Broadening Band of Wind Speed for Aeroelastic Energy Scavenging of a Cylinder through Buffeting in the Wakes of a Squared Prism

Small-scale energy harvesting from ambient vibration induced by aerodynamic instabilities can be used for wireless sensing applications. )e configuration with a bluff body attached to a piezoelectric cantilever has been exploited in many studies. For low-wind energy harvesting, vortex-induced vibration is investigated more frequently than other types of flow-induced motions, such as galloping and flutter, because of its quasisteady behavior called the potential lock-in phenomenon. In practice, a stationary square column is placed before the energy harvester to generate wake shedding, which can broaden the bandwidth of the energy harvester compared with a pure energy harvester equipped with a single bluff body. )is paper presents a proposed CFD method coupled with an electromechanical model to predict the performance of the energy harvester. )e proposed approach is verified with our experimental setup.)e time history of the voltage output and the frequency response is obtained by performing the relevant experiments. A subsequent CFD study is performed to investigate the flow patterns of the present energy harvesting system.


Introduction
Recently, the development of renewable energy technology motivated the development of low-power level piezoelectric energy harvesting, which is expected to solve the issue of energy supply for small wireless sensors and microelectromechanical system (MEMS) [1][2][3].ere are many ambient energy sources (including mechanical vibrations, human motions, and fluid flows) that can be harvested based on reasonable energy harvesting devices [4][5][6][7][8].Vibration is a common phenomenon in the natural world.Generally, starting approximately one decade ago, the study of piezoelectric energy harvesting from vibration has become quite mature [9][10][11][12].Many studies have been performed on harvesting energy from base vibrations using piezoelectric materials.In contrast, piezoelectric energy harvesting from wind flow has received relatively little attention compared with energy harvesting from vibrations.Wind energy harvesting can be generally divided into flutter, galloping, and vortex-induced vibration-based energy harvesters.e flutter phenomenon occurs when the two modal resonant frequencies of torsion and bending modes coalesce with each other.Bryant and Garcia [13] originally proposed a flutterbased aeroelastic energy harvester; they found that the harvester oscillated in a limited cycle at higher wind speeds above a critical wind speed.Aquino et al. [14] modeled a flutter-based aeroelastic energy harvester using computational fluid dynamics (CFD) and experimentally obtained a peak-to-peak voltage of 8.72 V and a short-circuit current of 1 mA when subjected to a wind speed of 2.3 m/s.Galloping occurs on a flexible base supported with a bluff body.Ewere et al. [15] experimentally investigated galloping piezoelectric energy harvesters with square bluff bodies.Yang et al. [16] experimentally investigated the influence of the bluff body shape on the energy harvesting performance of galloping piezoelectric energy harvesters.Weinstein et al. [17] tested the energy harvesting performance of a piezoelectric beam in the real heating, ventilation, and air conditioning flow.Zhang et al. [18] numerically investigated synchronization phenomenon in VIV energy harvesters.Recently, Dai et al. [19] explored the influence of a fixed cylinder on the energy harvesting performance of an aeroelastic energy harvester and experimentally verified the enhanced performance.Hobeck and Inman [20] presented a dual cantilever flutter and experimentally verified the large-amplitude vibration and high velocity of the two cantilever beams in the flutter.ese results demonstrate that the dual cantilever flutter can be used to efficiently harvest energy from wind flow.However, the coupling physical phenomenon between an energy harvester and a stationary