Galloping-based Energy Harvester Research Articles

Effect of Nonlinear Magnetic Forces on Transverse Galloping Dynamics of Square Cylinders

Under the influence of cross-fluid flow, a cylinder of a square cross-section may gallop. Galloping is a self-excited vibration mode that can be utilized for low-power harvesting applications. The harvested power depends on several factors, including upstream flow velocity and system dynamics. This study explores the potential of magnetically-induced nonlinear stiffness to improve the power output of galloping-based energy harvesters. In this experimental study, the vibration response of a square rod with a mass ratio of 10 is investigated at a Reynolds number of 200. The vibration behavior of two identical coaxial square rods with magnetic monopoles at opposite ends is analyzed. Results reveal that the magnets’ configuration and strength significantly affect vibration amplitude and the critical flow velocity necessary for the onset of galloping.

Performance enhancement of a galloping-based energy harvester with different groove depths on square bluff body

This paper focuses on the effects of a V-shaped groove depth on the performance of a galloping-based energy harvester. The study simulated air flow over cylindrical, square, and different depth grooved square bluff bodies using a computational fluid dynamics program with a user defined function added. An experiment using the particle-image velocimetry technique in a closed-loop wind tunnel was also conducted to validate and explain the results. The results show that the energy harvester and square bluff body with a ratio of 0.25 groove depth to the side generated the most power of 15.24 mW, which is 1.34 times higher than the power generated by the square bluff body at 9 m/s wind speed. This is because the groove on the windward side of the square bluff body increased the striking area of the fluid force and triggered the formation of a large vortex beside the bluff body. This results in a larger vibration amplitude and in an increased generation of electrical power. The discrepancy between the simulated and experimental results was also discovered to be due to a twist of the bluff body and hence a common used one-dimension oscillation assumption might be invalid.

An enhanced galloping-based piezoelectric energy harvester with non-rotational bluff body

This study proposes a bluff body non-rotational galloping-based piezoelectric wind energy harvester (BNRGH) for overall output performance enhancement. The bluff body used in this structure is designed to be available to rotate with respect to the free end of two cantilever beams by the connection of rotatable hinges. A series of performance comparisons are conducted experimentally in a wind tunnel between the proposed structure and the conventional galloping-based piezoelectric energy harvester, which commonly configured with a single beam. The results show that the proposed structure is capable of preventing the variation of the attack angle due to the self-rotation of the bluff body caused by the deflection of a common single beam, thus avoiding the amplitude saturation of the bluff body at a higher wind velocity range. It shows that the output voltage remains a continuous linear increase within elastic deformation range of the cantilever beam even in higher wind velocity range, which is helpful in accomplishing a broad wind range for a significant improvement of the overall performance. Overall, the proposed BNRGH provides a design guidance for a small size galloping-based energy harvester to achieve an excellent output performance, which holds great potential to promote its application in wireless node networks for self-power supply.

Performance investigation of a crossing angle adjustable galloping-based energy harvester

In this study, we proposed a crossing angle adjustable galloping-based piezoelectric energy harvester (CAGPEH) configured with a lambda-shaped beam to improve the energetic performance. The proposed structure can overcome the limitation of the installation capability of a conventional galloping energy harvester with a single cantilever beam by varying the crossing angle. This structure can change the crossing angle between primary and secondary beams so that the bluff body always faces the changing wind direction to ensure an efficient harvesting performance. A distributed parameter model was established using Euler-Bernoulli beam theory and Lagrange method, and a series of numerical analyses was performed to uncover the dynamical behaviors of the aero-electromechanical coupled system. The first two modes were considered to obtain a comprehensive understanding of the dynamic behaviors at different crossing angles. We validated the theoretical model through amplitude and output voltage comparisons between numerical and experimental results. The results show that a larger crossing angle and a smaller length proportional factor of the primary and secondary beams help reduce the critical wind velocity. The results show that a significant increase rate of 103% in the overall average output power (OAOP) can be achieved with a crossing angle of 30° and a proportional factor of 0.6. It is expected that the CAGPEH can help develop self-power systems for applications in wireless sensor systems.

