Session A11: Bubbles I: Cavitation, Nucleation and Ventilation

Pressures induced by collapsing cavitation bubbles near boundaries

A pulsed Nd:YAG laser was used to produce single cavitation bubbles both in the free field and near solid and compliant boundaries in a quiescent flow. High-speed videography was used to record the growth and collapse of these bubbles. Simultaneously, the local impulse created by the bubbles was measured using a needle hydrophone. The goal of the study is to determine how impulses are created during both the initial collapse of the bubble during re-entrant jetting flow and the final collapse of the bubble after jet impact. The needle probe was used to spatially and temporally resolve the creation of force normal to the surface of the boundary. Results will be used to validate numerical simulations of single cavitation bubble collapse testing several bubble dynamics models.   

Inertial cavitation threshold in nonlinear viscoelastic media

Thresholds for inertial cavitation in tissue are studied through spherical bubble models coupled to viscoelastic constitutive relationships. Therapeutic ultrasound treatments aim to exploit the large strains and shockwaves caused by large-amplitude bubble oscillations, but metrics for the onset of inertial cavitation in soft tissue do not readily carry over from water-based cavitation. Tissue is represented by a Zener-type model that incorporates viscosity, neo-Hookean elasticity, and upper-convected Maxwell relaxation. The partial differential equations for stress are solved via a spectral collocation method. The bubble dynamics are described by the Keller-Miksis equation with thermal effects. New metrics for viscoelastic cavitation thresholds are proposed and compared against past metrics. The influence of viscoelastic parameters and choice of constitutive relationship on bubble behavior is investigated in detail.   

Cavitation dynamics in a viscoelastic medium with nonlinear elasticity

Past methods for modeling the dynamics of a spherical cavitation bubble in a viscoelastic medium (e.g., soft tissue) usually assume the elasticity to be linear. In this work, we develop a general framework to study cavitation in nonlinear (visco)elastic media, which are expected to be more accurate for large-amplitude bubble oscillations. By following an approach based on deformation tensors and Cauchy stresses, the models presented here not only take into account the usual viscous, inertial, pressure and surface tension effects, but also complex nonlinear elasticity directly derived from specific strain-energy functions. The present results are consistent with past studies of linear viscoelasticity, but additional elastic terms with different exponents emerge in the bubble dynamics equation (e.g., Rayleigh-Plesset) for more complicated strain-energy functions. Key quantities in cavitation dynamics (bubble natural frequency, minimum radius, etc.) are reported for the neo-Hookean model, the simplest nonlinear elastic model. This approach also readily leads to a full description of the physical variables of the medium where the bubble oscillates (pressure, strain/strain rate, stress, etc.).   

Detailed Simulations of Bubble-Cluster Collapse Adjacent Material Surfaces

The collapse of bubble clusters adjacent material surfaces is thought to be an important damage mechanism, in both engineering and biomedical applications. Homogeneous models of these clusters have been able to reproduce some of their gross dynamics, however diagnostic challenges leave it unclear how important the bubble dynamics are for important quantities such as peak pressures on the surface. We study in detail the dynamics of small clusters collapsing adjacent to a wall using a numerical scheme that faithfully represents bubble-scale dynamics. It is based on a recently developed interface capturing method that is asymptotically consistent with a well-posed mixture model for the two phases. For collapse near a rigid wall, we show strong inward focusing of re-entrant jets, which enhances the impulsive pressures generated on the wall. The homogeneous model we compare with fails to capture the true peak pressures on the walls. We further apply our scheme to simulate cluster collapse near a viscous fluid as a model for soft tissue, as in therapeutic ultrasound. In this case, the low impedance mismatch at the wall leads to significantly different dynamics. Simulations suggest that clusters can actually be relatively protective when compared to single-bubble collapses.   

