Approximate methods for modelling cavitation bubbles near boundaries

Abstract

Approximate methods are developed for modelling the growth and collapse of clouds of cavitation bubbles near an infinite and semi-infinite rigid boundary, a cylinder, between two flat plates and in corners and near edges formed by planar boundaries. Where appropriate, comparisons are made between this approximate method and the more accurate boundary integral methods used in earlier calculations. It is found that the influence of nearby bubbles can be more important than the presence of boundaries. In confined geometries, such as a cylinder, or a cloud of bubbles, the effect of the volume change due to growth or collapse of the bubble can be important at much larger distances. The method provides valuable insight into bubble cloud phenomena.

A Boundary Integral Approach for Three-Dimensional Underwater Explosion Bubble Dynamics

“…The calculation indicates the formation of a ring jet around the lower circumference of the bubble. Similar calculations with bubbles between two infinite plates, where the attractive force of the plates oppose one another, have been made in axyismmetric conditions by Kucera and Blake (1989), with a 3-D code by Chahine (1982), and was observed by Chahine (1989). In these calculations, the bubble forms a ring jet about its circumference which eventually separates the bubble, in an hourglass fashion, into two bubbles.…”

Cloud Cavitation Dynamics

“…https://doi.org/10.1017/S1446181109000133 204 M. Wilson, J. R. Blake and P. M. Haese [6] become unstable. To resolve beyond initial stages of deformation, therefore, the internal singularity is repositioned at the mean centroid position…”

“…In past studies, Lagally's theorem has been extremely successful at predicting the dynamics of a few bubbles situated within various flow geometries. For example, Kucera and Blake [6] used a source-dipole representation of the bubble to model its growth and collapse near complex rigid boundaries. Their results indicated that such a model may be generally at most 3% in error, for such quantities as the bubble volume, Kelvin impulse, and bubble trajectory toward the boundary.…”

Conserved quantities for axisymmetric cavities near boundaries

“…On the surface J3 w e have the following, p + pgx = poo ----u z = poo + < so that the only contribution from the integral over ^ * n (3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19) …”

“…The five conservation principles would thus provide just sufficient conditions 216 R. Paull and J.R. Blake [2] to determine a simple global model for cavitation. A more detailed discussion on the conservation of linear momentum (the Kelvin impulse) may also be found in the review paper by Blake [4], while an approximate method to model the growth and collapse of cavitation bubbles near a rigid boundary have recently been developed by Kucera and Blake [6].…”