Axisymmetric Lattice Boltzmann Model For Multiphase Flows And Its Application

Multiphase fluid flows are common in both nature and engineering fields,such as enhanced oil recovery process,droplet splashing process on liquid film,droplet or bubble generation in microchannel and so on,which have attracted extensive attention from scholars in science and engineering fields.Multiphase fluid flow problems often involve complex phase interface changes,which makes experimental methods and traditional numerical methods have some limitations in solving these problems.With the rapid development of computer technology,numerical simulation methods have attracted great attention,especially lattice Boltzmann method.It has some advantages in dealing with multi-phase fluid flow problems,such as the simplicity of its algorithm,good parallel performance and simple implementation of complex boundary.In order to further enrich the theoretical system of lattice Boltzmann method,in this paper a novel lattice Boltzmann(LB)model based on the Allen-Cahn phase-field theory is proposed for simulating axisymmetric multiphase flows.The most striking feature of the model is that it enables to handle multiphase flows with large density ratio,which are unavailable in all previous axisymmetric LB models.The present model utilizes two LB evolution equations,one of which is used to solve fluid interface,and another is adopted to solve hydrodynamic properties.To simulate axisymmetric multiphase flows effectively,the appropriate source term and equilibrium distribution function are introduced into the LB equation for interface tracking,and simultaneously,a simple and efficient forcing distribution function is also delicately designed in the LB equation for hydrodynamic properties.Unlike many existing LB models,the source and forcing terms of the model arising from the axisymmetric effect include no additional gradients,and consequently,the present model contains only one non-local phase field variable,which in this regard is much simpler.In addition,to enhance the model's numerical stability,an advanced multiple-relaxation-time(MRT)model is also applied for the collision operator.We further conducted the Chapman-Enskog analysis to demonstrate the consistencies of our present MRT-LB model with the axisymmetric Allen-Cahn equation and hydrodynamic equations.A series of numerical examples,including static droplet,oscillation of a viscousdroplet,breakup of a liquid thread,and bubble rising in a continuous phase,are used to test the performance of the proposed model.The steady-state problem of static droplet with a density ratio of 1000 is first simulated,and it is found that the current model can accurately capture the interface and achieve a smaller spurious velocity than the previous axisymmetric model.Two dynamic problems,namely droplet collision and breakup of a liquid thread,were then simulated.The simulation results show that the model can predict the oscillation frequency of droplet and the size of satellite droplets in the range of density ratio.Finally,we simulated the rising of single bubble driven by buoyancy with a density ratio of 1000.The simulation results are in good agreement with the experimental results.