Effect of curved profiles on the drag response of riblet-textured surfaces in boundary layer flows: an experimental study

Skin of fast-swimming sharks such as Mako are covered with micro-scale rib-like structures in the streamwise direction, which are believed to be the reason for their ability to swim faster than other species in the ocean. Inspired by such natural textures, engineers have designed two-dimensional textured surfaces also known as riblets. Riblets have been considered in various cross-sectional shapes, such as triangular, semi-circular, and rectangular. However, there is still a lack of quantitative definition to distinguish among the various cross-sectional shapes used. To complement this, here, we introduce a family of curved textures, defined by second order polynomials where a curvature parameter is used to vary the level of concavity/convexity of the textures. We present the results of experiments performed over fully textured samples with varying height-to-half-spacing and curvature parameters, in a water tunnel where simultaneous load and velocity measurements are conducted via load-cell and high-resolution PIV respectively. We use the velocity measurements to first evaluate the local velocity profiles and shear stress distributions along the length of the samples. Then decompose the total drag into viscous and pressure dependent components as a function of the Reynolds number and the introduced geometric parameters and compare against the total load measured via the load cell. Ultimately, we use the analysis to discuss the effect of the shape of the cross-sectional profile of the textures on the frictional response of the entire sample in high Reynolds number laminar boundary layer flows, in terms of the two geometric parameters, the height-to-half-spacing, and curvature parameter.