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Microbubble enhanced high intensity focused ultrasound (HIFU) is of great interest to tissue ablation for solid tumor treatments such as in liver and brain cancers, in which contrast agents/microbubbles are injected into the targeted region to promote heating and reduce prefocal tissue damage. A compressible Euler–Lagrange coupled model has been developed to accurately characterize the acoustic and thermal fields during this process. This employs a compressible Navier–Stokes solver for the ultrasound acoustic field and a discrete singularities model for bubble dynamics. To address the demanding computational cost relevant to practical medical applications, a multilevel hybrid message-passing interface (MPI)-open multiprocessing (OpenMP) parallelization scheme is developed to take advantage of both scalability of MPI and load balancing of OpenMP. At the first level, the Eulerian computational domain is divided into multiple subdomains and the bubbles are subdivided into groups based on which subdomain they fall into. At the next level, in each subdomain containing bubbles, multiple OpenMP threads are activated to speed up the computations of the bubble dynamics. For improved throughput, the OpenMP threads are more heavily distributed to subdomains where the bubbles are clustered. By doing this, MPI load imbalance issue due to uneven bubble distribution is mitigated by OpenMP speedup locally for those subdomains hosting more bubbles than others. The hybrid MPI-OpenMP Euler–Lagrange solver is used to conduct simulations and physical studies of bubble-enhanced HIFU problems containing a large number of microbubbles. The phenomenon of acoustic shadowing caused by the bubble cloud is then analyzed and discussed. Efficiency tests on two different machines with 48 processors are conducted and indicate 2–3 times speedup with the same hardware by introducing an OpenMP parallelization in combination with the MPI parallelization.

The effects of the viscoelastic shell properties of ultrasound contrast agents on heat deposition in bubble enhanced high intensity focused ultrasound (HIFU) are studied numerically using a model that solves the ultrasound acoustic field and the multi-bubble dynamics. The propagation of the nonlinear acoustic waves in the test medium is modeled using the compressible Navier-Stokes equations in a fixed Eulerian grid, while the microbubbles are modeled as discrete flow singularities, which are tracked in a Lagrangian fashion. These two models are intimately coupled such that both the acoustic field and the bubbles influence each other at each time step. The resulting temperature rise in the field is then calculated by solving a heat transfer equation applied over a much longer time scale than the computed high frequency dynamics. Three shell models for the contrast agent are considered, and the effect of each of these models on the heat deposition at the focus is studied. The differences obtained in the bubble dynamics results between the shell models are discussed. The importance of modeling the elasticity of the shell is addressed by comparing the results between Newtonian and non-Newtonian shell models. Next, a parametric study varying the shell properties is carried out, and the relative roles of the shell viscosity and elasticity in affecting the heat deposition are discussed. These observations are then used to give recommendations for the design of innovative contrast agents, specifically for the purpose of obtaining higher heat deposition in bubble enhanced HIFU.

Importance-performance analysis (IPA) is a convenient tool for service quality evaluation. Likewise, SERVQUAL and the model of service quality is also another useful tool for service quality evaluation. How hot spring service providers position themselves and differentiate themselves from competitors is critical to their success. In this study, both IPA and SERVQUAL and the model of service quality are used to evaluate a hot spring service provider in Taiwan for comparisons. A modified SERVQUAL questionnaire was distributed to hot spring resort customers with 300 valid responses. Results from IPA indicated the “Reliability” as the service weakness, while SERVQUAL and the model of service quality identified the “Responsiveness” as the largest service gap. Using these tools, the service providers can identify the critical factors for improvements from different perspectives. Implications of both tools for service providers and researchers were discussed.

Microbubble enhanced High Intensity Focused Ultrasound (HIFU) is of great interest to tissue ablation for solid tumor treatments such as in liver and brain cancers, in which contrast agents/microbubbles are injected into the targeted region to promote heating and reduce pre-focal tissue damage. A compressible Euler-Lagrange coupled model has been developed to accurately characterize the acoustic and thermal fields during this process. This employs a compressible Navier-Stokes solver for the ultrasound acoustic field and a discrete singularities model for bubble dynamics. To address the demanding computational cost in practical biological applications, a multi-level hybrid MPI-OpenMP parallelization scheme is developed to take advantage of both scalability of MPI and load balancing of OpenMP. At the first level, the Eulerian computational domain is divided into multiple subdomains and the bubbles are subdivided in groups based on which subdomain they fall into. At the next level, in each subdomain containing bubbles, multiple OpenMP threads are activated to speed up the bubble computations. More OpenMP threads are used inside each subdomain where the bubbles are clustered. By doing this, MPI load imbalance issue due to non-uniformity of bubble presence is compensated. The hybrid MPI-OpenMP Euler-Lagrange solver is used to conduct simulations and physical studies of bubble-enhanced HIFU problems containing a large number of microbubbles. The phenomenon of acoustic shadowing caused by the bubble cloud is then analyzed and discussed. Hybrid parallelization efficiency tests and demonstration of its advantages against using MPI alone are presented.

