Research On The Chemical-potential-based Multiphase Lattice Boltzmann Method

The widespread phenomenon of multiphase flow in nature is widely used in industrial and agricultural production,scientific research and daily life.It involves the surface phenomena,the balance of thermodynamics and fluid mechanics,and the existence of heat transfer,mass transfer and chemical reaction.Therefore,the study of multiphase flow has been a hot topic in the field of fluid mechanics.Computational Fluid Dynamics(CFD)is a discipline that has evolved in the long-term practice of numerical and discrete methods to study the complex fluid motion,including multiphase flow,which have made a great success.However,since the multiphase flow often presents a very complex geometric interface,and with the intense interface topological deformation(such as droplet polymerization and splitting,etc.),the traditional CFD method for further study of multiphase flow will encounter bottlenecks.That is to say,The Navier-Stokes equations under the complex geometric boundary are not easy to solve,and it is very difficult to track the interface with violent topological deformation.Lattice Boltzmann method(LBM),based on molecular dynamics,is a special discrete scheme of continuous Boltzmann equation.It belongs to the emerging mesoscopic method,which has the advantages of continuous theory and microscopic method.In the study of complex fluid Sports has achieved remarkable success,especially in the multi-phase flow research has outstanding performance,and has been highly recognized by people.Compared with the traditional CFD method,there are at least the following advantages:1.The algorithm is simple,without the need to directly solve the complex Navier-Stokes equations and only need to solve the simple lattice Boltzmann equation;2.Easy to deal with complex geometric boundary conditions,To track the interface,the interface changes naturally contained in a simple evolution process;3.LBM evolution has a local,very suitable for high-performance parallel computing.After nearly 30 years of development and improvement,LBM has become a new and irreplaceable computational fluid dynamics method,which has played an important role in the study of multiphase flow and has become one of the mainstream research methods.So far,the LBM multiphase flow model,which has been widely recognized and widely used and successfully applied,mainly has the pseudo-potential model and the free energy model.However,both models and their subsequent improvements can not satisfy the Galilean invariance And thermodynamic consistency-the pseudo-potential model does not have thermodynamic consistency,while the free energy model can not satisfy the Galilean invariance.Models that do not have thermodynamic consistency will not be able to accurately characterize the thermodynamic behavior of the system,and the model that does not satisfy the Galilean invariance does not accurately describe the characteristics of the motion system.On the basis of the principle of free energy and pressure tensor calculation,the lattice Boltzmann multiphase flow based on pressure tensor is proposed on the basis of the principle of the two models.(EPL,112(2015)44002),and from the theoretical and numerical experiments,it is proved that the new model has both thermodynamic consistency and Galilean invariance.The algorithm is simple and easy to implement,and the simulation The phase transition between the two phases is better than that of the theory,and it is expected to be further popularized and applied.Although the pressure tensor model has obvious advantages in theory and value,it also has a good prospect of popularizing and applying.However,this paper has found that the model has further improved and improved space.First,through the pressure tensor or not the best,but not the only way to calculate the non-ideal force of the effective way,the system of free energy,chemical potential and entropy are very good description of the system thermodynamic behavior of the macro,in particular,Phase equilibrium and chemical equilibrium.On the other hand,the pressure-wetting boundary condition of the constrained multiphase flow system is difficult to be directly expressed by the pressure tensor,and the effective density expression is also complicated,and the chemical potential is described The interaction between the solid phase and the liquid phase in the wetting may be more convenient.In this paper,the original pressure tensor model is explored and improved from the chemical potential.The lattice Boltzmann multiphase flow model based on chemical potential is constructed by deducing the formula of non-ideal force based on chemical potential.Potential model),the same from the chemical potential of the development of a set of chemical potential based on the flow of wetting boundary conditions(referred to as:chemical potential wetting boundary conditions).By the theory and numerical experiments,the new model and the wetting boundary condition proposed in this paper have the following advantages and characteristics:1.Because of the improvement and perfection of the original pressure tensor model,the chemical potential model still has the thermodynamic consistency while satisfying the Galilean invariance,and the chemical potential model and the wetting boundary condition through the chemical potential are theoretically unified and self-,In the numerical calculation to achieve mutual coordination and sharing.2.The chemical potential model and the wetting boundary condition are more concise than the pressure tensor model.The simulation results show that the new chemical potential model has the advantages of computational precision,computational efficiency and stability.To varying degrees to enhance,fully explain its value also has a systematic,comprehensive advantage.3.The first-order phase transition and van der Waals droplet deformation simulation of several commonly used non-ideal fluids(including van der waals,Peng-Robinson,Redlich-Kwong Soave and Carnahan-Starling fluids)show that the chemical potential model is numerically Can well describe the coexistence of two-phase non-ideal fluid,but also accurately meet the Galilean invariance.4.The application of van der Waals droplet wetting on the solid wall surface is sufficient to show that the chemical potential model and the wetting boundary condition are convenient and feasible.In the numerical experiments,it is found that the wetting contact angle is almost linear with the specified chemical potential of the solid wall.It is very simple to adjust the surface chemical potential in order to obtain the required contact angle.Therefore,the chemical potential model and wetting The boundary conditions applied to the study of surface wetting have sufficient advantages.5.Since the chemical potential is an important and universal macro quantity that describes the thermodynamic system,the chemical potential model and the wetting boundary condition can be directly applied to the study of a multiphase flow system with an electromagnetic field environment or a chemical reaction.The above advantages and characteristics show that the chemical potential model and the wetting boundary condition have a solid theoretical basis and excellent numerical performance,which is expected to be popularized and applied in the field of multiphase flow.