Todd A. Hay

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Greens function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.

Model of coupled pulsation and translation of a gas bubble and rigid particle

A model of the interaction of a spherical gas bubble and a rigid spherical particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model accounts for pulsation and translation of the bubble as well as translation of the particle in an infinite, incompressible liquid. The model derived here is accurate to order R(5)d(5), where R is a characteristic radius and d is the separation distance between the bubble and particle. This order is the minimum accuracy required to account for the interaction of the bubble and particle. Dependence on the size and density of the particle is demonstrated through numerical integration of the dynamical equations for both the free and forced response of the system. Numerical results are presented for models accurate to orders higher than R(5)d(5) to demonstrate the consequences of truncating the equations at order R(5)d(5).

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability.

Models of cylindrical bubble pulsation

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23-26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion.

Model for the dynamics of a spherical bubble undergoing small shape oscillations between parallel soft elastic layers

A model is developed for a pulsating and translating gas bubble immersed in liquid in a channel formed by two soft, thin elastic parallel layers having densities equal to that of the surrounding liquid and small, but finite, shear moduli. The bubble is nominally spherical but free to undergo small shape deformations. Shear strain in the elastic layers is estimated in a way which is valid for short, transient excitations of the system. Coupled nonlinear second-order differential equations are obtained for the shape and position of the bubble, and numerical integration of an expression for the liquid velocity at the layer interfaces yields an estimate of the elastic layer displacement. Numerical integration of the dynamical equations reveals behavior consistent with laboratory observations of acoustically excited bubbles in ex vivo vessels reported by Chen et al. [Phys. Rev. Lett. 106, 034301 (2011) and Ultrasound Med. Biol. 37, 2139-2148 (2011)].

Final Report DE-EE0005380: Assessment of Offshore Wind Farm Effects on Sea Surface, Subsurface and Airborne Electronic Systems

Offshore wind energy is a valuable resource that can provide a significant boost to the US renewable energy portfolio. A current constraint to the development of offshore wind farms is the potential for interference to be caused by large wind farms on existing electronic and acoustical equipment such as radar and sonar systems for surveillance, navigation and communications. The US Department of Energy funded this study as an objective assessment of possible interference to various types of equipment operating in the marine environment where offshore wind farms could be installed. The objective of this project was to conduct a baseline evaluation of electromagnetic and acoustical challenges to sea surface, subsurface and airborne electronic systems presented by offshore wind farms. To accomplish this goal, the following tasks were carried out: (1) survey electronic systems that can potentially be impacted by large offshore wind farms, and identify impact assessment studies and research and development activities both within and outside the US, (2) engage key stakeholders to identify their possible concerns and operating requirements, (3) conduct first-principle modeling on the interactions of electromagnetic signals with, and the radiation of underwater acoustic signals from, offshore wind farms to evaluate the effect of such interactions on electronic systems, and (4) provide impact assessments, recommend mitigation methods, prioritize future research directions, and disseminate project findings. This report provides a detailed description of the methodologies used to carry out the study, key findings of the study, and a list of recommendations derived based the findings.

Green’s functions for a volume source in an elastic half-space

Greens functions are derived for elastic waves generated by a volume source in a homogeneous isotropic half-space. The context is sources at shallow burial depths, for which surface (Rayleigh) and bulk waves, both longitudinal and transverse, can be generated with comparable magnitudes. Two approaches are followed. First, the Greens function is expanded with respect to eigenmodes that correspond to Rayleigh waves. While bulk waves are thus ignored, this approximation is valid on the surface far from the source, where the Rayleigh wave modes dominate. The second approach employs an angular spectrum that accounts for the bulk waves and yields a solution that may be separated into two terms. One is associated with bulk waves, the other with Rayleigh waves. The latter is proved to be identical to the Greens function obtained following the first approach. The Greens function obtained via angular spectrum decomposition is analyzed numerically in the time domain for different burial depths and distances to the receiver, and for parameters relevant to seismo-acoustic detection of land mines and other buried objects.

A model for noise radiated by submerged piles and towers in littoral environments

Pile driving in shallow water during the construction of bridges and other structures can produce transient broadband noise of sufficient intensity to kill fish and disturb marine mammals. Sustained tonal noise radiated by towers supporting offshore wind turbines contains energy in frequency bands that may inhibit detection of coastal activities via passive sonar and seismic sensors. Understanding the generation and propagation of underwater noise due to pile driving and wind farms is important for determining the best strategies for mitigating the environmental impact of these noise sources. An analytic model, based on a Greens function approach, is presented for the sound radiated in the water column by a submerged cylindrical structure embedded in horizontally stratified layers of sediment. The sediment layers are modeled as viscoelastic media and the Greens function is derived via angular spectrum decomposition. Noise radiation due to both vibration of the structure and impulses delivered to the sed...

Effects of quadrupole and octupole modes on coupled nonlinear bubble interactions.

Photographs of bubble cluster dynamics have shown that under sufficiently intense acoustic excitation, neighboring bubbles may undergo shape deformation and even form opposing liquid jets. Jetting is one of the chief mechanisms thought responsible for cavitation‐induced erosion. Therefore, a better understanding of the phenomenon would be beneficial in improving the efficacy of and reducing collateral damage during medical procedures such as shock wave lithotripsy. Previous efforts to model aspherical collapse of a bubble near an interface have utilized purely numerical methods. In this presentation we derive dynamical equations for the coupled motion of two translating, aspherical gas bubbles. Deformation of the initially spherical bubble surfaces is taken into account by including quadrupole and octupole spherical harmonics in the boundary conditions on each bubble. For an axisymmetric geometry, this results in a set of eight coupled second‐order ordinary differential equations that may be integrated numerically in time. The effect of surface tension and shear viscosity on quadrupole and octupole contributions is included in a consistent manner. Simulation results agree qualitatively with measurements and predict the formation of opposing liquid jets for bubbles which are sufficiently close to one another. [Work supported by NIH DK070618.]

Green’s function for a volume source in a viscoelastic cylindrical tube.

A model based on Green’s functions that has been reported at previous meetings describes the field produced by a volumetric source in a bounded viscoelastic medium. Proposed applications of this model include scattering of sound in biological media and by objects buried in soil. The model was also adapted to study acoustically driven bubble pulsations near the surface of a viscoelastic medium, including calculation of the stress and strain in the medium. The methodology is generalized here to include cylindrical tubes. The Green’s function is obtained for a volumetric source at an arbitrary location in a viscoelastic or viscous fluid‐filled cylindrical tube. All modes of propagation in the elastic tube are taken into account as well as waves reflected from the tube wall. The Green’s function is expanded both as a Fourier integral with respect to the axial coordinate and as a Fourier series with respect to the polar angle. Amplitudes of the Fourier coefficients are determined by boundary conditions for displacements and stresses at the tube wall and by matching conditions on the cylindrical surface containing the source. The Green’s function is obtained in closed form and expressed through Hankel functions. [Work supported by NIH DK070618.]