Shallow Flows Over a Permeable Medium: The Hydrodynamics of Submerged Aquatic Canopies

Aquatic flow over a submerged vegetation canopy is a ubiquitous example of flow adjacent to a permeable medium. Aquatic canopy flows, however, have two important distinguishing features. Firstly, submerged vegetation typically grows in shallow regions. Consequently, the roughness sublayer, the region where the drag length scale of the canopy is dynamically important, can often encompass the entire flow depth. In such shallow flows, vortices generated by the inflectional velocity profile are the dominant mixing mechanism. Vertical transport across the canopy–water interface occurs over a narrow frequency range centered around f _v (the frequency of vortex passage), with the vortices responsible for more than three-quarters of the interfacial flux. Secondly, submerged canopies are typically flexible, coupling the motion of the fluid and canopy. Importantly, flexible canopies can exhibit a coherent waving (the monami) in response to vortex passage. This waving reduces canopy drag, allowing greater in-canopy velocities and turbulent stresses. As a result, the waving of an experimental canopy reduces the canopy residence time by a factor of four. Finally, the length required for the set-up and full development of mixing-layer-type canopy flow is investigated. This distance, which scales upon the drag length scale, can be of the same order as the length of the canopy. In several flows adjacent to permeable media (such as urban canopies and reef systems), patchiness of the medium is common such that the fully developed condition may not be representative of the flow as a whole.     

Coupling between countercurrent gas and solid flows in a moving granular bed: The role of shear bands at the walls

We extended the standard approach to countercurrent gas–solid flow in vertical vessels by explicitly coupling the gas flow and the rheology of the moving bed of granular solids, modelled as a continuum, pseudo-fluid. The method aims at quantitatively accounting for the presence of shear in the granular material that induces changes in local porosity, affecting the gas flow pattern through the solids. Results are presented for the vertical channel configuration, discussing the gas maldistribution both through global and specific indexes, highlighting the effect of the relevant parameters such as solids and gas flowrate, channel width, and wall friction. Non-uniform gas flow distribution resulting from uneven bed porosity is also discussed in terms of gas residence time distribution (RTD). The theoretical RTD in a vessel of constant porosity and Literature data obtained in actual moving beds are qualitatively compared to our results, supporting the relevance under given circumstances of the coupling between gas and solids flow.     

The Slip Velocity at the Edge of a Porous Medium: Effects of Interior Resistance and Interface Curvature

Singularity methods are used to analyze creeping planar flow in the annulus between concentric cylinders, when a portion of the annulus is filled with an array of regularly spaced rods adjacent to the inner cylinder. The rods are evenly spaced on concentric circles, and the circles are spaced such that the array resembles a square lattice bent into a circle. The rods and inner cylinder are stationary, and steady rotation of the outer cylinder generates the flow. The quantity of interest is the slip velocity, the mean velocity at the interface between the array and the unfilled portion of the annulus. The primary part of the study concerns the influence of the interior rods on the interfacial velocity, and to this end the velocity is found as successive circles of rods are removed, starting with the circle closest to the inner cylinder. The calculations are carried out for solid volume fractions from 0.0001 to 0.1, and these show that the slip velocity is virtually unchanged as the interior circles of rods are removed, until only one circle remains and then the velocity is of order 10% larger than that for the full array. Hence the velocity at the edge of a sparse porous medium depends minimally on the hydrodynamic resistance of the obstacles in the interior. In the secondary part of the study, it is found that curvature of the interface does not influence the velocity there.