upper middle parts of the graphics window. The water depth is obtained through the water depth input unit and the specific heat ratio of the gas is obtained through the specific heat ratio input unit. The default value of the specific heat ratio of the gas is 1.25. S13. A calculation mode selection module, including a forward deduction mode selection unit and a reverse deduction mode selection unit, is arranged in the graphics window to receive the calculation mode selected by the user. S14. A maximum bubble radius acquisition method selection module, including an automatic calculation selection unit and a manual input selection unit, is arranged in the middle right position of the graphics window. When in forward deduction mode, the automatic calculation selection unit calls the Cole empirical formula to automatically calculate the maximum bubble radius based on the charge mass and water depth. The manual input selection unit allows users to directly input the maximum bubble radius value given by external calculation, experiment or literature. S15. A manual maximum bubble radius input module and a calculation trigger module are arranged in the lower center of the graphics window. The manual maximum bubble radius input module is connected to the maximum bubble radius acquisition method selection module. When the manual input selection unit is selected, the manual maximum bubble radius input module switches to an editable state. When the automatic calculation selection unit is selected, the manual maximum bubble radius input module remains in an uneditable state. The calculation trigger module is used to read the parameters in the current interface and start the subsequent calculation process. S16, as Figure 3 As shown, a result display module is arranged at the bottom of the graphics window. The result display module is connected to the calculation trigger module and is used to output forward deduction results or backward deduction results. S17. Establish an exception prompt module. Connect the exception prompt module to the parameter input module, the calculation trigger module and the background calculation process through a try-catch structure. When the input parameters are unreasonable, the nonlinear equation has no roots, or the iterative solution fails, the exception prompt information will be output in the result display module.

[0038] In a specific implementation, as a preferred embodiment of the present invention, step S2, namely obtaining the charge mass and determining the maximum bubble radius, includes: S21. Arrange the explosive mass input unit in the graphics window to receive the explosive mass input by the user; S22. Provides a function to select the maximum bubble radius acquisition method, and receives the user's selection instruction for the acquisition method; the acquisition method includes automatic calculation method and manual input method; S23. When the automatic calculation method is selected, based on the underwater explosion bubble dynamics described by the unified bubble equation theory, the maximum bubble radius is automatically calculated using the Cole empirical formula according to the obtained charge mass and water depth. Simultaneously, the manual maximum bubble radius input control is set to an uneditable state to avoid conflicts between user error input and the automatic calculation results; wherein: The bubble unification equation unifies the Rayleigh-Plesset equation, the Gilmore equation, and the Keller-Miksis equation. Its complete form is as follows:

[0039] in, Indicates the instantaneous radius of the bubble. Indicates the speed of the bubble wall movement. This represents the acceleration of the bubble wall. This represents the speed of sound in water. Indicates the bubble migration speed. This represents the potential energy term in the unified bubble theory. Indicates time; When environmental flow and bubble migration are not considered, the unified bubble equation simplifies to:

[0040] in, Represents the velocity potential function; The bubble radius variation curves with time for different charge masses at different water depths were solved using the unified bubble equation, yielding the maximum bubble radius as shown in the following formula:

[0041] in, Indicates the maximum bubble radius. Indicates the quality of the explosive charge. Indicates water depth; S24. When the manual input method is selected, the manual maximum bubble radius input control is set to an editable state, receiving the maximum bubble radius value given by external calculation, experiment or literature directly input by the user, and using this value as the maximum bubble radius.

[0042] In a specific implementation, as a preferred embodiment of the present invention, step S3, which involves calculating the environmental hydrostatic pressure based on the water depth, includes: S31. Set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure; S32. Based on the set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure, and according to the water depth, the environmental hydrostatic pressure is calculated using the following formula:

[0043] in, This indicates the density of water. ; Indicates standard atmospheric pressure. ; Represents gravitational acceleration. .

[0044] In a specific implementation, as a preferred embodiment of the present invention, step S4, which involves constructing a nonlinear equation regarding the initial bubble radius by simultaneously applying the Rayleigh-Plesset equation and the empirical formula for the initial pressure based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio, includes: S41. Based on the relationship between the initial bubble volume and the initial bubble radius, and the empirical formula for the initial pressure, establish a functional relationship between the initial bubble pressure and the initial bubble radius; S42. Solve the Rayleigh-Plesset equations simultaneously, as follows:

[0045] in, Indicates the ambient hydrostatic pressure; Indicates the internal pressure of the bubble. ; S43. Set boundary conditions: The bubble at the initial moment... When the surface velocity is zero, the bubble expands to its maximum radius. The surface velocity is zero at that time; S44. Substituting the established functional relationship, the bubble internal pressure formula, and the boundary conditions into the Rayleigh-Plesset equation, and rearranging, we obtain the initial bubble radius... The coupled nonlinear equations are as follows:

[0046] in, This indicates the specific heat ratio of high-pressure gases.

