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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: frohnapfel@kit.edu
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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 

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