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

Abstract

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.