Ionic Polymer Metal Composites (IPMCs): Smart Multi-Functional Materials and Artificial Muscles, Volume 2
Chapter 14: Energy Exchange between Coherent Fluid Structures and Ionic Polymer Metal Composites, toward Flow Sensing and Energy Harvesting
Published:19 Nov 2015
Sean D. Peterson, Maurizio Porfiri, 2015. "Energy Exchange between Coherent Fluid Structures and Ionic Polymer Metal Composites, toward Flow Sensing and Energy Harvesting", Ionic Polymer Metal Composites (IPMCs): Smart Multi-Functional Materials and Artificial Muscles, Volume 2, Mohsen Shahinpoor, Mohsen Shahinpoor
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Coherent fluid structures, such as vortex rings and pairs, are potential energy sources for powering small-scale electronics in underwater environments. Ionic polymer metal composites (IPMCs) are well suited as harvesting devices for scavenging energy from such coherent fluid structures due to their high compliance, ability to work in wet environments, and large electrical capacitance. In this chapter, we review recent investigations into the energy exchange between advecting coherent fluid structures and IPMCs during impact events. Experimental demonstrations include the impact of a vortex ring with a cantilever IPMC strip and with an annular IPMC. The impulsive loading from the fluid impact produces a cascade of chemo-electro-mechanical phenomena, which ultimately result in a current through the IPMC. Deeper insight into this unsteady fluid–structure interaction is obtained through analytical and numerical modeling. A fully coupled potential flow model is proposed, consisting of a Kirchhoff–Love plate immersed in an ideal fluid where a vortex pair is propagating. The potential flow model necessarily neglects fluid viscosity, which is found to play a significant role in the impact dynamics via a series of computational fluid dynamics simulations.
The growing integration of small-scale electronics into modern life, ranging from consumer to research-grade devices, provides continuous impetus for the investigation of smart material-based energy harvesting to extend battery lifetime and enhance functionalities.1–5 Beyond well-studied structural vibrations, energy sources that have been considered in the design of miniature energy harvesting systems include human and animal locomotion,6–8 jaw movements,9 and heartbeats,10 to name a few. While these studies widely differ in their target applications, they are all based upon energy extraction from mechanical deformation of a solid body with which they interact. Recently, research efforts have been focused on expanding the range of energy harvesting sources to encompass fluid flows.
The majority of these studies have employed piezoelectric transducers to convert small-scale fluid energy into a usable electrical form. The first instance of energy conversion from a fluid flow is the so-called harvesting eel,11,12 which utilizes the Kármán vortex street shed from a cylinder in a cross flow to deform a piezoelectric element. Building on this concept, higher Reynolds numbers and different geometric configurations have been explored over subsequent years.13–16 Fluid–structure interactions associated with flutter instabilities from a mean flow and vibrations from a moving base have also been considered.17–20 In addition, hydraulic fluctuations and hydroelastic impacts have been demonstrated to be viable means for energy extraction.21,22
To afford large structural deformations and lower the operation frequency, recent studies have proposed the integration of ionic polymer metal composites (IPMC)23–28 into fluid energy harvesting. Upon mechanical deformation, a complex cascade of chemo-electro-mechanical processes takes place within the ionomer core and especially at the ionomer–electrode interfaces, resulting in an electric potential sensed across the electrodes.29–33 By shunting the IPMC electrodes with an external resistor, a small fraction of the mechanical energy is converted into electrical form and then dissipated as heat.19,34–36 Thus, IPMCs have been used to harvest energy from the flutter instability of a heavy flag,37 hydroelastic impact,38 fluid-induced buckling,39 hydroelastic interactions in arrays of flexible structures,40 fluid–structure interactions from a compliant miniature turbine,41 and the beating of an artificial fish tail.8
Coherent fluid structures are persistent, organized collections of rotational fluid parcels that are ubiquitous in nature, examples of which include vortex rings,42,43 Kármán vortex streets,44 and hairpin vortices.45 These fluid structures arise from such diverse sources as an undulating fish tail,46 the propulsion of some invertebrate marine animals,47 the shear layer of a jet,48 the oscillation of a sharp-edged structure in a quiescent fluid,49 the wake of a bluff body,44 and in turbulent boundary layers.45,50 The energy associated with these coherent structures is regulated by salient geometric features and local flow circulation.42,43,51 As an example, the energy of a vortex ring is a function of the vortex core structure, ring radius, and circulation.42,43
The advection and diffusion of coherent fluid structures are influenced by interactions with neighboring vortices and solid boundaries, comprising confining walls and nearby compliant bodies.52 For example, in the absence of viscosity, potential flow can be used to predict the kinematics of a pair of vortices approaching a rigid wall of infinite extent,53 including deformation of the core.54 The role of viscosity on impact dynamics has been subsequently elucidated through computational fluid dynamics (CFD).55 The inclusion of viscosity results in complex vortex dynamics due to the generation of secondary and tertiary structures on no-slip or porous boundaries.56–58 Scaling laws for the generation of vorticity on no-slip boundaries have been determined, along with the role of the angle of impact.59–61 The three-dimensional (3D) impact of a vortex ring with a wall has been addressed both numerically and experimentally.62,63
Here, we summarize recent work exploring the energy exchange between coherent fluid structures and IPMCs during impact events.64–68 We specifically focus on impulsive loading of compliant IPMC strips and annuli from self-propagating vortex rings. Beyond experimental evidence in favor of the potential of sensing and energy extraction during short-duration fluid–structure interactions, we propose potential flow and CFD solutions to offer insight into the physics of the impact.
