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.

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 Cavitation and bubble dynamics: the Kelvin impulse and its applications

2015 ◽  
Vol 5 (5) ◽  
pp. 20150017 ◽  
Author(s):  
John R. Blake ◽  
David M. Leppinen ◽  
Qianxi Wang
Keyword(s):  
Cavitation Bubble ◽  
High Speed ◽  
Bubble Dynamics ◽  
Clinical Medicine ◽  
Bubble Collapse ◽  
Rigid Boundary ◽  
Design Problems ◽  
Practical Applications ◽  
Wide Range ◽  
Naval Engineering

Cavitation and bubble dynamics have a wide range of practical applications in a range of disciplines, including hydraulic, mechanical and naval engineering, oil exploration, clinical medicine and sonochemistry. However, this paper focuses on how a fundamental concept, the Kelvin impulse, can provide practical insights into engineering and industrial design problems. The pathway is provided through physical insight, idealized experiments and enhancing the accuracy and interpretation of the computation. In 1966, Benjamin and Ellis made a number of important statements relating to the use of the Kelvin impulse in cavitation and bubble dynamics, one of these being ‘One should always reason in terms of the Kelvin impulse, not in terms of the fluid momentum…’. We revisit part of this paper, developing the Kelvin impulse from first principles, using it, not only as a check on advanced computations (for which it was first used!), but also to provide greater physical insights into cavitation bubble dynamics near boundaries (rigid, potential free surface, two-fluid interface, flexible surface and axisymmetric stagnation point flow) and to provide predictions on different types of bubble collapse behaviour, later compared against experiments. The paper concludes with two recent studies involving (i) the direction of the jet formation in a cavitation bubble close to a rigid boundary in the presence of high-intensity ultrasound propagated parallel to the surface and (ii) the study of a ‘paradigm bubble model’ for the collapse of a translating spherical bubble, sometimes leading to a constant velocity high-speed jet, known as the Longuet-Higgins jet.

Dynamics of bubbles near a rigid surface subjected to a lithotripter shock wave. Part 2. Reflected shock intensifies non-spherical cavitation collapse

2008 ◽  
Vol 616 ◽  
pp. 63-97 ◽  
Author(s):  
M. L. CALVISI ◽  
J. I. ILORETA ◽  
A. J. SZERI
Keyword(s):  
Shock Wave ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Bubble Collapse ◽  
Destructive Interference ◽  
Rigid Surface ◽  
Initial State ◽  
Rigid Boundary ◽  
Bony Tissue ◽  
Reflected Shock

In this paper we use the boundary integral method to model the non-spherical collapse of bubbles excited by lithotripter shock waves near a rigid boundary. The waves we consider are representative of those developed by shock wave lithotripsy or shock wave therapy devices, and the rigid boundaries we consider are representative of kidney stones and reflective bony tissue. This study differs from previous studies in that we account for the reflection of the incident wave and also the asymmetry of the collapse caused by the presence of the rigid surface. The presence of the boundary causes interference between reflected and incident waves. Quantities such as kinetic energy, Kelvin impulse and centroid translation are calculated in order to illuminate the physics of the collapse process. The main finding is that the dynamics of the bubble collapse depend strongly on the distance of the bubble relative to the wall when reflection is taken into account, but much less so when reflection is omitted from the model. The reflection enhances the expansion and subsequent collapse of bubbles located near the boundary owing to constructive interference between incident and reflected waves; however, further from the boundary, the dynamics of collapse are suppressed owing to destructive interference of these two waves. This result holds regardless of the initial radius of the bubble or its initial state at the time of impact with the lithotripter shock wave. Also, the work done by the lithotripter shock wave on the bubble is shown to predict strongly the maximum bubble volume regardless of the standoff distance and the presence or absence of reflection; furthermore, allowing for non-sphericity, these predictions match almost exactly those of a previously developed spherical model.

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