Study On The Nonlinear Interaction And Coalescence Of Multiple Bubbles

Multiple-bubbles interaction has wide applications in the naval architecture and ocean engineering,such as multiple underwater explosions,seabed exploration,water barrier,bubble curtain and so on.The existence of a bubble provides a special boundary condition to other bubbles.Therefore,comparing to the single bubble case,the dynamics of multiplebubbles collapse,no doubt,will change.The understanding of the interactions between multiple bubblesunder different boundaryconditionshas importantimplications for both fundamental studies and practical engineeringapplications.In this study,we have developed a numerical model for the nonlinear interaction between multiple bubblesbased on the Boundary Integral Method(BIM).This thesis focuses on some challenging problems,such as the coalescence of 3D bubbles,the interaction between multiple toroidal bubbles,the motion of free surface after jet impact and the fast algorithm for the interaction between bubbles with different scales.Detailed parametric studies are performed to understand the physical mechanisms.Firstly,the applications involving multiple-bubbles interaction in the naval architecture and ocean engineering are briefly introduced,and basic physical phenomena and their corresponding mechanisms are stated.Then,the latest developments concerning the multiple-bubbles interaction are summarized from the experimental,theoretical and numerical aspects.We noticed that there are some shortcomings and challenges with the current study ofthe bubble dynamics.For example,there are fewerstudies withthe multiple bubbles interaction than those with single bubble;in most published works,computations were restricted to the stage before jet impact;only a few numerical studies are concerned with the interaction between a toroidal bubble and a singly-connected one,the interaction between toroidal bubbles has never been considered;and there are few studies on the interaction between multiscale bubbles.In addition,the modelling for coalescence of 3D bubbles has not been established yet,which is mainly due to the difficulty with the large mesh deformation.Such a deformation arises when the multiple bubbles locating close to different boundaries.This thesis aims to provide a series of solution to some of the above mentioned problems.Based on the incompressible potential flow theory,the BIM is adopted to study the nonlinear interaction between multiple bubbles.After jet impact,a numerical model is established based on the ‘vortex ring model',and the single vortex ring model is extended to multiplevortex rings model in the present study.This model enables the simulation of the toroidal bubbles interaction.Since there are too many parameters involving within multiplebubbles interaction,we have first studied the interaction between two bubbles in free field.The effects of different parameters on the pressure load in the flow field are investigated.To vividly show the interaction between two equal-size bubbles,we have also performedcomputations with two other cases for comparison.The first case considers a single bubble with its size same as the two equal-size bubbles,while the second case deals with a big bubble with its energy equaling to the sum of two bubbles' energy.The motion of two bubbles near a rigid wall is also considered and the effect of the parameters on bubble collapse patterns is numerically investigated.In addition,the jet impact strengthened by out-of-phase bubble is studied,and the optimal parameters are given to provide reference for weapon design.If the distance between two bubbles is small enough,coalescence may occur in the expansion phase.The film thinning process during coalescence is dominated by inertia and viscosity can be safely ignored.We have developed a 3D coalescence model based on the BIM and some techniques have been used to deal with the topology.Meanwhile,the density potential method is improved to control the mesh quality.The results obtained based on the3 D numerical model agrees well with the ones based on the axisymmetric BIM model for axisymmetric cases and also the experimental results captured by high-speed camera.Then we studied the bubble coalescence in three configurations and the influence of various dimensionless parameters is discussed.Some new phenomena are observed and their inherent physical mechanisms are revealed.The coalescence of three and four bubbles is also studied.Besides,the coalescence of two 3D bubbles near a rigid wall or free surface is modelled and the validity of our numerical model is confirmed by experimental observation.Finally,the influence of the relative position,the buoyancy parameter and the distance parameter on the coalescence is investigated.The long-time motion of free-surface spike induced by multiple bubbles draws our attention because of the practical application of water barrier.In experiments,the spike continues to risefor a long time after jet impact.Obvious evolution of the spike occurs and an interesting phenomenon called ‘crown spike'appears.A three dimensional model is developed to study thecrown spike induced by bubbles,and the validation is confirmed by comparing the experimental and numerical results for single-and two-bubbles cases.A parametric study is performed for to reveal the characteristics of free-surface spike in two-bubble cases.In addition,the interaction between three or more bubbles with free surface is discussed.It is found that if bubbles are arranged in a horizontal line,a tall and wide water wall can beformed and the defense range is extended.To further improve the defense effect,bubbles can be arranged in several arrays to form multiple water walls.We have also studied the interaction between a large-scale underwater explosion bubble and small-scale air bubbles.We first perform a mechanism study by considering the interaction between an oscillating bubble and an air bubble.It's found that the existence of an air bubble reduces the pressure peak caused by the oscillating bubble and the pulsation of the air bubble leads to the fluctuation in the pressure curve.However,the efficiencyfor the BIM applied to the interaction between an explosion bubble and a group of air bubbles is low.Therefore,we have combined the BIM and an improved Rayleigh-Plesset(RP)equation to model the interaction between bubbles with different scales.In some details,the BIM is adopted to simulate the non-spherical motion of the large-scale oscillating bubble and the improved RP equation is used to solve the pulsation of small-scale air bubbles.The induced pressure is calculated by considering the coupling effect.We have demonstrated that the results obtained with this combined method agree well with the ones obtained by using the BIM for all bubbles,and that and the computational cost of the combined technique is dramatically reduced.After that,the interaction between an oscillating bubble and a group of air bubbles is investigated by using the proposed BIM-RP model.It's found that the pressure peak decays to a larger extent when bubble curtain is perpendicular to the line connecting the oscillating bubble center and the measure point.More bubble curtains show better performance in the reduction of the pressure peak,and two bubble curtains are recommended considering the economic applicability.