A Contact-Mode Triboelectric Nanogenerator for Energy Harvesting from Marine Pipe Vibrations

sensors

Article A Contact-Mode Triboelectric Nanogenerator for Energy Harvesting from Marine Pipe Vibrations

Rui Li, He Zhang * , Li Wang and Guohua Liu

College of Civil Engineering & Architecture, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China; [email protected] (R.L.); [email protected] (L.W.); [email protected] (G.L.) * Correspondence: [email protected]; Tel.: +86-135-8873-1346

Abstract: Structural health monitoring is of great significance to ensure the safety of marine pipes, while powering the required monitoring sensors remains a problem because the ocean environment is not amenable to the traditional ways of providing an external power supply. However, mechanical energy due to the vortex-induced vibration of pipelines may be harvested to power those sensors, which is a convenient, economic and environmentally friendly way. We here exploit a contact-separation mode triboelectric nanogenerator (TENG) to create an efficient energy harvester to transform the mechanical energy of vibrating pipes into electrical energy. The TENG device is com- posed of a tribo-pair of dielectric material films that is connected to a mass-spring base to guarantee the contact-separation motions of the tribo-pair. Experimental tests are conducted to demonstrate the output performance and long-term durability of the TENG device by attaching it to a sample pipe. A theoretical model for the energy harvesting system is developed for predicting the electrical output performance of the device. It is established that the normalized output power depends only on two compound variables with all typical factors taken into consideration simultaneously. The simple scale law is useful to reveal the underlying mechanism of the device and can guideline the optimization of the device based on multi-parameters analyses. The results here may provide Citation: Li, R.; Zhang, H.; Wang, L.; references for designing contact-mode TENG energy harvesting devices based on the vibration of Liu, G. A Contact-Mode Triboelectric marine pipes and similar structures. Nanogenerator for Energy Harvesting from Marine Pipe Keywords: mechanical energy harvesting; triboelectric nanogenerator; marine pipelines; optimiza- Vibrations. Sensors 2021, 21, 1514. https://doi.org/10.3390/s21041514 tion design; scaling law

Academic Editor: Fabio Viola

Received: 13 January 2021 1. Introduction Accepted: 17 February 2021 Vortex-induced vibration (VIV) [1] of marine pipes is a typical type of vibration caused Published: 22 February 2021 by the vortex shedding phenomenon of the fluid flowing through the pipe. VIV may finally lead to fatigue or damage of the pipe after long-term service in the deep ocean Publisher’s Note: MDPI stays neutral environment. To ensure the safety of marine pipes, health monitoring systems are of with regard to jurisdictional claims in great importance. Distributed optical fiber sensors [2–5] are the most popular sensing published maps and institutional affil- devices for pipeline status monitoring. However, these types of devices are usually driven iations. by traditional external power supplies. Considering the high cost on infrastructure for traditional power supplies and the corresponding energy loss in the process of long- distance power transmission, it is essential to develop self-powered sensing technologies [6] to free the health monitoring system from traditional power supplies. Copyright: © 2021 by the authors. A self-powered system may operate sustainably by scavenging electrical energy from Licensee MDPI, Basel, Switzerland. the ambient environment. The technologies of piezoelectric generators [7–10] and tribo- This article is an open access article electric generators (TENG) [11–13] represent the most popular technologies for harvesting distributed under the terms and energy from environmental mechanical motions. Piezoelectric generators have been pro- conditions of the Creative Commons posed as a good energy harvesting strategy using the vibrations of pipelines [14–17] with Attribution (CC BY) license (https:// a power conversion efficiency of more than 50% [18]. In contrast to the piezoelectric ef- creativecommons.org/licenses/by/ fect, the TENG technology, pioneered by Wang and his co-workers [19], is more feasible 4.0/).

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for scavenging energy from environment vibrations with low frequencies, such as ocean waves and the vibrations of pipelines, bridges, and the like. As a kind of blue energy, the ocean wave energy exhibits a series of merits like sustainability in application and friendliness for the environment. Recently, TENG devices with different designs were developed in this application area [20–28]. Chen et al. [20] proposed a network design made of TENGs for large-scale harvesting of kinetic water energy. Subsequently, Jiang et al. [29] improved the energy conversion efficiency of TENG devices by developing a wavy-structured conductor-dielectric-conductor film. To further enhance the output performance, Zhao et al. [30] modified the surfaces of tribo-layers by introducing a nanostructured morphology. To avoid the influence of high humidity, Xu et al. [31] developed a fully packaged TENG. The energy harvested by each TENG from ocean waves is roughly capable of powering a sensor. To achieve more electric power, a network of TENG devices floating on the water surface was proposed [20]. The output power of this device combination can reach 1.15 MW and the instantaneous energy conversion efficiency reaches 55% for a one-kilometer square water surface. In addition to ocean waves, vibrating marine pipes are also an effective host for energy harvesting. For the purpose of providing a power source for pipeline monitoring systems, we propose to exploit contact-mode TENG to create a high-performance energy harvester. This device can harvest the mechanical energy of vibrating pipes by converting it into electric power, which may offer then a power supply for the pipeline health monitoring system. The device is supposed to be attached on the surface of the pipeline, so that it may vibrate with the pipeline due to the ocean flow. It is designed with two dielectric films, which are connected by a mass-spring system for the restoring force. An alternating current will be produced by the device during the contact-separation oscillation process [32] induced by the pipe vibrations. A series of experimental tests will be carried out to investigate the output performance of the TENG device due to different pipe motions and electrical circuit resistance. To validate the feasibility of the TENG device, a theoretical model is established to predict dynamical responses of pipes, the oscillation of the mass- spring base and the electric output of TENG devices. Parameter analyses are performed to examine the influences of the installation position of the device on the pipe, the natural frequency of the mass-spring base, the effective thickness of the dielectric films and the circuit loading resistances. Finally, a simple scaling law is established based on the multi- parameter analyses to reveal the underlying correlation between the normalized output power and normalized system parameters. The results indicate that the application of TENG has potential in propelling wireless sensing and battery free detection in marine pipeline monitoring systems.

2. Materials and Methods TENG devices are used to scavenge mechanical energy of a vibrating pipeline which can power the monitoring system to realize the sensing and signal transmission. The TENG device consists of a tribo-pair, two electrodes, two acrylic plates, several springs and a waterproof package (Figure1). The movable acrylic plate and four springs form a mass- spring base, which is designed as the carrier for the tribo-pair to facilitate the energy conversion through the contact-separation oscillations. The acrylic plates serve as the carrier of the tribo-pair, which make it become flat so that the tribo-pair may contact intimately and prevent the leakage of electrons from copper foil to the external environment. The copper foils are bonded outside of the tribo-pair and inside of the acrylic plates as the conductive electrodes. Here we use polytetrafluoroethylene (PTFE) and nylon as the dielectric materials of the tribo-pair. The springs fixed between the two acrylic plates offer the restoring force when the tribo-pair are forced into contact. The whole TENG device is sealed by a waterproof box to protect the TENG device and restrict the lateral deformation of TENG devices. Sensors 2021, 21, 1514 3 of 21 Sensors 2021, 21, x FOR PEER REVIEW 3 of 24

(a) (b) (e) Offshore platform

Cloud servers

Accelerometer Temp. Detector Displacement sensor Stress gauges Power generator Springs Power supply to

Copper foil Acrylic plate

Figure 1. AFigure sketch 1. of A the sketch developed of the developed TENG devices TENG in devices application in application of ocean pipe of ocean vibration pipe energyvibration harvesting. energy (a,b) are the perspectiveharvesting. of the device (a,b arrangement) are the perspective at pipe; ( cof,d the) are device illustration arrangement of the energy at pipe; harvesting (c,d) are illustration system and of detailed the structural diagram ofenergy the tribo-pair harvesting of TENG system device; and detailed (e) is the structural fabrication diagram of the TENGof the tribo device-pair sealed of TENG by a waterproofdevice; (e) is box. the fabrication of the TENG device sealed by a waterproof box. When TENG devices are fixed on the outer surface of the pipeline, the vibration of When TENGthe devices host pipe are willfixed force on the the out TENGer surface devices of intothe pipeline, periodic the oscillations. vibration of In each working the host pipe willcycle, force four the stagesTENGoccur devices in into sequence: periodic fully oscillations. contacting, In separating, each working separating cycle, to a maximal four stages occurgap, in approaching.sequence: fully In contacting, the first stage separating, (Figure2 separatina), the pipeg to is a bent maximal under gap, the ocean current approaching. Inexcitation the first stage and the(Figure tribo-pair 2a), the comes pipe into is ben contact.t under The the electrons ocean current transfer excita- from nylon to PTFE tion and the tribodue-pair to staticcomes induction, into contact. so that The the electrons two layers transfer carry from equivalent nylon to opposite PTFE due charges. In stage II to static induction,(Figure so 2thatb), thethecurrent two layers excitation carry isequi reduced,valent andopposite the pipe charges. reverts In backstage and II the tribo-pair (Figure 2b), the beginscurrent to excitation separate. is A reduced, potential and drop the will pipe be reverts generated back betweenand the tribo electrodes-pair deposited on begins to separate.the topA potential and the drop bottom will surfaces be generated of two between dielectric electrodes films. To deposited balance the on potential drop, the top and the freebottom electrons surfaces in theof two electrode dielectric attached films. to To PTFE balance will the flow potential to the electrode drop, free attached to nylon electrons in thethrough electrode external attached circuit, to PTFE which will generates flow to a voltagethe electrode pulse withattached a positive to nylon amplitude. In stage through externalIII circuit, (Figure which2c), the generates current excitation a voltage keepspulse reducing,with a positiv and thee amplitude. pipe keeps In bending in the stage III (Figureopposite 2c), the current direction excitation due to inertia keeps and reducing, the tribo-pair and the gets pipe separated keeps bending to the maximum in distance. the opposite directionThe free due electrons to inertia stop and transferring the tribo and-pair the gets tribo-pair separated reaches to the a newmaximum electrical equilibrium. distance. The freeIn stageelectrons IV (Figure stop transferring2d), with the and increasing the tribo of-pair the oceanreaches current a new excitation, electricalthe pipe bends equilibrium. In instage the flowIV (Figure direction 2d), and with the the dielectric increasing material of the films ocean of current the tribo-pair excitation, begins to approach. the pipe bends Freein the electrons flow direction comeback and tothe the dielectric electrode materia connectedl films to of PTFE the tribo when-pair the betribo-pair contact gins to approach.again Free (Figure electrons2a), andcome a negativeback to the voltage electrode pulse connected generates. to In PTFE this way, when an alternatingthe output tribo-pair contactvoltage again in (Figure external 2a), circuit and a of negative TENG devices voltage occurs pulse duegenerates. to the flow-In this induced way, vibrations of an alternating outputthe pipe. voltage in external circuit of TENG devices occurs due to the flow- induced vibrations of the pipe.

