Evolutionary optimization of an anisotropic compliant surface for turbulent friction drag reduction

Abstract

Direct numerical simulation (DNS) of the channel flow with an anisotropic compliant surface is performed in order to investigate its drag reduction effect in a fully developed turbulent flow. The computational domain is set to be 3δ×2δ×3δ, where δ is the channel half-width. The surface is passively driven by the pressure and wall-shear stress fluctuations, and the surface velocity provides a boundary condition for the fluid velocity field. An evolutionary optimization method (CMA-ES) is used to optimize the parameters of the anisotropic compliant surface. The optimization identifies several sets of parameters that result in a reduction of the friction drag with a maximum reduction rate of 8%. The primary mechanism for drag reduction is attributed to the decrease of the Reynolds shear stress (RSS) near the wall induced by the kinematics of the surface. The resultant wall motion is a uniform wave traveling downstream. The compliant wall, with the parameters found in the optimization study, is also tested in a computational domain that is doubled in the streamwise direction. The drag, however, is found to increase in the larger computational domain due to excessively large wall-normal velocity fluctuations.

Keywords:

• turbulence control
• drag reduction
• compliant surface
• direct numerical simulation
• evolutionary optimization

Acknowledgments

We would like to thank two anonymous reviewers for their constructive comments.We also wish to acknowledge support by the University of Tokyo—ETH Züurich exchange agreement. This work was partly supported by Keio Gijuku Academic Development Funds.