Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-26T08:00:17.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent flow over superhydrophobic surfaces with streamwise grooves

Published online by Cambridge University Press:  14 April 2014

S. Türk ,
G. Daschiel ,
A. Stroh ,
Y. Hasegawa  and
B. Frohnapfel
S. Türk
Affiliation:
Graduate School of Computational Engineering, Technische Universität Darmstadt, Dolivostr. 15, 64293 Darmstadt, Germany
G. Daschiel
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstr. 10, 76131 Karlsruhe, Germany
A. Stroh
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstr. 10, 76131 Karlsruhe, Germany
Y. Hasegawa
Affiliation:
Institute of Industrial Science, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8505, Japan
B. Frohnapfel*
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstr. 10, 76131 Karlsruhe, Germany
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the effects of superhydrophobic surfaces (SHS) carrying streamwise grooves on the flow dynamics and the resultant drag reduction in a fully developed turbulent channel flow. The SHS is modelled as a flat boundary with alternating no-slip and free-slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. In all computations, a constant pressure gradient condition is employed, so that the drag reduction effect is manifested by an increase of the bulk mean velocity. To capture the flow properties that are induced by the non-homogeneous boundary conditions the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. It is observed that the alternating no-slip and free-slip boundary conditions lead to the generation of Prandtl’s second kind of secondary flow characterized by coherent streamwise vortices. A mathematical relationship between the bulk mean velocity and different dynamical contributions, i.e. the effective slip length and additional turbulent losses over slip surfaces, reveals that the increase of the bulk mean velocity is mainly governed by the effective slip length. For a small spanwise periodicity of the streamwise grooves, the effective slip length in a turbulent flow agrees well with the analytical solution for laminar flows. Once the spanwise width of the free-slip area becomes larger than approximately 20 wall units, however, the effective slip length is significantly reduced from the laminar value due to the mixing caused by the underlying turbulence and secondary flow. Based on these results, we develop a simple model that allows estimating the gain due to a SHS in turbulent flows at practically high Reynolds numbers.

JFM classification

Flow Control: Drag reduction Flow Control: Flow Control Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 747 , 25 May 2014 , pp. 186 - 217
Copyright
© 2014 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.)

References

Busse, A. & Sandham, N. D. 2012 Influence of an anisotropic slip-length boundary condition on turbulent channel flow. Phys. Fluids 24 (5), 055111.CrossRefGoogle Scholar
Cassie, A. B. D. & Baxter, S. 1944 Wettability of porous surfaces. Trans. Faraday Soc. 40, 546–551.CrossRefGoogle Scholar
Daniello, R., Waterhouse, N. & Rothstein, J. 2009 Drag reduction in turbulent flows over superhydrophobic surfaces. Phys. Fluids 21 (8), 085103.CrossRefGoogle Scholar
Frohnapfel, B., Hasegawa, Y. & Quadrio, M. 2012 Money versus time: evaluation of flow control in terms of energy consumption and convenience. J. Fluid Mech. 700, 406–418.CrossRefGoogle Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73.CrossRefGoogle Scholar
Fukagata, K., Kasagi, N. & Koumoutsakos, P. 2006 A theoretical prediction of friction drag reduction in turbulent flow by superhydrophobic surfaces. Phys. Fluids 18 (5), 051703.Google Scholar
Fukagata, K., Kobayashi, M. & Kasagi, N. 2010 On the friction drag reduction effect by a control of large-scale turbulent structures. J. Fluid Sci. Technol. 5 (3), 574–584.CrossRefGoogle Scholar
Gad-El-Hak, M. 2007 Flow Control: Passive, Active, and Reactive Flow Management. Cambridge University Press.Google Scholar
Goldstein, D. B. & Tuan, T. -C. 1998 Secondary flow induced by riblets. J. Fluid Mech. 363, 115–151.CrossRefGoogle Scholar
Hasegawa, Y., Frohnapfel, B. & Kasagi, N. 2011 Effects of spatially varying slip length on friction drag reduction in wall turbulence. J. Phys.: Conf. Ser. 318 (2), 022028.Google Scholar
Hasegawa, Y. & Kasagi, N. 2007 Effects of interfacial velocity boundary condition on turbulent mass transfer at high Schmidt numbers. Intl J. Heat Fluid Flow 28 (6), 1192–1203.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Lauga, E. & Stone, H. A. 2003 Effective slip in pressure-driven Stokes flow. J. Fluid Mech. 489, 55–77.CrossRefGoogle 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.CrossRefGoogle 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 (6), 065102.CrossRefGoogle Scholar
Marusic, I., Joseph, D. D. & Mahesh, K. 2007 Laminar and turbulent comparisons for channel flow and flow control. J. Fluid Mech. 570, 467–477.CrossRefGoogle 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 (9), 093603.CrossRefGoogle Scholar
Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction drag. Phys. Fluids 16 (7), L55.CrossRefGoogle Scholar
Navier, C. 1823 Memoire sur les dois du mouvement des fluides. Mem. Acad. Sci. Inst. Fr. 6, 389–440.Google Scholar
Nikuradse, J. 1926 Untersuchungen über die Geschwindigkeitsverteilung in turbulenten Strömungen. vol. 281. VDI Forschungsheft.Google Scholar
Ou, J., Perot, B. & Rothstein, J. P. 2004 Laminar drag reduction in microchannels using ultrahydrophobic surfaces. Phys. Fluids 16 (12), 4635.CrossRefGoogle Scholar
Philip, J. R. 1972 Flows satisfying mixed no-slip and no-shear conditions. Z. Angew. Math. Phys. 23 (3), 353–372.CrossRefGoogle Scholar
Pöschl, Th. 1926 Zweiter internationaler kongreß für technische mechanik in Zürich. (12. bis 17. September 1926). Naturwissenschaften 14, 1029–1032.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (02), 263–288.CrossRefGoogle Scholar
Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Annu. Rev. Fluid Mech. 42 (1), 89–109.CrossRefGoogle Scholar
Schoppa, W. & Hussain, F. 1998 A large-scale control strategy for drag reduction in turbulent boundary layers. Phys. Fluids 10 (5), 1049–1051.CrossRefGoogle Scholar
Spalart, P. R. & McLean, J. D. 2011 Drag reduction: enticing turbulence, and then an industry. Phil. Trans. R. Soc. A 369 (1940), 1556–1569.CrossRefGoogle ScholarPubMed
Van Driest, E. R. 1956 On turbulent flow near a wall. J. Aeronaut. Sci. (Inst. Aeronaut. Sci.) 23 (11), 1007–1011.CrossRefGoogle Scholar
Woolford, B., Maynes, D. & Webb, B. W. 2008 Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions. Microfluid. Nanofluid. 7 (1), 121–135.CrossRefGoogle Scholar