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Boundary Layer

Due to their height, riblets mainly interact with the viscous sublayer of the boundary layer, where they impede cross-stream translation of streamwise vortices. This reduces the ejection of these vortices into the outer boundary layers und subsequently their momentum transfer through twisting and tangling. The reduction of energy transferred away from the average flow direction immediately translates to a reduction in fluid drag.

Drag increase due to the larger wetted surface area stays minimal, as the vortices of turbulent flow form above the riblets and stay there, interacting only with the small area of the tips. This confines the higher velocities and shear stresses to those small areas as well. The flow velocity in the valleys is much smaller and therefore produces smaller shear stresses on most of the riblets’ surface. If any secondary vortices do form in the valleys, their shear stress increase is also small due to the low velocities.

The difference in flow speed and the displacement of vortices away from the surface creates an apparent shift of the flow origin, which affects the effective protrusion height. This height describes how much riblet height is left after deducting the shift of the flow origin.

In figure 1 below, the change of the velocity profile can be seen. Compared to the velocity profile without riblets (black), the velocity in the valleys (blue) increases slower, reducing friction drag on the surface. From the tips (green) outward the velocity increases rapidly and reaches free stream velocity faster, indicating a lower loss of momentum due to vortices. This distribution corresponds well to the illustration of the boundary sublayers in figure 2, where it becomes apparent that riblets drastically reduce the speed in the laminar sublayer and the buffer zone.

Fig.1: Velocity profile (u… velocity, y… wall distance)
Fig. 2: Velocities in boundary sub-layers (laminar – buffer – turbulent)
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