# Numerical Assessment and Parametric Optimization of a Piezoelectric Wind Energy Harvester for IoT-Based Applications

^{1}

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## Abstract

**:**

^{−1}stiffness generates the optimum electrical response of the harvester.

## 1. Introduction

^{−}

^{1}wind speed [23]. In the recent past, the design of an energy harvester based on PZT-Stack has been proposed to observe the voltage-power characteristics of a piezoelectric transducer. A transition system is also noticed, which was used to transfer the mechanical vibration from the industrial machine to PZT-Stack and the harvester is capable of producing a voltage of 3.85 V [24]. Moreover, for the last few years, researchers have been developing optimized vibrational scavengers for harvesting wind energy. A mathematical model of the cantilever-based harvester is studied to analyze the interrelationships between piezoelectric voltage and parameters of wind energy. The influence of change in length and location of piezo patches on the harvester’s output is also observed. It is noticed that the output response of the harvester is maximum only when the resonant frequency of a cantilever matches the vortex shedding frequency. Furthermore, 1.02 W power is practically observed with the variation in the wind velocity ranging from 9–10 ms

^{−}

^{1}[25]. Theoretical analysis based on ten bimorph sensors has been investigated to observe the generated electrical energy from a prototype of the wind energy harvester. Interestingly, the harvester can produce sufficient energy even at a frequency range less than the resonant frequency of bimorph materials. A comparison between analytical and experimental design has been carried out, and 7.5 mW power is noticed at a wind speed of 4.47 ms

^{−}

^{1}[26]. An analytical model of the novel piezoelectric energy harvester is studied to investigate the electrical response after the flutter velocity. The designed harvester works on the non-linear aerodynamics’ principle, and thus, generated electrical energy is due to the excitations produced by limit cycle oscillations (LCOs). Additionally, the authors have checked the efficiency of the harvester by considering two different PZT materials; PZT-5A and Barium Titanate (BaTiO

_{3}). It is observed that the harvester based on PZT-5A generates more electrical output as compared to BaTiO

_{3}[27]. The performance of piezoelectric wind energy harvesters is highly dependent on the conversion of aerodynamic forces into accelerated mechanical vibrations. Therefore, a piezoelectric wind energy harvester based on the bluff body has been developed in which a transition from vortex-induced vibration to galloping is done by Y-shaped attachments. It is observed that the attachment of y-structures to the bluff body increases the amplitude of mechanical vibration. Consequently, the designed harvester produces sufficient electrical energy even at low wind speeds [28]. Zhang et al., utilized a concept of nonlinear magnetic forces to increase the output response of the energy harvester based on the vortex-induced vibrations. Interestingly, the authors have investigated the effect of the relative distance between the magnets on the natural frequency of the harvester [29]. The conversion of aerodynamic forces into a reliable form of electrical energy is highly dependent on a particular category of the energy harvester [30]. Therefore, in one of the articles, researchers have modeled torsional-flutter wind energy harvester and correspondingly analyzed the electrical efficiency by tuning the electromechanical nature of the harvester. Based on the outcomes, the authors have recommended utilizing this harvester for low-power applications [31]. Similarly, Elahi et al., worked on various mechanisms for the transformation of airflow into useful electrical energy by using piezoelectric sensors having applications in the field of structural health monitoring and self-powered IoT devices [32,33,34]. The concept of fluttering plays a vital role in determining the effectiveness of wind energy harvesters. Therefore, researchers have been trying to design and develop wind energy harvesters based on the flutter phenomenon [35,36]. A concept of fluid-structure interaction (FSI) is also getting popular in the designing of piezoelectric energy harvesters. Elahi et al. presented a cantilever-flag-based piezoelectric energy harvester that was analyzed by considering the PZT and aluminum (Al) patches to check the stability of the harvester. The design was simulated on MSC Nastran and the performance of the harvester was experimentally evaluated by varying the resistive load. The maximum electrical power was found to be 1.12 mW at an optimal resistive load of 66.6 kΩ [37]. Elvin et al. proposed a novel approach to analyze the fluctuations in the flutter speed and output voltage of the harvester for a passive PZT damping at time-variant loading conditions. It is observed that the open circuit stiffness increases the flutter speed of the designed harvester. Furthermore, the authors have justified that the electromechanical coupling coefficient plays a noteworthy role in determining the range of flapping behavior and is having a direct relationship to the electrical energy of the harvester [38]. Bae et al., analyzed the performance of a two-degree of freedom (DOF) wind energy harvester based on the piezoelectric technique. It is contemplated that the pitch-to-plunge and frequency ratios are the two important variables in acquiring the effective power density from a non-linear wind energy harvester. The authors demonstrated that linear wind energy harvester can generate electrical energy only in the range of flutter velocity. On the contrary, LCOs are obtained for a nonlinear energy harvester which in turn force the PZT material to generate sufficient voltage [39]. A novel approach to harvest wind energy is analyzed in which the turbine operates at a low Reynold’s number (2 × 10

