Resistance of a grooved surface to parallel flow and cross-flow

Abstract

A study is undertaken of both parallel flow and cross-flow in the viscous sublayer generated by a fluid streaming along a grooved surface, with the aim of clarifying the phenomena that underlie the reduction of turbulent drag by such surfaces. A quantitative characterization of the effectiveness of different groove profiles in retarding secondary cross-flow is given in terms of the difference of two ‘protrusion heights’. Analytical calculations of limit cases and a boundary-element computer code for the analysis of general profiles are illustrated, and several examples are presented and discussed.

Riblets Induced Drag Reduction on a Spatially Developing Turbulent Boundary Layer

“…Finally, w rms is somewhat increased above y + = 10. Note that only the spanwise component w rms is damped in the riblets vicinity, in agreement with Luchini's vision of riblets as device impeding selectively the transverse over the longitudinal flow [14].…”

“…The rib angle is α = 30 • and the height-over-width ratio is fixed to h rib /s rib = 0.5. This riblets design leads to a "protrusion height" of ∆ h ≈ 0.10s rib = 0.20h rib , a value which can be compared to the optimal limit ∆ h max ≈ 0.13s rib computed analytically by Luchni et al [14]. Further increasing our ∆ h requires to sharpen the riblets even more and would lead to technologically unfeasible design.…”

“…García-Mayoral & Jiménez [8] identified drag-reduction regimes, gathering in one previously proposed theories [14,4,9,10]. For low Reynolds number or small riblets, effects are well-characterized by ∆ h. When size or Reynolds increases, break-down mechanisms, based on Kelvin-Helmotz instabilities, cancel out the beneficial viscous effect.…”

“…Based on viscous analyses, Luchini et al [14] observed that, above both a clean and a ribbed surfaces, the Stokes flows converge asymptotically to the same far-field solution, providing the appropriate relative position of the two walls. For a given riblet geometry, one can thus compute the "virtual origin" h at which a flat plate should be located to produce asymptotically the same Stokes flow.…”

Effective slip lengths for immobilized superhydrophobic surfaces

“…If a curved meniscus happens to be a no-slip surface -that is, it has been immobilized by some means -then we are equivalently dealing with a corrugated no-slip wall with circulararc 'riblets', and it is more common then to refer to these effective slip lengths as protrusion heights (Bechert & Bartenwerfer 1989;Luchini, Manzo & Pozzi 1991). In the latter context, since the choice of the y-origin is arbitrary, the only physically significant quantity is the difference λ || − λ ⊥ , which is independent of the choice of y-origin, and quantifies how much a corrugated no-slip wall impedes a transverse shear relative to a longitudinal shear.…”