The effects of heat transfer on vapour, gas and vapour-gas cavity bubbles

The dynamics of cavity bubbles both in a liquid of infinite extent and near a rigid boundary is studied. A technique is developed for mathematical modelling of bubble dynamics. In the mathematical modellings heat transfer between the bubble contents and the surrounding liquid, evaporation and condensation and the buoyancy forces are considered. The bubbles could be vapour bubbles (filled with vapour), gas bubbles (filled with a non-condensable gas) or bubbles filled with a mixture of vapour and a non-condensable gas. The properties of vapour are extracted from thermodynamic tables and those of the non-condensable gas are related by the equation of state of an ideal gas. The surrounding liquid is assumed to be invicid and incompressible and the flow field irrotational. For isolated bubbles the flow field is simulated by the flow field of a sink or a source and for bubbles near a rigid surface the boundary element method is utilised for the solution of the flow field. Three sets of differential equations have been derived for three types of the above mentioned bubbles. These sets of differential equations are solved by the Runge-Kutta method. dual reciprocity boundary element method is adopted and modified to solve the equation of energy in the liquid domain thereby heat transfer across the bubble-liquid interface is determined. The method, while retaining accuracy, found to be more efficient than other domain methods such as finite element methods regarding computational time, computer storage and time for preparation of input data. Different aspects of bubble dynamics such as the rate of change of volume, the pressure and temperature inside the bubbles, the velocity of liquid jets, the movement of the bubble centroid and the effect of heat transfer on each of these parameters are investigated.