Electro-hydrodynamic synchronization of piezoelectric flags

Abstract Hydrodynamic coupling of flexible flags in axial flows may profoundly influence their flapping dynamics, in particular driving their synchronization. This work investigates the effect of such coupling on the harvesting efficiency of coupled piezoelectric flags, that convert their periodic deformation into an electrical current. Considering two flags connected to a single output circuit, we investigate using numerical simulations the relative importance of hydrodynamic coupling to electrodynamic coupling of the flags through the output circuit due to the inverse piezoelectric effect. It is shown that electrodynamic coupling is dominant beyond a critical distance, and induces a synchronization of the flags’ motion resulting in enhanced energy harvesting performance. We further show that this electrodynamic coupling can be strengthened using resonant harvesting circuits.

[1]  Andrew G. Glen,et al.  APPL , 2001 .

[2]  R. Krasny.  Desingularization of periodic vortex sheet roll-up , 1986 .

[3]  C. G. Broyden.  A Class of Methods for Solving Nonlinear Simultaneous Equations , 1965 .

[4]  Cesare Stefanini,et al.  Piezoelectric Energy Harvesting Solutions , 2014, Sensors.

[5]  Jean-François Deü,et al.  Placement and dimension optimization of shunted piezoelectric patches for vibration reduction , 2012 .

[6]  Daniel J. Inman,et al.  Piezoelectric Energy Harvesting , 2011 .

[7]  Beverley J. Glover,et al.  Vortex shedding model of a flapping flag , 2008, Journal of Fluid Mechanics.

[8]  C. Eloy,et al.  Coupled flutter of parallel plates , 2009 .

[9]  Olivier Doar'e,et al.  Influence and optimization of the electrodes position in a piezoelectric energy harvesting flag , 2015, 1501.04303.

[10]  Silas Alben,et al.  The flapping-flag instability as a nonlinear eigenvalue problem , 2008 .

[11]  D. Inman,et al.  A Review of Power Harvesting from Vibration using Piezoelectric Materials , 2004 .

[12]  Jun Zhang,et al.  Flapping and Bending Bodies Interacting with Fluid Flows , 2011 .

[13]  Sébastien Michelin,et al.  Linear stability analysis of coupled parallel flexible plates in an axial flow , 2009 .

[14]  A. Smits,et al.  Energy harvesting eel , 2001 .

[15]  Silas Alben,et al.  Simulating the dynamics of flexible bodies and vortex sheets , 2009, J. Comput. Phys..

[16]  Luoding Zhu,et al.  An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments , 2011, J. Comput. Phys..

[17]  Earl H. Dowell,et al.  Power extraction from aeroelastic limit cycle oscillations , 2011 .

[18]  Olivier Doaré,et al.  Energy harvesting efficiency of piezoelectric flags in axial flows , 2012, Journal of Fluid Mechanics.

[19]  C. Peskin,et al.  Interaction of two flapping filaments in a flowing soap film , 2003 .

[20]  Daniel J. Inman,et al.  An experimentally validated bimorph cantilever model for piezoelectric energy harvesting from base excitations , 2009 .

[21]  Olivier Doare,et al.  Piezoelectric coupling in energy-harvesting fluttering flexible plates: linear stability analysis and conversion efficiency , 2011, 1104.3732.

[22]  Silas Alben,et al.  Wake-mediated synchronization and drafting in coupled flags , 2009, Journal of Fluid Mechanics.

[23]  Deniz Tolga Akcabay,et al.  Hydroelastic response and energy harvesting potential of flexible piezoelectric beams in viscous flow , 2012 .

[24]  B. M. Fulk.  MATH , 1992 .

[25]  Jun Zhang,et al.  Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind , 2000, Nature.

[26]  M. Porfiri,et al.  Underwater energy harvesting from a heavy flag hosting ionic polymer metal composites , 2011 .

[27]  A. Preumont.  Vibration Control of Active Structures , 1997 .

[28]  Henry A. Sodano,et al.  A review of power harvesting using piezoelectric materials (2003–2006) , 2007 .

[29]  S. Alben,et al.  Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. , 2008, Physical review letters.

[30]  Dejan Vasic,et al.  Energy harvesting of two cantilever beams structure: interfacing circuit discussion , 2015, Smart Structures.

[31]  Synchronized flutter of two slender flags , 2016, Journal of Fluid Mechanics.

[32]  D. Guyomar,et al.  Toward energy harvesting using active materials and conversion improvement by nonlinear processing , 2005, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[33]  Jun Zhang,et al.  Anomalous hydrodynamic drafting of interacting flapping flags. , 2008, Physical review letters.

[34]  Qiang Zhu,et al.  A review on flow energy harvesters based on flapping foils , 2014 .

[35]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[36]  Kiran Singh,et al.  The effect of non-uniform damping on flutter in axial flow and energy-harvesting strategies , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[37]  Yifan Xia,et al.  Fluid-Solid-Electric Lock-In of Energy-Harvesting Piezoelectric Flags , 2014, 1501.02191.

[38]  Dejan Vasic,et al.  Synchronized switch harvesting applied to piezoelectric flags , 2016 .

[39]  Daniele Dessi,et al.  Aeroelastic behavior of a flag in ground effect , 2015 .

[40]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[41]  Sébastien Michelin,et al.  Falling cards and flapping flags: understanding fluid–solid interactions using an unsteady point vortex model , 2010 .

[43]  Yifan Xia,et al.  Resonance-induced enhancement of the energy harvesting performance of piezoelectric flags , 2015, 1512.05532.