interrupting bluff body remains to be investigated.From the physical point of view, the cycled wake shedding effect of a bluff body may enhance the vibration of the harvesters and may improve the energy harvesting performance; this process is called buffeting.ere exists a fundamental type of VIV called buffeting, which is caused by the unsteadiness of the incoming flow.Buffeting is also a common and widespread natural phenomenon.Natural turbulence combined with the presence of the wake of the forward bluff body induces buffeting.In aeronautics, it is crucially important to predict the threshold of the buffeting.
e essential elements of buffeting are as follows: flow separation on the surface of the body, instability caused by the upstream obstacle (such as vortex shedding from other bluff bodies), and complex turbulence phenomena.Flow separation often occurs as the dynamic response of flight wings at high angles of attack.When the response of wings holds a wide frequency band of excitation, buffeting can be excited on aircrafts.As the second and most important source, the von Kármán vortex street that arises from wake oscillations behind a blunt body can directly lead to a socalled wake buffeting.Wake buffeting is a quite commonly observed phenomenon in many urban areas with many tall buildings.Wake buffeting generally contains two components of frequencies.e third source, pressure fluctuation of buffeting, can cause significant vertical and torsional motions, even at low flow speeds.Because of the three source types, buffeting can occur in a wide range of flow speeds, i.e., there is no critical onset wind velocity nor is there a limited range.
Buffeting is mostly dynamic in nature; as a result, altering the stiffness or damping of the structure will not necessarily change the fatigue load [21].Although the amplitude of oscillation due to buffeting is typically smaller than that for VIV, the frequency range over which it can occur is greater, from 0.1 to 60 Hz [22].Recently, it has been found that a freshly killed fish is capable of moving upstream within the Kármán vortex street generated by a D-shape cylinder [23].Furthermore, Beal et al. showed that live fish can swim upstream without any energy of their own; they extract the required energy from the oncoming large-scale vortices [24].
is observation is also important in the development of low-drag energy harvesting devices.
To exploit this important phenomenon in energy harvesting, the "eel" concept for energy harvesting was first presented by Allen and Smith [25]; the authors placed an array of slender PVDF under a stationary round sectioned bluff body and obtained milliwatt-level energy output.VIV-based energy harvesters efficiently work when the vortex-shedding frequency becomes nearly equal to one of the natural frequencies of the dynamical structure.In the year 2012, Akaydin et al. [26] experimentally obtained a peak power of 0.1 mW at a wind speed of 1.192 m/s.Goushcha et al. [27] explored the driving mechanisms of VIV energy harvesting by using particle image velocimetry.Despite these studies, there remains a lack of study of the performance of a VIV cylinder energy harvester placed behind a stationary bluff body producing a vortex-shedding street.
Accordingly, the present work aims to study a new configuration of buffeting energy harvesting containing a PEH and a stationary square column placed in front of the PEH.e square column was used to generate a Kármán vortex street, and the effect of different spacing between the stationary column and the VIV energy harvester was investigated.e purpose of the present study was to obtain an appropriate spacing to enhance the potential wind energy harvesting capability.Wind tunnel tests were performed to investigate the influence of the spacing between the stationary column and the VIVPEH on the voltage output and on the efficient wind speed region.To provide a complement of the wind tunnel test, CFD was conducted to analyze the vortex-shedding patterns in the vibration system.

