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A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method

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Abstract

This study investigates the pattern of flow past two staggered array cylinders using the spectral element method by varying the distance between the cylinders and the angle of incidence (α) at low Reynolds numbers (Re = 100-800). Six flow patterns are identified as Shear layer reattachment (SLR), Induced separation (IS), Vortex impingement (VI), Synchronized vortex shedding (SVS), Vortex pairing and enveloping (VPE), and Vortex pairing splitting and enveloping (VPSE). These flow patterns can be transformed from one to another by changing the distance between the cylinders, the angle of incidence, or Re. SLR, IS and VI flow patterns appear in regimes with small angles of incidence (i.e., α ≤ 30° ) and hold only a single von Karman vortex shedding in a wake with one shedding frequency. SVS, VPE and VPSE flow patterns appear in regimes with large angles of incidence (i.e., 30° ≤ α ≤ 50° ) and present two synchronized von Karman vortices. Quantitative analyses and physical interpretation are also conducted to determine the generation mechanisms of the said flow patterns.

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References

  1. K. Liu, D.-J. Ma, D.-J. Sun and X.-Y. Yin, Wake patterns of flow past a pair of circular cylinders in side-by-side arrangements at low Reynolds numbers, Journal of Hydrodynamics. Ser.B, 19 (6) (2007) 690–697.

    Article  Google Scholar 

  2. S.-M. Hesam and N. Navid, Numerical simulation of flow over two side-by-side circular cylinders, Journal of Hydrodynamics, 23 (6) (2011) 792–805.

    Article  Google Scholar 

  3. D. Sumner, S. J. Price and M. P. Paidoussis, Flow-pattern identification for two staggered circular cylinders in crossflow, Journal of Fluid Mechanics, 411 (2000) 263–303.

    Article  MATH  Google Scholar 

  4. M. H. Akbari and S. J. Price, Numerical investigation of flow patterns for staggered cylinder pairs in cross-flow, Journal of Fluids and Structures, 20 (2005) 533–554.

    Article  Google Scholar 

  5. D. Sumner, M. D. Richards and O. O. Akosile, Two staggered circular cylinders of equal diameter in cross-flow, Journal of Fluids and Structures, 20 (2005) 255–276.

    Article  Google Scholar 

  6. M. M. Alam and J. P. Meyer, Global aerodynamic instability of twin cylinders in cross flow, Journal of Fluids and Structures, 41 (2013) 135–145.

    Article  Google Scholar 

  7. A. T. Patera, A spectral element method for fluid dynamics: Laminar flow in a channel expansion, Journal of Computational Physics, 54 (1984) 468–488.

    Article  MATH  Google Scholar 

  8. S. A. Orszag and L. C. Kells, Transition to turbulence in plane poiseuille and plane couette flow, Journal of Fluid Mechanics, 96 (1980) 159–205.

    Article  MATH  Google Scholar 

  9. W. Jester and Y. Kallinderis, Numerical study of incompressible flow about fixed cylinder pairs, Journal of Fluids and Structures, 17 (2003) 561–577.

    Article  Google Scholar 

  10. S. Mittal, V. Kumar and A. Raghuvanshi, Unsteady incompressible flows past two cylinders in tandem and staggered arrangements, International Journal for Numerical Methods in Fluids, 25 (1997) 1315–1344.

    Article  MATH  Google Scholar 

  11. J. Park, K. Kwon and H. Choi, Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160, KSME International Journal, 12 (6) (1998) 1200–1205.

    Article  Google Scholar 

  12. D. Barkley and R. D. Henderson, Three-dimensional floquet stability analysis of the wake of a circular cylinder, Journal of Fluid Mechanics, 322 (1996) 215–241.

    Article  MATH  Google Scholar 

  13. O. Posdziech and R. Grundmann, A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder, Journal of Fluids and Structures, 23 (2007) 479–499.

    Article  Google Scholar 

  14. C. Lange, Numerical predictions of heat and momentum transfer from a cylinder in crossflow with implications to hot-wire anemometry, Ph.D. Thesis, University Erlangen-Nürnberg (1997).

    Google Scholar 

  15. C. Norberg, An experimental investigation of the flow around a circular cylinder: Influence of aspect ratio, Journal of Fluid Mechanics, 258 (1994) 287–316.

    Article  Google Scholar 

  16. C. H. K. Williamson and G. L. Brown, A series in 1 /Re to represent the Strouhal-Reynolds number relationship of the cylinder wake, Journal of Fluids and Structures, 12 (1998) 1073–1085.

    Article  Google Scholar 

  17. H. Ding, C. Shu, K. S. Yeo and D. Xu, Numerical simulation of flows around two circular cylinders by mesh-free least square-based finite difference methods, International Journal for Numerical Methods in Fluids, 53 (2) (2007) 305–332.

    Article  MATH  Google Scholar 

  18. A. B. Harichandan and A. Roy, Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme, International Journal of Heat and Fluid Flow, 31 (2010) 154–171.

    Article  Google Scholar 

  19. J. R. Meneghini, F. Saltara, C. L. R. Siqueira and J. A. Ferrari, Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements, Journal of Fluids and Structures, 15 (2) (2001) 327–350.

    Article  Google Scholar 

  20. K. Lee and K.-S. Yang, Flow patterns past two circular cylinders in proximity, Computers & Fluids, 38 (2009) 778–788.

    Article  MATH  Google Scholar 

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Correspondence to Li-Chieh Hsu.

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Recommended by Associate Editor Jungil Lee

Li-Chieh Hsu is currently an Associate Professor of the Department of Mechanical Engineering at the National Yunlin University of Science and Technology in Taiwan. His research interests include the spectral element method, adaptive meshes, vortex flow, fluid dynamics around cylinders, fluidstructure interactions, boiling heat transfer, and electronics cooling.

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Hsu, LC., Chen, CL. & Ye, JZ. A study of flow patterns for staggered cylinders at low Reynolds number by spectral element method. J Mech Sci Technol 31, 2765–2780 (2017). https://doi.org/10.1007/s12206-017-0520-7

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  • DOI: https://doi.org/10.1007/s12206-017-0520-7

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