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.

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 Bubble dynamics in a compressible liquid in contact with a rigid boundary

2015 ◽  
Vol 5 (5) ◽  
pp. 20150048 ◽  
Author(s):  
Qianxi Wang ◽  
Wenke Liu ◽  
A. M. Zhang ◽  
Yi Sui
Keyword(s):  
Shock Waves ◽  
Thin Layer ◽  
High Speed ◽  
Bubble Radius ◽  
Time History ◽  
Bubble Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Imaging Method ◽  
Rigid Boundary

A bubble initiated near a rigid boundary may be almost in contact with the boundary because of its expansion and migration to the boundary, where a thin layer of water forms between the bubble and the boundary thereafter. This phenomenon is modelled using the weakly compressible theory coupled with the boundary integral method. The wall effects are modelled using the imaging method. The numerical instabilities caused by the near contact of the bubble surface with the boundary are handled by removing a thin layer of water between them and joining the bubble surface with its image to the boundary. Our computations correlate well with experiments for both the first and second cycles of oscillation. The time history of the energy of a bubble system follows a step function, reducing rapidly and significantly because of emission of shock waves at inception of a bubble and at the end of collapse but remaining approximately constant for the rest of the time. The bubble starts being in near contact with the boundary during the first cycle of oscillation when the dimensionless stand-off distance γ = s / R m < 1, where s is the distance of the initial bubble centre from the boundary and R m is the maximum bubble radius. This leads to (i) the direct impact of a high-speed liquid jet on the boundary once it penetrates through the bubble, (ii) the direct contact of the bubble at high temperature and high pressure with the boundary, and (iii) the direct impingement of shock waves on the boundary once emitted. These phenomena have clear potential to damage the boundary, which are believed to be part of the mechanisms of cavitation damage.

Growth and collapse of cavitation bubbles near a curved rigid boundary

2002 ◽  
Vol 466 ◽  
pp. 259-283 ◽  
Author(s):  
Y. TOMITA ◽  
P. B. ROBINSON ◽  
R. P. TONG ◽  
J. R. BLAKE
Keyword(s):  
Boundary Integral ◽  
Bubble Collapse ◽  
Liquid Jet ◽  
High Speed Photography ◽  
Bubble Motion ◽  
Mean Flow ◽  
Rigid Boundary ◽  
Convex Boundary ◽  
Cavitation Bubbles ◽  
Toroidal Bubble

Laser-induced cavitation bubbles near a curved rigid boundary are observed experimentally using high-speed photography. An image theory is applied to obtain information on global bubble motion while a boundary integral method is employed to gain a more detailed understanding of the behaviour of a liquid jet that threads a collapsing bubble, creating a toroidal bubble. Comparisons between the theory and experiment show that when a comparable sized bubble is located near a rigid boundary the bubble motion is significantly influenced by the surface curvature of the boundary, which is characterized by a parameter ζ, giving convex walls for ζ < 1, concave walls for ζ > 1 and a flat wall when ζ = 1. If a boundary is slightly concave, the most pronounced migration occurs at the first bubble collapse. The velocity of a liquid jet impacting on the far side of the bubble surface tends to increase with decreasing parameter ζ. In the case of a convex boundary, the jet velocity is larger than that generated in the flat boundary case. Although the situation considered here is restricted to axisymmetric motion without mean flow, this result suggests that higher pressures can occur when cavitation bubbles collapse near a non-flat boundary. Bubble separation, including the pinch-off phenomenon, is observed in the final stage of the collapse of a bubble, with the oblate shape at its maximum volume attached to the surface of a convex boundary, followed by bubble splitting which is responsible for further bubble proliferation.

