Forward modeling prediction method for bubble pulsating pressure wavelets in shallow water area

Abstract

The invention relates to a forward prediction method for bubble pulsating pressure wavelets in a shallow water area, belongs to the field of deep sea resource exploration and ship structure protection, and aims to solve the problem of forward prediction of bubble pulsating pressure in the shallow water area in existing engineering. The method comprises the steps of inputting bubble initial conditions, environmental parameters and pressure measuring point positions, judging the influence of a water area boundary, designing a correction term expression, substituting into an equation to carry out time advance, calculating and considering physical quantity propagation time, and finally outputting a pressure curve based on a Bernoulli equation. On the basis of the Kelvin impulse theory, buoyancy parameter deviation induced by non-spherical deformation of the bubbles is corrected, the Kelvin impulse theory solution of the large-scale bubbles under the influence of different water area boundaries is calculated through the mirror image bubble method, and the purpose of rapidly predicting the jet flow direction of the underwater large-scale bubbles is achieved. And a theoretical basis and a basic technical support are provided for engineering construction.

Description

Technical Field

[0001] The invention relates to a forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters, and belongs to the field of deep-sea resource exploration and ship structure protection. Background Art

[0002] In the exploration of marine resources, high-pressure airgun bubbles have been favored by many explorers because of their low cost, high efficiency and green environmental protection. In the process of marine resource exploration, the exploration tools need to be able to emit strong signals and penetrate thick seawater layers, so the exploration source needs to have sufficient power. Large-scale airgun bubble seismic source is a means of generating pulsating sub-wave signals by releasing high-pressure gas in water. It is clean and environmentally friendly and has been widely used in recent years. However, in the exploration process, the far-field pressure sub-waves generated by large-scale underwater bubble pulsations will pose a serious threat to the safety of ship equipment and exploration personnel. The same engineering problem also exists in applications such as underwater explosions. Large-scale underwater explosion bubbles generate strong pulsating shock waves, which can be used to attack enemy targets, but also avoid their safety threats to our structures. Therefore, the prediction of large-scale underwater bubble pulsation pressure is crucial for practical engineering applications.

[0003] The bubble pulsation pressure is affected by two factors: the initial condition of the bubble and the boundary effect. For example, in the airgun bubble test used for seabed resource exploration, when the airgun test is carried out in waters near the coast or near islands and reefs, the dynamic characteristics of the airgun bubble will be affected by the boundaries of the water surface and the seabed, which will greatly increase the difficulty of analyzing the bubble source signal; for example, in underwater explosive devices arranged in nearshore waters, if the water depth is large relative to the bubble scale, the bubble will be affected by the seabed and coastal boundaries. The location of the bubble generation point, the water depth, and the selection of initial parameters will significantly affect the pressure sub-waves radiated by the pulsating bubble. Accurately predicting the pulsating pressure radiated by the bubble source is of great significance for the efficient and rational use of the bubble pulsation energy. The bubble dynamics theory based on the spherical bubble hypothesis provides a good tool for predicting the bubble pulsation pressure sub-wave, improves the efficiency of forward prediction, and greatly reduces the cost of directly conducting numerical simulations or mechanistic experiments.

[0004] Most existing technologies use domain grid numerical simulation to predict bubble pulsation pressure, and conduct research by establishing two-phase flow numerical models under different boundary conditions. However, the computational cost of three-dimensional numerical simulation is huge, especially when the influence of underwater structures is taken into account. The discretization of far-field water area grids can easily cause the calculation time to increase exponentially and the discrete error will become larger and larger. In addition, the numerical simulation of bubble domain grids with strong buoyancy effects cannot simulate the late stage of bubble rebound. Summary of the invention

[0005] The present invention proposes a forward prediction method for bubble pulsation pressure wavelet in shallow waters, and introduces a correction term for shallow water boundary effect to solve the forward prediction problem of bubble pulsation pressure in shallow waters in existing engineering.

