Bubble Simulation Using Level Set-Boundary Element Method

In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We propose a formulation for the update of a potential function in the level set context. This potential function is non-physical off the bubble surface but consistent with the physics on the bubble surface. We consider only axisymmetric cavitation bubbles in this paper. Included in the paper are some preliminary results and findings.Singapore-MIT Alliance (SMA

A refined numerical investigation of a large equivalent shallow-depth underwater explosion

The large equivalent shallow-depth explosion problem is very significant in the field of naval architecture and ocean engineering, as such explosions can be used to attack and demolish ships and anti-ship missiles. In the current work, a refined numerical study of the flow-field characteristics of a large equivalent shallow-depth explosion is carried out using a self-developed Eulerian finite element solver. Firstly, the numerical model is validated against theoretical results and a small equivalent explosion test in a tank. The numerical results are found to agree well with the theoretical and experimental results. In the next step, the cavitation cut-off effect is added to the underwater explosion model, and the cavitation phenomenon is quantitatively analyzed through the flow-field pressure. In addition, the dynamic characteristics of the bubble and water hump under various initial conditions for different stand-off parameters are analyzed. The effect of gravity on these physical processes is also discussed. The bubble pulsation period, taking into account the free surface effect, is then quantitatively studied and compared with Cole's experimental formula for an underwater explosion. Overall, when the stand-off parameter > 2, the influence of the free surface on the empirical period of the bubble is not significant. Our investigation provides broad insights into shallow-depth underwater explosions from theoretical, experimental, and numerical perspectives

SPH-BEM simulation of underwater explosion and bubble dynamics near rigid wall

A process of underwater explosion of a charge near a rigid wall includes three main stages: charge detonation, bubble pulsation and jet formation. A smoothed particle hydrodynamics (SPH) method has natural advantages in solving problems with large deformations and is suitable for simulation of processes of charge detonation and jet formation. On the other hand, a boundary element method (BEM) is highly efficient for modelling of the bubble pulsation process. In this paper, a hybrid algorithm, fully utilizing advantages of both SPH and BEM, was applied to simulate the entire process of free and near-field underwater explosions. First, a numerical model of the free-field underwater explosion was developed, and the entire explosion process– from the charge detonation to the jet formation–was analysed. Second, the obtained numerical results were compared with the original experimental data in order to verify the validity of the presented method. Third, a SPH model of underwater explosion for a column charge near a rigid wall was developed to simulate the detonation process. The results for propagation of a shock wave are in good accordance with the physical observations. After that, the SPH results were employed as initial conditions for the BEM to simulate the bubble pulsation. The obtained numerical results show that the bubble expanded at first and then shrunk due to a differences of pressure levels inside and outside it. Here, a good agreement between the numerical and experimental results for the shapes, the maximum radius and the movement of the bubble proved the effectiveness of the developed numerical model. Finally, the BEM results for a stage when an initial jet was formed were used as initial conditions for the SPH method to simulate the process of jet formation and its impact on the rigid wall. The numerical results agreed well with the experimental data, verifying the feasibility and suitability of the hybrid algorithm. Besides, the results show that, due to the effect of the Bjerknes force, a jet with a high speed was formed that may cause local damage to underwater structures

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method [109]. A nodally perfect matched definition of the interface is used [57, 25] and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data.El desarrollo de métodos eficientes para modelar la dinámica de implosión presenta varios desafíos. El primero es una representación eficaz de la dinámica del sistema acoplado de aire-agua. El segundo es que el método tiene que permitir una detección exacta o un seguimiento adecuado de la interfase entre ambas fases. Por último el método tiene que ser capaz de resolver cualquier choque que podría generar en el aire o en el agua, sobre todo en la última fase del colapso. Nosotros presentamos un método numérico compresible y totalmente Lagrangiano para simular la implosión bajo el agua. Tanto el aire como el agua se consideran compresibles y las ecuaciones Lagrangianos para la hidrodinámica del choque se estabilizan mediante un método multiescala que es variacionalmente consistente [109]. Se utiliza una definición de interfase que coincide perfectamente con los nodos [57, 25]. Ésta, nos facilita duplicar eficazmente las variables cinéticas como la presión y la densidad en los nodos de la interfase. Con el fin de obtener suficiente resolución alrededor de la interfase, la malla se genera de forma adaptativa y respetando la posición de la interfase. A continuación el método desarrollado se utiliza para simular la implosión bajo el agua de una burbuja cilíndrica del tamaño de un centímetro. Varios fenómenos se han capturado durante el colapso: un ciclo inmediato de colapso-crecimiento de la burbuja que ocurre en un espacio (0.3mm) y tiempo (0.1ms) bastante limitado, aparición de inestabilidades de tipo Rayleigh-Taylor en la interfase y formaron de varias ondas de choque que viajan tanto en el agua como en el aire. Después, seguimos el desarrollo del método para modelar la implosión bajo el agua de un contenedor metálico considerando una interacción monolítica de fluido y estructura. El cilindro de aluminio, que a su vez contiene aire a presión atmosférica y está rodeada de agua en alta presión, se modelando con elementos de lámina de tres nodos y sin grados de libertad de rotación. El cilindro se somete a deformaciones transitorias suficientemente rápidos y enormes hasta llegar a colapsar. Un nuevo modelo elástico de contacto sin considerar la fricción se ha desarrollado para detectar el contacto y calcular las fuerzas en el dominio discretizado entre las superficies medianas de las laminas. Dos esquemas temporales están considerados, uno es implícito utilizando el método de Bossak y otro es explícito utilizando Forward Euler. Al final los resultados de ambos casos se comparan con los resultados experimentales