Performance Enhancement of a Galloping-Based Energy Harvester with Different Groove Depths on Square Bluff Body

Performance Enhancement of a Galloping-Based Energy Harvester with Different Groove Depths on Square Bluff Body

A unified equivalent circuit and impedance analysis method for galloping piezoelectric energy harvesters

In the past decade, galloping-based energy harvesters (GPEH) connected with various interface circuits have been developed and analytical models have been built. However, the power performances of these advanced structures and circuits are always treated separately, and a general model is missing to gain insights at a system level. To tackle this issue, this paper proposes a unified analysis framework for GPEHs. Its results are consistent with validated (but disconnected) results in the literature. The method provides an integrated view of the physics of linear GPEHs in multiple domains at the system level, and elucidates the similarities and differences among power behaviors of GPEHs connected with various interface circuits. The framework is based on two major elements: an equivalent circuit that represents the entire system, and an equivalent impedance that represents the interface circuit. Firstly, the electromechanical system is linearized and modeled in the electrical domain by an equivalent self-excited circuit with a negative resistive element representing the external aerodynamic excitation, and a general load impedance representing the interface circuit. Then, a closed-form, analytical expression of the harvested power is obtained based on the Kirchhoff’s Voltage Law, from which the optimal load, maximum power, power limit, and critical electromechanical coupling (minimum coupling to reach the power limit) are determined. In this unified analysis, the exact type of energy harvesting interface circuit is not assumed. After that, the power characteristics of a GPEH connected with five representative interface circuits are analytically derived and discussed, by using the particular equivalent impedance of the interface circuit of interest. It is shown that they are subjected to the same power limit. However, the critical electromechanical coupling depends on the type of circuit. Throughout the discussions, impedance plots are used to illustrate the relationship between the internal system characteristics and external load impedance, facilitating the understanding of system power behavior.

Improving the performance of wind energy galloping harvesting with magnetic coupling

In a realistic environment, the wind speed generally is relatively low, which impedes the further promotion of energy harvesting efficiency. This letter proposes an advanced monostable galloping-based energy harvester (AM-GEH), in which magnetic coupling is introduced to improve harvesting efficiency. By arranging a magnet at the beam tip and three magnets on the arch-shaped fixture, the stiffness of the structure will be softened, which is beneficial for generating large-amplitude deflection for low-speed wind. It is designed so that the middle magnet provides a repulsive force, while the magnets at the two sides provide attractive forces. The combined forces could make the system keep a monostable one, but with a wide flat potential energy. The parameter analysis is carried out to investigate the influence of wind speed and impedance on the output power. For validation, corresponding experiments were carried out. We compare this configuration with the linear galloping-based energy harvester (L-GEH) and the weak-coupled monostable galloping-based energy harvester (WM-GEH). The experimental results show that the cut-in wind speed of AM-GEH is decreased by 55% and 18.2%, respectively, and its RMS voltage is increased by 69.92% and 14.7%, respectively.

Magnetically coupled piezoelectric galloping-based energy harvester using a tandem configuration

Herein, we propose a piezoelectric galloping-based energy harvester that uses a magnetic coupling effect to improve its energetic performance. This proposed structure includes two elastic structures with bluff bodies arranged in a tandem configuration and a pair of repulsive magnets installed between the two bluff bodies to enable the use of their mutual interaction. A nonlinear coupled aero-electro-mechanical model is established using the extended Hamilton principle to gain a comprehensive understanding of the nonlinear dynamic behaviors of the proposed system. The mechanism of the magnetic interaction between the outer and inner bluff bodies was thoroughly investigated through time histories, phase portrait, and frequency spectrum analysis. The experimental results exhibited good agreement with the analytic results, highlighting that the present model is considerably accurate and reliable. Compared with the conventional system without the engagement of the magnetic coupling effect, a maximum overall average output power of 8.09 mW and power improvement rate of 65% could be obtained for the proposed energy harvesting system with the optimal magnetic gap distance. The proposed energy harvesting system is expected to be a promising alternative for the convenient and practical development of efficient wind energy harvesters.