[0006] A forward modeling prediction method for bubble pulsation pressure sub-wave in shallow waters, the forward modeling prediction method for bubble pulsation pressure sub-wave in shallow waters comprising the following steps:

[0007] S100, inputting the initial conditions of the bubble, environmental parameters and the position of the pressure measuring point;

[0008] S200, judging whether the influence of the water area boundary needs to be considered based on the maximum size of the bubble and the distance between the initial center of the bubble and the water area boundary;

[0009] S300, designing an expression for a correction term for the background pressure at the center of the bubble based on the distance between the bubble and the water boundary;

[0010] S400, substituting the expression of the correction term into the Keller-Miksis equation, advancing the time from the initial condition of the bubble, and recording the time history of the bubble radius, bubble pulsation velocity, bubble translation velocity, and bubble surface enthalpy difference;

[0011] S500, based on the distance between the pressure measuring point and the bubble, calculating the time required for each physical quantity to propagate from the center of the bubble to the measuring point, and interpolating to obtain the delay amount of each physical quantity;

[0012] S600. Based on the Bernoulli equation, calculate and output the bubble pulsation pressure time history curve at the pressure measuring point.

[0013] Furthermore, in S100, the initial conditions and environmental parameters include the initial radius of the bubble, the initial internal pressure of the bubble, the water depth at the bubble's location, the environmental fluid density, the sea depth, the distance between the water boundary and the bubble, the free surface reflection coefficient and the atmospheric pressure.

[0014] Further, in S200, whether the water area boundary affects the bubble pulsating pressure is considered based on the ratio between the water area boundary and the maximum bubble radius, and whether the influence of the water area boundary needs to be considered is determined based on the following parameter range:

[0015] d f ≤6R max (1)

[0016] d w ≤4R max (2)

[0017] where d f is the distance between the bubble and the water surface, d w is the distance between the bubble and the bottom of the water, Rmax is the maximum radius of the bubble, when d f ≤6R max The influence of the water surface needs to be considered when d w ≤4R max The influence of the wall needs to be considered.

[0018] In S200, the maximum size of the bubble is obtained by the initial radius of the bubble and the subsequent dynamic change law under a specific environment.

[0019] Furthermore, in S200, if the water area boundary information does not satisfy equations (1) and (2), there is no need to use the method of the present invention for calculation.

[0020] Further, in S300, under the influence of the water surface and the bottom, the number of correction items is 8, each of which contains a position vector, which is determined by the following formula:

[0021] o 1 =o+2d f n f

[0022] o 2 =o+2d w n w

[0023] o i =mod(i,2)[o i-1 -(2o i-1 ·n f ) f ]+[mod(i,2)+1][o max(i-3,0) -(2o max(i-3,0) ·n w ) w ],i=3,...,8 (3)

[0025] Where o is the position vector of the bubble, o i is the position vector of the i-th mirror bubble, n f and n w are the unit external normal vectors of the water surface and bottom respectively;

[0026] When there is a structure near the bubble, the number of correction items is 17 under the combined influence of the water surface, the bottom of the water and the underwater structure. The position vector contained in each item is calculated as follows:

[0027] o 1 =o+2d f n f

[0028] o 2 =o+2d bn b

[0029] o i =mod(i,2)[o i-1 -(2o i-1 ·n f ) f ]+[mod(i,2)+1][o max(i-3,0) -(2o max(i-3,0) ·n b ) b ],i=3,...,8

[0030] o i =o i-8 +2d s n s ,i=9,...,16

[0031] o 17 =o+2d s n s (4)

[0033] According to the above position vector, the bubble center background pressure correction term is calculated as follows:

[0034]

[0035] Where ρ is the density of water, d r is the distance between the bubble and the pressure measuring point, is the first-order time derivative of the bubble radius R, and E is the enthalpy difference on the bubble surface. The enthalpy difference is calculated as follows:

[0036]

[0037] Where P is the pressure on the bubble surface, P ∞ is the hydrostatic pressure at the location of the bubble;

[0038] The bubble surface pressure P in formula (6) is calculated according to the state equation under the adiabatic assumption:

[0039]

[0040] Among them, P 0 is the initial internal pressure of the bubble, R 0 is the initial radius of the bubble, κ is the insulation coefficient, P v is the saturated vapor pressure.

