Development of a three-dimensional boundary integral method and its application to bubble formation from submerged orifices

A three dimensional boundary integral method is developed to study formation of gas bubbles from an underwater orifice. Since the bubble growth process is highly transient in small viscosity liquids like water, the flow field is assumed to be irrotational. Based upon this simplification, a potential-flow boundary-integral formulation is adopted to model the bubble growth. This study involves complicated geometries that are easily handled with the three dimensional code. Numerical instabilities leading to zig-zag patterns on the bubble surface commonly associated with the boundary integral technique are found to be even more severe for the three dimensional cases. An artificial damping term of Laplacian type is introduced to eliminate these instabilities. In addition, an artificial repulsive force that is proportional to the inverse of the square of the normal distance between a free surface and a solid wall is also introduced to simulate the lubrication layer that is neglected in the potential flow framework.;Numerical simulations are carried out to investigate bubble formation from a submerged orifice under various conditions. The liquid/gas system is compromised of air bubbles formed in water. Bubble injection in a cross liquid flow is the primary three dimensional case that has been extensively studied and compared with experiments in this work. Systematic simulations demonstrate the influence of liquid inertia, bubble's added mass, buoyancy as well as the geometry of the bubble injection device on the bubble size and shape. A good agreement is found between the simulations and the experiment for air bubbles of radii in the range from a few hundred microns to a millimeter. A good agreement is also achieved in simulations of three dimensional bubble formation from a tilted needle in an unbounded liquid domain. In addition, simulations of the process of bubble removal at an orifice are carried out, revealing potential difficulties in eliminating numerical instabilities for this case. The results demonstrate, for the first time. the effectiveness and reliability of the three dimensional boundary integral technique as a research tool in these flows.