Coupled lattice Boltzmann–large eddy simulation model for three-dimensional multiphase flows at large density ratio and high Reynolds number

A coupled lattice Boltzmann–large eddy simulation model is developed for modeling three-dimensional multiphase flows at large density ratios and high Reynolds numbers. In the framework of the lattice Boltzmann method, the model is proposed based on the standard Smagorinsky subgrid-scale approach, and a reconstructed multiple-relaxation-time collision operator is adopted. The conservative Allen-Cahn equation and Navier-Stokes equations are solved through the lattice Boltzmann discretization scheme for the interface tracking and velocity field evolution, respectively. Relevant benchmark cases are carried out to validate the performance of this model in simulating multiphase flows at a large density ratio and a high Reynolds number, including a stationary droplet, the process of spinodal decomposition, the Rayleigh-Taylor instability, the phenomenon of a droplet splashing on a thin liquid film, and the liquid jet breakup process. The maximum values of density ratio and Re number are 1000 and 10 240, respectively. The capability and reliability of the proposed model have been demonstrated by the good agreement between simulation results and the analytical solutions or the previously available results.

Figure 1

D3Q7 lattice model.

Figure 2

D3Q15 lattice model.

Figure 3

Numerical validation by Laplace's law.

Figure 4

Density profiles at $y=LY/2$ and $z=LZ/2$.

Figure 5

Maximum kinetic energy versus time.

Figure 6

Separation of binary fluid: distribution of order parameters shown in grayscale.

Figure 7

The domain size $R$ versus time step t.

Figure 8

Schematic diagram for the Rayleigh-Taylor instability.

Figure 9

Snapshots of the interface evolution at $\mathrm{Re}=1024$ (left) and $\mathrm{Re}=10000$ (right).

Figure 10

Comparison of the bubble, saddle, and spike front positions at $\mathrm{Re}=1024$ between present results and those of He et al. [61].

Figure 11

Evolution of the fluid interface at the planes of $x=0, x=0.5d$, and $x=y$ ($t*=1.0$, 2.0, 3.0, and 4.0 from left to right).

Figure 12

Schematic diagram for a droplet splashing on a thin liquid film.

Figure 13

Evolution of interface morphology for droplet splashing on a thin liquid film (time $t^{*}$ is 1.0, 1.5, 2.0, 2.5, 3.0, and 3.5 from left to right for both cases).

Figure 14

Vertical cross sections of the splashing lamella for case 2.

Figure 15

Evolutions of the radial distance of splashing lamella for case 1 and case 2.

Figure 16

Schematic diagram for liquid jet simulation.

Figure 17

Simulation results of case 1 in the dripping regime of the liquid-liquid system.

Figure 18

Simulation results of case 2 in the varicose regime of the liquid-liquid system.

Figure 19

Simulation results of case 3 in the sinuous regime of the liquid-liquid system.

Figure 20

Simulation results of case 4 in the atomization regime of the liquid-liquid system.

Figure 21

Locations of four cases on the Oh-Re map of the liquid-liquid system proposed by Saito et al. [69].

Figure 22

Simulation results of case 1 in the varicose regime of the liquid-gas system.

Figure 23

Simulation results of case 2 in the sinuous regime of the liquid-gas system.

Figure 24

Simulation results of case 3 in the atomization regime of the liquid-gas system.

Figure 25

Locations of three cases on the Oh-Re map of the liquid-gas system proposed by Kolev [70].