The influence of Reynolds number upon the apparent permeability of spatially periodic arrays of cylinders

Abstract

Flow fields within spatially periodic arrays of cylinders arranged in square and hexagonal lattices are calculated, with microscale Reynolds number ranging between zero and 200, employing a finite element numerical scheme. The terminology of an ‘‘apparent permeability’’ is introduced to establish a relationship existing between mean velocity and macroscopic pressure gradient characterized by a finite Reynolds number flow. In contrast with the low Reynolds number ‘‘true ’’ permeability, the apparent permeability is shown here to generally depend upon the direction of the applied pressure gradient, owing to nonlinearities existing within the local fluid motion. The orientation-dependent permeabilities of both square and hexagonal monodisperse arrays are observed to diminish with increasing Reynolds number. Similar behavior is also observed for a bidisperse square array, though the apparent permeability of the latter is shown less sensitive to Darcy velocity orientation at large Reynolds numbers in comparison to the corresponding monodisperse square array, for all cylinder concentrations examined.

Simulation of Liquid Flow Permeability for Dendritic Structures during Solidification Process

“…cylinders as the function of Reynolds numbers for three ranges of low, moderate, and high Reynolds number (Cai & Berdichevsky, 1993;Edwards et al, 1990;Eidsath et al, 1983;Ghaddar, 1995;Koch & Ladd, 1997;McCartney, 1994;Nagelhout et al, 1995;Sangani & Mo, 1994;Sangani & Yao, 1988;Thom & Aplelt, 1961). Particularly noteworthy is the work of Koch & Ladd (1997) for modeling permeability and drag force based on Reynolds number using a Lattice-Boltzmann formulation.…”

Simulating micorotransport in realistic porous media

“…Many authors have studied the influence of fluid flow on the drag force for a large range of pore patterns. A large part of this research has concentrated on porous media composed of cylinders or spheres [10,12,16,17,26,56,67]. Others have considered porous media composed of rectangular shapes [38,39].…”

“…A well established closure model for the drag force [63] correlates flow effects arising at pore-scales with the averaged fluid velocity in a relation involving two transport parameters: the Darcy's law permeability tensor [11,5] and the Forchheimer tensor [63]. By incorporating both parameters into a single phenomenological dependency, quantifying the permeable nature of a porous medium, we form the apparent permeability [12]. Accurate macroscale flow predictions in porous media require an accurate parameterization of the apparent permeability.…”

“…While filtering reduces the complexity of the problem it also creates a closure problem regarding the physical effects of sub-filter scales on the larger macroscopic scales. Our interest in this chapter is the parameterization and quantification, through pore-scale simulations, of the so-called apparent permeability [12], i.e., a transport parameter that characterizes sub-filter scale fluid resistance. The apparent permeability takes into account both the geometrical complexity of the porous medium (i.e., pore size, shape and porosity) as well as the flow in it [12]; this in contrast to the permeability based on Darcy's law, which is a strict material property [5,11].…”

“…Our interest in this chapter is the parameterization and quantification, through pore-scale simulations, of the so-called apparent permeability [12], i.e., a transport parameter that characterizes sub-filter scale fluid resistance. The apparent permeability takes into account both the geometrical complexity of the porous medium (i.e., pore size, shape and porosity) as well as the flow in it [12]; this in contrast to the permeability based on Darcy's law, which is a strict material property [5,11]. We will compute the apparent permeability for a porous medium composed of an infinitely extending array of staggered square rods.…”