Mitigating the sound of a flapping airfoil using optimal structural properties distributions

Author(s): 
Michael Weidenfeld (Israel Institute of Technology), Eran Arad (RD&E Division, RAFAEL)

CHALLENGE - This study investigated the effect of non-uniform thickness distribution on the sound radiation of an elastic, leading-edge actuated, two-dimensional thin airfoil, in a low-Mach potential uniform flow.

SOLUTION - Using thin airfoil theory along with a discrete wake model, the near-field dynamics was obtained and introduced as an effective dipole-type source term to the Powell-Howe acoustic analogy, to obtain the far-field sound. The aeroacoustic setup, was then introduced into an optimization scheme performed in modeFRONTIER where optimal material properties and thickness distribution was sought. The objective was to minimize flapping sound with respect to a rigid heaving configuration while retaining the rigid setup lift-amplitude value. Configurations which did not evolve to a periodic state were filtered out. A wide tolerance value was assigned to the lift constraint for faster convergence and to obtain an effective Pareto front, reflecting the compromise between aerodynamic efficiency and sound.

BENEFITS - The Pareto front was found to exhibit an approximated linear relation between sound reduction and lift-amplitude ratio, exhibiting a further substantial sound reduction of up to ∼30 [dB] for smaller lift amplitude values. The marginal gain obtained by higher order polynomials was found negligible, accept for lower lift ratio values, where an additional sound reduction of ∼10 [dB] was obtained, amounting to a total of ∼40 [dB] reduction compared with the rigid airfoil, at the cost of 33% of the lift-amplitude.