[0041] Furthermore, in S400, the Keller-Miksis equation used to describe the bubble pulsation is:

[0042]

[0043] in is the second-order time derivative of the bubble radius R, is the first-order derivative of the bubble surface enthalpy difference E with respect to time, C is the speed of sound in water,

[0044] The bubble center background pressure correction term given by equation (6) is added to the hydrostatic pressure term p in the Keller-Miksis equation ∞ In order to take into account the influence of the water boundary on the bubble pulsation, the second-order time derivative of the bubble radius is calculated as follows:

[0045]

[0046] Based on the initial conditions of the bubble and equation (9), time is advanced to record the time history of the bubble radius, bubble pulsation velocity, and bubble surface enthalpy difference. The time step is calculated as follows:

[0047]

[0048] Among them C 0 is the time step empirical coefficient, which is taken as 0.01.

[0049] According to the bubble radius, bubble pulsation speed and bubble surface enthalpy difference at each moment, the bubble translation speed is calculated and recorded as follows:

[0050]

[0051] in is the translational acceleration of the bubble, u is the translational velocity of the bubble, g is the gravitational acceleration, C d is the drag force coefficient,

[0052] According to the translational velocity and translational acceleration of the bubble at each moment, the displacement of the bubble at the current moment is obtained by integrating along time. According to the displacement of the bubble, the distance value between the bubble and the pressure measuring point is updated.

[0053] Furthermore, in S500, based on the distance between the pressure measuring point and the bubble, the time required for each physical quantity to propagate from the center of the bubble to the measuring point is calculated, and each physical quantity is interpolated on the time axis to obtain the corresponding physical quantity d before the current moment. r / C value at the moment.

[0054] Further, in S600, based on the Bernoulli equation, the bubble pulsation pressure time history curve at the pressure measuring point is calculated and outputted, and is calculated as follows:

[0055]

[0056] Where P ris the pressure at the pressure measuring point, and the subscript yc indicates the corresponding physical quantity d before the current moment r / C value at the moment.

[0057] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters.

[0058] 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 forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters.

[0059] The beneficial effects of the invention are as follows: the invention proposes a forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters, which can quickly predict large-scale underwater bubble pulsation pressures; corrects the buoyancy parameter deviation induced by the non-spherical deformation of the bubble, and uses the mirror bubble method to calculate the Kelvin impulse theory solution, which can quickly predict the direction of large-scale underwater bubble jets, providing a theoretical basis and basic technical support for engineering construction; compared with the existing domain grid numerical simulation prediction method, the invention improves the forward modeling prediction efficiency, reduces the cost, avoids the problem of exponential increase in calculation time and increase in discrete error due to the inclusion of the influence of the underwater structure, and can also simulate the late stage of the bubble rebound stage. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a method flow chart of a forward prediction method for bubble pulsation pressure sub-wave in shallow waters of the present invention;

[0061] Figure 2 It is a time history curve effect diagram of the bubble radius after taking into account the shallow water boundary effect in a forward prediction method of bubble pulsation pressure sub-wave in shallow waters according to the present invention;

[0062] Figure 3 It is a time history curve effect diagram of bubble displacement after taking into account the shallow water boundary effect in a forward prediction method of bubble pulsation pressure sub-wave in shallow waters according to the present invention;

[0063] Figure 4 It is a time history curve effect diagram of the bubble pulsating pressure after taking into account the shallow water boundary effect in a forward modeling prediction method of the bubble pulsating pressure sub-wave in shallow waters according to the present invention. DETAILED DESCRIPTION

[0064] 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.

[0065] Reference Figure 1 As shown, a forward modeling prediction method for bubble pulsation pressure sub-wave in shallow waters, the forward modeling prediction method for bubble pulsation pressure sub-wave in shallow waters comprises the following steps:

[0066] S100, inputting the initial conditions of the bubble, environmental parameters and the position of the pressure measuring point;

[0067] S200, judging whether the influence of the water area boundary needs to be considered based on the maximum size of the bubble and the distance between the initial center of the bubble and the water area boundary;

[0068] S300, designing an expression for a correction term for the background pressure at the center of the bubble based on the distance between the bubble and the water boundary;

[0069] S400, substituting the expression of the correction term into the Keller-Miksis equation, advancing the time from the initial condition of the bubble, and recording the time history of the bubble radius, bubble pulsation velocity, bubble translation velocity, and bubble surface enthalpy difference;

[0070] S500, based on the distance between the pressure measuring point and the bubble, calculating the time required for each physical quantity to propagate from the center of the bubble to the measuring point, and interpolating to obtain the delay amount of each physical quantity;

[0071] S600. Based on the Bernoulli equation, calculate and output the bubble pulsation pressure time history curve at the pressure measuring point.