Heat enhancement at the target in a High Intensity Focused Ultrasound (HIFU) field is investigated by considering the effects of the injection of microbubbles in the vicinity of the tumor to be ablated. The interaction between the bubble cloud and the HIFU field is investigated using a three-dimensional numerical model. The propagation of non-linear ultrasonic waves in the tissue or in a phantom medium is modeled using the compressible Navier-Stokes equations on a fixed Eulerian grid, while the microbubbles dynamics and motion are modeled as discrete singularities, which are tracked in a Lagrangian framework. These two models are coupled to each other such that both the acoustic field and the bubbles influence each other. The resulting temperature rise in the field is calculated by solving a heat transfer equation applied over a much longer time scale. The compressible continuum part of the model is validated by conducting axisymmetric HIFU simulations without microbubbles and comparing the pressure and temperature fields against available experiments. The coupled Eulerian-Lagrangian approach is then validated against existing experiments conducted with a phantom tissue. The bubbles are distributed randomly in a 3D fashion inside a cylindrical volume while the background acoustic field is assumed axisymmetric. The presence of microbubbles modifies the ultrasound field in the focal region and significantly enhances heat deposition. The various mechanisms through which heat deposition is increased are then examined. Among these effects, viscous damping of the bubble oscillations is found to be the main contributor of the enhanced heat deposition. The effects of the initial void fraction in the cloud are then sought by considering the changes in the attenuation of the primary ultrasonic wave and the modifications of the enhanced heat deposition in the focal region. It is observed that while high bubble void fractions lead to increased heat deposition, they also cause significant pre-focal heating due to acoustic shielding. The effects of the microbubble cloud size and its location in the focal region are studied and the effects of these parameters in altering the temperature rise and the location of the temperature peak are discussed. It is shown that concentrating the bubbles adjacent to the focus and farther away from the acoustic source leads to effective heat deposition. Finally, the presence of a shell at the bubble surface, as in contrast agents, is seen to reduce heat deposition by restraining bubble oscillations.

Cavitation bubble dynamics and interaction with a polymeric coating material can be scaled in space and time using spark-generated bubbles near an appropriate soft material and can be simulated using fluid-structure interaction (FSI) modelling. In this paper, cavitation bubble dynamics in a high-pressure cavitating jet eroding a Polyurea layer on a rigid substrate is simulated using spark-generated bubbles operating at reduced pressures near an Agar layer of a properly selected concentration. Geometric scaling is based on the ratio of bubble maximum radii in the two configurations, and fluid dynamics scaling follows the Rayleigh scaling, i.e. lengths are normalized by the bubble maximum radius and times by the Rayleigh time. Scaling of the materials properties is achieved by equating the ratio of the materials mechanical properties (Young's and shear moduli) to the ratio of the local ambient pressures collapsing the bubble. Full FSI numerical simulations conducted at different scales with the two materials indicate the validity of the scaling.

Microbubble enhanced High Intensity Focused Ultrasound (HIFU) is of great interest to tissue ablation for tumor treatment such as in liver and brain cancers, in which ultrasonic contrast agent microbubbles are injected to the targeted region to promote local heating while reducing pre-focal damage. To accurately characterize the acoustic and thermal fields during this process, a compressible Euler-Lagrange model is used. The non-linear ultrasound field is modeled using compressible N-S equations on an Eulerian grid, while the microbubbles are tracked as discrete singularities in a Lagrangian fashion with their dynamics computed. Their intimate coupling is realized through the local void fraction, which is computed from the instantaneous bubble volumes and locations, and then fed to the fluid continuum model. Owing to demanding computational cost in real applications, schemes for significant speedup are highly desirable. We present here a MPI parallelization scheme based on domain decomposition for both the continuum fluid and the discrete bubbles. The Eulerian computational domain is subdivided into several subdomains having each the same number of grids, while the bubbles are subdivided based on their locations corresponding to each subdomain. During each computation time step, MPI processors, each handling one subdomain, are 1) first used to execute the fluid computation, and 2) then to execute the bubble computations, 3) followed by the coupling procedure, which maps the void fraction from the Lagrangian bubble solutions into the Eulerian grids. Steps 1) and 2) are relatively straightforward by routinely following regular MPI procedures. However, step 3) becomes challenging as the effect of the bubbles through the void fraction at an Eulerian point near a subdomain border will require information from bubbles located in different subdomains. Similarly, a bubble near a border between subdomains will spread its contribution to the void fraction of different subdomains. This is addressed by a special utilization of ghost cells surrounding each fluid subdomain, which allows bubbles to spread their void fraction effects across subdomain edges without the need of exchanging directly bubble information between subdomains and significantly increasing overhead. This void fraction implementation is verified by gas volume conservation before and after spreading the bubble effects. Other bubble effects such as thermal effects are handled in a similar way. This parallelization scheme is validated and illustrated on a typical microbubble enhanced HIFU problem, followed by parallelization scaling tests and efficiency analysis.

Modeling the dynamics of microbubbles inside confined spaces has many potential applications in biomedicine, sonoporation being one classic example. Sonoporation is the permeabilization of a blood vessel’s endothelial cell membrane by acoustic waves in order to non-invasively deliver large-sized drug molecules into cells for therapeutic applications. By controlled activation of ultrasound contrast agents (UCA) in a microvessel, one can achieve better permeabilization without causing permanent damage associated with high intensity ultrasound. This paper considers numerically, the fluid-structure interactions (FSI) of UCA microbubbles with a microvessel accounting for large deformations. The modeling approach is based on a multi-material compressible flow solver that uses a Lagrangian treatment for numerical discretization of cells containing an interface between two phases and an Eulerian treatment for cells away from material interfaces. A re-mapping procedure is employed to map the Lagrangian solution back to the Eulerian grid. The model is first validated by simulating a microbubble oscillating due to an imposed ultrasound inside a microvessel and good agreement with experiments is obtained for both the bubble and vessel dynamics. The effect of vessel elasticity is then studied and it is shown that increasing the vessel elasticity damps the bubble oscillations. Then the effect of placing the bubble away from the axis of vessel is studied and it is shown that bubbles closer the vessel wall are capable of creating maximum deformation on the wall compared to those away from the wall.

