Piezoelectric transducer placement impacts energy harvesting from fluttering aerofoils
Transducer Placement and the Limits of a Four-State Reduced Model in Post-Flutter Piezoelectric Energy Harvesting from a Pitch-Plunge-Flap Aerofoil
Computational Engineering, Finance, and Science
Summary
Fluttering in aircraft wings is usually a problem, but it creates steady motion that can be used to generate electricity with a piezoelectric device. The authors studied a wing model with three movements and a flap, adding a device that converts this motion into power. They found that where the device is placed changes how much energy can be harvested and affects when flutter starts. They also showed that simplified mathematical models need to be carefully designed to accurately predict the power output.
What this means in practice
- •For aerospace engineers: Improve design of energy-harvesting devices on aircraft wings by selecting optimal transducer placement to maximize power from flutter-induced motion.
- •For wind energy developers: Design robust, low-order models for piezoelectric energy harvesters on aerofoils to better predict power output from airflow-induced vibrations.
Authors
Nikolaos D. Tantaroudas, Ilias Karachalios, Andrew J. McCracken
Abstract
Aeroelastic ?utter is normally a failure mode to be designed against, yet the limit-cycle oscillations (LCOs) that follow it convert flow energy into sustained structural motion that a piezoelectric transducer can turn into electrical power. A transducer is embedded in a three-degree-of-freedom pitch-plunge aerofoil with a finite-mass trailing-edge flap and unsteady strip-theory aerodynamics, giving a fifteen-state electro-aeroelastic system with a cubic hardening pitch spring, and the system is reduced by biorthonormal projection of the Taylor-expanded residual onto eigenvectors of the coupled Jacobian. The testbed is deliberately low order, so that every reduced prediction can be checked against the full-order system it replaces. The degree of freedom that carries the transducer is a first-order design variable, since it sets both the sign of the shift in the flutter boundary and the magnitude of the harvested power. The error of the reduced model is dominated not by the size of the retained basis but by how the reduced operator is made to depend on low speed. Expanding the retained eigenvalues leaves the reduced operator block-diagonal, with no coupling between the retained modes at any order of the expansion, whereas re-projecting the exact Jacobian onto the same frozen basis supplies that coupling and restores the structural response without enlarging the basis. It is found that the error that remains lies in the harvested voltage, which the equilibrium eigenvectors carry in a fixed proportion to the motion, and this is not removed by adding the electrical modes to the basis, whereas the flap detection, which the same basis also misses, is recovered by retaining the flap modes. The accuracy of a harvester reduced-order model must therefore be reported on the harvested quantity itself.