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Theoretical prediction of turbulent skin friction on geometrically complex surfaces

Phys. Fluids 21, 105105 (2009); doi:10.1063/1.3241993

Published 28 October 2009

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Yulia Peet and Pierre Sagaut
Institut Jean le Rond d'Alembert, Université Pierre et Marie Curie—Paris 6, 75252 Paris Cedex 05, France
This article can be considered as an extension of the paper of Fukagata et al. [Phys. Fluids 14, L73 (2002)] which derived an analytical expression for the constituent contributions to skin friction in a turbulent channel, pipe, and plane boundary layer flows. In this paper, we extend the theoretical analysis of Fukagata et al. (formerly limited to canonical cases with two-dimensional mean flow) to a fully three-dimensional situation allowing complex wall shapes. We start our analysis by considering arbitrarily shaped surfaces and then formulate a restriction on a surface shape for which the current analysis is valid. A theoretical formula for skin friction coefficient is thus given for streamwise and spanwise homogeneous surfaces of any shape, as well as some more complex configurations, including spanwise-periodic wavy patterns. The theoretical analysis is validated using the results of large eddy simulations of a turbulent flow over straight and wavy riblets with triangular and knife-blade cross-sections. Decomposition of skin friction into different constituent contributions allows us to analyze the influence of different dynamical effects on a skin friction modification by riblet-covered surfaces. ©2009 American Institute of Physics
History: Received 16 December 2008; accepted 1 September 2009; published 28 October 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/105105/1
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1070-6631 (print)   1089-7666 (online)
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