Effect of Reynolds number on turbulent channel flow over a superhydrophobic surface

The slip boundary and the near-wall statistics of a fully developed turbulent channel flow over a superhydrophobic surface (SHS) was investigated in a low Reynolds number (Re) range. The Re was varied from 6200 to 9400, based on the bulk velocity and the full-channel height. The root-mean-square of the surface roughness, normalized by the inner flow scaling, varied from 0.26 to 0.35 with increasing Re. Time-resolved, two-dimensional particle tracking velocimetry (PTV) was used to obtain the mean velocity profile in the linear viscous sublayer. Furthermore, time-resolved three-dimensional PTV was applied to obtain the Reynolds stresses. The estimated wall shear stress showed that the drag reduction of the SHS increased slightly from 37% to 42% when Re increased. With increasing Re, the slip velocity increased linearly from 0.25 m/s to 0.34 m/s, and the slip length reduced from 97.5 mu m to 69.6 mu m. When normalized using inner scaling, slip velocity and length remained constant with increasing Re. The mean velocity of the SHS demonstrated a log-law with the universal von Karman constant but shifted upward by an amount equal to the normalized slip velocity. The SHS increased the dimensional Reynolds stresses in the near-wall region and attenuated them farther away from the wall. With increasing Re, the differences between the dimensional Reynolds stresses of the smooth surface and the SHS increased. However, when Reynolds stresses were normalized using friction velocity, the Reynolds stresses of the SHS overlapped for all the investigated Re and were larger than the normalized Reynolds stresses of the smooth surface.