We present two experimental demonstrations of IPMC-based energy harvesting from coherent fluid structures. Specifically, we first review bending deformation of a cantilevered IPMC strip,65 followed by axisymmetric bending of an IPMC annulus, due to the impact of a vortex ring.64 Particle image velocimetry (PIV) is utilized in both studies to resolve the attendant flow field. The IPMCs are fabricated in-house from Nafion-117 membranes plated with platinum electrodes,23 which are held short-circuited to offer evidence for the possibility of energy conversion.
14.2.1 Impulsive Loading of a Cantilever Strip
The vortex is generated by a piston plunged through a cylinder submersed in the water, as shown in Figure 14.1. The vortex ring has circulation Γ, velocity Vvr, and diameter a. The vortex ring is launched so that it impacts the IPMC of length L orthogonally, with its center at the tip. A Cartesian coordinate system is introduced, with the x-axis along the IPMC and the y-axis aligned with the direction of the vortex propagation (see Figure 14.1). The circulation Γ is computed from the line integral of the velocity around each of the two vortices in the 2D slice captured by PIV.
As the piston plunges into the cylinder, water is ejected, forming a vortex ring. At the end of the plunger stroke, the vortex ring pinches off and advects towards the IPMC at a nearly constant speed. Once the vortex ring is approximately within 1.5 L of the IPMC, the IPMC bends away from it with negligible influence on the flow physics. Upon impact, the vortex ring breaks down and the IPMC suddenly deflects as energy is transferred from the ring to the structure.
The IPMC tip deflection δ as a function of time t superimposed with the short-circuit current is presented in Figure 14.2 for a representative instance of impact. The maximum deflection of the IPMC is as large as 0.6 L and is attained after vortex ring breakup. Specifically, when the vortex ring reaches the initial position of the IPMC, the deflection is on the order of 0.2 L, after which the IPMC tip speed increases rapidly, implying that breakdown of the vortex ring is a determinant of energy exchange. Such an exchange is revealed by the concomitant increase in the short-circuit current, which closely follows IPMC deformation. An estimate of the energy conversion is obtained from the strain and electrical energy in the IPMC, which amounts to roughly 0.001%.
14.2.2 Impulsive Loading of an Annulus
The problem of a vortex ring advecting through a placid fluid and orthogonally impacting a co-axial IPMC annulus is explored. The experimental setup consists of a custom vortex ring facility comprising a mechanically actuated piston/cylinder vortex generator immersed in a water tank (see Figure 14.3a). Rings of varying circulation are formed by controlling the piston stroke. The IPMC annulus is clamped along its outer radius through a custom fixture with embedded electrodes (see Figure 14.3b).
The velocity and vorticity fields of the advecting vortex ring pre- and post-impact are presented in Figure 14.4 for a representative experiment. The gray region in each frame represents the clamped IPMC. The vortex ring core is evident in the contours of vorticity, appearing as regions of red and blue, indicting opposite signs of vorticity. As in the previous study, the vortex ring advects towards the IPMC through self-induction.
Trailing vorticity is found behind the vortex ring as a result of the formation process.51 As seen in Figure 14.4c, a vortex ring exists post-impact, suggesting that the fluid passing through the annulus rolls up into another coherent structure of lower circulation.
The time traces of the displacement and current follow those presented in the previous study,65 whereby just after impact the IPMC attains its maximum deflection, which is accompanied by a substantial increase in the short-circuit current. Likely due to the different impact geometries, we observe a modest deflection of the IPMC towards the approaching ring prior to impact. This was not observed in the previous study due to the relatively high stagnation pressure at the tip of the IPMC strip. A further difference between the response of the annulus and the strip is the drastically reduced deformation levels experienced by the annular structure, due to the increased stiffness associated with the 2D axisymmetric bending. Despite the differences in deformation, the energy conversion is within the same order of magnitude.
