Vertically clamped flexible flags in an oncoming Poiseuille flow were numerically modeled to investigate the hydrodynamic interaction and dynamics of the flexible flags using the immersed boundary method. The number of flags modeled was increased step by step: a single flag, double flags, triple flags, and a large array of multiple flags were modeled. The flexible flags displayed a flapping mode or a fully deflected mode, depending on the relationship between the elastic inner force and the hydrodynamic force. The bending angle (α), flapping amplitude (A), and period (T) of the single flag decreased as the bending rigidity (γ) increased. In the double and triple flag systems, the bending angle of the first flag reached a steady state as the gap distance (d) increased. The gap distance affected the position of the flag relative to the vortical structures. The vortical structures merged and formed a large vortex. Small vortical structures penetrated the large gap to drive flag flapping and force flag bending. In a large array of multiple flags, all flags were present in the fully deflected mode for a small gap distance. As the gap distance increased, the interactions between the flags increased. The flags were significantly influenced by the inlet and exit conditions.
REFERENCES
1.
Belmonte
, A.
, Shelley
, M. J.
, Eldakar
, S. T.
, and Wiggins
, C. H.
, “Dynamic patterns and self-knotting of a driven hanging chain
,” Phys. Rev. Lett.
87
(11
), 114301
(2001
).2.
Bi
, X. B.
and Zhu
, Q.
, “Fluid-structure investigation of a squid-inspired swimmer
,” Phys. Fluids
31
, 101901
(2019
).3.
Connell
, B. S. H.
and Yue
, D. K. P.
, “Flapping dynamics of a flag in a uniform stream
,” J. Fluid Mech.
581
, 33
–67
(2007
).4.
Dong
, G. J.
and Lu
, X. Y.
, “Characteristics of flow over travelling wavy foils in a side-by-side arrangement
,” Phys. Fluids
19
, 057107
(2007
).5.
Eloy
, C.
, Souilliez
, C.
, and Schouveiler
, L.
, “Flutter of a rectangular plate
,” J. Fluids Struct.
23
, 904
–919
(2007
).6.
Favier
, J.
, Li
, C.
, Kamps
, L.
, Revell
, A.
, O’Connor
, J.
, and Brücker
, C.
, “The PELskin project—Part I: Fluid-structure interaction for a row of flexible flaps: A reference study in oscillating channel flow
,” Meccanica
52
(8
), 1767
–1780
(2017
).7.
Ghisalberti
, M.
, “Mixing layers and coherent structures in vegetated aquatic flows
,” J. Geophys. Res.
107
(C2
), 3-1
–3-11
, (2002
).8.
Glowinski
, R.
, Pana
, T.-W.
, Hesla
, T. I.
, and Joseph
, D. D.
, “A distributed Lagrange multiplier/fictitious domain method for particulate flows
,” Int. J. Multiphase Flow
25
, 755
–794
(1999
).9.
Goldstein
, D.
, Handler
, R.
, and Sirovich
, L.
, “Modeling a no-slip flow boundary with an external force field
,” J. Comput. Phys.
105
, 354
–366
(1993
).10.
Guo
, Z.
, Kim
, S. Y.
, and Sung
, H. J.
, “Pulsating flow and heat transfer in a pipe partially filled with a porous medium
,” Int. J. Heat Mass Transfer
40
, 4209
–4218
(1997
).11.
Harwood
, A. R. G.
, O’Connor
, J.
, Muñoz
, J. S.
, Santasmasas
, M. C.
, and Revell
, A. J.
, “LUMA: A many-core, fluid-structure interaction solver based on the Lattice–Boltzmann method
,” SoftwareX
7
, 88
–94
(2018
).12.
Huang
, W.-X.
, Shin
, S. J.
, and Sung
, H. J.
, “Simulation of flexible flags in a uniform flow by the immersed boundary method
,” J. Comput. Phys.
226
, 2206
–2228
(2007
).13.
Huang
, W.-X.
and Sung
, H. J.
, “An immersed boundary method for fluid-flexible structure interaction
,” Comput. Methods Appl. Mech. Eng.
198
, 2650
–2661
(2009
).14.
Huang
, W.-X.
and Sung
, H. J.
, “Three-dimensional simulation of a flapping flag in a uniform flow
,” J. Fluid Mech.
653
, 301
–336
(2010
).15.
Kadapa
, C.
, Dettmer
, W. G.
, and Perić
, D.
, “A stabilised immersed framework on hierarchical b-spline grids for fluid-flexible structure interaction with solid–solid contact
,” Comput. Methods Appl. Mech. Eng.
335
, 472
–489
(2018
).16.
Kim
, M. J.
and Lee
, J. H.
, “Flapping dynamics of a flexible flag clamped vertically in a viscous uniform flow
,” J. Mech. Sci. Technol.
33
(3
), 1243
–1256
(2019
).17.
Kim
, S.
, Huang
, W.-X.
, and Sung
, H. J.
, “Constructive and destructive interaction modes between two tandem flexible flags in viscous flow
,” J. Fluid Mech.
661
, 511
–521
(2010
).18.
Lee
, J. B.
, Park
, S. G.
, Kim
, B.