The dynamics of a bubble cloud excited by a sinusoidal pressure field near a rigid wall is studied using a novel Eulerian/Lagrangian two-phase flow model. The effects of key parameters such as the amplitude and frequency of the excitation pressure, the cloud and bubble sizes, the void fraction, and the initial standoff distance on the bubbles’ collective behavior and the resulting pressure loads on the nearby wall are investigated. The study shows that nonlinear bubble cloud dynamics becomes more pronounced and results in higher pressure loading at the wall as the excitation pressure amplitude increases. The strongest collective bubble behavior occurs at a preferred resonance frequency. At this resonance frequency, pressure peaks orders of magnitudes higher than the excitation pressure result from the bubble interaction when the amplitude of the pressure excitation is high. The numerically obtained resonance frequency is significantly different from the reported natural frequency of a spherical cloud derived from linear theory, which assumes small amplitude oscillations in an unbounded medium. At high amplitudes of the excitation, the resonance frequency decreases almost linearly with the ratio of excitation pressure amplitude to ambient pressure until the ratio is larger than one.

The limited amount of liquids and gases that can be carried to space makes it imperative to recycle and reuse these fluids for extended human operations. During recycling processes gas and liquid phases are often intermixed. In the absence of gravity, separating gases from liquids is challenging due to the absence of buoyancy. This paper describes development of a passive phase separator that is capable of efficiently and reliably separating gas-liquid mixtures of both high and low void fractions in a wide range of flow rates that is applicable to for both space and earth applications.

A multiscale two-phase flow model based on a coupled Eulerian/Lagrangian approach is applied to capture the sheet cavitation formation, development, unsteady breakup, and bubble cloud shedding on a hydrofoil. No assumptions are needed on mass transfer. Instead natural free field nuclei and solid boundary nucleation are modelled and enable capture of the sheet and cloud dynamics. The multiscale model includes a micro-scale model for tracking the bubbles, a macro-scale model for describing large cavity dynamics, and a transition scheme to bridge the micro and macro scales. With this multiscale model small nuclei are seen to grow into large bubbles, which eventually merge to form a large scale sheet cavity. A reentrant jet forms under the sheet cavity, travels upstream, and breaks the cavity, resulting in the emission of high pressure peaks as the broken pockets shrink and collapse while travelling downstream. The method is validated on a 2D NACA0015 foil and is shown to be in good agreement with published experimental measurements in terms of sheet cavity lengths and shedding frequencies. Sensitivity assessment of the model parameters and 3D effects on the predicted major cavity dynamics are also discussed.

Numerical modeling of cavitating bubbly flows is challenging due to the wide range of characteristic lengths of the physics at play: from micrometers (e.g., bubble nuclei radius) to meters (e.g., propeller diameter or sheet cavity length). To address this, we present here a multiscale approach which integrates a Discrete Singularities Model (DSM) for dispersed microbubbles and a two-phase Navier Stokes solver for the bubbly medium, which includes a level set approach to describe large cavities or gaseous pockets. Inter-scale schemes are used to smoothly bridge the two transitioning subgrid DSM bubbles into larger discretized cavities. This approach is demonstrated on several problems including cavitation inception and vapor core formation in a vortex flow, sheet-to-cloud cavitation over a hydrofoil, cavitation behind a blunt body, and cavitation on a propeller. These examples highlight the capabilities of the developed multiscale model in simulating various form of cavitation.

Surface cleaning using cavitation bubble dynamics is investigated numerically through modeling of bubble dynamics, dirt particle motion, and fluid material interaction. Three fluid dynamics models; a potential flow model, a viscous model, and a compressible model, are used to describe the flow field generated by the bubble all showing the strong effects bubble explosive growth and collapse have on a dirt particle and on a layer of material to remove. Bubble deformation and reentrant jet formation are seen to be responsible for generating concentrated pressures, shear, and lift forces on the dirt particle and high impulsive loads on a layer of material to remove. Bubble explosive growth is also an important mechanism for removal of dirt particles, since strong suction forces in addition to shear are generated around the explosively growing bubble and can exert strong forces lifting the particles from the surface to clean and sucking them toward the bubble. To model material failure and removal, a finite element structure code is used and enables simulation of full fluid–structure interaction and investigation of the effects of various parameters. High impulsive pressures are generated during bubble collapse due to the impact of the bubble reentrant jet on the material surface and the subsequent collapse of the resulting toroidal bubble. Pits and material removal develop on the material surface when the impulsive pressure is large enough to result in high equivalent stresses exceeding the material yield stress or its ultimate strain. Cleaning depends on parameters such as the relative size between the bubble at its maximum volume and the particle size, the bubble standoff distance from the particle and from the material wall, and the excitation pressure field driving the bubble dynamics. These effects are discussed in this contribution.

The modification of the bubble nuclei population by the presence of a finite-span hydrofoil is modeled numerically using an Eulerian-Lagrangian approach. The unsteady liquid flow field is simulated using Navier-Stokes equations, while the bubbles, initiating from nuclei in the free stream and emitted from boundaries, are tracked using a Lagrangian approach. The effects of including gas diffusion, wall nucleation, and bubble breakup on nuclei distribution downstream of hydrofoil are studied. The inclusion of gas diffusion is found to significantly increase the size of the bubbles downstream. Also, inclusion of boundary nucleation is found to significantly increase the total number of large bubbles collected in the wake as compared to accounting for free nuclei alone. Bubble breakup, modeled using instability analysis and experimental observations, is seen to result in a significant increase in the number of small and mid-size bubbles, at the expense of the large size bubbles.

