Inner and outer layer turbulence over a superhydrophobic surface with low roughness level at low Reynolds number

Abstract

The inner and outer layers of a turbulent channel flow over a superhydrophobic surface (SHS) are characterized using simultaneous long-range microscopic particle tracking velocimetry (micro-PTV) and particle image velocimetry, respectively. The channel flow is operated at a low Reynolds number of ReH = 4400 (based on full channel height and 0.174 m/s bulk velocity), equivalent to Reτ = 140 (based on half channel height and friction velocity). The SHS is produced by spray coating, and the root-mean-square of wall roughness normalized by wall-unit is k+rms = 0.11. The micro-PTV shows 0.023 m/s slip velocity over the SHS (about 13% of the bulk velocity), which corresponds to a slip-length of ∼200 μm. A drag reduction of ∼19% based on the slope of the linear viscous sublayer and 22% based on an analytical expression of Rastegari and Akhavan [J. Fluid Mech. 773, R4 (2015)] realized. The reduced Reτ over the SHS based on the corresponding friction velocity is ∼125, which is in the lower limit of a turbulence regime. The results show the increase of streamwise Reynolds stresses 〈u2〉 for the SHS in the linear viscous sublayer due to the slip boundary condition. The 〈u2〉 peak does not change in magnitude while it is displaced closer to the wall in physical distance. The wall-normal Reynolds stress 〈v2〉 over the SHS and smooth surface is observed to overlap near the wall at y+ < 10, while 〈v2〉 for the SHS is smaller further away from the wall in physical dimensions. At y+ = 30, 〈v2〉 is 30% smaller for the SHS. A small increase of Reynolds shear stress for the SHS is observed at y+ < 10, while about 30% reduction is observed at y+ = 30. The observed variation of Reynolds stresses is associated with the relatively small roughness of the surface. If Reynolds stresses are normalized based on the corresponding friction velocity, the non-dimensional stresses show a large increase of 〈u2〉 and a small increase of 〈uv〉 over the SHS at y+ < 20. Farther away from the wall at y+ > 20, the scaling of Reynolds stresses based on the corresponding uτ results in their overlap for the smooth and SHSs. The drag reduction is mainly associated with the reduction of viscous wall-shear stress, while the variation in Reynolds shear stress at the wall is negligible. The quadrant analysis of turbulent fluctuations shows attenuation of stronger sweep motions at y+ < 15, while ejections are attenuated in the buffer layer at y+ = 20 until 30.