Finite-volume WENO scheme for viscous compressible multicomponent flows

Investigations on the shock wave induced by collapse of a toroidal bubble

When bubbles collapse near a wall, they typically experience an asymmetric deformation. This collapse leads to the creation of a jet that strikes the bubble interface, causing the formation of a toroidal bubble and the subsequent release of a water-hammer shock. In this study, we present a systematic analysis of the collapse of a toroidal bubble in an open field or adjacent to a flat wall using high-fidelity numerical simulation. To maintain the sharpness of the interface, we employ the interface compression technique and the boundary variation diminishing approach within the two-phase model. Our findings demonstrate that shock waves emitted from the toroidal bubble consistently propagate toward the central axis of the torus, resulting in significant pressure shocks along the axis, similar to the water-hammer shock formed during the collapse of a spherical bubble. In contrast, weak pressure waves are generated in the transverse directions, leading to relatively weaker pressure peaks. Furthermore, the wall-pressure peak induced by the toroidal bubble is approximately three times higher than that induced by the spherical bubble. Based on the directional characteristics of pressure wave propagation from collapsing toroidal bubbles, toroidal-shaped pressure vessels can be designed as buoyancy materials for deep submersibles. This design enables the focused release of energy in a specific direction, effectively minimizing the destructive chain reaction caused by the implosion.

Investigation of the ultrasound-induced collapse of air bubbles near soft materials

A numerical investigation into the ultrasound-induced collapse of air bubbles near soft materials, utilizing a novel multi-material diffuse interface method (DIM) model with block-structured adaptive mesh refinement is presented. The present work expands from a previous five-equation DIM by incorporating Eulerian hyperelasticity. The model is applicable to any arbitrary number of interacting fluid and solid material. A single conservation law for the elastic stretch tensor enables tracking the deformations for all the solid materials. A series of benchmark cases are conducted, and the solution is found to be in excellent agreement against theoretical data. Subsequently, the ultrasound-induced bubble-tissue flow interactions are examined. The bubble radius was found to play a crucial role in dictating the stresses experienced by the tissue, underscoring its significance in medical applications. The results reveal that soft tissues primarily experience tensile forces during these interactions, suggesting potential tensile-driven injuries that may occur in relevant treatments. Moreover, regions of maximal tensile forces align with tissue elongation areas. It is documented that while early bubble dynamics remain relatively unaffected by changes in shear modulus, at later stages of the penetration processes and the deformation shapes, exhibit notable variations. Lastly, it is demonstrated that decreasing standoff distances enhances the interaction between bubbles and tissue, thereby increasing the stress levels in the tissue, although the behavior of the bubble dynamics remains largely unchanged.

Numerical simulation data of an elongated cavitation bubble induced by long-pulsed laser

The simulation data presented in this paper describes the formation and growth of an elongated bubble induced by a long-pulsed laser. The simulation is performed using the M2C solver, which is a recently developed three-dimensional finite volume Navier-Stokes CFD solver. The solver is used to simulate the fluid dynamics of the liquid water, the laser radiation, the laser-induced vaporization, and the fluid dynamics of the bubble after its formation. The data presented in this paper corresponds to a representative case of the cavitation induced by a narrow Gaussian beam (cf. [1]). Simulation data include laser radiance, fluid velocity, pressure, temperature, and bubble dynamics. The input files and the workflow to perform this simulation are also provided. With the information provided in this paper, researchers can repeat this simulation, and use it as a starting point to study related problems involving laser-induced cavitation, continuous vaporization, and bubble dynamics in general.

Investigating the migration of immiscible contaminant fluid flow in homogeneous and heterogeneous aquifers with high-precision numerical simulations

Numerical modeling of the migration of three-phase immiscible fluid flow in variably saturated zones is challenging due to the different behavior of the system between unsaturated and saturated zones. This behavior results in the use of different numerical methods for the numerical simulation of the fluid flow depending on whether it is in the unsaturated or saturated zones. This paper shows that using a high-resolution shock-capturing conservative method to resolve the nonlinear governing coupled partial differential equations of a three-phase immiscible fluid flow allows the numerical simulation of the system through both zones providing a unitary vision (and resolution) of the migration of an immiscible contaminant problem within a porous medium. In particular, using different initial scenarios (including impermeable "lenses" in heterogeneous aquifers), three-dimensional numerical simulation results are presented on the temporal evolution of the contaminant migration following the saturation profiles of the three-phases fluids flow in variably saturated zones. It is considered either light nonaqueous phase liquid with a density less than the water, or dense nonaqueous phase liquid, which has densities greater than the water initially released in unsaturated dry soil. Our study shows that the fate of the migration of immiscible contaminants in variably saturated zones can be accurately described, using a unique mathematical conservative model, with different evolution depending on the value of the system's physical parameters, including the contaminant density, and accurately tracking the evolution of the sharp (shock) contaminant front.