This paper describes a three-dimensional Eulerian–Lagrangian method for the modeling and simulation of high-speed multi-material dynamics. The equations for conservation of mass, momentum, and energy are solved on a fixed Cartesian grid using a fully conservative higher order MUSCL scheme. The dilatational response of each material is handled using a suitable equation of state. The embedded interfaces are handled using a mixed-cell approach. This approach uses an Eulerian treatment for the computational cells away from the interface and a Lagrangian treatment for the cells including interface elements, resulting in a fully conservative method for multi-material interactions. The method has shown capability to resolve and capture non-linear waves such as shock waves, rarefaction waves, and contact discontinuities in complex geometries. This work mainly emphasizes the handling of shock-wave interaction with bubbles, bubbly media, and multi-fluid interfaces in a compressible flow framework. Several numerical examples are shown to demonstrate the validity and robustness of the method.

For applications involving large bubble volume changes such as in cavitating flows and in bubbly two-phase flows involving shock and pressure wave propagation, the dynamics, relative motion, deformation, and interaction of bubbles with the surrounding medium play crucial roles and require accurate modeling. We present in this paper a fundamental study of the dynamic oscillations of a “primary” bubble in a bubbly mixture using a two-way coupled Euler–Lagrange model. It addresses a simplified spherical configuration while using the full three-dimensional code. A main objective of the study is to investigate how the dynamics of a “primary” bubble is affected by the presence of a surrounding bubbly medium and how it differs from its behavior in a pure liquid. This helps elucidate the physics at play for this relatively simple configuration. The model simulates the mixture as a continuum and solves the corresponding Navier Stokes equations with grids moving with the interface of the primary bubble wall. The surrounding microbubbles are tracked in a Lagrangian fashion accounting for their volume evolution. The two-way coupling between the bubbly medium and the primary bubble dynamics is realized through the local density of the mixture obtained from the tracking of the microbubbles and the determination of their volumes and spatial distribution. The simulations clearly indicate that the surrounding microbubbles absorb energy emitted from the primary bubble during its oscillations. This results in a reduction of the maximum radius and the period of oscillations of the primary bubble as compared to the dynamics in the pure liquid. Also, accounting for the dynamics of the field bubbles brings out the presence in the two-phase medium of a phase shift between density and pressure distributions. Such a shift is not captured by two-phase homogeneous medium models. These effects increase with increase in the mixture void fraction and in the initial bubble sizes in the mixture. The numerical observations are found to be in good qualitative agreements with previously published experimental data ( Jayaprakash et al., 2011 ) investigating spark generated bubble dynamics in a bubbly medium.

Cavitation erosion studies require a well-defined measure of the aggressiveness of the subject cavitation field. One proposed method of cavitation field strength evaluation is to use pitting tests on a selected material sample subjected to the cavitation field. These relatively short duration tests record pits or permanent deformations from individual cavitation events during the cavitation incubation period. The pitting test results are dependent on the load and the material used in the tests and a good understanding of the pit formation mechanism is required to correlate the loads with the deformations. In this study, finite element numerical simulations are conducted to examine the response of several selected materials to imposed loads representing cavitation events. The magnitude, duration, and spatial extent of the loads are varied, and the effects of these on the material deformations are studied. Next, the effects of material properties, such as yield stress, Young’s modulus, and plastic modulus on the pitting characteristics are elucidated. Material responses are found to be drastically different between metals and compliant materials and to depend significantly on load duration and spatial extent in addition to the magnitude.

Tandem bubble (TB) interactions have been shown to produce directional jets that can be used to create membrane poration on single cells. Jet speed and associated flow field produced around the TB have been postulated to play an important role in TB–induced bioeffects. In this study, dynamics of tandem bubble interaction in a microfluidic channel (25 µm in height) was analyzed by high-speed imaging and simulated using 3DYNAFS-BEM© (DYNAFLOW, INC.). The results suggest that jet size and geometry are primarily controlled by the maximum diameter of the first bubble (D1) while jet speed is about linearly correlated with maximum diameter of the second bubble (D2).

Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.

The effects of gravity on a phase separator are studied numerically using an Eulerian/Lagrangian two-phase flow approach. The separator utilizes high intensity swirl to separate bubbles from the liquid. The two-phase flow enters tangentially a cylindrical swirl chamber and rotate around the cylinder axis. On earth, as the bubbles are captured by the vortex formed inside the swirl chamber due to the centripetal force, they also experience the buoyancy force due to gravity. In a reduced or zero gravity environment buoyancy is reduced or inexistent and capture of the bubbles by the vortex is modified. The present numerical simulations enable study of the relative importance of the acceleration of gravity on the bubble capture by the swirl flow in the separator. In absence of gravity, the bubbles get stratified depending on their sizes, with the larger bubbles entering the core region earlier than the smaller ones. However in presence of gravity, stratification is more complex as the two acceleration fields — due to gravity and to rotation — compete or combine during the bubble capture.

The limited amount of liquids and gases that can be carried to space makes it imperative to recycle and reuse these fluids for extended human operations. During recycling processes gas and liquid phases are often intermixed. In the absence of gravity, separating gases from liquids is challenging due to the absence of buoyancy. This paper discusses a phase separator that is capable of efficiently and reliably separating gas-liquid mixtures of both high and low void fractions in a wide range of flow rates that is applicable to reduced and zero gravity environments. The phase separator consists of two concentric cylindrical chambers. The fluid introduced in the space between the two cylinders enters the inner cylinder through tangential slots and generates a high intensity swirling flow. The geometric configuration is selected to make the vortex swirl intense enough to lead to early cavitation which forms a cylindrical vaporous core at the axis even at low flow rates. Taking advantage of swirl and cavitation, the phase separator can force gas out of the liquid into the central core of the vortex even at low void fraction. Gas is extracted from one end of the cylinder axial region and liquid is extracted from the other end. The phase separator has successfully demonstrated its capability to reduce mixture void fractions down to 10−8 and to accommodate incoming mixture gas volume fractions as high as 35% in both earth and reduced gravity flight tests. The phase separator is on track to be tested by NASA on the International Space Station (ISS). Additionally, the phase separator design exhibits excellent scalability. Phase separators of different dimensions, with inlet liquid flow rates that range from a couple of GPMs to a few tens of GPMs, have been built and tested successfully in the presence and absence of the gravity. Extensive ground experiments have been conducted to study the effects of main design parameters on the performance of the phase separator, such as the length and diameter of the inner cylinder; the size, location, and layout of injection slots and exit orifices, etc., on the swirling flow behavior, and on the gas extraction performance. In parallel, numerical simulations, utilizing a two-phase Navier-Stokes flow solver coupled with bubble dynamics, have been conducted extensively to facilitate the development of the phase separator. These simulations have enabled us to better understand the physics behind the phase separation and provided guideline for system parts optimization. This paper describes our efforts in developing the passive phase separator for both space and ground applications.

