In the previous two posts of this blog series I introduced the different sensing mechanism that aquatic animals possess to create spatial images of the largely turbulent flow fields around them. Flow sensing has been shown to serve as a means of communication in schooling fish, for orientation in currents and for sensing the surrounding environment when the tactile or visual senses are impaired [1]. In 1936, Gray used a simple hydrodynamic model of a rigid dolphin with a turbulent boundary layer to calculate the power required to overcome the drag exerted by the water [2]. Quite surprisingly, the results suggested that the calculated drag could not be overcome by the available dolphin muscle power…
This controversy has since been known as “Gray’s Paradox”, and Gray concluded that dolphins must possess some sort of mechanism to reduce skin friction drag by maintaining a fully laminar boundary layer. Today it has been shown that basic assumptions in Gray’s analysis were flawed and that experimental data on the muscle power of dolphins was largely underestimated [3 – 4]. Nevertheless, the idea that dolphins are capable of maintaining a laminar boundary layer became the basic premise for research into dolphin drag reduction for almost 60 years. While it is now known that the boundary layer around swimming dolphins is largely turbulent, this focus of research has led to some interesting observations that may give useful insight into bio-mimetic applications for future aircraft or marine vehicles.
The study of dolphins and sharks is especially interesting because they have undergone millions of years of natural selection and, according to Darwin’s argument, are therefore pretty “fit” for survival in the aquatic environment. For dolphins the streamlined “teardrop” shape (Figure 1) provides the most drag reduction and other perceived “wonder-mechanisms” such as skin-folds observed by Essapian [5] do not contribute to any reductions in drag. In actual fact, the skin-folds observed by Essapian occur due to the compliance of the soft dolphin skin and are also observed for swimming humans [6]. The streamlined shape of the dolphin has a point of maximum thickness at 45% of the body length, and since adverse pressure gradients only occur beyond this point, the “teardrop” profile helps to confine boundary layer separation to a posterior section of the body, thus resulting in less pressure drag. Unsurprisingly, this streamlined profile has since been exploited in modern boat hulls and submarines such as the 1953 USS Albacore (Figure 2).
Fig. 1 Streamlined teardrop profile of dolphin (4)
Fig. 2. USS Albacore. Profile inspired by streamlined bodies found in nature (12)
An active control mechanism employed by many fish to reduce the high skin friction drag inherent of a turbulent boundary layer is mucus excretion. Fish secrete a combination of polysaccharides, lipids and lipoproteins through pores on the skin into the boundary layer to fill irregularities of the surface and improve streamlining. Most importantly, the mucus has a lower viscosity than the water around the fish, which helps to reduce the frictional shear stresses arising from the “stickiness” or viscosity of water. As can be observed in Figure 3 the velocity gradient at the wall is consequently less pronounced resembling a laminar boundary layer with reduced skin friction drag (Figure 4). In the oil industry soluble, long-chain polymer additives have achieved very promising results. A ratio as small as one-in-a-million of these additives in oil pipelines has reduced skin friction drag by up to 30% [7].
Fig. 3. Classic turbulent boundary layer profile and quasi-laminar boundary layer due to mucus excretion
Fig. 4. Contribution of different forms of drag for laminar and turbulent flow (13)
Similar to the flat plate parallel to oncoming flow discussed in the hydrodynamics post, flow measurements of swimming dolphins show that boundary layer is fully turbulent along the posterior section of the body while laminar and transitional boundary layers are observed towards the head. Kramer showed that dolphins are able to delay the transition to turbulent flow using their soft, compliant skin and therefore achieve some reductions in skin friction drag [8 – 9]. The viscoelastic properties of the skin interact with the flow over the body as a viscous damper and absorb energy from pressure oscillations known as “Tollmien-Schlichting waves” that can trip the boundary layer to go turbulent (Figure 5). Dolphins sense these pressure oscillations using canal neuromasts and then activate controlled muscular microvibrations to produce tremor-like skin vibrations of up to 5 mm amplitude at 7 – 13 Hz that destructively interfere with the Tollmien-Schlichting pressure waves (Figure 6). The transition to a turbulent boundary layer is thus delayed in order to achieve the best compromise of lower laminar skin-friction drag towards the head and allow turbulent flow in the posterior parts of the body to prevent boundary layer separation.
Fig. 5 Tollmien-Schichting Wave over compliant dolphin skin.
Fig. 6. Compliant dolphin skin acting as a viscous damper (14)
Rather than trying to delay the onset of turbulent flow, sharks have evolved with an incredibly clever system of reducing turbulent skin friction drag using their denticle scales. At the same time the scales also serve to passively (without any muscular effort from the shark) prevent boundary layer separation. During the 1980’s research at NASA Langley revealed that a turbulent boundary layer on a surface with longitudinal ribs develops lower shear stress and consequently exerts less drag than the same flow profile on a smooth surface. In the previous post I explained that the exchange of fluid normal to the surface in a turbulent boundary layer causes a steeper velocity gradient and therefore higher skin friction drag. In 3-D flow this momentum transfer will also occur in the lateral z-direction by cross flow vortices (Figure 7).Ribs on the surface aligned in the mean flow direction prevent this lateral transfer of momentum and result in a more gradual velocity profile with less shear stress. With optimal ribbed blade height of half the rib spacing Bechert et al. [7] showed a drag reduction of 9.9% using a metal plate. Unsurprisingly such a ribbed profile is also present on the scales of sharks (Figure 8).
