Calculation method for dynamic characteristics of underwater array explosion bubbles in limited drainage basin

Abstract

The invention relates to a calculation method for dynamic characteristics of underwater array explosion bubbles in a limited drainage basin, belongs to the field of ship and maritime work structure protection, and aims to solve the problem of prediction of the dynamic characteristics and flow field load of the underwater array explosion bubbles in existing engineering. According to the method, initial parameters including the quantity of explosives and the like are input firstly, relevant conditions are determined, then multi-step calculation is carried out, such as determining the initial radius and the internal pressure and establishing an equation set, and finally calculation and analysis of the bubble characteristics and the flow field pressure are achieved. According to the method, a calculation model of the dynamic characteristics of the underwater array explosion bubbles in a finite field is established based on a one-dimensional bubble pulsation and migration differential equation, so that the problem of predicting the dynamic characteristics and the flow field load of the underwater array explosion bubbles in the existing engineering is solved; the purpose of rapidly predicting the dynamic characteristics of the underwater array explosion bubbles in the limited drainage basin is achieved, and theoretical means and technical support are provided for engineering practice.

Description

Technical Field

[0001] The invention relates to a calculation method for dynamic characteristics of underwater array explosion bubbles in a limited flow domain, and belongs to the field of ship and marine engineering structure protection. Background Art

[0002] Underwater explosions seriously threaten the safety and vitality of ships or marine structures. The loads of underwater explosions mainly include shock waves and bubbles. The pressure peak of shock waves is high and the action time is extremely short. Bubbles are formed after the shock waves. Due to the action of inertial force, bubbles will expand and contract rapidly. In this process, high-speed jets may be generated, causing further damage to marine structures. Underwater array explosions can greatly increase the power of bubble pulsation and even produce a multiplier effect. It is of great significance to improve the protection capability of ship structures. It can better design ship structures and materials to improve their explosion resistance and also help develop more effective protection measures to protect the safety of crew members. When underwater explosions occur in a limited flow domain, the motion characteristics of bubbles and their induced load characteristics will change unpredictably. This is widely present in actual engineering applications, such as underwater explosions near ports, in narrow waterways, and between multiple ship structures. Therefore, the calculation of the dynamic characteristics of underwater array explosion bubbles in a limited flow domain is very important for the protection of ships and marine structures.

[0003] Due to the complexity and difficulty of underwater explosion bubble dynamics, there are many challenges in predicting the dynamic characteristics of underwater array explosion bubbles. By solving the one-dimensional differential equations of bubble pulsation and translation, the pulsation and migration history of the bubble can be quickly solved. Based on the potential flow theory that bubble pulsation can be regarded as a variable intensity point source, the bubble pulsation and migration characteristics in the bubble array can be corrected and simulated by superimposing multiple variable intensity point sources. The influence of the finite domain boundary can be simulated based on the fluid mechanics idea of ​​the mirror bubble equivalent rigid boundary. By solving the one-dimensional bubble pulsation and translation equations corrected by the bubble array and finite domain boundary effects, the dynamic characteristics of underwater array explosion bubbles in the finite flow domain can be quickly predicted, which can be applied to the engineering design of underwater array explosions, and has important practical application value.

[0004] The existing technology requires complex grid processing whether through domain grid numerical simulation or multi-level expansion boundary element simulation, and the calculation after the second cycle of bubble pulsation often has the characteristics of instability and low precision. However, for underwater array explosions, the movement details of the bubbles are not the focus of calculation. In engineering applications, we only care about the pulsation and translation process of the bubbles and the pressure waves radiated outward by the pulsation. For this purpose, it is very advantageous to use one-dimensional bubble pulsation and translation equations to carry out calculations. Summary of the invention

[0005] The invention proposes a calculation method for the dynamic characteristics of underwater array explosion bubbles in a limited flow domain, so as to solve the problem of predicting the motion characteristics and flow field load of underwater array explosion bubbles in existing engineering.