Physical Model and Experimental Setup
Figure 1 shows a schematic of the proposed system; it mainly consists of one piezoelectric energy harvester with one MFC piece that can oscillate freely, as well as one stationary square column.
e VIV bluff body suffers simultaneously two types of flow-induced force: the wake-induced and flowinduced forces.
e square column is used to produce a vortex-shedding wake, which induces the vibration of the energy harvester.In this work, the diameter d and the length l b of the circular cylinder are 32 mm and 125 mm, respectively, and the length of side l s and total length L of the square column are also 32 mm and 125 mm, respectively.L is the center-to-center distance of the two bluff bodies in the equilibrium position.

Mathematical Model
Based on the Euler-Bernoulli beam theory, the Rayleigh-Ritz method, the assumed-modes method, the system identification, etc., the proposed harvester shown in Figure 1 has the following equivalent nonlinear electromechanical governing equations based on the following Erturk model [28]: Shock and Vibration where M eff is the equivalent mass of a piezoelectric cantilever system; C eff is the equivalent damping related to the damping coe cient ξ, which can be obtained by free decay experiments; K eff is the equivalent sti ness of the system; and θ is the electromechanical coupling coe cient of the system that can be derived from equation group (2).In equation group (2), C p is the permittivity measured experimentally, ω n is the natural frequency of the system that can be obtained by free decay experiments, δ is the ratio of the amplitude before and after the free decay experiment, R L is the external load of the system, and V(t) is the output voltage of the system.F MIN is the ow-induced force caused by the incoming wind force and F EIM is the interactional force caused by the vortex shedding from the upper square column.
In the past few decades, researchers have made a substantial e ort to model the aerodynamic force of owinduced vibration.e force of a single blu body can be easily modeled for the vortex-induced vibration and galloping processes; however, to model the force of multiple blu bodies, it is di cult to objectively consider the phase di erence or other time-dependent physical variables.For modeling the vortex-induced vibration force of a single blu body, the van der Pol wake oscillator model is the most commonly used model because of its ease of understanding and its good match with the experimental results.
e van der Pol wake oscillator model was rst developed by Bishop and Hassan [29], Hartlen and Currie [30], Gri n et al. [31], and Skop and Gri n [32] to directly represent the body and wake oscillator equations coupled through common terms.Subsequently, to describe VIV and the lock-in phenomenon, Nayfeh [33], Facchinetti et al. [34], and Farshidianfar and Zanganeh [35] improved the traditional models.Note that all the wake oscillator models are sensitive to the coupling term introduced in the form of displacement, velocity, and acceleration.e quasisteady hypothesis is often used in modeling the galloping aerodynamic force; for example, from experimental results, the aerodynamic force of a galloping blu body is found to be a function of the angle of attack and can be expressed as a polynomial expansion [22].
However, there is a lack of research on the modeling vortex-induced vibration between multiple blu bodies that are either all in motion or partly in motion because it is di cult to model the force caused by the vortex-shedding street of the upper blu body.us, an experimental method is the most commonly used in the relevant research studies.Unfortunately, restricting factors, such as visualization, sizing, and ow speeds, make it di cult to conduct such experiments.As a result, usually, one cannot obtain the mechanism accurately.
In this work, a numerical method was utilized to obtain the aerodynamic force, and the Gauss law was solved based on the computational results of force and the displacement from the numerical codes.
e results of the Gauss law computation also in uence the numerical simulations.During this process, the aero-electromechanical coupling problem was solved.
As shown in Figure 2, when the uniform ow is rst combined with the vortex-shedding street of the square Shock and Vibration column that passes over the VIVPEH, a Lattice Boltzmann Method (LBM) is employed to solve the external force on the VIVPEH.Next, by coupling back to the M-C-K equation and the Gauss law, the force connects the ow eld and the electromechanical system.us, according to the criterion of the equation, one can obtain the vibration amplitude, velocity, accelerated velocity, and voltage output of the system; thus, the signal of vibration amplitude of the VIV blu body is sent back to the LBM as the initial position of the next timestep.

Stationary column Harverter
e updated aerodynamic force obtained by the LBM is sent to the electromechanical coupling system again.e unstable distribution of the ow eld and the alternative voltage output the VIVPEH can be available in such an iterative process, which stops if the precision is con rmed.
In this work, the LBM is used to predict the strength of ow-induced vibration of the tandem cylinders in a commercial X ow code.e advantages of the LBM in solving the uid-structure interaction problem are as follows: there is no need to solve the Laplace equation at each timestep to satisfy the continuity equation of incompressible, unsteady ows, as is required in solving the Navier-Stokes (NS) equation, and in the LBM, a dynamic mesh is unnecessary in solving the moving boundaries.e Boltzmann's transport equation is de ned as follows: where n i is the statistical distribution functions with real variables, based on the conservation of mass, linear momentum and energy; C i represents the velocity component in one of the predetermined direction at discrete time of the particles; and Ω is the collision operator.By employing a Bhatnagar-Gross-Krook (BGK) approximation, the operator is simpli ed as where τ is the relaxation time and n eq i is the local equilibrium function.For de ning the uid-structure interaction problem, the external force term should be considered, as shown in the following equation: where c Δ r/Δt is the velocity of the particle and F i is the external force.

