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Flexible ring flapping in a uniform flow

  • Boyoung Kim (a1), Wei-Xi Huang (a2), Soo Jai Shin (a1) and Hyung Jin Sung (a1)
Abstract
Abstract

An improved version of the immersed boundary (IB) method for simulating an initially circular or elliptic flexible ring pinned at one point in a uniform flow has been developed. The boundary of the ring consists of a flexible filament with tension and bending stiffness. A penalty method derived from fluid compressibility was used to ensure the conservation of the internal volume of the flexible ring. At , two different flapping modes were identified by varying the tension coefficient for a fixed bending stiffness, or by changing the bending coefficient for a fixed tension coefficient. The optimal tension and bending coefficients that minimize the drag force of the flexible ring were found. Visualization of the vorticity field showed that the two flapping modes correspond to different vortex shedding patterns. We observed the hysteresis property of the flexible ring, which exhibits bistable states over a range of flow velocities depending on the initial inclination angle, i.e. one is a stationary stable state and the other a self-sustained periodically flapping state. The Reynolds number range of the bistability region and the flapping amplitude were determined for various aspect ratios . For , the hysteresis region arises at the highest Reynolds number and the flapping amplitude in the self-sustained flapping state is minimized. A new bistability phenomenon was observed: for certain aspect ratios, two periodically flapping states coexist with different amplitudes in a particular Reynolds number range, instead of the presence of a stationary stable state and a periodically flapping state.

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Email address for correspondence: hjsung@kaist.ac.kr
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1. S. Alben & M. J. Shelley 2008 Flapping states of a flag in an inviscid fluid: bistability and the transition to chaos. Phys. Rev. Lett. 100, 074301.

2. H. Bailey 2000 Motion of a hanging chain after the free end is given an initial velocity. Am. J. Phys. 68, 764767.

3. A. Belmonte , M. J. Shelley , S. T. Eldakar & C. H. Wiggins 2001 Dynamic patterns and self-knotting of a driven hanging chain. Phys. Rev. Lett. 87, 114301.

5. R. Cortez & M. Minion 2000 The blob projection method for immersed boundary problems. J. Comput. Phys. 161, 428453.

6. R. Cortez , C. S. Peskin , J. M. Stockie & D. Varela 2004 Parametric resonance in immersed elastic boundaries. SIAM J. Appl. Maths 65, 494520.

8. D. J. J. Farnell , T. David & D. C. Barton 2004 Numerical simulations of a filament in a flowing soap film. Intl J. Numer. Meth. Fluids 44, 313330.

9. F. E. Fish & G. V. Lauder 2006 Passive and active flow control by swimming fishes and mammals. Annu. Rev. Fluid Mech. 38, 193224.

10. R. Glowinski , T.-W. Pana , T. I. Hesla & D. D. Joseph 1999 A distributed Lagrange multiplier/fictitious domain method for particulate flows. Intl J. Multiphase Flow 25, 755794.

11. D. Goldstein , R. Handler & L. Sirovich 1993 Modeling a no-slip flow boundary with an external force field. J. Comput. Phys 105, 354366.

12. W.-X. Huang , S. J. Shin & H. J. Sung 2007 Simulation of flexible filaments in a uniform flow by the immersed boundary method. J. Comput. Phys. 226, 22062228.

14. S. Jung , K. Mareck , M. Shelley & J. Zhang 2006 Dynamics of a deformable body in a fast flowing soap film. Phys. Rev. Lett. 97, 134502.

15. K. Kim , S.-J. Baek & H. J. Sung 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38, 125138.

16. Y. Kim & C. S. Peskin 2007 Penalty immersed boundary method for an elastic boundary with mass. Phys. Fluids 19, 053103.

18. Z. Li & M.-C. Lai 2001 The immersed interface method for the Navier–Stokes equations with singular forces. J. Comput. Phys. 171, 822842.

19. J. C. Liao , D. N. Beal , G. V. Lauder & M. S. Triantafyllou 2003 Fish exploiting vortices decrease muscle activity. Science 302, 15661569.

21. Z. Peng , R. J. Asaro & Q. Zhu 2010 Multiscale simulation of erythrocyte membrane. Phys. Rev. E 81, 031904.

23. C. S. Peskin & B. F. Printz 2002 Improved volume conservation in the computation of flows with immersed elastic boundaries. J. Comput. Phys. 105, 3346.

24. D. Qi 2007 A new method for direct simulations of flexible filament suspensions in non-zero Reynolds number flows. Intl J. Numer. Meth. Fluids 54, 103118.

25. S. J. Shin , W.-X. Huang & H. J. Sung 2008 Assessment of regularized delta functions and feedback forcing schemes for an immersed boundary method. Intl J. Numer. Meth. Fluids 58, 263286.

26. M. J. Shelley , N. Vandenberghe & J. Zhang 2005 Heavy flags undergo spontaneous oscillations in flowing water. Phys. Rev. Lett. 94, 094302.

28. A. Thess , O. Zikanov & A. Nepomnyashchy 1999 Finite-time singularity in the vortex dynamics of a string. Phys. Rev. E 59, 36373640.

29. A.-K. Tornberg & M. J. Shelley 2004 Simulating the dynamics and interactions of flexible fibres in Stokes flows. J. Comput. Phys. 196, 840.

30. M. Uhlmann 2006 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448476.

31. C. H. K. Williamson & A. Roshko 1988 Vortex formation in the wake of an oscillating cylinder. J. Fluids Struct. 2, 355381.

32. Z. Yu 2005 A DLM/FD method for fluid/flexible-body interactions. J. Comput. Phys. 207, 127.

33. J. Zhang , S. Childress , A. Libchaber & M. Shelley 2000 Flexible filaments in a flowing soap film as a model for one-dimensional flags in a two-dimensional wind. Nature 408, 835839.

34. L. J Zhang & J. D. Eldredge 2009 A viscous vortex particle method for deforming bodies with application to biolocomotion. Intl J. Numer. Meth. Fluids 59, 12991320.

35. L. Zhu & C. S. Peskin 2002 Simulation of a flapping flexible filament in a flowing soap film by the immersed boundary method. J. Comput. Phys. 179, 452468.

36. L. Zhu & C. S. Peskin 2003 Interaction of two flapping filaments in a flowing soap film. Phys. Fluids 15, 19541960.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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