E7 Friction Reduction

Topic

Drag reduction in fish is a field that integrates surface tribology, boundary-layer fluid mechanics, and fish tissue biology. Fish have evolved various physical strategies to minimize the drag encountered while swimming: a mucus coating that modifies fluid behavior within the boundary layer; scales with surface microstructures similar to those of sharks; a fusiform body shape that minimizes adverse pressure rise along the body; and active control of skin stiffness to suppress the onset of turbulence.

The total drag experienced by a moving body within a fluid—including a fish—comprises two distinct components: skin-friction drag, resulting from the integration of viscous shear over the entire wetted surface area (which dominates in slender bodies like those of most fish); and pressure (or form) drag, resulting from the pressure difference between the front and rear of the body (which dominates in blunter bodies). Skin-friction drag depends on fluid density, the square of the swimming speed, the wetted surface area, and a friction coefficient specific to the body in question.

When the boundary layer around the fish's body is laminar, this friction coefficient decreases with the square root of the body's Reynolds number, in accordance with the Blasius correlation: the higher the Reynolds number, the lower the laminar friction coefficient. If the boundary layer transitions to a turbulent regime, the friction coefficient typically increases five- to tenfold for the same Reynolds number; thereafter, it decreases much more slowly with the Reynolds number than in the laminar regime, following the Prandtl-Schlichting correlation for turbulent boundary layers. Within that same laminar boundary layer, the thickness increases along the fish's body in proportion to the distance from the leading edge—scaled by the square root of the local Reynolds number at each point—meaning the boundary layer thickness grows more slowly than the distance traveled along the body.

The mucus secreted by the fish's epidermis is a non-Newtonian, viscoelastic fluid that acts as a drag-reducing additive similar to the Toms effect; by modifying the turbulence structure right next to the body surface, this mucus can reduce skin-friction drag by up to sixty percent compared to the drag the same body would experience in pure water without mucus. This reduction is quantified by comparing the friction coefficient of the mucus-covered fish with the friction coefficient it would have in pure water: the greater the relative difference between the two coefficients, the greater the drag reduction achieved by the mucus.

The microstructures of the ctenoid scales mentioned earlier in this model function differently from the mucus: they form channels aligned with the flow direction—resembling the drag-reducing ridges found on shark skin—and these channels reduce the interaction between the small vortices forming right next to the body surface and the surface itself, achieving drag reductions of between five and ten percent.

The pressure (or form) drag of the fish's fusiform body—also mentioned at the beginning of this model—depends on fluid density, the square of the swimming speed, the body's frontal area, and a pressure drag coefficient specific to that fusiform shape, which is precisely the shape that minimizes this component of total drag. The total drag on the fish is the sum of the friction drag and pressure drag described in this model, and the fish's net drag coefficient is obtained by normalizing this total drag by the flow's dynamic pressure and the body's frontal area. The expected outcome is that, thanks to the combination of all the drag-reduction strategies described at the beginning of this model—mucus, scale microstructures, a fusiform body, and active control of skin stiffness—the total drag on a fish is between two and five times lower than that of an equivalent rigid body of the same volume moving at the same swimming speed.

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