Phase-field-based lattice Boltzmann modeling of large-density-ratio two-phase flows

Abstract

In this paper, we present a simple and accurate lattice Boltzmann (LB) model for immiscible two-phase flows, which is able to deal with large density contrasts. This model utilizes two LB equations, one of which is used to solve the conservative Allen-Cahn equation, and the other is adopted to solve the incompressible Navier-Stokes equations. A forcing distribution function is elaborately designed in the LB equation for the Navier-Stokes equations, which make it much simpler than the existing LB models. In addition, the proposed model can achieve superior numerical accuracy compared with previous Allen-Cahn type of LB models. Several benchmark two-phase problems, including static droplet, layered Poiseuille flow, and spinodal decomposition are simulated to validate the present LB model. It is found that the present model can achieve relatively small spurious velocity in the LB community, and the obtained numerical results also show good agreement with the analytical solutions or some available results. Lastly, we use the present model to investigate the droplet impact on a thin liquid film with a large density ratio of 1000 and the Reynolds number ranging from 20 to 500. The fascinating phenomena of droplet splashing is successfully reproduced by the present model and the numerically predicted spreading radius exhibits to obey the power law reported in the literature.

A generalized lattice Boltzmann model for fluid flow system and its application in two-phase flows

“…From the generalized model, we can not only get some existing models, but also derive new models. Among these derived models, we can get an incompressible model for N-S equations with a mass source term, and we present a modified scheme to calculate the pressure p, which is more accurate than the previ- First, we conducted a detailed comparison between present scheme and the previous one [27,31,35]. The result shows that there is a significant difference between the two pressure schemes when S 1 = 0, and theoretically, the present pressure scheme is more accurate.…”

“…The governing equations for nearly incompressible fluid flows with a mass source term can be written as [12,30,31] ∂ρ ∂t…”

“…We would also like to point out that the present pressure expression is different from that in Refs. [27,31,35] which can be expressed as…”

“…The layered Poiseuille flow between two parallel plates is also a classical twophase problem which provides a good benchmark for validating the LB models [50,25,52,38,53,31].…”

“…We then simulated the layered Poiseuille flow with another density ratio ρ A /ρ B = 3, and viscosity ratio is equal to 3. Here the dynamic viscosity is given by [35,31] The other parameters are the same as those stated above. From Fig.…”