A method for calculating the dynamics of underwater array explosion bubbles in a limited drainage basin

Abstract

The present application relates to a kind of for the calculation method of underwater array explosion bubble dynamics characteristics in limited drainage area, belong to the protection field of ship and marine structure, to solve the prediction problem of existing engineering underwater array explosion bubble movement characteristics and flow field load.The present application first input includes initial parameters such as explosive quantity, determine relevant conditions, then by multi-step calculation, such as determining initial radius and internal pressure, equation set is established, etc., finally realize the calculation and analysis of bubble characteristics and flow field pressure.The present application will be based on one-dimensional bubble pulsation and migration differential equation to establish the calculation model of underwater array explosion bubble dynamics characteristics in limited drainage area, solve the prediction problem of existing engineering underwater array explosion bubble movement characteristics and flow field load, reach the purpose of quickly predicting underwater array explosion bubble dynamics characteristics in limited drainage area, provide theoretical means and technical support for engineering practice.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for calculating the underwater array explosion bubble dynamics characteristics in a limited flow field, belonging to the field of ship and offshore structure protection. BACKGROUND

[0002] Underwater explosion seriously threatens the safety and viability of ships or offshore structures. The load of underwater explosion mainly includes shock wave and bubble. The pressure peak of shock wave is high, and the action time is extremely short. Bubble is formed after the shock wave, and due to the effect of inertial force, the bubble will rapidly expand and contract. During this process, high-speed jet may be produced, which can further damage the offshore structure. Underwater array explosion can greatly improve the power generated by bubble pulsation, and even produce a multiplication effect. It is of great significance to improve the protection ability of ship structure, better design ship structure and materials to improve their anti-explosion performance, and help develop more effective protection measures to protect the safety of crew. When underwater explosion occurs in a limited flow field, the motion characteristics of the bubble and the induced load characteristics will change unpredictably, which widely exists in actual engineering applications, such as underwater explosion near the port, in narrow waterway and between multiple ship structures. Therefore, the calculation of underwater array explosion bubble dynamics characteristics in a limited flow field is very important for ship and offshore structure protection.

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

[0004] The existing technology needs complex grid processing whether through domain grid numerical simulation or multi-level expansion boundary element simulation, and the calculation after the second period of bubble pulsation often has the characteristics of instability and low precision. However, for underwater array explosion, the details of bubble motion are not the focus of calculation, and the engineering application only cares about the pulsation and translation process of bubble and the pressure wave radiated outward by pulsation. For this goal, it has great advantages to use one-dimensional bubble pulsation and translation equation to carry out calculation SUMMARY

[0005] The application provides a calculation method for underwater array explosion bubble dynamics in a limited flow field.

[0006] The application provides a calculation method for underwater array explosion bubble dynamics in a limited flow field, which comprises the following steps:

[0007] S1, input initial parameters of underwater array explosion, and determine initial characteristics and environmental conditions of the underwater explosion array;

[0008] S2, determine 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 one-dimensional bubble pulsation and translation equations, establish bubble array pulsation and migration equation groups according to the initial characteristics and environmental conditions of the underwater explosion array;

[0010] S4, correct the influence of the limited domain boundary according to the mirror image theory, and determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equation groups;

[0011] S5, time-propagate the bubble pulsation and migration equation groups to obtain the volume and displacement time history curves of each bubble in the bubble array;

[0012] S6, according to the obtained volume time-varying process of each bubble in the bubble array, superimposedly solve the flow field pressure, and record and post-process the bubble characteristic parameters and flow field measuring point pressure.

[0013] Further, in S1, the initial parameters of underwater array explosion are input, the initial parameters include the number of explosives, the position of each explosive, the water depth, the equivalent, the form of the limited flow field boundary and the distance between each explosive and the water area 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 the 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] Wherein, W is the equivalent of the explosive, 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 maximum volume moment respectively, ΔP is the difference between the hydrostatic pressure and the saturated vapor pressure at the position 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 at which the explosive is located, and the initial radius of the bubble is obtained by solving equation (1) iteratively by the bisection method.