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Figure 2. FourFigure process 2. Four steps process for a TENG steps for device a TENG to convert device the to mechanicalconvert the energymechanical of a vibratingenergy of pipea vibrating into electricity. (a) In the fully contactpipe into process, electricity. the pipe (a) is In bended the fully under contact the process, current the excitation, pipe is bended and the under tribo-pair the current are getting excita- into contact; (b) In the separatingtion, and process, the tribo the current-pair are excitation getting into is reduced, contact; ( andb) In the the pipe separating reverts backprocess, and the the current tribo-pair excit startsation to separate; (c) In the separatingis reduced, to aand maximal the pipe gap reverts process, back the and current the tribo excitation-pair starts keeps to separate; reducing, (c and) In thethe pipeseparating keeps to bending a in the opposite directionmaximal due gap to inertiaprocess, and the the current tribo-pair excitation gets separated keeps reducing, to the maximum and the pipe distance; keeps ( dbending) In the approachingin the process, opposite direction due to inertia and the tribo-pair gets separated to the maximum distance; (d) In the current excitation increases, and the pipe returns to its original state and the dielectric material ﬁlms of the tribo-pair the approaching process, the current excitation increases, and the pipe returns to its original state begins to approach. and the dielectric material films of the tribo-pair begins to approach.

3. Experimental3. ExperimentalTest Test To investigateTo the investigate output performance the output performance of a TENG device, of a TENG a series device, of aexperimental series of experimental tests tests will be carriedwill be out carried to test out th toe electrical test the electricaloutput of output the TENG of the device TENG due device to different due to different pipe pipe motions andmotions electrical and electricalcircuit resistance circuit resistances.s. The experiment The experimentalal setup includes setup includes the TENG the TENG device, device, a polyvinyla polyvinyl chloride chloride (PVC) (PVC) pipe, pipe,a vibration a vibration exciter, exciter, a signal a signal amplifier amplifier and a and gal- a galvanometer vanometer andand an anosc oscilloscopeilloscope (Figure (Figure 3).3 ).The The simply simply supported supported PVC PVC pipe, pipe, of of which which the the two ends are two ends are hingedhinged by by a apair pair of of pliers pliers and and the the middle middle is isadhered adhered to tothe the exciter, exciter, is isused used as as the host for the host for TENGTENG devices. devices. The The pipe pipe is 1.2 is 1.2m in m length in length and and0.01 0.01 m in m diameter. in diameter. The TheTENG TENG device is µ device is pastedpasted on the on top the topof the of thepipe. pipe. The The smooth smooth nylon nylon film film with with a athickness thickness of of 100 100 m/smooth PTFE film with a thickness of 50 µm (triboelectric layers) are utilized for the tribo-pair. μm/smooth PTFE film with a thickness of 50 μm (triboelectric layers) are utilized for the In the test, a periodic harmonic load with the loading amplitude of 3 mm and frequency tribo-pair. In the test, a periodic harmonic load with the loading amplitude of 3 mm and of 9 Hz is applied on the middle of pipe by the exciter. Other corresponding parameters frequency of 9 Hz is applied on the middle of pipe by the exciter. Other corresponding are presented in Table1. To demonstrate the practical use of the proposed TENG device, parameters are presented in Table 1. To demonstrate the practical use of the proposed the TENG attached on the simply supported PVC pipe is loaded to light up 14 LEDs with TENG device, the TENG attached on the simply supported PVC pipe is loaded to light up the external resistance of 1.14 MΩ, as shown in Video S1. 14 LEDs with the external resistance of 1.14 MΩ, as shown in Video S1.

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(a) (b) Spring PTFE

Acrylic Wire Nylon Galvanometer

Signal amplifier

Pipeline model

Exciter Resistance

Figure 3. AA photo photo of of the the experimental experimental setup. setup. (a ()a The) The experimental experimental setup setup consists consists of a of PVC a PVC pipe, pipe, ; twotwo bearings,bearings, anan exciter,exciter, a a galvanometer, galvanometer, a a TENG TENG device device and and external external resistances; resistances (b) ( Theb) The PTFE PTFE layer, layer, nylon layer and the acrylic base. nylon layer and the acrylic base.

Table 1. Parameters of pipe and the energy harvesting system. Table 1. Parameters of pipe and the energy harvesting system. Parameter Value Parameter Value Pipe length L 1.2 m Pipe lengthPipeL diameter D 1.2 m 0.02 m Pipe diameter D 0.02 m Dielectric constant of PTFE  r1 2.55 Dielectric constant of PTFE εr1 2.55 Dielectric constantDielectric of constant nylon εr2 of nylon  r 2 4.55 4.55 Thickness of PTFE d1 0.05 mm Thickness of PTFE d1 0.05 mm Thickness of nylon d2 0.05 mm Number ofThickness springs n of nylon d2 4 0.05 mm Number of springNumber coils Nofc springs n 8 4 Spring diameter Dc 4 mm Number of spring coils Nc 8 Spring wire diameter dc 0.15 mm Mass of the mass −Springspring diameter base mT Dc 19.46 g 4 mm Natural frequency of the TENG f 7.1 Hz Spring wire diameter dc 0.15 mm Circuit resistance R 100 MΩ Mass of the mass-spring base m −12 Vacuum dielectric co-efﬁcient ε0 T 8.854 × 10 19.46 g SurfaceNatural charge frequency density σ of the TENG f 5–20 µC/m2 7.1 Hz T ◦ TemperatureCircuit resistance R 20 C 100 MΩ Humidity 40% −12 DimensionsVacuum of tribo-pair dielectric co-efficient 0 5 cm × 5 cm8.854  10 Surface charge density  5–20 μC/m2 As the TENG device isTemperature attached at the T pipeline, the vibration amplitude and20 °C frequency of pipeline are considered crucialHumidity factors affecting the output performance of TENG40% device. To investigate the relationshipDimensions between of tribo them,-pair the output current of TENG5 devicecm  5 attachedcm at the pipe is tested under different mechanical loads. Firstly, the output current of the TENGAs devices the TENG under device different is attached excitation at frequencies the pipeline, is measured the vibration and the amplitude output voltage and fre- is obtainedquency of according pipeline to are Ohm’s considered law: V crucial = IR. The factor externals affecting excitation the output starts with performance the loading of

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frequency varying from 4 Hz to 10 Hz under a loading amplitude of 4 mm. The results (Figure4a,b) show that the voltage amplitude increases with loading frequency in the range of 4 Hz to 7 Hz, and then reaches a relatively stable value (about 102 V) when the frequency exceeds 7 Hz. The average output power of TENG is calculated according to the Sensors 2021, 21, x FOR PEER REVIEWoutput voltage signals. As Figure4b shows, the maximum average output power (11.67 ofµ W)24

occurs when the excitation frequency is 9 Hz.

(a) (b)

4Hz 5Hz 6Hz 7Hz 8Hz 9Hz 10Hz

(V)

( P

(V) amplitude Voltage Voltage Power

t (s) f (H z )

0.5 1 1.5 2 2.5 3 3.5 4 4.5 W)

(V) μ

( P

(V) amplitude Voltage Voltage Power

t (s) A (mm)

(e) (f) 1M 2M 5M 10M 50M 100M 200M 500M

W) (V)

(

(V) amplitude Voltage

Voltage Power

R (M ) t (s) FigureFigure 4. 4. ElectricElectric output output of of TENG TENG device at different physicalphysical andand electricalelectrical conditions. conditions. ( a(,ab,b)) are are the the influence influence of of mechanical mechanicalloading loading frequency frequency ranging ranging from from 4 Hz–10 4 Hz Hz on10 theHz outputon the performanceoutput performance of TENG of device; TENG (c device;,d) are the (c,d influence) are the of influence mechanical of mechanicalloading amplitude loading appliedamplitude on theapplied pipe rangingon the pipe from ranging 0.5 mm–4.5 from mm 0.5 mm on the - 4.5 output mm performanceon the output of p TENGerformance device; of (TENGe,f) are device;the influence (e,f) are of the circuit influence loading of resistancecircuit loading ranging resistance from 1 MrangingΩ–500 from MΩ on1 MΩ the - output 500 MΩ performance on the output of theperformance TENG device. of the TENG device. Next, the output performance of TENG device due to different pipe vibration ampli- tudesThe is tested.long-term The durability exciter is set of upthe to TENG make device the pipe is vibrate also a critical with an issue amplitude for a mechanical in the range energyof 0.5–4.5 harvester mm and. Thus, a frequency the tests offor 8 measuring Hz. The results the cycling (Figure performance4c,d) show of that the the TENG voltage de- viceamplitude during increases10,000 cycles with are the carried vibration out amplitude at the loading of pipe. frequency The maximum of 8 Hz averageand excitation output amplitudepower (11.2 of µ3.5W) mm occurs (Fig whenure 5a the,b). vibrationFigure 5a amplitudepresents the of output the pipe current is 4.5 mm.signals of TENG deviceTo after further 100, study500, 1000, the output 2000 and performance 10,000 cycles of the, respectively TENG device. In Figure due to different5b, both the electrical peak currentload resistances, and the average the output output current power of has TENG no significant device is measureddegradation as after the external 10,000 recipro- loading cating cycles, indicating an excellent stability and durability of the TENG device.

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resistors range from 1 MΩ to 500 MΩ. According to the two tests above (Figure4a–d), a mechanical excitation with frequency of 8 Hz and amplitude of 4 mm is facilitated by the exciter (Figure4e,f). The results show that the peak voltage increases as the load resistance increases, and reaches a stable value at load resistance of 200 MΩ. The average output power increases ﬁrstly and then decreases with the peak of 14.0 µW at a circuit resistance of 200 MΩ. The long-term durability of the TENG device is also a critical issue for a mechanical energy harvester. Thus, the tests for measuring the cycling performance of the TENG device during 10,000 cycles are carried out at the loading frequency of 8 Hz and excitation amplitude of 3.5 mm (Figure5a,b). Figure5a presents the output current signals of TENG device after 100, 500, 1000, 2000 and 10,000 cycles, respectively. In Figure5b, both the peak current Sensors 2021, 21, x FOR PEER REVIEW 8 of 24 and the average output power has no signiﬁcant degradation after 10,000 reciprocating cycles, indicating an excellent stability and durability of the TENG device.

