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PIEZOAEROELASTIC
         ENERGY HARVESTING

                     Vagner Candido de Sousa – vagner@sc.usp.br
                                   Aeronautical Engineering Department
                                          Sao Carlos Engineering School
                                         University of Sao Paulo – Brazil




                    PASI Workshop 2012
Computational 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

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  me )h  d h h  k h h  v p   L
                          
                                           l

          vp
C vp 
  
  eq
  p             h  0
                  
          Rl
State-space representation

I   0   0    0  x        0         I     0         0  x 
0            0          K                                

     
     M   0         x     
                                       B    D       Θs   x 
                                                              
0                   
     0   I    0  x a       E1       E2     F         0  x a 
              eq                                           
0
    0   0         
             C p  v p      0        Θe     0      1 / Rl   v p 

           0          I            0               0           
        M 1K
                      
                    M 1B         
                                   M 1D         
                                                M 1Θ s         
       
     A                                                        
          E1          E2            F                0          
                                                               
       
           0     1 / C  Θ
                       eq
                       p       e    0      1 / C p  (1 / Rl ) 
                                                  eq
                                                                

                    
                    x  Ai x  a i
                          
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
                             I   ( I   b(c  a ) S  )   S h  d   k   f fp ( )  M 
                                                                    
                                           k  fp          fp
                                         
                             f fp ( )      0          fp     fp
                                          k                fp
                                           fp
2-DOF with bilinear spring




                                                                      3-DOF with bilinear spring




                              Sousa et al., 2011, Smart Mat. Struc.

                                                                                                   3-DOF: Power with airspeed (70% ~ 98% ULF)
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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Piezoaeroelastic Energy Harvesting

  • 1. PIEZOAEROELASTIC ENERGY HARVESTING Vagner Candido de Sousa – vagner@sc.usp.br Aeronautical Engineering Department Sao Carlos Engineering School University of Sao Paulo – Brazil PASI Workshop 2012 Computational Material Science for Energy Generation and Conversion January 9 – 20, Santiago, Chile
  • 2. 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
  • 3. 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)
  • 4. 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)
  • 5. Piezoaeroelastic equations of motion 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  me )h  d h h  k h h  v p   L     l vp C vp   eq p  h  0  Rl
  • 6. State-space representation I 0 0 0  x   0 I 0 0  x  0 0      K      M 0  x     B D Θs   x    0   0 I 0  x a   E1 E2 F 0  x a   eq     0  0 0   C p  v p   0 Θe 0 1 / Rl   v p   0 I 0 0   M 1K     M 1B  M 1D  M 1Θ s   A  E1 E2 F 0      0 1 / C  Θ eq p e 0 1 / C p  (1 / Rl )  eq   x  Ai x  a i  
  • 8. 2-DOF Linear piezoaeroelastic response • Load resistances (Rl): 102, 103, 104, 105 and 106 Ω 2-DOF ULF = 12 m/s
  • 10. 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
  • 11. Nonlinear model • Structural nonlinearities can induce subcritical LCOs • The linear torsional spring is replaced by a bilinear spring I   ( I   b(c  a ) S  )   S h  d   k   f fp ( )  M        k  fp    fp  f fp ( )   0  fp     fp  k     fp   fp 2-DOF with bilinear spring 3-DOF with bilinear spring Sousa et al., 2011, Smart Mat. Struc. 3-DOF: Power with airspeed (70% ~ 98% ULF)
  • 12. 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
  • 13. Thank you! Questions? • The author gratefully acknowledge – PASI 2012 CMS4E organizing committee – CNPq