Optimal Pulse Control of Unsteady Separation Over a Cambered Airfoil: Right Place, Right Time

We present a data‑driven study of a two‑dimensional separated shear layer over a NACA‑65(12) airfoil at Re = 2×10⁴, employing zero-mass Gaussian pulses to manipulate separated shear-layer dynamics. Brief, spatially localized, phase-locked excitations at certain locations and timings trigger shear-layer instabilities; by tuning both pulse location and timing, the flow can induce reattachment of the separated flow, yielding up to 30% lift improvement. Using high‑fidelity CFD snapshots, we first leverage a data-driven convex optimization method to construct a modal reduced‑order model of the flow whose long‑term boundedness is guaranteed by computing the minimal invariant energy bound, ensuring reliable predictions under transient disturbances. Next, we employ a sparse nonlinear optimal perturbation approach to identify critical modes that maximize transient energy growth under perturbation, revealing the flow's most responsive structures. Finally, continuous wavelet–based time–frequency analysis uncovers which flow structures are most amplified at specific phases and spatial locations, enabling determination of optimal actuation locations and timings to drive instabilities towards flow reattachment. By combining guaranteed model stability with targeted, low‑energy perturbations, this workflow lays the foundation for robust, energy‑efficient control of separated flows in aerospace and industrial applications.