When riblets were being extensively studied as drag-reduction devices several years ago, the protrusion height was introduced [1] as an important parameter quantifying their effectiveness. The underlying idea is that riblets are small enough that flow in their neighbourhood is governed by the Stokes equations, even when the surrounding flow is turbulent, and therefore their action is linear and can be replaced by the asymptotic solution of the Stokes equations themselves; this is a Couette velocity profile originating at a virtual wall located at a certain height, which takes the name of protrusion height. More precisely, as established in [6], there are two protrusion heights, one for flow along and one for flow across the riblets, and since the reference plane from which these heights are measured is arbitrary and has no physical meaning, only the protrusion-height difference is the relevant physical parameter. The whole idea of protrusion height reappears in the form of the slip length that is today used to describe the drag-reducing action of superhydrophobic surfaces; however the distinction between a longitudinal and a transverse protrusion height and the importance of their difference does not seem to have been realized yet in this context.

THE RELEVANCE OF LONGITUDINAL AND TRANSVERSE PROTRUSION HEIGHTS FOR DRAG REDUCTION BY A SUPERHYDROPHOBIC SURFACE

LUCHINI, Paolo
2015-01-01

Abstract

When riblets were being extensively studied as drag-reduction devices several years ago, the protrusion height was introduced [1] as an important parameter quantifying their effectiveness. The underlying idea is that riblets are small enough that flow in their neighbourhood is governed by the Stokes equations, even when the surrounding flow is turbulent, and therefore their action is linear and can be replaced by the asymptotic solution of the Stokes equations themselves; this is a Couette velocity profile originating at a virtual wall located at a certain height, which takes the name of protrusion height. More precisely, as established in [6], there are two protrusion heights, one for flow along and one for flow across the riblets, and since the reference plane from which these heights are measured is arbitrary and has no physical meaning, only the protrusion-height difference is the relevant physical parameter. The whole idea of protrusion height reappears in the form of the slip length that is today used to describe the drag-reducing action of superhydrophobic surfaces; however the distinction between a longitudinal and a transverse protrusion height and the importance of their difference does not seem to have been realized yet in this context.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4668416
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