Aeroelastic Limit Cycles As A Small Scale Energy Source

Transcription

1 Aeroelastic Limit Cycles As A Small Scale Energy Source Jared Dunnmon 8 th Int. Conf. on Multibody Systems, Nonlinear Dynamics, and Control Advised by Professor Earl Dowell, Duke University August 29, 2011

2 The Idea: Research Concept and Goals Utilize aeroelastically induced 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

3 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

4 Experimental Demonstration: Pre-Flutter Behavior at 30 m/s

5 Experimental Demonstration: Post-Flutter Behavior at 31.5 m/s

6 Experimental Demonstration: Frequency Matched Behavior at 27 m/s

7 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

8 Modeling: Basic Equations Coupled Nonlinear ODEs for Aeroelectroelastic Beam and Electrical Circuit Nonlinear Inertial Forces Mass Matrix Nonlinear Curvature Force State Space Discretization of ODE System and Coupling to Vortex Lattice Aerodynamics Full Aeroelectroelastic State Space Equation

9 Modeling: Basic Equations Coupled Nonlinear ODEs for Aeroelectroelastic Beam and Electrical Circuit State Space Discretization of ODE System and Coupling to Vortex Lattice Aerodynamics Full Aeroelectroelastic State Space Equation

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

11 Results: Frequency Measures FFT of Experimental Signal FFT of Theoretical Signal Frequency vs. Amplitude

12 Results: Amplitude Measures Amplitude vs. Velocity Experimental Strain vs. Velocity

13 Results: Voltage Time Histories Experimental Voltage Time History Theoretical Voltage Time History

14 Results: Power Extraction Measures Power Extracted vs. Physical Amplitude Power Extracted vs. Resistance (U=27 m/s)

15 Results: Efficiency Measures Capture efficiency estimated by the following equation: Capture Efficiency vs. Physical Amplitude Remains approximately constant over all observed amplitudes Promising potential for a harvester that operates efficiently over a large velocity band

16 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

17 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

18 Results: Voltage Linearity Measures Voltage Amplitude vs. Physical Amplitude Linear Fit of Voltage to Physical Amplitude

19 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