A forward prediction method for bubble pulsation pressure subwave in shallow water

Abstract

The present application relates to a kind of for shallow water area bubble pulsating pressure subwave forward prediction method, belong to deep sea resource exploration and ship structure protection field, to solve the existing engineering shallow water area bubble pulsating pressure forward prediction problem.The present application inputs bubble initial condition, environmental parameter and pressure measuring point position, judges water area boundary influence, designs correction term expression, substitutes into equation and carries out time advance, calculates and considers the propagation time of physical quantity, finally based on Bernoulli equation exports pressure curve.The present application is based on kelvin impulse theory, corrects the buoyancy parameter deviation induced by the nonspherical deformation of bubble, using mirror bubble method to calculate the kelvin impulse theory solution of large-scale bubble under the influence of different water area boundary, to quickly predict the purpose of large-scale bubble jet direction underwater, provides theoretical basis and basic technical support for engineering construction.

Description

Technical Field

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

[0002] In marine resource exploration, high-pressure airgun bubbles have gained widespread favor due to their low cost, high efficiency, and environmentally friendly nature. Marine resource exploration requires tools capable of emitting strong signals and penetrating thick seawater layers, thus requiring a sufficiently powerful source. Large-scale airgun bubble sources, which generate pulsating wavelet signals by releasing high-pressure gas into water, are clean and environmentally friendly, and have been widely used in recent years. However, during exploration, the far-field pressure wavelets generated by large-scale underwater bubble pulsations can pose a serious threat to the safety of shipboard equipment and exploration personnel. Similar engineering challenges also exist in applications such as underwater explosions. Large-scale underwater explosion bubbles generate strong pulsating shock waves, which can be used to strike enemy targets while preventing them from posing a threat to the safety of domestic structures. Therefore, predicting the pulsating pressure of large-scale underwater bubbles is crucial for practical engineering applications.

[0003] The pulsating pressure of bubbles is affected by two factors: the initial conditions of the bubbles and the boundary effects. For example, in airgun bubble tests used for seabed resource exploration, when the airgun test is conducted in waters near the coast or near islands and reefs, the dynamic characteristics of the airgun bubbles will be affected by the boundaries of the water surface and the seabed, which greatly increases the difficulty of analyzing the bubble source signal. Another example is underwater explosive devices deployed in nearshore waters. If the water depth is large relative to the bubble scale, the bubbles 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 wavelet 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 bubble pulsation energy. The bubble dynamics theory based on the spherical bubble assumption provides an excellent tool for predicting bubble pulsating pressure wavelets, improving the efficiency of forward prediction and greatly reducing the cost of direct numerical simulation 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 the far-field water area grid can easily cause the calculation time to increase exponentially and the discretization error will become larger and larger. In addition, for bubble domain grid numerical simulations with strong buoyancy effects, it is impossible to 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, which 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 projects.

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

[0007] S100, input 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 correction term expression into the Keller-Miksis equation, advancing the time from the initial bubble condition, 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 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 density of the ambient fluid, the depth of the sea area, the distance between the water area boundary and the bubble, the free surface reflection coefficient and the atmospheric pressure.

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

[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 specific conditions.

[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] Furthermore, 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]

[0022] 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;

[0023] 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 and the underwater structure. The position vector contained in each item is calculated as follows:

[0024]

[0025] According to the above position vector, the bubble center background pressure correction term is calculated as follows:

[0026]

[0027] 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:

[0028]

[0029] Where P is the pressure on the bubble surface, P ∞ is the hydrostatic pressure at the location of the bubble;

[0030] The bubble surface pressure P in formula (6) is calculated based on the state equation under the adiabatic assumption:

[0031]

[0032] Where P0 is the initial internal pressure of the bubble, R0 is the initial radius of the bubble, κ is the adiabatic coefficient, P v is the saturated vapor pressure.

[0033] Furthermore, in S400, the Keller-Miksis equation used to describe bubble pulsation is:

[0034]

[0035] 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,

[0036] 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:

[0037]

[0038] Based on the initial conditions of the bubble and formula (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 according to the following formula:

[0039]

[0040] Where C0 is the time step empirical coefficient, which is taken as 0.01.

[0041] 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:

[0042]

[0043] in is the translational acceleration of the bubble, u is the translational velocity of the bubble, g is the acceleration due to gravity, C d is the drag force coefficient,

[0044] 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.