Simulation of humpback whale bubble-net feeding models

Humpback whales can generate intricate bubbly regions, called bubble nets, via blowholes. Humpback whales appear to exploit these bubble nets for feeding via loud vocalizations. A fully-coupled phase-averaging approach is used to model the flow, bubble dynamics, and corresponding acoustics. A previously hypothesized waveguiding mechanism is assessed for varying acoustic frequencies and net void fractions. Reflections within the bubbly region result in observable waveguiding for only a small range of flow parameters. A configuration of multiple whales surrounding and vocalizing towards an annular bubble net is also analyzed. For a range of flow parameters, the bubble net keeps its core region substantially quieter than the exterior. This approach appears more viable, though it relies upon the cooperation of multiple whales. A spiral bubble net configuration that circumvents this requirement is also investigated. The acoustic wave behaviors in the spiral interior vary qualitatively with the vocalization frequency and net void fraction. The competing effects of vocalization guiding and acoustic attenuation are quantified. Low void fraction cases allow low-frequency waves to partially escape the spiral region, with the remaining vocalizations still exciting the net interior. Higher void fraction nets appear preferable, guiding even low-frequency vocalizations while still maintaining a quiet net interior.

High-speed video microscopy and numerical modeling of bubble dynamics near a surface of urinary stone

Ultra-high-speed video microscopy and numerical modeling were used to assess the dynamics of microbubbles at the surface of urinary stones. Lipid-shell microbubbles designed to accumulate on stone surfaces were driven by bursts of ultrasound in the sub-MHz range with pressure amplitudes on the order of 1 MPa. Microbubbles were observed to undergo repeated cycles of expansion and violent collapse. At maximum expansion, the microbubbles' cross-section resembled an ellipse truncated by the stone. Approximating the bubble shape as an oblate spheroid, this study modeled the collapse by solving the multicomponent Euler equations with a two-dimensional-axisymmetric code with adaptive mesh refinement for fine resolution of the gas-liquid interface. Modeled bubble collapse and high-speed video microscopy showed a distinctive circumferential pinching during the collapse. In the numerical model, this pinching was associated with bidirectional microjetting normal to the rigid surface and toroidal collapse of the bubble. Modeled pressure spikes had amplitudes two-to-three orders of magnitude greater than that of the driving wave. Micro-computed tomography was used to study surface erosion and formation of microcracks from the action of microbubbles. This study suggests that engineered microbubbles enable stone-treatment modalities with driving pressures significantly lower than those required without the microbubbles.

Bubble cloud dynamics in an ultrasound field

The dynamics of bubble clouds induced by high-intensity focused ultrasound are investigated in a regime where the cloud size is similar to the ultrasound wavelength. High-speed images show that the cloud is asymmetrical; the bubbles nearest the source grow to a larger radius than the distal ones. Similar structures of bubble clouds are observed in numerical simulations that mimic the laboratory experiment. To elucidate the structure, a parametric study is conducted for plane ultrasound waves with various amplitudes and diffuse clouds with different initial void fractions. Based on an analysis of the kinetic energy of liquid induced by bubble oscillations, a new scaling parameter is introduced to characterize the dynamics. The new parameter generalizes the cloud interaction parameter originally introduced by d'Agostino & Brennen (1989). The dynamic interaction parameter controls the energy localization and consequent anisotropy of the cloud. Moreover, the amplitude of the far-field, bubble-scattered acoustics is likewise correlated with the proposed parameter. Findings of the present study not only shed light on the physics of cloud cavitation, but may also be of use to quantification of the effects of cavitation on outcomes of ultrasound therapies including HIFU-based lithotripsy.

Experimental observations and numerical modeling of lipid-shell microbubbles with calcium-adhering moieties for minimally-invasive treatment of urinary stones

A novel treatment modality incorporating calcium-adhering microbubbles has recently entered human clinical trials as a new minimally-invasive approach to treat urinary stones. In this treatment method, lipid-shell gas-core microbubbles can be introduced into the urinary tract through a catheter. Lipid moities with calcium-adherance properties incorporated into the lipid shell facilitate binding to stones. The microbubbles can be excited by an extracorporeal source of quasi-collimated ultrasound. Alternatively, the microbubbles can be excited by an intraluminal source, such as a fiber-optic laser. With either excitation technique, calcium-adhering microbubbles can significantly increase rates of erosion, pitting, and fragmentation of stones. We report here on new experiments using high-speed photography to characterize microbubble expansion and collapse. The bubble geometry observed in the experiments was used as one of the initial shapes for the numerical modeling. The modeling showed that the bubble dynamics strongly depends on bubble shape and stand-off distance. For the experimentally observed shape of microbubbles, the numerical modeling showed that the collapse of the microbubbles was associated with pressure increases of some two-to-three orders of magnitude compared to the excitation source pressures. This in-vitro study provides key insights into the use of microbubbles with calcium-adhering moieties in treatment of urinary stones.

