Outi Supponen

Numerical simulation of a collapsing bubble subject to gravity

The present paper focuses on the simulation of the expansion and aspherical collapse of a laser-generated bubble subjected to an acceleration field and comparison of the results with instances from high-speed videos. The interaction of the liquid and gas is handled with the volume of fluid method. Compressibility effects have been included for each phase to predict the propagation of pressure waves. Initial conditions were estimated through the Rayleigh Plesset equation, based on the maximum bubble size and collapse time. The simulation predictions indicate that during the expansion the bubble shape is very close to spherical. On the other hand, during the collapse the bubble point closest to the bottom of the container develops a slightly higher collapse velocity than the rest of the bubble surface. Over time, this causes momentum focusing and leads to a positive feedback mechanism that amplifies the collapse locally. At the latest collapse stages, a jet is formed at the axis of symmetry, with opposite direction to the acceleration vector, reaching velocities of even 300 m/s. The simulation results agree with the observed bubble evolution and pattern from the experiments, obtained using high speed imaging, showing the collapse mechanism in great detail and clarity.

Geometrical influence on vortex shedding in turbulent axisymmetric wakes

We investigate the structures generated by the vortex shedding mechanism in turbulent axisymmetric wakes of non-axisymmetric plates, including a square plate and a series of fractal plates, and compare the results to a disk. For a given characteristic length l, all plates have the same frontal area A, since l = A0.5, but the length of the perimeter and the irregularity of the perimeter were varied in a fractal manner thus allowing us to investigate the effect of boundary conditions. Measurements were taken over a large range of downstream and radial distances in order to obtain a more robust measure for the vortex shedding energy. It was found that the fractal plates are able to reduce the vortex shedding energy by as much as 60% compared to the disk and square plates. It was also found that the frequency at which the vortex shedding structures are generated and the manner in which they organise themselves in the wake are independent of the boundary conditions of the wake generator. The results suggest th...

Simulation of bubble expansion and collapse in the vicinity of a free surface

The present paper focuses on the numerical simulation of the interaction of laser-generated bubbles with a free surface, including comparison of the results with instances from high-speed videos of the experiment. The Volume Of Fluid method was employed for tracking liquid and gas phases while compressibility effects were introduced with appropriate equations of state for each phase. Initial conditions of the bubble pressure were estimated through the traditional Rayleigh Plesset equation. The simulated bubble expands in a non-spherically symmetric way due to the interference of the free surface, obtaining an oval shape at the maximum size. During collapse, a jet with mushroom cap is formed at the axis of symmetry with the same direction as the gravity vector, which splits the initial bubble to an agglomeration of toroidal structures. Overall, the simulation results are in agreement with the experimental images, both quantitatively and qualitatively, while pressure waves are predicted both during the expansion and the collapse of the bubble. Minor discrepancies in the jet velocity and collapse rate are found and are attributed to the thermodynamic closure of the gas inside the bubble.

Scaling laws for jets of single cavitation bubbles

Fast liquid jets, called micro-jets, are produced within cavitation bubbles experiencing an aspherical collapse. Here we review micro-jets of different origins, scales and appearances, and propose a unified framework to describe their dynamics by using an anisotropy parameter zeta >= 0, representing a dimensionless measure of the liquid momentum at the collapse point (Kelvin impulse). This parameter is rigorously defined for various jet drivers, including gravity and nearby boundaries. Combining theoretical considerations with hundreds of high-speed visualisations of bubbles collapsing near a rigid surface, near a free surface or in variable gravity, we classify the jets into three distinct regimes: weak, intermediate and strong. Weak jets (zeta 0.1) pierce the bubble early during the collapse. The dynamics of the jets is analysed through key observables, such as the jet impact time, jet speed, bubble displacement, bubble volume at jet impact and vapour-jet volume. We find that, upon normalising these observables to dimensionless jet parameters, they all reduce to straightforward functions of zeta, which we can reproduce numerically using potential flow theory. An interesting consequence of this result is that a measurement of a single observable, such as the bubble displacement, suffices to estimate any other parameter, such as the jet speed. Remarkably, the dimensionless parameters of intermediate and weak jets (zeta < 0.1) depend only on zeta, not on the jet driver (i.e. gravity or boundaries). In the same regime, the jet parameters are found to be well approximated by power laws of zeta, which we explain through analytical arguments.

The inner world of a collapsing bubble

Note: FNSFlash and Splash Reference EPFL-ARTICLE-214200doi:10.1063/1.4931098View record in Web of Science Record created on 2015-12-02, modified on 2017-05-10

Shock waves from nonspherical cavitation bubbles

We present detailed observations of the shock waves emitted at the collapse of single cavitation bubbles using simultaneous time-resolved shadowgraphy and hydrophone pressure measurements. The geometry of the bubbles is systematically varied from spherical to very nonspherical by decreasing their distance to a free or rigid surface or by modulating the gravity-induced pressure gradient aboard parabolic flights. The nonspherical collapse produces multiple shocks that are clearly associated with different processes, such as the jet impact and the individual collapses of the distinct bubble segments. For bubbles collapsing near a free surface, the energy and timing of each shock are measured separately as a function of the anisotropy parameter zeta, which represents the dimensionless equivalent of the Kelvin impulse. For a given source of bubble deformation (free surface, rigid surface, or gravity), the normalized shock energy depends only on zeta, irrespective of the bubble radius R-0 and driving pressure Delta p. Based on this finding, we develop a predictive framework for the peak pressure and energy of shock waves from nonspherical bubble collapses. Combining statistical analysis of the experimental data with theoretical derivations, we find that the shock peak pressures can be estimated as jet impact-induced hammer pressures, expressed as p(h) = 0.45(rho c(2) Delta p)(1/2) zeta(-1) at zeta > 10(-3). The same approach is found to explain the shock energy decreasing as a function of zeta(-2/3).

Luminescence from cavitation bubbles deformed in uniform pressure gradients

Presented here are observations that demonstrate how the deformation of millimetric cavitation bubbles by a uniform pressure gradient quenches single-collapse luminescence. Our innovative measurement system captures a broad luminescence spectrum (wavelength range, 300-900 nm) from the individual collapses of laser-induced bubbles in water. By varying the bubble size, driving pressure, and perceived gravity level aboard parabolic flights, we probed the limit from aspherical to highly spherical bubble collapses. Luminescence was detected for bubbles of maximum radii within the previously uncovered range, R_{0}=1.5-6 mm, for laser-induced bubbles. The relative luminescence energy was found to rapidly decrease as a function of the bubble asymmetry quantified by the anisotropy parameter ζ, which is the dimensionless equivalent of the Kelvin impulse. As established previously, ζ also dictates the characteristic parameters of bubble-driven microjets. The threshold of ζ beyond which no luminescence is observed in our experiment closely coincides with the threshold where the microjets visibly pierce the bubble and drive a vapor jet during the rebound. The individual fitted blackbody temperatures range between T_{lum}=7000 and T_{lum}=11500 K but do not show any clear trend as a function of ζ. Time-resolved measurements using a high-speed photodetector disclose multiple luminescence events at each bubble collapse. The averaged full width at half-maximum of the pulse is found to scale with R_{0} and to range between 10 and 20 ns.

Detailed Jet Dynamics in a Collapsing Bubble

We present detailed visualizations of the micro-jet forming inside an aspherically collapsing cavitation bubble near a free surface. The high-quality visualizations of large and strongly deformed bubbles disclose so far unseen features of the dynamics inside the bubble, such as a mushroom-like flattened jet-tip, crown formation and micro-droplets. We also find that jetting near a free surface reduces the collapse time relative to the Rayleigh time.