Effect of Reynolds Number on Turbulent Drag Reduction by Superhydrophobic Surface Textures

Abstract

In turbulent flows over streamwise-aligned superhydrophobic surface (SHS) textures, the percent drag reduction is dependent on Reynolds number. This dependence is examined using direct numerical simulations of channel flow over SHS texture at three bulk Reynolds numbers, Re b = 2800, 6785 and 10975.Simulations of regular no-slip channel flows at the same bulk velocities are also performed for comparison. Changes in the flow due to the SHS texture are examined with particular focus on phase averaged statistics and coherent turbulent motions. As the Reynolds number is increased, the texture performance, or the percent drag reduction, is enhanced. In terms of turbulent motions, the weakened The enhanced performance is therefore due to a significant drop in the strength of small-and large-scale vortical structures. The weaker vortical motions yield a considerable reduction in the Reynolds shear stress and the transport of mean momentum. The SHS texture introduces a performance penalty in the form of a local increase in drag at the no-slip free-slip edge. This adverse effect is caused by the inhomogeneity of the near-wall flow field. However, the affected region narrows in width at higher Reynolds numbers. As a result, the percent drag reduction approaches the gas fraction of the texture.

Superhydrophobic drag reduction in high-speed towing tank

“…At low speeds, when the surface was found to be mostly dewetted (i.e. retained plastron appearing silvery bright), the drag ratio decreased with the Reynolds number, consistent with some previous experimental studies (Srinivasan et al 2015) and all numerical studies (Min & Kim 2004;Busse & Sandham 2012;Park et al 2013;Lee, Jelly & Zaki 2015). At high speeds, however, the wetted (dark) areas expanded, negating and eventually overshadowing the drag reduction created by the dewetted…”

“…Representing the drag ratio obtainable if the entire SHPo surface retained a proper plastron at all speeds, D c was added in figure 6(a) as hollow symbols connected by dotted lines. These 'projected' data by hypothetically assuming no plastron loss are in agreement with the numerical results that the drag ratio of a SHPo trench surface decreases with Reynolds number (Min & Kim 2004;Busse & Sandham 2012;Park et al 2013;Lee et al 2015). They also suggest that a larger pitch or gas fraction could drop the drag ratio further down in large-scale turbulent boundary-layer tests at high Reynolds numbers, similar to the trend found in small-scale turbulent boundary-layer tests at low Reynolds numbers by Park et al (2014), if the entire SHPo surface could remain properly dewetted.…”

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].…”

“…Since many different flow facilities are used, we compare the results using the friction Reynolds number on smooth surface Re τ = u τ •δ/ν by estimating it from the flow data in each report, similarly to Gose et al [17], where u τ is the friction velocity, δ is boundary layer thickness, and ν is kinematic viscosity. As a relevant trend for drag ratio, the effect of Reynolds number unveiled by numerical studies [9,10] has been observed in some experiments [15,24,27] but contradicted in some others [13,17,21]. Most importantly, all but one [13] experimental study were performed in a confined flow, e.g., water tunnel, whether internal or external.…”

“…So far, the only high Reynolds number SHPo experiment performed in open water [13] found drag reduction at low Reynolds numbers but drag increase at high Reynolds numbers due to the diminishing plastron. These inconsistent and discouraging experimental results 2331-7019/20/13(3)/034056 (10) 034056-1 © 2020 American Physical Society after decades-long research have started to cast doubts on whether SHPo surfaces will ever bring the level of impact once anticipated [15,33]. Meanwhile, microcavities whose top edges are shaped to be "re-entrant" were shown to be more stable against wetting transition [34,35].…”