(a) (b)

100 500 1000 2000 10,000

(V)

(

V P

(V) amplitude Voltage Voltage Power

t (s) Cycle Figure 5. Output performance of of TENG device after a certain period of operation. ( (aa)) is is the the time history results of the output current of TENG device after certai certainn cycles of operation; ( b) is inﬂuenceinfluence of the loading cycles on the peak output current and average power of TENG device.

IInn practice practice,, the the devices devices that that n needeed to be powered in thethe wirelesswireless pipelinepipeline monitoringmonitoring systemsystem mainly mainly includ includee sensors sensors and and wireless wireless signal signal transmission transmission device devices,s, for which for whicha micro- a wattmicrowatt level power level powerconsumption consumption can be estimated can be estimated [33]. According [33]. According to the measured to the measured output of theoutput TENG of thefabricated TENG fabricatedin this paper, in this the paper, output the may output meet may the meetpower the consumption power consumption require- mentsrequirements of these ofdevices. these devices.In addition, In addition, the TENGs the could TENGs be electrically could be electrically connected connectedin parallel or in inparallel series orto inform series a network to form aon network the surface on the of surfacea pipeline. of a The pipeline. network The will network greatly will enhance greatly theenhance output the of outputthe energy of the harvesting energy harvesting system sosystem that it could so that provide it could an provide adequate an green adequate en- ergygreen supply energy for supply the monitoring for the monitoring system instead system of instead using ofa traditional using a traditional power supply. power supply.

4.4. Theoretical Theoretical M Modellingodelling ToTo understand understand the the operation operation mechanism mechanism of ofTENG TENG in inscavenging scavenging the themechanic mechanicalal en- ergyenergy from from marine marine pipes pipes and provide and provide a better a betteroptimization optimization method method for the structure, for the structure, material andmaterial electric and circuit electric of the circuit energy of theharvesting energy system, harvesting we establish system, wea theoretical establish model a theoretical of the model of the energy harvesting system and predict the electrical output of the TENG energy harvesting system and predict the electrical output of the TENG device theoretically. device theoretically.

4.1.4.1. Dynamic Dynamic Responses Responses of of the the Pipe Pipe and and the the Mass Mass-Spring-Spring B Basease TheThe schematic schematic structural structural illustration illustration of of the the energy energy harvesting harvesting system system is shown is shown in Fig- in ureFigure 6. Firs6 . Firstly,tly, the the pipe pipe is is modelled modelled as as a simplysimply supported supported Bernoulli-Euler Bernoulli-Euler beam beam(Figure (Figure6a ) 6a)with with several several TENG TENG devices devices attached attached on it.on A it. Cartesian A Cartesian coordinate coordinate system system is used is used with with the theorigin origin at the at the left left end end of theof the beam beam with with the the axial axial direction direction of theof the beam beam the thex-axis. x-axis. The Th in-e incomingcoming ﬂow flow direction direction is is assumed assumed in in the the direction direction ofofz z-axis,-axis, withwith thethe laterallateral response of thethe pipe pipe in in yy directiondirection calculated. calculated. According According to the to theEuler Euler-Bernoulli-Bernoulli beam beam theory theory [34], [ 34the], governingthe governing equation equation of the of simply the simply-supported-supported cantilever cantilever beam beam can canbe writt be writtenen as Eq asuation Equa- (1). The vibration equations for TENG device is written as Equation (2) based on D’Alem- bert’s principle:

2 22  yppp( x , ty )( ,x )( ty , x ) t []+(EImcp ) t += (1) xxt222 p t

mT y T()()(,) t+ ky T t = − m T y p x T t (2)

in which E is the elastic modulus, I the cross-sectional moment of inertia, m the linear

mass density, cp the damping coefficient, yxtp (,) the cross-line displacement vector of pipe, and t represents the derivation of time, pt() the hydrodynamic fluid forces acted

on pipe, ytT () the displacement vector of TENG device, mT the mass of the TENG base,

xT the installation position of the TENG devices on the pipe, and k the springs’ stiffness.

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tion (1). The vibration equations for TENG device is written as Equation (2) based on D’Alembert’s principle:

2 2 2 ∂ ∂ yp(x, t) ∂ yp(x, t) ∂yp(x, t) [EI ] + m + c = p(t) (1) ∂x2 ∂x2 ∂t2 p ∂t .. .. mTyT(t) + kyT(t) = −mTyp(xT, t) (2) in which E is the elastic modulus, I the cross-sectional moment of inertia, m the linear mass density, cp the damping coefﬁcient, yp(x, t) the cross-line displacement vector of pipe, and t represents the derivation of time, p(t) the hydrodynamic ﬂuid forces acted on pipe, yT(t) Sensors 2021, 21, x FOR PEER REVIEW 9 of 24 the displacement vector of TENG device, mT the mass of the TENG base, xT the installation position of the TENG devices on the pipe, and k the springs’ stiffness.

(a) y x T TENG device The pipe x z

y (b) (c) (d) yxtT (,) Water Waterproof box z mT flow

k yxp (,) t

The pipe

Figure 6. SchematicFigure design 6. Schematic of the pipe design host. of (thea) the pipe integral host. ( pipea) the which integral is assumed pipe which to be is aassumed simply supportedto be a simply beam; (b) the cross section ofsupported the pipe; beam; (c) TENG (b) the device cross sealed section by of a water-proofthe pipe; (c) TENG box; (d device) the schematic sealed by designa water of-proof mass-spring box; (d) base of TENG device. the schematic design of mass-spring base of TENG device.

According toAccording the wake to oscillator the wake model oscillator [35] model, the hydrodynamic [35], the hydrodynamic fluid forces ﬂuid on forcespipe- on pipeline line may be mayexpressed be expressed as: as: 1 2 1 p(t) = CLρwDU cos 2π fst (3) p( tCDUf )cos2= t 2 (3) 2 Lw s in which CL is the lift coefﬁcient, ρw the water density, D the diameter of the pipe, U the

in which CﬂowL is the velocity, lift coefficient,fs = St · U /Dw thethe Strouhalwater density, frequency, D the and diameterSt the non-dimensionalof the pipe, U Strouhal S = the flow velocity,number (fSUDstt=0.2). the Strouhal frequency, and St the non-dimensional Based on the mode superposition method, a generalized expression for the displace- Strouhal number ( St = 0.2 ). ment of the pipe is written as: Based on the mode superposition method, a generalized expression for the displacement of the pipe is written as: n yp(x, t) = φ (x)q (t) (4) n ∑ j j j=1 yxp (,)()( txqt = )  jj (4) j=1 in which, φj(x) is the j-th mode shape, qj(t) the generalized displacement of j-th normal jπ in which, j ()x is the j-th mode shape, qtj () the generalized displacement of j-th normal mode in time domain. For simply supported beam, φj(x) = sin L x, in which, L is the length of the pipe. j mode in time domain. For simply supported beam,  (xx )= sin , in which, L is the Substituting Equations (3) and (4) into Equationj (2),L we have: length of the pipe. .. . 2 Substituting Equations (3) and (4)qj( intot) + E2quationζpjλpjqj (2+)λ, wepjqj have(t) =: Pj(t)/Mj (5)

2 qtqqtPjjjjjjjj( )2(++= )( tMppp ) (5)

EI in which, = ()j 2 is the natural circular frequency of pipe,  is the hysteretic pj mL4 pj

12 0.032 damping coefficient of the pipe defined by  pj =+0.008 j 2 [33], 2 j 2 j L LCLw DU (1−− ( 1) ) U  Pjt( tp )(==+ t ) ( x )dsin xS 2 t  and 0 j 22jD  L L M== m 2 ( x )d x m respectively the generalized loading and generalized mass of the jj0 2 j-th normal mode, L the length of the pipe. By solving Equation (5), the generalized displacement of the j-th normal mode will be:

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q = (j )2 EI in which, λpj π mL4 is the natural circular frequency of pipe, ζpj is the hys- = 1 2 + 0.032 ( ) = teretic damping coefﬁcient of the pipe deﬁned by ζpj 2 0.008j j2 [33], Pj t LC ρ DU2 1−(−1)j R L L w U π R L 2 L 0 p(t)φj(x)dx = 2jπ sin 2πSt D t + 2 and Mj = 0 mφj (x)dx = m 2 respectively the generalized loading and generalized mass of the j-th normal mode, L the length of the pipe. By solving Equation (5), the generalized displacement of the j-th normal mode will be:

4 2 U L CLρwDU (1 − cos jπ) sin 2πSt D t − βj qj(t) = q (6) 5 5 2 2 2 j π EI (1 − γpj) + 2ζpjγpj

= 2ζpjγpj in which, βj arctan − 2 is the phase difference of the generalized displacement of the 1 γpj j-th normal mode, γ = 2πStU the frequency ratio between the ﬂow excitation and the j-th pj Dλpj natural frequency of the pipe. Substituting Equation (6) into Equation (4), the vibration displacement of the pipe will be: j U jπx 4 2 n 1 − (−1) sin 2πSt t + β sin L CLρwDU D j L yp(x, t) = (7) 5 ∑ q 2 2 π EI j=1 5 2 j (1 − γpj) + 2ζpjγpj The dynamic oscillation of TENG is excited by the vibrations of the pipe, of which the displacement expression is shown in Equation (7). By introducing the vibration displacement of the pipe into the oscillation equation of TENG in Equation (2) and specifying the initial conditions, the vibration displacement of TENG will be obtained. Considering the initial condition that at t = 0, two dielectric material ﬁlms just get into contact, which can be expressed by yT(t = 0) = 0. Substituting this initial condition and Equation (7) into Equation (2), the vibration displacement of the mass-spring base of TENG is:

j x 4 2 n 1 − (−1) sin jπ T 1 + sin 2πt + β L CLρwDU L j yT(t) = r (8) ∑ 2 5 1 − j=1 5 2 2 π EI 2 1 j 1 − γ + 2ζpjγpj γT pj

in which γT is the frequency ratio between the ﬂow excitation and the natural frequency of the mass-spring base.

