Yoshinori Jinbo

Application of an Improved Ghost Fluid Method to the Collapse of Non-Spherical Bubbles in a Compressible Liquid

The ghost fluid method (GFM) is improved to investigate violent bubble collapse in a compressible liquid, in which the adaptive mesh refinement with multigrids, the surface tension, and the thermal diffusion through the bubble interface are taken into account. The improved multigrid GFM is applied to the interaction of an incident shock wave with a bubble. The multigrid GFM captures the fine interfacial and vortex structures of the toroidal bubble when the bubble collapses violently accompanied with the penetration of the liquid jet and the formation of the shock waves. The multigrid GFM is also applied to the bubble collapse near a tissue surface in which the tissue is modeled with gelatin in order to predict the tissue damage due to the bubble collapse; the motions of three phases for the gas inside the bubble, the liquid surrounding the bubble, and the gelatin boundary are solved directly by coupling the level set method with the improved GFM. Two kinds of level set functions are utilized for distinguishing the gas-liquid interface from the liquid-gelatin interface. It is shown that the impact of the shock waves generated from the collapsing bubble on the boundary leads to the formation of depression of the boundary; the toroidal bubble penetrates into the depression. Also, the surface tension effects are successfully included in the improved GFM. The thermal effects of internal gas on the bubble collapse are also discussed by considering the thermal diffusion across the interface in the GFM. The thermal boundary layers of the toroidal bubble are captured with the method. The result shows that the smaller the initial bubble radius becomes, the lower the maximum temperature inside the bubble becomes because of the thermal diffusion across the interface.Copyright

Direct numerical simulations of nonspherical bubble collapse with nonequilibrium phase transition by the improved ghost fluid method

The ghost fluid method is improved so as to consider the nonequilibrium phase transition through the interface of a collapsing nonspherical bubble. The adaptive zonal grids are utilized for capturing the gas-liquid interface structure. The present method is applied to the collapse of a spherical vapor bubble, and the numerical results are compared with the experiments by Akhatov et al. [Phys. Fluids 13, 2805-2819 (2001)]. It is shown that the present method can predict successfully the violent collapse of a spherical bubble even though the Eulerian grids are employed. The present method is also utilized to simulate the collapse of an axi-symmetric nonspherical vapor bubble induced by the interaction of an incident shock wave with the bubble. The results also show that the complicated interface structure is formed for the toroidal bubble after the liquid-jet impacts the bubble wall. The phase transition causes the decrease of the internal temperature of the toroidal bubble.

Numerical Investigations of Thermal Effects on the Interaction of Shock Waves With Bubbles

The present study deals with the collapse of nonspherical bubbles in a compressible liquid by taking the thermal diffusion into account. The ghost fluid method (GFM) is modified so as to consider the thermal diffusion through the bubble surface. The boundary condition for the temperature continuity at the interface is discussed for determining the values of the ghost fluids. The improved GFM is applied to the collapse of a single spherical bubble. The present results are in good agreement with those obtained from the equation of motion for a single bubble (Keller equation) coupling with the energy equation. The improved multigrid GFM is also applied to the interaction of a gas bubble with a strong shock wave. The non-spherical bubble collapse is simulated successfully by taking the thermal diffusion into account. The thermal boundary layers both inside and outside the bubble are captured with the present method although the thermal boundary layer in liquid is very thin. The bubble collapse due to the incident shock wave accompanies the formation of the liquid jets and shock waves leading to the high temperature field. The influence of thermal diffusion becomes more prominent when the initial bubble radius is small. It is shown that a large amount of heat outflows from the interior of the bubble to the liquid when the liquid jet hits the downstream surface of the bubble and the bubble rebounds. The increased thermal diffusion causes the decrease of the internal pressure and temperature in the bubble leading to more violent collapse.Copyright