Meso‐scale statistical properties of gas–solid flow—a direct numerical simulation (DNS) study

Abstract

Statistical properties of particles in heterogeneous gas–solid flow were numerically investigated based on the results of a three‐dimensional large‐scale direct numerical simulation (DNS). Strong scale‐dependence and local non‐equilibrium of these properties, especially the particle fluctuating velocity (PFV) or granular temperature, were observed to be related to the effect of meso‐scale structures formed by the compromise in competition between fluid and particle dominated mechanisms. To quantify such effects, the heterogeneous structures were partitioned into a gas‐rich dilute phase and a solid‐rich dense phase according to the particle‐scale voidage defined through the Voronoi tessellation. Non‐equilibrium features, such as the deviation of PFV from Gaussian distribution and anisotropy, were found even in phase‐specific properties. A new distribution function for the PFV well characterizing these features was obtained by fitting the DNS results, which takes a typical bi‐disperse mode, with phase‐specific granular temperatures. The implications of these findings to the kinetic theory of granular flow and traditional continuum models of gas–solid flow were also discussed. © 2016 American Institute of Chemical Engineers AIChE J, 63: 3–14, 2017

Particle‐level dynamics of clusters: Experiments in a gas‐fluidized bed

“…Identification of a cluster 2,3 is not unempirical, as reviewed in the literature 65,66 and discussed in the Introduction section. Most of these methods are not at the particle level except for the Voronoi diagram method, which has been used for determining the local concentration of particles in gas-solids flows 36,67 and characterization of the clustering of inertial particles in a turbulent flow. 37 For a random Poisson process (RPP) considering particle volume effects, its probability density function (PDF) is given as follows 68 :…”

Scale‐dependent nonequilibrium features in a bubbling fluidized bed

“…In greater detail, the PDF of particle velocity shows a non-Gaussian shape in a vibro-fluidized bed, where energy was injected from vibrating boundaries and dissipated through particle collisions. 28,[45][46][47][48][49] For a molecular equilibrium system, continuum hypothesis can be used to attach a definite meaning to the notion of local values of various macroscopic variables such as the density, velocity and temperature and these values are continuous functions of position and time. 34,38 The farther from the boundary, the more symmetrical is local PDF.…”

“…34,38 The farther from the boundary, the more symmetrical is local PDF. Most studies on this topic are based on simulation 28,48,49 and relevant experimental data are scarce. A skewed distribution and even a bimodal distribution can be found along vertical (driving) direction.…”

“…44 Besides PDF of particle velocity, other hydrodynamic quantities, like the granular density, velocity and granular temperature, also depend on spatio-temporal scales. 28,[45][46][47][48][49] For a molecular equilibrium system, continuum hypothesis can be used to attach a definite meaning to the notion of local values of various macroscopic variables such as the density, velocity and temperature and these values are continuous functions of position and time. 50 The meso-scale structures in fluidization, in forms of bubbles or clusters, prevent us to raise simple definitions on e.g.…”

“…the averaged velocity of particle and granular temperature. Most studies on this topic are based on simulation 28,48,49 and relevant experimental data are scarce.…”