Characteristics of Porescale Vortical Structures in Random and Arranged Packed Beds of Spheres

The characteristics of pore scale vortical structures observed in moderate Reynolds number flow through monodisperse packed beds of spheres are examined. Our results come from direct numerical simulations of flow through (i) a periodic, simple cubic arrangement of 54 spheres, (ii) a wall bounded, close packed arrangement of 216 spheres, and (iii) a realistic randomly packed tube containing 326 spheres with a tube diameter to sphere diameter ratio of 5.96. Pore Reynolds numbers in the steady inertial ( 10 . Re . 200) and unsteady inertial (Re ≈ 600) regimes are considered. Even at similar Reynolds numbers, the vortical structures observed in flows through these three packings are remarkably different. The interior of the arranged packings are dominated by multi-lobed vortex ring structures which align with the principal axes of the packing. The random packing and the near wall region of the close packed arrangement are dominated by helical vortices, elongated in the mean flow direction. In the simple cubic packing, unsteady flow is marked by periodic vortex shedding which occurs at a single frequency. Conversely, at a similar Reynolds number, the vortical structures in unsteady flow through the random packing oscillate with many characteristic frequencies. ∗Address all correspondence to this author. INTRODUCTION The flow of fluid through a packed bed of spheres is a fundamental problem, rich in its applicability to a variety of disciplines. For example, groundwater hydrologists [1, 2], chemical engineers [3] and nuclear reactor designers [4] often consider flow through strikingly similar arrangements of fixed, contacting spheres as a prototypical problem for more complex systems. Despite such broad importance, the existing body of knowledge related to the flow physics of such problems is limited, particularly at moderate to large flow rates. For Stokesian, creeping flow, fluid streamlines conform naturally to the boundary of the porespace. In this case, the general behavior of the flow may be adequately described using geometric or network models [5], and simple relationships are available for macroscale properties such as Darcy’s law for permeability. However, at larger flow rates, porous media and packed bed flows become highly non-linear and multiscale in nature due to the contribution of flow inertia. This makes a-priori determination of the flow characteristics difficult or impossible even for simple, homogeneous sphere packings. This multiscale nature of inertial flows through porous media and packed beds is illustrated in FIG. 1. The macroscale is often used to describe the largest representative scale encountered in the field or laboratory. The macroscale flow can be sim1 Copyright c © 2012 by ASME (a) macroscale Lm qm (-)Vm