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Superhydrophobic surfaces for drag reduction
No full textProperties of superhydrophobic materials are examined in light of their possible use for drag reduction in naval applications. To achieve superhydrophobicity a low-surface-energy material must be structured so as to minimize the liquid-solid interactions. The crucial aspect is that of maintaining a layer of gas in between the (rough) wall and the liquid, and this can be achieved by hierarchical micro- and nano-structuring of the solid surface, to ensure a sufficiently large apparent slip of the fluid at the wall, thus reducing skin friction. The behavior of the liquid is quantified by a slip length; recent results have shown that this length can be as large as 400 μm. As far as transition to turbulence is concerned, we show that superhydrophobic surfaces are effective (i.e. they delay the onset of travelling instability waves) only in channels with characteristic dimensions of a few millimeters. Conversely, when the fluid flow has already attained a turbulent state, the gain in term of drag reduction can be very significant also in macroscopic configurations. This occurs because the relevant length scale of the boundary layer is now the thickness of the viscous sub-layer, which can be of magnitude comparable to the slip length, so that an effective coupling emerges. Finally, some procedures to produce superhydrophobic surfaces are examined, in light of the possible application of such innovative coatings on the hull of ships
Flow over natural or engineered surfaces: an adjoint homogenization perspective
No full textNatural and eng (i) neered surfaces are ne (v) er smooth, but (i) rregular, rough at d (i) fferent scales, compl (i) ant, poss (i) bly porous, l (i) qu (i) d (i) mpregnated or superhydrophob (i) c. The correct numer (i) cal modell (i) ng of flu (i) d flow (i) ng through and around them (i) s (i) mportant but poses problems. For med (i) a character (i) zed by a per (i) od (i) c or quas (i) -per (i) od (i) c m (i) crostructure of character (i) st (i) c d (i) mens (i) ons smaller than the rele (v) ant scales of the flow, mult (i) scale homogen (i) zat (i) on can be used to study the effect of the surface, a (v) o (i) d (i) ng the numer (i) cal resolut (i) on of small deta (i) ls. Here, we re (v) (i) s (i) t the homogen (i) zat (i) on strategy us (i) ng adjo (i) nt (v) ar (i) ables to model the (i) nteract (i) on between a flu (i) d (i) n mot (i) on and regularly m (i) cro-textured, permeable or (i) mpermeable walls. The approach descr (i) bed allows for the easy der (i) (v) at (i) on of aux (i) l (i) ary/adjo (i) nt systems of equat (i) ons wh (i) ch, after a (v) erag (i) ng, y (i) eld macroscop (i) c tensor (i) al propert (i) es, such as permeab (i) l (i) ty, elast (i) c (i) ty, sl (i) p, transp (i) rat (i) on, etc. When the flu (i) d (i) n the ne (i) ghbourhood of the m (i) crostructure (i) s (i) n the Stokes reg (i) me, class (i) cal results are reco (v) ered. Adjo (i) nt homogen (i) zat (i) on, howe (v) er, perm (i) ts s (i) mple extens (i) on of the analys (i) s to the case (i) n wh (i) ch the flow d (i) splays nonl (i) near effects. Then, the propert (i) es extracted from the aux (i) l (i) ary systems take the name of effect (i) (v) e propert (i) es and do not depend only on the geometr (i) cal deta (i) ls of the med (i) um, but also on the m (i) croscop (i) c character (i) st (i) cs of the flu (i) d mot (i) on. Examples are shown to demonstrate the usefulness of adjo (i) nt homogen (i) zat (i) on to extract effect (i) (v) e tensor propert (i) es w (i) thout the need for < (i) tal (i) c>ad hoc parameters. In part (i) cular, notable results reported here (i) n (i) nclude:( (i) ) an or (i) g (i) nal formulat (i) on to descr (i) be f (i) ltrat (i) on (i) n porous med (i) a (i) n the presence of (i) nert (i) al effects; ( (i) (i) ) the m (i) croscop (i) c and macroscop (i) c equat (i) ons needed to character (i) ze flows through poroelast (i) c med (i) a; ( (i) (i) (i) ) an extended Na (v) (i) er's cond (i) t (i) on to be employed at the boundary between a flu (i) d and an (i) mpermeable rough wall, w (i) th roughness elements wh (i) ch can be e (i) ther r (i) g (i) d or l (i) nearly elast (i) c; ( (i) (v) ) the m (i) croscop (i) c problems needed to def (i) ne the rele (v) ant parameters for a Saffman-l (i) ke cond (i) t (i) on at the (i) nterface between a flu (i) d and a porous substrate; and ( (v) ) the macroscop (i) c equat (i) ons wh (i) ch hold at the d (i) (v) (i) d (i) ng surface between a free-flu (i) d reg (i) on and a flu (i) d-saturated poroelast (i) c doma (i) n
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