Coupled motion of two side-by-side inverted flags

The interaction and coupling between two inverted flags that are placed side-by-side in a uniform flow is investigated in an effort to determine the behavior of systems that are formed by arrays of cantilevered plates. Inverted flags are elastic plates that are free to move at their leading edge and clamped at their trailing edge. We show that placing two inverted flags of equal dimensions side-by-side will cause their motion to couple. In-phase, anti-phase, staggered, alternating and decoupled flapping modes are present, with the anti-phase mode being predominant at small flag distances and low wind speeds. Increases both in amplitude and frequency of flapping are observed in the two flag system with respect to a single flag. Two side-by-side inverted flags of different lengths are found to interact for small length differences, with the longer flag being able to induce a motion on the shorter flag even when the latter is outside of its flapping wind speed range.

[1]  Wei Jin,et al.  Free vibrations of two side-by-side cylinders in a cross-flow , 2001, Journal of Fluid Mechanics.

[2]  John E. Sader,et al.  Stability of slender inverted flags and rods in uniform steady flow , 2016, Journal of Fluid Mechanics.

[3]  R. Mittal,et al.  Energy harvesting by flow-induced flutter in a simple model of an inverted piezoelectric flag , 2016, Journal of Fluid Mechanics.

[4]  Djj Farnell,et al.  Coupled States of Flapping Flags , 2003 .

[5]  Y. Lau,et al.  NUMERICAL STUDIES OF TWO SIDE-BY-SIDE ELASTIC CYLINDERS IN A CROSS-FLOW , 2001 .

[6]  Morteza Gharib,et al.  Flow-induced vibrations of a side-by-side arrangement of two flexible circular cylinders , 2011 .

[7]  Hyung Jin Sung,et al.  Flapping dynamics of an inverted flag in a uniform flow , 2015 .

[8]  John O Dabiri,et al.  Fish schooling as a basis for vertical axis wind turbine farm design , 2010, Bioinspiration & biomimetics.

[9]  Joseph R. Burns,et al.  The Energy Harvesting Eel: a small subsurface ocean/river power generator , 2001 .

[10]  Michael P. Païdoussis,et al.  Cantilevered flexible plates in axial flow: Energy transfer and the concept of flutter-mill , 2009 .

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

[12]  D. Weihs Hydromechanics of Fish Schooling , 1973, Nature.

[13]  C. Williamson,et al.  Vortex-Induced Vibrations , 2004, Wind Effects on Structures.

[14]  C. Peskin Flow patterns around heart valves: A numerical method , 1972 .

[15]  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.

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

[17]  Transition Mode of Two Parallel Flags in Uniform Flow , 2013 .

[18]  Xi-Yun Lu,et al.  Dynamics of an inverted flexible plate in a uniform flow , 2015 .

[19]  Morteza Gharib,et al.  Flapping dynamics of an inverted flag , 2013, Journal of Fluid Mechanics.

[20]  Rajeev K. Jaiman,et al.  Self-induced flapping dynamics of a flexible inverted foil in a uniform flow , 2015, Journal of Fluid Mechanics.

[21]  M. Sugihara,et al.  AN EXPERIMENTAL STUDY OF PAPER FLUTTER , 2002 .

[22]  John E. Sader,et al.  THE EFFECT OF ASPECT RATIO AND ANGLE OF ATTACK ON THE TRANSITION REGIONS OF THE INVERTED FLAG INSTABILITY , 2014 .

[23]  Boyu Fan,et al.  Large-amplitude flapping of an inverted flag in a uniform steady flow – a vortex-induced vibration , 2016, Journal of Fluid Mechanics.

[24]  Fang Li,et al.  Coupling modes between two flapping filaments , 2007, Journal of Fluid Mechanics.

[25]  M. M. Zdravkovich,et al.  Flow induced oscillations of two interfering circular cylinders , 1985 .

[26]  Shengjun Shi,et al.  Coupling Motion and Energy Harvesting of Two Side-by-Side Flexible Plates in a 3D Uniform Flow , 2016 .

[27]  Laibing Jia,et al.  Force measurement on coupled flapping flags in uniform flow , 2016 .