Cavitation flow behind a blunt body is modeled using a physics-based numerical model of cavitation initiation and transition to larger cavities. The calculations initiate from the dynamics of nuclei, then tracks the dispersed bubble phase with a two-phase viscous model. This solver includes a level set method to model coalescence of the nuclei into large cavities and to track the dynamics of the resulting free surfaces. A transition scheme enables collection of the bubbles into a large cavity and also enables breakup of a large cavity into a bubble cloud. Using this model, simulations are conducted for different flow velocities and corresponding cavitation regimes. When the velocity is relatively small (i.e., large cavitation number), flow separation behind the body results in the shedding of vortices, which capture nuclei in their cores to form elongated vortical cavities. As the flow velocity increases (or as the ambient pressure decreases) the flow evolves into a separated flow with a large cavity behind the body. A reentrant jet may form and move upstream into the cavity towards the body. This jet periodically shears off portions of the cavity volume, resulting in large amounts of bubble clouds. These results are in good qualitative agreements with experimental observations.

A multi-bubble dynamics code accounting for gas diffusion in the liquid and through the bubble wall was developed and used to study the modification of a bubble nuclei population dynamics by a propeller. The propeller flow field was obtained using a Reynolds-Averaged Navier-Stokes (RANS) solver and bubble nuclei populations were propagated in this field. The numerical procedure enabled establishment of the possibility of production behind the propeller of relatively large visible bubbles starting from typical ocean nuclei size distributions. The resulting larger bubbles are seen to cluster in the blade wakes and tip vortices. Parametric investigations of the initial nuclei size distribution, the dissolved gas concentration, and the cavitation number were conducted to identify their effects on bubble entrainment and the resultant void fractions and bubble distribution modifications downstream from the propeller. Imposed synthetic turbulence-like fluctuations unto the average RANS flow field were also used to study the effect averaging in the RANS procedure has on the results.

This contribution presents experimental and numerical investigations of the concept jet propulsion augmentation using bubble injection. A half-3D (D-shaped cylindrical configuration to enable optimal visualizations) divergent-convergent nozzle was designed, built, and used for extensive experiments under different air injection conditions and thrust measurement schemes. The design, optimization, and analysis were conducted using numerical simulations. The more advanced model was based on a two-way coupling between an Eulerian description of the flow field and a Lagrangian tracking of the injected bubbles using our Surface Averaged Pressure (SAP) model. The numerical results compare very favorably with nozzle experiments and both experiments and simulations validation the thrust augmentation concept. For a properly designed nozzle and air injection system, air injection produces net thrust augmentation, which increases with the rate of bubble injection. Doubling of thrust was measured for a 50% air injection rate. This beneficial effect remains at 50% after account for liquid pump additional work to overcome increased pressure by air injection.

Cavitating jet technologies (DynaJets®) were investigated as a means of disinfection of gram-negative Escherichia coli, Klebsiellapneumoniae, Pseudomonas syringae, and Pseudomonas aeruginosa, and gram-positive Bacillus subtilis. The hydrodynamic cavitating jets were found to be very effective in reducing the concentrations of all of these species. In general, the observed rates of disinfection of gram-negative species were higher than for gram-positive species. However, different gram-negative species also showed significant differences (P. syringae 6-log(10) reduction, P. aeruginosa 2-log(10) reduction) under the same conditions. Disinfection of E. coli repeatedly showed five orders of magnitude reduction in concentration within 45-60-min at low nozzle pressure (2.1 bar). Optimization of nozzle design and operating pressures increased disinfection rates per input energy by several orders of magnitude. The power efficiencies of the hydrodynamic cavitating jets were found to be 10-100 times greater than comparable ultrasonic systems.

The stability of thick shell encapsulated bubbles is studied analytically. 3-D small perturbations are introduced to the spherical oscillations of a contrast agent bubble in response to a sinusoidal acoustic field with different amplitudes of excitation. The equations of the perturbation amplitudes are derived using asymptotic expansions and linear stability analysis is then applied to the resulting differential equations. The stability of the encapsulated microbubbles to nonspherical small perturbations is examined by solving an eigenvalue problem. The approach then identifies the fastest growing perturbations which could lead to the breakup of the encapsulated microbubble or contrast agent.

The growth, oscillation and collapse of vortex cavitation bubbles are examined using both two- and three-dimensional numerical models. As the bubble changes volume within the core of the vortex, the vorticity distribution of the surrounding flow is modified, which then changes the pressures at the bubble interface. This interaction can be complex. In the case of cylindrical cavitation bubbles, the bubble radius will oscillate as the bubble grows or collapses. The period of this oscillation is of the order of the vortex time scale, τV= 2πrc/uθ,max, wherercis the vortex core radius anduθ,maxis its maximum tangential velocity. However, the period, oscillation amplitude and final bubble radius are sensitive to variations in the vortex properties and the rate and magnitude of the pressure reduction or increase. The growth and collapse of three-dimensional bubbles are reminiscent of the two-dimensional bubble dynamics. But, the axial and radial growth of the vortex bubbles are often strongly coupled, especially near the axial extents of the bubble. As an initially spherical nucleus grows into an elongated bubble, it may take on complex shapes and have volume oscillations that also scale with τV. Axial flow produced at the ends of the bubble can produce local pinching and fission of the elongated bubble. Again, small changes in flow parameters can result in substantial changes to the detailed volume history of the bubbles.