^{4}) and an acceptable power coefficient is observed at the tip speed ratio of 0.7 [40]. Several optimization techniques are also investigated to improve the efficiency of the energy harvester [41,42]. One such method is based on optimizing the geometry of a cantilever beam, which is excited by lateral force to study different distributions of PZT layers. Finite element analysis (FEA) has been carried out on Ansys, and the verified model is also used to calculate the dissipated energy due to relative distributions of PZT beams [43]. Normally, the output response of the energy harvester does not produce enough voltage necessary to drive a wireless network. Therefore, the power quality enhancement circuit is also reported in the article in which authors have presented the static multicell converters to enhance and stabilize the electrical energy of wind energy harvesters [44]. Moreover, observations from the literature reveal that by minimizing the capacitive load on the PZT materials, the output response could be enhanced up to 95% as compared to energy obtained from conventional full-bridge rectifiers [45].

## 2. Analytical Model

_{B}) [46]. Besides that, in the recent past, J.X Tao and Q. Wang developed an analytical model for the piezoelectric wind energy harvester [47]. Therefore, in this research work, VEM is considered as a lever mechanism whose one end is fixed which is further divided into short and long moment arms denoted by ‘L

_{s}’ and ‘L

_{l}’ respectively. Additionally, it is also noticed that only harmonic motion is obtained by using RLC; therefore, it is necessary to utilize a combination of Hookean springs to attain useful mechanical vibration for the piezoelectric stack. Literature studies reveal that proof mass has a prominent role in displacing the structure to produce deformations in the piezoelectric materials. Researchers have already analyzed the piezoelectric energy harvester by varying the geometrical features of the proof mass. Therefore, in this research work, stiffness of VEM has been considered to analyze the performance of the piezoelectric wind energy harvester as shown in Figure 3. Furthermore, the magnifying ratio as given in Equation (2) plays a prominent role in the enhancement of alternative mechanical vibration for PZT-Stack.

## 3. Simulation and Analysis

## 4. Optimization Strategy for the Proposed Energy Harvester

#### Factorial Design of Experiment

## 5. Results and Discussions

#### 5.1. Outcomes of Simulation

^{−}

^{1}to 14 ms

^{−}

^{1}. This response of wind-PZT energy harvester is observed at the constant values of stiffness (40 Nm

^{−}

^{1}) and resistive load (50 Ω). Due to an increase in wind speed, the rotor of the windmill produces more rotational motion which will increase the amount of alternative mechanical vibrations obtained from the RLC mechanism. Therefore, the trendlines of Figure 7 show that the minimum speed at which the harvester produces sufficient energy is 1.5 ms

^{−}

^{1}, known as the cut-in speed of the energy harvester. Furthermore, it can also be observed that the wind speed has square and cubic relationships with the output voltage and power of the energy harvester respectively as shown in Figure 7 and Figure 8. Additionally, this analysis is accomplished through different trials based on the PZT thickness values of 2 mm, 4 mm, and 6 mm. It is found that PZT thickness has a positive linear impact on the response of wind energy harvester, which means that both output voltage and power will be increased with the values of PZT thickness.

^{−}

^{1}to 14 ms

^{−}

^{1}and Figure 8b shows the time-varying response in which the harvester produces a maximum output power of 1.8 W due to the dynamic input of wind speed. Additionally, it is also observed that under the specific condition of the input parameters, the electrical power is changed from 0.1705 to 1.757 W. One of the key reasons for this fluctuation is due to the external turbulences such as air pressure or temperature and air drag. Due to these reasons, average wind speed has been considered in the further analysis of the harvester to visualize the influence of piezoelectric transduction in harvesting wind energy.

^{−1}. It is observed that due to an increase in rotor angular velocity, the response of the energy harvester increases. When air particles move across the circular plane created by the number of blades, the thrust force is developed which in turn forces the rotor to produce some rotational motion. Since rotor velocity is directly related to wind speed, therefore, due to an increase in wind speed, the rotor rotates with higher angular velocity up to a certain limit known as the cut-out speed of the harvester. Consequently, mechanical vibration on PZT-Stack increases with rotor angular velocity, which in turn enhances the output response of the energy harvester as shown in Figure 9.

