Hostname: page-component-54dcc4c588-r5qjk Total loading time: 0 Render date: 2025-09-12T00:01:39.770Z Has data issue: false hasContentIssue false
  • English
  • Français

Coupling performance of tandem flexible inverted flags in a uniform flow

Published online by Cambridge University Press:  28 December 2017

Haibo Huang Open the ORCID record for Haibo Huang [Opens in a new window] ,
Heng Wei  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Haibo Huang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Heng Wei
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
Xi-Yun Lu*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, China
*
†Email address for correspondence: xlu@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

The interaction of tandem inverted flexible flags in a uniform flow is investigated. For the inverted flags, their ends are fixed with their heads freely flapping. A direct numerical simulation is performed for which the Reynolds number is of order 200. Large flapping amplitude as well as large drag force is preferred because more energy may be harvested if more bending energy is generated. For the simple case of two tandem inverted flags, the drag force and flapping amplitude of the rear flag are found to be smaller than those of an isolated inverted flag due to the destructive merging mode of vortices. However, it is still unknown whether more bending energy can be generated when coupled inverted flags are arranged properly. To explore the possibility, inverted flags are proposed to be arranged as two rows, which indicate two lines of inverted flags perpendicular to the direction of the incoming flow, and flags in the front and rear rows are in-line or staggered. First the results for infinite flags with periodic boundary condition are presented. In both the in-line and the staggered arrangements, due to the interactions between the front–rear flags, the flapping amplitude or the maximum bending deformation and bending energy of a flag in the rear row can be enhanced, which may be significantly higher than those of an isolated case. Meanwhile, the bending energy of a flag in the front row is close to that of an isolated case. Second, results for finite inverted flag groups show that antiphase synchronization is preferred. When the group number is large enough, the bending energies of the front and rear flags in the inner groups are close to those in the infinite case. This finding may be helpful for the designing of an efficient energy harvesting device using inverted flags.

JFM classification

Flow Control: Drag reduction Vortex Flows: Vortex interactions

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 837 , 25 February 2018 , pp. 461 - 476
Copyright
© 2017 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Alben, S. 2009 Wake-mediated synchronization and drafting in coupled flags. J. Fluid Mech. 641, 489–496.Google Scholar
Boschitsch, B. M., Dewey, P. A. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in an in-line configuration. Phys. Fluids 26 (5), 051901.Google Scholar
Dewey, P. A., Quinn, D. B., Boschitsch, B. M. & Smits, A. J. 2014 Propulsive performance of unsteady tandem hydrofoils in a side-by-side configuration. Phys. Fluids 26 (4), 041903.Google Scholar
Doyle, J. F. 2013 Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability. Springer Science & Business Media.Google Scholar
Goldstein, D., Handler, R. & Sirovich, L. 1993 Modeling a no-slip flow boundary with an external force field. J. Comput. Phys. 105 (2), 354–366.Google Scholar
Gurugubelli, P. S. & Jaiman, R. K. 2015 Self-induced flapping dynamics of a flexible inverted foil in a uniform flow. J. Fluid Mech. 781, 657–694.Google Scholar
He, X., Shan, X. & Doolen, G. D. 1998 Discrete Boltzmann equation model for nonideal gases. Phys. Rev. E 57 (1), R13.Google Scholar
Hua, R.-N., Zhu, L. & Lu, X.-Y. 2014 Dynamics of fluid flow over a circular flexible plate. J. Fluid Mech. 759, 56–72.Google Scholar
Huang, W.-X., Shin, S. J. & Sung, H. J. 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226 (2), 2206–2228.Google Scholar
Huang, Z., Olson, J. A., Kerekes, R. J. & Green, S. I. 2006 Numerical simulation of the flow around rows of cylinders. Comput. Fluids 35 (5), 485–491.Google Scholar
Kim, D., Cossé, J., Cerdeira, C. H. & Gharib, M. 2013 Flapping dynamics of an inverted flag. J. Fluid Mech. 736, R1.Google Scholar
Kim, S., Huang, W.-X. & Sung, H. J. 2010 Constructive and destructive interaction modes between two tandem flexible flags in viscous flow. J. Fluid Mech. 661, 511–521.Google Scholar
Michelin, S. & Doaré, O. 2013 Energy harvesting efficiency of piezoelectric flags in axial flows. J. Fluid Mech. 714, 489–504.Google Scholar
Mougel, J., Doaré, O. & Michelin, S. 2016 Synchronized flutter of two slender flags. J. Fluid Mech. 801, 652–669.Google Scholar
Orrego, S., Shoele, K., Ruas, A., Doran, K., Caggiano, B., Mittal, R. & Kang, S. H. 2017 Harvesting ambient wind energy with an inverted piezoelectric flag. Appl. Energy 194, 212–222.Google Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.Google Scholar
Ryu, J., Park, S. G., Kim, B. & Sung, H. J. 2015 Flapping dynamics of an inverted flag in a uniform flow. J. Fluids Struct. 57, 159–169.Google Scholar
Sader, J. E., Cossé, J., Kim, D., Fan, B. & Gharib, M. 2016a Large-amplitude flapping of an inverted flag in a uniform steady flow: a vortex-induced vibration. J. Fluid Mech. 793, 524–555.Google Scholar
Sader, J. E., Huertas-Cerdeira, C. & Gharib, M. 2016b Stability of slender inverted flags and rods in uniform steady flow. J. Fluid Mech. 809, 873–894.Google Scholar
Shoele, K. & Mittal, R. 2016 Energy harvesting by flow-induced flutter in a simple model of an inverted piezoelectric flag. J. Fluid Mech. 790, 582–606.Google Scholar
Tang, C., Liu, N.-S. & Lu, X.-Y. 2015 Dynamics of an inverted flexible plate in a uniform flow. Phys. Fluids 27 (7), 073601.Google Scholar
Tian, F.-B., Luo, H., Zhu, L. & Lu, X.-Y. 2011 Coupling modes of three filaments in side-by-side arrangement. Phys. Fluids 23 (11), 111903.Google Scholar
Uddin, E., Huang, W.-X. & Sung, H. J. 2013 Interaction modes of multiple flexible flags in a uniform flow. J. Fluid Mech. 729, 563–583.Google Scholar
Ye, H., Wei, H., Huang, H. & Lu, X.-Y. 2017 Two tandem flexible loops in a viscous flow. Phys. Fluids 29 (2), 021902.Google Scholar
Zhang, C., Huang, H. & Lu, X.-Y. 2017 Free locomotion of a flexible plate near the ground. Phys. Fluids 29 (4), 041903.Google Scholar
Zhang, J., Childress, S., Libchaber, A. & Shelley, M. 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408 (6814), 835–839.Google Scholar
Zhu, L. 2009 Interaction of two tandem deformable bodies in a viscous incompressible flow. J. Fluid Mech. 635, 455–475.Google Scholar
Zhu, X., He, G. & Zhang, X. 2014a Flow-mediated interactions between two self-propelled flapping filaments in tandem configuration. Phys. Rev. Lett. 113 (23), 238105.Google Scholar
Zhu, X., He, G. & Zhang, X. 2014b An improved direct-forcing immersed boundary method for fluid–structure interaction simulations. Trans. ASME J. Fluids Engng 136 (4), 040903.Google Scholar

Huang et al. supplementary movie 1

Supplemental material: Vorticity contours (upper and lower boundaries are periodic) with K = 0.3, Gx = 2.0, Gy=0 for the in-line arrangement. The red and blue contours represent the positive (anti clockwise) and negative (clockwise) vortices.

Download Huang et al. supplementary movie 1(Video)
Video 3.8 MB