Effects of side ratio on energy harvesting from transverse galloping of a rectangular cylinder

Rectangular cylinders have been identified as ideal bluff bodies for galloping-based energy harvesting, while a systematic study of the effects of the side ratio (i.e., the ratio between the cylinder width and the cylinder height) remains unavailable. This study investigates the influences of the side ratio on the piezoelectric energy harvesting from the transverse galloping of a rectangular cylinder based on a representative electro-aero-mechanical model, in which the aerodynamic force is calculated by the quasi-steady theory. The existing experimental aerodynamic coefficients for rectangular cylinders with side ratios of 0.62–3.0 are utilized as inputs of the quasi-steady aerodynamic force model. The influences of the side ratio and load resistance on the onset velocity, displacement, and power output of the galloping-based energy harvester are investigated. The results show that the onset velocity of galloping is dependent on the load resistance while this dependency becomes less significant with increasing the natural frequency. The onset galloping velocity of the energy harvester decreases with increasing the side ratio, and the lowest onset velocity is achieved by a rectangular cylinder with a side ratio of around 2.50. The largest vibration amplitude is achieved by the cylinder with a side ratio of 1.62 or 2.0 at low flow velocities, while the largest vibration amplitude is always achieved by the square cylinder at high flow velocities. Therefore, the side ratio of a galloping-based energy harvester should be designed according to its working environment: the optimal side ratio is around 1.0 if the harvester is expected to work at relatively high reduced flow velocities, while the optimal side ratio is around 1.62–2.0 if the harvester is expected to be effective at relatively low reduced flow velocities. These conclusions can provide references for designing galloping-based energy harvesters with rectangular cylinders as bluff bodies.

Experimental and Theoretical Study on Energy Harvesting Performance of Galloping-Based Energy Harvester Using Rotationally Oscillating Blade

Experimental and Theoretical Study on Energy Harvesting Performance of Galloping-Based Energy Harvester Using Rotationally Oscillating Blade

Investigation of transverse galloping in the presence of structural nonlinearities: theory and experiment

We formulate and experimentally validate a theoretical reduced-order model for the transverse galloping of nonlinear structures, namely a pair of identical, parallel-oriented cantilever beams whose free ends are attached to square prisms. We derive the structural nonlinearities from (a) a single-mode approximation of the nonlinear (truncated at cubic order) equation of motion, calculated for conservative cantilever beams augmented by a non-conservative aerodynamic force acting on a prism; and (b) phenomenological linear, quadratic, and cubic damping forces. We estimate the coefficients of the damping forces from the ring-down responses of the structures in still air. We analyze the deterministic dynamics of transverse galloping that stem from the aerodynamic force of the quasi-steady theory, and the stochastic effect of spectral line broadening that stem from turbulence-induced random fluctuations. Our findings clearly show that standard nonlinear macroscopic structures exhibit considerably different steady-state response curves than the universal curve of Parkinson obtained for linear mass–spring–damper structures. Importantly, the amplitudes of the oscillations are attenuated at high upstream velocities due to nonlinear damping, while the spectral line broadens due to turbulence-induced random fluctuations and an amplitude-to-phase noise conversion, which lowers the quality of the self-sustained oscillations. These two phenomena should be considered in the design of efficient transverse galloping-based energy harvesters—a rapidly growing field of research.

Enhancement of low-speed piezoelectric wind energy harvesting by bluff body shapes: Spindle-like and butterfly-like cross-sections

Fluid-structure interaction can be utilized to harvest the low-speed wind energy for sustaining the low-power sensors for structural health monitoring. To enhance the low-speed wind energy harvesting, this study proposes the novel spindle-like and butterfly-like bluff bodies by coupling both the vortex-induced vibration (VIV) and galloping phenomena. Comprehensive wind tunnel experiments are conducted to investigate the advantages of the two bluff bodies in terms of the bluff body cross-sections and installment directions. The experimental results demonstrate that for both the spindle-like and butterfly-like bluff bodies, the vertical installment and small width ratio are beneficial to the performance in a broad range of wind speeds. Compared to a conventional galloping-based energy harvester, owing to the coupling between the VIV and galloping, the vertical spindle-like bluff body with the smallest width ratio can reduce the threshold wind speed of activating the energy harvesting function by over 13%, and improve the maximum voltage output by over 160%. Finally, taking the spindle-like bluff body as an example, the computational fluid dynamics (CFD) studies are conducted by using XFlow software to interpret the physical insight of performance enhancement. The CFD results show that the vertical installment direction and a small width ratio play an important role. The two designs can lead to a stronger aerodynamic force due to the fast vortex shedding, which improves the energy conversion efficiency from the flow-induced vibrations.