4.2. The Electric Output of TENG Device In Section 4.1, we have established the expressions of the oscillation displacement of the mass-spring base of TENG device, which denotes the variation of the surface gap between the two substrates in Figure6c. As the dielectric plates and electrodes are closely attached at the substrates, the variation of the gap distance between the dielectric plates are equal to that of the two substrates (yT(t)). The dielectric plates get into contact when yT(t) = 0, and get separated to the max gap when yT(t) reaches the maximum value. Substituting yT(t) into the basic V-Q-x relationship of TENG device [36–38] with a load resistance R (Figure7), the output voltage of the tribo-pair ( V(t)) is expressed as:

( + ( )) h i V(t) = − σd0 + σ d0 yT t exp − 1 d t + R t y (t)dz ε0 ε0 RSε0 0 0 T + ( ) h i (9) + σd0 d0 yT t R t exp 1 d (z − t) + R z y (t)dr dz ε0 RSε0 0 RSε0 0 t T

here, S is the area size of the dielectric material film, ε0 the dielectric constants of the air gap, σ the charge density of each dielectric material film, R the electrical circuit resistance, d the effective thickness constant defined by d = d1 + d2 , d and d the thickness of two 0 0 εr1 εr2 1 2 dielectric plates, εr1 and εr2 the relative dielectric constants. Sensors 2021, 21, x FOR PEER REVIEW 11 of 24

here, S is the area size of the dielectric material film, 0 the dielectric constants of the air gap,  the charge density of each dielectric material film, R the electrical circuit re- dd d 12 d Sensors 2021, 21, 1514 sistance, 0 the effective thickness constant defined by d0 =+ , d1 and 102 ofthe 21 rr12

thickness of two dielectric plates,  r1 and  r 2 the relative dielectric constants.

Electrode

d1 Dielectric plate 1 R V(t) ＋＋＋＋＋＋ y T 

d2 Dielectric plate 2

FigureFigure 7. 7. TThehe schematic schematic design design of of the the tribo tribo-pair-pair of of TENG TENG device. device.

TThehe expression expression for for average average power power of of TENG TENG with with an an external external load load resistance resistance RR isis::

TT 1 1Z 2 P =PVtt= V2((t))dt (10) 0 d (10) RTRT0

in which, T = DD is the time period of the separation-contact cycle. in which, T = StU is the time period of the separation-contact cycle. SUt 4.3. Scaling Laws 4.3. ScalingUsing L theaws theoretical model for the TENG device, we may investigate the effect of each individualUsing the factor theoretical on the output model performance for the TENG of thedevice, device we with may the investigate others fixed. the However,effect of eachthe optimization individual factor work ison restricted the output by the performance single-parameter of the analysisdevice with which the does others not reflectfixed. However,the relationship the optimization between the work different is restr parametersicted by the and single the-parameter combined influenceanalysis which of them does on notthe reflect electrical the outputrelationship performance. between the In the different simulation, parameters the electric and the output combined performance influence is ofinfluenced them on the by theelectric typicalal output factors performance. (the dynamic In characteristics the simulation, of the the electric pipe and output spring-mass perfor- mancebase for is the influenced device, the by loading the typical resistance factors in the(the electrical dynamic circuit characteristics and the material of the propertiespipe and springof the- dielectricmass base films for the in tribo-pair,device, the etc.) loading simultaneously resistance in and the coherently. electrical circuit The change and the of ma- any terialfactor p mayroperties affect of the the optimized dielectric electricfilms in output tribo-pair, performance. etc.) simultaneously To overcome and the coherently. limitation Theof single-parameter change of any factor analysis may andaffect provide the optimized a general electric optimization output performance. method, we propose To over- a comenew theoretical the limitation model of to single predict-parameter the output analysis voltage and and powerprovide of a TENG general in dimensionless optimization method,forms. In we this propose way, the a new output theoretical performance model of TENGto predict will the be studiedoutput voltage with all and typical power factors of TENGtaken intoin dimensionless consideration forms. simultaneously. In this way, the output performance of TENG will be studied withTo investigateall typical factors the simultaneous taken into consideration effects of the simultaneously. typical parameters on output performance,To investigate here we establish the simultaneous a series of dimensionlesseffects of the typical expressions parameters of the on electric output output perfor- of mance,TENG device.here we In establish this theoretical a series model,of dimensionless all the typical expressions factors are of combinedthe electric into output dimen- of TENGsionless device. variables, In this including theoretical the model, gap distance all the typical of the tribo-pair.factors are Basedcombined on Equationinto dimen- (8), sionlessthe dimensionless variables, including expression the for gap gap distance distance of may the betribo expressed-pair. Based as: on Equation (8), the

dimensionless expression for gap distance may be expressed as: j m κ4y (τ) γ2 n 1 − (−1) sin(jπξT) p T T j y (τ) = =4 (12 + sin 2πt τ) n (11) T1 my2() 2  0 ∑ q(1−− ( 1)) sin(jT ) CLρwDUpT1 − γ T 5 5 22 2 ytT1( )= =T ( 1 + sin 2  0 j=)1 j π 1 − γ + 2ζ γ 22  pj 2 pj 2 pj (11) CL w DU 1− T j=1 5 5 2 j (12−+ pj) (  p j  p j ) in which, the ratio of vortex shedding frequency to the natural frequency of pipe is γpj,

inwhile which, the the ratio ratio of vortex of vortex shedding shedding frequency frequency to the to naturalthe natural frequency frequency of TENG of pipe is γ isT.  pj , In Equation (11), y (τ) is the dimensionless expressions of the gap distance of the while the ratio of vortex T1shedding frequency to the natural frequency of TENG is  T . tribo-pair which is inﬂuencedy () by the installation position of TENG device at pipe ξT, In Equation (11), T1 is the dimensionless expressions of the gap distance of the4 the characteristics of ocean ﬂow excitation (CL, U, ρw), the pipe structure (mp, D, κ ), tribo-pair which is influenced by the installation position of TENG device at pipe T , the

Sensors 2021, 21, 1514 11 of 21

and frequency ratio (γT, γpj). Substituting Equation (10) into Equation (8), the dimensionless output voltage is:

4 4 V(τ)ε0mpκ mpκ d0 d0t0 2 = VB τ, 2 , σCLρwDU CLρwDU RSε0 4 4 h 2 i mpκ d0 mpκ d0 d0t0 CLρwDU R τ = − 2 + 2 + y (τ) exp − τ + 4 y (λ)dλ (12) CLρwDU CLρwDU T1 RSε0 mpκ d0 0 T1 4 h 2 i d0t0 mpκ d0 R τ d0t0 CLρwDU R µ + 2 + y (τ) exp (µ − τ) + 4 y (λ)dλ dµ RSε0 CLρwDU T1 0 RSε0 mpκ d0 τ T1

Based on the normalized voltage, the dimensionless output power is given as follows:

2 8 4 ! Pε0mpκ d0t0 mpκ d0 d t Z 1 2 = P , 0 0 = V dτ (13) 2 2 2 2 4 A 2 A Sσ CLρwD U CLρwDU RSε0 0

4 mpκ d0 d0t0 Equations (12) and (13) contain two compound variables, 2 and . The for- CLρwDU RSε0 mer mainly reflects the coherent influence of the dynamical characteristics of ocean flow 4 excitation (CL, U, ρw) and pipeline host (D, κ , mp) on the dimensionless voltage, while the latter reflects influence of the structural properties of TENG (S, ε0, d0) and external circuit (R) on the output. Other corresponding parameters (ξT, γT, γpj) are not reflected directly in the two equations but they affect the output performance of TENG by influencing the gap distance of the tribo-pair according to Equation (10). The influence of ξT, γT, γpj on the electric output performance is investigated using theoretical simulation in Section5. The relations in Equations (11)–(13) reveal the coherent influence of several mechanical and electrical factors on the electric output performance of TENG. However, there is still a limitation in the dimensionless expressions because the optimization of the structural characteristics of TENG device is not reflected in these equations. The mass mT of the base and the springs’ stiffness k are important factors to reflect the dynamic characteristics of TENG device, such as the natural frequency of the base which greatly influences the variation of the gap distance between the tribo-pair, thereby making a remarkable contribution to the electric output of TENG. To reveal the relationship among the electric output performance, the gap distance and the natural frequency of the base, we propose another expression for normalized gap distance with mT and k taken into consideration:

m S2y (τ) y ( ) = p t T T2 τ C ρ D3 L w n 1−(−1)j sin(jπξ ) 4π2 T (14) = (1 + sin(2πt τ)) s t2k 0 ∑ 2 0 − 2 j=1 2 4t2κ4 m 4π j5π5 t2κ4− 4 +(2ζ ) 0 T 0 j4π2 pj j4π2

here, the dimensionless time τ = t and dimensionless installation position of the device t0 xT 4 EI at pipeline ξT = are defined, κ = 4 is the square of the natural frequency of pipe, L mp L t = D the period of the current excitation. 0 StU As shown in Equation (14), yT2(τ) is influenced by the characteristics of ocean flow excitation (CL, St, ρw), the pipe structure (mp, D) and the TENG structure (mT, k). Based on the dimensionless gap distance yT2(τ), the dimensionless expressions for voltage and power will be:

2 2 V(t)ε0mpSt d0mpSt d0t0 3 = V A τ, 3 , σCLρwD CLρwD RSε0 2 2 3 d0mpSt d0mpSt d0t0 CLρwD R τ = − 3 + 3 + yT2(τ) exp − RSε τ + 2 0 yT2(λ)dλ (15) CLρwD CLρwD 0 mpSt d0 2 3 d0t0 d0mpSt R τ d0t0 CLρwD R µ + RSε 3 + yT2(τ) 0 exp RSε (µ − τ) + 2 τ yT2(λ)dλ dµ 0 CLρwD 0 mpSt d0 Sensors 2021, 21, x FOR PEER REVIEW 13 of 24

As shown in Equation (14), yT2 () is influenced by the characteristics of ocean flow

excitation ( CL , St , w ), the pipe structure ( mp , D ) and the TENG structure ( mT , k). Based

on the dimensionless gap distance yT2 () , the dimensionless expressions for voltage and power will be:

Vtm( ) Sd m S22dt 0p0p tt= V  ,,00 33A  CDCDLwLw RS0

22 3   d0p0p m Sdtt m S d0 tCD 0Lw  =(−++−+ ) exp()d  yyT2T2  (15) CDCDm332 S d RS 0 LwLwp0  0 t

