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Lagrangian model with bubble dynamics for cavitating nuclei

Beelen, S.J. (2017) Lagrangian model with bubble dynamics for cavitating nuclei.

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Abstract:In this report a model for cavitating nuclei in a ow _eld and the possible extensions of this model are examined. In the paper by Johnson and Hsieh such a model is introduced. In this paper a simple equation of motion along with a quasi steady equation for the bubble growth is solved in a potential ow _eld. This model leads to a prediction of cavitation inception based on the critical pressure coe_cient. Cavitation inception is therefore also assumed to occur when the bubble starts to grow asymptotically. One could say that the model presented by Johnson and Hsies is the absolute basis. The equation of motion only has three terms, which is the minimum, the bubble growth is described by a quasy-steady equation and the ow _eld is a potential ow _eld. Step by step the complexity of (parts of) the model is increased. Starting with a bubble dynamics equation, the Rayleigh-Plesset equation is used at _rst. Eventually the Rayleigh-Plesset equation is replaced by the general Keller-Herring equation, which is a more advanced bubble dynamics equation and includes damping due to the emitted sound wave. The equation of motion is extended by using more forces, of which the buoyancy force is the most inuential. The volumechanging force (the force due to the changing volume of the wake of the bubble) turned out to be very dominant during collapses of the bubble. The model has the mass of the nucleus incorporated so that the model is suitable for solid particles. The history force has been included as the Basset force. This is done in an iterative way. The history force smears out the trajectory of the bubble, and is especially reactionary towards the volume-changing force as it is a very unsteady force. The Basset force turned out not to be a good choice for the history force, since it overestimates this force signi_cantly, especially over longer time spans. Finally a new ow _eld has been taken, in this ow _eld the simple equation of motion has been solved along with the general Keller-Herring equation. The result is a trajectory in this ow _eld. The trajectory has been compared with the results found in literature, it was found that locally taking the streamline as a trajectory was a good approximation. The trajectory has also been compared with the trajectory found in experiments which gave encouraging results regarding the trajectories. The bubble diameter was less comparable.
Item Type:Internship Report (Master)
Faculty:ET: Engineering Technology
Programme:Mechanical Engineering MSc (60439)
Keywords:Cavitation inception, Cavitation, Nuclei, Equation of motion, flow, Rayleigh Plesset, History force, Basset force, Interpolation
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