Verification of the Proposed Mathematical Method
A wind tunnel test is conducted to verify the precision of the simulation code in this work.e experimental setup is shown in Figure 3. e wind is produced by a round wind tunnel, with a diameter of 400 mm.e wind speed is measured by a hot-wire anemometer (Testo Co., USA).e metal substrate is made of pure aluminum, with dimensions of 200 × 20 × 0.5 mm 3 .An MFC-M2807-P2 (Smart Material Corp, Germany) piezoelectric patch has dimensions of  1-3.e wind speed is tested by the hot-wire anemometer and is adjusted by the frequency transducer.Figure 4 shows the relationship between the frequency transducer and the wind speed.To avoid the potential inuence of the anemometer, which could act as another blu body, the tted line of identifying the wind speed versus the frequency transducer is given based on a substantial amount of measured data.
As shown in Figure 3, a cantilever beam is used as a base layer, and an MFC piezoelectric sheet is bonded to the root of the cantilever beam. is arrangement constitutes a piezoelectric cantilever beam device that is placed at the end of the cantilever beam for generating the vortex-induced vibration.
We compare the results of the voltage output obtained by the CFD simulation with the wind tunnel test to verify the accuracy of the present LBM code.e schematic maps of di erent lattices are shown in Figures 5(a)-5(c), where L O is the outside lattice size, L R is the re ning region lattice size, and L N is the circular cylinder near wall lattice size.Before comparing the predicted results to the experimental results to verify the present simulation code, a lattice independence study was conducted to ensure the accuracy of simulation from.e computational results are shown in Table 4. e lift and drag force coe cients as well as the Strouhal numbers (de ned as S t f s D/U, f s is the vortex-shedding frequency) are very close for the lattice numbers of 24000 and 53100; thus, the lattice number of 24000 is used in the present work.e computational results of the voltage output are compared with the experimental results.As shown in Figure 6, the time history results of the present numerical method match well with the experimental results.e FFT results of the voltage output also show good agreement   between the simulation and the experiment; thus, the proposed model is validated.

Results and Discussions
First, we conducted the experiments of energy harvesting under different wind speeds.e internal impendence of the data collecting system is equal to R L � 1 MΩ.Figures 7-9 show the time history curves of the voltage output and the fast Fourier transform (FFT) results of the energy harvester under different wind speeds when l � 1-3L.

Voltage Output.
As shown in Figures 7(a) and 7(b), for l � 1L, in the upper region (U � 2.78 m/s), there obviously exists two components of vibration, which are the vibration caused by the incoming wind and the Kármán vortex shedding of the forward bluff body.e vibration curve exhibits a "beating"-like phenomenon, i.e., the vibration is dominated by a main frequency, which is the global natural frequency of the harvester.e maximum voltage output is approximately 15 V.Note that unlike a pure beating phenomenon of a single cylinder vibrating system, because of the influence of the vortex-shedding impact on the upper bluff body, the vortex-shedding frequency of the vibrating circular cylinder is quite chaotic, and the time history curve appears complicated, as shown in Figures 7(a) and 7(b).Figure 7(b) shows that before the resonance occurs, much noise exists in the vortex-shedding frequency of the circular cylinder.When the wind speed increases to 3.56 m/s, the time history curves of the voltage output become more sinusoidal and approach a harmonic response, as shown in Figure 7(c).It is demonstrated that during this stage, the frequency of the vibrating circular cylinder is locked at the global natural frequency.A maximum voltage up to approximately 54.5 V is observed in this stage.Figure 7(d) shows that in the current region, the vibration frequency is quite close to the vortex-shedding frequency of the square column, and the vibration becomes stronger than that shown in Figure 7(a).Figures 7(e) and 7(f ) show that when

Shock and Vibration
the wind speed increases, the vortex-shedding frequency continues to increase and departs from the natural frequency of the circular cylinder; moreover, the vibration amplitudes and the harvested power decrease.
e voltage and frequency response present a similar varying trend for l 2L and l 3L.For l 2L, the maximum voltage outputs are 24.2V, 50.5 V, and 23.3 V, respectively, as shown in Figures 8(a), 8(c), and 8(e).e "beating"-like phenomenon occurs again via the combined e ects of the vortex and the wake shedding-induced vibration.For l 3L, the maximum voltage outputs are 33.8V, 60.2 V, and 23 V, respectively, as shown in Figures 9(a), 9(c), and 9(e).Moreover, from the FFT results, we can conclude that there exist three di erent statuses according to the coexistence of the vortex-shedding frequency of the forward cylinder and the global natural frequency of the vibrating cylinder.
Figure 10 compares the in uences of wind speed on the voltage output for three di erent regimes with three harvester con gurations.First, unlike the VIV of a single cylinder, one can observe that for di erent space distances, there is a wind speed range of high amplitude vibration after the VIV lock-in regions.In other words, the circular cylinder encountered wake-induced bu eting via the wake shedding street of the square column in front.erefore, the proposed design is able to achieve a considerable enhancement in VIV-based wind energy harvesting.Second, the con guration of l 3L has wider wind speed bandwidth and higher voltage output than the con gurations of l 1L and l 2L.
Figure 11 shows a comparison of the computed voltage output with the wind tunnel experimental results for l 3L.It can be concluded that the predictions and measurements agree well with each other, thus verifying the present simulation method.e discrepancy is mainly attributed to the probabilistic error in the experimental process.