Fig. 7. Riblets preventing lateral crossflow of turbulent boundary layer (top) and graph of subsequent drag reduction (7)
Fig. 8. Shark scales (top) and ribbed plate tested by Bechert et al. (7)
Bechert et al. manufactured a representative wind-tunnel model of 800 plastic scales using electric discharge machining with compliant anchorings to model the bristling of the scales. With this model only a modest decrease in drag of 3.3% was achieved due to losses arising from the gaps between the scales. On the other hand a significant increase in drag of over 10% was measured if the scales were bristled, thus forced upright as observed on swimming sharks.
Consequently, the researchers were facing the question why shark scales bristle and not remain nicely attached to maintain a streamlined profile?
Boundary layer separation is initiated by a flow reversal in the boundary layer i.e. the flow locally flows opposite to the direction of motion (Figure 9). As the boundary layer is about to separate the flow reversal causes the scales to bristle and erect passively (without any input from the shark) acting as vortex generators, which on one hand increase friction drag, but on the other hand energise the boundary layer by forcing high momentum fluid from the free stream towards the skin surface [10] (Figure 10). Thus, just as the boundary layer is about to separate, bristling is automatically activated and boundary layer separation is prevented which would otherwise lead to a significant increase in pressure drag.
Fig. 9. Boundary layer separation initiated by local flow reversal (15)
Fig. 10. Bristled scales (right) and subsequent formation of vortices between scales (10)
The riblet research by NASA Langley led 3M to develop a riblet polymer film that could readily be coated on a surface like an exterior paint. This smart skin helped the American Stars and Stripes yacht win the America’s cup in 1987 before the technology was banned. Since then the technology has been tested on large civil aircraft such as the Airbus A320 and also smaller business jets and fighter aircraft with more moderate reductions in drag of around 2% [7]. At the same time researchers at MIT have been trying to emulate the canal neuromasts sensory system found in fish using a flexible membrane covering a number of cavities with integrated microelectromechanical systems (MEMS) to serve as pressure sensors for flow over a surface (Figure 11) [11].
Fig. 11. Pressure sensing skin using MEMS (11)
At the same time compliance of the elastomer membrane would allow active changes to the skin profile to either prevent boundary layer separation (e.g. via “bristling” controlled by skin buckling) or mitigate laminar-to-turbulent boundary layer transition (e.g. via skin vibrations). In this manner a truly multifunctional “smart” skin could be developed that actively senses the flow field around a body via the pressure sensors and then changes the profile of the skin by thin film deformations. However, considerable research is yet required to make such systems a reality in the future…
References
[1] Windsor, S., & McHenry, M. (2009). The influence of viscous hydrodynamics on the fish lateral-line system. Integrative
and Comparative Biology , 49, 691-701.
[2]Gray J 1936 Studies in animal locomotion: VI. The propulsive powers of the dolphin J. Exp. Biol. 13 192–9
[3]Williams T M, Friedl W A, Fong M L, Yamada R M, Sedivy P and Haun J E 1992 Travel at low energetic cost by swimming and wave-riding bottlenose dolphins Nature 355 821–3
[4] Fish, F. (2006). Thy myth and reality of Gray’s paradox: implication of dolphin drag reduction for technology. Bioinspiration & Biomechanics , 1, R17-R25.
[5] Essapian F S 1955 Speed-induced skin folds in the bottle-nosed porpoise Tursiops. truncatus. Breviora Mus. Comp. Zool. 43 1–4
[6] Aleyev Y G 1977 Nekton (The Hague: Junk)
[7] Bechert, D., et al. (2000). Fluid Mechanics of Biological Surfaces and their Technological Application. Naturwissenschaften , 87, 157-171.
[8] Kramer M O 1960a Boundary layer stabilization by distributed damping J. Am. Soc. Nav. Eng. 72 25–33
[9] Kramer M O 1960b The dolphins’ secret New Sci. 7 1118–20
[10] Lang, A., et al. (2008). Bristled shark skin: a microgeometry for boundary layer control? Bioinspration & Biomimetics , 3, 1-9.
[11] Stauffer, N. (2011). Going with the flow: Biomechanic pressure sensors help guide oceangoing vessels. MIT. MIT.
[12] http://www.britannica.com/EBchecked/media/142063/USS-Albacore
[13] Fish, F. Imaginative solutions by marine organisms for drag reduction. West Chester: West Chester University.
[14] Wiplier, O., & Ehrenstein, U. (2000). Numerical simulation of linear and nonlinear disturbance evolution in a boundary layer with compliant walls. Journal of Fluids and Structures , 14, 157-182.
[15] http://sci-fix.blogspot.co.uk/2010/08/paragliding-aerodynamics.html
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