Theoretical aspects of synchronization in transverse galloping aeroelastic instability

We investigate, for the first time to the best of our knowledge, theoretical aspects of synchronization in transverse galloping aeroelastic instability. The current study is a generalization of previous studies that considered the dynamics of a single-cylinder, and therefore, precluded the option to study synchronization. Here, we consider both the deterministic and stochastic dynamics of a system comprising two weakly coupled cylinders, which are attached to the ground with linear springs and dashpots, and are immersed in a high velocity airstream. We derive the conditions for the instability threshold. We give a detailed and simplified procedure to compute the amplitudes, phase differences, and frequencies of the synchronized solutions. We calculate quantitative measures of the amplitude and phase noises, including an explicit calculation of the phase noise reduction due to synchronization, which can enhance the performance of transverse galloping-based energy harvesters. Furthermore, we provide simple mappings for the amplitudes and phase difference dynamics, which we show to be highly useful for understanding both the deterministic and the stochastic dynamics of the amplitudes and the phase difference dynamics from geometric point of view.

A double-beam piezo-magneto-elastic wind energy harvester for improving the galloping-based energy harvesting

This study investigates the performance of a double-beam piezo-magneto-elastic wind energy harvester (DBPME-WEH) when exhibiting a galloping-based energy harvesting regime under wind excitation. The DBPME-WEH comprises two piezoelectric beams, each of which supports a prism bluff body embedded with a magnet at the tip. The magnets are oriented to repulse each other to introduce a bistable nonlinearity. Wind tunnel tests were conducted to compare performances of the DBPME-WEH and a double-beam piezoelectric wind energy harvester (DBP-WEH) that does not comprise the magnet-induced nonlinearity. The results reveal that compared to the DBP-WEH, the critical wind speed to activate the galloping vibration of DBPME-WEH can be reduced up to 41.9%. Thus, the results corroborate the significant performance enhancement by the DBPME-WEH. It can also be found that the distance of the two magnets affects the performance and the distance that achieves the weakly bistable nonlinearity is beneficial to energy harvesting in reducing the critical wind speed and improving the output voltage.

Effects of Electrical and Electromechanical Parameters on Performance of Galloping-Based Wind Energy Harvester with Piezoelectric and Electromagnetic Transductions

This paper presents an analysis of galloping-based wind energy harvesters with piezoelectric and electromagnetic transductions. The lumped parameter models of the galloping-based piezoelectric energy harvester (GPEH) and galloping-based electromagnetic energy harvester (GEMEH) are developed and the approximate analytical solutions of the equations are derived using the harmonic balance method (HBM). The accuracy of the approximate analytical solutions is validated by the numerical solutions. A parametric study is then conducted based on the validated models and solutions to understand the effects of the dimensionless load resistance, r, and electromechanical coupling strength (EMCS) on various quantities indicating the performance of the harvesters, including the dimensionless oscillating frequency, cut-in wind speed, displacement, and average power output. The results show that both r and EMCS can affect the dimensionless oscillating frequencies of the GPEH and GEMEH in a narrow frequency range around the natural frequency. A significant decrease in the displacement around r = 1 for GEPH and at a low r for GEMEH indicates the damping effect induced by the increase in EMCS. There are two optimal r to achieve the maximal power output for GPEH given strong EMCS while there is only one optimal r for GEMEH. Both GPEH and GEMEH show similar characteristics in that the optimal power outputs can reach saturation with an increase of the EMCS. The findings from the parametric study provide useful guidelines for the design of galloping-based energy harvesters with different energy conversion mechanisms.

Novel modeling of circular piezoelectric devices as vibration suppresser and energy harvester

In this paper, a simple model for circular piezoelectric energy harvester is theoretically and experimentally studied. For this reason, vibration behavior of a circular piezoelectric device, which simply called piezoelectric buzzer, is modeled as a changeable cross-section beam. A new quartic polynomial function is introduced to precisely describe the vibratory behavior of the circular piezoelectric device. The obtained electromechanical equations of motion are experimentally validated. As a case study, application of the presented circular piezoelectric device is studied when it is used in a galloping-based energy harvester. Finally, the optimized parameters of the presented energy harvester and vibration suppressor are presented and its efficiency is studied.

