A phase-field-based lattice Boltzmann method for two-phase flows with the interfacial mass/heat transfer

Abstract

In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass/heat transfer. Through the Chapman-Enskog analysis, we show that the present LB method can correctly recover the governing equations for phase field, flow field and concentration/temperature field. In particular, to derive the two-scalar equations for the mass/heat transfer, we propose a new LB model with an auxiliary source distribution function to describe the extra flux terms, and the discretizations of some derivative terms can be avoided. The accuracy and efficiency of the present method is also tested through several benchmark problems, and the influence of mass/heat transfer on the fluid viscosity is further considered by introducing an exponential relation. The numerical results show that the present LB method is suitable for the two-phase flows with interfacial mass/heat transfer.

Figures (12)

• Figure 1: The distributions of two-scalar and one-scalar models at the same instants for pseudo-single-phase case, and the time intervals between adjacent concentration profiles are identical.
• Figure 2: Evolutions of the concentrations $c_1$, $c_2$ and $c_1+K_{eq}c_2$ at different cases [(a) and (b): $D_1=D_2=K_{eq}=1$, (c) and (d): $D_1=D_2=1$ and $K_{eq}=1/3$, (e) and (f): $D_1=10$, $D_2=1$ and $K_{eq}=1/3$].
• Figure 3: Evolutions of the concentrations $c_1$, $c_2$ and $c_1+K_{eq}c_2$ at linear equilibrium cases [(a) and (b): $D_1=D_2=K_{eq}=1$, (c) and (d): $D_1=10$, $D_2=1$ and $K_{eq}=1$, (e) and (f): $D_1=D_2=1$ and $K_{eq}=1/3$].
• Figure 4: A comparison of one-scalar and two-scalar models for the case with large diffusivity ratio $D_1=1/D_2=10^{4}$ [(a) two-scalar model and (b) one-scalar model].
• Figure 5: The predicted profiles of heat content at $y=z=0.5$ [(a) $t=13$, (b) $t=40$, (c) $t=80$, and (d) $t=250$].