Cavitation inception in a ducted propulsor was studied numerically using Navier-Stokes computations and bubble dynamics models. Experimental observations of the propulsor model and previous numerical computations using Reynolds-averaged Navier-Stokes (RANS) codes indicated that cavitation inception occurred in the region of interaction of the leakage and trailing tip vortices. The RANS simulations failed, however, to predict correctly both the cavitation inception index value and the inception location. To improve the numerical predictions, we complemented here the RANS computations with a direct Navier-Stokes simulation in a reduced computational domain including the region of interaction of the two vortices. Initial and boundary conditions in the reduced domain were provided by the RANS solution of the full ducted propulsor flow. Bubble nuclei were released in this flow field, and spherical and nonspherical bubble dynamics models were exercised to investigate cavitation inception. This resulted in a solution in much better agreement with the experimental measurements than the original RANS solution. Both the value of the cavitation inception index and the location of the cavitation inception were very well captured. The characteristics of the emitted acoustic signals and of the bubble shapes during a cavitation event were also computed.

Material deformation and pitting from cavitation bubble collapse is investigated using fluid and material dynamics and their interaction. In the fluid, a novel hybrid approach, which links a boundary element method and a compressible finite difference method, is used to capture non-spherical bubble dynamics and resulting liquid pressures efficiently and accurately. The bubble dynamics is intimately coupled with a finite-element structure model to enable fluid/structure interaction simulations. Bubble collapse loads the material with high impulsive pressures, which result from shock waves and bubble re-entrant jet direct impact on the material surface. The shock wave loading can be from the re-entrant jet impact on the opposite side of the bubble, the fast primary collapse of the bubble, and/or the collapse of the remaining bubble ring. This produces high stress waves, which propagate inside the material, cause deformation, and eventually failure. A permanent deformation or pit is formed when the local equivalent stresses exceed the material yield stress. The pressure loading depends on bubble dynamics parameters such as the size of the bubble at its maximum volume, the bubble standoff distance from the material wall and the pressure driving the bubble collapse. The effects of standoff and material type on the pressure loading and resulting pit formation are highlighted and the effects of bubble interaction on pressure loading and material deformation are preliminarily discussed.

Cavitating and bubbly flows are encountered in many engineering problems involving propellers, pumps, valves, ultrasonic biomedical applications, etc. In this contribution, an openmp parallelized Euler–Lagrange model of two-phase flow problems and cavitation is presented. The two-phase medium is treated as a continuum and solved on an Eulerian grid, while the discrete bubbles are tracked in a Lagrangian fashion with their dynamics computed. The intimate coupling between the two description levels is realized through the local void fraction, which is computed from the instantaneous bubble volumes and locations, and provides the continuum properties. Since, in practice, any such flows will involve large numbers of bubbles, schemes for significant speedup are needed to reduce computation times. We present here a shared-memory parallelization scheme combining domain decomposition for the continuum domain and number decomposition for the bubbles; both selected to realize maximum speedup and good load balance. The Eulerian computational domain is subdivided based on geometry into several subdomains, while for the Lagrangian computations, the bubbles are subdivided based on their indices into several subsets. The number of fluid subdomains and bubble subsets matches with the number of central processing unit (CPU) cores available in a shared-memory system. Computation of the continuum solution and the bubble dynamics proceeds sequentially. During each computation time step, all selected openmp threads are first used to evolve the fluid solution, with each handling one subdomain. Upon completion, the openmp threads selected for the Lagrangian solution are then used to execute the bubble computations. All data exchanges are executed through the shared memory. Extra steps are taken to localize the memory access pattern to minimize nonlocal data fetch latency, since severe performance penalty may occur on a nonuniform memory architecture (NUMA) multiprocessing system where thread access to nonlocal memory is much slower than to local memory. This parallelization scheme is illustrated on a typical nonuniform bubbly flow problem, cloud bubble dynamics near a rigid wall driven by an imposed pressure function (Ma et al., 2013, “Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall,” International Mechanical Engineering Congress and Exposition, San Diego, CA, Nov. 15–21, Paper No. IMECE2013-65191 and Ma et al., 2015, “Euler–Lagrange Simulations of Bubble Cloud Dynamics Near a Wall,” ASME J. Fluids Eng., 137(4), p. 041301).

We present in this paper a two-way coupled Eulerian–Lagrangian model to study the dynamics of clouds of microbubbles subjected to pressure variations and the resulting pressures on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the Navier–Stokes equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting singularities representing moving and oscillating spherical bubbles, following a modified Rayleigh–Plesset–Keller–Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density determined by the bubbles' volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures at different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or nonsynchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressure. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall also affects significantly the resulting pressures. A bubble cloud collapsing very close to the wall exhibits a cascading collapse, with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and this results in very high pressure peaks at the wall. At farther cloud distances from the wall, the bubble cloud collapses quasi-spherically with the cloud center collapsing last.

