Numerical investigation of the strength of collapse of a harmonically excited bubble

Varga, Roxána; Paál, György

doi:10.1016/j.chaos.2015.03.007

Cited by 18 publications

(13 citation statements)

References 44 publications

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“…In the above case, where Δ w has a minimum, the values are between . These values meet the expectations that approximately below 1 bar excitation amplitude, the bubble oscillation lacks really strong collapses [30,38]. This means that the specific bubble oscillation studied here is probably not able to support effects of strong collapses, such as sonochemical applications.…”

Section: Resultssupporting

confidence: 84%

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High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

Varga

Mettin

2019

Period. Polytech. Mech. Eng.

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A parameter identification technique of an underlying bubble model of an experimentally observed single bubble in a cluster under dual-frequency external forcing is presented. The measurements are carried out via high-speed camera recordings at a rate of 162750 frames per second. The used frequencies during the experiment are 25 kHz and 50 kHz. With a digital image processing technique, the measured bubble radius as a function of time is determined. The employed governing equation for the parameter fitting is the Keller–Miksis equation being a second order ordinary differential equation. The unknown four-dimensional parameter space is composed by the two pressure amplitudes, the phase shift of the dual-frequency driving and the equilibrium size of the bubble. In order to obtain an optimal parameter set within reasonable time, an in-house initial value problem solver is used running on a graphics processing unit (GPU). The error function measuring the distance between the numerical simulations and the measurement is based on the identification of the maximum bubble radii during each subsequent period of the external forcing. The results show a consistent estimation of both pressure amplitudes. The optima of phase shift and equilibrium bubble size are less significant due to a valley-like shape of the error function. Nevertheless, reasonable values are found that lead to estimations of pressure and temperature peaks during bubble collapse.

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Section: Resultssupporting

confidence: 84%

“…The parameter set of this solution differs from the previous case only in the equilibrium radius R E . This confirms the observation that this parameter has a strong effect on the oscillation [38,39]. Comparing the average of the maxima and looking for the smallest difference MIN ∆ avg { } , one gets the solution presented in Fig.…”

Section: Resultssupporting

confidence: 84%

High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

Varga

Mettin

2019

Period. Polytech. Mech. Eng.

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“…The simple initial value problem solver, applied here, has been used for decades to investigate the bifurcation structure of various bubble oscillators with a variety of control parameters. The interested reader is referred to the publications [1,[33][34][35][36][37][38][39][40][41][42][43][44][45][46].…”

Section: Global Scan Of Stable Periodic Attractorsmentioning

confidence: 99%

Topological analysis of the periodic structures in a harmonically driven bubble oscillator near Blake's critical threshold: Infinite sequence of two-sided Farey ordering trees

Hegedűs

2016

Physics Letters A

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The topology of the stable periodic orbits of a harmonically driven bubble oscillator, the Rayleigh-Plesset equation, in the space of the excitation parameters (pressure amplitude and frequency) has been revealed numerically. This topology is governed by a hierarchy of two-sided Farey trees initiated from a unique primary structure defined also by a simple asymmetric Farey tree. The sub-topology of each of these building blocks is driven by a homoclinic tangency of a periodic saddle. This self-similar organization is a suitable basis for a general description, since it is in good agreement with partial results obtained in other periodically forced oscillators and iterated maps. The applied ambient pressure in the model is near but still below Blake's critical threshold. Therefore, this paper is also a straightforward continuation of the work of Hegedűs [1], who first found numerical evidence for the existence of stable, period 1 solutions beyond Blake's threshold. The present findings are crucial for the extension of the available numerical results from period 1 to arbitrary periodicity.

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“…From a fixed initial condition, the differential equation system was integrated forward in time until the transient solution converged to an attractor. After the convergence of a solution, its characteristic properties were saved such as points of the Poincaré section, period, or maximum bubble radius [21]. This is a very common method to examine nonlinear systems in general, for details see e.g.…”

Section: Numerical Toolsmentioning

confidence: 99%

“…The accumulated knowledge of this nonlinear behavior has been summarized in many reviews [18][19][20] and papers [1,[21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. The most important findings are the existence of period-doubling cascades in the bifurcation structure [1,21,30,31,35], the appearance of resonance horns in the amplitude-frequency plane of the driving [24,27,34] or the alternation of chaotic and periodic windows [21,23,33]. These structures show similarities with the results obtained on other nonlinear oscillators such as Toda [37], Duffing [38][39][40][41] and others [42], implying that they are universal features of nonlinear systems rather than unique properties of oscillating bubbles.…”

Section: Introductionmentioning

confidence: 99%

Classification of the bifurcation structure of a periodically driven gas bubble

Varga

Hegedűs

2016

Nonlinear Dyn

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The bifurcation structure of a periodically driven spherical gas/vapour bubble is examined by means of methods of nonlinear analysis. The study of Behnia and his coworkers [1] revealed that the bifurcation structures with the pressure amplitude of the excitation as control parameter are structurally similar provided that R E ω is kept constant. In the present paper, this problem is revisited. Analytical and numerical investigations of the bubble oscillator, which is the Keller-Miksis equation, are presented. It is shown that the validity range of Behnia's condition is governed by the viscosity and the surface tension, and holds only for relatively large bubbles. In water, the effect of viscosity is negligible, and the surface tension plays significant role at bubble size lower than approximately 5 µm.

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Numerical investigation of the strength of collapse of a harmonically excited bubble

Cited by 18 publications

References 44 publications

High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

High Dimensional Parameter Fitting of the Keller–Miksis Equation on an Experimentally Observed Dual-Frequency Driven Acoustic Bubble

Topological analysis of the periodic structures in a harmonically driven bubble oscillator near Blake's critical threshold: Infinite sequence of two-sided Farey ordering trees

Classification of the bifurcation structure of a periodically driven gas bubble

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