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Resolvent-analysis-based design of airfoil separation control

Published online by Cambridge University Press:  26 March 2019

Chi-An Yeh Open the ORCID record for Chi-An Yeh [Opens in a new window]  and
Kunihiko Taira Open the ORCID record for Kunihiko Taira [Opens in a new window]
Chi-An Yeh*
Affiliation:
Department of Mechanical Engineering, Florida State University, Tallahassee, FL 32310, USA
Kunihiko Taira
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA
*
†Email address for correspondence: [email protected]
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Abstract

We use resolvent analysis to design active control techniques for separated flows over a NACA 0012 airfoil. Spanwise-periodic flows over the airfoil at a chord-based Reynolds number of $23\,000$ and a free-stream Mach number of $0.3$ are considered at two post-stall angles of attack of $6^{\circ }$ and $9^{\circ }$. Near the leading edge, localized unsteady thermal actuation is introduced in an open-loop manner with two tunable parameters of actuation frequency and spanwise wavelength. To provide physics-based guidance for the effective choice of these control input parameters, we conduct global resolvent analysis on the baseline turbulent mean flows to identify the actuation frequency and wavenumber that provide large perturbation energy amplification. The present analysis also considers the use of a temporal filter to limit the time horizon for assessing the energy amplification to extend resolvent analysis to unstable base flows. We incorporate the amplification and response mode from resolvent analysis to provide a metric that quantifies momentum mixing associated with the modal structure. This metric is compared to the results from a large number of three-dimensional large-eddy simulations of open-loop controlled flows. With the agreement between the resolvent-based metric and the enhancement of aerodynamic performance found through large-eddy simulations, we demonstrate that resolvent analysis can predict the effective range of actuation frequency as well as the global response to the actuation input. We believe that the present resolvent-based approach provides a promising path towards mean flow modification by capitalizing on the dominant modal mixing.

JFM classification

Flow Control: Instability control Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 867 , 25 May 2019 , pp. 572 - 610
Copyright
© 2019 Cambridge University Press 

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