  Birds have a remarkable ability to perform complex maneuvers at post-stall
angles of attack. The passive deployment of self-actuating covert feathers in
response to unsteady flow separation while performing such maneuvers provides a
passive flow control paradigm for these aerodynamic capabilities. Most studies
involving covert-feathers-inspired passive flow control have modeled the
feathers as a rigidly attached or a freely moving flap on a wing. A flap
mounted via a torsional spring enables a configuration more emblematic of the
finite stiffness associated with the covert-feather dynamics. The performance
benefits and flow physics associated with this more general case remain largely
unexplored. In this work, we model covert feathers as a passively deployable,
torsionally hinged flap on the suction surface of a stationary airfoil. We
numerically investigate this airfoil-flap system at a low Reynolds number of
$Re=1{,}000$ and angle of attack of $20^\circ$ by performing high-fidelity
nonlinear simulations using a projection-based immersed boundary method. A
parametric study performed by varying the stiffness of the spring, mass of the
flap and location of the hinge yielded lift improvements as high as 27%
relative to the baseline flap-less case and revealed two dominant flow
behavioral regimes. A detailed analysis revealed that the stiffness-dependent
mean flap deflection and inertia-dependent amplitude and phase of flap
oscillations altered the dominant flow characteristics in both the regimes. Of
special interest for performance benefits were the flap parameters that
enhanced the lift-conducive leading-edge vortex while weakening the
trailing-edge vortex and associated detrimental effect of upstream propagation
of reverse flow. These parameters also yielded a favorable temporal
synchronization of flap oscillations with the vortex-shedding process in both
regimes.