CFD Computational Results.
To clarify the phenomenon of bu eting, as shown in Figure 10, we compared the vortexshedding patterns in di erent time regions during a complete vibration period.On the left hand side of Figure 12 (l 1L), as shown in Figures 12(a  ).e vortex shedding patterns of l � 2L and l � 3L are close to each other since the space between the stationary square column and the VIV circular cylinder is larger; thus, a typical "P + S" mode is obtained.

Conclusions
To enhance the efficiency of flow energy harvesting, higher vibration amplitudes and wider bandwidths are required.In this work, a numerical method combined with the electromechanical coupling model was employed to solve the aero-electromechanical coupling problem of piezoelectric energy harvesting from buffeting.In the proposed approach, the aerodynamic force response from fluid and structure interactions is solved by the LBM method and is then transferred to an electromechanical coupling platform; the vibration position and voltage output are solved and are then sent back to the LBM again as the initial position of the vibration cylinder in the next timestep to obtain the AC voltage time history of the energy harvester and the vibration displacement of the circular cylinder.ree different energy harvester configurations are investigated by varying the space length of the harvester and the interrupting stationary square cylinder.e time histories and the frequency responses of the voltage output are tested in both experiments and numerical simulations; good agreement was found between the experimental results and the simulations.ere exist two kinds of frequencies of vibration for the energy harvester according to the VIV and the interrupted vibration influenced by the vortex shedding of the stationary square cylinder.e configuration with l � 3L was found to perform better than the other two configurations considered, achieving wider wind speed bandwidth and higher voltage output.e "2P + S" and "P + S" patterns were obtained for l � 1L and l � 2 − 3L, respectively.Note that for the present energy harvester configurations, unlike the VIVPEH, the vibration could be sustained after the lock-in region.e present phenomenon may enhance the piezoelectric energy harvesting efficiency.

Data Availability
e data used to support the findings of this study are included within the article.Shock and Vibration

Figure 1 :
Figure 1: Schematic of the proposed harvester.(a) Physical system model and (b) schematic of the experimental setup.

Figure 2 :
Figure 2: e ow chart of the strong coupling computational process.

Figure 4 :Figure 3 :
Figure 4: e tted result of the wind speed versus the frequency transducer.

Figure 5 :Table 4 :Figure 6 :
Figure 5: Schematic maps of different lattices in the present simulation work.

Figure 7 :
Figure 7: Time histories and frequency responses of the voltage outputs for the presynchronous (a, b), synchronous (c, d), and postsynchronous (e, f ) regimes of l 1L.

Figure 8 :
Figure 8: Time histories and frequency responses of the voltage outputs for the presynchronous (a, b), synchronous (c, d), and postsynchronous (e, f ) regimes of l 2L.

Figure 9 :Figure 11 :Figure 12 :
Figure 9: Time histories and frequency responses of the voltage outputs for the presynchronous (a, b), synchronous (c, d), and postsynchronous (e, f ) regimes of l 3L.

Figure 10 :
Figure 10: Comparisons of the experimental voltage output versus the wind speed of four di erent regimes.e experimental data from regime-1(l 1L), regime-2(l 1L), regime-3(l 1L) and single harvester are drawn by rectangle, circles, triangle, and stars, respectively.

Table 1 :
Parameters of the piezoelectric cantilever beam.

Table 2 :
Parameters of the blu body.

Table 3 :
Measured parameters of the M-C-K system.