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

[0018]

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

[0020]

[0021] where c is the sound speed in water, p 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, P is the internal pressure of the bubble at the current time, u and are the translation velocity and acceleration vector of the bubble, is the hydrostatic pressure gradient at the bubble location, when the bubble is in a free field only subjected to gravity, g is the gravity acceleration vector, C d is the drag force coefficient, and the internal pressure P of the bubble at the current time is calculated as follows:

[0022]

[0023] where V0 is the bubble volume at the initial time, V is the bubble volume at the calculation time,

[0024] According to the characteristics of the underwater explosion array, the bubble array pulsation and translation equation set is established. First, the fluid particle velocity induced by the bubble 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 lower table d represents that the physical quantity is a time delay, i.e. the disturbance at r in the flow field at t time is caused by the bubble at an earlier t-(|r|-R) / C time, and the time delay needs to be interpolated on the time axis to obtain the physical quantity at t-(|r|-R) / C time in the calculation process, t is the current time, S is the enthalpy of the bubble surface, S=(P-P ∞) / p,

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

[0028]

[0029] The other bubbles in the bubble array are regarded as a number of compressible point sources, which cause pressure disturbance at the calculated bubble. The influence of the bubble array can be taken into account by superimposing the hydrostatic pressure at the calculated bubble. 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 equation groups of the bubble array respectively:

[0030]

[0031]

[0032] Where 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 i-th bubble at the N-th bubble, which is calculated according to formula (8).

[0033] Further, in S4, the influence of the finite field boundary is corrected according to the mirror image theory. The boundary condition in the finite flow field is composed of two parallel wall boundaries. According to the mirror image theory of fluid mechanics, the flow state on both sides of the rigid wall is exactly the same, so the bubble array is respectively symmetrical to the other side of the two water area boundaries. At this time, the surface enthalpy S j can be calculated as follows:

[0034]

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

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

[0037]

[0038] Where n1 and n2 are the unit outer normal vectors of the two rigid walls, and L is the position vector of the position where the real bubble is located. i Then it represents the position vector of the position where the corresponding i-th mirror image bubble is located.

[0039] Further, in S5, according to the surface enthalpy S jThe expressions of the bubble array in the limited flow field are as follows:

[0040]

[0041] The above two equations are solved by using the fourth-order Runge-Kutta method to perform time advancement, so that the volume and displacement time history of each bubble in the underwater explosion array under the condition of the limited domain can be obtained.

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

[0043] The all bubbles include the calculation bubble and the mirror bubble.

[0044] A storage medium, the storage medium stores a computer program, the computer program is executed by the processor to realize the above-mentioned one kind is used for the calculation method of the dynamic characteristics of the underwater array explosion bubble in the limited flow field.

[0045] A computer device, comprising: memory, processor and computer program stored on the memory and executable on the processor, the processor executes the program to realize the above-mentioned one kind is used for the calculation method of the dynamic characteristics of the underwater array explosion bubble in the limited flow field.

[0046] The beneficial effects of the present application: the present application is a kind of for the calculation method of the dynamic characteristics of the underwater array explosion bubble in the limited flow field, based on one-dimensional bubble pulsation and migration differential equation successfully constructs the calculation model of the dynamic characteristics of the underwater array explosion bubble in the limited flow field, effectively solves the problem that the motion characteristics of underwater array explosion bubble and flow field load in the existing engineering are difficult to accurately predict, can quickly and more accurately predict relevant dynamic characteristics, shows good flexibility and development potential in boundary condition processing, equation application expansion and other aspects, has important significance to promote the development of ship and marine structure protection and other related fields. BRIEF DESCRIPTION OF DRAWINGS

[0047] Figure 1 It is a flow chart of the calculation method of the dynamic characteristics of the underwater array explosion bubble in the limited flow field in the present application;

[0048] Figure 2 It is an explanatory diagram of the bubble array dynamic behavior calculation method in the present application;

[0049] Figure 3is a schematic diagram of the equivalent method of the limited flow domain boundary effect in the present application;

[0050] Figure 4 is an effect diagram of the time history change of the bubble radius and displacement of the underwater array explosion in the present application;

[0051] Figure 5 is an effect diagram of the pressure curve of the flow field induced by the bubble of the underwater array explosion calculated in the present application. DETAILED DESCRIPTION

[0052] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0053] Referring to Figure 1 As shown in the figure, a calculation method for the dynamic characteristics of the underwater array explosion bubble in a limited flow domain, the calculation method for the dynamic characteristics of the underwater array explosion bubble in a limited flow domain comprises the following steps:

[0054] S1, input the initial parameters of the underwater array explosion, determine the initial characteristics and environmental conditions of the underwater explosion array;

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

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

[0057] S4, according to the mirror image theory, correct the influence of the limited domain boundary, determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equation set;

[0058] S5, time advance the bubble pulsation and migration equation set, obtain the volume and displacement time history curve of each bubble in the bubble array;

[0059] S6, according to the obtained volume time-varying process of each bubble in the bubble array, superimpose and solve the flow field pressure, and record and post-process the bubble characteristic parameters and flow field measuring point pressure.

[0060] Specifically, the present application successfully solves the problem of difficult prediction of the motion characteristics and flow field load of underwater array explosion bubbles in a limited flow field by systematically performing a series of steps from inputting initial parameters to determine initial characteristics and environmental conditions of the explosion array, to determining initial dynamic conditions of bubble pulsation based on equivalent and water depth, then establishing equation groups by combining array characteristics and environmental conditions using one-dimensional equations, then correcting the boundary influence using mirror theory, then performing time advancement on the equation groups to obtain bubble volume and displacement curves, and finally superimposing and solving the flow field pressure and recording post-processing.

[0061] Further, in S1, initial parameters of underwater array explosion are inputted, the initial parameters including the number of explosives, the position of each explosive, the water depth, the equivalent, the form of the limited flow field boundary, and the distance between each explosive and the water area boundary, so as to determine the initial characteristics and environmental conditions of the underwater explosion array.

[0062] Specifically, in the present application, S1 can accurately determine the initial characteristics and environmental conditions of the underwater explosion array by inputting comprehensive initial parameters of underwater array explosion including the number of explosives, the position, the water depth, the equivalent, the form of the limited flow field boundary, and the distance between the explosive and the boundary. The number of explosives and the equivalent determine the scale and energy of the explosion generated bubble, the position affects the distribution pattern of the bubble, and the water depth and the boundary condition jointly act on the motion trajectory and dynamic process of the bubble. 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 and water depth of each explosive in the array, 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, the free-field bubble equation and the underwater explosion empirical formula being respectively:

[0064]

[0065]

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

[0067] Specifically, in S2, based on the equivalent of explosives in the array and the water depth, the initial radius and the initial internal pressure of the underwater explosion bubble pulse are determined by using the free-field bubble equation and the underwater explosion empirical formula. Through these formulas, the key physical parameters of the bubble in the initial stage can be accurately quantified, in which the equivalent of explosives and the 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 the adiabatic characteristics of the gas and the water pressure conditions of the position where the explosives are located, and the bisection iterative solution of formula (1) ensures the accuracy of the calculation of the initial radius. This step provides accurate initial conditions for the subsequent study of the dynamic change process of the bubble, making the entire technical scheme more scientific and rigorous in describing the dynamic characteristics of the underwater explosion bubble, and greatly improving the reliability and accuracy of the prediction of the behavior of the underwater array explosion bubble.

[0068] Further, 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 the specific physical relationship and the obtained initial radius, thereby completely determining the mechanical state of the bubble in the initial stage.

[0071] Further, in S3, based on the free-field one-dimensional bubble pulse and translation equation, the bubble array pulse and migration equation set is established. The free-field one-dimensional bubble pulse 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 sound speed 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, P is the current internal pressure of the bubble, u and are the translation velocity and acceleration vector of the bubble, is the static water pressure gradient at the bubble position, when the bubble is in a free field only affected by gravity, g is the gravity acceleration vector, C d is the drag coefficient, and the current internal pressure P of the bubble is calculated as follows:

[0074]

[0075] where V0 is the initial volume of the bubble, V is the volume of the bubble at the calculation time,

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

[0077]

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

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

[0080]

[0081] The influence on the motion of each bubble in the bubble array is regarded as two parts, one part is induced by the pressure difference between the internal pressure of the bubble and the ambient hydrostatic pressure, and the other part is induced by other bubbles in the bubble array, as shown in Figure 2 Therefore, other bubbles in the bubble array can be regarded as a number of compressible point sources, which cause pressure disturbance at the calculated bubble, and the influence of the bubble array can be taken into account by superimposing the hydrostatic pressure at the calculated bubble. 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 respectively as follows:

[0082]

[0083] Where 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 i-th bubble at the N-th bubble, which is calculated according to formula (8).

