Computational Studies of Turbulent Skin-Friction Drag Reduction with Super-Hydrophobic Surfaces and Riblets

Abstract

Skin-friction Drag Reduction (DR) with SuperHydrophobic (SH) surfaces and riblets was investigated using Direct Numerical Simulation (DNS) to study the scaling and mechanism of DR, and the pressure loads on SH surfaces in turbulent flow environments. The computations were performed using Lattice Boltzmann (LB) methods in turbulent channel flow at a bulk Reynolds number of 3600. SH surfaces composed of Longitudinal Micro-Grooves (LMGs) of size 4 to 128 Base-flow Wall Units (BWUs) with Shear-Free Fractions (SFFs) of 1/2, 7/8 and 15/16, transverse Micro-Grooves (MGs) of size 8 to 56 BWUs with SFFs of 1/2 and 7/8, and micro-posts of size 8 to 56 BWUs with SFFs of 1/4 and 49/64 were studied by DNS. The liquid/gas interfaces on the SH walls were modeled as `idealized' flat, shear-free boundaries in these simulations. Additionally, a second set of DNS studies, with SH LMGs and scallop-shaped riblets of size 14 to 56 BWUs with a MG width to MG pitch ratio of 7/8, were performed to investigate the effect of interface deformation on SH LMGs, and compare the results to riblets. The liquid/gas interfaces on the SH LMGs in these simulations were modeled as stationary curved, shear-free regions, with the meniscus shape obtained from the solution of the Young-Laplace equation. Interface protrusion angles of 0, -30, -60 and -90 degrees were investigated. The same geometries as those formed by the curved SH LMG interfaces were also studied as riblets. DRs of up to 83% and 10% were realized in DNS with the SH surfaces and riblets, respectively. By analysis of the governing equations, it is shown that in laminar or turbulent channel flow with any SH or riblet wall micro-pattern five elements contribute to DR: (i) the effective slip at the wall, (ii) changes in the normalized structure of turbulence due to the drop in the friction Reynolds number of the flow because of this wall slip, (iii) other changes in the normalized structure of turbulence, (iv) changes in the structure of mean flow, and (v) the minor flow rate through the wall micro-texture. Comparison of DNS results to this expression shows that over 90% of the DR with SH LMGs and all of the DR with riblets arises from effects (i, ii, v). Modifications to the normalized structure of turbulence (iii) were found to be always drag increasing with riblets and SH LMGs of size less than 20 wall units, and only mildly drag reducing with SH LMGs of size greater than 20 wall units. For riblets, this effect leads to diminishing DRs with riblets of size greater than 14 wall units. The presence of interface deformation in SH LMGs led to increases of 2% to 5% in the magnitude of DR at low protrusion angles (-30 degrees), and drops of -0.5% to -10% at high protrusion angles (-90 degrees), compared to flat interfaces. Furthermore, interface deformation led to significant drops in the magnitude of pressure fluctuations with SH LMGs of size ~14 BWUs at small protrusion angles (-30 degrees), compared to flat interfaces, offering new opportunities for improving the stability of SH LMGs in turbulent flows. With riblets, the highest DRs were always obtained at the largest MG depths, with the peak DR obtained with MGs of size ~14 BWUs.