Analysis of receptivity and sensitivity of laminar flow separation over three-dimensional tapered wings

The structural sensitivity and receptivity of flows over tapered wings are studied numerically to understand the effect of Reynolds number and planform geometry variation and ultimately inform flow control. Low aspect ratio swept and tapered NACA 0015 wings are considered at 200 ≤ Re ≤ 600. Direct and adjoint TriGlobal linear stability analysis is carried out to identify the wavemaker of the leading unstable mode; this is found to have a compact structure located inside the laminar separation bubble (LSB) with regions associated with the suction and pressure side shear layers. The receptivity to momentum forcing is found to be highest near the separation line on the suction side. Both regions follow the spanwise location of maximum recirculation of the LSB when the wing is swept and tapered. The combination of leading edge (LE) and trailing edge (TE) sweep angles, rather than the taper ratio itself, affects the spanwise position of both the wavemaker and receptivity fields. An increase of LE sweep moves these regions towards the wing tip, whereas the forward sweep of the TE has the opposite effect and causes movement towards the root. These insights from stability theory are then used to inform the positioning of jet actuators in experimental flow control investigations, and numerical results are found to be consistent with those of experiments under the same boundary conditions. The present results establish a theoretical basis for future studies on tapered wings at higher Reynolds numbers.