From drag-reducing riblets to drag-increasing ridges

Abstract

Small drag-reducing riblets and larger drag-increasing ridges are longitudinally invariant and laterally periodic surface structures that differ only in the details of their lateral periodicity and their size in viscous units. Due to their different drag behaviour, typically riblets and ridges have been analysed separately. By studying experimentally trapezoidal-grooved surfaces of different sizes, we address systematically the transition from riblet-like to ridge-like behaviour in a unified framework. The structure height and lateral wavelength are varied both physically, by considering eight different surfaces, and in their viscous-scaled form, by spanning a wide range of bulk Reynolds number $Re_b$ . The effective skin-friction coefficient $C_f$ is determined via pressure-drop measurement in a turbulent channel flow facility designed for accurate drag measurements. An unexpectedly rich drag behaviour is unveiled, in which different drag regimes are distinguished depending on the value of $l_g^+$ , the viscous-scaled square root of the groove area. The well-known drag-reducing regime of riblets that spans up to $l_g^+=17$ is followed by a regime in which the roughness function ${\rm \Delta} U^+$ increases logarithmically with $l_g^+$ , indicating an apparent fully rough behaviour up to $l_g^+\approx 40$ . Further increase of $l_g^+$ leads to a clear departure from the fully rough regime, and an unexpected non-monotonic behaviour of the roughness function ${\rm \Delta} U^+$ for $50< l_g^+<200$ is reported for the first time. For sufficiently large $Re_b$ and $l_g$ , it is shown that a single parameter, similar to the classical hydraulic diameter, is sufficient to describe the drag behaviour of ridges. We find that an appropriate definition of the effective channel height is crucial for interpreting the drag behaviour. When the longitudinal protrusion height of the structured surface is accounted for in the channel height definition, a laminar flow exhibits the same $C_f(Re_b)$ relation known for flat surfaces. This approach thus allows us to discern the modification of $C_f$ induced by turbulence. We provide predictive correlations for the fully rough regime and the high Reynolds number range of trapezoidal-grooved surfaces that become possible thanks to the chosen channel height definition.