  We combine three-dimensional (3D) large-eddy simulations (LES) and resolvent
analysis to design active separation control techniques on 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. For the
most successful control case that achieves full reattachment, we observe a
reduction in drag by up to $49\%$ and increase in lift by up to $54\%$. 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 high
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. By
comparing this metric from resolvent analysis and the LES results of controlled
flows, we demonstrate that resolvent analysis can predict the effective range
of actuation frequency as well as the global response to the actuation input.
Supported by the agreements between the results from resolvent analysis and
LES, we believe that this study provides insights for the use of resolvent
analysis in guiding future active flow control.
