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Reynolds-number dependence of turbulent skin-friction drag reduction induced by spanwise forcing

Published online by Cambridge University Press:  05 August 2016

Davide Gatti
Affiliation:
Institute of Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstraße 10, 76131 Karlsruhe, Germany
Maurizio Quadrio*
Affiliation:
Department of Aerospace Science and Technology, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
Email address for correspondence: maurizio.quadrio@polimi.it

Abstract

This paper examines how increasing the value of the Reynolds number $Re$ affects the ability of spanwise-forcing techniques to yield turbulent skin-friction drag reduction. The considered forcing is based on the streamwise-travelling waves of spanwise-wall velocity (Quadrio et al., J. Fluid Mech., vol. 627, 2009, pp. 161–178). The study builds upon an extensive drag-reduction database created via direct numerical simulation of a turbulent channel flow for two fivefold separated values of $Re$ , namely $Re_{\unicode[STIX]{x1D70F}}=200$ and $Re_{\unicode[STIX]{x1D70F}}=1000$ . The sheer size of the database, which for the first time systematically addresses the amplitude of the forcing, allows a comprehensive view of the drag-reducing characteristics of the travelling waves, and enables a detailed description of the changes occurring when $Re$ increases. The effect of using a viscous scaling based on the friction velocity of either the non-controlled flow or the drag-reduced flow is described. In analogy with other wall-based drag-reduction techniques, like riblets for example, the performance of the travelling waves is well described by a vertical shift of the logarithmic portion of the mean streamwise velocity profile. Except when $Re$ is very low, this shift remains constant with $Re$ , at odds with the percentage reduction of the friction coefficient, which is known to present a mild, logarithmic decline. Our new data agree with the available literature, which is however mostly based on low- $Re$ information and hence predicts a quick drop of maximum drag reduction with $Re$ . The present study supports a more optimistic scenario, where for an airplane at flight Reynolds numbers a drag reduction of nearly 30 % would still be possible thanks to the travelling waves.

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Papers
Copyright
© 2016 Cambridge University Press 

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