[0072] Specifically, the initial conditions, environmental parameters and the location of the pressure measuring point of the bubble are input through step S100, which provides a comprehensive data basis for subsequent predictions. In S200, whether the boundary effect needs to be considered is determined based on the maximum scale of the bubble and the distance from the water boundary, which makes the prediction more in line with the actual situation. The bubble center background pressure correction term expression designed in S300 further improves the accuracy of the prediction. The S400 step of substituting the correction term expression into the Keller-Miksis equation for time advancement records the time history of multiple physical quantities such as bubble radius and speed. S500 calculates the propagation time of the physical quantity based on the distance between the pressure measuring point and the bubble and interpolates to obtain the delay amount, which improves the details of the prediction. Finally, S600 calculates and outputs the bubble pulsating pressure time history curve at the pressure measuring point based on the Bernoulli equation, realizing the forward prediction of the bubble pulsating pressure sub-wave in shallow waters. The present invention can quickly predict the pulsating pressure of large-scale underwater bubbles, and correct the buoyancy parameter deviation induced by the non-spherical deformation of bubbles. The mirror bubble method is used to calculate the Kelvin impulse theory solution, so that the direction of large-scale underwater bubble jets can be quickly predicted, providing an important theoretical basis and basic technical support for engineering construction. At the same time, compared with the existing domain grid numerical simulation prediction method, this method improves the forward prediction efficiency, reduces the calculation cost, avoids the problems of exponential increase in calculation time and increase in discrete error due to the inclusion of underwater structure influence, and can also simulate to the late stage of bubble rebound, greatly improving the practicality and reliability of the prediction.

[0073] Furthermore, in S100, the initial conditions and environmental parameters include the initial radius of the bubble, the initial internal pressure of the bubble, the water depth at the bubble's location, the environmental fluid density, the sea depth, the distance between the water boundary and the bubble, the free surface reflection coefficient and the atmospheric pressure, etc. By modifying the above initial information parameters, the initial state of the bubble and the water environment conditions can be set.

[0074] Further, in S200, whether the water area boundary affects the bubble pulsating pressure is considered based on the ratio between the water area boundary and the maximum bubble radius, and whether the influence of the water area boundary needs to be considered is determined based on the following parameter range:

[0075] d f ≤6R max (1)

[0076] d w ≤4R max (2)

[0077] where d f is the distance between the bubble and the water surface, d w is the distance between the bubble and the bottom of the water, R max is the maximum radius of the bubble, when d f ≤6Rmax The influence of the water surface needs to be considered when d w ≤4R max The influence of the wall needs to be considered.

[0078] Specifically, the so-called "ratio between it and the maximum radius of the bubble" refers to the ratio between the distance between the bubble and the water surface and the distance between the bubble and the water bottom and the maximum radius of the bubble.

[0079] In S200, the maximum size of the bubble is obtained by the initial radius of the bubble and the subsequent dynamic change law under a specific environment.

[0080] Specifically, in S200, the influence of the water area boundary on the bubble pulsating pressure is considered according to the ratio of the distance between the bubble and the water surface, the water bottom and the maximum radius, and a parameter range is given to determine whether the boundary effect needs to be considered, and the method of obtaining the maximum size of the bubble is clarified. This can more accurately determine whether the boundary effect needs to be considered, make the forward prediction method more targeted, avoid unnecessary calculations, and determine the maximum size of the bubble according to scientific and reasonable rules, thereby providing an accurate basis for subsequent steps.

