Phase-field-simplified lattice Boltzmann method for modeling solid-liquid phase change

This article proposes a phase-field–simplified lattice Boltzmann method (PF-SLBM) for modeling solid-liquid phase change problems within a pure material. The PF-SLBM consolidates the simplified lattice Boltzmann method (SLBM) as the flow solver and the phase-field method as the interface tracking algorithm. Compared with conventional lattice Boltzmann modelings, the SLBM shows advantages in memory cost, boundary treatment, and numerical stability, and thus is more suitable for the present topic which includes complex flow patterns and fluid-solid boundaries. In contrast to the sharp interface approach, the phase-field method utilized in this work represents a diffuse interface strategy and is more flexible in describing complicated fluid-solid interfaces. Through abundant benchmark tests, comprehensive validations of the accuracy, stability, and boundary treatment of the proposed PF-SLBM are carried out. The method is then applied to the simulations of partially melted or frozen cavities, which sheds light on the potential of the PF-SLBM in resolving practical problems.

Figure 1

Streamlines of the flow past a stationary circular cylinder at $\mathrm{Re}=10$, 20, and 40.

Figure 2

Illustration of induction induced solidification and melting.

Figure 3

Accuracy test of the PF-SLBM for conduction induced melting.

Figure 4

Conduction induced solidification. Left: time history of the interface position; right: temperature distributions at 5, 15, and 30 s.

Figure 5

Conduction induced melting. Left: time history of the interface position; right: temperature distributions at 5, 15, and 30 s.

Figure 6

Configuration of the convection melting in a square cavity.

Figure 7

Interface locations (red lines), streamlines (black lines), and temperature contours of the convection melting in a square cavity at different time.

Figure 8

Time histories of the liquid fraction (left column) and the average Nusselt number on the left wall (right column) for the convection melting in a square cavity. Only the upper and the lower limits of the reference data are presented.

Figure 9

Temperature contours and interface locations of the convection melting in a square cavity obtained by the PF-SLBM on coarse mesh sizes at $\mathrm{Ra}=2.5\times {10}^4$.

Figure 10

Illustration of the convection melting in a concentric annulus.

Figure 11

Evolution of the liquid fraction for the convection melting in a concentric annulus.

Figure 12

Interface locations (red lines), streamlines (black lines), and temperature contours of the convection melting in a concentric annulus at different time.

Figure 13

Time histories of the liquid fraction (left) and the average Nusselt number on the left wall (right) for the partial melting or freezing in a square cavity.

Figure 14

Interface locations, streamlines, and temperature contours of the partial melting or freezing in a square cavity.

Figure 15

Time histories of the liquid fraction for the partial melting or freezing in a concentric annulus.

Figure 16

Interface locations, streamlines, and temperature contours of the partial melting or freezing in a concentric annulus.