Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T06:54:55.800Z Has data issue: false hasContentIssue false
  • English
  • Français

Predictions of the effective slip length and drag reduction with a lubricated micro-groove surface in a turbulent channel flow

Published online by Cambridge University Press:  12 July 2019

Jaehee Chang ,
Taeyong Jung ,
Haecheon Choi Open the ORCID record for Haecheon Choi [Opens in a new window]  and
John Kim
Jaehee Chang
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea
Taeyong Jung
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea
Haecheon Choi*
Affiliation:
Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Korea
John Kim
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We perform direct numerical simulations of a turbulent channel flow with a lubricated micro-grooved surface to investigate the effects of this surface on the slip characteristics at the interface and the friction drag. The interface between water and lubricant is assumed to be flat, i.e. the surface-tension effect is neglected. The solid substrate, where a lubricant is infused, is composed of straight longitudinal grooves. The flow rate of water inside the channel is maintained constant, and a lubricant layer under the interface is shear driven by the turbulent water flow above. A turbulent channel flow with a superhydrophobic (i.e. air-lubricated) surface having the same solid substrate configuration is also simulated for comparison. The results show that the drag reduction with the liquid-infused surface highly depends on the lubricant viscosity as well as the groove width and aspect ratio. The amounts of drag reduction with the liquid-infused surfaces are not as good as those with superhydrophobic surfaces, but are still meaningfully large. For instance, the maximum drag reduction by the heptane-infused surface is approximately 13 % for a rectangular groove whose spanwise width and depth in wall units are 12 and 14.4, respectively, whereas a superhydrophobic surface with the same geometry results in a drag reduction of 21 %. The mean slip length normalized by the viscosity ratio and groove depth depends on the groove aspect ratio. The ratio of fluctuating spanwise slip length to the streamwise one is between 0.25 (ideal surface without groove structures) and 1 (i.e. isotropic slip), indicating that the slip is anisotropic. Using the Stokes flow assumption, the effective streamwise and spanwise slip lengths are expressed as a function of groove geometric parameters and lubricant viscosity. We also suggest a predictive model for drag reduction with the heptane-lubricated surface by combining the predicted effective slip lengths with the drag reduction formula used for riblets (Luchini et al., J. Fluid Mech., vol. 228, 1991, pp. 87–109). The predicted drag reductions are in good agreements with those from the present and previous direct numerical simulations.

JFM classification

Flow Control: Drag reduction Turbulent Flows: Turbulence control Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 797 - 820
Check for updates
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: LG Electronics, 51, Gasan digital 1-ro, Geumcheon-gu, Seoul, Korea