[0081] In this embodiment, the maximum size of the bubble is obtained by the initial condition of the bubble, and the fourth-order Runge-Kutta method can be used to solve the following equation:

[0082]

[0083] Where ρ is the density of water, P 0 is the initial internal pressure of the bubble, is the first-order time derivative of the bubble radius R, is the second-order time derivative of the bubble radius R, R 0 is the initial radius of the bubble, κ is the insulation coefficient, P ∞ is the hydrostatic pressure at the location of the bubble.

[0084] Furthermore, in S200, if the water area boundary information does not satisfy equations (1) and (2), there is no need to use the method of the present invention for calculation.

[0085] Specifically, this embodiment avoids invalid calculations when the requirements are not met by reasonably setting the judgment conditions, saves computing resources and time, and improves the efficiency of the entire prediction method.

[0086] Further, in S300, under the influence of the water surface and the bottom, the number of correction items is 8, each of which contains a position vector, which is determined by the following formula:

[0087]

[0088] Where o is the position vector of the bubble, o iis the position vector of the i-th mirror bubble, n f and n w are the unit external normal vectors of the water surface and bottom respectively;

[0089] When there is a structure near the bubble, the number of correction items is 17 under the combined influence of the water surface, the bottom of the water and the underwater structure. The position vector contained in each item is calculated as follows:

[0090] o 1 =o+2d f n f

[0091] o 2 =o+2d b n b

[0092] o i =mod(i,2)[o i-1 -(2o i-1 ·n f ) f ]+[mod(i,2)+1][o max(i-3,0) -(2o max(i-3,0) ·n b ) b ],i=3,...,8

[0093] o i =o i-8 +2d s n s ,i=9,...,16

[0094] o 17 =o+2d s n s (4)

[0096] According to the above position vector, the bubble center background pressure correction term is calculated as follows:

[0097]

[0098] Where ρ is the density of water, d r is the distance between the bubble and the pressure measuring point, is the first-order time derivative of the bubble radius R, and E is the enthalpy difference on the bubble surface. The enthalpy difference is calculated as follows:

[0099]

[0100] Where P is the pressure on the bubble surface, P ∞ is the hydrostatic pressure at the location of the bubble;

[0101] The bubble surface pressure P in formula (6) is calculated according to the state equation under the adiabatic assumption:

[0102]

[0103] Among them, P 0 is the initial internal pressure of the bubble, R 0 is the initial radius of the bubble, κ is the insulation coefficient, P v is the saturated vapor pressure.

[0104] Specifically, in S300, this embodiment provides detailed correction item settings for different scenarios. When only the influence of the water surface and the bottom is considered, the number of correction items is determined to be 8 and a corresponding expression is given, which is based on the position vector of the bubble and the position vector of the mirror bubble and the unit external normal vector. Under such relatively simple boundary conditions, the background pressure at the center of the bubble can be corrected more accurately, taking into account the main influencing factors.

[0105] When there are structures near the bubble, the number of correction terms is further determined to be 17 and the corresponding expressions are determined. This is because the presence of structures will have an additional impact on the behavior of the bubble. Through these expressions, the correction of the background pressure at the center of the bubble can be adjusted more finely.

[0106] At the same time, the calculation method of the background pressure correction term at the center of the bubble is given, which comprehensively considers multiple physical quantities such as the density of water, the distance between the bubble and the pressure measuring point, the first-order time derivative of the bubble radius, and the enthalpy difference on the bubble surface. This calculation method that comprehensively considers multiple factors can more accurately reflect the actual physical process, so that the correction result is more in line with the actual situation.

[0107] Through these precise settings and calculation methods, this embodiment significantly improves the correction effect of the background pressure at the center of the bubble under different boundary conditions, thereby greatly improving the accuracy of the entire bubble pulsation pressure prediction method, and providing strong support for more accurate prediction of the bubble pulsation pressure.

