Buoyant and Forced Flows over Regularly Textured Surfaces and Porous Substrates

The complex interaction between textured walls/substrates and a fluid is analyzed in different buoyant and forced flow problems. Experimental surveys on natural convection along rib-roughened vertical surfaces are conducted, in addition to numerical analyses of laminar buoyant flows over ribbed surfaces and of laminar/turbulent forced flows in channels with rough/permeable boundaries. The numerical work comprises (i) full feature-resolving simulations and (ii) homogenized ones that exploit effective boundary conditions to macroscopically mimic the phenomena, thus bypassing expensive numerical resolution of the fields near/within wall corrugations. The theoretical/numerical work on buoyant flows along ribbed vertical surfaces focuses on the formulation and validation of high-order effective velocity and temperature boundary conditions at a fictitious plane interface next to the roughness elements. In the first experimental phase, the buoyant airflow over a heated vertical surface regularly roughened with wooden ribs of square cross section, either spanwise-elongated or truncated and arranged in a staggered pattern, is studied at relatively large Rayleigh numbers (Ra of order 10^8), and varying the rib height and pitch. The experiments utilize the schlieren method to visualize the thermal boundary layer and to estimate the local Nusselt number values along the vertical surface; also, miniature thermocouples are employed to measure the local air temperature near the wall. Exclusively for staggered ribs, heat transfer enhancement, sensitive to number of rib segments per row, is found, and the observations reveal the potential of truncated ribs to amplify thermal-field disturbances. The second phase of experiments is aimed at studying similar roughness geometries under conditions well within the laminar regime (Ra of order 10^7), which facilitates performing full/homogenized numerical simulations, to be validated against the experimental results. Both the continuous and the truncated rib patterns are found to degrade the convective heat transfer from the surface at such a low Rayleigh number. In regard to the forced flow problems, first, the fully developed, laminar flow in a channel bounded by rough/porous walls is considered, and the Beavers-Joseph-Saffman condition for the slip velocity is revisited. The boundary condition used for the longitudinal velocity, available from the homogenization theory, applies not only to permeable but also to rough surfaces, including the case of separated flow. Moreover, the near-wall advection is incorporated into the analysis by means of an Oseen’s approximation, and this widens the applicability range of the model considerably. Second, effective boundary conditions of the three velocity components are implemented to study turbulent channel flows over different porous substrates. The results demonstrate the possible drag-reducing effect of porous substrates with streamwise-preferential alignment of the solid inclusions, and show that the r.m.s. fluctuations of the transpiration velocity at the fictitious interface between the free-fluid region and the perturbed wall, ˜ Vrms, is a key control parameter of the roughness function, ΔU+; further analysis reveals that ˜ Vrms is strongly correlated to a single macroscopic quantity, Ψ, which comprises the upscaling coefficients of the model. Finally, a volume-averaging-based analysis of seepage in triply-periodic-minimal-surface- based porous structures is conducted, under conditions departing from Stokes’. An advection-sensitive “effective” permeability (rather than the merely geometry-dependent intrinsic permeability) in Darcy’s law stems from upscaling, and can be evaluated by solving a closure problem through a representative elementary volume of the medium. It is found that advection can significantly reduce permeability, particularly at large porosities.