Study On The Lattice Boltzmann Flux Solver For The Two-phase Flows

Two-phase flow problems are very common in the naval architecture and ocean engi-neering.The exploration of two-phase flows mechanism is beneficial for the development of ship drag reduction by the microbubbles,the superhydrophobic surfaces for drag reduction and the multiphase mixing transportation in the pipelines.Computational fluid dynamics(CFD)is an important tool to study two-phase flow problems,and studying the basic theory of CFD is helpful for breaking the foreign monopoly on CFD commercial software.Con-ventional Navier-Stokes(NS)equations based numerical methods are still very complicated when dealing with nonlinear convection terms and viscous terms containing higher-order derivatives,together with a rather cumbersome calculation for pressure.The lattice Boltz-mann method(LBM)can recover to the NS equations under certain conditions.Besides,the computation of LBM is simple and easy to implement.However,the LBM still faces some challenges such as the limitation of uniform grids,the coupling between the time step and the space step,the high memory cost,and the complex boundary processing caused by the transformation between the macroscopic quantities and the distribution functions.The newly developed lattice Boltzmann flux solver(LBFS)inherits the advantages of the LB-M and the conventional finite volume method(FVM),and avoids their shortcomings.The LBFS has shown great potential in the simulation of two-phase flows.In this solver,only the macroscopic variables at the cell centers are evolved,and the numerical fluxes at the cell in-terfaces are reconstructed by the solution of the LBM.However,the two-phase LBFS is still not mature enough.In this work,interface capturing models,flux reconstruction methods,and axisymmetric models are studied under the framework of LBFS.Besides,some typical problems are preliminarily simulated,such as the static bubbles,the bubbles merging,the bubble rising,and the droplet impacting on the dry or wetting surfaces.The main work in this dissertation is shown as follows:First,different LBFS models for interface capturing are developed and tested.Origi-nating from the LBM for interface capturing,the governing equations of the interface LBFS are derived by the Chapman-Enskog expansion muti-scale analysis,and are discretized by the FVM.In addition,the numerical interface fluxes of the LBFS are calculated by the re-constructed distribution functions for the order parameter.Numerical experiments show that under the LBFS framework,the effects of the interface capturing equations and the artifi-cial term on the results are different from those of the LBM.When the interface thickness is relatively small(?=2),the Allen-Cahn(AC)equation based LBFS generates obvi-ous unphysical disturbance while two Cahn-Hilliard(CH)equation based LBFS models can capture the phase interface accurately.Besides,for the CH equation,the additional artificial term has little influence on the results in the framework of the LBFS.This research provides an important reference for the selection and application of the interface capturing models under the framework of LBFS.Second,on the basis of the LBFS for interface capturing determined by the above study and the LBFS for flow field proposed by the formers,we develop a two-phase simpli-fied LBFS model.Unlike the original numerical fluxes reconstruction method,this strategy adopts the combination of the macroscopic variables and the distribution functions instead of the pure distribution functions,which avoids the calculation of some time-consuming dis-tribution functions and their velocity moments.The simplified model retains the accuracy and stability of the original method,and has the ability to simulate large-density-ratio and large-viscosity-ratio flows.Meanwhile,the code implementation is simplified and the com-putational efficiency is improved.The grid size is larger,the saved computational time for this simplified method is more.What's more,the proposed simplified strategy is meaningful for the whole LBFS framework and can also be extended to other LBFS models besides the multiphase flow.Third,a more stable two-phase LBFS is established for the flow field.For the phase field,the aforementioned simplified LBFS is directly employed.For the flow field,unlike the standard LBM based simplified LBFS model mentioned above,present model is deduced from the two-phase LBM,which naturally includes the effect of the source term for the density difference and the surface tension.However,the computation of the source term is not easy.To simplify the computational procedure,the simplified strategy is extended to the terms involving H_?which are directly given as the macroscopic variables.Numerical assessments suggest that the proposed model can simulate two-phase flows with complex interface change,large density ratio(up to 1000)and high Reynolds number(up to 10000).Compared with the above-mentioned simplified model,present model has better numerical stability but lower computational efficiency.Finally,considering the simplicity of the above-mentioned simplified LBFS model,we propose a mass-conserved fractional step axisymmetric two-phase LBFS on the basis of the simplified LBFS model.In the predictor step,the two-phase simplified LBFS is employed to predict the macroscopic variables.In the corrector step,the terms for the axisymmetric effect are considered.The application of the fractional method avoids the complicated processing of the axisymmetric source terms in the LBM.However,this method may break the law of the mass conservation due to its large numerical dissipation.We employ a modified CH equation and the mass correction term is discretized in the framework of axisymmetric model.Some axisymmetric problems close to the reality are simulated,such as the micro-droplet impacting on a dry hydrophobic plate and multiple bubbles merging.The numerical results are in good agreements with the theoretical and experimental results.The proposed model is capable of simulating large-density-ratio and large-viscosity-ratio flows.In this sense,present model is superior to most of the CH-based axisymmetric two-phase LBM models.