Luca d'Agostino

Linearized Dynamics of Spherical Bubble Clouds

The present work investigates the dynamics of the one-dimensional, steady flow of a spherical bubble cloud subject to harmonic far-field pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility and relative motion of the two phases are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. The results are then generalized by means of Fourier synthesis to the case of arbitrary far-field pressure excitation. The flow displays various regimes (sub-resonant, trans-resonant and super-resonant) with different properties depending on the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms. Finally the results for the case of Gaussian-shaped far-field pressure change are presented and the most important limitations of the theory are briefly discussed. The simple linearized dynamical analysis developed so far clearly deminstrates the importance of the complex phenomena connected to the interaction of the dynamics of the bubbles with the flow and provides an introduction to the more realistic study of the same flows with nonlinear bubble dynamics.

Acoustical absorption and scattering cross sections of spherical bubble clouds

The present work investigates the acoustical absorption and scattering cross sections of spherical bubble clouds subject to harmonic farfield pressure excitation. Bubble dynamics effects and energy dissipation due to viscosity, heat transfer, liquid compressibility, and relative motion of the two phases are included. The equations of motion for the average flow and for the bubble radius are linearized and a closed-form solution is obtained. Due to the presence of natural oscillatory modes and frequencies, the acoustical cross sections of the cloud are very different from those of each individual bubble in the cloud, as well as from the acoustical cross sections of a single large bubble with the same volume of vapor and gas. In general, the acoustical properties of any give volume of the dispersed phase depend strongly on the degree of dispersion because of the complex interactions of the dynamics of the bubbles with the whole flow.

Linearized Dynamics of Two-Dimensional Bubbly and Cavitating Flows Over Slender Surfaces

The present work investigates the dynamics of two-dimensional, steady bubbly flows over a surface and inside a symmetric channel with sinusoidal profiles. Bubble dynamics effects are included. The equations of motion for the average flow and the bubble radius are linearized and a closed-form solution is obtained. Energy dissipation due to viscous, thermal and liquid compressibility effects in the dynamics of the bubbles is included, while the relative motion of the two phases and viscous effects at the flow boundaries are neglected. The results are then generalized by means of Fourier synthesis to the case of surfaces with slender profiles of arbitrary shape. The flows display various flow regimes (subsonic, supersonic and superresonant) with different properties according to the value of the relevant flow parameters. Examples are discussed in order to show the effects of the inclusion of the various energy dissipation mechanisms on the flows subject to harmonic excitation. Finally the results for a flow over a surface with a Gaussian-shaped bump are presented and the most important limitations of the theory are briefly discussed.

A Cavitation Susceptibility Meter With Optical Cavitation Monitoring—Part Two: Experimental Apparatus and Results

This work is concerned with the design, development and operation of a Cavitation Susceptibility Meter based on the use of a venturi tube for the measurement of the content of active cavitation nuclei in water samples. The pressure at the venturi throat is determined from the upstream pressure and the local flow velocity without corrections for viscous effects because the flow possesses a laminar potential core in all operational conditions. The main considerations leading to the present design concept are illustrated and the implementation of the whole system is described.

On the Inviscid Stability of Parallel Bubbly Flows

This paper investigates the effects of bubbly dynamics on the stability of parallel bubbly flows of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability problem. This is then used for the stability analysis of two-dimensional shear layers, jets and wakes. Inertial effects associated with the bubbly response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problems for the modified Rayleigh equation are obtained by means of a multiple shooting method. Depending on the characteristic velocities of the various flows, the void fractions, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical stability results for a single-phase fluid.

Inviscid stability of bubbly jets

This paper investigates the effects of bubble dynamics on the stability of bubbly and cavitating jets of low void fraction. The equations of motion for the bubbly mixture are linearized for small perturbations and the parallel flow assumption is used to obtain a modified Rayleigh equation governing the inviscid stability of a two-dimensional jet. Inertial effects associated with the bubble response and energy dissipation due to the viscosity of the liquid, the heat transfer between the two phases, and the liquid compressibility are included. Numerical solutions of the eigenvalue problem for the modified Rayleigh equation of a Bickley jet are obtained by a multiple shooting method. Depending on the jet velocity, the void fraction, and the ambient pressure, the presence of air bubbles can induce significant departures from the classical results for a single phase fluid.