Lattice Boltzmann Method For Bubble Dynamics Simulation

Bubble dynamics phenomenon exists widely in the natural and chemical industry,navigation,military and other practical engineering fields.When bubbles rise under the action of buoyancy,a series of shape changes will be generated,from the original circle to ellipsoidal,oblate ellipsoidal cap and skirted shape.When bubbles are severely deformed,the skirted bubble breaks,resulting in the formation of sub-bubbles and its splashing.Therefore,the dynamic characteristics of bubbles are extremely complex,the motion mechanism of the bubbles under different physical parameters has not been fully understood.Traditional computational methods are limited in the study of such complex problems because it is difficult to deal with fluid interactions.The lattice Boltzmann method based on mesoscopic theory can easily describe the interaction between fluid and fluid,so it has certain advantages in the simulation of gas-liquid two-phase flow problem,and will be used in the present study of bubble dynamic behavior.For the water-air two-phase system with high density ratio,in this paper an improved lattice Boltzmann model based on the Allen-Cahn phase field theory will be used to systematically study the dynamic behavior of a single bubble and multiple bubbles in two-dimensional microchannel,and its main content includes the following aspects:(1)The rising motion of single bubble was first simulated to verify the Allen-Cahn phase field based lattice Boltzmann model.It is found that when the density ratio of gasliquid two-phase fluids reaches 1000,the numerical results for bubble motion shape and position are in good agreement with the literature data.(2)The motion of a single two-dimensional bubble with a density ratio of 1000 through a stationary fluid is studied.In this process,several important physical quantities are mainly investigated,including Eotvos number,Reynolds number,density ratio,viscosity ratio,bubble size and initial bubble shape,as well as their influences on the dynamic behavior of the bubble interface,the position of the center of mass and the rising speed.The numerical results show that the bubble undergoes a great deformation with the increase of the Eotvos number or Reynolds number,and even could break up into multiple satellite bubbles at a sufficiently large value of Eotvos number or Reynolds number.The terminal rising velocity of bubble at equilibrium shows to present an initial increase withthe Eotvos number and finally decreases with it,while increasing the Reynolds number could enhance the bubble rising velocity.In addition,other parameters will also have a series of influences on its motion.(3)This paper studies the rising process of two bubbles through static fluid when the density ratio reaches 1000 in the two-dimensional case,and mainly focuses on the influence of the bubble center distance,Eotvos number and Reynolds number on the merging state,motion trajectory and morphological change of two bubbles.In the research process,each case is specifically divided into vertical direction and horizontal direction,and the bubbles show different motion states under different placement conditions.Numerical results show that for the vertical case,the interaction between the two bubbles is more significant as the bubble centers are closer to each other,and thus the merger phenomenon is more likely to occur.For the horizontal case,the center distance has no significant effect on the merger,but under this condition,the bubbles will show the reciprocating phenomenon of mutual attraction and repulsion.Besides,it is found that both bubbles will deform sharply with the increase of the Eotvos number or Reynolds number.