, Ryu
, J.
, and Sung
, H. J.
, “Heat transfer enhancement by flexible flags clamped vertically in a Poiseuille channel flow
,” Int. J. Heat Mass Transf.
107
, 391
–402
(2017
).19.
Lee
, J. B.
, Park
, S. G.
, and Sung
, H. J.
, “Heat transfer enhancement by asymmetrically clamped flexible flags in a channel flow
,” Int. J. Heat Mass Transfer
116
, 1003
–1015
(2018
).20.
Luhar
, M.
, Infantes
, E.
, and Nepf
, H.
, “Seagrass blade motion under waves and its impact on wave decay
,” J. Geophys. Res.: Oceans
122
, 3736
–3752
, (2017
).21.
Luhar
, M.
and Nepf
, H.
, “Wave-induced dynamics of flexible blades
,” J. Fluids Struct.
61
, 20
–41
(2016
).22.
Mullarney
, J. C.
and Henderson
, S. M.
, “Wave-forced motion of submerged single-stem vegetation
,” J. Geophys. Res.
115
, C12061
, (2010
).23.
Nepf
, H. M.
, “Hydrodynamics of vegetated channels
,” J. Hydraul. Res.
50
(3
), 262
–279
(2012
).24.
O’Connor
, J.
and Revell
, A.
, “Dynamic interactions of multiple wall-mounted flexible flaps
,” J. Fluid Mech.
870
, 189
–216
(2019
).25.
Park
, S. G.
, Kim
, B.
, Chang
, C. B.
, Ryu
, J.
, and Sung
, H. J.
, “Enhancement of heat transfer by a self-oscillating inverted flag in a Poiseuille channel flow
,” Int. J. Heat Mass Transf.
96
, 362
–370
(2016
).26.
Park
, T. S.
and Sung
, H. J.
, “A nonlinear low-Reynolds number k-ε model for turbulent separated and reattaching flows. 1. Flow field computations
,” Int. J. Heat Mass Transf.
38
(14
), 2657
–2666
(1995
).27.
Peng
, Z. R.
, Huang
, H. B.
, and Lu
, X.-Y.
, “Hydrodynamic schooling of multiple self-propelled flapping plates
,” J. Fluid Mech.
853
, 587
–600
(2018
).28.
Peskin
, C. S.
, “Flow patterns around heart valves: A numerical method
,” J. Comput. Phys.
10
, 252
–271
(1972
).29.
Peskin
, C. S.
, “The immersed boundary method
,” Acta Numer.
11
, 479
–517
(2002
).30.
Shin
, S. J.
, Huang
, W.-X.
, and Sung
, H. J.
, “Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method
,” Int. J. Numer. Methods Fluids
58
, 263
–286
(2008
).31.
Shoele
, K.
and Mittal
, R.
, “Computational study of flow-induced vibration of a reed in a channel and effect on convective heat transfer
,” Phys. Fluids
26
, 127103
(2014
).32.
Singh
, R.
, Bandi
, M. M.
, Mahadevan
, A.
, and Mandre
, S.
, “Linear stability analysis for monami in a submerged seagrass bed
,” J. Fluid Mech.
786
, R1
(2016
).33.
Tornberg
, A. K.
and Shelley
, M. J.
, “Simulating the dynamics and interactions of flexible fibers in Stokes flows
,” J. Comput. Phys.
196
, 8
–40
(2004
).34.
Uddin
, E.
, Huang
, W.-X.
, and Sung
, H. J.
, “Interaction modes of multiple flexible flags in a uniform flow
,” J. Fluid Mech.
729
, 563
–583
(2013
).35.
Uddin
, E.
, Huang
, W.-X.
, and Sung
, H. J.
, “Actively flapping tandem flexible flags in a viscous flow
,” J. Fluid Mech.
780
, 120
–142
(2015
).36.
Uhlmann
, M.
, “An immersed boundary method with direct forcing for the simulation of particulate flows
,” J. Comput. Phys.
209
, 448
–476
(2005
).37.
Wang
, Y.
, Jimack
, P. K.
, and Walkley
, M. A.
, “A one-field monolithic fictitious domain method for fluid–structure interactions
,” Comput. Methods Appl. Mech. Eng.
317
, 1146
–1168
(2017
).38.
Yeh
, P. D.
and Alexeev
, A.
, “Free swimming of an elastic plate plunging at low Reynolds number
,” Phys. Fluids
26
, 053604
(2014
).39.
Yu
, Z.
, “A DLM/FD method for fluid/flexible-body interactions
,” J. Comput. Phys.
207
, 1
–27
(2005
).40.
Zhang
, J.
, Childress
, S.
, Libchaber
, A.
, and Shelley
, M.
, “Flexible flags in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind
,” Nature
408
, 835
–839
(2000
).41.
Zhu
, L.
and Peskin
, C. S.
, “Interaction of two flapping flags in a flowing soap film
,” Phys. Fluids
15
(7
), 1954
–1960
(2003
).42.
Zhu
, Q.
and Peng
, Z.
, “Mode coupling and flow energy harvesting by a flapping foil
,” Phys. Fluids
21
, 033601
(2009
).© 2020 Author(s).
2020
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