Improving application of galloping-based energy harvesters in realistic condition

In this study, the electromechanical equation of motion for a galloping-based energy harvesting system is derived and experimentally validated. This system consists of a bluff body that elastically mounted in fluid flow and a piezoelectric energy harvesting device, which is placed inside it. To confirm dynamic behavior of the system in fluid flow, periodic response of the variables is analytically obtained by employing the harmonic balance method. The validated equations are used to study effect of changing the system parameters on electromechanical behavior of the energy harvester. Then, application of the system is investigated in a realistic condition. Employing several user-oriented charts, the energy harvesting system is optimized and it is shown that this system can optimally be used in normal wind speed.

Role of the galloping force and moment of inertia of inclined square cylinders on the performance of hybrid galloping energy harvesters

Energy harvesting by a square cross-section cylinder, inclined at different angles from the incoming wind flow, prone to galloping oscillations is investigated. The cylinder is fixed at the tip of a cantilever beam at a definite angle, to which is attached a piezoelectric layer and a permanent magnet placed in the close vicinity of a coil. Existing aerodynamic-coefficient experimental values as a function of the incident angle of attack are utilized for determining the aerodynamic force on each inclined cylinder. Seven-order polynomial is recognized to be a convenient choice for performing the analyses in this study. After establishing the galloping aerodynamic force of each case, a reduced-order model is developed for the beam-cylinder energy harvester using Galerkin discretization. Moment of inertia of each case is calculated using transformation matrix and its impact on the natural frequency is determined. It is shown that the moment of inertia affects the linear characteristics of the galloping-based energy harvester when the inclination of the cylinder is changed. The nonlinear characteristics and performance of the energy harvester for various inclination angles are carried out. It is indicated that an upright zero inclined or a slight angle of cylinder till ten or fifteen degrees towards the wind flow is preferable for energy harvesting. Any forward inclination towards the wind flow greater than that or any backward angle of cylinder away from the wind flow are not suitable for attaining high levels of harvested power. This behavior actually opens the doors for using a movable cylinder at the tip of a beam with lock mechanism that can be tilted at a high forward or backward angle for extreme windy conditions to have reasonable practical power harvesting without damaging the harvester.

Galloping-based energy harvester considering enclosure effect

A galloping-based energy harvester, which is surrounded by structure(s) such as an enclosure, has an aerodynamic force change due to a change in flow caused by movement of the bluff body against the structure(s). Therefore, any model derived without considering this effect cannot predict the harvester’s behavioral or energetic characteristics accurately. The main goal of this study was to develop a model that could be used to accurately simulate a galloping-based energy harvester surrounded by an enclosure. To consider the effect of the enclosure on the aerodynamic force applied to the bluff body, a bivariate quasi-static aerodynamic force model was newly proposed, which was accomplished by performing an experiment involving two variables, the attack angle, and the distance from the nearest wall of the bluff body. A set of governing nonlinear field equations reflecting this force model were derived, and their perturbed solutions were obtained and validated by comparison with experimental results. The effect of the enclosure on the performance of the present energy harvester system was investigated and discussed using both theoretical and experimental methods.

Impacts of the aerodynamic force representation on the stability and performance of a galloping-based energy harvester

One of the challenging tasks in the analytical modeling of galloping systems is the representation of the galloping force. In this study, the impacts of using different aerodynamic load representations on the dynamics of galloping oscillations are investigated. A distributed-parameter model is considered to determine the response of a galloping energy harvester subjected to a uniform wind speed. For the same experimental data and conditions, various polynomial expressions for the galloping force are proposed in order to determine the possible differences in the variations of the harvester's outputs as well as the type of instability. For the same experimental data of the galloping force, it is demonstrated that the choice of the coefficients of the polynomial approximation may result in a change in the type of bifurcation, the tip displacement and harvested power amplitudes. A parametric study is then performed to investigate the effects of the electrical load resistance on the harvester's performance when considering different possible representations of the aerodynamic force. It is indicated that for low and high values of the electrical resistance, there is an increase in the range of wind speeds where the response of the energy harvester is not affected. The performed analysis shows the importance of accurately representing the galloping force in order to efficiently design piezoelectric energy harvesters.