# Pulse and power characteristics of a flexible piezoelectric nanogenerator in the Reynolds number range simulating ocean current

An increase in the specific surface area of ​​micro/nanostructured piezoelectric materials improves the output performance of PENGs due to an increase in the trapping region for charge transfer26. To increase the specific surface of the piezoelectric mesh in PVDF, we used the EHD jet printing technique, allowing a higher printing resolution compared to conventional inkjet printing techniques that work with a printing module. thermal or piezoelectric.27. By applying an electric field, ink droplets are propelled from the nozzle onto a target substrate in EHD print mode, allowing the formation of a high-resolution Taylor cone jet down to the micrometer scale or less. PVDF-based meshes with a width of 13 μm and a thickness of 1.54 μm [Fig. S2(a)] have been achieved. For PVDF-based mesh patterns, AgNP-based gate electrodes with a width of 18 μm and a thickness of 1.19 μm [Fig. S2(b)] were built using the EHD printing technique.

PVDF can have α, β, γ and δ phases28of which the β phase is desirable for PENG applications due to its spontaneous polarization behavior29. However, PVDF tends to crystallize in α phase rather than β phase30,31,32. Therefore, additional processes to change the α-phase to the β-phase are usually required. Nevertheless, according to Ye et al., the EHD jet printed PVDF mesh exhibits a dominant β-phase33. Moreover, the analysis of the FTIR spectra shown in Fig. S3 confirms that the β phase was dominant in the printed piezoelectric PVDF. Therefore, we did not perform any additional process to change α-phase to β-phase.

Vortex detachment occurs when fluid passes a bluffing body, producing a sinusoidal force. This is the origin of the vibration of PENGs with flexible layers. If the vortex shedding frequency approaches the frequencies of the PENG structure, then chaotic flapping or flapping motion of the PENG, which is desirable for feeding, may occur. In the case of a two-dimensional sheet with high longitudinal stiffness and low bending stiffness, the structural restoring force of the sheet is governed by the flow-induced tensionten. Accordingly, the dynamic effect of the sheet, the formation of surface vortices, the propagation of wake vortices, the structural inertia and the changing force of the main body due to bending stiffness must be taken into account to predict the mechanical response of the sheet to the detachment of the vortices. Therefore, Re, KBand M* were considered as the key parameters governing the mechanical response of the sheetten. Re, KBand M* are defined as follows:

$$Re= frac{{rho }_{f}uL}{{mu }_{f}},quad {K}_{B}=frac{E{h}^{3}/ 12(1-{v}^{2})}{{rho }_{f}{u}^{2}{L}^{3}},quad{M}^{*}=frac {{rho }_{s}h}{{rho }_{f}L}$$

where E, (v), (h), ({rho }_{f}, {rho }_{s}, u), Land ({mu }_{f}) denote Young’s modulus (MPa), Poisson’s ratio, thickness (m), fluid density (kg/m3), material density (kg/m3), flow velocity (m/s), two-dimensional body length (m), and fluid viscosity (kg/ms), respectively. According to Lumpkin et al., the global flow velocity distribution in the Pacific, Atlantic and Indian oceans ranges from 0.031 to 0.656 m/s, and the corresponding value Re values ​​range from 6200 to 13120034. We fix the Re range from 1 to 141,489 in current water channel experiments to simulate ocean currents.

Figure 2a presents the beating responses of the PENG to Re = 40,000 when KB= 0.00124 and M*= 0.01, and at Re = 60,000 when KB= 0.000046 and M* = 0.003, demonstrating that chaotic flapping and flapping motion can be achieved in the water channel. Figure S4 shows the response regime map as a function of M* versus Re , demonstrating steady and beating modes. The initial neutral mode was found at M* = 0.005 and Re = 10,000, and the boundary has been distributed at a higher level M* as Reincrease. Figure 2b presents the neutral curves between steady (i) and swing (ii and iii) motions, demonstrating that a KB a value less than 0.0024 can beat whatever the Reinterval. Gurugubelli et al. reported that the neutral curve for a conventional foil appeared at a KB value about 0.001 to Re35. Further, the regime in which flapping motion is dominant can be divided into flapping (ii) and chaotic flapping (iii) regimes.

As shown in Fig. 3, PIV was used to represent the distribution of the vortices and the velocity of the components at t = 0, 0.2 and 0.4 s under beating (Re= 40,000, KB= 0.00124, M*= 0.01) and chaotic beating regimes (Re= 60,000, KB= 0.000046, M*= 0.003). Independent of the PENG response, the vortex flow velocities exhibited a comparable level of 0.013 m/s. However, in the case of the chaotic beating regime, there were significant differences in flow velocities between the vortex and the surroundings, resulting in a pressure gradient along the y-axis. In contrast, the difference in flow velocities was insignificant in the beating regime. The steep pressure gradient due to the significant difference in flow velocity can be attributed to the greater displacement of the PENG in the chaotic beat regime than in the beat regime.

Figure 4 presents the output voltages and currents generated by the PENG under steady beat, beat and chaotic beat regimes. A schematic model of PENG interaction with water flow is shown in Fig. S5(a). A schematic illustration of the measurement circuit and electron flows as a function of PENG behaviors is given in Figures S5(b) and (c). The acquired currents are sinusoidal due to the repetitive bending of the PENGs, as shown in Fig. S5(d).

As expected, Figure 4 shows that there was no output voltage or current in the steady state due to the absence of vibration. In the beating and chaotic beating regimes, the PENG can generate electricity. The outputs generated in the chaotic beating regime (17 mV and 8 nA) were higher than those in the beating regime (9 mV and 4 nA), indicating that the PENG harvesting energy from the ocean current should be designed to exhibit a chaotic beating response from the power supply perspective.

Figure 5a presents a plot of current density as a function of KB measured in the Rerange of 40,000 to 60,000, which was chosen because it covers the beating and chaotic beating regimes with a change in the KB. A sharp increase from around 0.889 to 2.354 (upmu)A m2 has been observed in the current density below a KB value of 0.001, which can be attributed both to the resonance between the vortex detachment and to the increased displacement of the PENG due to the increase in its compliance. To test our hypothesis, we plotted the frequency of vortex detachment and KB value according to Re(Fig. 5b), and the natural frequency of the PENG and the vortex detachment frequency as a function of KB (Fig. 5c). With Reranging from 40,000 to 60,000, Figure 5b shows that the frequency of vortex detachment and KB the values ​​are distributed in the ranges of 5 to 25 and 0.000051 to 0.00062, respectively. Figure 5c shows that the natural frequency of the PENG 2 mode has approached the vortex detachment frequency as KB approached 0.00052. In contrast, the mode 1 frequency did not approach the vortex detachment frequency, indicating that the mode 2 resonance occurred more dominantly than mode 1. This analysis is in good agreement with the PIV image displayed in Fig. 2a, which shows mode 2 beating . The current density increased sharply (Fig. 5a) below a KB value of 0.00042, although the natural frequency of the PENG and the vortex detachment frequency have moved away. As stated earlier, we have assumed that the large displacement of the PENG with a small KB value may have led to the origin of the strong increase in power. The frequency of the output voltage in the chaotic beat region displayed in Figure 4 is about 4.33 Hz, which does not match the vortex detachment frequency (>6.67 Hz). This indicates that the resonance between the vortex shedding and PENG is not the cause of the strong increase in current density. Therefore, the large displacement of the PENG complies with a KB below 0.00042 is the main contributor to the high current. Our observations indicate that the flexible sheet type PENG should be designed to have a KB value less than the critical value to present a chaotic beat and generate significant power.