14.3 Insights from Modeling and Simulation
Here, we employ analytical modeling techniques and CFD to obtain further insights into the physics of the impact and associated energy transfer. Specifically, we report on a fully coupled potential flow-based fluid–structure interaction model for energy harvesting design66 and a discussion of its associated limitations. To address some of these drawbacks, we develop a CFD framework for refined analysis of the vortex dynamics.67,68
14.3.1 Potential Flow Modeling
To gain insight into the impact dynamics of a vortex ring with a deformable structure, we develop a modeling framework in 2D in which the vortex ring is represented as a pair of point vortices and the IPMC strip is modeled as a Kirchhoff–Love plate undergoing cylindrical bending in an ideal fluid. As such, the circulation of the vortices remains constant during the impact, and no new coherent fluid structures are shed from the strip. Using the potential flow model, the plate is assimilated to a vortex sheet with zero net circulation, and the pressure field is expressed in terms of the configuration of the impacting vortices and the distributed vorticity of the sheet. The pressure field is in turn utilized to compute the impulsive hydrodynamic loading on the strip, which determines the strip deformation. As the structure deforms, the boundary condition on the fluid changes, thus influencing the flow physics, namely the propagation of the free vortices and the vorticity distribution on the strip.
The coupled partial differential equations are solved by projecting the strip deflection onto a basis of Chebyshev polynomials, which is afforded through the introduction of Lagrange multipliers to enforce kinematic boundary conditions on the strip. A similar basis is used to project the vorticity distribution on the strip and ultimately transform the problem into a set of coupled ordinary differential equations in the complex domain.
Snapshots of the interaction between the strip and the vortex pair are detailed in Figure 14.5. In this figure, the left column depicts the vortex positions (dots) and the configuration of the strip (black line). The center column displays a magnified view of the strip shape, while the right column shows the hydrodynamic loading on the strip, which is computed from the pressure jump across the two faces. Similarly to our experimental findings,65 the stagnation pressure induced by the approaching vortices results in deflection of the strip away from the vortices. When the pair is in close proximity to the strip, the magnitude of the hydrodynamic loading dramatically increases. The model not only anticipates the drastic temporal variation in the loading prior to impact, but also predicts a distinct spatial pressure localization. Specifically, the hydrodynamic loading can alternate sign along the strip, with the strip being pushed away from the vortices in the region between the pair and being sucked towards them in the vicinity of their cores. Unlike the experimental observations, where vorticity can be generated along the IPMC and thus influence the vortex dynamics, resulting in the vortex ring breakdown, the vortex pair in the potential flow model simply passes around the plate and continues to advect away indefinitely, albeit possibly at a different speed.
The maximum tip deflection is shown in Figure 14.6a versus circulation of the vortices. The amplitude of vibration increases monotonically with circulation due to the larger induced pressure field associated with higher circulation vortices. For lower circulation strengths, the strip vibration is primarily along the fundamental mode shape of the cantilever, though higher modes are excited at higher circulation values. The strip energy, including kinetic and strain energies, is presented in dimensionless form in Figure 14.6b for various values of vortex circulation as a function of time. As the vortices approach, the energy of the strip increases due to the transfer of energy through the hydrodynamic loading, and as such an increase is modulated by the vortex circulation. As the vortex circulation increases, the strip undergoes larger deflection, which results in more energy transfer. After the interaction, the strip continues to vibrate in the fluid, maintaining a constant mean energy level, due to the absence of fluid viscosity and structural damping.
We note that in comparison with experiments,65 the potential flow model matches well in the early stages of the impact, where interaction between the advecting vortices and the vortex sheet co-located with the strip is relatively weak. However, viscous effects become important when the vortices are near the plate, and thus the potential flow model assumptions lose accuracy.
A similar framework has been proposed to model the experimental study of the interaction between a vortex ring and an annulus.64 However, due to the additional complexity of the coherent fluid structure and the minute deflection of the annulus observed in the experiments, the bi-directional coupling between the fluid flow and the annulus deformation has been neglected. Thus, vortex propagation is studied assuming a rigid annulus and the resulting hydrodynamic loading is independently imposed to predict the short-circuit current through the IPMC electrodes.
In an effort to overcome the limitations of the potential flow solution in resolving vortex dynamics during and after impact, we develop a CFD modeling framework.67,68 While the point vortex model is amenable to analytical treatment through the potential flow solution, it contains a singularity in the velocity field at the vortex core, hampering CFD. As such, we replace the vortex pair with a Lamb dipole69 for numerical analysis. Simulations are performed using the icoFoam incompressible flow solver in the open-source CFD package OpenFOAM, which solves the 3D Navier–Stokes equations using the finite volume method. Structural deformations of the plate are modeled by discretizing Kirchhoff–Love plate equations using a central finite difference approximation.