[0108] Furthermore, in S400, the Keller-Miksis equation used to describe the bubble pulsation is:

[0109]

[0110] in is the second-order time derivative of the bubble radius R, is the first-order derivative of the bubble surface enthalpy difference E with respect to time, C is the speed of sound in water,

[0111] The bubble center background pressure correction term given by equation (6) is added to the hydrostatic pressure term p in the Keller-Miksis equation ∞In order to take into account the influence of the water boundary on the bubble pulsation, the second-order time derivative of the bubble radius is calculated as follows:

[0112]

[0113] Based on the initial conditions of the bubble and equation (9), time is advanced to record the time history of the bubble radius, bubble pulsation velocity, and bubble surface enthalpy difference. The time history of the bubble radius is as follows: Figure 2 The time step is calculated as follows:

[0114]

[0115] Among them C 0 is the time step empirical coefficient, which is taken as 0.01.

[0116] According to the bubble radius, bubble pulsation speed and bubble surface enthalpy difference at each moment, the bubble translation speed is calculated and recorded as follows:

[0117]

[0118] in is the translational acceleration of the bubble, u is the translational velocity of the bubble, g is the gravitational acceleration, C d is the drag force coefficient,

[0119] According to the bubble translation speed and translation acceleration at each moment, the displacement of the bubble at the current moment is obtained by integrating along time. According to the displacement of the bubble, the distance value between the bubble and the pressure measuring point is updated. The time history of the bubble displacement is as follows: Figure 3 shown.

[0120] Specifically, the Keller-Miksis equation specified in S400 is the key theoretical basis for describing bubble pulsation. It provides a basic framework for us to understand the dynamic behavior of bubbles, so that we can study the changing laws of bubbles under different conditions based on this equation. After taking into account the influence of the water boundary, the second-order time derivative calculation method of the bubble radius given further improves this theoretical model. Through this precise calculation method, the change of the bubble radius under the influence of the boundary can be captured more accurately. This is crucial for studying the pulsation characteristics of bubbles, because the change of the bubble radius directly affects the pressure inside the bubble and the interaction with the surrounding environment. The determined time step calculation method is also an important contribution of this embodiment. Reasonable time step selection can ensure that when performing numerical calculations, the dynamic process of the bubble can be accurately reflected, and important details will not be lost due to too large a time step, or the amount of calculation will be too large due to too small a time step. This scientific and reasonable time step calculation method ensures the efficiency and accuracy of the entire calculation process. In addition, the calculation method of the bubble translation velocity is also of great significance. It enables us to understand that bubbles in water not only have pulsating behavior, but also translational motion. By calculating the translational velocity of the bubble, we can better understand the movement trajectory of the bubble in the entire water area, which plays an indispensable role in predicting the impact of the bubble on the surrounding environment and the ultimate prediction of the bubble pulsation pressure.

[0121] Furthermore, in S500, based on the distance between the pressure measuring point and the bubble, the time required for each physical quantity to propagate from the center of the bubble to the measuring point is calculated, and each physical quantity is interpolated on the time axis to obtain the corresponding physical quantity d before the current moment. r / C value at the moment.

[0122] Specifically, in S500, the time required for each physical quantity to propagate from the center of the bubble to the measuring point is calculated based on the distance between the pressure measuring point and the bubble, and the delay is obtained by interpolation. This embodiment enables the present invention to more accurately consider the time delay factor of physical quantity propagation, making the prediction result more consistent with the actual physical process.

[0123] Further, in S600, based on the Bernoulli equation, the bubble pulsation pressure time history curve at the pressure measuring point is calculated and output. The time history change process of the bubble pulsation pressure is as follows: Figure 4 The pressure formula is as follows:

[0124]

[0125] Where P r is the pressure at the pressure measuring point, and the subscript yc indicates the corresponding physical quantity d before the current moment r / C value at the moment.

[0126] Specifically, in S600, the bubble pulsation pressure time history curve at the pressure measuring point is calculated and output based on the Bernoulli equation. This embodiment can accurately calculate the bubble pulsation pressure change curve over time through the Bernoulli equation based on the various parameters and calculation results obtained in the previous steps, thereby intuitively presenting the dynamic change process of the bubble pulsation pressure, providing key data support for engineering applications, and further improving the practicality and value of the entire prediction method.

[0127] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters.