[0006] A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain, the method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain comprising the following steps:

[0007] S1. Input the initial parameters of the underwater array explosion to determine the initial characteristics and environmental conditions of the underwater explosion array;

[0008] S2. determining the initial dynamic conditions of underwater explosion bubble pulsation based on the equivalent of each explosive in the array and the water depth;

[0009] S3, based on the one-dimensional bubble pulsation and translation equations, establish a bubble array pulsation and migration equation group according to the initial characteristics and environmental conditions of the underwater explosion array;

[0010] S4. According to the mirror theory, the influence of the finite domain boundary is corrected to determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equations;

[0011] S5, advancing the bubble pulsation and migration equations in time to obtain a volume and displacement time history curve of each bubble in the bubble array;

[0012] S6. According to the obtained time-varying process of the volume of each bubble in the bubble array, the flow field pressure is solved by superposition, and the bubble characteristic parameters and the pressure of the flow field measuring point are recorded and post-processed.

[0013] Furthermore, in S1, the initial parameters of the underwater array explosion are input, and the initial parameters include the number of explosives, the position of each explosive, the water depth, the equivalent, the form of the finite basin boundary and the distance between each explosive and the water boundary, so as to determine the initial characteristics and environmental conditions of the underwater explosion array.

[0014] Further, in S2, based on the equivalent of each explosive in the array and the water depth, the initial radius and initial internal pressure of the underwater explosion bubble pulsation are determined according to the free field bubble equation and the underwater explosion empirical formula, and the free field bubble equation and the underwater explosion empirical formula are respectively:

[0015]

[0016] Where W is the explosive equivalent, γ is the adiabatic coefficient of the gas, R0 and R max are the radii of the underwater explosion bubble at the initial moment and the moment of maximum volume, respectively. ΔP is the difference between the hydrostatic pressure and the saturated vapor pressure at the location of the explosive. ΔP=P ∞ -Pv , P ∞ is the hydrostatic pressure at the location of the explosive, P v is the saturated vapor pressure, h is the water depth where the explosive is located, and the initial radius of the bubble is obtained by solving equation (1) iteratively using the bisection method.

[0017] Furthermore, in S2, after obtaining the initial radius of the bubble, the initial internal pressure of the bubble is obtained by formula (3):

[0018]

[0019] Furthermore, in S3, based on the free-field one-dimensional bubble pulsation and translation equations, the bubble array pulsation and migration equations are established. The free-field one-dimensional bubble pulsation equation is a compressible point source differential equation based on the wave equation, and the bubble translation equation is a differential form of the bubble momentum balance equation, which are respectively:

[0020]

[0021] Where c is the speed of sound in water, ρ is the density of water, R, and are the bubble radius, the first-order time derivative and the second-order time derivative of the bubble radius, respectively; P is the bubble internal pressure at the current moment; u and are the translational velocity and acceleration vector of the bubble, respectively. is the hydrostatic pressure gradient at the bubble position when the bubble is in a free field subject only to gravity. g is the gravitational acceleration vector, C d is the drag force coefficient, and the bubble internal pressure P at the current moment is calculated as follows:

[0022]

[0023] Where V0 is the bubble volume at the initial moment, V is the bubble volume at the calculation moment,

[0024] According to the characteristics of underwater explosion array, the bubble array pulsation and migration equations are established. First, the fluid particle velocity induced by bubbles in the flow field can be calculated as follows:

[0025]

[0026] Where r is the position vector of any point in the flow field, pointing from the bubble position to the flow field; in the above formula, the table d below represents that the physical quantity is a time delay quantity, that is, the disturbance at r in the flow field at time t is caused by the bubble at an earlier time t-(|r|-R) / C. The time delay quantity needs to be interpolated on the time axis during the calculation process to obtain the physical quantity at time t-(|r|-R) / C. t is the current time, S is the enthalpy of the bubble surface, S=(PP ∞) / ρ,

[0027] Combining the Bernoulli equation of fluid mechanics, the calculation formula for the dynamic pressure of the flow field at r is obtained:

[0028]

[0029] The other bubbles in the bubble array are regarded as several compressible point sources, which cause pressure disturbances at the calculated bubbles. The influence of the bubble array can be taken into account by superimposing the hydrostatic pressure at the calculated bubbles. Therefore, each bubble in the array composed of N underwater explosion bubbles has an independent pulsation and translation equation, which constitutes the pulsation and migration equations of the bubble array:

[0030]

[0031]

[0032] Wherein, the subscript i=1, 2, ..., N represents the number of each bubble in the bubble array; p iN represents the flow field pressure induced by the ith bubble at the Nth bubble, calculated according to formula (8).