A compressible Lagrangian framework for the simulation of underwater implosion problems

The development of efficient algorithms to understand implosion dynamics presents a number of challenges. The foremost challenge is to efficiently represent the coupled compressible fluid dynamics of internal air and surrounding water. Secondly, the method must allow one to accurately detect or follow the interface between the phases. Finally, it must be capable of resolving any shock waves which may be created in air or water during the final stage of the collapse. We present a fully Lagrangian compressible numerical framework for the simulation of underwater implosion. Both air and water are considered compressible and the equations for the Lagrangian shock hydrodynamics are stabilized via a variationally consistent multiscale method. A nodally perfect matched definition of the interface is used and then the kinetic variables, pressure and density, are duplicated at the interface level. An adaptive mesh generation procedure, which respects the interface connectivities, is applied to provide enough refinement at the interface level. This framework is then used to simulate the underwater implosion of a large cylindrical bubble, with a size in the order of cm. Rapid collapse and growth of the bubble occurred on very small spatial (0.3mm), and time (0.1ms) scales followed by Rayleigh-Taylor instabilities at the interface, in addition to the shock waves traveling in the fluid domains are among the phenomena that are observed in the simulation. We then extend our framework to model the underwater implosion of a cylindrical aluminum container considering a monolithic fluid-structure interaction (FSI). The aluminum cylinder, which separates the internal atmospheric-pressure air from the external high-pressure water, is modeled by a three node rotation-free shell element. The cylinder undergoes fast transient deformations, large enough to produce self-contact along it. A novel elastic frictionless contact model is used to detect contact and compute the non-penetrating forces in the discretized domain between the mid-planes of the shell. Two schemes are tested, implicit using the predictor/multi-corrector Bossak scheme, and explicit, using the forward Euler scheme. The results of the two simulations are compared with experimental data

3D full coupling model for strong interaction between a pulsating bubble and a movable sphere

In this study, we establish a full coupling model (FCM) to simulate strong bubble-sphere interactions based on a three-dimensional boundary integral method. Different from the conventional loose coupling model (LCM), FCM adopts several auxiliary functions to deal with the mutual dependence between the hydrodynamic force and the sphere acceleration. In addition, the weighted moving least square method, a mesh density control scheme and an adaptive mesh refinement scheme are implemented to improve the quality of mesh on the deformable bubble surface. To validate the present model, convergence tests on different mesh sizes and time steps are conducted at first. The numerical results are also compared with the axisymmetric model, in which consistent results have been achieved. We further make comparisons between the numerical results and those from several experiments under different boundary conditions. For weak interaction cases, both LCM and FCM can give the results that have good agreement with the experiment data. As the interaction effects become stronger, the advantage of the FCM over the LCM becomes increasingly obvious. Particularly, when the pulsating bubble is in contact with the sphere surface, the essential physical features of the experiments can be well reproduced by the FCM while the predictions by the LCM are significantly different from the experiment. The present 3D model can be further extended to study more complex underwater contact explosions, cavitation inception on a structure and airgun bubble dynamics

Scaling laws for jets of single cavitation bubbles

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter $\zeta$, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets ($\zeta<10^{-3}$) hardly pierce the bubble, but remain within it throughout the collapse and rebound. Intermediate jets ($10^{-3}<\zeta<0.1$) pierce the opposite bubble wall close to the last collapse phase and clearly emerge during the rebound. Strong jets ($\zeta>0.1$) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of $\zeta$, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets only depend on $\zeta$, not on the jet driver. In the same regime, the jet parameters are found to be well approximated by power-laws of $\zeta$, which we explain through analytical arguments

Computational Analysis of Bubble-Structure Interactions in Near-Field Underwater Explosion

The response of underwater structures to a near-field explosion is coupled with the dynamics of the explosion bubble and the surrounding water. This multiphase fluid-structure interaction process is investigated using a model problem that features the yielding and collapse of a thin-walled aluminum cylinder. A recently developed computational framework that couples a compressible fluid dynamics solver with a structural dynamics solver is employed. The fluid-structure and liquid-gas interfaces are tracked using embedded boundary and level set methods. The conservation law across the interfaces is enforced by solving one-dimensional bimaterial Riemann problems. The initial pressure inside the explosion bubble is varied by two orders of magnitude in different test cases. Three different modes of collapse are discovered, including an horizontal collapse (i.e. with one lobe extending towards the explosive charge) that appears counterintuitive, yet has been observed in previous laboratory experiments. Because of the transition of modes, the time it takes for the structure to reach self-contact does not decrease monotonically as the explosion magnitude increases. The flow fields, the bubble dynamics, and the transient structural deformation are visualized to elucidate the cause of each collapse mode and the mode transitions. The result suggests that the pressure pulse resulting from the contraction of the explosion bubble has significant effect on the structure's collapse. The phase difference between the structural vibration and bubble oscillation influences the structure's mode of collapse. Furthermore, the transient structural deformation has clear effect on the bubble dynamics, leading to a two-way interaction. A liquid jet that points away from the structure is observed. Compared to the liquid jets produced by bubbles collapsing near a rigid wall, this jet is in the opposite direction