Lattice Boltzmann modeling of fluid-particle interaction based on a two-phase mixture representation

In this work, we derive a lattice Boltzmann model for fluid-particle interaction by considering the system as a two-phase mixture. A partially saturated type scheme is achieved rigorously without any viscosity-dependent weight parameter. The scheme is of second-order accuracy in both space and time including the body-force term. Moreover, we devise a scheme suitable for the scenario where two or more particles intersect a single computational cell, typically occurring for particles in contact or close to contact. Good performance is found when the present scheme is validated against three classic problems, namely the flow past a stationary cylinder, a cylindrical particle settling in a channel under gravity, and the flow around two impacting cylinders.

Figure 1

Illustration of the vector $\mathit{r}$ for calculating the velocity, ${\mathit{V}}_p$.

Figure 2

Illustration of two particles “1” and “2” intersecting a computational cell around grid point ${\mathit{x}}_n$.

Figure 3

A time cycle of the present LBM modeling of fluid-particle interaction.

Figure 4

Computational domain for flows around a cylinder.

Figure 5

Accuracy of the present LBM simulations with MES-I and MES-II for a channel flow past a stationary cylinder. For convenience, a guide line of slope $-2$ is added.

Figure 6

Drag coefficient $C_d$ predicted by MES-II for unconfined flows past a cylinder at various Reynolds numbers. The experimental results in Ref. [52] are included for comparison.

Figure 7

Computational domain for case of a particle settling inside a channel under gravity.

Figure 8

Accuracy of MES-II and PSM for a cylindrical particle settling in a channel under gravity.

Figure 9

The setup of two infinite cylinders of diameter $D$ moving toward each other with an initial velocity of $U/2$. The initial gap of the two cylinders is $2D$.

Figure 10

Evolution of the drag coefficient for flow past two impacting cylinders against the dimensionless time $t^{*}$ at $\mathrm{Re}=50$ using two sets of $D/\mathrm{\Delta }x$. The results of Bampalas and Graham [55] are included for comparison.