^{−}

^{1}, and for three blades, the rotor of the windmill rotates with an optimal velocity of 4.45 rads

^{−}

^{1}.

^{−1}to 45 Nm

^{−1}. The wind speed, PZT thickness, and resistive load are set to be 8.5 ms

^{−1}, 4 mm, and 50 Ω respectively. The trendlines of Figure 12b reveal that by increasing the stiffness, the amplitude of mechanical vibrations on PZT-Stack increases; consequently, it will enhance the output response of wind piezoelectric energy harvesters. Figure 12b also shows that after the stiffness value of 40 Nm

^{−1}, the response of the harvester increases exponentially which is satisfying the theoretical analysis of the harvester; therefore, this value is considered as an optimal VEM-Stiffness for the proposed energy harvester.

#### 5.2. Outcomes of Optimization Strategy

#### Pareto and Contour Charts for Dominant Factors

^{−1}), rotor-blades (3), and PZT thickness (3 mm).

#### 5.3. A State of the Art-Comparison

^{3}at 1.5 mm piezoelectric thickness.

## 6. Conclusions

^{−1}. Additionally, the response of the wind harvester was investigated by varying wind speed, rotor angular velocity, piezoelectric thickness, and VEM stiffness to observe the various parametric relationships of the harvester. It was noticed that the electrical efficiency of the harvester is highly dependent on the stiffness of the vibration enhancement mechanism (VEM). Finally, the full factorial design of the experiment (DOE) was implemented to statistically optimize the input parameters of the proposed wind energy harvester. The optimization results are in good agreement with the simulation, and literature outcomes. Therefore, based on the outcomes of the proposed work, it is recommended to develop and utilize this low-cost, efficient, and robust proposed harvester to power the sensor nodes in wireless networking.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

A | Rotor Cross Sectional Area |

C_{33} | Elastic Stiffness |

C_{p} | Piezoelectric Capacitance |

d_{33} | Piezoelectric Coefficient |

E_{33} | Piezoelectric Constant |

F_{p} | Equivalent Piezoelectric force |

K_{b} | Stiffness of VEM |

K_{p} | Stiffness of Piezoelectric layer |

L_{p} | Piezoelectric Stack’s Length |

L_{b} | Length of rotor blade |

t_{p} | Thickness of Piezoelectric Stack |

w_{p} | Piezoelectric Stack’s Width |

Z | Distance between slider and slotted rod |

Z_{e} | Equivalent Displacement |

${\mathrm{\u014b}}_{\mathrm{m}}$ | Magnifying Ratio |

A | Level of Significance |

Acronyms | |

DOE | Design of Experiment |

DOF | Degree of Freedom |

FSI | Fluid Structure Interaction |

LCO | Limit Cycle Oscillation |

MATLAB | Matrix Laboratory |

PZT | Lead Zirconate Titanate |

RLC | Rotary to linear Converter |

VEM | Vibration Enhancement Mechanism |

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**Figure 8.**The response of the harvester. (

