Numerical Studies On Vapor-liquid Multiphase And Thermal Convection Using Lattice Boltzmann Method

Vapor-liquid two-phase flow, atmospheric circulation and oceancirculation are a common and complex phenomenon in the engineeringof fluid system of the nature. Recently, lattice Boltzmann method(LBM)is a new tools used to simulate vapor-liquid two phase flow, heatand mass transfer flow. LBM is based on the microscopic fluid modeland the mesoscopic dynamic equation. Compared with the traditionalnumerical methods which are based on the Navier-Stokes equation, LBMhas peculiar advantages, such as, easy treatment of boundaryconditions, high efficiency of computation, suitable for flow withlarge distortion and the nature of parallel computation.1. We present simply the single-component vapor-liquid two-phaselattice Boltzmann model: color model, the free energy model and thepseudo-potential model. The vapor-liquid two-phase process ofseparation, the process of integration of the two droplets andbubbles are simulated using the pseudo-potentialmodel.Meanwhile,the collision of two droplets is studied aboutdifferent Weber number using high density ratios model. Thedeformation and rupture of a single bubble is simulated in the shearflow.The simulations about deformation of a single bubble are in goodagreement with experimental results in the shear flow. Finally,thermal vapor-liquid two-phase lattice Boltzmann model is presented.Numerical results verify that the internal energy of the gas phaseis greater than the internal energy of the liquid phase.2. The reasons of the spurious velocities are presented bydifferent scholars who also introduce some methods of reducing thespurious velocities. Two methods of reducing the spurious velocities are presented. The first method is that a random densitydistribution is introduced in the lattice Boltzmann equation. Thismethod is able to eliminate eight spurious eddies around the bubble,and the spurious velocities are reduced.Secondly, the fractionalpropagation is used to reduce the spurious velocities for themultiphase lattice Boltzmann models. Numerical results show that themaximum spurious velocity at the interfaces could be reducedeffectively comparing with some early models. Eight spurious eddies,previously existing for the D2Q9model, at the interfaces oftwo-phase flows are completely eliminated.3. A double distribution function LBM is improved. The methodis used to simulate the Rayleigh-Bénard convection.Firstly,naturalconvetion of square cavity is simulated at different Rayleighnumbers.The Isotherms and flow pattern at steady states is consideredat different Rayleigh numbers. Comparison of Nusselt numberscomputed at different Rayleigh numbers using different grids withresults are presented.Secondly, the laminar Rayleigh-Bénardconvection is simulated. The Isotherms and flow pattern at steadystates is considered at different Rayleigh numbers. As shown, hotfluids near the bottom wall flow upward and increase the temperaturein the central portion of the channel, while cold fluids near thetop wall flow downward and decrease the temperature near the sideboundaries. As the Rayleigh numbers are increasing,two trends wereobserved for the temperature distribution: enhanced mixing of thehot andcold fluids, and an increase in the temperature gradients nearthe bottom and top boundaries. The calculated relationship betweenthe Nusselt number and the Rayleigh number is presented. Alsoincluded are the simulation results by Clever and Busse. As shown, our results are in good agreement with those by Clever and Busseand the theoretical values for Rayleigh numbers. The doubledistribution function LBM is firstly used to simulate the turbulenceRayleigh-Bénard convection.As times evolve,the thermal plumes in twodimentional are presented when Rayleigh number is equal toRa=3.5×10~9.As time evolves,the interactions of thermal plumes areshown, which leads to a breakdown of the large-scale flow. Thelarge-scale convection rolls are not continuously maintained.The three-dimensional turbulent Rayleigh-Bénard convection issimulated at different Rayleigh numbers. At the lowest Ra two pairsof plumes are rising and falling, and hence forming the typicalconvection rolls with their rotational axes orthogonal to thelongitudinal direction of the cell.The interaction of the thermalplumes still causes a large scale circulation of the flow. However,at this Rayleigh number the large-scale convection rolls are notcontinuously maintained, but appear to become unstable, whichtemporarily leads to a breakdown of the large-scale flow.Energyspectra of the velocity and temperature are studied, which are ingood agreement with the Kolmogorov-law and Bolgiano-law.