The vortex dynamics of a dipole impacting the tip of a rigid semi-infinite plate are presented in Figure 14.7 for a dipole Reynolds number of Re=1500, where the Reynolds number is based upon the initial dipole convection speed and radius. Initially, all of the vorticity in the domain is contained within the dipole. Prior to impact, positive vorticity is observed at the plate tip, while negative vorticity is generated in the thin boundary layer on the plate face. This induced vorticity is a viscous effect not captured in the potential flow model. The importance of this induced vorticity is evident during the impact, in which the top half of the initial dipole pairs with the induced vorticity along the wall, resulting in the formation of a secondary dipole. Similarly, the lower half of the initial dipole pairs with the vorticity shed from the tip, forming another secondary dipole. These secondary dipoles follow circular trajectories that result in subsequent impacts with the wall. Viscous dissipation slowly diffuses the vorticity within the domain, in contrast with the potential flow model in which vortices advect away from the plate, maintaining their circulation.
To elucidate the hydrodynamic loading on the wall, we compute the time-dependent tip load by integrating the pressure jump in a region that extends from the free end to one dipole initial radius. This resultant force is presented in Figure 14.8 for three dipole Reynolds numbers. Initially, as the dipole approaches the wall, the force increases slowly, which is in agreement with the potential flow model. Upon impact with the wall, the resultant force rapidly increases, attaining a maximum value when the dipole center reaches the wall. During this primary impact, we observe that the force is relatively insensitive to the dipole Reynolds number. Subsequent deviations of the resultant force for varying Reynolds numbers after primary impact are a result of the complex vortex dynamics shown in Figure 14.7.
This vortex dipole/rigid wall impact study is extended to fully coupled fluid–structure interaction simulations by replacing the semi-infinite wall with a finite length Kirchhoff–Love plate undergoing cylindrical bending.68 As the dipole approaches the plate, it deflects slowly, followed by a rapid deflection upon impact, which corresponds to a rapid increase in the strain energy. Similar to the rigid wall case, the impact results in the formation of two secondary dipoles, which return for subsequent interactions with the plate. These secondary impacts result in additional peaks in the deflection and strain energy. In comparison with the rigid wall case, the vorticity induced along the plate during impact is reduced due to the plate compliance. Consequently, the secondary dipoles remain much closer to the plate and have a stronger influence on the hydrodynamic loading. The primary impact is largely independent of the Reynolds number, as found in the rigid wall case; however, the interaction with the secondary dipoles and the associated plate dynamics and strain energy are highly dependent on the Reynolds number.
14.4 Summary and Conclusions
In this chapter, we have examined the impulsive loading of IPMCs by coherent fluid structures for the design of small-scale fluid energy harvesters. Dedicated experimental setups for simultaneous mechanical, fluid, and electrical measurements have been integrated with analytical and numerical schemes to elucidate the physics of the energy exchange.
We have demonstrated the feasibility of extracting energy from self-propagating vortex rings in aqueous environments through impact with IPMC strips and annuli. PIV measurements indicate that most of the energy exchange takes place as the vortex ring reaches the IPMC, which results in a sudden deflection of the IPMC and simultaneous vortex breakdown. For the annular geometry, the IPMC deflections tend to be modest due to the nature of the mechanical deformation and fluid passing through the hole in the IPMC rolling up into a second vortex ring of lower circulation that propagates away. For the strip geometry, large deflections are observed, along with complex vortex dynamics in the vicinity of the tip. The short-circuit current through the IPMCs is found to consistently follow the rapid deformation, occurring over a few milliseconds.
The fully coupled potential flow solution accurately predicts the early stage of the fluid–structure interaction, where the coupling between the impacting coherent fluid structure and induced vorticity on the IPMC is negligible. The model describes the impulsive hydrodynamic loading on the IPMC as a function of the locations of the vortices and the IPMC vibration. We predict the energy stored in the IPMC as the vortex pair advects away post-interaction and dissect the role of the vortex pair strength. CFD allows for resolving the vortex dynamics during the impact, which leads to the formation of secondary and tertiary coherent fluid structures that significantly contribute to the hydrodynamic loading experienced by the IPMC.
While we acknowledge that there is a significant gap between the power requirements of existing miniature electronic devices and the energy transduction capacity of IPMCs, our results offer compelling evidence for the feasibility of IPMC use in highly unsteady flow sensing applications, along with an experimental and theoretical framework to inform the design of energy harvesters.
This research was supported by the Natural Sciences and Engineering Research Council of Canada under grant number 386282-2010, the National Science Foundation under grant numbers CMMI-0745753, CMMI-0926791, and CBET-1332204, the Office of Naval Research under grant N00014-10-1-0988, and the Mitsui USA Foundation. The authors would like to thank Dr Youngsu Cha, Mr Jia Cheng Hu, Mr Eugene Zivkov, and Dr Serhiy Yarusevych, who have contributed to the research efforts summarized in this chapter.