[0047] In a specific implementation, as a preferred embodiment of the present invention, step S5, which involves using the Newton-Raphson iterative method to solve the nonlinear equation to obtain the initial bubble radius, includes: S51. Use half of the determined maximum bubble radius as the initial guess value; S52. Call the built-in fzero function in Matlab, set the iteration tolerance, maximum number of iterations and convergence criteria, and perform Newton-Raphson iterative numerical solution on the constructed coupled nonlinear equations. S53. Determine if the iteration converges. If the iteration does not converge or the equation has no feasible roots, output the solution failure information and reason through the exception prompt module so that the user can modify the input parameters and recalculate. If the iteration converges, the initial bubble radius is obtained. .

[0048] In a specific implementation, as a preferred embodiment of the present invention, step S6, which involves calculating the initial bubble volume based on the initial bubble radius, and calculating the initial bubble pressure based on the initial bubble volume, charge mass, and gas specific heat ratio, and outputting a forward derivation result including the maximum bubble radius, initial bubble radius, and initial bubble pressure, includes: S61, based on the initial bubble radius Calculate the initial bubble volume The formula is as follows:

[0049] S62, Based on the initial bubble volume Calculate the initial bubble pressure The formula is as follows:

[0050] S63. Output the maximum bubble radius, the initial bubble radius, and the initial bubble pressure to the result display module in tabular form, wherein the initial bubble pressure is displayed in megapascals. S64. The output maximum bubble radius, initial bubble radius, and initial bubble pressure are used as the initial conditions for underwater high-pressure bubble numerical simulation, bubble boundary motion calculation, or explosive equivalent back-calculation.

[0051] In a specific implementation, as a preferred embodiment of the present invention, steps S7 to S9 include the following reverse deduction: S71. Arrange the known bubble parameter input area in the graphics window, receive the known bubble parameters input by the user, and simultaneously obtain the water depth and gas specific heat ratio; S81. When the known bubble parameters include the maximum bubble radius and the initial bubble radius, the maximum bubble radius and the initial bubble radius in the known bubble parameters are taken as known quantities, the environmental hydrostatic pressure and the gas specific heat ratio are taken as known parameters, and the equivalent charge mass is taken as the only unknown quantity. These are substituted into the coupled nonlinear equation to establish a nonlinear equation with the equivalent charge mass as the unknown quantity. In this equation, the equivalent charge mass replaces the charge mass in the original equation, and the known maximum bubble radius and the initial bubble radius replace the corresponding parameters to be solved in the original equation. S82. Using the preset initial guess value as the initial value for iteration, call the built-in iterative solver of Matlab and use the Newton-Raphson iterative method to numerically solve the established nonlinear equation to obtain the equivalent charge mass. S83. If the iteration does not converge or the equation has no feasible roots, the solution failure information and the reason shall be output through the exception prompt module. S91. Output the equivalent charge mass in tabular form to the result display module; S92. The equivalent charge mass is used to assist in the design of underwater explosion similarity tests, analysis of the load of a vehicle emerging from or entering the water, assessment of the explosion resistance of ships and marine structures, estimation of the safe distance for near-field explosions, and design of small-yield alternative test schemes.

[0052] Throughout the entire operation, the software interface components of this calculator are arranged in a fixed position, without involving the displacement, rotation, or change of the shape of mechanical parts; what changes are the enabled status of the controls, the values ​​entered by the user, the variables calculated in the background, and the output content in the result display box.

