Liquid vorticity computation in non-spherical bubble dynamics

Аганин, А. А.; Khismatullina, N. A.

doi:10.1002/fld.816

Cited by 3 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, as shown in [10], in the problems considered in this paper, using central differences is acceptable because of the presence of dissipative viscous terms in (10). Our calculations show that on fine grids, central and upstream one-sided differences give the same numerical solution.…”

Section: Formulation Of the Problem Using Continuity And Motion Equatsupporting

confidence: 49%

“…In this case, due to the lower order of the approximation by one-sided differences, the computation time increases significantly. It has also been shown [10] that the approach employed in the present work is more effective than the Bubnov-Galerkin method and the collocation method. We also note that all the results presented in this study were tested for convergence by successive refinement of the computation grid.…”

Section: Formulation Of the Problem Using Continuity And Motion Equatmentioning

confidence: 90%

“…The change of variables ξ = R/r, ζ = t made according to the calculation procedure for problem (5)-(13) [10] results in the transformation of the spatial domain of integration R(t) r < ∞ of Eq. (10) to the interval 0 < ξ 1.…”

Section: Formulation Of the Problem Using Continuity And Motion Equatmentioning

confidence: 99%

See 2 more Smart Citations

Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Аганин

Ilgamov

Toporkov

2010

J Appl Mech Tech Phy

Self Cite

View full text Add to dashboard Cite

This paper studies the effect of the vortex fluid motion produced by periodic radial oscillations of a weakly nonspherical gas bubble on the variation in the small initial deviation from the spherical shape of this bubble. It is shown that the most intense vortex motion of the fluid occurs in the boundary layer (near field ), and in the far field, the vortex fluid motion rapidly transforms to potential motion. The ranges of problem parameters in which vortex motion in the far field flow does not affect bubble oscillations and the ranges in which accounting for this motion is necessary for a qualitatively correct description of the oscillations are determined.Key words: periodic action, stability of spherical bubble shape, deviation, effect of vortex motion, vorticity.Introduction. Bubble dynamics research has been stimulated by the discovery of stable periodic singlebubble sonoluminescence, by which is meant the periodic emission of short light pulses by a small gas bubble which oscillates at the antinode of an ultrasonic standing pressure wave [1,2]. In addition, there has been increased interest in the variation in the deviation of the bubble shape from a sphere during periodic oscillations. Until recently, the ranges of stable oscillations have been primarily determined [3,4].In this paper, we study the effect of the vortex fluid motion caused by periodic radial oscillations of a weakly nonspherical bubble on the variation in the small initial deviation of the bubble shape from a sphere. Emphasis is placed on the effect of vortex motion in the far (relative to the bubble) flow field. As is known, if a body placed in a weakly viscous fluid performs high-frequency oscillations whose amplitude is small compared to the body size, the most intense vortex motion of the fluid occurs in the boundary layer (near field) of thickness δ c ∼ 2ν/ω c , where ω c is the oscillation frequency and ν is the kinematic viscosity [5]. At distances larger than δ c (in the far field), the fluid motion rapidly becomes potential; therefore, in many cases, the vortex motion in the far field can be neglected. This assumption is made in most of the well-known approximate methods of taking into account the effect of viscosity on the dynamics of gas bubbles (see, for example, [6]). If the frequency and amplitude of nonspherical oscillations vary widely, the intensity ratio of the vortex motion in the near and far (in the region r > R + δ c ) fields can vary. In the present work, we use a model in which the evolution of the deviation of the bubble shape from sphericity is described by an equation [7] which takes into account vortex fluid motion in both the near and far field.It is shown that during stable radial oscillations, the variation in the deviation from period to period can be not only exponential (as is the case under the effect of the near vorticity field) but much slower (power-law) due to the effect of vortex fluid motion in the far field. In addition, the deviation value can alternatively decrease and increase from period to per...

show abstract

Section: Formulation Of the Problem Using Continuity And Motion Equatsupporting

confidence: 49%

Section: Formulation Of the Problem Using Continuity And Motion Equatmentioning

confidence: 90%

See 1 more Smart Citation

Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Аганин

Ilgamov

Toporkov

2010

J Appl Mech Tech Phy

Self Cite

View full text Add to dashboard Cite

show abstract

“…This function is determined from a partial differential equation with an integral boundary condition. In contrast to other studies (see [54,56]), in this paper, the vorticity diffusion is calculated by a finite-difference method [57].The system of equations is solved numerically using a Runge-Kutta method of high-order accuracy [58] with a variable time step.…”

Section: Introductionmentioning

confidence: 99%

Evolution of deviations from the spherical shape of a vapor bubble in supercompression

Нигматулин

Аганин

Ilgamov

et al. 2014

J Appl Mech Tech Phy

Self Cite

View full text Add to dashboard Cite

This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3, . . . with the wavelength λ = 2πR/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.

show abstract

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

Shaw¹

2009

Physics of Fluids

View full text Add to dashboard Cite

The volume oscillations, translation, and axisymmetric deformation of a bubble in an acoustic traveling wave are considered. Assuming the bubble translation and deformation is small, but placing no restriction on the volume oscillations, a combination of the Rayleigh dissipation function and perturbation analysis is employed to account for the effects of viscosity in the absence of vorticity to third order in the small interaction terms. Contributions from the acoustic field are also determined to this order, while the free oscillation terms are drawn from a previously derived model correct to the same order of analysis. To permit the study of large amplitude acoustic forcing, appropriate compressibility terms are phenomenologically added to the volume pulsation equation. Stability maps of driving pressure versus driving frequency and driving pressure versus the equilibrium bubble radius are presented. A predominant number of results are for micron-sized bubbles driven in the ultrasonic regime, but the behavior of larger bubbles driven at frequencies in the kilohertz range is also considered. In all cases, bubbles driven above the natural frequency of their respective volume oscillations are markedly more stable with regard to the acoustic driving amplitude, consistent with previous observations. Below these respective natural frequency values, the stability/instability fronts display a much more complex structure. Accounting for shape mode viscous damping causes a general increase in bubble stability, together with a reduction in the stability/instability front complexity. In the case of micron-sized bubbles this stabilization is markedly more significant for bubbles driven above the natural frequency of the respective volume mode oscillations; for larger bubbles driven in the kilohertz range, the influence of shape mode damping is less significant.

show abstract

Liquid vorticity computation in non-spherical bubble dynamics

Cited by 3 publications

References 16 publications

Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Effect of vortex fluid motion on nonspherical oscillations of a gas bubble

Evolution of deviations from the spherical shape of a vapor bubble in supercompression

The stability of a bubble in a weakly viscous liquid subject to an acoustic traveling wave

Contact Info

Product

Resources

About