The formation of toroidal bubbles upon the collapse of transient cavities

1993 ◽  
Vol 251 ◽  
pp. 79-107 ◽  
Author(s):  
J. P. Best
Keyword(s):  
High Speed ◽  
Pressure Field ◽  
Boundary Integral ◽  
Liquid Jet ◽  
Rigid Boundary ◽  
Damage Mechanisms ◽  
Cavity Collapse ◽  
It Impacts ◽  
Toroidal Bubble ◽  
Flow Domain

A spectacular feature of transient cavity collapse in the neighbourhood of a rigid boundary is the formation of a high-speed liquid jet that threads the bubble and ultimately impacts upon the side of the bubble nearest to the boundary. The bubble then evolves into some toroidal form, the flow domain being doubly connected. In this work, the motion of the toroidal bubble is computed by connecting the jet tip to the side of the bubble upon which it impacts. This connection is via a cut introduced into the flow domain and across which the potential is discontinuous, the value of this discontinuity being equal to the circulation in the flow. A boundary integral algorithm is developed to account for this geometry and some example computations are presented. Consideration of the pressure field in the fluid has implications for possible damage mechanisms to structures due to nearby cavity collapse.

Tropylium Salt Promoted Hydroboration Reactions: Mechanistic Insights via Experimental and Computational Studies

2021 ◽  
Author(s):  
Nhan Nu Hong Ton ◽  
Binh Khanh Mai ◽  
Thanh Vinh Nguyen
Keyword(s):  
Dft Calculations ◽  
Lewis Acids ◽  
Experimental Studies ◽  
Cross Coupling ◽  
Computational Studies ◽  
Metal Free ◽  
Hydride Abstraction ◽  
Novel Method ◽  
Tropylium Salts

Abstract: Hydroboration reaction of alkynes is one of the most synthetically powerful tools to access organoboron compounds, versatile precursors for cross coupling chemistry. This type of reaction has traditionally been mediated by transition metal or main group catalysts. Herein, we report a novel method using tropylium salts, typically known as organic oxidants and Lewis acids, to efficiently promote the hydroboration reaction of alkynes. A broad range of vinylboranes can be easily accessed via this metal-free protocol. Similar hydroboration reactions of alkenes and epoxides can also be efficiently catalyzed by the same tropylium catalysts. Experimental studies and DFT calculations suggested that the reaction follows an uncommon mechanistic paradigm, which is triggered by a hydride abstraction of pinacolborane with tropylium ion. This is followed by a series of <i>in situ</i> counterion-activated substituent exchanges to generate boron intermediates that promote the hydroboration reaction.

scholarly journals Microbubble dynamics in a viscous compressible liquid near a rigid boundary

2019 ◽  
Vol 84 (4) ◽  
pp. 696-711 ◽  
Author(s):  
Qianxi Wang ◽  
WenKe Liu ◽  
David M Leppinen ◽  
A D Walmsley
Keyword(s):  
Potential Flow ◽  
Stokes Equations ◽  
Bubble Surface ◽  
Compressible Liquid ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Viscous Effects ◽  
Rigid Boundary ◽  
Viscous Potential Flow ◽  
Viscous Compressible Liquid

Abstract This paper is concerned with microbubble dynamics in a viscous compressible liquid near a rigid boundary. The compressible effects are modelled using the weakly compressible theory of Wang & Blake (2010, Non-spherical bubble dynamics in a compressible liquid. Part 1. Travelling acoustic wave. J. Fluid Mech., 730, 245–272), since the Mach number associated is small. The viscous effects are approximated using the viscous potential flow theory of Joseph & Wang (2004, The dissipation approximation and viscous potential flow. J. Fluid Mech., 505, 365–377), because the flow field is characterized as being an irrotational flow in the bulk volume but with a thin viscous boundary layer at the bubble surface. Consequently, the phenomenon is modelled using the boundary integral method, in which the compressible and viscous effects are incorporated into the model through including corresponding additional terms in the far field condition and the dynamic boundary condition at the bubble surface, respectively. The numerical results are shown in good agreement with the Keller–Miksis equation, experiments and computations based on the Navier–Stokes equations. The bubble oscillation, topological transform, jet development and penetration through the bubble and the energy of the bubble system are simulated and analysed in terms of the compressible and viscous effects.