Shear stresses and temperatures during the collapse of a bubble near a rigid wall

The collapse of a cavitation bubble is the central problem in cavitation erosion. In naval and biomedical applications, this process is known to lead to structural damage, whether intended or not. In the present work, the collapse of an initially spherical bubble, filled with non-condensable gas, near a rigid wall is simulated numerically using a high-order shock- and interface-capturing scheme. This computational approach prevents both temperature and pressure errors by using appropriate transport equations for the variables entering the equation of state. By directly solving the axisymmetric compressible Navier-Stokes equations, the viscous stresses and temperatures produced along the neighboring wall are computed. The quantities are critical when considering compliant bodies and polymeric coatings on metallic surfaces. The simulations show that substantial increases in temperature in the liquid may be produced. Characterization of the temperatures and viscous stresses along the neighboring wall will be presented.   

Why does a beer bottle foam up after a sudden impact on its mouth?

A sudden vertical impact on the mouth of a beer bottle generates a compression wave that propagates through the glass towards the bottom. When this wave reaches the base of the bottle, it is transmitted to the liquid as an expansion wave that travels to free surface, where it bounces back as a compression wave. This train of expansion-compression waves drives the forced cavitation of existing air pockets, leading to their violent collapse. A cloud of very small daughter bubbles are generated upon these collapses, that expand much faster than their mothers due to their smaller size. These rapidly growing bubble clusters effectively act as buoyancy sources, what leads to the formation of bubble-laden plumes whose void fraction increases quickly by several orders of magnitude, eventually turning most of the beverage into foam. In this talk, we will analyze quantitatively these processes in order to explain the extremely high efficiency of the degasification process that occurs in the bottle within the few seconds that follow the impact. This work has been supported by Spanish Ministries of Science and of Economy and Competitiveness through grants: DPI2008-06369 and DPI2011-28356-C03-02.   

Bubble cloud nucleation induced by the interaction between multiple laser-induced shocks and bubbles

Multifocal laser-induced optical breakdown in water is used to nucleate microscopic bubble clouds. The liquid is ruptured via the interaction of multiple shocks and bubbles. We find that the liquid is fractured at localized regions defined by the planes bisecting each pair of foci on the array, where rarefaction waves (reflected from the laser bubbles) merge. For laser pulses focused at two spots we measure the probability for nucleation as a function of separation between the foci and the maximum tensions are calculated with Euler flow simulations.   

Ventilation of an hydrofoil wake

Ventilation physics plays a role in a variety of important engineering applications. For example, hydroturbine ventilation is used for control of vibration and cavitation erosion and more recently for improving the dissolved oxygen content of the flow through the turbine. The latter technology has been the focus of an ongoing study involving the ventilation of an hydrofoil wake to determine the velocity and size distribution of bubbles in a bubbly wake. This was carried out by utilizing particle shadow velocimetry (PSV). This technique is a non-scattering approach that relies on direct in-line volume illumination by a pulsed source such as a light-emitting diode (LED). The data are compared with previous studies of ventilated flow. The theoretical results of Hinze suggest that a scaling relationship is possible that can lead to developing appropriate design parameters for a ventilation system.   

Improved Performance With Ventilation

Drag reduction and/or speed augmentation of marine vehicles by means of supercavitation is a topic of great interest. During the initial launch of a supercavitating vehicle, ventilation is required to supply an artificial cavity until conditions at which a natural supercavity can be sustained are reached. Various aspects of the flow physics of a supercavitating vehicle have been under investigation for several years at Saint Anthony Falls Laboratory. Both steady flow and simulated flow below a wave train have been studied. Using a high speed camera and the proper software, it is possible to synchronize cavity dimensions with pressure measurements taken inside the cavity to permit an in-depth study of unsteadiness. It was found that flow unsteadiness caused a decrease in the overall length of the supercavity while having only a minimal effect on the maximum diameter. Results regarding supercavity shape, ventilation demand, cavitation parameters and closure methods are reviewed in light of new studies that focused on various closure mechanisms.