Particle velocity distributions and velocity fluctuations of non-Brownian settling particles by particle-resolved direct numerical simulation

Settling dynamics of non-Brownian particles is investigated using particle-resolved direct numerical simulations. There are two aims of this paper: first is to study the variation of particle velocity fluctuations with solid volume for a wide range of settling Reynolds number; second is to investigate the effects of solid volume fraction and settling Reynolds number on the distribution of particle velocity fluctuations after reaching the steady state. Simulations are performed in the periodic domain and the settling Reynolds number and solid volume fraction are varied from 0.5 to 400 and 0.01 to 0.2, respectively. It is observed that particle velocity fluctuations increase with increase in solid volume fraction for settling Reynolds number less than 100. Further increase in the settling Reynolds number alters the behavior of settling particles, making the particle velocity fluctuations either remain nearly constant or even decrease with the increase in solid volume fraction. For dense suspensions, it is observed by simulations that the distribution of particle velocities has Gaussian form during settling. However, for dilute and moderately dense suspensions, particle velocity distribution becomes non-Gaussian for the studied range of settling Reynolds number. At the end of paper, the physics behind the scaling of particle velocity fluctuations with solid volume fraction and the distribution of particle velocity fluctuations during settling is explained.

Figure 1

DEM model.

Figure 2

Particle velocity fluctuations (a) along the settling direction and (b) perpendicular to the settling direction.

Figure 3

Ratio of particle velocity fluctuations parallel to the settling direction to the particle velocity fluctuations perpendicular to the settling direction.

Figure 4

PDF of particle velocities distribution in settling direction (a) $\mathrm{Re}=0.5$, (b) $\mathrm{Re}=50$, and (c) $\mathrm{Re}=400.$

Figure 5

PDF of particles velocity distribution perpendicular to settling direction (a) $\mathrm{Re}=0.5$, (b) $\mathrm{Re}=50$, and (c) $\mathrm{Re}=400$.

Figure 6

Skewness of particle velocity distribution (a) along the settling direction and (b) perpendicular to the settling direction.

Figure 7

Kurtosis of particle velocity distribution (a) along the settling direction and (b) perpendicular to the settling direction.

Figure 8

Particle clusters nondimensionalized by clusters formed in random particle arrangements: (a) singlets, (b) doublets, (c) triplets, and (d) more than triplets.

Figure 9

Radial distribution function in spherical coordinates (a) $\phi =0.01$ and $\mathrm{Re}=0.5$, (b) $\phi =0.01$ and $\mathrm{Re}=50$, (c) $\phi =0.01$ and $\mathrm{Re}=400$, (d) $\phi =0.05$ and $\mathrm{Re}=0.5$, (e) $\phi =0.05$ and $\mathrm{Re}=50$, and (f) $\phi =0.05$ and $\mathrm{Re}=400$.

Figure 10

Visualization of vortices around single particles using isosurfaces of ${\nabla }^{2}p=2\times {10}^6$: (a) $\mathrm{Re}=50$, (b) $\mathrm{Re}=100$, (c) $\mathrm{Re}=200$, (d) $\mathrm{Re}=300$, and (e) $\mathrm{Re}=400$.

Figure 11

Distribution of particles in the computational domain after Stokes time $\cong 2500$ for $\mathrm{Re}=400$ and (a) $\phi =0.005$, (b) $\phi =0.05$, and (c) $\phi =0.2$.

Figure 12

Variation of interparticle distance during DKT of particles for $\mathrm{Re}=0.5$ and 50 ($d_1$ is the initial interparticle distance).

Figure 13

Variation of average velocity fluctuations of two settling particles for $\mathrm{Re}=10$, 50, and 100 by increasing the length of the computational domain perpendicular to the settling direction.

Figure 14

Distribution of particles in the top view of the computational domain at (a) Stokes time $\cong 0$, (b) Stokes time $\cong 1000$, (c) Stokes time $\cong 2000$, and (d) Stokes time $\cong 3000$.