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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Instability and Transition

Phys. Fluids 24, 024102 (2012); http://dx.doi.org/10.1063/1.3682373 (22 pages)

Secondary instability in the near-wake past two tandem square cylinders

Choon-Bum Choi1, Yong-Jun Jang2, and Kyung-Soo Yang1

1Department of Mechanical Engineering, Inha University, Incheon 402-751, Republic of Korea
2Railway Environment Research Department, Korea Railroad Research Institute, Kyonggi-Do 437-757, Republic of Korea

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(Received 10 April 2011; accepted 31 October 2011; published online 8 February 2012)

Floquet stability analysis has been carried out to detect the onset of the secondary instability in the laminar flow past two identical square cylinders in tandem. Presence of a neighbouring cylinder alters flow topology, leading to change of stability characteristics. A parametric study has been performed with the gap between the two square cylinders as the key parameter. Three distinct patterns of base flow are found depending on the gap, and distinctive modes of the secondary instability are identified for each pattern of the base flow. The modes exhibit either odd reflection-translation symmetry or even RT symmetry. The critical Reynolds number and the corresponding dominant spanwise wavelength are presented for a wide range of the gap. Temporal and spatial characteristics of the dominant Floquet modes are described in detail. A hysteresis is also noticed in a certain range of the gap. Neutral stability curves are presented for some selected values of the gap. The averaged in-plane vorticity of the dominant normalized Floquet mode is depicted as a function of the downstream distance from the rear face of the cylinder that sheds vortices. Comparison of stability characteristics is also made between the current flow and the flow past two circular cylinders in tandem arrangements.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FORMULATION AND NUMERICAL METHODS
    1. Base flow
    2. Floquet stability analysis
  3. RESULTS AND DISCUSSION
    1. Review of the secondary instability for flow past a single square cylinder
    2. Patterns of base flow
    3. Hysteresis of base flow
    4. Characteristics of three-dimensional instability modes
      1. Mode TB1/TA1 (0.8 ≤ L x /h ≤ 1.1)
      2. Mode TB2 (1.2 ≤ L x /h ≤ 3.2)
      3. Mode TA2 (3.0 ≤ L x /h ≤ 3.5)
      4. Mode TA3 (3.0 ≤ L x /h ≤ 6.0)
    5. Coexisting three-dimensional instabilities
    6. Mode exchange due to hysteresis of base flow
    7. Neutral stability curves
    8. Comparison with the results of two circular cylinders in tandem
  4. CONCLUSION

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KEYWORDS and PACS

Keywords

external flows, flow instability, laminar flow, pattern formation, vortices, wakes

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3682373

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. Sohankar, C. Norberg, and L. Davidson, “Simulation of three-dimensional flow around a square cylinder at moderate Reynolds numbers,” Phys. Fluids 11, 288 (1999)PHFLE6000011000002000288000001.

    D.-H. Yoon, K.-S. Yang, and C.-B. Choi, “Flow past a square cylinder with an angle of incidence,” Phys. Fluids 22, 043603 (2010)PHFLE6000022000004043603000001.

    J. Mizushima and N. Suehiro, “Instability and transition of flow past two tandem circular cylinders,” Phys. Fluids 17, 104107 (2005)PHFLE6000017000010104107000001.

    S. Kang, “Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers,” Phys. Fluids 15, 2486 (2003)PHFLE6000015000009002486000001.

    J. Robichaux, S. Balachandar, and S. P. Vanka, “Three-dimensional Floquet instability of the wake of square cylinder,” Phys. Fluids 11, 560 (1999)PHFLE6000011000003000560000001.

    Y. Tasaka, S. Kon, L. Schouveiler, and P. L. Gal, “Hysteretic mode exchange in the wake of two circular cylinders in tandem,” Phys. Fluids 18, 084104 (2006)PHFLE6000018000008084104000001.


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