Effect of texture randomization on the slip and interfacial robustness in turbulent flows over superhydrophobic surfaces

Abstract

Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of roughness, such as spray coating and etched process. However, most of previous analyses of the interaction between flows and superhydrophobic surfaces studied periodic geometries that are economically feasible only in lab-scale experiments. In order to assess the drag reduction effectiveness as well as interfacial robustness of superhydrophobic surfaces with randomly distributed textures, we conduct direct numerical simulations of turbulent flows over randomly patterned interfaces considering a range of texture widths w + ≈ 4−26, and solid fractions φ s = 11% to 25%. Slip and no-slip boundary conditions are implemented in a pattern, modeling the presence of gas-liquid interfaces and solid elements. Our results indicate that slip of randomly distributed textures under turbulent flows are about 30% less than those of surfaces with aligned features of the same size. In the small texture size limit w + ≈ 4, the slip length of the randomly distributed textures in turbulent flows is well described by a previously introduced Stokes flow solution of randomly distributed shear-free holes. By comparing DNS results for patterned slip and no-slip boundary against the corresponding homogenized slip length boundary conditions, we show that turbulent flows over randomly distributed posts can be represented by an isotropic slip length in streamwise and spanwise direction. The average pressure fluctuation on gas pocket is similar to that of the aligned features with the same texture size and gas fraction, but the maximum interface deformation at the leading edge of the roughness element is about twice larger when the textures are randomly distributed. The presented analyses provide insights on implications of texture randomness on drag reduction performance and robustness of superhydrophobic surfaces. arXiv:1709.05605v2 [physics.flu-dyn]

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

“…This approach, similar to that recently proposed by Zampogna, Magnaudet & Bottaro (2019) for rough walls, allows for a huge reduction of the computational cost of a direct numerical simulation (DNS) of channel flow: Seo & Mani (2016) have recently shown that a DNS using heterogeneous slip/no-slip boundary conditions would need a 12 times more refined computational grid compared to an equivalent computation using a homogeneous slip boundary condition. Recent DNS of turbulent flows over spatially heterogeneous boundary conditions, resolved up to the scale of the texture roughness (Seo & Mani 2016), have confirmed the trend found in experiments for both laminar (Choi et al 2003;Ou et al 2004) and turbulent regimes (Daniello et al 2009;Zhang et al 2015Zhang et al , 2016, as well as the theoretical predictions by Fukagata et al (2006), Seo & Mani (2018). Given the texture geometry, in most flow conditions the slip length L s is linearly dependent on the texture characteristic size L, up to a threshold value for which the high shear and pressure fluctuations will induce gas bubble depletion, resulting in a wetted (Wenzel 1936) state, providing an overall increase of the drag (Zhang et al 2016;Seo et al 2017;Gose et al 2018).…”

“…They also confirm that the solid fraction is the main parameter controlling both gas depletion and drag reduction: increasing this parameter ensures wetting-stable gas pockets, although providing a limited decrease of the friction. If on the one hand the presence of the plastron film produces a complex two-way interaction between the boundary and the external flow (Huang, Lv & Duan 2019), on the other hand, Seo & Mani (2018) have proven that the velocity and displacement of the gas-liquid interface is small enough to be neglected, provided that the surface texture is small enough not to trigger the onset of characteristic upwind travelling capillary waves. 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).…”

“…If on the one hand the presence of the plastron film produces a complex two-way interaction between the boundary and the external flow (Huang, Lv & Duan 2019), on the other hand, Seo & Mani (2018) have proven that the velocity and displacement of the gas-liquid interface is small enough to be neglected, provided that the surface texture is small enough not to trigger the onset of characteristic upwind travelling capillary waves. 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).…”

Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air–water interfaces

“…Next, we include more practical considerations to the presented analysis to make it more relevant to realistic applications. Our recent finding on the effect of texture randomness (Seo & Mani 2017) indicates that the maximum deformation angle of the randomly distributed textured SHS is about twice of the perfectly aligned posts considered in this study. For randomly distributed textured SHS, by spray coating or etched process, this geometric randomness will push the boundaries imposed by our analysis from aligned, periodic textured SHS as shown in figure 24(b).…”

“…• Considering realistic surfaces that typically involve random posts, it is useful to extend the present DNS investigations to the case of surfaces with randomly distributed posts. In the limit of flat interface, Seo & Mani (2017) investigated the effects of randomness and quantified their impact on increased maximum stagnation pressure and deterioration of drag reduction performance. In the figures presented in Section 7, same trends were hypothesized for the capillary wave mechanism, but confirming this hypothesis requires a thorough and original investigation.…”