2 3 dt d m S d tCD +( )ex00 0pt + y  p()dd0 0Lw(−+) y RS CD 3 T2 0 RS m S2 d  T2 0 Lw 0 p0t

2 4 2 Sensors 2021, 21, 1514 1 12 of 21 P0 m p Stt d 0 t 0 d 0 m p S dt00 2 =PVAA , = d (16) 2 2 2 6 3 0 CDSCDL  w L  w RS0

According to Equations (14) and (152 ),4 we may understand 2 the simultaneous! 1 effects Pε0mpSt d0t0 d0mpS d t Z 2 of the loading resistance R, the area size of the =dielectricP materialst , 0 S0, the= chargeV ddensityτ (16) 2 2 2 6 A 3 A σ CLρwD S CLρwD RSε0 0  , the effective thickness of the dielectric material films d0 , the characteristics of ocean According to Equations (14) and (15), we may understand the simultaneous effects flow excitation ( CL , St , w ) and the pipe structure ( mp , D ) on the dimensionless output of the loading resistance R, the area size of the dielectric materials S, the charge density σ, voltage and power. We can also optimize the structural characteristics of TENG ( mT , k) the effective thickness of the dielectric material films d0, the characteristics of ocean flow to improve the electric output performance of TENG device through theoretical case study excitation (CL, St, ρw) and the pipe structure (mp, D) on the dimensionless output voltage according to Equations (14) – (16). and power. We can also optimize the structural characteristics of TENG (mT, k) to improve In this section,the electric we established output performance two sets of ofdimensionless TENG device expressions through theoretical of output case per- study according formances withto two Equations dimensionless (14)–(16). compound parameters to optimize the factors of the energy harvesting system.In this section,With Equati we establishedons (11) – (16 two), we sets provide of dimensionless a general guideline expressions for of output per- the optimizationformances of the output with twoperformance dimensionless of TENG, compound which may parameters help us toto optimizeunderstand the factors of the the simultaneousenergy influence harvesting of all typical system. factors With Equationson the electric (11)–(16), output. we provide a general guideline for the optimization of the output performance of TENG, which may help us to understand 5. Theoretical Ctheas simultaneouse Study influence of all typical factors on the electric output. 5.1. Validation of the Theoretical Model 5. Theoretical Case Study In Section 3, we tested the output performance of energy harvesting system with 5.1. Validation of the Theoretical Model TENG devices, in which we obtain the electric output performance of TENG due to different mechanical orIn electrical Section3, weconditions tested the. As output Figure performance 8 shows, the of energytheoretical harvesting simulation system with TENG for the output voltagedevices, of in TENG which is wein high obtain agreement the electric with output the experiments performance at either of TENG a load- due to different ing resistance mechanicalof 1 MΩ or or10 electrical MΩ, which conditions. proved Asthe Figureaccuracy8 shows, of theoretical the theoretical prediction simulation for the method. Correspondingoutput voltage parameters of TENG are isshown in high in Table agreement 1 (see withSection the 3) experiments and Table 2 at(see either a loading Section 5.2). resistance of 1 MΩ or 10 MΩ, which proved the accuracy of theoretical prediction method. Corresponding parameters are shown in Table1 (see Section3) and Table2.

Figure 8. Comparison of the simulated and experimental voltage output with the loading resistance of (a) 1 MΩ and (b) 10 MΩ.

Table 2. Parameters of the marine pipeline and ocean current.

Parameter Value Pipe length 400 m The external diameter of pipeline 0.324 m The inner diameter of pipeline 0.284 m The water current velocity 0.3 m/s Lift coefﬁcient of the current 0.9

5.2. Individual Parameter Analysis of Output Performance Further, we investigated the output performance of the energy harvesting system due to ocean current through theoretical analysis. The inﬂuence of four typical factors including the installation position of the device, the dynamic characteristics of the spring-mass base for the device, the loading resistance in the electrical circuit and the material properties of the dielectric ﬁlms in tribo-pair on the electric output of TENG device are studied, which may provide guidelines for the design and arrangement of TENG devices on marine Sensors 2021, 21, 1514 13 of 21

pipelines. The corresponding parameters are shown in Table1 (see Section3) and Table2 (see Section 5.1). To obtain the feasible installation position of TENG devices on pipelines, the TENG devices are supposed to be arranged every two meters on a pipeline with the circuit resistance of 10 MΩ. The peak values for the dynamic response amplitude of pipeline, the oscillation response of the mass-spring base and the electric output of the TENG devices Sensors 2021, 21, x FOR PEER REVIEW 15 of 24 are shown in Figure9, in which the time history analysis at 1/8, 1/4 and 1/2 span of the pipeline are presented, respectively.

(a) (b)

1/8 span 1/4 span 1/2 span

P y

(m)

of Amplitude (m) Mode superposition method Finite element analysis

t (s) x (m)

1/8 span 1/4 span 1/2 span

T y

(m) Amplitude of of Amplitude (m)

t (s) x (m)

(e) (f) 1/8 span 1/4 span 1/2 span

(V)

(V) Voltage Peak

Average Power Power Average (

t (s) x (m) FigureFigure 9. Influence 9. Influence of the install of theation installation position position of the TENG of the device TENG at device pipeline at on pipeline its output on its performance. output performance. (a,b) is the (influencea,b) is the of the positioninfluence at pipeline of the on position the dynamic at pipeline response on theof pipeline; dynamic (c response,d) is the ofinfluence pipeline; of ( cthe,d) installation is the influence position of the of installationTENG at pipeline position on the dynamicof TENG response at pipeline of the mass on the-spring dynamic base; response(e,f) is the of influence the mass-spring of the installation base; (e,f) position is the influence of TENG of at the pipeline installation on its position electric output. of TENG at pipeline on its electric output. As one of the factors which may greatly affect the electric output of TENG device, the time histories of the gap distance between the tribo-pair is dependent on the dynamic characteristics of the mass-spring base. To provide an accordance for the structural design of the mass-spring base, we investigate the output performance of TENG device with different natural frequencies (Figure 10a–d). As shown in Figure 10b, with increasing of the natural frequency, the amplitude for the gap distance between the tribo-pair shows expo- -2 nential drop, which could be expressed by the equation of yT,maxT= 0.205 . The peak voltage and average power also show exponential drop with the expression of −0.998 −3.193 VpeakT= 6.296 and P = 0.9T , respectively (Figure 10d). The results indicate that reducing the natural frequency of the mass-spring base may help improve the output performance of the TENG device. The influence of the effective thickness of the dielectric layer d0 is also studied (Figure 10f), the peak voltage and average power have similar variation trends with the increase of d0. The peak voltage (5.6 V) and power (0.014 μW) reaches its maximum value when d0 is 0.036 mm. The corresponding results provide an accordance for the design of dielectric

Sensors 2021, 21, 1514 14 of 21

Results show that the displacement amplitude of the pipeline, the gap distance between the tribo-pair, the peak voltage and average power of the TENG devices have similar trends as the installation positions are changed. The peak output voltage (2.1 V) and average output power (0.028 µW) of the TENG device reach their maximum values when x = 60 m and 340 m. When installed in the range of 40 m to 360 m, the TENG devices maintain a relatively high and stable electric output. That is to say, within this area, large quantities of TENG devices could be arranged to form a network to greatly improve the total electric output. As one of the factors which may greatly affect the electric output of TENG device, the time histories of the gap distance between the tribo-pair is dependent on the dynamic characteristics of the mass-spring base. To provide an accordance for the structural design of the mass-spring base, we investigate the output performance of TENG device with different natural frequencies (Figure 10a–d). As shown in Figure 10b, with increasing of the natural frequency, the amplitude for the gap distance between the tribo-pair shows exponential −2 drop, which could be expressed by the equation of yT,max = 0.205λT . The peak voltage −0.998 and average power also show exponential drop with the expression of Vpeak = 6.296λT −3.193 and P = 0.9λT , respectively (Figure 10d). The results indicate that reducing the natural frequency of the mass-spring base may help improve the output performance of the TENG device. The inﬂuence of the effective thickness of the dielectric layer d0 is also studied (Figure 10f), the peak voltage and average power have similar variation trends with the increase of d0. The peak voltage (5.6 V) and power (0.014 µW) reaches its maximum value when d0 is 0.036 mm. The corresponding results provide an accordance for the design of dielectric ﬁlms in tribo-pair. In circuit design analysis, the best electrical resistance for the system is 180 MΩ (Figure 10h). Sensors 2021, 21, x FOR PEER REVIEW 16 of 24

Sensors 2021, 21, 1514 15 of 21 films in tribo-pair. In circuit design analysis, the best electrical resistance for the system is 180 MΩ (Figure 10h).

(a) (b)

2Hz 4Hz 6Hz 8Hz 10Hz

T y

(m)

T y

−2

yT,peakT= 0.205 Amplitude of of Amplitude (m)

t (s) T ( H z )

2Hz 4Hz 6Hz 8Hz 10Hz

μ P

(V)

V −0.998 VpeakT= 6.296

Peak Voltage (V) Voltage Peak Average Power Power Average ( −3.193 P = 0.9T

t (s) T (Hz)

(e) (f) W) μ P

(V)

V Peak Voltage (V) Voltage Peak

Average Power Power Average (

0.01mm 0.03mm 0.16mm 0.64mm

t (s) d0 (mm)

(g) (h) W) μ P

(V) V

(V) Voltage Peak Average Power Power Average (

2M 20M 200M 2,000M

R ( ) t (s) FigureFigure 10 10.. InfluenceInfluence ofof thethe natural natural frequency frequency of of the the mass-spring mass-spring bass, bass, effective effective thickness thickness of the of dielectric the dielectric films andfilms the and circuit the circuitresistance resistance on the on output the output performance performance of TENG of TENG device. device. (a,b) are (a,b the) are influence the influence of the naturalof the natural frequency frequency of the of mass-spring the mass- springbase on base the on dynamic the dynamic response response of the base;of the ( cbase;,d) are (c, thed) are influence the influence of the naturalof the natural frequency frequency of the mass-springof the mass-spring base on base the electric output of TENG device; (e,f) are the influence of the effective thickness of the dielectric layer on the electric output of TENG device; (g,h) are the influence of the circuit loading resistance on the electric output of TENG device.

