General Propagation Lattice Boltzmann Model for Flow and Mass Transfer of Multicomponent Mixtures
Author:Guo Xiu Zuo
Supervisor:shi bao chang
Multi-component gas transport is widespread in the fields of greenhouse gas storage and design of fuel cells,which has become a common scientific problem to be solved urgently in environment,resources and clean energy,with the development of high-tech industries with a lower energy consumption.According to the previous work,multi-component gas mixtures not only contain the collision of the same kind of molecules during the processes of flow and diffusion,but also the interactions among different molecules and/or molecules and the wall surface.In this case,the classical Fick law will be invalid,while the coupled advection-diffusion equations based on the Maxwell-Stefan theory must be considered.However,the multi-component system involves the characteristics of particle property and the multi-field coupling,which brings a great challenge in the study of such complex problems by experimental or traditional numerical methods.In recent years,in view of the microscopic nature and mesoscopic characteristics,the kinetic-based mesoscopic latticeBoltzmann(LB)method has some distinct advantages in depicting the interactions among molecules and dealing with complex boundary,which further promote the application of this method in the investigation of multi-component gas transport.Now,although many researchers have made some academic achievements in the study of the LB models for multi-component gas mixtures and their transport processes,there are still some basic problems that have not yet been resolved.For example,due to the fact that physically,different kinds of molecules have different molecular velocities,the multiple meshes or the complicated interpolations are usually needed in the LB models,which greatly reduces the numerical stability and computational efficiency.To solve this problem,in this thesis we first develop a general propagation LB model for advection-diffusion equations,which can be used to study the mass transfer of a binary mixture,and also construct a bounce-back boundary scheme of this LB model.Then we extend the general propagation LB model to the case of the multi-component mixtures,and also perform a study of the multi-component diffusion in porous media.Our main work include the following aspects:(1)Firstly,a general propagation LB model is proposed for advection-diffusion equations with variable coefficients,and the Chapman-Enskog analysis shows that the macroscopic equations can be recovered correctly from the present model.In addition,we also can find that the classical Lax-Wendroff and fractional propagation schemes are special cases of this model.The numerical results indicate that by properly adjusting the two free parameters introduced into the streaming step,the present model could be more stable and more accurate than the standard BGK model.(2)To solve the advection-diffusion equations with Robin boundary conditions,a bounce-back boundary scheme of general propagation LB model is constructed.A rigorous multiscale analysis technique – asymptotic analysis is also conducted to show that the present boundary scheme has a second-order accuracy in space theoretically.Compared with some existing boundary schemes,the present scheme is more accurate.In order to eliminate the numerical slip,we also perform an analysis on the discrete effect.The equivalent finite-difference scheme and the optimal relation between the relaxation time and the two free parameters have been derived.(3)We develop a general propagation LB model for multi-component mixtures with different molecular mass ratios,which can be used to overcome the shortcoming of multiple meshes or interpolations used in some existing LB models.Through the Chapman-Enskog analysis,the Navier-Stokes equations(describing the gas flow)and the Maxwell-Stefan equations(depicting the component diffusion)can be correctly recovered from the present model.Furthermore,the model is suitable for mixtures with large molecular mass ratios and different viscosities.By conducting some quantitative comparisons with previous experimental,theoretical or numerical results,we find that the present model still works well,and can capture the curious phenomenon existing in the multi-component system,such as reverse diffusion.(4)Based on the above proposed LB model,we further study the diffusion of binary mixture in porous media.To handle the complex geometry of porous media more conveniently,the proposed bounce-back boundary scheme is adopted here.After conducting some simulations for binary mixture with two different mass ratios,we find that the distribution of density obtained by present model is nonlinear and smooth for both cases.However,for the mixtures with different molecular mass ratios,the diffusion of the component with small molecular weight is much faster than that with larger molecular weight.In summary,we not only develop the LB models for advection-diffusion equations and multi-component gas transport,but also propose a bounce-back boundary scheme,which can be applied to the study of the complex multi-component fluid flows.Furthermore,based on the above work,we also carry out a preliminary study on a binary mixture in porous media,which laies a necessary basis for future work on the transport mechanism of multi-component mixtures.