Bubble Collapse Inside Rigid Ellipsoid Using Boundary Integral Method in Axisymmetric Configuration.

Hawchin Jabar Ahmed; Kawa M.A. Manmi

doi:10.21271/ZJPAS.35.2.8

Authors

Hawchin Jabar Ahmed Department of Mathematics, Faculty of Science, Soran University, Soran -Erbil, Kurdistan Region, Iraq.
Kawa M.A. Manmi Department of Mathematic, College of Science, Salahaddin University-Erbil, Kurdistan Region, Iraq

DOI:

https://doi.org/10.21271/ZJPAS.35.2.8

Keywords:

Bubble Collapse, Boundary Integral Method, Rigid Ellipsoid.

Abstract

A high-speed liquid jet forms toward the closest side of the boundary when a bubble collapses near a solid boundary. This is associated with important applications in cleaning microdevices, chemical reactions (sonochemistry) and biomedical ultrasound. In this work, bubble expansion, collapse and jet formation inside a rigid ellipsoid boundary have been investigated using the boundary integral method (BIM) in an axisymmetric configuration. We assume that the fluid flows satisfy the potential flow theory and the bubble is initially spherical with high gas pressure. Then the bubble growth and subsequently collapse non-spherically. Eventually high-speed liquid jet forms toward the nearby rigid boundary(s). The numerical results validated with the Rayleigh-Plesset equation for a spherical bubble oscillation at infinite fluid for several cycles as well as self-validating with considering image and without image method for using Green’s function in the BIM. Then, three different vertical standoff distances from the center of the bubble to the boundary of the ellipsoid have been considered to investigate the bubble motion behavior including jet velocity, jet width, Kelvin impulse and centroid movement. It was concluded that the standoff distances and ellipsoid radius were significant factors on the bubble behaviour.

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