Effects of porous substrates on the structure of turbulent boundary layers

Abstract

Three different porous substrates (with different pore sizes, $s$ , and permeabilities, $K$ ) are used to examine their effect on the structure of boundary layer flow over them. The flow is characterised with single-point hot-wire measurements as well as planar particle image velocimetry. In order to elucidate differences in shallow and deep flows past porous substrates, foams with two different thicknesses ( $h$ ) are used (for all three substrates). A wide range of friction Reynolds numbers ( $2000< Re_\tau <13\,500$ ) and permeability-based Reynolds numbers ( $1< Re_K< 50$ ) are attained. For substrates with $Re_K \sim 1$ , the flow behaviour remains similar to flow over impermeable smooth walls and as such Townsend's hypothesis remains valid. Very large-scale motions are observed over permeable foams even when the $Re_K > 1$ . In contrast, a substantial reduction in velocity disturbances and associated length scales is achieved for permeable foams with intermediate values of pore density and relative foam thickness ( $h/s$ ), which affects outer-layer similarity. As permeability is increased by increasing pore size, the foam becomes sparse relative to viscous scales at high Reynolds numbers. For such foams, the flow conforms to outer-layer similarity and is more akin to flow over rough surfaces. Permeability attenuates the wavelengths associated with the outer-layer peak.