[0033] Furthermore, in S4, the influence of the finite domain boundary is corrected according to the mirror theory. The boundary conditions in the finite domain are composed of two parallel wall boundaries. According to the mirror theory of fluid mechanics, the flow state of the flow field on both sides of the rigid wall is exactly the same. Therefore, the bubble array can be symmetrically moved to the other side of the two water boundaries. At this time, the surface enthalpy S of the jth bubble is j It can be calculated as follows:

[0034]

[0035] Where m ij is the flow field pressure generated by the i-th mirror bubble at bubble j, which can be calculated according to formula (8), M is the number of mirror bubbles,

[0036] For each bubble in the underwater explosion array, there are 4 mirror bubbles, so M = 4N, and the position vector of the mirror bubble can be determined as follows:

[0037]

[0038] Where n1 and n2 are the unit external normal vectors of the two rigid walls, L is the position vector of the real bubble, and L i It represents the position vector of the corresponding i-th mirror bubble.

[0039] Furthermore, in S5, according to the bubble surface enthalpy S jThe pulsation and translation equations of the underwater explosion bubble array in the finite flow domain are:

[0040]

[0041] The fourth-order Runge-Kutta method is used to solve the above two equations and perform time advancement to obtain the volume and displacement time history of each bubble in the underwater explosion array under finite domain conditions.

[0042] Further, in S6, the pressure induced by each bubble in the flow field is calculated in combination with formula (8), and the pressure induced by all bubbles in the flow field is superimposed to obtain the flow field pressure induced by the underwater array explosion bubbles. The radius, displacement and flow field pressure of the underwater array explosion bubbles are recorded and post-processed. The post-processing includes drawing a bubble radius and displacement time history diagram and a flow field pressure curve.

[0043] All the bubbles include calculation bubbles and mirror bubbles.

[0044] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain.

[0045] A computer device comprises: a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-mentioned method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain.

[0046] Beneficial effects of the invention: A calculation method for the dynamic characteristics of underwater array explosion bubbles in a finite flow domain of the invention successfully constructs a calculation model for the dynamic characteristics of underwater array explosion bubbles in a finite domain based on one-dimensional bubble pulsation and migration differential equations, effectively solving the problem that the motion characteristics of underwater array explosion bubbles and flow field loads in existing projects are difficult to accurately predict, and can quickly and relatively accurately predict related dynamic characteristics, showing good flexibility and development potential in terms of boundary condition processing and equation application expansion, and is of great significance to promoting the development of related fields such as ship and marine structure protection. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 It is a flow chart of a method for calculating dynamic characteristics of underwater array explosion bubbles in a limited flow domain in the present invention;

[0048] Figure 2 is an explanatory diagram of a method for calculating the dynamic behavior of a bubble array in the present invention;

[0049] Figure 3It is an illustration of the finite flow domain boundary effect equivalent method in the present invention;

[0050] Figure 4 It is a rendering of the time history change of the radius and displacement of the underwater array explosion bubble in the present invention;

[0051] Figure 5 It is a rendering of the flow field pressure curve induced by the underwater array explosion bubbles calculated in the present invention. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0053] Reference Figure 1 As shown, a method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain, the method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain comprises the following steps:

[0054] S1. Input the initial parameters of the underwater array explosion to determine the initial characteristics and environmental conditions of the underwater explosion array;

[0055] S2. determining the initial dynamic conditions of underwater explosion bubble pulsation based on the equivalent of each explosive in the array and the water depth;

[0056] S3, based on the one-dimensional bubble pulsation and translation equations, establish a bubble array pulsation and migration equation group according to the initial characteristics and environmental conditions of the underwater explosion array;

[0057] S4. According to the mirror theory, the influence of the finite domain boundary is corrected to determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equations;

[0058] S5, advancing the bubble pulsation and migration equations in time to obtain a volume and displacement time history curve of each bubble in the bubble array;

[0059] S6. According to the obtained time-varying process of the volume of each bubble in the bubble array, the flow field pressure is solved by superposition, and the bubble characteristic parameters and the pressure of the flow field measuring point are recorded and post-processed.

