Multi-physics Simulation of a Wind Piezoelectric Energy Harvester Validated by Experimental Results Giuseppe Acciani, Filomena Di Modugno, Ernesto Mininno, Pasquale Montegiglio giuseppe.acciani@poliba.it, filomena.dimodugno@poliba.it, ernesto.mininno@poliba.it, pasquale.montegiglio@poliba.it

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Results/3 Time (s) Electric potential (V) 0.4 0.00996 0.6 0.01102 0.8 0.01107 1 0.01109 1.2 0.01118 1.4 0.01136 1.6 0.01212 1.8 0.01207 2 0.01275 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

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

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