[0128] Specifically, a storage medium of this embodiment implements the prediction method of the present invention when a computer program stored thereon is executed by a processor. This embodiment provides a carrier for implementing the prediction method, so that the method can be applied and implemented on a storage medium through a computer program, which facilitates the promotion and use of the technology and provides software-level support and guarantee for the prediction of bubble pulsation pressure in actual engineering.

[0129] 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 forward modeling prediction method for bubble pulsation pressure sub-waves in shallow waters.

[0130] Specifically, a computer device of this embodiment includes a memory, a processor and a related computer program, which can implement the prediction method of the present invention. This embodiment integrates the prediction method into the computer device, so that the method can run efficiently, improves the calculation speed and processing ability, provides a hardware foundation and guarantee for the accurate prediction of bubble pulsation pressure, and promotes the application and implementation of this technology in practical engineering.

[0131] The present invention relies on the Kelvin impulse theory to correct the buoyancy parameter deviation caused by the non-spherical deformation of the bubble. With the help of the mirror bubble method, the Kelvin impulse theory solution is calculated for the situation where large-scale bubbles are affected by the boundaries of different water areas. Through this series of operations, the purpose of quickly predicting the direction of underwater large-scale bubble jets is achieved, thereby providing solid theoretical support and basic technical guarantees for engineering construction.

[0132] In this process, the correction of the buoyancy parameter deviation can more accurately reflect the actual stress state of the bubble in a complex water environment. The use of the mirror bubble method cleverly takes into account the boundary conditions of different waters, making the calculation of the theoretical solution more in line with the actual situation. This ability to quickly predict the direction of large-scale underwater bubble jets is of vital importance in engineering construction. For example, in the process of deep-sea resource exploration, it can help construction personnel understand in advance the impact that bubble jets may have on exploration equipment and personnel, so as to take corresponding protective measures; in terms of ship structure protection, it can also provide a key theoretical basis for the design of protective structures to ensure the safety of ships in bubble pulsating pressure environments.

[0133] 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.

[0134] 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 forward prediction method for bubble pulsation pressure sub-waves in shallow waters, characterized in that: The forward prediction method for bubble pulsation pressure sub-wave in shallow waters comprises the following steps: S100, input the initial conditions of the bubble, environmental parameters and the position of the pressure measuring point; S200, judging whether the influence of the water area boundary needs to be considered based on the maximum size of the bubble and the distance between the initial center of the bubble and the water area boundary; S300, designing an expression for a correction term for the background pressure at the center of the bubble based on the distance between the bubble and the water boundary; S400, substituting the expression of the correction term into the Keller-Miksis equation, advancing the time from the initial condition of the bubble, and recording the time history of the bubble radius, bubble pulsation velocity, bubble translation velocity, and bubble surface enthalpy difference; S500, based on the distance between the pressure measuring point and the bubble, calculating the time required for each physical quantity to propagate from the center of the bubble to the measuring point, and interpolating to obtain the delay amount of each physical quantity; S600. Based on the Bernoulli equation, calculate and output the bubble pulsation pressure time history curve at the pressure measuring point.

2. A forward prediction method for bubble pulsation pressure sub-wave in shallow waters according to claim 1, characterized in that: In S100, the initial conditions and environmental parameters include the initial radius of the bubble, the initial internal pressure of the bubble, the water depth at the bubble's location, the environmental fluid density, the sea depth, the distance between the water boundary and the bubble, the free surface reflection coefficient and the atmospheric pressure.

3. A forward prediction method for bubble pulsation pressure sub-wave in shallow waters according to claim 2, characterized in that: In S200, whether the water area boundary affects the bubble pulsating pressure is considered based on the ratio between the water area boundary and the maximum bubble radius, and whether the influence of the water area boundary needs to be considered is determined based on the following parameter ranges: d f ≤6R max (1) d w ≤4R max (2) where d f is the distance between the bubble and the water surface, d w is the distance between the bubble and the bottom of the water, R max is the maximum radius of the bubble, when d f ≤6R max The influence of the water surface needs to be considered when d w ≤4R max The influence of the wall needs to be considered.

4. A forward prediction method for bubble pulsation pressure sub-wave in shallow waters according to claim 3, characterized in that: In S200, if the water area boundary information does not satisfy equations (1) and (2), there is no need to use the method of the present invention for calculation.