[0060] Specifically, the present invention systematically executes a series of steps, from inputting initial parameters to determine the initial characteristics and environmental conditions of the explosion array, to determining the initial dynamic conditions of the bubble pulsation based on the equivalent and water depth, and then using a one-dimensional equation to combine the array characteristics and environmental conditions to establish a group of equations, and then using the mirror theory to correct the boundary influence, and then time-advancing the group of equations to obtain the bubble volume and displacement curve, and finally superimposing and solving the flow field pressure and recording post-processing. The present invention successfully solves the problem that the motion characteristics of underwater array explosion bubbles and flow field loads in a limited flow domain are difficult to predict, provides accurate and effective theoretical and technical support for engineering practice, and strongly promotes the research and application progress of underwater explosion bubble phenomena in related fields.

[0061] Furthermore, in S1, the initial parameters of the underwater array explosion are input, and the initial parameters include the number of explosives, the position of each explosive, the water depth, the equivalent, the form of the finite basin boundary and the distance between each explosive and the water boundary, so as to determine the initial characteristics and environmental conditions of the underwater explosion array.

[0062] Specifically, in the present invention, S1 can accurately determine the initial characteristics and environmental conditions of the underwater explosion array by inputting comprehensive underwater array explosion initial parameters including the number of explosives, position, water depth, equivalent, limited watershed boundary form, and distance between explosives and boundaries. The number and equivalent of explosives determine the scale and energy of bubbles generated by the explosion, the position affects the distribution pattern of bubbles, and the water depth and boundary conditions act together on the motion trajectory and dynamic process of bubbles. The accurate acquisition of these parameters ensures the reliability and effectiveness of the subsequent analysis of the behavior of underwater explosion bubbles.

[0063] Further, in S2, based on the equivalent of each explosive in the array and the water depth, the initial radius and initial internal pressure of the underwater explosion bubble pulsation are determined according to the free field bubble equation and the underwater explosion empirical formula, and the free field bubble equation and the underwater explosion empirical formula are respectively:

[0064]

[0065]

[0066] Where W is the explosive equivalent, γ is the adiabatic coefficient of the gas, R0 and R max are the radii of the underwater explosion bubble at the initial moment and the moment of maximum volume, respectively. ΔP is the difference between the hydrostatic pressure and the saturated vapor pressure at the location of the explosive. ΔP=P ∞ -P v , P ∞ is the hydrostatic pressure at the location of the explosive, P v is the saturated vapor pressure, h is the water depth where the explosive is located, and the initial radius of the bubble is obtained by solving equation (1) iteratively using the bisection method.

[0067] Specifically, in S2, based on the equivalent of explosives in the array and the water depth, it is of great significance to use the free-field bubble equation and the underwater explosion empirical formula to determine the initial radius and initial internal pressure of the underwater explosion bubble pulsation. Through these formulas, the key physical parameters of the bubble in the initial stage can be accurately quantified, among which the explosive equivalent and water depth are the core factors affecting the initial state of the bubble. The combination of the free-field bubble equation and the underwater explosion empirical formula fully considers factors such as the adiabatic properties of the gas and the water pressure conditions at the location of the explosive, and the binary iterative solution of formula (1) ensures the accuracy of the initial radius calculation. This step provides accurate starting conditions for subsequent research on the dynamic change process of the bubble, making the entire technical solution more scientific and rigorous in describing the dynamic characteristics of underwater explosion bubbles, greatly improving the reliability and accuracy of the prediction of the behavior of underwater array explosion bubbles.

[0068] Furthermore, in S2, after obtaining the initial radius of the bubble, the initial internal pressure of the bubble is obtained by formula (3):

[0069]

[0070] Specifically, in S2, formula (3) can accurately calculate the initial internal pressure of the bubble based on a specific physical relationship and the obtained initial radius, thereby completely determining the mechanical state of the bubble in the initial stage.

