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Yutaka Hasegawa
Research Center for Advanced Energy Conversion, Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-8603; Department of Mechanical Engineering Nagaoka University of Technology, Nagaoka, Niigata 940-2133, Japan

Sebastian Tuerk
Graduate School of Computational Engineering Numerical Methods in Mechanical Engineering Technical University of Darmstadt Dolivostr. 15, 64293 Darmstadt, Germany

Alexander Stroh
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Karlsruhe, 76131, Germany

Getraud Daschiel
Institute of Fluid Mechanics Karlsruhe Institute of Technology Kaiserstr. 10, 76131 Karlsruhe, Germany

Bettina Frohnapfel
International Research Training Group Darmstadt-Tokyo on Mathematical Fluid Dynamics; Institut fur Stromungsmechanik, Karlsruher Institut fur Technologie, Kaiserstr. 10, Geb. 10.23, 76131 Karlsruhe, Germany


We investigate the effects of superhydrophobic surface carrying streamwise micro grooves on the flow dynamics and the resultant gain in the flow rate in a fully developed turbulent channel flow under a constant pressure gradient. The superhydrophobic surface is modeled as a flat boundary with alternating no-slip and slip conditions, and a series of direct numerical simulations is performed with systematically changing the spanwise periodicity of the streamwise grooves. It is observed that the alternating no-slip and slip boundary conditions cause a spanwise inhomogeneity of the Reynolds shear stress near the superhydrophobic surface, and consequently generate Prandtl's second kind of secondary flow characterized by coherent streamwise vortices. Accordingly, the instantaneous turbulent flow is decomposed into the spatial-mean, coherent and random components. The detailed turbulent statistics of the three components are obtained and the effect of the secondary flow on the resultant drag reduction is discussed.