[0084] Specifically, in S3, the free-field one-dimensional bubble pulsation equation is based on 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. It fully considers many key physical quantities such as the speed of sound in water, water density, bubble radius and its derivative, internal bubble pressure, translational velocity, and acceleration, accurately describing the motion of a single bubble in a free field. By calculating the fluid particle velocity induced by the bubble in the flow field and combining it with Bernoulli's equation to derive the dynamic pressure calculation formula, and by constructing a set of equations by superimposing the influence of other bubbles as compressible point sources, it can comprehensively and accurately reflect the complex interactions between bubbles and the overall dynamic changes in the underwater explosion array. This invention enables a systematic analysis from the microscopic motion of a single bubble to the macroscopic behavior of the bubble array, greatly enhancing the understanding and prediction capabilities of the dynamic characteristics of underwater array explosion bubbles, and providing a solid theoretical foundation 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 flow domain consist of two parallel wall boundaries. According to the mirror theory of fluid mechanics, the flow state on both sides of the rigid wall is exactly the same. Therefore, the bubble array can be symmetrically mapped to the other side of the two water boundaries, as shown in the reference. Figure 3 As shown, the surface enthalpy S of the j-th bubble at this time j It can be calculated using the following formula:

[0086]

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

[0088] For each bubble in the underwater explosion array, there are 4 mirror bubbles, therefore M = 4N. The position vector of the mirror bubbles can be determined by the following formula:

[0089]

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

[0091] Specifically, in S4, the influence of the finite field boundary is corrected according to the mirror theory. For the case that the finite flow field is composed of two parallel wall boundaries, the mirror theory is used to handle the boundary effect by symmetrizing the bubble array to the other side of the boundary. The enthalpy on the surface of the jth bubble is calculated by a specific formula, the flow field pressure generated by the mirror bubble is considered, and it is clear that there are four mirror bubbles (M = 4N) for each underwater explosion array bubble, and the mirror bubble position vector calculation formula is given, and the factors such as the unit outer normal vector of the rigid wall and the real bubble position are fully considered. The processing method enables the present application to accurately incorporate the boundary conditions into the bubble dynamics analysis, greatly improves the accuracy of the prediction of the motion characteristics of the underwater array explosion bubble in the finite flow field environment, makes up for the shortcomings of the previous research in handling the boundary effect, and lays a solid foundation for the subsequent accurate calculation of the motion and pressure parameters of the bubble.

[0092] Further, in S5, according to the expression of the bubble surface enthalpy S j , the pulsation and translation equation groups of the underwater explosion bubble array in the finite flow field are respectively:

[0093]

[0094] The above two equations are solved by using the fourth-order Runge-Kutta method to perform time advancement, that is, the volume and displacement time history process of each bubble in the underwater explosion array under the condition of the finite field can be obtained.

[0095] Specifically, in S5, the above two equations are solved by using the fourth-order Runge-Kutta method to perform time advancement, that is, the volume and displacement time history process of each bubble in the underwater explosion array under the condition of the finite field can be obtained, as shown in Figure 4 This step can fully utilize the conditions and parameters determined in the previous steps to solve complex equation groups through accurate mathematical calculation. The fourth-order Runge-Kutta method has high precision and stability, and in the time advancement process, the dynamic change process of the bubble under the condition of the finite field with time can be simulated in detail, so that the volume and displacement time history curve of each bubble in the underwater explosion array can be accurately obtained. This enables the present application to convert theoretical analysis into actual quantifiable results, and provides key data support for in-depth study of the behavior of bubbles in the underwater explosion process.

[0096] Further, in S6, the pressure induced by each bubble in the flow field is calculated according to formula (8), and the pressure induced by all bubbles (including the calculated bubbles and the mirror bubbles) in the flow field is superimposed to obtain the flow field pressure induced by the underwater array explosion bubble, as shown in Figure 5 The radius, displacement, flow field pressure and other parameters of the underwater array explosion bubble are recorded and post-processed, and the post-processing includes drawing the bubble radius and displacement time history graph, the flow field pressure curve, etc.

