Numerical simulation of spherical bubble collapse by a uniform bubble pressure approximation and detailed description of heat and mass transfer with phase transition

摘要

A mathematical model for the simulation of the dynamics of spherical vapor-air bubbles and its numerical implementation is presented. Heat and mass transfer and phase transition in terms of evaporation and condensation as well as air absorption and desorption are considered. Flow variables are discretized by a mixed finite volume / finite difference scheme and solved either by a Crank-Nicolson or Runge-Kutta scheme. Due to the assumption of homogeneous bubble pressure (homobaricity), the solution of momentum equations is restricted to the Rayleigh-Plesset equation which makes the model computationally efficient. The model is validated by measurement data for bubble growth and applied to bubble collapse and rebound. By a comparison with Navier-Stokes results from literature, the homobaricity assumption is shown to be appropriate even in the last stage of bubble collapse. The relation of the local velocity and temperature field with heat and mass transfer is discussed. Equilibrium bubble interface conditions (liquid and gaseous side have the same temperature and chemical potential) are compared to non-equilibrium conditions and are shown to yield the same local velocity and temperature field for each stage of bubble collapse and rebound.