Interaction of pressure and momentum driven flows with thin porous media: Experiments and modeling.

摘要

Flow interaction with thin porous media arise in a variety of natural and man-made settings. Examples include flow through thin grids in electronics cooling, and NOx emissions reduction by means of ammonia injection grids, pulsatile aquatic propulsion with complex trailing anatomy (e.g., jellyfish with tentacles) and microbursts from thunderstorm activity over dense vegetation, unsteady combustion in or near porous materials, pulsatile jet-drying of textiles, and pulsed jet agitation of clothing for trace contaminant sampling. Two types of interactions with thin porous media are considered: (i) forced convection or pressure-driven flows, where fluid advection is maintained by external forces, and (ii) inertial or momentum-driven flows, in which fluid motion is generated but not maintained by external forces.; Forced convection analysis through thin permeable media using a porous continuum approach requires the knowledge of porous medium permeability and form coefficients, K and C, respectively, which are defined by the Hazen-Dupuit-Darcy (HDD) equation. Their determination, however, requires the measurement of the pressure-drop per unit of porous medium length. The pressure-drop caused by fluid entering and exiting the porous medium, however, is not related to the porous medium length. Hence, for situations in which the inlet and outlet pressure-drops are not negligible, e.g., for short porous media, the definition of Kand C via the HDD equation becomes ambiguous. This aspect is investigated analytically and numerically using the flow through a restriction in circular pipe and parallel plates channels as preliminary models. Results show that inlet and outlet pressure-drop effects become increasingly important when the inlet and outlet fluid surface fraction &phis; decreases and the Reynolds number Re increases for both laminar and turbulent flow regimes. A conservative estimate of the minimum porous medium length beyond which the core pressure-drop predominates over the inlet and outlet pressure-drop is obtained by considering a least restrictive porous medium core. Finally, modified K and C are proposed and predictive equations, accurate to within 2.5%, are obtained for both channel configurations with Re ranging from 10-2 to 102 and &phis; from 6% to 95%.; When momentum driven flows interact with thin porous media, the interaction of vortices with the media's complex structure gives way to a number of phenomena of fundamental and applied interest, such as unsteady flow separation. A special case that embodies many of the key features of these flows is the interaction of a vortex ring with a permeable flat surface. Although fundamental, this complex flow configuration has never been considered. The present investigation experimentally studies the fluid mechanics of the interaction of a vortex ring impinging directly on thin permeable flat targets. The vortex ring is formed in water using a piston-cylinder mechanism and visualized using planar laser-induced fluorescence (PLIF). The rings are formed for jet Reynolds numbers of 3000 and 6000, and piston stroke-to-diameter ratios of 1.0, 3.0, and 6.0. Thin screens of similar geometry having surface opening fractions of 44, 60, 69, and 79% are targeted by the rings. The flow that emerges downstream of the screens reforms into a new, "transmitted" vortex ring. For the lower porosity targets, features that are characteristic of vortex ring impingement on walls are also observed, such as primary vortex ring rebound and reversal, flow separation, formation of secondary vortices and mixing. As the interaction proceeds, however, the primary vortex ring and secondary vortices are drawn toward the symmetry axis of the flow by fluid passing through the permeable screen. Quantitative flow measurements using digital particle image velocimetry (DPIV), indicate the transmitted vortex ring has lower velocity and less (total) kinetic energy than the incident ring. Ring trajectories and total ki