Phase-Field Lattice Boltzmann Method For Flow And Heat Transfer Of Multiphase Fluid

Multiphase fluid flow and heat transfer are universal in both nature and industrial processes,such as inkjet printing,the capture of crude oil,microfluidics,and so on,which are key scientific problems in significant requirements of countries,such as resources,environment and clean energy.The basic characteristics of multiphase fluid flow are the interaction of flow,heat transfer,mass transfer,interfacial dynamics and so on.It is a multi-field coupling problem,including flow field,phase field and temperature field.However,the flow and heat transfer of multiphase fluids involve the complexity in dealing with a moving interface between different phases and the coupling interactions,which brings some difficulty in the study of such complicated problems by theoretical and experimental methods.With the development of computer technology,numerical simulation has become an effective method to study such problems.However,when studying these multiphase fluid problems,the traditional numerical methods will suffer from many shortcomings,including the complexity in treating boundary conductions,the difficulty to deal with the multi-field coupling problems and the low parallel efficiency.In recent years,the kinetic-based lattice Boltzmann method(LBM),has a great advantage in studying the flow and heat transfer of multiphase fluids.Now,the phase-field based LBM,has drawn great attention in the study of multiphase flows.However,in this method,there are still some fundamental problems that have not been solved.First,most of the existing works are focused on the lattice Boltzmann(LB)models for Cahn-Hilliard(C-H)equation,but these models suffer from the poor stability,difficulty in simulating the large density ratio problems,and the nonlocal collision.Second,most of the existing LB models based on the phase-field theory are only suitable for isothermal multiphase flow problems.Thirdly,in the standard LBM,the discrete velocity is coupled with the space step,which makes the method difficult to use non-uniform grids,and also leads to a low computational efficiency.For above problems,we have carried out the following works:(1)A new LB model for the Allen-Cahn(A-C)equation is first proposed,where the equilibrium distribution function and the source term distribution function are delicately designed to recover the A-C equation correctly.In addition,we developed a local scheme for the spatial gradient under the framework of LBM,such that the collision process can be implemented locally.Finally,from the theoretical and numerical points of view,a comparative study on the LB models for the A-C and C-H equations in tracking the interface is performed.The results show that the LB model for A-C equation is more accurate and more stable for the problems with large P?eclet number,and also has a capacity in the study of large-density ratio problems.(2)Based on the above developed LB model,we further established an LB model for solving the non-isothermal multiphase flow problems.Through the Chapmann-Enskog analysis,the model not only can recover the temperature field equation accurately,but also can ensure that the collision process is implemented locally,since the spatial gradient in the model can be computed by the nonequilibrium part of the distribution function.Then we validate the model with the thermocapillary flow problems.The results show that the proposed model is more accurate and more stable than the existing model.(3)A finite-difference LB model is developed for the general nonlinear convectiondiffusion equation.On the one hand,different from the standard LB model,the discrete velocity and spatial step in this model are decoupled such that it is more convenient to study convection-diffusion problem with the non-uniform grid.On the other hand,the model not only preserves the advantage of standard LB model that the complex-valued convectiondiffusion equation can be solved directly,but also can be used to solve anisotropic problems.The von Neumann stability analysis is also conducted to discuss the stability region which can be used to determine the free parameters appeared in the model.Finally,we validate the model with some classical examples.The results show that the proposed model can improve the computational efficiency of LB method.Moreover,the finite-difference LB model has better stability and accuracy than the standard LB model.(4)The developed finite-difference LB model is first used to solve the A-C and C-H equations.To this end,the source term distribution function is delicately designed to recover the A-C and C-H equations exactly.In addition,we validate the model with some classic interface problems.The numerical results show that the stability and accuracy of the finitedifference LB model are better than those of the standard LB model in solving large P?eclet number or convection dominant problems.In conclusion,this thesis not only develops a more accurate and more stable LB model for the A-C equation,but also explores the advantages of such interface capture equation in the study of multiphase flow and heat transfer.In addition,a comparative study on the LB models for the A-C and C-H equations in tracking the interface is also performed,which provides a reference for the further study on the specific multiphase flow problems.