[0071] Furthermore, in S3, based on the free-field one-dimensional bubble pulsation and translation equations, the bubble array pulsation and migration equations are established. The free-field one-dimensional bubble pulsation equation is a compressible point source differential equation based on the wave equation, and the bubble translation equation is a differential form of the bubble momentum balance equation, which are respectively:

[0072]

[0073] Where c is the speed of sound in water, ρ is the density of water, R, and are the bubble radius, the first-order time derivative and the second-order time derivative of the bubble radius, respectively; P is the bubble internal pressure at the current moment; u and are the translational velocity and acceleration vector of the bubble, respectively. is the hydrostatic pressure gradient at the bubble position when the bubble is in a free field subject only to gravity. g is the gravitational acceleration vector, C d is the drag force coefficient, and the bubble internal pressure P at the current moment is calculated as follows:

[0074]

[0075] Where V0 is the bubble volume at the initial moment, V is the bubble volume at the calculation moment,

[0076] According to the characteristics of underwater explosion array, the bubble array pulsation and migration equations are established. First, the fluid particle velocity induced by bubbles in the flow field can be calculated as follows:

[0077]

[0078] Where r is the position vector of any point in the flow field, pointing from the bubble position to the flow field; in the above formula, the table d below represents that the physical quantity is a time delay quantity, that is, the disturbance at r in the flow field at time t is caused by the bubble at an earlier time t-(|r|-R) / C. The time delay quantity needs to be interpolated on the time axis during the calculation process to obtain the physical quantity at time t-(|r|-R) / C. t is the current time, S is the enthalpy of the bubble surface, S=(PP ∞ ) / ρ,

[0079] Combining the Bernoulli equation of fluid mechanics, the calculation formula for the dynamic pressure of the flow field at r is obtained:

[0080]

[0081] The influence on the movement of each bubble in the bubble array is considered to be two parts, one is induced by the pressure difference between the bubble internal pressure and the hydrostatic pressure of the ambient flow field, and the other is induced by other bubbles in the bubble array. Figure 2 As shown, the other bubbles in the bubble array can be regarded as several compressible point sources, which cause pressure disturbances at the calculated bubbles. The influence of the bubble array can be taken into account by superimposing the hydrostatic pressure at the calculated bubbles. Therefore, each bubble in the array composed of N underwater explosion bubbles has an independent pulsation and translation equation, and the pulsation and migration equations of the bubble array are:

[0082]

[0083] Wherein, the subscript i=1, 2, ..., N represents the number of each bubble in the bubble array; p iN represents the flow field pressure induced by the ith bubble at the Nth bubble, calculated according to formula (8).

[0084] Specifically, in S3, the free-field one-dimensional bubble pulsation equation is based on the differential form of the compressible point source differential equation of the wave equation and the bubble translation equation is based on the differential form of the bubble momentum balance equation, which fully considers many key physical quantities such as the speed of sound in water, the density of water, the bubble radius and its derivative, the bubble internal pressure, the translation velocity and acceleration, and accurately describes the motion law of a single bubble in a free field. By calculating the fluid particle velocity induced by the bubble in the flow field, and combining the Bernoulli equation to derive the flow field dynamic pressure calculation formula, and constructing a set of equations by treating other bubbles as compressible point sources and superimposing their influence, it is possible to comprehensively and accurately reflect the complex interactions and overall dynamic changes between bubbles in the underwater explosion array. This enables the present invention to conduct a systematic analysis from the microscopic single bubble movement to the macroscopic bubble array behavior, greatly enhancing the understanding and prediction capabilities of the dynamic characteristics of underwater array explosion bubbles, and providing a solid theoretical basis for subsequent steps.

