Improved thermal multiple-relaxation-time lattice Boltzmann model for liquid-vapor phase change

In this paper, an improved thermal multiple-relaxation-time (MRT) lattice Boltzmann (LB) model is proposed for simulating liquid-vapor phase change. A temperature equation is first derived for liquid-vapor phase change, where the latent heat of vaporization is decoupled with the equation of state. Therefore, the latent heat of vaporization can be arbitrarily specified in practice, which significantly improves the flexibility of the present LB model for liquid-vapor phase change. The Laplacian term of temperature is avoided in the proposed temperature equation and the gradient term of temperature is calculated through a local scheme. To solve the temperature equation accurately and efficiently, an improved MRT LB equation with nondiagonal relaxation matrix is developed. The implicit calculation of the temperature, caused by the source term and encountered in previous works, is avoided by approximating the source term with its value at the previous time step. As demonstrated by numerical tests, the results by the present LB model agree well with analytical results, experimental results, or the results by the finite difference method where the fourth-order Runge-Kutta method is employed to implement the discretization of time.

Figure 1

Simulation of droplet evaporation in open space. Snapshots of the density contours obtained by Gong and Cheng's model [22] (a), Li et al.'s model [24] (b), the present LB model (c), and the FDM (d). The snapshots are taken at $t^{*}=0.1,0.25,\mathrm{and}0.5$ (from left to right).

Figure 2

Simulation of droplet evaporation in open space. Variation of the square of the dimensionless diameter ${\left(D^{*}\right)}^2$ with the dimensionless time $t^{*}$.

Figure 3

Simulation of droplet evaporation in open space. Comparison of the present LB model and the FDM.

Figure 4

Simulation of droplet evaporation on a heated substrate. Variation of the dimensionless radius $r^{*}$ with the dimensionless time $t_1^{*}$.

Figure 5

Simulation of droplet evaporation on a heated substrate. The errors between the numerical results and experimental results.

Figure 6

Simulation of droplet evaporation on a heated substrate. Variation of the dimensionless radius $r^{*}$ with the dimensionless time $t_2^{*}$.

Figure 7

Simulation of droplet evaporation on a heated substrate. Comparison of the present LB model with FDM.

Figure 8

Simulation of bubble nucleation and departure ($g=2.75\times {10}^{-5}$, $h_{lv}=0.120$). Snapshot of the density contours. The snapshots are taken at $t=140000{\delta }_t$, $t=146000{\delta }_t$, $t=148500{\delta }_t$ (from left to right).

Figure 9

Simulation of bubble nucleation and departure ($g=2.75\times {10}^{-5}$, $h_{lv}=0.145$). Snapshot of the density contours. The snapshots are taken at $t=161000{\delta }_t$, $t=164000{\delta }_t$, $t=166000{\delta }_t$ (from left to right).

Figure 10

Simulations of bubble nucleation and departure. Variation of detachment bubble diameter with gravity acceleration. $h_{lv}=0.120$ (a) and $h_{lv}=0.145$ (b).