Turbulent boundary layers over substrates with streamwise-preferential permeability

Abstract

Recent numerical studies have suggested the potential of substrates with streamwise-preferential permeability to reduce drag in turbulent boundary layers. Such a substrate is theorized to facilitate relaxation of the no-slip condition and thereby reduce the skin friction. So far, these beneficial effects have not been demonstrated experimentally yet and therefore the scope of this work is to present this concept in air flow where the substrate geometry satisfies the theoretical permeability requirements for an expected reduction in drag. For this, a three-dimensional-printed structure with anisotropic permeability (φxz=2.7, φxy=3.9) and small pores (s≈250μm), akin to an acoustic liner, was developed. The substrate was investigated using direct force measurements and 2D-2C PIV in the range of U∞≈5-35 ms-1, corresponding to frictional Reynolds numbers of Reτ≈430-1960. Results show an increase in drag of 0%<ΔCD<8% and, while contrasting the model predictions, this agrees with DNS data on structures with similar geometric properties when using the inverse wall-normal Forchheimer coefficient, or inertial permeability, as the equivalent roughness parameter. Hence the present results constitute the first experimental evidence that this is the governing property for the drag behavior of acoustic liners. The absence of the predicted beneficial flow modulation effects is attributed to the investigated substrate not strictly satisfying the theoretical framework assumptions on characteristic length scales. However, to expand beyond this structural limitation, we analytically derive that, for realistic, geometrically resolved cases, this length scale mismatch is unavoidable and thereby render it unfeasible to model the substrate as a continuum for the virtual-origin approach. We expect that translating the abstraction of substrates with streamwise-preferential permeability into physical realisations relevant for practical applications would result in structures very similar to riblets.