[0045] 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 bubble center 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.

[0046] Furthermore, 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:

[0047]

[0048] Among them, 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.

[0049] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned forward prediction method for bubble pulsation pressure wavelets in shallow waters.

[0050] 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 prediction method for bubble pulsation pressure wavelets in shallow waters.

[0051] The beneficial effects of the present invention are as follows: the present invention proposes a forward prediction method for bubble pulsation pressure sub-waves in shallow waters, which can quickly predict large-scale bubble pulsation pressure underwater; corrects the buoyancy parameter deviation induced by the non-spherical deformation of the bubble, and adopts the mirror bubble method to calculate the Kelvin impulse theory solution, which can quickly predict the direction of large-scale bubble jet underwater, providing a theoretical basis and basic technical support for engineering construction; compared with the existing domain grid numerical simulation prediction method, the present invention improves the forward prediction efficiency, reduces the cost, avoids the problem of exponential increase in calculation time and increase in discrete error due to the influence of underwater structures, and can also simulate the late stage of bubble rebound. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 This is a flow chart of a method for forward prediction of bubble pulsation pressure wavelets in shallow waters according to the present invention;

[0053] Figure 2 This 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 wavelet in shallow water according to the present invention;

[0054] Figure 3 This 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 wavelet in shallow water according to the present invention;

[0055] Figure 4The present invention is a forward prediction method for bubble pulsation pressure wavelet in shallow waters, which is an effect diagram of a time history curve of bubble pulsation pressure after taking into account the shallow water boundary effect. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0057] Reference Figure 1 As shown, a forward modeling prediction method for bubble pulsation pressure wavelet in shallow waters, the forward modeling prediction method for bubble pulsation pressure wavelet in shallow waters includes the following steps:

[0058] S100, input the initial conditions of the bubble, environmental parameters and the position of the pressure measuring point;

[0059] 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;

[0060] 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;

[0061] S400, substituting the correction term expression into the Keller-Miksis equation, advancing the time from the initial bubble condition, and recording the time history of the bubble radius, bubble pulsation velocity, bubble translation velocity, and bubble surface enthalpy difference;

[0062] 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 of each physical quantity;

[0063] S600: Based on the Bernoulli equation, calculate and output the bubble pulsation pressure time history curve at the pressure measuring point.

[0064] Specifically, the initial conditions, environmental parameters and the position of the pressure measuring point of the bubble are input through step S100, providing a comprehensive data basis for subsequent predictions. In S200, whether the boundary influence 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 correction term expression is substituted into the Keller-Miksis equation for time advancement in step S400, which 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, thereby improving the details of the prediction. Finally, S600 calculates and outputs the bubble pulsation pressure time history curve at the pressure measuring point based on the Bernoulli equation, realizing the forward prediction of the bubble pulsation pressure sub-wave in shallow waters. This method can rapidly predict the pulsating pressure of large-scale underwater bubbles, correct for buoyancy parameter deviations induced by the non-spherical deformation of bubbles, and employ the mirror bubble method to calculate the Kelvin impulse theory solution, thereby rapidly predicting the direction of large-scale underwater bubble jets. This provides an important theoretical basis and fundamental technical support for engineering construction. Furthermore, compared to existing domain grid numerical simulation prediction methods, this method improves forward prediction efficiency, reduces computational costs, and avoids the problems of exponentially increased computational time and increased discrete errors caused by incorporating the effects of underwater structures. It can also simulate the late stage of bubble rebound, greatly enhancing the practicality and reliability of predictions.

[0065] 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 density of the environmental fluid, the depth of the sea area, 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.

[0066] Furthermore, in S200, whether the water boundary affects the bubble pulsating pressure is considered based on the ratio between the water boundary and the maximum bubble radius, and whether the influence of the water boundary needs to be considered is determined based on the following parameter ranges:

[0067] d f ≤6R max (1)

[0068] d w ≤4R max (2)

[0069] 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.

[0070] Specifically, the so-called "ratio between the distance 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.

[0071] In S200 , the maximum size of the bubble is obtained by the initial radius of the bubble and the subsequent dynamic change law under specific conditions.

[0072] Specifically, in S200, the effect of the water boundary on the bubble's pulsating pressure is considered based on the ratio of the bubble's distance to the water surface, the water bottom, and the maximum radius. A parameter range is defined to determine whether boundary effects should be considered, and the method for obtaining the maximum bubble size is clarified. This allows for a more accurate determination of whether boundary effects should be considered, making the forward prediction method more targeted, avoiding unnecessary calculations, and determining the maximum bubble size based on scientific and reasonable rules, providing an accurate basis for subsequent steps.

