Fluid flow over and through a regular bundle of rigid fibres

Abstract

The interaction between a fluid flow and a transversely isotropic porous medium is described. A homogenized model is used to treat the flow field in the porous region, and different interface conditions, needed to match solutions at the boundary between the pure fluid and the porous regions, are evaluated. Two problems in different flow regimes (laminar and turbulent) are considered to validate the system, which includes inertia in the leading-order equations for the permeability tensor through a Oseen approximation. The components of the permeability, which characterize microscopically the porous medium and determine the flow field at the macroscopic scale, are reasonably well estimated by the theory, both in the laminar and the turbulent case. This is demonstrated by comparing the model's results to both experimental measurements and direct numerical simulations of the Navier-Stokes equations which resolve the flow also through the pores of the medium

Effects of porosity and inertia on the apparent permeability tensor in fibrous media

“…These authors show that, for arrays of fibers, the apparent permeability decreases with the increase of the Reynolds number, and the rate of this decrease depends on the geometry of the array; also, the Reynolds number is found to have a stronger influence on the apparent permeability when the medium is highly porous. The results of the work by Edwards et al (1990) agree with those by Zampogna and Bottaro (2016) and with our own work (as shown later), all for the case of cylindrical fibers, although some issues remain on the persistence of steady solutions in the simulations by Edwards et al (1990) in cases for which a limit cycle should have set in. A fully three-dimensional porous medium, more complex than those discussed so far, has been considered by Soulaine and Quintard (2014) , confirming the decreasing trend of the apparent permeability with the Reynolds number.…”

“…This of course implies knowledge of the microscopic velocity field. A Oseen-like approximation which relaxes this constraint has been proposed by Zampogna and Bottaro (2016) .…”

Drag-model sensitivity of Kelvin-Helmholtz waves in canopy flows

“…The effective interface between the inertial region and the slow, viscosity-dominated region does not coincide with the edge of the canopy; in fact, the rapid outer flow penetrates through the upper part of the vegetation and an effective matching between outer and inner flows must be enforced some distance δ below the canopy's edge. 20 This distance, a penetration depth, has been successfully computed by Zampogna and Bottaro 21 for a few cases and is found to increase with the Reynolds number of the flow; for experiment G discussed below it is δ ≈ 0.40. 22 On account of the results shown in Fig.…”

“…One model is based on the use of a single drag coefficient to express the force exerted by the vegetation on the fluid, the second considers the canopy as an orthotropic porous medium and is based on Darcy's equation with a tensorial permeability. 21 Both models have advantages and drawbacks. The main advantage of the first model is that the drag coefficient can be taken to vary across the canopy; whether this positive consideration, based on macroscopic experimental measurements, [14][15][16] carries over to the stability problem remains to be established.…”

“…Such parameters and components of the transversely isotropic permeability tensor K i j arise from the solution of a local Oseen problem. 21 The drawback of the second model is the fact that an interface (whether real or effective) appears, and adequate matching conditions must be enforced there. Despite much work since the seminal contribution by Beavers and Joseph, 23 a consensus on the "best" interface conditions between a pure fluid region and a porous medium has not yet emerged.…”