5. A forward prediction method for bubble pulsation pressure sub-wave in shallow waters according to claim 4, characterized in that: In S300, under the influence of the water surface and the bottom, the number of correction items is 8, each of which contains a position vector, which is determined by the following formula: o1=o+2d f n f o2=o+2d w n w o i =mod(i,2)[o i-1 -(2o i-1 ·n f )n f ]+[mod(i,2)+1][o max(i-3,0) -(2o max(i-3,0) ·n w )n w ],i=3,...,8(3) Where o is the position vector of the bubble, o i is the position vector of the i-th mirror bubble, n f and n w are the unit external normal vectors of the water surface and bottom respectively; When there is a structure near the bubble, the number of correction items is 17 under the combined influence of the water surface, the bottom of the water and the underwater structure. The position vector contained in each item is calculated as follows: o1=o+2d f n f o2=o+2d b n b o i =mod(i,2)[o i-1 -(2o i-1 ·n f )n f ]+[mod(i,2)+1][o max(i-3,0) -(2o max(i-3,0) ·n b )n b ],i=3,...,8 o i =o i-8 +2d s n s ,i=9,...,16 o 17 =o+2d s n s (4) According to the above position vector, the bubble center background pressure correction term is calculated as follows: Where ρ is the density of water, d r is the distance between the bubble and the pressure measuring point, is the first-order time derivative of the bubble radius R, and E is the enthalpy difference on the bubble surface. The enthalpy difference is calculated as follows: Where P is the pressure on the bubble surface, P ∞ is the hydrostatic pressure at the location of the bubble; The bubble surface pressure P in formula (6) is calculated according to the state equation under the adiabatic assumption: Where P0 is the initial internal pressure of the bubble, R0 is the initial radius of the bubble, κ is the insulation coefficient, and P v is the saturated vapor pressure.

6. A forward prediction method for bubble pulsation pressure sub-waves in shallow waters according to claim 5, characterized in that: In S400, the Keller-Miksis equation used to describe bubble pulsation is: in is the second-order time derivative of the bubble radius R, is the first-order derivative of the bubble surface enthalpy difference E with respect to time, C is the speed of sound in water, The bubble center background pressure correction term given by equation (6) is added to the hydrostatic pressure term p in the Keller-Miksis equation ∞ In order to take into account the influence of the water boundary on the bubble pulsation, the second-order time derivative of the bubble radius is calculated as follows: Based on the initial conditions of the bubble and equation (9), time is advanced to record the time history of the bubble radius, bubble pulsation velocity, and bubble surface enthalpy difference. The time step is calculated as follows: Where C0 is the time step empirical coefficient, which is taken as 0.

01. According to the bubble radius, bubble pulsation speed and bubble surface enthalpy difference at each moment, the bubble translation speed is calculated and recorded as follows: in is the translational acceleration of the bubble, u is the translational velocity of the bubble, g is the gravitational acceleration, C d is the drag force coefficient, According to the translational velocity and translational acceleration of the bubble at each moment, the displacement of the bubble at the current moment is obtained by integrating along time. According to the displacement of the bubble, the distance value between the bubble and the pressure measuring point is updated.

7. A forward prediction method for bubble pulsation pressure sub-wave in shallow waters according to claim 6, characterized in that: In S500, based on the distance between the pressure measuring point and the bubble, the time required for each physical quantity to propagate from the center of the bubble to the measuring point is calculated, and each physical quantity is interpolated on the time axis to obtain the corresponding physical quantity d before the current time. r / C value at the moment.

8. A forward prediction method for bubble pulsation pressure sub-waves in shallow waters according to claim 7, characterized in that: In S600, based on the Bernoulli equation, the bubble pulsation pressure time history curve at the pressure measuring point is calculated and outputted as follows: Where P r is the pressure at the pressure measuring point, and the subscript yc indicates the corresponding physical quantity d before the current moment r / C value at the moment.

9. A storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the forward prediction method for bubble pulsation pressure sub-waves in shallow waters 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 forward prediction method for bubble pulsation pressure sub-waves in shallow waters as described in any one of claims 1 to 8.

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