[0097] Specifically, in S6, the induced pressure of each bubble in the flow field is calculated by combining formula (8), and the pressures of all bubbles (including the calculated bubbles and the mirror bubbles) are superimposed, so that the flow field pressure induced by the underwater array explosion bubble can be accurately obtained, and 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 the flow field pressure curve are drawn, and the above visualized results can intuitively present the dynamic change process of the bubble and the distribution and change trend of the flow field pressure, which helps researchers to deeply analyze the behavior law of the underwater array explosion bubble, and provides detailed and easy-to-understand reference for engineering practice.

[0098] A storage medium has a computer program stored thereon, and the computer program is executed by a processor to implement the above-mentioned calculation method for the dynamic characteristics of underwater array explosion bubbles in a limited flow field.

[0099] Specifically, when the processor executes the program, the calculation method for the dynamic characteristics of underwater array explosion bubbles in a limited flow field can be realized, and a series of steps are included, such as inputting initial parameters to determine the characteristics of underwater explosion array and environmental conditions, determining the initial conditions of bubble pulsation based on the equivalent of explosives and water depth, establishing and solving the equation set of bubble array pulsation and migration, correcting the influence of limited domain boundary, and calculating and post-processing related parameters, which effectively solves the problem that the motion characteristics and flow field load of underwater array explosion bubbles in a limited flow field are difficult to predict, provides efficient and accurate theoretical analysis and data support means for engineering practice, and greatly improves the ability and efficiency of related fields in underwater explosion research and application.

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

[0101] Specifically, the computer device, the memory and the processor of the present application work cooperatively to run a specific computer program to realize the calculation method for the dynamic characteristics of underwater array explosion bubbles in a limited flow field. Through this method, the complex situation of underwater explosion can be accurately processed, from determining the initial parameters, calculating the initial conditions of bubble pulsation, to constructing and solving the equation set, correcting the boundary influence, and subsequent data processing and analysis, and a series of steps, effectively overcoming the difficulties in predicting the motion characteristics and flow field load 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 application discloses a calculation method for underwater array explosion bubble dynamic characteristics in a limited flow field.

[0103] It should be noted that, in this document, relational terms such as "first" and "second", and the like can be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises", "comprising", or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but can also include other elements not expressly listed or inherent to such process, method, article, or apparatus. Furthermore, this document refers to "a", "an", "the", "other", and "at least one" to describe one or more of the items; however, the use of these terms does not preclude the presence of more than one of the items at the same time.

[0104] Finally, it should be noted that the above examples are merely used to illustrate the technical solutions of the present application, rather than limiting the same; even though the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced by equivalent features; and such modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for calculating the dynamics of an underwater array explosion bubble in a limited flow domain, characterized by, The method for calculating the dynamic characteristics of underwater array explosion bubbles in a limited flow field comprises the following steps: S1, input initial parameters of underwater array explosion, determine initial characteristics and environmental conditions of the underwater explosion array; S2, based on the equivalent weight of each explosive in the array and the water depth, determine the initial dynamic conditions of the underwater explosion bubble pulsation; S3, based on one-dimensional bubble pulsation and translation equations, establish bubble array pulsation and migration equation set according to the initial characteristics and environmental conditions of the underwater explosion array, In S3, based on the one-dimensional bubble pulsation and translation equations in the free field, the bubble array pulsation and migration equation set is established, the one-dimensional bubble pulsation equation in the free field 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 sound speed in water, p is the density of water, R, and are the bubble radius, the first and second time derivative of the bubble radius, respectively, P is the current time instant bubble internal pressure, u and are the bubble translational velocity and acceleration vectors, respectively, is the hydrostatic pressure gradient at the bubble location, when the bubble is in a free field subject to gravity only, g is the gravity acceleration vector, C d is the drag force coefficient, the current time instant bubble internal pressure P is calculated as follows: Where V0 is the initial volume of the bubble, V is the volume of the bubble at the calculation time, According to the characteristics of the underwater explosion array, the bubble array pulsation and migration equation set is established. First, the fluid particle velocity induced by the bubble 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 location to the flow field; the lower table d in the above equation represents the time delay quantity, i.e. the disturbance at r in the flow field at time t is caused by the bubble at an earlier time t-(|r|-R) / C, which needs to be interpolated on the time axis in 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=(P-P ∞ ) / p, Combined with the Bernoulli equation of fluid mechanics, the dynamic pressure calculation formula of the flow field at r is obtained: The other bubbles in the bubble array are regarded as a number of compressible point sources, which cause pressure disturbance at the calculated bubble. By superimposing the static water pressure at the calculated bubble, the influence of the bubble array can be taken into account. 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 equation set of the bubble array, respectively: where 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 i-th bubble at the N-th bubble, calculated according to equation (8); S4, according to the mirror image theory, the influence of the limited domain boundary is corrected to determine the expression of the bubble surface enthalpy in the bubble array pulsation and migration equation set; S5, time marching is performed on the bubble pulsation and migration equation set to obtain the volume and displacement time history curves of each bubble in the bubble array; S6, according to the volume time-varying process of each bubble in the bubble array, the flow field pressure is superimposed and solved, and the bubble characteristic parameters and flow field pressure are recorded and post-processed.

