Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-30T17:31:50.457Z Has data issue: false hasContentIssue false

Numerical Investigation of the Dynamics of a Flexible Filament in the Wake of Cylinder

Published online by Cambridge University Press:  03 June 2015

Ru-Nan Hua
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
Luoding Zhu
Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, 402 North Blackford Street, Indianapolis, IN 46202, USA
Xi-Yun Lu*
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230026, China
*Corresponding author. URL:
Get access


Fluid-structure-interaction problems are ubiquitous, complicated, and not yet well understood. In this paper we investigate the interaction of a leading rigid circular cylinder and a trailing compliant filament and analyze the dynamic responses of the filament in the wake of the cylinder. It is revealed that there exist two flapping states of the filament depending on the cylinder-filament separation distance and the relevant critical distance distinguishing the two states is associated with the Reynolds number and the filament length. It is also found that the drag coefficient of the cylinder is reduced but that of the filament may be increased or decreased depending on its length. Compared with a single filament in a uniform flow, the filament of the same mechanical properties flapping in the wake of the cylinder has a lower frequency and a greater amplitude.

Research Article
Copyright © Global-Science Press 2014

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.)


[1] Xia, Z., Connington, K. W., Rapaka, S., Yue, P., Feng, J. J. and Chen, S., Flow patterns in the sedimentation of an elliptical particle, J. Fluid Mech., 625 (2009), pp. 249272.Google Scholar
[2] Mittal, R., Seshadri, V. and Udaykumar, H. S., Flutter, tumble and vortex induced autoro-tation, Theor. Comput. Fluid Dyn., 17 (2004), pp. 165170.CrossRefGoogle Scholar
[3] Zhang, J., Childress, S., Libchaber, A. and Shelley, M., Flexible filaments in afowing soap film as a model for one-dimensional flags in a two-dimensional wind, Nature, 408 (2000), pp. 835839.CrossRefGoogle Scholar
[4] Zhu, L. and Peskin, C. S., Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method, J. Comput. Phys., 179 (2002), pp. 452468.Google Scholar
[5] Lee, J., Shin, J. and Lee, S., Fluid-structure interaction of a flapping flexible plate in quiescent fluid, Comput. Fluids, 57 (2012), pp. 124137.Google Scholar
[6] Michelin, S. and Smith, S. G. L., Resonance and propulsion performance of a heaving flexible wing, Phys. Fluids, 21 (2009), pp. 071902.Google Scholar
[7] Sui, Y., Chen, X. B., Chew, Y. T., Roy, P. and Low, H. T., Numerical simulation of capsule deformation in simple shear flow, Comput. Fluids, 39 (2010), pp. 242250.Google Scholar
[8] Sui, Y., Low, H. T., Chew, Y. T. and Roy, P., A front-tracking lattice Boltzmann method to study flow-induced deformation of three-dimensional capsules, Comput. Fluids, 39 (2010), pp. 499511.Google Scholar
[9] Kang, C.-K., Aono, H., Cesnik, C.E.S., and Shyy, W., Effects of flexibility on the aerodynamic performance of flapping wings, J. Fluid Mech., 689 (2011), pp. 3274.Google Scholar
[10] Liao, J. C., Beal, D. N., Lauder, G. V. and Triantafyllou, M. S., The Karman gait: novel body kinematics of rainbow trout swimming in a vortex street, J. Exp. Biol., 206 (2003), pp. 10591073.Google Scholar
[11] Beal, D. N., Hover, F. S., Triantafyllou, M. S., Liao, J. C. and Lauder, G. V., Passive propulsion in vortex wakes, J. Fluid Mech., 549 (2006), pp. 385402.CrossRefGoogle Scholar
[12] Eldredge, J. D. and Pisani, D., Passive locomotion of a simple articulated fish-like system in the wake of an obstacle, J. Fluid Mech., 607 (2008), pp. 279288.Google Scholar
[13] Sui, Y., Chew, Y.-T., Roy, P. and Low, H.-T., A hybrid immersed-boundary and multi-block lattice boltzmann method for simulating fluid and moving-boundaries interactions, Intl J. Numer. Meth. Fluids, 53 (2007), pp. 17271754.Google Scholar
[14] Jia, L.-B. and Yin, X.-Z., Response modes of a flexible filament in the wake of a cylinder in a flowing soap film, Phys. Fluids, 21 (2009), pp. 101704.Google Scholar
[15] Wang, S.-Y., Jia, L.-B. and Yin, X.-Z., Kinematics and forces of a flexible body in Karman vortex street, Chin. Sci. Bull., 54 (2009), pp. 556561.Google Scholar
[16] Tian, F.-B., Luo, H., Zhu, L. and Lu, X.-Y., Interaction between a flexible filament and a downstream rigid body, Phys. Rev. E, 82 (2010), pp. 026301.Google Scholar
[17] Zdravkovich, M. M., Review of flow interference between two circular cylinders in various arrangement, J. Fluids Eng., 99 (1977), pp. 618633.Google Scholar
[18] Ristroph, L. and Zhang, J., Anomalous hydrodynamic drafting of interacting flapping flags, Phys. Rev. Lett., 101 (2008), pp. 194502.Google Scholar
[19] Zhu, L., Interaction of two tandem deformable bodies in a viscous incompressible flow, J. Fluid Mech., 635 (2009), pp. 455475.Google Scholar
[20] Tian, F.-B., Luo, H., Zhu, L., Liao, J. C. and Lu, X.-Y., An efficient immersed boundary-lattice Boltzmann method for the hydrodynamic interaction of elastic filaments, J. Comput. Phys., 230 (2011), pp. 72667283.CrossRefGoogle ScholarPubMed
[21] Yu, D., Mei, R. and Shyy, W., A multi-block lattice Boltzmann method for viscous fluid flows, Intl J. Numer. Meth. Fluids, 39 (2002), pp. 99120.Google Scholar
[22] Kim, Y. and Peskin, C. S., Penalty immersed boundary method for an elastic boundary with mass, Phys. Fluids, 19 (2007), pp. 053103.Google Scholar
[23] Feng, Z.-G. and Michaelides, E. E., Proteus: a direct forcing method in the simulations of particulate flows, J. Comput. Phys., 202 (2005), pp. 2051.Google Scholar
[24] Tian, F.-B., Luo, H., Zhu, L. and Lu, X.-Y., Coupling modes of three filaments in side-by-side arrangement, Phys. Fluids, 23 (2011), pp. 111903.Google Scholar
[25] Connell, B. S. H. and Yue, D. K. P., Flapping dynamics of a flag in a uniform stream, J. Fluid Mech., 581 (2007), pp. 3367.Google Scholar
[26] Apelt, C. J., West, G. S. and Szewczyk, A. A., The effects of wake splitter plates on the flow past a circular cylinder in the range 104 < Re < 5 × 104, J. Fluid Mech., 61 (1973), pp. 187198.CrossRefGoogle Scholar