Simulation on the interaction between multiple bubbles and free surface with viscous effects

Based on the boundary layer theory, a general Bernoulli equation involving normal and tangential stresses has been derived and the weak viscous effects have been considered. Three-dimensional boundary element method and Green's function have been adopted to solve the interaction between bubbles and free surface. Numerical results have been validated by convergence study and comparison with published results. On this basis, two in-phase and out-phase bubbles in the vicinity of free surface are chosen as cases at different Froude number. Influence of fluid viscosity or Reynolds number is mainly investigated. Physical relevance of numerical computation and the range of validity of numerical simulation are further discussed. It is found that viscous effects depress the interaction between bubbles and free surface, which hinders the formation of the downward jet on the upper bubble surface and declines bubble volume and the height of free-surface spike.