Aeroelastic Limit Cycles As A

Small Scale Energy Source

Jared Dunnmon

8th Int. Conf. on Multibody Systems, Nonlinear Dynamics, and Control

Advised by Professor Earl Dowell, Duke University

August 29, 2011

The Idea: Research Concept and Goals

• Utilize aeroelasticallyinduced LCO as a source of energy

• Experimentally investigate capturing energy in the LCO of a cantilevered metal beam with piezoelectric laminates

• Computationally model full “aeroelectroelastic” system behavior

Experimental Methods:

Aeroelectroelastic Beam Experiments

• Self-excited subcritical

LCO occur over a

significant hysteresis band

from 31.5 m/s to 26 m/s

• Normalized amplitudes of

0.46 at 31.5 m/s

• RMS power output of 2.5

mW at 27 m/s

Experimental Demonstration:

Pre-Flutter Behavior at 30 m/s

Experimental Demonstration:

Post-Flutter Behavior at 31.5 m/s

Experimental Demonstration:

Frequency Matched Behavior at 27 m/s

Modeling: Conceptual Framework

• Three dimensional vortex lattice aerodynamic model

• Discontinuous piezoelectric beam electrostructural model

• Experimental natural frequencies and physical parameters input

• In vacuo modeshapes used as an approximation to discontinuous modeshapes

• Essential Mathematics– Bernoulli’s Equation

– Laplace’s Equation

– Velocity Potential-Downwash Boundary Condition

– Hodges-Dowell Equations

Modeling: Basic EquationsCoupled Nonlinear ODEs for Aeroelectroelastic Beam and Electrical Circuit

Full Aeroelectroelastic State Space Equation

State Space Discretization of ODE System and Coupling to Vortex Lattice Aerodynamics

Mass Matrix

Nonlinear Curvature Force

Nonlinear Inertial Forces

Modeling: Basic EquationsCoupled Nonlinear ODEs for Aeroelectroelastic Beam and Electrical Circuit

Full Aeroelectroelastic State Space Equation

State Space Discretization of ODE System and Coupling to Vortex Lattice Aerodynamics

Results: Flutter Speed PredictionTheoretical Damping vs. Flow Velocity Theoretical Root-Locus

Results: Frequency MeasuresFFT of Experimental Signal FFT of Theoretical Signal

Frequency vs. Amplitude

Results: Amplitude MeasuresAmplitude vs. Velocity Experimental Strain vs. Velocity

Results: Voltage Time HistoriesExperimental Voltage Time History Theoretical Voltage Time History

Results: Power Extraction Measures

Power Extracted vs. Physical Amplitude Power Extracted vs. Resistance (U=27 m/s)

Results: Efficiency Measures

• Capture efficiency estimated by the following equation:

• Remains approximately constant over all observed amplitudes

• Promising potential for a harvester that operates efficiently over a large velocity band

Capture Efficiency vs. Physical Amplitude

Summary: Conclusions and Next Steps

• Conclusions– Rudimentary piezoelectric

aeroelastic energy harvester able to generate significant amounts of power

– Aeroelectroelastic state space model with linear piezoelectric terms approximates system behavior well

– Subcritical LCO potentially desirable for this particular applications

• Next Steps– Optimization

• Electrical components

• Piezoelectric placement

– Advanced Modeling• Wind tunnel walls

• Subcritical LCO

• Advanced electrical network

– New Prototype• Root piezoelectric clamping

• Specialized electronics housing

• SSHI circuit integration

Acknowledgements

Many thanks to the following individuals for their time, effort, and guidance in supporting this project:

Earl Dowell

Deman Tang

Brian Mann

Sam Stanton

Chad Gibbs

Pat McGuire

Casey Dunn

Results: Voltage Linearity Measures

Voltage Amplitude vs. Physical Amplitude Linear Fit of Voltage to Physical Amplitude

Ongoing Theoretical Work: Ducted Flow

First approximation of “stationary” mirror suggests that including

the wind tunnel wall may be necessary to accurately model the

flutter condition and LCO amplitude in ducted flow