Modelling bubble clusters in compressible liquids
D. Fuster and T. Colonius. J. Fluid Mech. 2011.
We present a new model for bubbly cavitating flows. Based on volume-averaged equations, a subgrid model is added to account for a bubble, or multiple bubbles, within each computational cell. The model converges to the solution of ensemble-averaged bubbly flow equations for weak oscillations and monodisperse systems. In the other extreme, it also converges to the theoretical solution for a single oscillating bubble, and captures the bubble radius evolution and the pressure disturbance induced in the liquid. A substantial saving of computational time is achieved compared to ensemble-averaged models for polydisperse mixtures.
Liquid compressibility effects during the collapse of a single cavitating bubble.
D. Fuster, C. Dopazo and G. Hauke. J. Acoust. Soc. Am. 2011.
The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, it is unclear the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh-Plesset equation. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh-Plesset type equations accounting for compressibility effects, proposed by Keller \& Miksis, Gilmore, and Tomita \& Shima, are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh-Plesset type equations, whereas the amplitudes of the rebounds are smaller.
Influence of the accommodation coefficient on nonlinear bubble oscillations
D. Fuster, G. Hauke and C. Dopazo. J. Acoust. Soc. Am. 2010.
This paper numerically investigates the effect of mass transfer processes on spherical single bubble dynamics using the Hertz-Langmuir-Knudsen approximation for the mass flux across the interface. Bubble behavior, with and without mass transfer, is studied for different values of pressure wave amplitude and frequency, as well as initial bubble radius. Whereas mass transfer processes do not seem to play a significant role on the bubble response for pressure amplitudes smaller than 0.9 atm, they appear to have an important effect when the amplitude is greater than or equal to 1 atm. For the later case, where the minimum liquid pressure reaches values around its vapor pressure, the importance of mass transfer depends on frequency. For frequencies in the 10-100 kHz range and initial bubble radii of the order of tens of microns, bubble implosions with and with no mass transfer are significantly different; smaller radii display a lower sensitivity. In this regime, accurate model predictions must, therefore, carefully select the correct value of the accommodation coefficient. For frequencies greater than 100 kHz, as a first approximation mass transfer can be ignored.
Parametric analysis for a single collapsing bubble
D. Fuster, C. Dopazo and G. Hauke. J. Flow Turb. Comb. 2008.
This work presents a sensitivity analysis for cavitation processes, studying in detail the effect of various model parameters on the bubble collapse. A complete model (Hauke,2007) is used to obtain how different parameters influence the collapse in SBSL experiments, providing some clues on how to enhance the bubble implosion in real systems. The initial bubble radius, the frequency and the amplitude of the pressure wave are the most important parameters determining under which conditions cavitation occurs. The range of bubble sizes inducing strong implosions for different frequencies is computed; the initial radius is the most important parameter characterized the intensity of the cavitation processes. However, other parameters like the gas and liquid conductivity or the liquid viscosity can have an important effect under certain conditions. It is shown that mass transfer processes play an important role in order to correctly predict the trends related with the effect of the liquid temperature, which translates into the bubble dynamics. Moreover, under some particular circumstances, evaporation can be encountered during the bubble collapse; this can be profitably exploited in order to feed reactants when the most extreme conditions inside the bubbles are reached. Thus, this paper aims at providing a global assessment of the effect of the different parameters...
Dynamics of a single cavitating and reacting bubble
G.Hauke, D. Fuster and C. Dopazo. Phys. Rev. E. 2007.
A part of the studies on the dynamics of cavitating bubbles often consider simplified sub-models assuming uniform fluid properties within the gas bubbles, ignoring chemical reactions and suppressing fluid transport phenomena across the bubble interphase. Another group of works, to which the present contribution belongs, include the radial dependence of the fluid variables. Important fluid processes that take part inside the gas bubble, such as chemical reactions, and across the bubble interphase, such as heat and mass transfer phenomena, are here also considered. As a consequence, this model should yield more realistic results. In particular, it is found that water evaporation/condensation is a fundamental transport phenomena to estimate the dissociation reactions of water into OH. The thermal and mass boundary layers and the radial variation of the chemical concentrations seem as well essential for accurate predictions.
(Click to play video)Response of a bubble cluster to a sinusoidal perturbation of 1.2 atm. Pressure field. The bubbles implode violently generating pressure waves which propagate throughout the bubble cluster. Advisor: Tim Colonius (Caltech 2010) |
(Click to play video)Comparison in the response of a bubble cluster to a sinusoidal perturbation of 1.2 atm for a monodisperse (left) and polydisperse system. Pressure field. In the non-linear regime, polydispersity tend to increase the violence of the implosions. Advisor: Tim Colonius (Caltech 2010) |
(Click to play video)3D simulation of the response of a bubble cluster to a weak sinusoidal perturbation. Advisor: Tim Colonius (Caltech, 2010) |
(Click to play video)Comparisson of the radial pressure profiles in the liquid in a spherical vibrating flask with and without bubble (dots and lines respectively). Advisors: Cesar Dopazo and Guillermo Hauke (AMF, 2004-07). |