On the boundary integral method for the rebounding bubble

2007 ◽  
Vol 570 ◽  
pp. 407-429 ◽  
Author(s):  
M. LEE ◽  
E. KLASEBOER ◽  
B. C. KHOO
Keyword(s):  
Energy Loss ◽  
Integral Method ◽  
Bubble Radius ◽  
Experimental Studies ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Bubble Collapse ◽  
Solid Boundary ◽  
Bubble System ◽  
Toroidal Bubble

The formation of a toroidal bubble towards the end of the bubble collapse stage in the neighbourhood of a solid boundary has been successfully studied using the boundary integral method. The further evolution (rebound) of the toroidal bubble is considered with the loss of system energy taken into account. The energy loss is incorporated into a mathematical model by a discontinuous jump in the potential energy at the minimum volume during the short collapse–rebound period accompanying wave emission. This implementation is first tested with the spherically oscillating bubble system using the theoretical Rayleigh–Plesset equation. Excellent agreement with experimental data for the bubble radius evolution up to three oscillation periods is obtained. Secondly, the incorporation of energy loss is tested with the motion of an oscillating bubble system in the neighbourhood of a rigid boundary, in an axisymmetric geometry, using a boundary integral method. Example calculations are presented to demonstrate the possibility of capturing the peculiar entity of a counterjet, which has been reported only in recent experimental studies.

scholarly journals Multi-oscillations of a bubble in a compressible liquid near a rigid boundary

2014 ◽  
Vol 745 ◽  
pp. 509-536 ◽  
Author(s):  
Qianxi Wang
Keyword(s):  
Cavitation Erosion ◽  
Bubble Radius ◽  
Experimental Studies ◽  
Classical Problem ◽  
Boundary Integral ◽  
Computational Studies ◽  
Rigid Boundary ◽  
Toroidal Bubble ◽  
Damped Oscillation ◽  
Collapse Phase

AbstractBubble dynamics near a rigid boundary are associated with wide and important applications in cavitation erosion in many industrial systems and medical ultrasonics. This classical problem is revisited with the following two developments. Firstly, computational studies on the problem have commonly been based on an incompressible fluid model, but the compressible effects are essential in this phenomenon. Consequently, a bubble usually undergoes significantly damped oscillation in practice. In this paper this phenomenon will be modelled using weakly compressible theory and a modified boundary integral method for an axisymmetric configuration, which predicts the damped oscillation. Secondly, the computational studies so far have largely been concerned with the first cycle of oscillation. However, a bubble usually oscillates for a few cycles before it breaks into much smaller ones. Cavitation erosion may be associated with the recollapse phase when the bubble is initiated more than the maximum bubble radius away from the boundary. Both the first and second cycles of oscillation will be modelled. The toroidal bubble formed towards the end of the collapse phase is modelled using a vortex ring model. The repeated topological changes of the bubble are traced from a singly connected to a doubly connected form, and vice versa. This model considers the energy loss due to shock waves emitted at minimum bubble volumes during the beginning of the expansion phase and around the end of the collapse phase. It predicts damped oscillations, where both the maximum bubble radius and the oscillation period reduce significantly from the first to second cycles of oscillation. The damping of the bubble oscillation is alleviated by the existence of the rigid boundary and reduces with the standoff distance between them. Our computations correlate well with the experimental data (Philipp & Lauterborn, J. Fluid Mech., vol. 361, 1998, pp. 75–116) for both the first and second cycles of oscillation. We have successively reproduced the bubble ring in direct contact with the rigid boundary at the end of the second collapse phase, a phenomenon that was suggested to be one of the major causes of cavitation erosion by experimental studies.

The Boundary Integral Method Applied to Non-Spherical Cavitation Bubble Growth and Collapse Close to a Rigid Boundary

2015 ◽  
Author(s):  
Ali Alhelfi ◽  
Bengt Sunden
Keyword(s):  
Cavitation Bubble ◽  
Integral Method ◽  
Bubble Dynamics ◽  
Boundary Integral ◽  
Solid Surfaces ◽  
Boundary Integral Method ◽  
Bubble Collapse ◽  
Surface Erosion ◽  
Rigid Boundary ◽  
Cavitation Phenomenon

Recently much attention has been paid to studies concerning bubble dynamics in the cavitation phenomena and this topic has been the subject of many research works. In fact, the simulation of non-spherical bubble dynamics and its interaction with solid boundaries have received much less attention due to the complexity of the problem. One of the main reasons of the structural damages in the cavitation phenomenon is due to the formation of micro jets generated due to the bubble collapse and impinging on the solid surfaces or boundaries. The boundary integral method (BIM) based on Green’s function is used to model the oscillation and collapse of a cavitation bubble close to a rigid boundary. The liquid is considered to be incompressible, inviscid, and irrational around the bubble. These assumptions satisfy the conditions for the Laplacian equation. The theory permits one to predict correctly the interaction between the bubble and the rigid boundary, which is of great importance in the study of cavitation damage due to a bubble collapsing close to the boundaries. The results reveal that the amplitude of bubble oscillation depends on the bubble location away from a rigid surface. Also, the theory for the cavitation bubble dynamics presented in this study has many advantages in various situations and might be helpful to understand effects of the cavitation phenomenon such as generation of excessive vibration, surface erosion and undesirable acoustic emission.

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