Sensors 2021, 21, 1514 16 of 21

5.3. Multiple Parameters Analysis of Output Performance Based on the dimensionless expressions of the electrical output, the theoretical analysis is developed to reveal a clear correlation between the normalized output performance and the dimensionless compound parameters using Equations (11)–(16). The simulation is carried out using multi-parameter analysis, so that it can be utilized in the design for the energy harvesting system with any structure or material parameters. The scaling laws relating the dimensionless output and the two compound variables 2 d0t0 d0mpSt ( RSε and C ρ D3 ) are presented in Figure 11. According to the possible range of the corre- Sensors 2021, 21, x FOR PEER REVIEW 0 L w 18 of 24 sponding parameters of TENG and the pipe in actual applications, the compound parameter 2 d0t0 −5 2 d0mpSt −2 5 is evaluated in the range of 10 to 10 with 3 in the range of 10 to 10 . RSε0 CLρwD

4 (a) 105 10 (b) 105 108 6 104 103 104 10 4 3 2 3 10 10 10 10 2 3 2 3 2 10 2 2 t 10 t 10 10 ρ ρ 1 0p 0p Lw Lw dmS 10 dmS 10 CD 1 CD 10−2 1 − 1 10 1 10−4 − 1 −1 −6 10 10−2 10 10 −2 −2 −8 10 10 − − − − − 10 10−5 10−4 10−3 10−2 10−1 1 10 102 103 10 5 10 4 10 3 10 2 10 1 1 10 102 103 dt dt00 00 ε RSε RS 0 0 (c) 4 (d) 10 107 103 105 103 102 2

t 1 3 10

10 t 10−1 ε 24 Lw Lw −

CD 3 0p 00

1 CDS peak 0 p

222 6 10 σρ − ε − VmS 4 4

PmSdt σρ − −1 10 5 10 10 −1 10 −1 dt00 10 dt 10 10−7 00 −2 RSε 10 ε 10 10 0 RS 0 2 102 10−9 10 −3 10 − − 10−2 10−1 1 10 102 103 104 105 10 2 10 1 1 10 102 103 104 105 2 2 dmS0pt dmS0pt ρ 3 ρ 3 CDLw CDLw

Figure 11. Analysis of the output performance ideal energy harvesting system with dimensionless parameters. (a,b) are Figure 11. Analysis of the output performance ideal energy harvesting system2 with dimensionless parameters. (a,b) are power d0t0 d0mpSt power maps for the two dimensionless parameters RSε and2 C D3 . The color represents the dimensionless peak voltage dt00 dmS0p0 t Lρw maps for the two dimensionless parameters and . The color represents the dimensionless peak voltage V2 and RSε CDρ 3 d0mpSt n1 V and average power P , respectively.0 (c,d) showLw restricted optimization voltage and power versus 3 with n1 n1 CLρw D 2 d0t0 dmS ﬁxed. 0pt dt00 averageRS εpower0 P , respectively. (c,d) show restricted optimization voltage and power versus with fixed. n1 ρ 3 ε CDLw RS 0 2 d0mpSt d0t0 In Figure 11a,b for the relationship between the compound variables ( 3 and ) To investigate the relationship between the output performance andCLρ wtheD dynamicRSε0 2 d0mpSt characteristicson the dimensionless of the system output, in it detail, is obvious anothe thatr scaling the increasing law is exhibited of 3inmay Figure enhance 12 based the CLρwD on Equations (11) – (13). The results show that2 the dimensionless compound2 4 parameters ( Vpeakε0mpSt Pε0mpSt d0t0 4 dimensionlessmdκ peak voltage Vn1 ( 3 ) and power Pn1 ( 2 2 2 6 ) no matter how p0 dt00 σCLρwD σ CLρwD S 2 and d m )S 2have a larger optimal range for the best output performance than CDUd0t0ρ RS0ε p t 4 5 d0t0 Lwvaries. When 0 3 is in the range of 10 –10 and in the range of 1–10, both the RSε0 C ρwD RSε0 L εκ4 dimensionless voltage and power reaches the optimalVmpeak 0 value. p Thus, as long as the two that in Figure 11. The dimensionless voltage V ( ) in Figure 12a reaches to its compound variables are evaluated in these rangesn2 σρ through device2 design and parameter CDULw analysis, the electric output of TENGmdκ 4 may be maximized. dt maximum value (0.5) when p0 ranges in 1 - 105 with 00 from 10-5 to 4. ρ 2 ε CDULw RS 0 mdκ 4 The dimensionless power reaches the maximum value when p0 ranges from 10 ρ 2 CDULw dt dt to 5 with 00 ranging from 1 to 102 . In Figure 12c,d, for each 00 , the value of 10 ε ε RS 0 RS 0 Pmεκ28 dt mdκ 4 V and P ( 0p 00 ) increases monotonically with p0 and approaches n2 n2 σρ222 24 ρ 2 SCLw DU CDULw mdκ 4 mdκ 4 to a constant when p0=10 , which implies that optimal p0is over 10. In ρ 2 ρ 2 CDULw CDULw

Sensors 2021, 21, 1514 17 of 21

2 d0mpSt For better understanding of the influence of 3 on electric output performance CLρwD 2 d0mpSt of TENG, we present the restricted optimization voltage and power versus 3 with CLρwD d0t0 fixed (Figure 11c,d). As can be seen, for each d0t0 , both the dimensionless voltage V RSε0 RSε0 n1 2 d0mpSt and power Pn1 increase rapidly with 3 firstly, and then tend to a stable value when CLρwD 2 2 d0mpSt 4 d0mpSt 4 5 3 reaches 10 . Thus, the optimal range of 3 is 10 –10 . In real applications, CLρwD CLρwD the Strouhal number St, water density ρw and Lift coefficient CL in this variable reflect the characteristics of the ocean flow and may be not adjustable. For optimization of the output performance, we can design the structural characteristics of the pipe (mp, D) and TENG (d0) to make the compound variable in the optimal range. To investigate the relationship between the output performance and the dynamic characteristics of the system in detail, another scaling law is exhibited in Figure 12 based on Equations (11)–(13). The results show that the dimensionless compound parameters 4 mpκ d0 d0t0 ( 2 and ) have a larger optimal range for the best output performance than that in CLρwDU RSε0 4 Vpeakε0mpκ Figure 11. The dimensionless voltage Vn2 ( 2 ) in Figure 12a reaches to its maximum σCLρwDU 4 mpκ d0 5 d0t0 −5 value (0.5) when 2 ranges in 1–10 with from 10 to 4. The dimensionless CLρwDU RSε0 4 mpκ d0 5 d0t0 power reaches the maximum value when 2 ranges from 10 to 10 with ranging CLρwDU RSε0 Pε m2 κ8d t 2 d0t0 0 p 0 0 from 1 to 10 . In Figure 12c,d, for each RSε , the value of Vn2 and Pn2 ( 2 2 2 2 4 ) 0 Sσ CLρwD U 4 4 mpκ d0 mpκ d0 increases monotonically with 2 and approaches to a constant when 2 = 10, CLρwDU CLρwDU 4 4 mpκ d0 mpκ d0 5 which implies that optimal 2 is over 10. In short, when 2 ranges in 10–10 CLρwDU CLρwDU with d0t0 from 1 to 4, both the dimensionless power and voltage reaches the maximum RSε0 value simultaneously. Arranging the two variables in these ranges, we may obtain the best output voltage and power of TENG device at the same time. 2 4 d0t0 d0mpSt mpκ d0 Based on Figures 11 and 12, we obtain the optimal range of , 3 and 2 RSε0 CLρwD CLρwDU for the best dimensionless voltage and power of TENG device, respectively. Besides, we can also carry out single-parameter analysis to improve the output performance based on the results. For example, the influence of current excitation period t0, area S of the tribo-pair, load resistance R and the effective thickness of the dielectric material films d0 on the output voltage V can be realized in Figure 11a,b. After obtaining the best combination of d0t0 n1 RSε0 2 d0mpSt and 3 , we can study one of above parameters (t0, S, R, D, mp and d0) with other CLρwD parameters remaining fixed. To investigate the influence of frequency ratio between the flow excitation, the pipe and TENG on the output performance, the normalized voltage and power versus γp and 4 4 d0t0 mpκ d0 d0t0 mpκ d0 γT with specific and 2 are presented in Figures 13 and 14. and 2 RSε0 CLρwDU RSε0 CLρwDU are selected in the range where normalized voltage and power reaches the optimal value according to Figure 12a,b. It is observed that all voltage and power curves reach the maximum values when γp = 1, which will lead to the resonance of pipe and the device. The similar tendency of the dimensionless voltage and power versus the frequency ratio between the current excitation and the mass-spring base of TENG device is shown in Figure 14. In practice, the resonance phenomenon is harmful for the structural safety of the system and should be prevented. However, when γp is less than 1 and γT greater than 1 the dimensionless voltage and power both reach a considerable and stable value. We can carry out structural design to make the energy harvesting system achieve this value, thereby enhancing the electric output of the TENG device. Sensors 2021, 21, x FOR PEER REVIEW 19 of 24

mdκ 4 dt short, when p0 ranges in 10 - 105 with 00 from 1 to 4, both the dimension- ρ 2 ε CDULw RS 0 less power and voltage reaches the maximum value simultaneously. Arranging the two variables in these ranges, we may obtain the best output voltage and power of TENG device at the same time. dt dmS2 Based on Figures 11 and 12, we obtain the optimal range of 00 , 0pt and ε ρ 3 RS 0 CDLw mdκ 4 p0 for the best dimensionless voltage and power of TENG device, respectively. ρ 2 CDULw Besides, we can also carry out single-parameter analysis to improve the output perfor-

mance based on the results. For example, the influence of current excitation period t0 , area S of the tribo-pair, load resistance R and the effective thickness of the dielectric ma-

terial films d 0 on the output voltage Vn1 can be realized in Figure 11a,b. After obtaining dt dmS2 Sensors 2021, 21, 1514 the best combination of 00 and 0pt , we can study one of above parameters ( t , 18 of 21 ε ρ 3 0 RS 0 CDLw

S, R, D, mp and d 0 ) with other parameters remaining fixed.

