As far as plastron is sustained, superhydrophobic (SHPo) surfaces are expected to reduce skin-friction drag in any flow conditions including large-scale turbulent boundary-layer flows of marine vessels. However, despite many successful drag reductions reported using laboratory facilities, the plastron on SHPo surfaces was persistently lost in high-Reynolds-number flows on open water, and no reduction has been reported until a recent study using certain microtrench SHPo surfaces underneath a boat (Xu et al., Phys. Rev. Appl. , vol. 13, no. 3, 2020, 034056). Since scientific studies with controlled flows are difficult with a boat on ocean water, in this paper we test similar SHPo surfaces in a high-speed towing tank, which provides well-controlled open-water flows, by developing a novel $0.7\ \textrm {m} \times 1.4\ \textrm {m}$ towing plate, which subjects a $4\ \textrm {cm} \times 7\ \textrm {cm}$ sample to the high-Reynolds-number flows of the plate. In addition to the 7 cm long microtrenches, trenches divided into two in length are also tested and reveal an improvement. The skin-friction drag ratio relative to a smooth surface is found to be decreasing with increasing Reynolds number, down to 73 % (i.e. 27 % drag reduction) at $Re_x\sim 8\times 10^6$ , before starting to increase at higher speeds. For a given gas fraction, the trench width non-dimensionalized to the viscous length scale is found to govern the drag reduction, in agreement with previous numerical results.
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Sustainability of the plastron on nano-grass-covered micro-trench superhydrophobic surfaces in high-speed flows of open water
This paper studies the sustainability of plastrons on superhydrophobic (SHPo) surfaces made of longitudinal micro-trenches covered by nano-grass with the main interest on hydrodynamic friction drag reduction in high-speed flows of open water, which represent the operating conditions of common watercraft. After revising the shear-driven drainage model to address the air diffusion for SHPo surfaces, the existing theories are combined to reveal the trends of how the immersion depth, air saturation level and shear stress affect the maximum attainable plastron length. Deviations from the theories by the dynamic effect at the two ends of the trench, the interfacial contaminations and turbulent fluctuation are also discussed. A combinatorial series of well-defined SHPo trench surfaces (4 cm × 7 cm in size with varying trench widths, depths, lengths and roughnesses) is microfabricated and attached underneath a 4 m long motorboat on seawater in turbulent flows up to 7.2 m s −1 (shear rate ∼83 000 s −1 and friction Reynolds number ∼5500). Because the plastron can provide a substantial slip only while its air–water interfaces are pinned (or only slightly depinned) at the trench top, two underwater cameras are employed to differentiate the pinned (and slightly depinned) interfaces from the depinned (and no) interfaces. In addition to achieving pinned plastrons on 6 cm long trenches aligned to high-speed flows in open water, the experimental results corroborate the theoretical estimations, supporting the design of SHPo surfaces for field applications.
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- Award ID(s):
- 2030404
- PAR ID:
- 10451567
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 962
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Superhydrophobic (SHPo) surfaces have been investigated vigorously since around 2000 due in large part to their unique potential for hydrodynamic frictional drag reduction without any energy or material input. The mechanisms and key factors affecting SHPo drag reduction have become relatively well understood for laminar flows by around 2010, as has been reviewed before [Lee et al. Exp Fluids 57:176 (2016)], but the progress for turbulent flows has been rather tortuous. While improved flow tests made positive SHPo drag reduction in fully turbulent flows more regular since around 2010, such a success in a natural, open water environment was reported only in 2020 [Xu et al. Phys Rev Appl 13:034056 (2020b)]. In this article, we review studies from the literature about turbulent flows over SHPo surfaces, with a focus on experimental studies. We summarize the key knowledge obtained, including the drag-reduction mechanism in the turbulent regime, the effect of the surface roughness morphology, and the fate and role of the plastron. This review is aimed to help guide the design and application of SHPo surfaces for drag reduction in the large-scale turbulent flows of field conditions.
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In this work, we experimentally investigated the impact of surface roughness on drag reduction as well as the plastron stability of superhydrophobic surfaces (SHSs) in turbulent flows. A series of SHSs were fabricated by spraying hydrophobic nanoparticles on sandpapers. By changing the grit size of sandpapers from 240 to 1500, the root mean square roughness height (krms) of the SHSs varied from 4 to 14 μm. The experiments were performed in a turbulent channel flow facility, where the mean flow speed (Um) varied from 0.5 to 4.4 m/s, and the Reynolds number (Rem) based on Um and channel height changed from 3400 to 26 400. The drag reduction by SHSs was measured based on pressure drops in the fully developed flow region. The plastron status and gas fraction (φg) were simultaneously monitored by reflected-light microscopy. Our results showed a strong correlation between drag reduction and krms+ = krms/δv, where δv is the viscous length scale. For krms+ < 1, drag reduction was independent of krms+. A maximum 47% drag reduction was observed. For 1 < krms+ < 2, less drag reduction was observed due to the roughness effect. And for krms+ > 2, the SHSs caused an increase in drag. Furthermore, we found that surface roughness influenced the trend of plastron depletion in turbulent flows. As increasing Rem, φg reduced gradually for SHSs with large krms, but reduced rapidly and maintained as a constant for SHSs with small krms. Finally, we found that as increasing Rem, the slip length of SHS reduced, although φg was nearly a constant.
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Measurements of turbulence, as rate of dissipation of turbulent kinetic energy (ε), adjacent to the air-water interface are rare but essential for understanding of gas transfer velocities (k) used to compute fluxes of greenhouse gases. Variability in ε is expected over diel cycles of stratification and mixing. Monin-Obukhov similarity theory (MOST) predicts an enhancement in ε during heating (buoyancy flux, β+) relative to that for shear (u*w 3/κz where u*w is water friction velocity, κ is von Karman constant, z is depth). To verify and expand predictions, we quantified ε in the upper 0.25 m and below from profiles of temperature-gradient microstructure in combination with time series meteorology and temperature in a tropical reservoir for winds <4 m s−1. Maximum likelihood estimates of near-surface ε during heating were independent of wind speed and high, ∼5 × 10−6 m2 s−3, up to three orders of magnitude higher than predictions from u*w 3/κz, increased with heating, and were ∼10 times higher than during cooling. k, estimated using near-surface ε, was ∼10 cm hr−1, validated with k obtained from chamber measurements, and 2–5 times higher than computed from wind-based models. The flux Richardson number (Rf) varied from ∼0.4 to ∼0.001 with a median value of 0.04 in the upper 0.25 m, less than the critical value of 0.2. We extend MOST by incorporating the variability in Rf when scaling the influence of β+ relative to u*w 3/κz in estimates of ε, and by extension, k, obtained from time series meteorological and temperature data.more » « less
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ε ), was similar to buoyancy flux computed from the surface energy budget, indicating convection dominated turbulence production. Under heating, turbulence was suppressed unless winds in the adjacent open water exceeded 1 m/s. Gas transfer velocities obtained from chamber measurements ranged from 1 to 5 cm/hr and were similar to or slightly less than predicted using a turbulence‐based surface renewal model computed with measuredε andε predicted from wind and cooling.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2023.184