Energy shielding by cavitation bubble clouds in burst wave lithotripsy

Combined laboratory experiment and numerical simulation are conducted on bubble clouds nucleated on the surface of a model kidney stone to quantify the energy shielding of the stone caused by cavitation during burst wave lithotripsy (BWL). In the experiment, the bubble clouds are visualized and bubble-scattered acoustics are measured. In the simulation, a compressible, multi-component flow solver is used to capture complex interactions among cavitation bubbles, the stone, and the burst wave. Quantitative agreement is confirmed between results of the experiment and the simulation. In the simulation, a significant shielding of incident wave energy by the bubble clouds is quantified. The magnitude of shielding can reach up to 90% of the energy of the incoming burst wave that otherwise would be transmitted into the stone, suggesting a potential loss of efficacy of stone comminution. There is a strong correlation between the magnitude of the energy shielding and the amplitude of the bubble-scattered acoustics, independent of the initial size and the void fraction of the bubble cloud within a range addressed in the simulation. This correlation could provide for real-time monitoring of cavitation activity in BWL.

Eulerian-Lagrangian method for simulation of cloud cavitation

We present a coupled Eulerian-Lagrangian method to simulate cloud cavitation in a compressible liquid. The method is designed to capture the strong, volumetric oscillations of each bubble and the bubble-scattered acoustics. The dynamics of the bubbly mixture is formulated using volume-averaged equations of motion. The continuous phase is discretized on an Eulerian grid and integrated using a high-order, finite-volume weighted essentially non-oscillatory (WENO) scheme, while the gas phase is modeled as spherical, Lagrangian point-bubbles at the sub-grid scale, each of whose radial evolution is tracked by solving the Keller-Miksis equation. The volume of bubbles is mapped onto the Eulerian grid as the void fraction by using a regularization (smearing) kernel. In the most general case, where the bubble distribution is arbitrary, three-dimensional Cartesian grids are used for spatial discretization. In order to reduce the computational cost for problems possessing translational or rotational homogeneities, we spatially average the governing equations along the direction of symmetry and discretize the continuous phase on two-dimensional or axi-symmetric grids, respectively. We specify a regularization kernel that maps the three-dimensional distribution of bubbles onto the field of an averaged two-dimensional or axi-symmetric void fraction. A closure is developed to model the pressure fluctuations at the sub-grid scale as synthetic noise. For the examples considered here, modeling the sub-grid pressure fluctuations as white noise agrees a priori with computed distributions from three-dimensional simulations, and suffices, a posteriori, to accurately reproduce the statistics of the bubble dynamics. The numerical method and its verification are described by considering test cases of the dynamics of a single bubble and cloud cavitaiton induced by ultrasound fields.

A Source Term Approach for Generation of One-way Acoustic Waves in the Euler and Navier-Stokes equations

We derive a volumetric source term for the Euler and Navier-Stokes equations that mimics the generation of unidirectional acoustic waves from an arbitrary smooth surface in three-dimensional space. The model is constructed as a linear combination of monopole and dipole sources in the mass, momentum, and energy equations. The singular source distribution on the surface is regularized on a computational grid by convolution with a smeared Dirac delta function. The source is implemented in the Euler equations using a Cartesian-grid finite-volume WENO scheme, and validated by comparing with analytical solution for unidirectional planar and spherical acoustic waves. Using the scheme, we emulate a spherical piezoelectric transducer and a multi-array transducer to simulate focused ultrasound fields in water. The simulated ultrasound fields show favorable agreement with previous experiments.

Modeling and experimental analysis of acoustic cavitation bubbles for Burst Wave Lithotripsy

A combined modeling and experimental study of acoustic cavitation bubbles that are initiated by focused ultrasound waves is reported. Focused ultrasound waves of frequency 335 kHz and peak negative pressure 8 MPa are generated in a water tank by a piezoelectric transducer to initiate cavitation. The resulting pressure field is obtained by direct numerical simulation (DNS) and used to simulate single bubble oscillation. The characteristics of cavitation bubbles observed by high-speed photography qualitatively agree withs the simulation result. Finally, bubble clouds are captured using acoustic B-mode imaging that works in synchronization with high-speed photography.

Central upwind scheme for a compressible two-phase flow model

In this article, a compressible two-phase reduced five-equation flow model is numerically investigated. The model is non-conservative and the governing equations consist of two equations describing the conservation of mass, one for overall momentum and one for total energy. The fifth equation is the energy equation for one of the two phases and it includes source term on the right-hand side which represents the energy exchange between two fluids in the form of mechanical and thermodynamical work. For the numerical approximation of the model a high resolution central upwind scheme is implemented. This is a non-oscillatory upwind biased finite volume scheme which does not require a Riemann solver at each time step. Few numerical case studies of two-phase flows are presented. For validation and comparison, the same model is also solved by using kinetic flux-vector splitting (KFVS) and staggered central schemes. It was found that central upwind scheme produces comparable results to the KFVS scheme.