5 5 (a) 10 (b) 10 −1 0.5 10 104 104 −3 103 0.4 103 10 2 2 102 102 10−5

4 0.3 4

κ κ p0 ρ p0 ρ Lw md 10 10 Lw md −7 CDU 0.2 CDU 10 1 1 −9 − 0.1 − 10 10 1 10 1

−2 −2 −11 10 0 10 − − − − − 10 10−5 10−4 10−3 10−2 10−1 1 10 102 103 10 5 10 4 10 3 10 2 10 1 1 10 102 103 dt00 dt00 ε ε RS 0 RS 0 (c)0.6 (d) 1 0.5 10−2

2 0.4 Sensors 2021, 21, x FOR4 PEER REVIEW 20 of 24

10−4

εκ 0.3 28 Lw Lw

−4 0p 00 −

peak 0 p 6 CDU 10 εκ 222 24 10 −4 Vm σρ 0.2 dt −1 Pm dt σρ 10 4 00 10 SC DU dt −1 mdp0 00 10 ε 10 − RareS 0 selected in the range8 where normalized εvoltage and power reaches the 0.1 2 2 10 RS 0 10 10 2 C DULw 10 0 10-10 optimal value according to Figure 12a,b.− It −is observed that2 all3 voltage4 5 and power curves 10−2 10−1 1 10 102 103 104 105 10 2 10 1 1 10 10 10 10 10 κ 4 κ 4 reach themdp0 maximum values when  p =1, which willmd p0lead to the resonance of pipe and the CDUρ 2 CDUρ 2 deviceLw. The similar tendency of the dimensionless voltageLw and power versus the frequency ratio between the current excitation and the mass-spring base of TENG device is shown FigureFigure 12. AnalysisAnalysis of of the the output output performance performance ideal idealenergy energy harvesting harvesting system with system dimensionless with dimensionless parameters. parameters.(a,b) are power (a maps,b) are in Figuredt 14. In practice,mdκ 4 the resonance4 phenomenon is harmful for the structural safety of 00 p0d0t0 mpκ d0 for the two dimensionless parameters and . The color represents the dimensionless peak voltage Vn2 and average power maps for the two dimensionlessthe systemε parameters and shouldρ 2beand prevented.2 .However, The color when represents  is the less dimensionless than 1 and peak T greater voltage RS 0 CDULwRSε0 CLρw DU p m κ4d than 1 the dimensionless voltage and power both mdreachκ 4 a considerable and stablep value.0 Vn2 and average power Pn2, respectively; (c,d) show restricted optimization voltagep0 and powerdt00 versus 2 with power P , respectively; (c,d) show restricted optimization voltage and power versus with fixed. CLρw DU n2 We can carry out structural design to make the CDUenergyρ 2 harvestingRSε system achieve this d0t0 ﬁxed. Lw 0 RSε0 value, thereby enhancing the electric output of the TENG device. To investigate the influence of frequency ratio between the flow excitation, the pipe and4 TENG on the output performance, the normalized voltage and power versus γ and md dt00 p p0 10−2 1 102 104 = 0.1 2 κ 4 RS CDULw dt00 mdp0 0 dt00 γ with specific and 102 are presented in Figures 13 and 14. and T ε ρ 2 (b) ε (a) RS 0 CDULw RS 0 1

2 −2 4 10 −2 10 −4

28 10 

0 p 0 0

2 2 2 2 4

peak 0 p C DU

 −6

P m d t  −4 10 10 SCDU 10−8

−6 −10 10 10 −2 10−2 10−1 1 10 102 10 102   p p

dt md 4 00 10−4 10−2 1 p0=100 RS 2 0 CDULw (c) (d)

10−2

10−2 10−4

10−6 10−4 10−8 10−6 10−10

d0t0 Figure 13. The normalized voltage Vn2 and Pn2 versus γp.(a,b) are normalized voltage and power versus γp with dt00 RSε0 Figure 13. The normalized voltage Vn2 and Pn2 versus  p . (a,b) are normalized4 voltage and power versus  p with fixed; mpκ d0 RS0 ﬁxed; (c,d) are normalized voltage and power versus γp with C ρ DU2 ﬁxed. 4 L w mdp0 (c,d) are normalized voltage and power versus  p with 2 fixed. CLw DU

SensorsSensors 20212021,, 2121,, x 1514 FOR PEER REVIEW 2119 of of 24 21

4 md dt00 p0 10−2 1 102 104 = 0.1 2 RS CDULw 0 102 (a) (b)

1 2 4 10−2

−2 28 −4 

10 Lw 10

0 p 0 0

peak 0 p

C DU

2 2 2 2 4 

Vm −6

 P m d t 10 10−4 SCDU 10−8

10−6 10−10 10−2 10−1 1 10 102 10−2 102  T  T 4 dt00 −4 −2 mdp0 10 10 1 2 =100 RS 0 CLw DU (c) (d)

10−2

−2 10 10−4 10−6 10−4 10−8 −6 10 10−10   T T

d0t0 Figure 14. The normalized voltage Vn2 and Pn2 versus γT.(a,b) are normalized voltage and power versus γT with dt00 Figure 14. The normalized voltage V and P versus  . (a,b) are normalized voltage and power versus  with RSε0fixed; n2 n2 T 4 T mpκ d0 RS0 fixed; (c,d) are normalized voltage and power versus γT with 2 fixed. 4 CLρw DU mdp0 (c,d) are normalized voltage and power versus  T with 2 fixed. 6. Conclusions CDULw In this paper, we use a contact-mode triboelectric nanogenerator (TENG) to scavenge 6mechanical. Conclusion energys from vibrating marine pipes. The TENG device is fabricated with PTFE, nylonIn dielectricthis paper material, we use a films, contact acrylic-mode base, triboelectric springs nanogenerator and a waterproof (TENG box.) to The scavenge output mechanicalperformance energy of the fromTENG vibrating is tested bymarine experiment pipes. Themeans, TENG which device proves is the fabricated feasibility with of PTFE,TENG. nylon Theoretical dielectric simulations material arefilms, carried acrylic out base, to investigate springs and the a influencewaterproo off typicalbox. The factors outputon theperformance electric output, of the such TENG as theis tested dynamic by experiment characteristics means, of the which pipe andproves spring-mass the feasibility base offor TENG. the device, Theoretical the loading simulations resistance are in carried the electrical out to circuitinvestigate and the the material influence properties of typical of factorsthe dielectric on the filmselectric in output, tribo-pair. such In as addition, the dynamic two groups characteristi of dimensionlesscs of the pipe expressions and spring for- massnormalized base for electric the device, output the versus loading two resistance compound in variablesthe electri arecal establishedcircuit and the to provide material a propertiesgeneral optimization of the dielectric method films of thein tribo energy-pair. harvesting In addition, system. two groups Based on of thedimensionless experiment expressionstests and theoretical for normalized simulation electric in thisoutput paper, vers theus two main compound conclusion variables is obtained are established as below: to provide(1) The a general experimental optimization tests confirm method that of thethe electricalenergy harvesting output of system. TENG mayBased meet on the the experimentrequirement tests of theand monitoring theoretical systemsimulation in pipes. in this The paper, output the main power conclusion of TENG reachesis obtained the 2 asmaximum below: value of 14.0 µW with the power density of 5.56 mW/m at the electrical circuit resistance(1) The of experimental 200 MΩ. If all tests TENG confirm devices that are the connected electrical inoutput series of with TENG large may quantities meet the to requirementform a network, of the the monitoring output of thesystem energy in pipes. harvesting The output system power will be of enhanced TENG reaches greatly the to maximumprovide adequate value of energy 13.9 μW for with the monitoringthe power density system of in 5.56 pipes. mW/m2 at the electrical circuit resistance(2) The of output200 MΩ performance. If all TENG of devices TENG isare further connected investigated in series by with theoretical large quantities simulations, to formwith a the network, influence the of outpu fourt typicalof the energy factors harvesting on the output system performance will be enhanced of TENG greatly devices to provideobtained. adequate It is observed energy for that the the monitoring peak dynamic system response in pipes. amplitude of occurs near the 1/8 span(2) The of pipe.output Thus, performance installing of TENG TENG devices is further near investigated the 1/8 span by of theoretical the pipe may simula- help tions,maximize with the influence electric output. of four Thetypical results factors also on provide the output a guideline performance for structural of TENG andde- material design for TENG devices. Reducing the natural frequency of the mass-spring base vices obtained. It is observed that the peak dynamic response amplitude of occurs near can help enhance the electric output of TENG devices, and the optimal effective thickness of the 1/8 span of pipe. Thus, installing TENG devices near the 1/8 span of the pipe may help

Sensors 2021, 21, 1514 20 of 21

the tribo-pair is 0.036 mm. Moreover, it is found that the maximum output power appears at the resistance of 180 MΩ, which is close to the resistance (200 MΩ) in the experiment and proves again the accuracy of the theoretical model. (3) The multiple-parameters analysis reveals the relationship between the normalized electric output and the normalized system parameters. With regard to ﬁrst set of the scaling law, both the normalized voltage Vn1 and power Pn1 reaches their maximum value 2 d0mpSt 4 5 d0t0 simultaneously when the compound variable 3 ranges from 10 to 10 with in CLρwD RSε0 the range of 1–10. For another set of dimensionless expressions, the normalized voltage 4 mpκ d0 Vn2 and power Pn2 reaches the maximum value with the compound variable 2 in CLρwDU the range of 10–105 and d0t0 in the range of 1 to 4. Moreover, the inﬂuence of the natural RSε0 frequency of the system on the electric output of TENG is investigated. It is observed that TENG has a considerable and stable electric output when γp is less than 1 or γT greater than 1. Arranging these variables in their optimal ranges through structural design and parameters adjustment, the best normalized voltage and power may be achieved. The feasibility of using TENG to scavenge mechanical energy from marine pipes is proved by experiment tests and theoretical simulations. Through the theoretical simulation, the optimal ranges for the typical factors are presented, which provides a guideline for the structural and material design of the proposed energy harvesting system. In the future, the application of TENG devices is expected to be a feasible approach to power monitoring systems for marine pipelines.