[0085] Furthermore, in S4, the influence of the finite domain boundary is corrected according to the mirror theory. The boundary conditions in the finite domain are composed of two parallel wall boundaries. According to the mirror theory of fluid mechanics, the flow state of the flow field on both sides of the rigid wall is exactly the same. Therefore, the bubble array can be symmetrically moved to the other side of the two water boundaries. Figure 3 As shown, at this time, the surface enthalpy of the jth bubble is S j It can be calculated as follows:

[0086]

[0087] Where m ij is the flow field pressure generated by the i-th mirror bubble at bubble j, which can be calculated according to formula (8), M is the number of mirror bubbles,

[0088] For each bubble in the underwater explosion array, there are 4 mirror bubbles, so M = 4N, and the position vector of the mirror bubble can be determined as follows:

[0089]

[0090] Where n1 and n2 are the unit external normal vectors of the two rigid walls, L is the position vector of the real bubble, and L i It represents the position vector of the corresponding i-th mirror bubble.

[0091] Specifically, in S4, the influence of the finite domain boundary is corrected according to the mirror theory. In view of the situation that the finite flow domain is composed of two parallel wall boundaries, the bubble array is symmetrical to the other side of the boundary using the mirror theory to deal with the boundary effect. The surface enthalpy of the jth bubble is calculated by a specific formula, the flow field pressure generated by the mirror bubble is taken into account, and it is clarified that there are 4 mirror bubbles (M=4N) for each underwater explosion array bubble, and a formula for calculating the mirror bubble position vector is given, which fully considers factors such as the unit external normal vector of the rigid wall and the real bubble position. This processing method enables the present invention to accurately incorporate boundary conditions into the bubble dynamics analysis, greatly improving the accuracy of predicting the motion characteristics of underwater array explosion bubbles in a finite flow environment, making up for the shortcomings of previous studies in dealing with boundary effects, and laying a solid foundation for the subsequent accurate calculation of bubble motion and pressure parameters.

[0092] Furthermore, in S5, according to the bubble surface enthalpy S j The pulsation and translation equations of the underwater explosion bubble array in the finite flow domain are:

[0093]

[0094] The fourth-order Runge-Kutta method is used to solve the above two equations and perform time advancement to obtain the volume and displacement time history of each bubble in the underwater explosion array under finite domain conditions.

[0095] Specifically, in S5, the fourth-order Runge-Kutta method is used to solve the above two equations and perform time advancement to obtain the volume and displacement time history of each bubble in the underwater explosion array under finite domain conditions, as follows: Figure 4 As shown. This step can make full use of the conditions and parameters determined in the previous steps to solve the complex set of equations through precise mathematical calculations. The fourth-order Runge-Kutta method has high accuracy and stability. During the time advancement process, it can carefully simulate the dynamic change process of bubbles under finite domain conditions over time, thereby accurately obtaining the volume and displacement time history curve of each bubble in the underwater explosion array. This enables the present invention to transform theoretical analysis into actual quantifiable results, providing key data support for in-depth research on the behavior of bubbles during underwater explosions.

[0096] Furthermore, in S6, the pressure induced by each bubble in the flow field is calculated by combining formula (8), and the pressure induced by all bubbles (including calculated bubbles and mirror bubbles) in the flow field is superimposed to obtain the flow field pressure induced by the underwater array explosion bubbles, as follows: Figure 5 The radius, displacement, flow field pressure and other parameters of the underwater array explosion bubble are recorded and post-processed, including drawing bubble radius and displacement time history diagrams, flow field pressure curves, etc.

[0097] Specifically, in S6, by combining formula (8) to calculate the induced pressure of each bubble in the flow field, and superimposing the pressures of all bubbles (including calculated bubbles and mirror bubbles), the flow field pressure induced by the underwater array explosion bubbles can be accurately obtained. At the same time, the parameters such as bubble radius, displacement and flow field pressure are recorded and post-processed, and the bubble radius and displacement time history diagram and flow field pressure curve are drawn. The above visualization results can intuitively present the dynamic change process of the bubbles and the distribution and change trend of the flow field pressure, which helps researchers to deeply analyze the behavior laws of underwater array explosion bubbles and provide a detailed and easy-to-understand reference basis for engineering practice.

[0098] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain.

