A non-singular boundary element method for modelling bubble dynamics in viscoelastic fluids
| Autor: | Timothy Nigel Phillips, Michael Walters |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Physics
Jet (fluid) Applied Mathematics Mechanical Engineering General Chemical Engineering Bubble Boundary (topology) 02 engineering and technology Mechanics Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Vortex ring Deborah number Physics::Fluid Dynamics 020303 mechanical engineering & transports Classical mechanics 0203 mechanical engineering Inviscid flow 0103 physical sciences No-slip condition General Materials Science QA Boundary element method |
| ISSN: | 0377-0257 |
| Popis: | When a cavity forms near a solid boundary a liquid jet can form directed towards the boundary, causing the generation of high pressures at the wall (potentially causing damage) and the formation of a toroidal bubble. In this paper several recent developments in the boundary element modelling of the dynamics of cavitation bubbles in viscoelastic fluids are presented. The standard formulation of the boundary element method (BEM) is in terms of a boundary integral equation with a singular kernel. A reformulation of the BEM in terms of a non-singular kernel is shown to provide enhanced stability. In situations when a liquid jet forms and impacts the far side of the bubble there is a transition to a toroidal form. This topological singularity in bubble geometry is modelled by placing a vortex ring inside the bubble to account for the circulation in the fluid and the discontinuity in potential following jet impact. The bubble dynamics are dependent on the initial stand-off distance from the boundary as well as the viscous and elastic properties of the fluid. It is shown that, while the viscosity of the fluid inhibits jet formation, the dynamics are particularly dependent on the relative strength of viscous, elastic and inertial forces. In particular, if the Deborah number is large enough elastic effects effectively negate fluid viscosity and behaviour similar to the inviscid case is recovered in terms of liquid jet formation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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