PIEZOAEROELASTICENERGY HARVESTING
Vagner Candido de Sousa – [email protected] Engineering Department
Sao Carlos Engineering SchoolUniversity of Sao Paulo – Brazil
PASI Workshop 2012Computational Material Science for Energy Generation and Conversion
January 9 – 20, Santiago, Chile
Outline
• Vibration-based energy harvesting• E.H. from aeroelastic vibrations• Piezoelectrically coupled airfoil typical section
• Case Studies– Linear model (interaction power - aeroelastic response)– Nonlinear model (broadband generation)
• Conclusions
Vibration-based energy harvesting
• Motivation– Vibrations are available in the environment– Additional (long-term) power source– Reduced power requirement of small devices
• Flow-induced energy harvesting– Aeroelastic vibrations– Potential application: UAV
• Piezoelectric transduction (direct effect)
Airfoil section for energy harvesting
2-DOF (Erturk et al., 2010) 3-DOF (Tang and Dowell, 2010)
• DOFs: plunge (h), pitch (α) and control surface rotation (β)
Piezoaeroelastic equations of motion
( ( ) )
( ( ) )
( )
0
e h h p
peqp p
l
I I b c a S S h d k M
I b c a S I S h d k M
S S m m h d h k h v Ll
vC v h
R
State-space representation
1 2
1/
s
a aeqp p pe lC v vR
I 0 0 0 x x0 I 0 0
0 M 0 0 x xK B D Θ
0 0 I 0 x xE E F 0
0 0 0 0 Θ 0
1 1 1 1
1 2
1/ 1/ (1/ )
s
eq eqp e p lC C R
0 I 0 0
M K M B M D M ΘA E E F 0
0 Θ 0
i i x A x a
The experimental system
2-DOF Linear piezoaeroelastic response
• Load resistances (Rl): 102, 103, 104, 105 and 106 Ω
2-DOF ULF = 12 m/s
2-DOF Linear piezoaeroelastic response
The “linear problem”
• U∞ < ULF: damped oscillation
• U ∞ > ULF: growing amplitudes of oscillation
• U ∞ = ULF: the ideal scenario for energy harvesting
– U ∞ = ULF is a very particular situation
• Nonlinear model– Opportunity for persistent power generation
Nonlinear model
• Structural nonlinearities can induce subcritical LCOs• The linear torsional spring is replaced by a bilinear spring
Sousa et al., 2011, Smart Mat. Struc.
( ( ) ) ( )
( ) 0
fp
fp fp
fp fp fp
fp fp
I I b c a S S h d k f M
k
f
k
3-DOF: Power with airspeed (70% ~ 98% ULF)
2-D
OF
with
bili
near
spr
ing
3-D
OF
with
bili
near
spr
ing
Summary and conclusions
• Piezoaeroelastically coupled typical section for energy harvesting
• Harvests energy from linear and nonlinear aeroelastic vibrations
• Nonlinear aeroelastic phenomena can provide persistent power generation in a wide range of airflow velocities
Thank you! Questions?
• The author gratefully acknowledge– PASI 2012 CMS4E organizing committee– CNPq
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