**a**) Electrical power via wind speed, (

**b**) Time varying trends of the harvester.

**Figure 9.**The response of energy harvester via angular velocity of rotor. (

**a**) Output voltage, (

**b**) Output current.

**Figure 10.**Output response. (

**a**) Electrical power via angular velocity, (

**b**) Dynamic input-output of the harvester.

**Figure 11.**Measurement of output response of harvester via PZT thickness. (

**a**) Output voltage, (

**b**) Output current.

**Figure 14.**Variation of output voltage in response to dominant factors. (

**a**) Wind Speed-Piezoelectric Thickness, (

**b**) Piezoelectric Thickness-Stiffness of VEM.

Sr# | Parameters | Symbol | Unit | Values |
---|---|---|---|---|

1 | Elastic Stiffness | C_{33} | Nm^{−2} | 11.09 × 10^{10} |

2 | Radius of Rotor | R | m | 0.25 |

3 | Swept Area | A_{s} | m^{2} | 0.19 |

4 | Number of Blades | - | - | 3–5 |

5 | VEM Stiffness | K | Nm^{−1} | 10–40 |

6 | Proof Mass | m_{p} | kg | 0.5 |

7 | Piezoelectric Charge Constant | d_{33} | C/N | 450 × 10^{−12} |

8 | Piezoelectric Coefficient | g_{33} | m^{2}C^{−1} | 24 × 10^{−3} |

9 | Permittivity | Ɛ_{33} | Fm^{−1} | 706 × 10^{−11} |

10 | Density | ρ | Kgm^{−3} | 7750 |

11 | Piezoelectric Stack’s Length | L_{p} | mm | 10 |

12 | Piezoelectric Stack’s Width | w_{p} | mm | 20 |

13 | Piezoelectric Stack’s Thickness | t_{p} | mm | 0.5–4 |

Independent Factors | Unit | Low Level | High Level |
---|---|---|---|

Wind Speed | ms^{−1} | 5.5 | 8.5 |

Piezoelectric Thickness | mm | 1.5 | 3.0 |

Stiffness of VEM | Nm^{−1} | 30 | 40 |

Number of Blades | - | 3 | 4 |

Terms | Coefficient | SE Coeff. | t-Value | p-Value |
---|---|---|---|---|

Wind-Speed | 1.110 | 0.208 | 5.33 | 0.004 |

Piezoelectric Thickness | 1.727 | 0.208 | 8.29 | 0.001 |

Stiffness of VEM | 1.668 | 0.208 | 8.01 | 0.002 |

Number of blades | −0.740 | 0.208 | −3.55 | 0.005 |

Piezoelectric Thickness * Stiffness of VEM | 0.556 | 0.208 | 2.67 | 0.023 |

References | Authors | Publication Year | Approach | Piezoelectric Dimensions | Cut-In Speed | Output Power |
---|---|---|---|---|---|---|

[25] | Wu. N et.al. | 2013 | Analytical | 0.12 × 0.15 × 0.0125 m^{3} | - | 1.02 W @ 9 ms^{−1} |

[50] | Zhao. L et.al. | 2013 | Analytical | 61 × 30 × 0.5 mm^{3} | ~2.1 ms^{−1} | 40 mW @ 14 ms^{−1} |

[28] | Zhou. S et.al. | 2019 | Analytical and Experimental | - | 1.3 ms^{−1} | 1.2 mW @ 2.2 ms^{−1} |

[51] | Wei et.al. | 2020 | Analytical and Experimental | 46 × 10 × 1 mm^{3} | 2 ms^{−1} | 35.6 µW @ 5.45 ms^{−1} |

[52] | Wang. K et.al. | 2020 | Analytical and Numerical | 100 × 30 × 0.3mm^{3} | 6 ms^{−1} | 0.12 W @ 17–18 ms^{−1} |

[53] | Sitharthan. R et.al. | 2021 | Experimental | 0.00234 m^{3} | <3 ms^{−1} | 2.6 W @ 9–11 ms^{−1} |

[54] | Shi.T et.al. | 2021 | Experimental | - | ~2.1 ms^{−1} | 3 mW @ 4 ms^{−1} |

[55] | Silva et.al. | 2021 | Numerical and Experimental | 12.9 mm^{3} | - | 2.06 mW |

Proposed work | Sheeraz et.al. | - | Numerical | 10 × 20 × 3 mm^{3} | ~1.5 ms^{−1} | 2.622 W @ 8.5 ms^{−1} |

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**MDPI and ACS Style**

Sheeraz, M.A.; Malik, M.S.; Rehman, K.; Elahi, H.; Butt, Z.; Ahmad, I.; Eugeni, M.; Gaudenzi, P.
Numerical Assessment and Parametric Optimization of a Piezoelectric Wind Energy Harvester for IoT-Based Applications. *Energies* **2021**, *14*, 2498.
https://doi.org/10.3390/en14092498

**AMA Style**

Sheeraz MA, Malik MS, Rehman K, Elahi H, Butt Z, Ahmad I, Eugeni M, Gaudenzi P.
Numerical Assessment and Parametric Optimization of a Piezoelectric Wind Energy Harvester for IoT-Based Applications. *Energies*. 2021; 14(9):2498.
https://doi.org/10.3390/en14092498

**Chicago/Turabian Style**

Sheeraz, Muhammad Abdullah, Muhammad Sohail Malik, Khalid Rehman, Hassan Elahi, Zubair Butt, Iftikhar Ahmad, Marco Eugeni, and Paolo Gaudenzi.
2021. "Numerical Assessment and Parametric Optimization of a Piezoelectric Wind Energy Harvester for IoT-Based Applications" *Energies* 14, no. 9: 2498.
https://doi.org/10.3390/en14092498