The acoustic pressure generated by cavitation inception in a tip vortex flow was simulated in water containing a realistic bubble nuclei size distribution using a surface-averaged pressure (SAP) spherical bubble dynamics model. The flow field was obtained by the Reynolds-averaged Navier–Stokes computations for three geometrically similar scales of a finite-span elliptic hydrofoil. An “acoustic” criterion, which defines cavitation inception as the flow condition at which the number of acoustical “peaks” above a pre-selected pressure level exceeds a reference number per unit time, was applied to the three scales. It was found that the scaling of cavitation inception depended on the reference values (pressure amplitude and number of peaks) selected. Scaling effects (i.e., deviation from the classical σi∝Re0.4) increase as the reference inception criteria become more stringent (lower threshold pressures and less number of peaks). Larger scales tend to detect more cavitation inception events per unit time than obtained by classical scaling because a relatively larger number of nuclei are excited by the tip vortex at the larger scale due to simultaneous increase of the nuclei capture area and of the size of the vortex core. The average nuclei size in the nuclei distribution was also found to have an important impact on cavitation inception number. Scaling effects (i.e., deviation from classical expressions) become more important as the average nuclei size decreases.

A spherical and a nonspherical bubble dynamics models were developed to study cavitation inception, scaling, and dynamics in a vortex flow. The spherical model is a modified Rayleigh–Plesset model to account for bubble slip velocity and for nonuniform pressures around the bubble. The nonspherical model is embedded in an unsteady Reynolds-averaged Navier–Stokes code with appropriate free-surface boundary conditions and a moving chimera grid scheme around the bubble. The effect of nonspherical deformation and bubble/flow interaction on bubble dynamics is illustrated by comparing spherical and nonspherical models. It is shown that nonspherical deformations and bubble/flow interactions are important for an accurate prediction of cavitation inception. The surface-averaged pressure-modified Rayleigh–Plesset scheme is a significant improvement over the conventional spherical model, and is able to capture the volume changes of a bubble during its capture. It is also a fast scheme for studying scaling. In a preliminary study, the scaling effects on cavitation inception were examined using two different Reynolds numbers owing to two different chord lengths. The nuclei-size effect on the prediction of cavitation inception was also studied, and its important effects are highlighted.

We have developed a three-dimensional BEM based code (3DYNAFS©) to study nonlinear free surface flows. The code is being used here to study bubble dynamics, such as that due to an underwater explosion, beneath surface piercing bodies. Six degree-of-freedom rigid body motion of the surface piercing bodies are modeled producing a fully coupled fluid-structure interaction effect simulation. Validation of the code is presented by comparison of simulations with laboratory experimental data obtained from high speed video recordings of surface piercing bodies interacting with bubbles generated by electric spark discharge. Two cylindrical body configurations are considered under both free floating and rigidly constrained conditions. The results of the numerical simulation show very good comparison to the experimental data in terms of bubble shapes and periods, the time evolution of the bubble and the induced motion of the bodies.

The current study considers the prediction of tip vortex cavitation inception at a fundamental physics based level. Starting form the observation that cavitation inception detection is based on the “monitoring” of the interaction between bubble nuclei and the flow field, the bubble dynamics is investigated in detail. A spherical model coupled with a bubble motion equation is used to study numerically the dynamics of a nucleus in an imposed flow field. The code provides bubble size and position versus time as well as the resulting pressure at any selected monitoring position. This model is used to conduct a parametric study. Bubble size and emitted sound versus time are presented for various nuclei sizes and flow field scales in the case of an ideal Rankine vortex to which a longitudinal viscous core size diffusion model is imposed. Based on the results, one can deduce cavitation inception with the help of either an “optical inception criterion” (maximum bubble size larger than a given value) or an “acoustical inception criterion” (maximum detected noise higher than a given background value). We use here such criteria and conclude that scaling effects can be inherent to the way in which these criteria are exercised if the bubble dynamics knowledge is not taken into account.

This work uses a compressible Eulerian multi-material solver with three modeling approaches to examine shock and pressure wave propagation in a bubbly medium. These approaches represent different levels of complexity from fully resolving the dispersed bubbles to treating the bubbly medium as a homogeneous mixture. An intermediate approach is based on treating bubbles as discrete singularities. Propagation of the pressure wave through the bubbly medium is compared between the simplified approaches and the fully resolved bubble simulation. Different scenarios demonstrating the effect of pressure amplitude, void fraction, and bubble size distribution are presented to further understand wave propagation in bubbly media.Copyright © 2014 by ASME

Cavitating bubbly flows are encountered in many engineering problems involving propellers, pumps, valves, ultrasonic biomedical applications, … etc. In this contribution an OpenMP parallelized Euler-Lagrange model of two-phase flow problems and cavitation is presented. The two-phase medium is treated as a continuum and solved on an Eulerian grid, while the discrete bubbles are tracked in a Lagrangian fashion with their dynamics computed. The intimate coupling between the two description levels is realized through the local void fraction, which is computed from the instantaneous bubble volumes and locations, and provides the continuum properties. Since, in practice, any such flows will involve large numbers of bubbles, schemes for significant speedup are needed to reduce computation times. We present here a shared-memory parallelization scheme combining domain decomposition for the continuum domain and number decomposition for the bubbles; both selected to realize maximum speed up and good load balance. The Eulerian computational domain is subdivided based on geometry into several subdomains, while for the Lagrangian computations, the bubbles are subdivided based on their indices into several subsets. The number of fluid subdomains and bubble subsets are matched with the number of CPU cores available in a share-memory system. Computation of the continuum solution and the bubble dynamics proceeds sequentially. During each computation time step, all selected OpenMP threads are first used to evolve the fluid solution, with each handling one subdomain. Upon completion, the OpenMP threads selected for the Lagrangian solution are then used to execute the bubble computations. All data exchanges are executed through the shared memory. Extra steps are taken to localize the memory access pattern to minimize non-local data fetch latency, since severe performance penalty may occur on a Non-Uniform Memory Architecture multiprocessing system where thread access to non-local memory is much slower than to local memory. This parallelization scheme is illustrated on a typical non-uniform bubbly flow problem, cloud bubble dynamics near a rigid wall driven by an imposed pressure function.