References

Aljallis, E., Sarshar, M. A., Datla, R., Sikka, V., Jones, A. & Choi, C.-H. 2013 Experimental study of skin friction drag reduction on superhydrophobic flat plates in high Reynolds number boundary layer flow. Phys. Fluids 25, 025103.Google Scholar
Bechert, D. W., Brus, M., Hage, W., Van der Hoeven, J. G. T. & Hoppe, G. 1997 Experiment on drag-reduction surfaces and their optimization with an adjustable geometry. J. Fluid Mech. 338, 59–87.Google Scholar
Belyaev, A. V. & Vinogradova, O. I. 2010 Effective slip in pressure-driven flow past super-hydrophobic stripes. J. Fluid Mech. 652, 489–499.Google Scholar
Bidkar, R. A., Leblac, L., Kulkarni, A. J., Bahadur, V., Ceccio, S. L. & Perlin, M. 2014 Skin-friction drag reduction in the turbulent regime using random-textured hydrophobic surfaces. Phys. Fluids 26, 085108.Google Scholar
Busse, A. & Sandham, N. D. 2012 Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24, 055111.Google Scholar
Busse, A., Sandham, N. D., Mchale, G. & Newton, M. I. 2013 Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface. J. Fluid Mech. 727, 488–508.Google Scholar
Cartagena, E. J. G., Arenas, I., Bernardini, M. & Leonardi, S. 2018 Dependence of the drag over super hydrophobic and liquid infused surfaces on the textured surface and Weber number. Flow Turbul. Combust. 100, 945–960.Google Scholar
Cheng, Y. P., Teo, C. J. & Khoo, B. C. 2009 Microchannel flows with superhydrophobic surfaces: effects of Reynolds number and pattern width to channel height ratio. Phys. Fluids 21 (12), 122004.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503.Google Scholar
Cottin-Bizonne, C., Barentin, C., Charlaix, É., Bocquet, L. & Barrat, J. L. 2004 Dynamics of simple liquids at heterogeneous surfaces: molecular-dynamics simulations and hydrodynamic description. Eur. Phys. J. E 15 (4), 427–438.Google Scholar
Daniello, R. J., Waterhouse, N. E. & Rothstein, J. P. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21, 085103.Google Scholar
Fairhall, C. T. & García-Mayoral, R. 2018 Spectral analysis of the slip-length model for turbulence over textured superhydrophobic surfaces. Flow Turbul. Combust. 100, 961–978.Google Scholar
Fu, M. K., Arenas, I., Leonardi, S. & Hultmark, M. 2017 Liquid-infused surfaces as a passive method of turbulent drag reduction. J. Fluid Mech. 824, 688–700.Google Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin-friction in wall-bounded flows. Phys. Fluids 14, L73–L76.Google Scholar
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18, 051703.Google Scholar
García-Mayoral, R. & Jiménez, J. 2011 Drag reduction by riblets. Phil. Trans. R. Soc. Lond. A 369, 1412–1427.Google Scholar
Ge, Z., Holmgren, H., Kronbichler, M., Brandt, L. & Kreiss, G. 2018 Effective slip over partially filled microcavities and its possible failure. Phys. Rev. Fluids 3, 054201.Google Scholar
Golovin, K. B., Gose, J. W., Perlin, M., Ceccio, S. L. & Tuteja, A. 2016 Bioinspired surfaces for turbulent drag reduction. Phil. Trans. R. Soc. Lond. A 374 (2073), 20160189.Google Scholar
Greidanus, A. J., Delfos, R. & Westerweel, J. 2011 Drag reduction by surface treatment in turbulent Taylor–Couette flow. J. Phys.: Conf. Ser. 318 (8), 082016.Google Scholar
Henoch, C., Krupenkin, T., Kolodner, P., Taylor, J., Hodes, M., Lyons, A., Peguero, C. & Breuer, K. 2006 Turbulent drag reduction using superhydrophobic surfaces. In Proceedings of the 3rd AIAA Flow Control Conference, vol. 2, pp. 840–844. AIAA.Google Scholar
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.Google Scholar
Jiménez, J. 1994 On the structure and control of near wall turbulence. Phys. Fluids 6, 944.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jung, T., Choi, H. & Kim, J. 2016 Effects of the air layer of an idealized superhydrophobic surface on the slip length and skin-friction drag. J. Fluid Mech. 790, R1.Google Scholar
Jung, Y. C. & Bhushan, B. 2010 Biomimetic structures for fluid drag reduction in laminar and turbulent flows. J. Phys.: Condens. Matter 22, 035104.Google Scholar
Kim, J., Kim, D. & Choi, H. 2001 An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput. Phys. 171, 132–150.Google Scholar
Lauga, E. & Stone, H. 2003 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 489, 55–77.Google Scholar
Lee, J., Jelly, T. O. & Zaki, T. A. 2015 Effect of Reynolds number on turbulent drag reduction by superhydrophobic surface textures. Flow Turbul. Combust. 95, 277–300.Google Scholar
Li, Y., Alame, K. & Mahesh, K. 2017 Feature-resolved computational and analytical study of laminar drag reduction by superhydrophobic surfaces. Phys. Rev. Fluids 2 (5), 054002.Google Scholar
Ling, H., Srinivasan, S., Golovin, K., Mckinley, G. H., Tuteja, A. & Katz, J. 2016 High-resolution velocity measurement in the inner part of turbulent boundary layers over super-hydrophobic surfaces. J. Fluid Mech. 801, 670–703.Google Scholar
Liu, Y., Wexler, J. S., Schönecker, C. & Stone, H. A. 2016 Effect of viscosity ratio on the shear-driven failure of liquid-infused surfaces. Phys. Rev. Fluids 1 (7), 074003.Google Scholar