Supplementary Materials: The following are available online at https://www.mdpi.com/1424-822 0/21/4/1514/s1, Video S1: LEDs powered by TENG. Author Contributions: H.Z., G.L.: Conceptualization, Methodology, Investigation, Writing—review & editing. R.L.: Data curation, Writing—original draft, Investigation, Software. L.W.: Data curation, Investigation, Software. All authors have read and agreed to the published version of the manuscript. Funding: This work was funded by Zhejiang Provincial Natural Science Foundation for Distin- guished Young Scholar under grant No. LR20E080003, the National Natural Science Foundation of China under the grant Nos. 51978609, 11925206, 11472244. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References 1. Gabbai, R.D.; Benaroya, H. An overview of modeling and experiments of vortex-induced vibration of circular cylinders. J. Sound Vib. 2005, 282, 575–616. [CrossRef] 2. Lu, P.; Lalam, N.; Badar, M.; Liu, B.; Ohodnicki, P.R. Distributed optical fiber sensing: Review and perspective. Appl. Phys. Rev. 2019, 6, 041302. [CrossRef] 3. Nishimoto, T.; Miyahara, T.; Takehana, H.; Tateno, F. Development of 66kV XLPE submarine cable using optical fiber as a mechanical-damage-detection-sensor. IEEE T Power Deliv. 2002, 10, 1711–1717. [CrossRef] 4. Zhou, Z.; Zhang, J.; Huang, X.; Zhang, J.; Guo, X. Trend of soil temperature during pipeline leakage of high-pressure natural gas: Experimental and numerical study. Measurement 2020, 153, 107440. [CrossRef] 5. Ren, L.; Jiang, T.; Jia, Z.G.; Li, D.S.; Yuan, C.L.; Li, H.N. Pipeline corrosion and leakage monitoring based on the distributed optical fiber sensing technology. Measurement 2018, 57–65. [CrossRef] 6. Xia, H.; Xia, Y.; Ye, Y.; Qian, L.; Shi, G. Simultaneous Wireless Strain Sensing and Energy Harvesting from Multiple Piezo-Patches for Structural Health Monitoring Applications. IEEE T Ind. Electron 2019, 66, 8235–8243. [CrossRef] 7. Othmani, C.; Zhang, H.; Lü, C. Effects of initial stresses on guided wave propagation in multilayered PZT-4/PZT-5A composites: A polynomial expansion approach. Appl Math Model 2020, 78, 148–168. [CrossRef] 8. Zhang, Y.; Zhang, H.; Lü, C.; Chen, Y.; Wang, J. Piezoelectric energy harvesting from roadway deformation under various traffic flow conditions. J. Intel. Mat. Syst. Str. 2020, 31, 1751–1762. [CrossRef] 9. Zhang, H.; Huang, K.; Zhang, Z.; Xiang, T.; Quan, L. Piezoelectric Energy Harvesting From Roadways Based on Pavement Compatible Package. Journal of Applied Mechanics 2019, 86.[CrossRef] Sensors 2021, 21, 1514 21 of 21

10. Zhang, H.; Ye, G.; Zhang, Z. Acoustic Radiation of a Cylindrical Piezoelectric Power Transformer. Journal of Applied Mechanics 2013, 80.[CrossRef] 11. Zhang, H.; Yao, L.; Quan, L.; Zheng, X. Theories for triboelectric nanogenerators: A comprehensive review. Nanotechnol Rev. 2020, 9, 610–625. [CrossRef] 12. Zhang, H.; Wang, H.; Zhang, J.; Zhang, Z.; Dong, S. A Novel Rhombic-shaped Paper-based Triboelectric Nanogenerator for Harvesting Energy from Environmental Vibration. Sensors Actuators A Phys. 2019, 302, 111806. [CrossRef] 13. Zhang, H.; Yang, C.; Yu, Y.; Zhou, Y.; Luo, J. Origami-tessellation-based triboelectric nanogenerator for energy harvesting with application in road pavement. Nano Energy 2020, 78, 105177. [CrossRef] 14. Okosun, F.; Cahill, P.; Hazra, B.; Pakrashi, V. Vibration-based leak detection and monitoring of water pipes using output-only piezoelectric sensors. Eur. Phys. J. Spec. Top. 2019, 228, 1659–1675. [CrossRef] 15. Rui, X.; Zeng, Z.; Zhang, Y.; Li, Y.; Xu, T. An intelligent self-powered pipeline inner spherical detector with piezoelectric energy harvesting. IEEE Access. 2019, 7, 104621–104629. [CrossRef] 16. Cao, D.; Duan, X.; Guo, X.; Lai, S. Design and performance enhancement of a force-amplified piezoelectric stack energy harvester under pressure fluctuations in hydraulic pipeline systems. Sens. Actuators A Phys. 2020, 309, 112031. [CrossRef] 17. Aramendia, I.; Fernandez-Gamiz, U.; Zulueta Guerrero, E.; Lopez-Guede, J.M.; Sancho, J. Power Control Optimization of an Underwater Piezoelectric Energy Harvester. Appl. Sci. 2018, 8, 389. [CrossRef] 18. Aphayvong, S.; Yoshimura, T.; Murakami, S.; Kanda, K.; Fujimura, N. Investigation of efficient piezoelectric energy harvesting from impulsive force. Jpn. J. Appl. Phys. 2020, 59, SPPD04. [CrossRef] 19. Wang, Z.L. Triboelectric Nanogenerators as New Energy Technology for Self-Powered Systems and as Active Mechanical and Chemical Sensors. Acs Nano 2013, 7, 9533–9557. [CrossRef] 20. Chen, J.; Yang, J.; Li, Z.; Fan, X.; Zi, Y.; Jing, Q.; Guo, H.; Wen, Z.; Pradel, K.C.; Niu, S. Networks of Triboelectric Nanogenerators for Harvesting Water Wave Energy: A Potential Approach toward Blue Energy. ACS Nano 2015, 9, 3324–3331. [CrossRef] 21. Wen, Z.; Guo, H.; Zi, Y.; Yeh, M.; Wang, X.; Deng, J.; Wang, J.; Li, S.; Hu, C.; Zhu, L.; et al. Harvesting Broad Frequency Band Blue Energy by a Triboelectric–Electromagnetic Hybrid Nanogenerator. Acs Nano 2016, 10, 6526–6534. [CrossRef][PubMed] 22. Wang, Z.L.; Jiang, T.; Xu, L. Toward the blue energy dream by triboelectric nanogenerator networks. Nano Energy 2017, 39, 9–23. [CrossRef] 23. Chen, H.; Xing, C.; Li, Y.; Wang, J.; Xu, Y. Triboelectric nanogenerators for a macro-scale blue energy harvesting and self-powered marine environmental monitoring system. Sustain Energ Fuels 2020, 4, 1063–1077. [CrossRef] 24. Xi, Y.; Guo, H.; Zi, Y.; Li, X.; Wang, J.; Deng, J.; Li, S.; Hu, C.; Cao, X.; Wang, Z.L. Multifunctional TENG for Blue Energy Scavenging and Self-Powered Wind-Speed Sensor. Adv. Energy Mater. 2017, 7, 1602397. [CrossRef] 25. Saadatnia, Z.; Asadi, E.; Askari, H.; Esmailzadeh, E.; Naguib, H.E. A heaving point absorber-based triboelectric-electromagnetic wave energy harvester: An efficient approach toward blue energy. Int. J. Energy Res. 2018, 42, 2431–2447. [CrossRef] 26. Shao, H.; Wen, Z.; Cheng, P.; Sun, N.; Shen, Q.; Zhou, C.; Peng, M.; Yang, Y.; Xie, X.; Sun, X. Multifunctional Power Unit by Hybridizing Contact-Separate Triboelectric Nanogenerator, Electromagnetic Generator and Solar Cell for Harvesting Blue Energy. Nano Energy 2017, 39, 608–615. [CrossRef] 27. Wang, Y.; Yu, X.; Yin, M.; Wang, J.; Gao, Q.; Yu, Y.; Cheng, T.; Wang, Z.L. Gravity triboelectric nanogenerator for the steady harvesting of natural wind energy. Nano Energy 2021, 82, 105740. [CrossRef] 28. Guo, H.; Wen, Z.; Zi, Y.; Yeh, M.; Wang, J.; Zhu, L.; Hu, C.; Wang, Z.L. A Water-Proof Triboelectric–Electromagnetic Hybrid Generator for Energy Harvesting in Harsh Environments. Adv. Energy Mater. 2016, 6, 1501593. [CrossRef] 29. Jiang, T.; Zhang, L.M.; Chen, X.; Han, C.B.; Tang, W.; Zhang, C.; Xu, L.; Wang, Z.L. Structural Optimization of Triboelectric Nanogenerator for Harvesting Water Wave Energy. Acs Nano 2015, 9, 12562–12572. [CrossRef][PubMed] 30. Zhao, X.J.; Zhu, G.; Fan, Y.J.; Li, H.Y.; Wang, Z.L. Triboelectric Charging at the Nanostructured Solid/Liquid Interface for Area-Scalable Wave Energy Conversion and Its Use in Corrosion Protection. ACS Nano 2015, 9, 7671–7677. [CrossRef][PubMed] 31. Xu, L.; Pang, Y.; Zhang, C.; Jiang, T.; Chen, X.; Luo, J.; Tang, W.; Cao, X.; Wang, Z.L. Integrated triboelectric nanogenerator array based on air-driven membrane structures for water wave energy harvesting. Nano Energy 2017, 31, 351–358. [CrossRef] 32. Wang, Z.L. On Maxwell’s displacement current for energy and sensors: The origin of nanogenerators. Mater. Today 2017, 20, 74–82. [CrossRef] 33. Totovic, A.R.; Dabos, G.; Passalis, N.; Tefas, A. Femtojoule per MAC Neuromorphic Photonics: An Energy and Technology Roadmap. Ieee J Sel Top Quant 2020, 26, 1–15. [CrossRef] 34. Paultre, P. Dynamics of Structures; John Wiley & Sons: Hoboken, NJ, USA, 2013. 35. Farshidianfar, A.; Zanganeh, H. A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio. J. Fluids Struct. 2010, 26, 430–441. [CrossRef] 36. Niu, S.; Wang, S.; Lin, L.; Liu, Y.; Zhou, Y.S.; Hu, Y.; Wang, Z.L. Theoretical study of contact-mode triboelectric nanogenerators as an effective power source. Energy Environ. Sci. 2013, 6, 3576–3583. [CrossRef] 37. Zhang, H.; Quan, L.; Chen, J.; Xu, C.; Zhang, C.; Dong, S.; Lü, C.; Luo, J. A general optimization approach for contact-separation triboelectric nanogenerator. Nano Energy 2019, 56, 700–707. [CrossRef] 38. Zhang, H.; Zhang, C.; Zhang, J.; Quan, L.; Huang, H.; Jiang, J.; Dong, S.; Luo, J. A theoretical approach for optimizing sliding-mode triboelectric nanogenerator based on multi-parameter analysis. Nano Energy 2019, 61, 442–453. [CrossRef]