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On the mechanism of turbulent drag reduction with super-hydrophobic surfaces

  • Amirreza Rastegari (a1) and Rayhaneh Akhavan (a1)


The mechanism of turbulent drag reduction (DR) with super-hydrophobic (SH) surfaces is investigated by direct numerical simulation (DNS) and analysis of the governing equations in channel flow. The DNS studies were performed using lattice Boltzmann methods in channels with ‘idealized’ SH surfaces on both walls, comprised of longitudinal micro-grooves (MG), transverse MG, or micro-posts. DRs of $5\,\%$ to $83\,\%$ , $-4\,\%$ to $20\,\%$ , and $14\,\%$ to $81\,\%$ were realized in DNS with longitudinal MG, transverse MG, and micro-posts, respectively. By mathematical analysis of the governing equations, it is shown that, in SH channel flows with any periodic SH micro-pattern on the walls, the magnitude of DR can be expressed as $DR=U_{slip}/U_{bulk}+O({\it\varepsilon})$ , where the first term represents the DR resulting from the effective slip on the walls, and the second term represents the DR or drag increase (DI) resulting from modifications to the turbulence dynamics and any secondary mean flows established in the SH channel compared to a channel flow with no-slip walls at the same bulk Reynolds number as the SH channel. Comparison of this expression to DNS results shows that, with all SH surface micro-patterns studied, between 80 % and 100 % of the DR in turbulent flow arises from the effective slip on the walls. Modifications to the turbulence dynamics contribute no more than 20 % of the total DR with longitudinal MG or micro-posts of high shear-free fraction (SFF), and a DI with transverse MG or micro-posts of moderate SFF. The effect of the SH surface on the normalized dynamics of turbulence is found to be small in all cases, and confined to additional production of turbulence kinetic energy (TKE) within a thin ‘surface layer’ of thickness of the order of the width of surface micro-indentations. Outside of this ‘surface layer’, the normalized dynamics of turbulence proceeds as in a turbulent channel flow with no-slip walls at the friction Reynolds number of the SH channel flow.


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Benzi, R., Biferale, L., Sbragaglia, M., Succi, S. & Toschi, F. 2006 Mesoscopic modelling of heterogeneous boundary conditions for microchannel flows. J. Fluid Mech. 548, 257280.
Bushnell, D. & Hefner, J. N.1990 Viscous drag reduction in boundary layers. Progress In Astronautics and Aeronautics (ed. D. Bushell & N. J. Hefner), vol. 123. AIAA.
Davis, A. M. J. & Lauga, E. 2009 Geometric transition in friction for flow over a bubble mattress. Phys. Fluids 21, 011701.
Davis, A. M. J. & Lauga, E. 2010 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 661, 402411.
Daniello, R. J., Waterhouse, N. E. & Rothstein, J. P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21, 085103.
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin-friction in wall-bounded flows. Phys. Fluids 14, L73L76.
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703.
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Jelly, T. O., Jung, S. Y. & Zaki, T. A. 2014 Turbulence and skin friction modification in channel flow with streamwise-aligned superhydrophobic surface texture. Phys. Fluids 26, 095102.
Karatay, E., Haase, A. S., Visser, C. W., Sun, C., Lohse, D., Tsai, P. A. & Lammertink, R. G. 2013 Control of slippage with tunable bubble mattresses. Proc. Natl Acad. Sci. USA 110, 84228426.
Lauga, E. & Stone, H. A. 2003 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 489, 5577.
Martel, M., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 3141.
Martel, M. B., Rothstein, J. P. & Perot, J. B. 2010 An analysis of superhydrophobic turbulent drag reduction mechanisms using direct numerical simulation. Phys. Fluids 22, 065102.
Min, T. & Kim, J. 2004 Effect of superhydrophobic surfaces on skin-friction drag. Phys. Fluids 16, L55.
Ou, J., Perot, J. B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16, 4635.
Ou, J. & Rothstein, J. P. 2005 Direct velocity measurements of the flow past drag reducing ultrahydrophobic surfaces. Phys. Fluids 17, 103606.
Park, H., Park, H. & Kim, J. 2013 A numerical study of the effects of superhydrophobic surface on skin-friction drag in turbulent channel flow. Phys. Fluids 25, 110815.
Park, H., Sun, G. & Kim, C.-J. 2014 Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722734.
Peet, Y. & Sagaut, P. 2009 Theoretical prediction of turbulent skin friction on geometrically complex surfaces. Phys. Fluids 21, 105105.
Peguero, C. & Bruer, K. 2009 On drag reduction in turbulent channel flow over superhydrophobic surfaces. In Advances in Turbulence XII (ed. Eckhardt, B.), pp. 233236. Springer.
Perkins, H. J. 1970 The formation of streamwise vorticity in turbulent flow. J. Fluid Mech. 44, 721740.
Philip, J. R. 1972 Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23, 353372.
Rastegari, A. & Akhavan, R. 2013 Lattice Boltzmann simulations of drag reduction by super-hydrophobic surfaces. In Proceedings of 14th European Turbulence Conference, September 1–4, 2013.
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89109.
Sbragaglia, M. & Prosperetti, A. 2007 A note on the effective slip properties for microchannel flows with ultrahydrophobic surfaces. Phys. Fluids 19, 043603.
Succi, S. 2001 The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press.
Steinberger, A., Cottin-Bizonne, C., Kleimann, P. & Charlaix, E. 2007 High friction on a bubble mattress. Nat. Mater. 6, 665668.
Tsai, P., Peters, A. M., Pirat, C., Wessling, M., Lammertink, R. G. H. & Lohse, D. 2009 Quantifying effective slip length over micropatterned hydrophobic surfaces. Phys. Fluids 21, 112002.
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186217.
Voronov, R. S. & Papavassiliou, D. V. 2008 Review of fluid slip over superhydrophobic surfaces and its dependence on the contact angle. Ind. Eng. Chem. Res. 47, 24552477.
Watanabe, K., Ugadawa, Y. & Ugadawa, H. 1999 Drag reduction of Newtonian fluid in a circular pipe with a highly water-repellent wall. J. Fluid Mech. 381, 225238.
Woolford, B., Prince, J., Maynes, D. & Webb, B. W. 2009 Particle immage velocimetry charactrization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21, 085106.
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On the mechanism of turbulent drag reduction with super-hydrophobic surfaces

  • Amirreza Rastegari (a1) and Rayhaneh Akhavan (a1)


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