Compressible aerodynamics and rigid-body support motion in post-flutter piezoelectric energy harvesting from a pitch-plunge-flap aerofoil

Abstract

A piezoelectric transducer on a pitching and plunging aerofoil with a trailing edge flap turns the limit cycle that follows flutter into electrical power, and two modelling changes to that harvester have been studied separately. Replacing incompressible strip theory by the compressible Euler equations reduces the stabilising effect of a transducer mounted on the pitch, where the electrical time constant meets the flutter frequency, and raises the harvested power, and letting the section react against a fuselage free to translate, instead of rigid ground, does the same two things by about the same amounts. Here both changes are put in one model, which needs no new mesh motion in the flow solver, since the support's translation displaces the wall exactly as the plunge does. On the harvested power the two published corrections simply multiply. On the flutter boundary they more than compound, and at strong enough coupling they reverse the sign of the transducer's effect at the load resistance where both companion papers harvest, although neither change alone reverses it. The free support widens the band of resistance over which the two aerodynamic models disagree in sign, carrying its upper edge out by about a factor of three. Above the resistance where the electrical pole meets the flutter frequency, where the transducer acts as an added stiffness, the product of the published corrections predicts the shift to within seven parts in a thousand. Below it, where the transducer acts as a damper whose effect depends on phase, the product is wrong by a factor of up to fourteen, and on the pitch mounting by a sign. The same transducer lowers the boundary while flattening the growth of the instability above it. Whether corrections found one change at a time may be multiplied therefore depends on the quantity and, for the flutter boundary, on the regime of the transducer.