[0073] 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:

[0074]

[0075] Where ρ is the density of water, P0 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, R0 is the initial radius of the bubble, κ is the adiabatic coefficient, P ∞ is the hydrostatic pressure at the location of the bubble.

[0076] 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.

[0077] 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.

[0078] Furthermore, 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:

[0079]

[0080] Where o is the position vector of the bubble, o i is the position vector of the i-th mirror bubble, nf and n w are the unit external normal vectors of the water surface and bottom respectively;

[0081] 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 and the underwater structure. The position vector contained in each item is calculated as follows:

[0082]

[0083] According to the above position vector, the bubble center background pressure correction term is calculated as follows:

[0084]

[0085] 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:

[0086]

[0087] Where P is the pressure on the bubble surface, P ∞ is the hydrostatic pressure at the location of the bubble;

[0088] The bubble surface pressure P in formula (6) is calculated based on the state equation under the adiabatic assumption:

[0089]

[0090] Where P0 is the initial internal pressure of the bubble, R0 is the initial radius of the bubble, κ is the adiabatic coefficient, P v is the saturated vapor pressure.

[0091] Specifically, in S300, this embodiment provides detailed correction term settings for different scenarios. When considering only the effects of the water surface and bottom, the number of correction terms is determined to be eight, and a corresponding expression is provided. This expression is based on factors such as the bubble's position vector, the mirror bubble's position vector, and the unit external normal vector. This allows for relatively accurate correction of the background pressure at the bubble's center under these relatively simple boundary conditions, taking into account the main influencing factors.

[0092] When structures are present near the bubble, the number of correction terms is further determined to be 17, along with the corresponding expressions. This is because the presence of structures can have an additional effect on the bubble's behavior. These expressions allow for more precise adjustment of the correction to the background pressure at the bubble's center.

[0093] The proposed calculation method for the background pressure correction term at the bubble center comprehensively considers multiple physical quantities, including water density, the distance between the bubble and the pressure measurement point, the first-order time derivative of the bubble radius, and the enthalpy difference at the bubble surface. This comprehensive calculation method can more accurately reflect the actual physical process, making the correction results more consistent with actual conditions.

[0094] 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 bubble pulsation pressure.

[0095] Furthermore, in S400, the Keller-Miksis equation used to describe bubble pulsation is:

[0096]

[0097] 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,

[0098] 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:

[0099]

[0100] Based on the initial conditions of the bubble and equation (9), the time evolution of the bubble radius, bubble pulsation velocity, and bubble surface enthalpy difference is recorded. The time evolution of the bubble radius is as follows: Figure 2 As shown. The time step is calculated as follows

[0101]

[0102] Where C0 is the time step empirical coefficient, which is taken as 0.01.

[0103] 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:

[0104]

[0105] in is the translational acceleration of the bubble, u is the translational velocity of the bubble, g is the acceleration due to gravity, C d is the drag force coefficient,

[0106] 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. The temporal change process of the bubble displacement is as follows: Figure 3 shown.

[0107] Specifically, the Keller-Miksis equation, specified in S400, is a key theoretical foundation for describing bubble pulsation. It provides a fundamental framework for understanding the dynamic behavior of bubbles, enabling us to study their behavior under different conditions based on this equation. The proposed method for calculating the second-order time derivative of the bubble radius, after accounting for the influence of the water boundary, further refines this theoretical model. This precise calculation method allows for more accurate capture of the changes in bubble radius under boundary influences. This is crucial for studying the pulsating characteristics of bubbles, as changes in bubble radius directly affect the pressure inside the bubble and its interaction with the surrounding environment. The defined time step calculation method is also a key contribution of this embodiment. A reasonable time step selection ensures that numerical calculations accurately reflect the dynamic process of the bubble while avoiding the loss of important details due to an excessively large time step or the excessive computational effort due to an excessively small time step. This scientifically sound time step calculation method ensures the efficiency and accuracy of the entire calculation process. Furthermore, the method for calculating the bubble translational velocity is equally significant. It allows us to understand that bubbles in water exhibit not only 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 is indispensable for predicting the impact of the bubble on the surrounding environment and the ultimate bubble pulsation pressure prediction.

