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Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces

Published online by Cambridge University Press:  22 October 2015

J. Seo ,
R. García-Mayoral  and
A. Mani
J. Seo
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
R. García-Mayoral
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
A. Mani*
Affiliation:
Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA
*
†Email address for correspondence: alimani@stanford.edu
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Abstract

Superhydrophobic surfaces can entrap gas pockets within their grooves when submerged in water. Such a mixed-phase boundary is shown to result in an effective slip velocity on the surface, and has promising potential for drag reduction and energy-saving in hydrodynamic applications. The target flow regime, in most such applications, is a turbulent flow. Previous analyses of this problem involved direct numerical simulations of turbulence with the superhydrophobic surface modelled as a flat boundary, but with a heterogeneous mix of slip and no-slip boundary conditions corresponding to the surface texture. Analysis of the kinematic data from these simulations has helped to establish the magnitude of drag reduction for various texture topologies. The present work is the first investigation that, alongside a kinematic investigation, addresses the robustness of superhydrophobic surfaces by studying the load fields obtain from data from direct numerical simulations (DNS). The key questions at the focus of this work are: does a superhydrophobic surface induce a different pressure field compared to a flat surface? If so, how does this difference scale with system parameters, and when does it become significant that it can deform the air–water interface and potentially rapture the entrapped gas pockets? To this end, we have performed DNS of turbulent channel flows subject to superhydrophobic surfaces over a wide range of texture sizes spanning values from $L^{+}=6$ to $L^{+}=155$ when expressed in terms of viscous units. The pressure statistics at the wall are decomposed into two contributions: one coherent, caused by the stagnation of slipping flow hitting solid posts, and one time-dependent, caused by overlying turbulence. The results show that the larger texture size intensifies the contribution of stagnation pressure, while the contribution from turbulence is essentially insensitive to $L^{+}$. The two-dimensional stagnation pressure distribution at the wall and the pressure statistics in the wall-normal direction are found to be self-similar for different $L^{+}$. The scaling of the induced pressure and the consequent deformations of the air–water interface are analysed. Based on our results, an upper bound on the texture wavelength is quantified that limits the range of robust operation of superhydrophobic surfaces when exposed to high-speed flows. Our results indicate that when the system parameters are expressed in terms of viscous units, the main parameters controlling the problem are $L^{+}$ and a Weber number based on inner dimensions; We obtain good collapse when all our results are expressed in wall units, independently of the Reynolds number.

JFM classification

Flow Control: Drag reduction Interfacial Flows (free surface): Interfacial Flows (free surface) Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 783 , 25 November 2015 , pp. 448 - 473
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Copyright
© 2015 Cambridge University Press 

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Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P13.

Download Seo et al. supplementary movie(Video)
Video 18 MB

Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P13.

Download Seo et al. supplementary movie(Video)
Video 6.9 MB

Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P26.

Download Seo et al. supplementary movie(Video)
Video 16.7 MB

Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P26.

Download Seo et al. supplementary movie(Video)
Video 8.1 MB

Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P39.

Download Seo et al. supplementary movie(Video)
Video 16.3 MB

Seo et al. supplementary movie

Instantaneous wall-normal vorticity contours at y=0 for case P39.

Download Seo et al. supplementary movie(Video)
Video 7.8 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P39.

Download Seo et al. supplementary movie(Video)
Video 12.4 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P39.

Download Seo et al. supplementary movie(Video)
Video 8.1 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P13.

Download Seo et al. supplementary movie(Video)
Video 16.1 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P13.

Download Seo et al. supplementary movie(Video)
Video 8.4 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P26.

Download Seo et al. supplementary movie(Video)
Video 16.5 MB

Seo et al. supplementary movie

Instantaneous pressure contours at y=0 for case P26.

Download Seo et al. supplementary movie(Video)
Video 7.9 MB