Numerical Prediction of Various Cavitation Erosion Mechanisms

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Ignacijo Biluš ◽  
Marko Hočevar ◽  
Matevž Dular ◽  
Luka Lešnik
Keyword(s):  
Experimental Work ◽  
High Speed ◽  
Cavitation Erosion ◽  
Cavitating Flow ◽  
Numerical Prediction ◽  
Quantitative Prediction ◽  
Navier Stokes ◽  
Erosion Mechanisms ◽  
Recent Experimental Work ◽  
Collapse Phase

Abstract Numerical prediction of cavitation erosion is a great scientific and technological challenge. In the past, many attempts were made—many successful. One of the issues when a comparison between a simulation and erosion experiments is made, is the great difference in time scale. In this work, we do not attempt to obtain quantitatively accurate predictions of erosion process but concentrate qualitatively on cavitation mechanisms with quantitative prediction of pressure pulses which lead to erosion. This is possible, because of our recent experimental work on simultaneous observation of cavitating flow and cavitation erosion by high speed cameras. In this study, the numerical simulation was used to predict details of the cavitation process during the vapor collapse phase. The fully compressible, cavitating flow simulations were performed to resolve the formation of the pressure waves at cavitation collapse. We tried to visualize the mechanisms and dynamics of vapor structures during collapse phase at the Venturi geometry. The obtained results show that unsteady Reynolds-averaged Navier–Stokes (URANS) simulation of cavitation is capable of reproducing four out of five mechanisms of cavitation erosion, found during experimental work.

Experimental and Computational Studies of Chaotic Stirring in Complex 3D Flows

2002 ◽  
Author(s):  
Fotis Sotiropoulos ◽  
Tahirih C. Lackey ◽  
S. Casey Jones
Keyword(s):  
Swirling Flow ◽  
Experimental Studies ◽  
Computational Studies ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Numerical Studies ◽  
Helical Vortices ◽  
3D Flows ◽  
Confined Flows ◽  
Particle Paths

Recent progress in experimental and computational studies of complex chaotically advected 3D flows is reviewed for the confined swirling flow in a cylindrical container with a rotating bottom and the open flow in a helical static mixer. The concept of Lagrangian averaging along particle paths, whose theoretical foundation stems from ergodic theory, is proposed as a powerful tool for constructing Poincare´ maps in numerical studies of confined flows. The same concept has also been employed to develop the first non-intrusive experimental technique for constructing Poincare´ maps in complex 3D flows. The potential of these ergodic concepts is demonstrated in computational and experimental studies for the confined swirling flow. Numerical computations for the helical mixer flow show that increasing the Reynolds number from Re = 100 to 500 leads to the appearance of unmixed islands in the flow. The mechanism that leads to the formation of such islands is shown to be linked to the growth of coherent helical vortices in the flow.

scholarly journals Approximate methods for modelling cavitation bubbles near boundaries

1990 ◽  
Vol 41 (1) ◽  
pp. 1-44 ◽  
Author(s):  
A. Kucera ◽  
J.R. Blake
Keyword(s):  
Boundary Integral ◽  
Valuable Insight ◽  
Flat Plates ◽  
Confined Geometries ◽  
Rigid Boundary ◽  
Approximate Methods ◽  
Boundary Integral Methods ◽  
Integral Methods ◽  
Cavitation Bubbles ◽  
Insight Into

Approximate methods are developed for modelling the growth and collapse of clouds of cavitation bubbles near an infinite and semi-infinite rigid boundary, a cylinder, between two flat plates and in corners and near edges formed by planar boundaries. Where appropriate, comparisons are made between this approximate method and the more accurate boundary integral methods used in earlier calculations. It is found that the influence of nearby bubbles can be more important than the presence of boundaries. In confined geometries, such as a cylinder, or a cloud of bubbles, the effect of the volume change due to growth or collapse of the bubble can be important at much larger distances. The method provides valuable insight into bubble cloud phenomena.

Study on splitting of a toroidal bubble near a rigid boundary

2015 ◽  
Vol 27 (6) ◽  
pp. 062102 ◽  
Author(s):  
A. M. Zhang ◽  
S. Li ◽  
J. Cui
Keyword(s):  
Rigid Boundary ◽  
Toroidal Bubble
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