[0053] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, characterized in that, include: S1. Establish a two-way forward and backward inference calculation process in the Matlab environment, obtain common basic parameters and determine the calculation mode. The common basic parameters include water depth and gas specific heat ratio, and the calculation modes include forward inference mode and backward inference mode. S2. Obtain the charge mass and determine the maximum bubble radius; S3. Calculate the ambient hydrostatic pressure based on the water depth; S4. Based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio, the Rayleigh-Plesset equation and the empirical formula for initial pressure are combined to construct a nonlinear equation for the initial bubble radius. S5. Solve the nonlinear equations using the Newton-Raphson iterative method to obtain the initial bubble radius; S6. Calculate the initial bubble volume based on the initial bubble radius, and calculate the initial bubble pressure based on the initial bubble volume, charge mass, and gas specific heat ratio. Output the forward derivation result including the maximum bubble radius, initial bubble radius, and initial bubble pressure. When in the reverse derivation mode, execute steps S7 to S9 sequentially. S7. Obtain known bubble parameters, including at least one of the maximum bubble radius, initial bubble radius, and initial bubble pressure; S8. Based on the known bubble parameters, water depth, and gas specific heat ratio, a nonlinear equation for the equivalent charge mass is constructed using the coupling relationship between the Cole empirical formula, the initial pressure empirical formula, and the Rayleigh-Plesset equation. The Newton-Raphson iterative method is then used to solve the equation and obtain the equivalent charge mass. S9. Output includes the reverse deduction results of the equivalent charge mass.

2. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S1, establishing a bidirectional forward and inverse inference calculation process in the Matlab environment, obtaining common basic parameters, and determining the calculation mode includes: S11. Create a fixed-size graphics window in the Matlab environment and name the window "Bubble Initial Condition Calculator" to serve as the unified interface for the bidirectional forward and reverse inference calculation process. S12. A parameter input module including a water depth input unit and a specific heat ratio input unit is arranged in the upper and upper middle parts of the graphics window. The water depth is obtained through the water depth input unit and the specific heat ratio of the gas is obtained through the specific heat ratio input unit. S13. A calculation mode selection module, including a forward deduction mode selection unit and a reverse deduction mode selection unit, is arranged in the graphics window to receive the calculation mode selected by the user. S14. A maximum bubble radius acquisition method selection module, including an automatic calculation selection unit and a manual input selection unit, is arranged in the middle right position of the graphics window. When in forward deduction mode, the automatic calculation selection unit calls the Cole empirical formula to automatically calculate the maximum bubble radius based on the charge mass and water depth. The manual input selection unit allows users to directly input the maximum bubble radius value given by external calculation, experiment or literature. S15. A manual maximum bubble radius input module and a calculation trigger module are arranged in the lower center of the graphics window. The manual maximum bubble radius input module is connected to the maximum bubble radius acquisition method selection module. When the manual input selection unit is selected, the manual maximum bubble radius input module switches to an editable state. When the automatic calculation selection unit is selected, the manual maximum bubble radius input module remains in an uneditable state. The calculation trigger module is used to read the parameters in the current interface and start the subsequent calculation process. S16. A result display module is arranged at the bottom of the graphics window. The result display module is connected to the calculation trigger module and is used to output forward deduction results or backward deduction results. S17. Establish an exception prompt module. Connect the exception prompt module to the parameter input module, the calculation trigger module and the background calculation process through a try-catch structure. When the input parameters are unreasonable, the nonlinear equation has no roots, or the iterative solution fails, the exception prompt information will be output in the result display module.

3. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S2, obtaining the charge mass and determining the maximum bubble radius includes: S21. Arrange the explosive mass input unit in the graphics window to receive the explosive mass input by the user; S22. Provides a function to select the maximum bubble radius acquisition method, and receives the user's selection instruction for the acquisition method; the acquisition method includes automatic calculation method and manual input method; S23. When the automatic calculation method is selected, based on the underwater explosion bubble dynamics described by the unified bubble equation theory, the maximum bubble radius is automatically calculated using the Cole empirical formula according to the obtained charge mass and water depth. Simultaneously, the manual maximum bubble radius input control is set to an uneditable state to avoid conflicts between user error input and the automatic calculation results; wherein: The bubble unification equation unifies the Rayleigh-Plesset equation, the Gilmore equation, and the Keller-Miksis equation. Its complete form is as follows: in, Indicates the instantaneous radius of the bubble. Indicates the speed of the bubble wall movement. This represents the acceleration of the bubble wall. This represents the speed of sound in water. Indicates the bubble migration speed. This represents the potential energy term in the unified bubble theory. Indicates time; When environmental flow and bubble migration are not considered, the unified bubble equation simplifies to: in, Represents the velocity potential function; The bubble radius variation curves with time for different charge masses at different water depths were solved using the unified bubble equation, yielding the maximum bubble radius as shown in the following formula: in, Indicates the maximum bubble radius. Indicates the quality of the explosive charge. Indicates water depth; S24. When the manual input method is selected, the manual maximum bubble radius input control is set to an editable state, receiving the maximum bubble radius value given by external calculation, experiment or literature directly input by the user, and using this value as the maximum bubble radius.

4. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S3, the calculation of the environmental hydrostatic pressure based on the water depth includes: S31. Set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure; S32. Based on the set environmental constant parameters, including water density, gravitational acceleration, and standard atmospheric pressure, and according to the water depth, the environmental hydrostatic pressure is calculated using the following formula: in, Indicates the density of water; Indicates standard atmospheric pressure; It represents the acceleration due to gravity.

5. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S4, the nonlinear equation for the initial bubble radius is constructed by simultaneously applying the Rayleigh-Plesset equation and the empirical formula for the initial pressure, based on the maximum bubble radius, charge mass, ambient hydrostatic pressure, and gas specific heat ratio. This includes: S41. Based on the relationship between the initial bubble volume and the initial bubble radius, and the empirical formula for the initial pressure, establish a functional relationship between the initial bubble pressure and the initial bubble radius; S42. Solve the Rayleigh-Plesset equations simultaneously, as follows: in, Indicates the ambient hydrostatic pressure; Indicates the internal pressure of the bubble. ; S43. Set boundary conditions: The bubble at the initial moment... When the surface velocity is zero, the bubble expands to its maximum radius. The surface velocity is zero at that time; S44. Substituting the established functional relationship, the bubble internal pressure formula, and the boundary conditions into the Rayleigh-Plesset equation, and rearranging, we obtain the initial bubble radius... The coupled nonlinear equations are as follows: in, This indicates the specific heat ratio of high-pressure gases.

6. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S5, the step of using the Newton-Raphson iterative method to solve the nonlinear equation to obtain the initial bubble radius includes: S51. Use half of the determined maximum bubble radius as the initial guess value; S52. Call the built-in fzero function in Matlab, set the iteration tolerance, maximum number of iterations and convergence criteria, and perform Newton-Raphson iterative numerical solution on the constructed coupled nonlinear equations. S53. Determine if the iteration converges. If the iteration does not converge or the equation has no feasible roots, output the solution failure information and reason through the exception prompt module so that the user can modify the input parameters and recalculate. If the iteration converges, the initial bubble radius is obtained. .

7. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In step S6, the initial bubble volume is calculated based on the initial bubble radius, and the initial bubble pressure is calculated based on the initial bubble volume, charge mass, and gas specific heat ratio. The output includes a forward extrapolation result comprising the maximum bubble radius, the initial bubble radius, and the initial bubble pressure, including: S61, based on the initial bubble radius Calculate the initial bubble volume The formula is as follows: S62, Based on the initial bubble volume Calculate the initial bubble pressure The formula is as follows: S63. Output the maximum bubble radius, the initial bubble radius, and the initial bubble pressure to the result display module in tabular form, wherein the initial bubble pressure is displayed in megapascals. S64. The output maximum bubble radius, initial bubble radius, and initial bubble pressure are used as the initial conditions for underwater high-pressure bubble numerical simulation, bubble boundary motion calculation, or explosive equivalent back-calculation.

8. The method for bidirectional forward and inverse extrapolation calculation of initial parameters and explosive equivalent of underwater high-pressure bubbles based on Matlab, as described in claim 1, is characterized in that... In steps S7 to S9, the reverse deduction includes: S71. Arrange the known bubble parameter input area in the graphics window, receive the known bubble parameters input by the user, and simultaneously obtain the water depth and gas specific heat ratio; S81. When the known bubble parameters include the maximum bubble radius and the initial bubble radius, the maximum bubble radius and the initial bubble radius in the known bubble parameters are taken as known quantities, the environmental hydrostatic pressure and the gas specific heat ratio are taken as known parameters, and the equivalent charge mass is taken as the only unknown quantity. These are substituted into the coupled nonlinear equation to establish a nonlinear equation with the equivalent charge mass as the unknown quantity. In this equation, the equivalent charge mass replaces the charge mass in the original equation, and the known maximum bubble radius and the initial bubble radius replace the corresponding parameters to be solved in the original equation. S82. Using the preset initial guess value as the initial value for iteration, call the built-in iterative solver of Matlab and use the Newton-Raphson iterative method to numerically solve the established nonlinear equation to obtain the equivalent charge mass. S83. If the iteration does not converge or the equation has no feasible roots, the solution failure information and the reason shall be output through the exception prompt module. S91. Output the equivalent charge mass in tabular form to the result display module; S92. The equivalent charge mass is used to assist in the design of underwater explosion similarity tests, analysis of the load of a vehicle emerging from or entering the water, assessment of the explosion resistance of ships and marine structures, estimation of the safe distance for near-field explosions, and design of small-yield alternative test schemes.

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