Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Smith, Warren R.; Wang, Qianxi

doi:10.1063/1.4999940

Cited by 10 publications

(10 citation statements)

References 49 publications

(58 reference statements)

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“…In the past few decades, a large amount of works have been undertaken to understand the characteristics of bubble collapse [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Lauterborn recorded the process of a single bubble collapsing near a rigid wall, in which the shock wave emission was captured by a schlieren system [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the Collapse of Multiple Bubbles and the Energy Conversion during Bubble Collapse

Zhang

Deng

2019

Water

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This paper investigates numerically the collapses of both a single cavitation bubble and a cluster consisting of 8 bubbles, concerning mainly on the conversions between different forms of energy. Direct numerical simulation (DNS) with volume of fluid (VOF) method is applied, considering the detailed resolution of the vapor-liquid interfaces. First, for a single bubble near a solid wall, we find that the peak value of the wave energy, or equivalently the energy conversion rate decreases when the distance between the bubble and the wall is reduced. However, for the collapses of multiple bubbles, this relationship between the bubble-wall distance and the conversion rate reverses, implying a distinct physical mechanism. The evolutions of individual bubbles during the collapses of multiple bubbles are examined. We observe that when the bubbles are placed far away from the solid wall, the jetting flows induced by all bubbles point towards the cluster centre, while the focal point shifts towards the solid wall when the cluster is very close to the wall. We note that it is very challenging to consider thermal and acoustic damping mechanisms in the current numerical methods, which might be significant contributions to the energy budget, and we leave it open to the future studies.

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Section: Introductionmentioning

confidence: 99%

Numerical Study of the Collapse of Multiple Bubbles and the Energy Conversion during Bubble Collapse

Zhang

Deng

2019

Water

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“…(3) This model, together with our recent research on strongly nonlinear analysis (Smith & Wang 2017, 2018, 2021, is the basis of our objective to simulate bubble growth over many millions of cycles of oscillation.…”

Section: Discussionmentioning

confidence: 99%

A theoretical model for the growth of spherical bubbles by rectified diffusion

Smith

Wang

2022

J. Fluid Mech.

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Rectified diffusion is a bubble growth phenomenon that occurs in acoustic fields. Despite the existence of a well-established spherically symmetric mathematical model, theoretical results have been unsuccessful in reproducing the bubble growth even in the case of a single spherical bubble in the bulk. In the latter case, the influence of surfactants and acoustic microstreaming have been speculated as the explanation for this disagreement. In this article, an exact solution for the leading-order concentration of gas in the liquid is determined. Using this exact solution, the well-established mathematical model is reduced to a system of two ordinary differential equations for the spherical bubble radius and the mass of gas in the bubble. This simplified model predicts the rapid bubble growth observed in experiments of a single spherical bubble in the bulk. The new results show that the bubble growth is asymptotically larger than at later times when the mass flux is limited by the slow diffusion of gas in a much larger region of the liquid surrounding the bubble. The new results also show that this bubble growth is relatively insensitive to a reduction in surface tension.

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“…The assumption that the solvability conditions of the Navier-Stokes equations correspond to reformulations of (2.1)-(2.2) should be viewed in the context of the literature. We consider three nonlinear differential equations in which the first correction is not self-adjoint: KdV [33], the Rayleigh-Plesset equation [37] and the single-mode rate equations [36]. In all three cases, the null space of the adjoint equation may be entirely determined and the solvability conditions all correspond to reformulations of the original equations.…”

Section: Solvability Conditionsmentioning

confidence: 99%

Asymptotic analysis of the attractors in two-dimensional Kolmogorov flow

Smith

Wissink

2017

Eur. J. Appl. Math

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The high Reynolds-number structure of the laminar, chaotic and turbulent attractors is investigated in a two-dimensional Kolmogorov flow. The laminar attractors include the families of multi-phased travelling waves and quasi-periodic standing waves both of which form the backbone of the transition to a turbulent flow. At leading order, each laminar attractor under study is obtained by solving the Euler equations on a manifold subject to the appropriate periodicity and symmetry conditions. The manifold is determined by a finite number of vorticity equations, these being required to suppress the secular terms at the next order. Our results show that, for the multi-phased travelling waves, the first phase velocity can be determined by an integral conservation law for kinetic energy and the subsequent phase velocities can be evaluated by a non-linear eigenvalue problem. The results also reveal that whereas viscosity determines the smallest scales and controls the amplitude of the flow, the inertial terms govern the shape and form of the flow. The comparison of our analytical predictions for evaluating the stable single-phased travelling wave with the direct numerical simulation of the Navier–Stokes equations has been undertaken, the agreement being excellent. For sufficiently high Reynolds number, after the bifurcation to chaotic flow, all of the multi-phased travelling waves and quasi-periodic standing waves become unstable non-wandering sets. Based on the above new findings for these unstable non-wandering sets and other travelling and standing waves of this kind in phase space, necessary conditions for the invariant manifolds of the chaotic and turbulent attractors are obtained, these necessary conditions being conjectured to be also sufficient.

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Viscous decay of nonlinear oscillations of a spherical bubble at large Reynolds number

Cited by 10 publications

References 49 publications

Numerical Study of the Collapse of Multiple Bubbles and the Energy Conversion during Bubble Collapse

Numerical Study of the Collapse of Multiple Bubbles and the Energy Conversion during Bubble Collapse

A theoretical model for the growth of spherical bubbles by rectified diffusion

Asymptotic analysis of the attractors in two-dimensional Kolmogorov flow

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