An optimization method based on a genetic algorithm (GA) and a boundary element method is applied to solve an electrical impedance tomography problem. The scheme is applied to reconstruct highly irregular shapes and to image and count objects inside a host medium of different impedance. A Pareto multiobjective optimization method is applied to improve the performance of the GA. Comparisons between the GA and a calculus-based method for selected test problems show that the calculus-based method outperforms the GA in simple cases but that for more complex cases the GA reaches the correct solution whereas the calculus-based method does not. A hybrid scheme that we developed combining a calculus-based method and the GA is shown to be the most efficient and robust even when applied to the complex cases we tested. The sensitivity of the current scheme is evaluated in the presence of noise.

The uniform flow past a rotating marine propeller was studied using incompressible Reynolds-averaged Navier-Stokes computations with the Baldwin-Barth turbulence model. Extensive comparison with the experimental data was made to validate the numerical results. The general characteristics of the propeller flow were well predicted. The current numerical method, however, produced an overly diffusive and dissipative tip vortex core. Modification of the Baldwin-Barth model to better predict the Reynolds stress measurements also improved the prediction of the mean velocity field. A modified tip geometry was also tested to show that an appropriate cross section design can delay cavitation inception in the tip vortex without reducing the propeller performance.

The tip-vortex flow over a finite-span hydrofoil with laminar separation on the hydrofoil surface was numerically studied by computing the three-dimensional unsteady Navier-Stokes equations. The computations were direct numerical simulations of all resolvable structures without adding a turbulence model. The topological structure of unsteady separated flow and the influence of the unsteady laminar separated flow on the tip vortex for both swept and unswept hydrofoils were qualitatively investigated. The secondary flow induced by the swept planform played an important role in the unsteadiness of the tip vortex. The interaction between the tip vortex and the unsteady laminar separated flow became stronger as the sweep angle was increased

The Rayleigh-Plesset bubble dynamics equation coupled with the bubble motion equation developed by Johnson and Hsieh was applied to study the real flow effects on the prediction of cavitation inception in tip vortex flows. A three-dimensional steady-state tip vortex flow obtained from a Reynolds-Averaged Navier-Stokes computation was used as a prescribed flow field through which the bubble was passively convected. A “window of opportunity” through which a candidate bubble must pass in order to be drawn into the tip-vortex core and cavitate was determined for different initial bubble sizes. It was found that bubbles with larger initial size can be entrained into the tip-vortex core from a larger window size and also had a higher cavitation inception number.

The flow over a finite-span hydrofoil creating a tip vortex was numerically studied by computing the full Navier-Stokes equations. A good agreement in pressure distribution and oil flow pattern was achieved between the numerical solution and available experimental data. The steady-state roll-up process of the tip vortex was described in detail from the numerical results. The effect of the angle of attack, the Reynolds number, and the hydrofoil planform on the tip vortex was investigated. The axial and tangential velocities within the tip-vortex core in the near-field wake region were greatly influenced by the angle of attack. A jet-like profile in the axial velocity was found within the tip-vortex core at high angle of attack, while a wake-like profile in the axial velocity was found at low angle of attack. Increasing the Reynolds number was found to increase the maximum axial velocity, but only had a slight impact on the tangential velocity. Finally, a swept hydrofoil planform was found to attenuate the strength of the tip vortex due to the low-momentum boundary layer traveling into the tip vortex on the suction side.

This paper addresses the issue of transposing laboratory scale results of cavitation on a propeller to other geometrically similar propellers of larger sizes. A particular emphasis is placed on nuclei dynamics and similarities and differences in the behavior of the bubbles at the different scales. Considering a realistic nuclei size distribution, an Eulerian–Lagrangian method is used to numerically model propeller flow and the motion, dynamics, and collection of the bubbles for a set of propeller sizes. Strong scaling effects are found for propellers operating under the same cavitation number and advance coefficient and in waters, which have the same nuclei density distribution. Inclusion of strong bubble interactions in the simulations is required for future cavitation erosion modeling efforts. A multi-bubble interaction model is introduced in the second part of the paper and a preliminary study of potential collective effects on the cavitation impulsive loads is presented.

We present in this paper a two-way coupled Eulerian-Lagrangian model to study the dynamics of microbubble clouds exposed to incoming pressure waves and the resulting pressure loads on a nearby rigid wall. The model simulates the two-phase medium as a continuum and solves the N-S equations using Eulerian grids with a time and space varying density. The microbubbles are modeled as interacting spherical bubbles, which follow a modified Rayleigh-Plesset-Keller-Herring equation and are tracked in a Lagrangian fashion. A two-way coupling between the Euler and Lagrange components is realized through the local mixture density associated with the bubbles volume change and motion. Using this numerical framework, simulations involving a large number of bubbles were conducted under driving pressures of different frequencies. The results show that the frequency of the driving pressure is critical in determining the overall dynamics: either a collective strongly coupled cluster behavior or non-synchronized weaker multiple bubble oscillations. The former creates extremely high pressures with peak values orders of magnitudes higher than that of the excitation pressures. This occurs when the driving frequency matches the natural frequency of the bubble cloud. The initial distance between the bubble cloud and the wall is also critical on the resulting pressure loads. A bubble cloud collapsing very close to the wall exhibits a cascading collapse with the bubbles farthest from the wall collapsing first and the nearest ones collapsing last, thus the energy accumulates and then results in very violent pressure peaks at the wall. Farther from the wall, the bubble cloud collapses quasi spherically with the cloud center collapsing last.