Comparison between super-hydrophobic, liquid infused and rough surfaces: a direct numerical simulation study

Abstract

Direct Numerical Simulations of two superposed fluids in a channel with a textured surface on the lower wall have been carried out. A parametric study varying the viscosity ratio between the two fluids has been performed to mimic both idealised superhydrophobic and liquid-infused surfaces and assess its effect on the frictional, form and total drag for three different textured geometries: longitudinal square bars, transversal square bars and staggered cubes. The interface between the two fluids is assumed to be slippery in the streamwise and spanwise directions and not deformable in the vertical direction, corresponding to the ideal case of infinite surface tension. To identify the role of the fluid-fluid interface, an extra set of simulations with a single fluid has been carried out. Comparison with the cases with two fluids reveals the role of the interface in suppressing turbulent transport between the lubricating layer and the overlying flow decreasing the overall drag. In addition, the drag and the maximum wall-normal velocity fluctuations were found to be highly correlated for all the surface configurations, whether they reduce or increase the drag. This implies that the structure of the near-wall turbulence is dominated by the total shear and not by the local boundary condition of

Effective boundary conditions at a rough wall: a high-order homogenization approach

“…The incompressible two-dimensional creeping flow equations for the generic unknown (u, p) are solved with a finite element method using the FreeFEM open source code [29]. The approach is based on a weak formulation of the equations, which means This provides an indication also of the geometries to be preferentially tested in cases where the microcavities are filled with an immiscible lubricant fluid (such as air or vapor, when considering superhydrophobic coatings); first order results [28] confirm this indication and feature-resolving direct numerical simulations of turbulence in a channel bound by lubricantimpregnated walls [30] further highlight the significance of wall-normal velocity fluctuations and their strong correlation to the total drag. The high-order approach described here can easily be extended to the case of lubricant-filled micro-cavities, to better capture phenomena which, to date, have only been modelled using the (first-order) Navier condition.…”

Laminar–turbulent transition in channel flow with superhydrophobic surfaces modelled as a partial slip wall

“…The flat air-liquid interface approximation used to model superhydrophobic surfaces sustaining laminar-turbulent transitional flows has been a posteriori justified by Seo & Mani (2018), who reported no appreciable flow modification in considering the free-surface dynamics while measuring drag reduction compatible with the ones measured by Gose et al (2018). Thus, considering 'vanishingly small' textures (Fairhall, Abderrahaman-Elena & García-Mayoral 2018) for which the gas-liquid surface dynamics is negligible with respect to other factors (Arenas et al 2019), it is generally agreed that the surface can be modelled by a flat wall characterised by alternating no-slip and shear-free zones, as discussed, to cite a few, by Ybert et al (2007), Martell, Perot & Rothstein (2009), Jelly, Jung & Zaki (2014) and Rastegari & Akhavan (2015). Even though such approximations allow for the use of the single phase, incompressible Navier-Stokes equations, accurate simulations remain computationally demanding (Seo & Mani 2016).…”

Superhydrophobic Drag Reduction for Turbulent Flows in Open Water

“…The plastron loss is accelerated by the high shear of turbulent flows and further exacerbated by the hydrostatic pressure as well as many environmental variables [7] inevitable in open-water tests. For turbulent flows, while numerical studies have shown definite drag reduction and brought insights into the drag-reducing mechanism [9][10][11][12], experimental studies have reported mixed results, varying from substantial to negligible drag reduction, and even drag increase. Figure 1 summarizes the recent experimental studies of SHPo drag reduction in turbulent flows [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”