Effect of Reynolds Number on Turbulent Drag Reduction by Superhydrophobic Surface Textures

In turbulent flows over streamwise-aligned superhydrophobic surface (SHS) textures, the percent drag reduction is dependent on Reynolds number. This dependence is examined using direct numerical simulations of channel flow over SHS texture at three bulk Reynolds numbers, R e (b) = 2800, 6785 and 10975. Simulations of regular no-slip channel flows at the same bulk velocities are also performed for comparison. Changes in the flow due to the SHS texture are examined with particular focus on phase averaged statistics and coherent turbulent motions. As the Reynolds number is increased, the texture performance, or the percent drag reduction, is enhanced. In terms of turbulent motions, the weakened shear stresses are manifest as a decrease in the population of the small-scale vortical structures and a weakening of large-scale motions. The influence of stochastic fluctuations near the large-scale motions diminishes at higher Reynolds number. The enhanced performance is therefore due to a significant drop in the strength of small- and large-scale vortical structures. The weaker vortical motions yield a considerable reduction in the Reynolds shear stress and the transport of mean momentum. The SHS texture introduces a performance penalty in the form of a local increase in drag at the no-slip free-slip edge. This adverse effect is caused by the inhomogeneity of the near-wall flow field. However, the affected region narrows in width at higher Reynolds numbers. As a result, the percent drag reduction approaches the gas fraction of the texture.