Moderate-Reynolds-number flows in ordered and random arrays of spheres

Abstract

Lattice-Boltzmann simulations are used to examine the effects of fluid inertia, at moderate Reynolds numbers, on flows in simple cubic, face-centred cubic and random arrays of spheres. The drag force on the spheres, and hence the permeability of the arrays, is calculated as a function of the Reynolds number at solid volume fractions up to the close-packed limits of the arrays. At Reynolds numbers up to O(102), the non-dimensional drag force has a more complex dependence on the Reynolds number and the solid volume fraction than suggested by the well-known Ergun correlation, particularly at solid volume fractions smaller than those that can be achieved in physical experiments. However, good agreement is found between the simulations and Ergun's correlation at solid volume fractions approaching the close-packed limit. For ordered arrays, the drag force is further complicated by its dependence on the direction of the flow relative to the axes of the arrays, even though in the absence of fluid inertia the permeability is isotropic. Visualizations of the flows are used to help interpret the numerical results. For random arrays, the transition to unsteady flow and the effect of moderate Reynolds numbers on hydrodynamic dispersion are discussed.

Particle-resolved direct numerical simulation of homogeneous isotropic turbulence modified by small fixed spheres

“…For uniform flow over a regular particle array, the hydrodynamic actions can be very strong (Hill et al 2001). Figure 12 in that paper is particularly interesting in the present context, as it shows the drag force obtained from particle-resolved simulations of uniform flows over a simple cubic particle array for a volume fraction of 0.001 and a particle Reynolds number around 10.…”

Assessing Eulerian–Lagrangian simulations of dense solid-liquid suspensions settling under gravity

“…In such cases, the fluid flow time scales are much shorter than the time scales over which particle configurations change so that one can view drag as the result of the gas flowing through static (and random) assemblies of particles. Nowadays fully resolved simulations of fluid flow through assemblies of static particles are standard routine [19][20][21][22] and a great many correlations have been proposed based on such simulations. As shown by [23], the situation for liquid-solid systems that have low to intermediate Stokes numbers is very different.…”

Characterization of fluid-particle interactions in poly-disperse systems

“…Even semi-analytical treatments of low-Reynolds-number flow through periodic arrays have been proposed in the literature [1][2][3]. In the last decade, fully resolved numerical simulations have allowed developing more accurate expressions for the drag force acting on individual particles [4][5] and to introduce useful elements for a formulation of the problem in poly-disperse systems [5][6]. However, the problem of a sufficiently general and validated theory for modelling the fluid-particle interaction in poly-disperse systems is still open, as will be discussed below.…”