Effects of settling particles on the bubble formation in a gas-liquid-solid flow system studied through a coupled numerical method

In this paper, the numerical investigation of the bubble formation and rise in gas-liquid-solid flow systems has been done through a coupled numerical method, the so-called volume of fluid (VOF) method, and a discrete element model (DEM). VOF is used to capture the interface of the bubble and DEM is employed to track the movement of particles. This coupled numerical method is validated through the good consistency of our calculated results to those experimental data (from other literature) of a bubble rising in a gas-liquid-solid system. The calculation results in this paper disclose that the detachment time of the first formed bubble is longer for case I (when particles are lying at the bottom of the container) than for case II (when the particles are settling freely). The main reason is that a stronger circulation (induced by the sedimentation of particles) near the bottom of the container plays a stronger cutting role and speeds up the detachment of the bubble. Then, the effects of some factors including particle volume fractions, gas velocities, orifice sizes, surface tensions, and liquid densities on the bubble formation and rise have also been investigated systematically. This work is useful for further research on the gas-liquid-solid fluidized bed system.

Figure 1

Simulation results of the bubble rising velocity with different mesh sizes.

Figure 2

Effects of gas velocities on bubble behavior with different mesh sizes. (a) Detachment time vs $V_g$. (b) Bubble diameter vs $V_g$.

Figure 3

Falling velocity vs time for a single particle falling from the air into a liquid phase under various viscosities $\mu$ and particle initial heights $z$. (a) $\mu =1\times {10}^{-3}\mathrm{Pa}\mathrm{s}, z=6\mathrm{mm}$; (b) $\mu =1\times {10}^{-3}\mathrm{Pa}\mathrm{s}, z=7\mathrm{mm}$; (c) $\mu =5\times {10}^{-4}\mathrm{Pa}\mathrm{s}, z=6$ mm; (d) $\mu =5\times {10}^{-4}\mathrm{Pa}\mathrm{s}, z=7\mathrm{mm}$.

Figure 4

Snapshots of particles falling into water.

Figure 5

Height of the water surface at time $t=0$ s and $t=1.0$ s.

Figure 6

(a) Comparison of the velocity of the rising bubble from the simulation to those from the experiment [41]. (b) Comparison of the aspect ratio of the rising bubble from the simulation to those from the experiment [41].

Figure 7

Formation and detachment of the first bubble when particles are lying at the bottom. (a) $t=0.3$ s, (b) $t=0.45$ s, (c) $t=0.6$ s, and (d) $t=0.85$ s.

Figure 8

Simulation results of bubble formation and rising when particles are lying at the bottom. (a) $t=0.9$ s, (b) $t=1.0$ s, (c) $t=1.2$ s, (d) $t=1.4$ s, (e) $t=1.5$ s, and (f) $t=1.6$ s.

Figure 9

Velocity vectors during the bubble formation for (a) $t=0.3$ s, (b) $t=0.45$ s, (c) $t=0.6$ s, and (d) $t=0.85$ s. The directions of velocity vectors are indicated by arrows with a uniform length. Thus, the length of the arrow does not represent the magnitude of the velocity vector, but the color does.

Figure 10

Velocity vectors at the bottom of the container during the first bubble formation. (a) $t=0.3$ s, (b) $t=0.45$ s, (c) $t=0.6$ s, and (d) $t=0.85$ s.

Figure 11

Formation and detachment of the first bubble when particles are settling freely in the liquid phase. (a) $t=0.1$ s, (b) $t=0.2$ s, (c) $t=0.25$ s, and (d) $t=0.35$ s.

Figure 12

Bubble formation and rising when particles are settling freely in the liquid phase. (a) $t=0.5$ s, (b) $t=0.6$ s, (c) $t=0.7$ s, (d) $t=0.8$ s, (e) $t=1.0$ s, and (f) $t=1.2$ s.

Figure 13

Velocity vector in the bubble formation process shown in Fig. 11. (a) $t=0.1$ s, (b) $t=0.2$ s, (c) $t=0.25$ s, and (d) $t=0.35$ s.

Figure 14

Velocity vectors at the bottom of the container during the first bubble formation. (a) $t=0.1$ s, (b) $t=0.2$ s, (c) $t=0.25$ s, and (d) $t=0.35$ s.

Figure 15

Formation and rise of bubbles at different volume fractions of solid particles suspended in the liquid phase. (a) ${\varepsilon }_p=0.2234\%$, (b) ${\varepsilon }_p=0.2979\%$, and (c) ${\varepsilon }_p=0.4467\%$.

Figure 16

Effects of gas velocities and orifice sizes on bubble behaviors in the gas-liquid-solid flow. (a) Detachment time vs $V_g$. (b) Detachment velocity vs $V_g$. (c) Bubble diameter vs $V_g$.

Figure 17

Effects of surface tensions and liquid densities on bubble behaviors in a gas-liquid-solid flow system. (a) Effects on the detachment time. (b) Effects on the bubble diameter.