Luchini, P., Manzo, F. & Pozzi, A. 1991 Resistance of a grooved surface to parallel flow and cross-flow. J. Fluid. Mech. 228, 87–109.Google Scholar
MacDonald, M., Chung, D., Hutchins, N., Chan, L., Ooi, A. & García-Mayoral, R. 2017 The minimal-span channel for rough-wall turbulent flows. J. Fluid Mech. 816, 5–42.Google Scholar
Martell, M. B., Perot, J. B. & Rothstein, J. P. 2009 Direct numerical simulations of turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 620, 31–41.Google Scholar
Martell, 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.Google Scholar
Maynes, D., Jeffs, K., Woolford, B. & Webb, B. W. 2007 Laminar flow in a microchannel with hydrophobic surface patterned microribs oriented parallel to the flow direction. Phys. Fluids 19, 093603.Google Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16, L55.Google Scholar
Nizkaya, T. V., Asmolov, E. S. & Vinogradova, O. I. 2014 Gas cushion model and hydrodynamic boundary condition for superhydrophobic textures. Phys. Rev. E 90, 043017.Google Scholar
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.Google Scholar
Park, H., Sun, G. & Kim, C.-J. C. 2014 Superhydrophobic turbulent drag reduction as a function of surface grating parameters. J. Fluid Mech. 747, 722–734.Google Scholar
Peguero, C. & Breuer, K. 2009 On drag reduction in turbulent channel flow over superhydrophobic surfaces. In Advance in Turbulence XII (ed. Eckhardt, B.), pp. 233–236. Springer.Google Scholar
Rastegari, A. & Akhavan, R. 2015 On the mechanism of turbulent drag reduction with superhydrophobic surfaces. J. Fluid Mech. 773, R4.Google Scholar
Rastegari, A. & Akhavan, R. 2018 The common mechanism of turbulent skin-friction drag reduction with superhydrophobic longitudinal microgrooves and riblets. J. Fluid Mech. 838, 68–104.Google Scholar
Rosenberg, B. J., Van Buren, T., Fu, M. K. & Smits, A. J. 2016 Turbulent drag reduction over air- and liquid- impregnated surfaces. Phys. Fluids 28, 015103.Google Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42, 89–109.Google Scholar
Sangani, A. S. & Acrivos, A. 1982 Slow flow through a periodic array of spheres. Intl J. Multiphase Flow 14 (4), 343–360.Google Scholar
Schönecker, C., Baier, T. & Hardt, S. 2014 Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state. J. Fluid Mech. 740, 168–195.Google Scholar
Schönecker, C. & Hardt, S. 2013 Longitudinal and transverse flow over a cavity containing a second immiscible fluid. J. Fluid Mech. 717, 376–394.Google Scholar
Schönecker, C. & Hardt, S. 2015 Assessment of drag reduction at slippery, topographically structured surfaces. Microfluid Nanofluid 19, 199–207.Google Scholar
Seo, J., García-Mayoral, R. & Mani, A. 2015 Pressure fluctuations and interfacial robustness in turbulent flows over superhydrophobic surfaces. J. Fluid Mech. 783, 448–473.Google Scholar
Seo, J., García-Mayoral, R. & Mani, A. 2018 Turbulent flows over superhydrophobic surfaces: flow-induced capillary waves, and robustness of air-water interfaces. J. Fluid Mech. 835, 45–85.Google Scholar
Seo, J. & Mani, A. 2016 On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces. Phys. Fluids 28, 025110.Google Scholar
Solomon, B. R., Khalil, K. S. & Varanasi, K. K. 2014 Drag reduction using lubricant-impregnated surfaces in viscous laminar flow. Langmuir 30 (36), 10970–10976.Google Scholar
Sun, R. & Ng, C. O. 2017 Effective slip for flow through a channel bounded by lubricant-impregnated grooved surfaces. Theor. Comput. Fluid Dyn. 31 (2), 189–209.Google Scholar
Teo, C. J. & Khoo, B. C. 2009 Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves. Microfluid. Nanofluid. 7, 353–382.Google Scholar
Türk, S., Daschiel, G., Stroh, A., Hasegawa, Y. & Frohnapfel, B. 2014 Turbulent flow over superhydrophobic surfaces with streamwise grooves. J. Fluid Mech. 747, 186–217.Google Scholar
Van Buren, T. & Smits, A. J. 2017 Substantial drag reduction in turbulent flow using liquid-infused surfaces. J. Fluid Mech. 827, 448–456.Google Scholar
Vinogradova, O. I. 1995 Drainage of a thin liquid film confined between hydrophobic surfaces. Langmuir 11, 2213–2220.Google Scholar
Walsh, M. J. 1983 Riblets as a viscous drag reduction technique. AIAA J. 21, 485–486.Google Scholar
Wexler, J. S., Jacobi, I. & Stone, H. A. 2015 Shear-driven failure of liquid-infused surfaces. Phys. Rev. Lett. 114 (16), 168301.Google Scholar
Wong, T. S., Kang, S. H., Tang, S. K., Smythe, E. J., Hatton, B. D., Grinthal, A. & Aizenberg, J. 2011 Bioinspired self-repairing slippery surfaces with pressure-stable omniphobicity. Nature 477, 443–447.Google Scholar
Woolford, B., Prince, J., Maynes, D. & Webb, B. W. 2009 Particle image velocimetry characterization of turbulent channel flow with rib patterned superhydrophobic walls. Phys. Fluids 21, 085106.Google Scholar
Ybert, C., Barentin, C., Cottin-Bizonne, C. C., Joseph, P. & Bocquet, L. R. 2007 Achieving large slip with superhydrophobic surfaces: Scaling laws for generic geometries. Phys. Fluids 19, 123601.Google Scholar
You, J., Choi, H. & Yoo, J. 2000 A modified fractional step method of keeping a constant mass flow rate in fully developed channel and pipe flows. KSME Intl J. 14 (5), 547–552.Google Scholar