Influence of particle-fluid density ratio on the dynamics of finite-size particles in homogeneous isotropic turbulent flows

In this paper, direct numerical simulations of particle-laden homogeneous isotropic turbulence are performed using lattice Boltzmann method incorporating interpolated bounce-back scheme. Four different particle-fluid density ratios are considered to explore how particles with different particle-fluid density ratios respond to the turbulence. Overall particle dynamics in the homogeneous isotropic turbulence such as the Lagrangian statistics of single particle and the preferential concentration of particles are investigated. Results show that particle acceleration and angular acceleration are more intermittent than velocity and angular velocity for finite-size particles with different particle-fluid density ratios. The preferential concentration of particles is investigated using radial distribution function and Voronoï tessellation, and the preferential concentration is more profound for particles with two intermediate particle-fluid density ratios. The Voronoï analysis indicates that the distribution of Voronoï cells satisfy the log-normal distribution better than the gamma distribution. The mechanism of preferential concentration is analyzed using the sweep-stick mechanism and drift mechanism. Results show that although a higher probability of having particles located near the sticky points is found, the sticky mechanism is very weak for large density ratios. The particle clustering is then found to be better qualitatively described by the drift mechanism.

Figure 1

A two-dimensional sketch of the bounce-back scheme. The red circle is the particle surface, the black spheres are the fluid nodes, the red squares are the solid nodes, the black vectors represent the known molecular distribution functions during streaming step and the red vectors are the unknown molecular distribution functions which are determined using interpolated bounce-back scheme. The interpolated bounce-back scheme uses different number of fluid nodes to construct the unknown distributions in different situations.

Figure 2

Three-dimensional isosurface of vortical structures identified by $Q$ criteria with $Q/\langle 2r_{ij}{r}_{ij}\rangle =2.5$ for Case 1, and a small portion of the particles (30%) are shown to clearly see the vortical structures.

Figure 3

The distribution of three velocity components for ${\rho }_p/{\rho }_f=100$, the red dash line represents the Gaussian distribution.

Figure 4

The distribution of three angular velocity components for ${\rho }_p/{\rho }_f=100$, the red dash line represents the Gaussian distribution.

Figure 5

The distributions of three particle acceleration components for different cases, the red dash line is the empirical equation proposed by Qureshi [8, 9].

Figure 6

The distribution of angular acceleration in z direction for different cases, the red dash line is the fitting curve in Eq. (3), the fitting parameter is the average over different cases which corresponds to 0.69.

Figure 7

PDF of particle Reynolds number for different cases, the red dashed line is the gamma distribution suggested by Uhlmann et al. [25] for particles with particle-fluid density ratio 1.5.

Figure 8

(a) Sketch of the alignment angle $\left({\theta }_{\text{align}}\right)$ between particle and fluid velocity and (b) PDF of the alignment angle $\left({\theta }_{\text{align}}\right)$ between particle and fluid velocity. As the particle-fluid density ratio increases, the ability of particles to follow the local fluid motion becomes weaker as the peak value becomes smaller and the distribution becomes wider, and the heavy particles exhibit an almost uniform distribution.

Figure 9

Radial distribution function for different cases, the $x$ axis is the distance from particle center normalized by particle radius. The inset shows a zoom of the region near the peak.

Figure 10

2D visualization for different cases on a slice at $x=127.5$, figures for the same case are at the same time step. Panels (a), (d), (g), (j) are the vorticity fields, the color represents the magnitude of vorticity. High-vorticity regions near particle surfaces in all cases especially in Case 4 can be observed. Panels (b), (e), (h), (k) are the Voronoï diagrams, the particles insect with the plane are also shown and are represented by the skyblue spheres. Panels (c), (f), (i), (l) show spatial locations of particles and sticky points, the black dots are sticky points and the skyblue spheres are particles.

Figure 11

Centered and normalized PDF of the logarithm of Voronoï cell volumes, the red dash is a Gaussian distribution for comparison.

Figure 12

PDF of the normalized Voronoï cells, RPP represents results from random Poisson process.

Figure 13

PDF of the largest eigenvalue ${\lambda }_1$ of symmetric part of the fluid acceleration gradient, ${\rho }_p/{\rho }_f=100$.

Figure 14

Particle conditional RDF as a function of the distance from particle surface normalized by particle radius for different cases. (a) ${\rho }_p/{\rho }_f=1$, (b) ${\rho }_p/{\rho }_f=5$, (c) ${\rho }_p/{\rho }_f=20$, and (d) ${\rho }_p/{\rho }_f=100$.

Figure 15

Regions of different signs of the coarse-grained $Q$ using the $Q$ criterion, the red color represents the region where $\tilde{S}:\tilde{S}-\tilde{R}:\tilde{R}<0$, the blue color represents the region where $\tilde{S}:\tilde{S}-\tilde{R}:\tilde{R}>0$, and the green color represents the solid particles. (a) ${\rho }_p/{\rho }_f=1$, (b) ${\rho }_p/{\rho }_f=5$, (c) ${\rho }_p/{\rho }_f=20$, and (d) ${\rho }_p/{\rho }_f=100$.