Georges L. Chahine

The final stage of the collapse of a cavitation bubble near a rigid wall

During the collapse of an initially spherical cavitation bubble near a rigid wall, a reentrant jet forms from the side of the bubble farthest from the wall. This re-entrant jet impacts and penetrates the bubble surface closest to the wall during the final stage of the collapse. In the present paper, this phenomenon is modelled with potential flow theory, and a numerical approach based on conventional and hypersingular boundary integral equations is presented. The method allows for the continuous simulation of the bubble motion from growth to collapse and the impact and penetration of the reentrant jet. The numerical investigations show that during penetration the bubble surface is transformed to a ring bubble that is smoothly attached to a vortex sheet. The velocity of the tip of the re-entrant jet is always directed toward the wall during penetration with a speed less than its speed before impact. A high-pressure region is created around the penetration interface. Theoretical analysis and numerical results show that the liquid-liquid impact causes a loss in the kinetic energy of the flow field. Variations in the initial distance from the bubble centre to the wall are found to cause large changes in the details of the flow field. No existing experimental data are available to make a direct comparison with the numerical predictions. However, the results obtained in this study agree qualitatively with experimental observations.

The Use of Cavitating Jets to Oxidize Organic Compounds in Water

This paper reports on the application of hydrodynamic cavitation by the use of submerged cavitating liquid jets to trigger widespread cavitation and induce oxidation of organic compounds in the bulk liquid solution with a two order of magnitude increase in energy efficiency compared to the ultrasonic means. The results are compared to a bubble dynamics model that includes heat and mass transport, collective bubble effects, and a first order Arrhenius reaction rate model. Comparison of model results with experiment indicated the reactions were limited by contaminant transport to the bubble surface rather than by radical generation or the intensity of bubble collapse. Other findings are the desirability of operating at atmospheric ambient pressure and low driving pressures and of maximizing cavity surface area. These results suggest a great potential for the use of jet cavitation in practical scale waste treatment and remediation systems.

Boundary element techniques for efficient 2-D and 3-D electrical impedance tomography

This paper presents applications of boundary element methods to electrical impedance tomography. An algorithm for imaging the interior of a domain that consists of regions of constant conductivity is developed, that makes use of a simpler parametrization of the shapes of the regions to achieve efficiency. Numerical results from tests of this algorithm on synthetic data are presented, and show that the method is quite promising.

Bubble counting using an inverse acoustic scattering method

A nuclei size measurement technique is developed, based on a dispersion relation for propagation of sound waves through a bubbly liquid. This is used to relate the attenuation and phase velocity of a sound wave to the bubble population, leading to two integral equations. These equations are ill posed, and require special treatment for solution. Algorithms based on a minimization method that imposes a number of physical constraints on the solution, rendering the equation well posed, are developed. The procedure is first tested on analytical data with varying artificial noise added, and found to be successful in recovering the bubble density function, and to perform much better than other published solution techniques. Then, bubbles were generated using electrolysis and air injection through porous tubes, and bubble populations measured. Short monochromatic bursts of sound at different frequencies were emitted and received using hydrophones. The received signals were then processed and analyzed to obtain the attenuation and phase velocity. The void fraction and known experimental errors were also obtained and were fed as constraints to the inverse problem solution procedure. This resulted in bubble populations which compare favorably to those obtained by microphotography.

Efficient 2D and 3D electrical impedance tomography using dual reciprocity boundary element techniques

Abstract Numerical algorithms based on boundary element methods are developed for application to problems in Electrical Impedance Tomography (EIT). Two types of EIT problems are distinguished. In the first type internal boundaries of domains of constant conductivity are imaged. For such problems an algorithm based on identifying the shape of the included region is developed, and uses conventional BEM techniques. For problems where a distribution of conductivity is to be imaged algorithms that use dual reciprocity techniques are developed. The size of the inverse problem required to be solved is much reduced, offering substantial speed-ups over conventional techniques. Further, the present algorithms use simple parametrization of the unknowns to achieve efficiency. Numerical results from tests of this algorithm on synthetic data are presented, and these show that the method is quite promising.

Dynamical Interactions in a Multi-Bubble Cloud

Results of studies on the dynamics of clouds of bubbles via both an analytical technique using asymptotic expansions, and via numerical simulation using a three-dimensional boudary element technique (BEM) are reported. The asymptotic method relies on the assumption that the characteristic bubble size is much smaller than the characteristic inter-bubble distance. Result obtained from the two methods are compared, and are found to agree in the domain of validity of the asymptotic technique, which is for very low void fractions

Modeling of surface cleaning by cavitation bubble dynamics and collapse

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.

Advanced Experimental and Numerical Techniques for Cavitation Erosion Prediction

This book provides a comprehensive treatment of the cavitation erosion phenomenon and state-of-the-art research in the field. It is divided into two parts. Part 1 consists of seven chapters, offering a wide range of computational and experimental approaches to cavitation erosion. It includes a general introduction to cavitation and cavitation erosion, a detailed description of facilities and measurement techniques commonly used in cavitation erosion studies, an extensive presentation of various stages of cavitation damage (including incubation and mass loss), and insights into the contribution of computational methods to the analysis of both fluid and material behavior. The proposed approach is based on a detailed description of impact loads generated by collapsing cavitation bubbles and a physical analysis of the material response to these loads. Part 2 is devoted to a selection of nine papers presented at the International Workshop on Advanced Experimental and Numerical Techniques for Cavitation Erosion (Grenoble, France, 1-2 March 2011), representing the forefront of research on cavitation erosion. Innovative numerical and experimental investigations illustrate the most advanced breakthroughs in cavitation erosion research.

Dilute polymer solution effects on bubble growth and collapse

Spark‐generated bubble behavior was observed in an unbounded fluid and in the vicinity of a wall, both for water and a polymer solution. The formation of the re‐entering jet close to the wall is retarded in the presence of polymer additives.

Growth, oscillation and collapse of vortex cavitation bubbles

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 =2 πrc/uθ,max ,w hererc is the vortex core radius and uθ,max is 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.