Degree Name

Doctor of Philosophy


Department of Mathematics


The boundary integral method is used to model the growth and collapse of axisymmetric cavitation bubbles near two types of boundary; a rigid boundary, and a free surface. The fluid is assumed to be incompressible, inviscid and irrotational, and surface tension forces have been ignored. This method involves only the values of the potential and its normal derivative on the surface, thus avoiding the need to solve the Laplace's equation in the domain occupied by the fluid.

This study is particularly useful in predicting the interaction between the bubble and the boundaries, which is of great importance in the study of cavitation damage due to the bubble collapsing near a rigid boundary.

The growth and collapse of transient vapour bubbles near a rigid boundary in the presence of buoyancy forces and an incident axisymmetric stagnation point flow are also studied. Bubble shapes, particle pathlines, movement of the bubble centroid, and pressure contours are used to illustrate the numerical results. Migration of the bubble and subsequent jet formation during the collapse phase may be directed either towards or away from the rigid boundary, depending on the relative magnitude and orientation of the physical parameters used in the study. In particular, for the case of stagnation point flow, a "toroidal jet" forms at the side of the collapsing bubble splitting it into two parts.

Finally, the growth and collapse of a buoyant vapour bubble near a free surface is considered. It is found that, without buoyancy forces the bubble always moves away from the free surface. However, when buoyancy forces are present, the direction of motion of the collapsing vapour bubble depends on the initial location of the bubble relative to the free surface and the strength of the buoyancy forces.