[0108] 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 bubble center 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.

[0109] 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 the physical quantity propagation, making the prediction result more consistent with the actual physical process.

[0110] Furthermore, 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:

[0111]

[0112] Among them, 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.

[0113] Specifically, in S600, a bubble pulsating pressure time history curve at the pressure measurement point is calculated and output based on the Bernoulli equation. This embodiment accurately calculates the bubble pulsating pressure time history curve using the Bernoulli equation based on the various parameters and calculation results obtained in the previous steps, thereby intuitively presenting the dynamic changes in bubble pulsating pressure. This provides critical data support for engineering applications and further enhances the practicality and value of the entire prediction method.

[0114] A storage medium stores a computer program, which, when executed by a processor, implements the above-mentioned forward prediction method for bubble pulsation pressure wavelets in shallow waters.

[0115] Specifically, this embodiment provides a storage medium storing a computer program that, when executed by a processor, implements the prediction method described herein. This embodiment provides a medium for implementing the prediction method, enabling the method to be applied and implemented on the storage medium via the computer program. This facilitates the promotion and use of the technology and provides software-level support and assurance for bubble pulsation pressure prediction in practical engineering applications.

[0116] 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 prediction method for bubble pulsation pressure wavelets in shallow waters.

[0117] Specifically, this embodiment provides a computer device comprising a memory, a processor, and a related computer program, capable of implementing the prediction method described herein. This embodiment integrates the prediction method into the computer device, enabling efficient operation of the method, improving computational speed and processing power. This provides a hardware foundation and guarantee for accurate prediction of bubble pulsation pressure, thereby promoting the application and implementation of this technology in practical engineering projects.

[0118] This invention, based on Kelvin impulse theory, corrects for buoyancy parameter deviations caused by non-spherical bubble deformation. Using the mirror bubble method, the Kelvin impulse theory solution is calculated for large-scale bubbles under the influence of different water boundaries. This series of operations achieves the goal of rapidly predicting the direction of large-scale underwater bubble jets, providing solid theoretical support and fundamental technical assurance for engineering construction.

[0119] 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 application of the mirror bubble method cleverly takes into account the boundary conditions of different water areas, 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, during deep-sea resource exploration, it can help construction personnel understand in advance the possible impact of bubble jets on exploration equipment and personnel, so that they can 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.

[0120] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device that includes 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 document are all referenced to the placement states shown in the accompanying drawings.

[0121] 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 various embodiments of the present invention.

Claims

1. A forward prediction method for bubble pulsation pressure wavelets in shallow waters, characterized in that: The forward prediction method for bubble pulsation pressure wavelet 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. Based on the distance between the bubble and the water boundary, design an expression for the background pressure correction term at the bubble center. Under the influence of the water surface and the bottom, the number of correction terms is 8, each of which contains a position vector, determined by the following formula: 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 and the underwater structure. The position vector contained in each item is calculated as follows: 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 based on 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 adiabatic coefficient, P v is the saturated vapor pressure; S400, substituting the correction term expression into the Keller-Miksis equation, advancing the time from the initial bubble condition, 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 of each physical quantity; S600, based on the Bernoulli equation, calculates and outputs the bubble pulsation pressure history curve at the pressure measuring point, calculated as follows: Among them, 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.

2. A forward prediction method for bubble pulsation pressure wavelets 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 where the bubble is located, the density of the ambient fluid, the depth of the sea area, the distance between the water area boundary and the bubble, the free surface reflection coefficient and the atmospheric pressure.

3. A forward prediction method for bubble pulsation pressure wavelets in shallow waters according to claim 2, characterized in that: In S200, whether the water boundary affects the bubble pulsating pressure is considered based on the ratio between the water boundary and the maximum bubble radius, and whether the influence of the water boundary needs to be considered is determined based on the following parameter ranges: d f ≤6R max (1), or 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 wavelets 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. The forward prediction method for bubble pulsation pressure wavelet in shallow water according to claim 4, 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 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 formula (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 according to the following formula: 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 acceleration due to gravity, 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.

6. A forward prediction method for bubble pulsation pressure wavelets in shallow waters according to claim 5, 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 bubble center 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.

7. 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 wavelets in shallow waters according to any one of claims 1 to 6 is implemented.

8. 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 wavelets in shallow waters as described in any one of claims 1 to 6.

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