inertia

One of the essential areas of the study of transport in porous medium is the flow phenomena at the onset of inertia. While this area has attracted considerable research interest, many fundamental questions remain. Such questions relate to things such as the nature of the multi-dimensional velocities of the flow, the evolution of inertia, the differences in flow phenomena at various complexity of porous media, and the best constitutive equation for the flow. To resolve some of these questions, the present research program was designed to experimentally investigate pressure-driven flow through two- and three-dimensional porous media at the onset of inertia. Specifically, the goals in view were to obtain velocity data and pressure measurements, apply the benchmark experimental data to study the evolution of inertia, distinguish differences in such evolution with respect to the parameters of the porous media, and to establish the constitutive equation that best describes the porous media flow when inertia sets in. What particularly sets this work apart, is the use of particle image velocimetry (PIV) – an experimental technique that captures multi-dimensional flow quantities, as opposed to mere flow rates. Using PIV then, detailed velocity measurements were conducted for flows through model porous media of solid volume fraction 6%, 12%, and 22%. The velocities were spatially averaged to obtain average streamwise and transverse components. In addition to the velocity measurements, differential pressure measurements were obtained using pressure-measurement gauges and transducers. The pressure and velocity data sets were then statistically analyzed and presented to provide a complete set of experimental data to characterize the flow through the model porous media. The results show that the velocity flow domain is dictated by the streamwise velocities, which are at least an order of magnitude greater than the transverse components. Furthermore, pressure drag was found to increase with compactness and complexity of the porous media. While inertia increases exponentially from particle Reynolds number ~ 1 – 3 onwards, it is apparently subdued by the form drag that tends to dominate the flow through complex media. Overall, the flow at the onset of inertia is best described by a power law. These results provide insights that are applicable to flows such as those near well bores and fractures where seepage velocities are relatively high.