PIEZOAEROELASTICENERGY HARVESTING

Vagner Candido de Sousa – vagner@sc.usp.brAeronautical 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