High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces

Abstract

Digital holographic microscopy is used for characterizing the profiles of mean velocity, viscous and Reynolds shear stresses, as well as turbulence level in the inner part of turbulent boundary layers over several super-hydrophobic surfaces (SHSs) with varying roughness/texture characteristics. The friction Reynolds numbers vary from 693 to 4496, and the normalized root mean square values of roughness $(k_{rms}^{+})$ vary from 0.43 to 3.28. The wall shear stress is estimated from the sum of the viscous and Reynolds shear stress at the top of roughness elements and the slip velocity is obtained from the mean profile at the same elevation. For flow over SHSs with $k_{rms}^{+}<1$, drag reduction and an upward shift of the mean velocity profile occur, along with a mild increase in turbulence in the inner part of the boundary layer. As the roughness increases above $k_{rms}^{+}\sim 1$, the flow over the SHSs transitions from drag reduction, where the viscous stress dominates, to drag increase where the Reynolds shear stress becomes the primary contributor. For the present maximum value of $k_{rms}^{+}=3.28$, the inner region exhibits the characteristics of a rough wall boundary layer, including elevated wall friction and turbulence as well as a downward shift in the mean velocity profile. Increasing the pressure in the test facility to a level that compresses the air layer on the SHSs and exposes the protruding roughness elements reduces the extent of drag reduction. Aligning the roughness elements in the streamwise direction increases the drag reduction. For SHSs where the roughness effect is not dominant ($k_{rms}^{+}<1$), the present measurements confirm previous theoretical predictions of the relationships between drag reduction and slip velocity, allowing for both spanwise and streamwise slip contributions.

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

“…The deleterious effect of increasing texture size on the drag observed by these DNS studies is qualitatively consistent with theoretical analysis [28], and experimental investigations [13,15,29].…”

“…Another, texture-related dimensionless parameter is the solid fraction, φ s . A typical range of φ s is 10% − 20% and does not vary by order of magnitude [13][14][15]. In the present study we considered φ s = 1/9, 1/6, and 1/4.…”

“…Bidkar et al [13] and Ling et al [15] showed that the non-dimensional surface roughness in wall unit, k + , was needed to be significantly smaller than the viscous sublayer to obtain successful drag reduction. All previous investigations of turbulent flows over SHS are experimental [13][14][15], while analyses from above-mentioned DNSs only considered geometries with regularly aligned textures. Systematic investigations of texture randomization in DNS can augment quantitative understanding of turbulent flows over the randomly distributed texture.…”

A theory for the slip and drag of superhydrophobic surfaces with surfactant

“…Substituting k = k * /M a and Γ = Γ * /M a into (5), (14) and (13), with the Henry kinetics (18) and (19), we obtain a set of equations where k and M a have been combined to form k * , thereby reducing by one the number of dimensionless groups. This can be verified by examining the updated version of the complete set of equations (2)- (13), which becomes…”

The effect of slip and surface texture on turbulence over superhydrophobic surfaces

“…Experimental studies have also observed that for sufficiency large roughness size, expressed in wall units, superhydrophobic surfaces resulted in a drag increase rather than a drag decrease. This has been attributed to the protrusion of roughness elements introducing additional drag and roughness-like effects (Bidkar et al 2014;Ling et al 2016;Gose et al 2018). Ling et al (2016) also investigated the effect of increasing the roughness protrusion, for the same texture, by increasing the overlying fluid pressure in their experiments.…”