Multiphase lattice Boltzmann method and its applications in phase-change heat transfer

Abstract

<p indent=0mm>In the past three decades, the lattice Boltzmann (LB) method has been developed into an efficient numerical method for simulating fluid flow and heat transfer. It is a mesoscopic numerical approach, sitting in the middle between the molecular dynamic method and conventional numerical methods based on the continuum assumption. Unlike conventional numerical methods, the LB method is built on the mesoscopic kinetic equation. It tracks the evolution of a particle distribution function and then accumulates the particle distribution function to obtain the macroscopic properties. Owing to its kinetic nature, the LB method has exhibited many advantages over conventional numerical methods. For example, in the LB equation the convective operator is linear, whereas the convective terms of the Navier-Stokes equations are nonlinear. Moreover, in the LB simulations the complex boundary conditions can be formulated with the elementary mechanical rules such as the bounce-back rule according to the interaction of the “LB particles” with the solid walls. Furthermore, the LB method is ideal for parallel computing because of its explicit scheme and local interactions. Particularly, the intermolecular interactions of fluids can be easily incorporated into the LB method. As a result, the interface between different phases can arise, deform, and migrate naturally in the LB modeling without using any techniques to track or capture the interface, which is often required in the VOF or Level Set method. The existing multiphase LB models can be generally classified into four categories, i.e., the color-gradient model, the pseudopotential model, the free-energy model, and the phase-field model. In the color-gradient LB model, two distribution functions are introduced to represent two different fluids and a color-gradient-based perturbation operator is employed to generate surface tension. Moreover, a recoloring step is used in the color-gradient model so as to separate different phases. The pseudopotential LB model is the simplest and the most popular multiphase LB model. In this model, the fluid interactions are mimicked by an interparticle potential, through which the separation of different phases or components can be achieved naturally. Accordingly, the interface between different phases can arise, deform and migrate naturally. The free-energy LB model was developed based on thermodynamics considerations, which modifies the second-order moment of the particle equilibrium distribution function so as to include a non-ideal thermodynamic pressure tensor. The phase-field LB model is based on the phase-field theory, in which the interface dynamics is described by an order parameter that obeys the Cahn-Hilliard equation or a Cahn-Hilliard-like equation. In this paper we briefly review some recent advances in these multiphase LB models. Particularly, recent progress in the pseudopotential LB model is highlighted. It is shown that the thermodynamic consistency of the pseudopotential model can be achieved by adjusting the mechanical stability condition via an improved forcing scheme. Furthermore, an alternative approach is presented to tune the surface tension of the pseudopotential model and an improved contact angle scheme is introduced, which retains the advantages of the original virtual-density scheme but does not suffer from an unphysical thick mass-transfer layer near the solid boundary. Moreover, the applications of the pseudopotential LB model to boiling and condensation heat transfer are outlined.