J. Fluid Mech. (2009), vol. 620, pp. 31–41. c  2009 Cambridge University Press doi:10.1017/S0022112008004916 Printed in the United Kingdom 31 Direct numerical simulations of turbulent flows over superhydrophobic surfaces MICHAEL B. MARTELL, J. BLAIR PEROT† AND JONATHAN P. ROTHSTEIN Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA (Received 10 October 2008 and in revised form 6 November 2008) Direct numerical simulations (DNSs) are used to investigate the drag-reducing per- formance of superhydrophobic surfaces (SHSs) in turbulent channel flow. SHSs combine surface roughness with hydrophobicity and can, in some cases, support a shear-free air–water interface. Slip velocities, wall shear stresses and Reynolds stresses are considered for a variety of SHS microfeature geometry configurations at a friction Reynolds number of Re τ ≈ 180. For the largest microfeature spacing studied, an average slip velocity over 75% of the bulk velocity is obtained, and the wall shear stress reduction is found to be nearly 40 %. The simulation results suggest that the mean velocity profile near the superhydrophobic wall continues to scale with the wall shear stress but is offset by a slip velocity that increases with increasing microfeature spacing. 1. Introduction Significant effort has been placed on the development of surfaces which reduce the amount of drag experienced by a fluid as it passes over the surface. Drag reduction in turbulent flows can be achieved through a number of very different mechanisms including the addition of polymers (Lumley 1969), riblets (Bechert et al. 1997), compliant walls (Hahn, Je & Choi 2002) and active blowing and suction (Kim 1999). Laminar drag reduction is much harder to achieve. Macroscale laminar drag reduction is possible with liquids, using surface or fluid electric charges (Maynes & Webb 2003) and via surface hydrophobicity (Tretheway & Meinhart 2002). Recent work (see Ou, Perot & Rothstein 2004; Ou & Rothstein 2005; Joseph et al. 2006) has shown that liquid laminar drag reduction is achievable in larger channels, using superhydrophobic surfaces (SHSs). SHSs combine hydrophobic chemistry with micron-scale topological features which can, in some cases, support a shear-free air–water interface resulting in slip lengths of the order of tens of microns in laminar flows. In this work, we will demonstrate that SHSs can also produce significant drag reduction for liquids operating in the turbulent regime. Experiments by Gogte et al. (2005) using hydrophobically modified sand paper and recent results from Daniello, Waterhouse & Rothstein (2008) using precisely patterned hydrophobic microridges and microposts were at high enough Reynolds numbers to be turbulent and showed that drag reduction could be achieved. A theoretical analysis by Fukagata, Kasagi & Koumoutsakos (2006) suggests how a small alteration of the laminar sublayer can † Email address for correspondence: perot@ecs.umass.edu