A comparison of measured and modeled velocity fields for a laminar flow in a porous medium

Abstract

Obtaining highly-resolved velocity data from experimental measurements in porous media is a significant challenge. The goal of this work is to compare the velocity fields measured in a randomly-packed porous medium obtained from particle image velocimetry (PIV) with corresponding fields predicted from direct numerical simulation (DNS). Experimentally, the porous medium was comprised of 15 mm diameter spherical beads made of optical glass placed in a glass flow cell to create the packed bed. A solution of ammonium thiocyanate was refractive-index matched to the glass creating a medium that could be illuminated with a laser sheet without distortion. The bead center locations were quantified using the imaging system so that the geometry of the porous medium was known very accurately. Two-dimensional PIV data were collected and processed to provide high-resolution velocity fields at at a single planes within the porous medium. A Cartesian-grid-based fictitious domain approach was adopted for the direct numerical simulation of flow through the same geometry as the experimental measurements and without any adjustable parameters. The uncertainties associated with characterization of the pore geometry, PIV measurements, and DNS predictions were all systematically quantified. Although uncertainties in bead position measurements led to minor discrepancies in the comparison of the velocity fields, the axial and normal velocity deviations exhibited normalized root mean squared deviations (N RM SD) of only 11.32% and 4.74% respectively. The high fidelity of both the experi-1

Micro- and Macro-Scale Measurement of Flow Velocity in Porous Media: A Shadow Imaging Approach for 2D and 3D

“…Color bars represent the planar velocity magnitude √ u 2 + v 2 in mm/s. As shown in Figure 10, the fluid accelerates in the narrower regions, satisfying the continuity equation, Equation (1). By comparing Figure 10a-f, it appears that the magnitude of the in-plane velocity vectors ( √ u 2 + v 2 ) diminishes by increasing the distance from the front window that is located at z = 0 (see Figure 2).…”

“…This implies that the liquid flows faster near the window compared to the central region of the porous medium that can be due to the smaller resistance against the flow near the side windows. The out-of-plane component of velocity (w) at different planes was computed from the continuity equation, Equation (1). As w calculated from this approach strongly depends on the gradients of the in-plane velocities (∂u/∂x and ∂v/∂y) rather than the velocities (u,v) themselves (see Equation (1)), the in-plane velocities (u,v) need to be smoothed before being introduced into Equation (1) to get a coherent w from the continuity equation.…”

“…Understanding flow behavior at the micro scale inside a porous medium is as important as understanding macro behavior in the development of technological knowledge. For instance, while Darcy's law provides an overall estimation for flow transport in porous media, the fundamental foundations require detailed information about pore-scale flow patterns [1]. This becomes important in a variety of processes such as heat transfer [2], emulsion properties [3], oil extraction [4], colloidal transport [5] and separation industries, where porous media are often implemented as a filter medium [6].…”

Pore-scale investigation of complex flow behaviour in porous media

“…i.e.medium's permeability stays unchanged. In contrast, experimental investigations using nuclear magnetic resonance velocimetry [31][32][33][34][35][36][37] and optical imaging techniques [38][39][40][41][42][43][44] have demonstrated extensive variations of pore fluid velocity distributions in porous media. This research aims to investigate systematically the flow structures at the pore scale in conventional and complex flow systems and provide insights about their potential impacts on the transport properties of the medium.…”

“…and[7]), but not to the flow rate. However, experimental investigations using nuclear magnetic resonance velocimetry[31][32][33][34][35][36][37][184][185][186] and optical imaging techniques[39][40][41][42][43][44]187] have demonstrated extensive variations of pore-scale fluid velocity in porous media.As important features affecting the transport properties of porous media, dead-end and closed pore structures have been investigated for several decades[52,94]. Moreover, stagnant zones in porous systems, such as eddies or low-speed regions among the preferential flow paths have been numerically observed, either at low or high Reynold's numbers[95,96,188].…”