1. Multi-physics Simulation of a Wind Piezoelectric Energy Harvester Validated by Experimental Results
Giuseppe Acciani, Filomena Di Modugno, Ernesto Mininno, Pasquale Montegiglio

2. Summary Aim of the paper; Simulations; Definitions; Results;
State of art;
Ongoing Research;
Experimental setup;
Conclusion.
Mathematical model;
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

3. Aim of the paper
The aim of this paper is to evaluate the experimental and simulated behaviour and performances of an energy harvester, with the shape of a piezoelectric cantilever beam, subjected to wind induced-vibrations.
The comparison between experimental and simulated data validates the simulation method.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

4. Definitions
Energy Harvesting (EH): “Capturing minute amounts of energy from one or more of the surrounding energy sources, accumulating them and storing them for later use”. (Heung Soo, Joo-Hyon, Jaehwan)
Piezoelectric materials: smart materials able to convert mechanical energy into electric one because of the direct piezoelectric effect.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

5. State of Art
In recent years, many EH techniques using piezoelectric materials and cantilever beams, both in large and small-scale, have been developed.
A great interest is directed to piezoelectric transducers stressed by natural vibrations, such as those induced by rain or wind.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

6. State of Art/2
The studies about harvester devices are often sustained by suitable simulations to accurately reproduce the transducers and their behaviour under induced- vibrations.
The earliest simulations were based on the isolated observation of a single physical phenomenon.
In the last years, sophisticated software packages, based on Finite Element Method (FEM), are able to reproduce multiphysics phenomena, as they really fulfill in nature.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

7. Experimental Setup Oscilloscope, anemometer, cantilever beam
Anemometer as seen from above and wind direction
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

8. Experimental Setup/2 Structure of cantilever beam
Parameter
Value
Unit
Silver Layer
Short length B 30 mm
Width 12
Thickness
6+6 µm
PVDF
Length A 41 28
Piezo Strain Constant d31
23E-12
C/N
Piezo Strain Constant d33
-33E-12
Piezo Stress Constant g31
216E-3
Vm/N
Piezo Stress Constant g33
-330E-3
Electromechanical coupling factor k31
0.12
Plastic coat
Negligible
Structure of cantilever beam
Properties and dimensions of Cantilever Beam
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

9. Mathematical Model Fluid Model
Based on the Reynolds Averaged Navier-Stokes (RANS) formulation with the k- model for turbulent flow.
Described by the Navier-Stokes equations, the continuity equation for incompressible flow and the transport equation for k and .
Fluid density
Fluid velocity
Fluid dynamic viscousity p
Fluid pressure
Turbulent kinetic energy F
External forces applied
turbulent dissipation rate μT
turbulent viscosity
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

10. Mathematical Model/2 Solid Mechanics Model
stress
Volume forces u
Velocity of solid
Electric displacement
Elasticity matrix
Dielectric matrix e
Piezoelectric matrix
transpose matrix
Electromechanical coupling Model
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

11. Simulations
Comsol Multiphysics is the software environment used to simulate experimental situations.
The interaction air-cantilever and the piezoelectric effect were simulated using three different physics environment of Comsol Multiphysics: the Fluid-Structure Interaction, the Solid Mechanics and the Electrostatics.
The cantilever was built with the same shape, dimensions and materials of that used in experimental setup. It reacts to fluid-wind pressure with a deformation, which develops electric potential.
SILVER
SILVER
PVDF
Details of cantilever beam
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

12. Simulations/2 A rectangular wind channel is set;
the wind is studied as air that flows in the channel;
the wind enters through inlet in the channel with an initial velocity, moves with a turbulent flow, and leaves the channel through outlet;
The fluid interacts with the cantilever beam, deforming it.
channel
outlet
inlet
Cantilever beam
Channel and cantilever beam
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

13. Simulations/3 Boundary conditions
The cantilever is ‘free’ to move except for its lowest surface that is locked;
the channel is completely fixed;
the input for the model is the inlet fluid velocity with a direction normal to the inlet surface. Input wind velocities are the same detected by the anemometer in the experimental setup;
The initial condition for fluid velocity and solid displacement fields are both set to zero;
a zero pressure boundary condition is applied at the outlet section.
locked
Inlet fluid velocity
Channel and cantilever beam
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

14. Simulations/4
Mesh
The most difficult aspect inherent the simulation described was the creation of a good mesh.
The aspect ratio of the experimental piezoelectric cantilever beam has the magnitude order of 103 : a good mesh needs elements with aspect ratio close to unity.
A too refined mesh has a good quality but requires too long computational time.
Minimum mesh quality: an important parameter to build a good mesh. A number between 0 and 1. An acceptable mesh quality is larger than 0.1.
Mesh quality
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

15. Simulations/5 Adopted Strategies
Simulation of a two-dimensional and not a three-dimensional system;
aspect ratio closed to 15 was considered good.
the cantilever beam was implemented with a mapped structured mesh of 450 elements on the longest dimension.
Free triangular and mapped mesh
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

16. Results Simulation of 2 [s] with initial velocity of 1.4 [m/s]
Von Mises stress and the velocity magnitude

17. Results/2 Cantilever deformation under wind effect
Electric potential developed
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

18. Results/3 Time (s) Electric potential (V) 0.4 0.00996 0.6 0.01102 0.8 1
1.2
1.4
1.6
1.8 2
Average Electrical Potential Values (wind velocity = 1.4 [m/s])
Comparison between measured and simulated data
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

19. Ongoing Research Limits Investigating improvements
Problems with convergence of FEM simulation for initial velocity higher than 2.0 [m/s];
High noise for input data.
Investigating improvements
Higher iteration numbers for solutors of FEM simulations;
Bigger dimensions of the channel than actual;
Different experimental apparatus.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio

20. Conclusion
The paper proposes a model and simulation of a piezoelectric cantilever beam as energy harvester to expose to wind vibrations.
The comparison between experimental and simulated data validates the simulation method.
The paper suggests an improvement on the existing literature because of the inclusion of an extended and numerical model for the multiphysics interaction between fluid and piezoelectric device, with experimental validation.
Multi-physics Simulation of a Wind Piezoelectric Energy Harvester
Validated by Experimental Results
Acciani, Di Modugno, Mininno, Montegiglio