2. The method for calculating the dynamic characteristics of the bubble of underwater array explosion in a limited flow field according to claim 1, characterized in that, In S1, the initial parameters of underwater array explosion are input, including the number of explosives, the position of each explosive, the water depth, the equivalent weight, the form of the limited flow field boundary and the distance between each explosive and the water area boundary, so as to determine the initial characteristics and environmental conditions of the underwater explosion array.

3. The method for calculating the dynamic characteristics of the bubble generated by an underwater array explosion in a limited flow field according to claim 2, characterized in that, In S2, based on the equivalent weight 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, 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 maximum volume moment 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, and h is the water depth at which the explosive is located. The initial radius of the bubble is obtained by solving equation (1) iteratively using the bisection method.

4. The method for calculating the dynamic characteristics of the bubble of underwater array explosion in a limited flow field 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. The method for calculating the dynamic characteristics of the bubble of underwater array explosion in a limited flow field according to claim 4, characterized in that, In S4, the influence of the finite field boundary is corrected according to the mirror theory. The boundary condition in the finite flow field is composed of two parallel wall boundaries. According to the mirror theory of fluid mechanics, the flow states on both sides of the rigid wall are completely the same. Therefore, the bubble array is respectively symmetrical to the other side of the two water area boundaries, that is, the surface enthalpy Sj of the jth bubble can be calculated as follows: j This can be calculated as follows: where m ij The flow field pressure generated by the ith mirror bubble at bubble j can be calculated according to equation (8), where M is the number of mirror bubbles. For each bubble in the underwater explosion array, there are four mirror bubbles, so M=4N. The position vector of the mirror bubble can be determined as follows: where n1and n2are the unit outward normal vectors of the two rigid walls, L is the position vector of the position where the real bubble is located, and L i represents the position vector of the position where the corresponding i-th mirror bubble is located.

6. The method for calculating the dynamic characteristics of the bubble of underwater array explosion in a limited flow field according to claim 5, characterized in that, In S5, according to the expression of bubble surface enthalpy S j The pulsating and translating equations of the bubble array of underwater explosion in the limited flow domain are respectively as follows: The fourth-order Runge-Kutta method is used to solve the above two equations to perform time marching, so as to obtain the volume and displacement time history process of each bubble in the underwater explosion array under the condition of limited domain.

7. The method for calculating the dynamic characteristics of the bubble of underwater array explosion in a limited flow field according to claim 6, characterized in that, In S6, the pressure induced by each bubble in the flow field is calculated according to formula (8), and the pressure induced by all the bubbles in the flow field is superimposed to obtain the flow field pressure induced by the underwater array explosion bubble, and the radius, displacement and flow field pressure of the underwater array explosion bubble are recorded and post-processed, the post-processing including drawing the bubble radius and displacement time history diagram, the flow field pressure curve, The all bubbles include the calculation bubble and the mirror bubble.

8. A storage medium having stored thereon a computer program, characterized in that The computer program is executed by the processor to implement the calculation method for the dynamic characteristics of the underwater array explosion bubble in the limited flow field according to any one of claims 1-7.

9. A computer device, comprising: Comprise: A memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor executes the program to implement the calculation method for the dynamic characteristics of the underwater array explosion bubble in the limited flow field according to any one of claims 1-7.

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