Skip to main content
SpringerLink
Log in

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

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

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, R e 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 shear stresses are manifest as a decrease in the population of the small-scale vortical structures and a weakening of large-scale motions. The influence of stochastic fluctuations near the large-scale motions diminishes at higher Reynolds number. 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cassie, A., Baxter, S.: Wettability of porous surfaces. Trans. Faraday Soc. 40, 546–551 (1944)

    Article  Google Scholar 

  2. Daniello, R.J., Waterhouse, N.E., Rothstein, J.P.: Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21, 085103 (2009)

    Article  Google Scholar 

  3. Wenzel, R.: Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 29, 988–994 (1936)

    Article  Google Scholar 

  4. Woolford, B., Prince, J., Maynes, D., Webb, B.W.: Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21, 085106 (2009)

    Article  Google Scholar 

  5. Aljallis, E., Sarshar, M.A., Datla, R., Sikka, V., Jones, A., Choi, C.-H.: Experimental study of skin friction drag reduction on superhydrophobic flat plates in high Reynolds number boundary layer flow. Phys. Fluids 25, 025103 (2013)

    Article  Google Scholar 

  6. Lee, C., Kim, C.-J.: Influence of surface hierarchy of superhydrophobic surfaces on liquid slip. Langmuir 27, 4243–4248 (2011)

    Article  Google Scholar 

  7. Lee, C., Kim, C.-J.: Underwater restoration and retention of gases on superhydrophobic surfaces for drag reduction. Phys. Rev. Lett. 106, 014502 (2011)

    Article  Google Scholar 

  8. Philip, J.R.: Flows satisfying mixed no-slip and no-shear conditions. J. Appl. Math. Phys. 23, 353–372 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  9. Martell, M.B., Perot, J.B., Rothstein, J.P.: Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41 (2009)

    Article  MATH  Google Scholar 

  10. Martell, M.B., Perot, J.B., Rothstein, J.P.: An analysis of superhydrophobic turbulent drag reduction mechanisims using direct numerical simulation. Phys. Fluids, 22 (2010)

  11. Choi, H., Moin, P., Kim, J.: Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Türk, S., Daschiel, A., Stroh, A., Hasegawa Y., Frohnapfel, B.: Turbulent flow over superhydrophobic surface with streamwise grooves. J. Fluid Mech. 747, 186–217 (2014)

    Article  Google Scholar 

  13. Jelly, T.O., Jung, S.Y., Zaki, T.A.: Turbulence and skin-friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26, 095102 (2014)

    Article  Google Scholar 

  14. Park, H., Park, H., Kim, J.: A numerical study of the effects of superhydrophobic surface on the skin-friction drag in turbulent channel flow. Phys. Fluids 25, 110815 (2013)

    Article  Google Scholar 

  15. Lauga, E., Stone, H.: Effective slip in pressure-driven stokes flow. J. Fluid Mech. 489, 55–77 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ybert, C., Barentin, C., Cottin-Bizonne, C., Joseph, P., Bocquet, L.: Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries. Phys. Fluids 19, 123601 (2007)

    Article  Google Scholar 

  17. Davis, A.M.J., Lauga, E.: Hydrodynamic friction of fakir-like superhydrophobic surfaces. J. Fluid Mech. 661, 402–411 (2010)

    Article  MATH  Google Scholar 

  18. Zaki, T.A.: From streaks to spots and on to turbulence: exploring the dynamics of boundary layer transition. Flow Turbul. Combust. 91, 451–473 (2013)

    Article  Google Scholar 

  19. Nolan, K.P., Zaki, T.A.: Conditional sampling of transitional boundary layers in pressure gradients. J. Fluid Mech. 728, 306–339 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  20. Lee, J., Jung, S.Y., Sung, H.J., Zaki, T.A.: Effect of wall heating on turbulent boundary layer with temperature-dependent viscosity. J. Fluid Mech. 726, 196–225 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  21. Lee, J., Jung, S.Y., Sung, H.J., Zaki, T.A.: Turbulent thermal boundary layers with temperature-dependent viscosity. Int. J. Heat Fluid Flow. 49, 43–52 (2014)

    Article  Google Scholar 

  22. Hussain, A.K.M.F., Reynolds, W.C.: The mechanisms of an organized wave in turbulent shear flow. J. Fluid Mech. 31, 241–258 (1970)

    Article  Google Scholar 

  23. Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to R e t =590. Phys. Fluids 11, 943–945 (1999)

    Article  MATH  Google Scholar 

  24. Min, T., Kim, J.: Effect of hydrophobic surface on skin-friction drag. Phys. Fluids 7, 55–58 (2004)

    Article  Google Scholar 

  25. Fukagata, K., Kasagi, N., Koumoustaskos, P.: A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703 (2006)

    Article  Google Scholar 

  26. Busse, A., Sandham, N.D.: Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24, 055111 (2012)

    Article  Google Scholar 

  27. Fukagata, K., Iawmoto, K., Kasagi, N.: Contribution of Reynolds stress distribution to the skin friction in wall–bounded flows. Phys. Fluids 14, 73–76 (2002)

    Article  Google Scholar 

  28. Jeong, J., Hussain, F.: On the identification of a vortex. J. Fluid Mech. 285, 69–94 (2009)

    Article  MathSciNet  Google Scholar 

  29. Adrian, R.J., Christensen, K.T., Liu, Z.C.: Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275–290 (2000a)

    Article  Google Scholar 

  30. Adrian, R.J., Meinhart, C.D., Tomkins, C.D.: Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54 (2000b)

    Article  MATH  MathSciNet  Google Scholar 

  31. Ganapathisubramani, B., Longmire, E.K., Marusic, I.: Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46 (2003)

    Article  MATH  Google Scholar 

  32. Hutchins, N., Hambleton, W.T., Marusic, I.: Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 21–54 (2005)

    Article  MATH  Google Scholar 

  33. Monty, J.P., Stewart, J.A., Williams, R.C., Chong, M.S.: Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147–156 (2007)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA

    Jin Lee & Tamer A. Zaki

  2. Department of Mechanical Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Thomas O. Jelly & Tamer A. Zaki

Authors
  1. Jin Lee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas O. Jelly
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tamer A. Zaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tamer A. Zaki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, J., Jelly, T.O. & Zaki, T.A. Effect of Reynolds Number on Turbulent Drag Reduction by Superhydrophobic Surface Textures. Flow Turbulence Combust 95, 277–300 (2015). https://doi.org/10.1007/s10494-015-9627-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-015-9627-z

Keywords

Search

Navigation