Energy dissipation of pulsating bubbles in compressible fluids using the Eulerian finite-element method

Energy dissipation mechanisms of bubble pulsation in compressible fluids have always been a significant aspect of research into bubble dynamics. In this paper, bubble dynamics in compressible fluids are investigated numerically with the Eulerian finite-element method (EFEM), and the energy dissipation due to the wave effects of the compressible surrounding fluid is analyzed. The present model is validated by comparing with experimental results. Results from both the simulation and experiment show that bubble fragmentation also contributes to the energy dissipation, which has seldom been discussed before. It is also shown that the initial discontinuity is significant to the energy dissipation which is non-trivial to simulate in 1-dimensional bubble dynamics equations like the Gilmore equation. Then, the relationship between dissipated energy and bubble maximum radii in adjacent pulsating cycles is formulated to quantitatively evaluate the energy dissipation during a pulsating cycle. At last, based on the linearized theory of the energy conservation of the bubble system, a new non-dimensional parameter M _a is modified from the Mach number to represent the energy dissipation due to wave effects. With simulation and discussion on cases with different initial pressure and sound speed, it is found that the dissipated energy is related linearly to M _a, which can be used to predict the energy dissipation of a new case.