[0099] Specifically, when the processor executes the program, it can implement a calculation method for the dynamic characteristics of underwater array explosion bubbles in a finite flow domain. Through a series of steps, including inputting initial parameters to determine the underwater explosion array characteristics and environmental conditions, determining the initial conditions of bubble pulsation based on explosive equivalent and water depth, establishing and solving a group of bubble array pulsation and migration equations, correcting the influence of finite domain boundaries, and calculating and post-processing related parameters, etc., it effectively solves the problem of difficult prediction of underwater array explosion bubble motion characteristics and flow field loads in a finite flow domain, provides efficient and accurate theoretical analysis and data support means for engineering practice, and greatly improves the capabilities and efficiency of related fields in underwater explosion research and application.

[0100] A computer device comprises: a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the above-mentioned method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain.

[0101] Specifically, the computer device, memory and processor of the present invention work together to run a specific computer program to implement a calculation method for the dynamic characteristics of underwater array explosion bubbles in a limited flow domain. Through this method, the complex situation of underwater explosion can be accurately handled, from determining initial parameters, calculating initial conditions of bubble pulsation, to constructing and solving a set of equations, correcting boundary effects, and performing subsequent data processing and analysis. A series of steps effectively overcome the difficulties in predicting the motion characteristics and flow field loads of underwater array explosion bubbles in the past, providing strong technical support and efficient computing power for engineering practice, and greatly promoting the research depth and application breadth of related fields.

[0102] The present invention provides a calculation method for the dynamic characteristics of underwater array explosion bubbles in a finite flow domain. Based on one-dimensional bubble pulsation and migration differential equations, a calculation model for the dynamic characteristics of underwater array explosion bubbles in a finite domain is successfully constructed, which effectively solves the problem that the motion characteristics of underwater array explosion bubbles and flow field loads in existing projects are difficult to accurately predict. The method can quickly and relatively accurately predict the relevant dynamic characteristics, and shows good flexibility and development potential in terms of boundary condition processing, equation application expansion, etc., which is of great significance to promoting the development of related fields such as ship and marine structure protection.

[0103] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In addition, "front", "back", "left", "right", "upper" and "lower" in this article are all referenced to the placement state shown in the accompanying drawings.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain, characterized in that: The method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain comprises the following steps: S1. Input the initial parameters of the underwater array explosion to determine the initial characteristics and environmental conditions of the underwater explosion array; S2. determining the initial dynamic conditions of underwater explosion bubble pulsation based on the equivalent of each explosive in the array and the water depth; S3, based on the one-dimensional bubble pulsation and translation equations, establish a bubble array pulsation and migration equation group according to the initial characteristics and environmental conditions of the underwater explosion array; S4. According to the mirror theory, the influence of the finite domain boundary is corrected to determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equations; S5, advancing the bubble pulsation and migration equations in time to obtain a volume and displacement time history curve of each bubble in the bubble array; S6. According to the obtained time-varying process of the volume of each bubble in the bubble array, the flow field pressure is solved by superposition, and the bubble characteristic parameters and the pressure of the flow field measuring point are recorded and post-processed.

2. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 1, characterized in that: In S1, the initial parameters of the underwater array explosion are input, and the initial parameters include the number of explosives, the position of each explosive, the water depth, the equivalent, the form of the finite basin boundary and the distance between each explosive and the water boundary, so as to determine the initial characteristics and environmental conditions of the underwater explosion array.

3. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 2, characterized in that: In S2, based on the equivalent of each explosive in the array and the water depth, the initial radius and initial internal pressure of the underwater explosion bubble pulsation are determined according to the free field bubble equation and the underwater explosion empirical formula, wherein the free field bubble equation and the underwater explosion empirical formula are respectively: Where W is the explosive equivalent, γ is the adiabatic coefficient of the gas, R0 and R max are the radii of the underwater explosion bubble at the initial moment and the moment of maximum volume, respectively. ΔP is the difference between the hydrostatic pressure and the saturated vapor pressure at the location of the explosive. ΔP=P ∞ -P v , P ∞ is the hydrostatic pressure at the location of the explosive, P v is the saturated vapor pressure, h is the water depth where the explosive is located, and the initial radius of the bubble is obtained by solving equation (1) iteratively using the bisection method.

4. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 3, characterized in that: In S2, after obtaining the initial radius of the bubble, the initial internal pressure of the bubble is obtained by formula (3):

5. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 4, characterized in that: In S3, based on the free-field one-dimensional bubble pulsation and translation equations, the bubble array pulsation and migration equations are established. The free-field one-dimensional bubble pulsation equation is a compressible point source differential equation based on the wave equation, and the bubble translation equation is a differential form of the bubble momentum balance equation, which are respectively: Where c is the speed of sound in water, ρ is the density of water, R, and are the bubble radius, the first-order time derivative and the second-order time derivative of the bubble radius, respectively; P is the bubble internal pressure at the current moment; u and are the translational velocity and acceleration vector of the bubble, respectively. is the hydrostatic pressure gradient at the bubble position when the bubble is in a free field subject only to gravity. g is the gravitational acceleration vector, C d is the drag force coefficient, and the bubble internal pressure P at the current moment is calculated as follows: Where V0 is the bubble volume at the initial moment, V is the bubble volume at the calculation moment, According to the characteristics of underwater explosion array, the bubble array pulsation and migration equations are established. First, the fluid particle velocity induced by bubbles in the flow field can be calculated as follows: Where r is the position vector of any point in the flow field, pointing from the bubble position to the flow field; in the above formula, the table d below represents that the physical quantity is a time delay quantity, that is, the disturbance at r in the flow field at time t is caused by the bubble at an earlier time t-(|r|-R) / C. The time delay quantity needs to be interpolated on the time axis during the calculation process to obtain the physical quantity at time t-(|r|-R) / C. t is the current time, S is the enthalpy of the bubble surface, S=(PP ∞ ) / ρ, Combining the Bernoulli equation of fluid mechanics, the calculation formula for the dynamic pressure of the flow field at r is obtained: The other bubbles in the bubble array are regarded as several compressible point sources, which cause pressure disturbances at the calculated bubbles. The influence of the bubble array can be taken into account by superimposing the hydrostatic pressure at the calculated bubbles. Therefore, each bubble in the array composed of N underwater explosion bubbles has an independent pulsation and translation equation, which constitutes the pulsation and migration equations of the bubble array: Wherein, the subscript i=1, 2, ..., N represents the number of each bubble in the bubble array; p iN represents the flow field pressure induced by the ith bubble at the Nth bubble, calculated according to formula (8).

6. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 5, characterized in that: In S4, the influence of the finite domain boundary is corrected according to the mirror theory. The boundary conditions in the finite domain are composed of two parallel wall boundaries. According to the mirror theory of fluid mechanics, the flow state of the flow field on both sides of the rigid wall is exactly the same. Therefore, the bubble array can be symmetrically moved to the other side of the two water boundaries. At this time, the surface enthalpy S of the jth bubble is j It can be calculated as follows: Where m ij is the flow field pressure generated by the i-th mirror bubble at bubble j, which can be calculated according to formula (8), M is the number of mirror bubbles, For each bubble in the underwater explosion array, there are 4 mirror bubbles, so M = 4N, and the position vector of the mirror bubble can be determined as follows: Where n1 and n2 are the unit external normal vectors of the two rigid walls, L is the position vector of the real bubble, and L i It represents the position vector of the corresponding i-th mirror bubble.

7. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 6, characterized in that: In S5, according to the bubble surface enthalpy S j The pulsation and translation equations of the underwater explosion bubble array in the finite flow domain are: The fourth-order Runge-Kutta method is used to solve the above two equations and perform time advancement to obtain the volume and displacement time history of each bubble in the underwater explosion array under finite domain conditions.

8. A method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain according to claim 7, characterized in that: In S6, the pressure induced by each bubble in the flow field is calculated by combining formula (8), and the pressure induced by all bubbles in the flow field is superimposed to obtain the flow field pressure induced by the underwater array explosion bubbles. The radius, displacement and flow field pressure of the underwater array explosion bubbles are recorded and post-processed. The post-processing includes drawing a bubble radius and displacement time history diagram, and a flow field pressure curve. All the bubbles include calculation bubbles and mirror bubbles.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain as described in any one of claims 1 to 8 is implemented.

10. A computer device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow domain as described in any one of claims 1 to 8.

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