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Variation of wake patterns and force coefficients of the flow past square bodies aligned inline

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Abstract

In this numerical study, the variation of wake patterns and force coefficients of the flow past four square bodies aligned inline are investigated. A two-dimensional numerical code is developed using the Lattice Boltzmann method (LBM) for this study. The code is first validated for the flow past a single and two tandem square cylinders. The results are compared to those available in literature and found to be in good agreement. After validation the calculations are further performed to investigate the effect of gap spacing (g) for the flow past four inline square cylinders at two different Reynolds numbers (Re) 100 and 200. The gap spacing is chosen in the range 0.25 ≤ g ≤ 7. Six different flow patterns: Single slender body, alternate reattachment, quasi steady reattachment, intermittent shedding, chaotic flow and periodic flow are found in this study with successive increment in spacing. It is found that some flow patterns existing at Re = 100 do not exist at Re = 200. The generated vortices at Re = 200 are much stronger as compared to those at Re = 100. The spacing value g = 3 is found to be critical at Re = 100 while at Re = 200 the spacing value g = 2 is critical due to abrupt changes in flow characteristics. At some spacing values the downstream cylinders have higher values of average drag coefficients as compared to upstream ones. In general the upstream cylinder (c1) have higher drag forces at Re = 200 than at Re = 100. The root mean square values of lift coefficient are found to be greater than the corresponding root mean square values of drag coefficient.

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References

  1. M. M. Zdravkovich, The effects of interference between circular cylinders in cross flow, Journal of Fluids and Structures, 1 (1987) 239–261.

    Article  Google Scholar 

  2. W. C. L. Shih, C. Wang, D. Coles and A. Roshko, Experiments on flow past rough circular cylinders at large Reynolds numbers, Journal of Wind Engineering and Industrial Aerodynamics, 49 (1993) 351–368.

    Article  Google Scholar 

  3. H. J. Niemann and N. Holscher, A review of recent experiments on the flow past circular cylinders, Journal of Wind Engineering and Industrial Aerodynamics, 33 (1990) 197–209.

    Article  Google Scholar 

  4. S. Manzoor, J. Khawar and N. A. Sheikh, Vortex-induced vibrations of a square cylinder with damped free-end conditions, Advances in Mechanical Engineering (2013) 1–12.

  5. R. Franke, W. Rodi and B. Schonung, Numerical calculation of laminar vortex-shedding flow past cylinders, Journal of Wind Engineering and Industrial Aerodynamics, 35 (1990) 237–257.

    Article  Google Scholar 

  6. A. k. Saha, k. Muralidhar and G. Biswas, Transition and chaos in two-dimensional flow past a square cylinder, Journal of Engineering Mechanics, 126 (2000) 523–532.

    Article  Google Scholar 

  7. M. Cheng, D. S. Whyte and J. Lou, Numerical simulation of flow around a square cylinder in uniform-shear flow, Journal of Fluids and Structures, 23 (2007) 207–226.

    Article  Google Scholar 

  8. S. Dutta, P. K. Panigrahi and K. Muralidhar, Experimental investigation of flow past a Square cylinder at an angle of incidence, Journal of Engineering Mechanics, 134 (2008) 788–803.

    Article  Google Scholar 

  9. A. Sohankar, L. Davidson and C. Norberg, Numerical simulation of unsteady flow around a square two-dimensional cylinder, Twelfth Australian Fluid Mechanics Conference, The University of Sydney, Australia (1995) 517–520.

  10. N. Mahir, Three-dimensional flow around a square cylinder near a wall, Ocean Engineering, 36 (2009) 357–367.

    Article  Google Scholar 

  11. G. Xu and Y. Zhou, Strouhal numbers in the wake of two inline cylinders, Experiments in Fluids, 37 (2004) 248–256.

    Article  Google Scholar 

  12. M. K. Kim, D. K. Kim, S. H. Yoon and D. H. Lee, Measurements of the flow fields around two square cylinders in a tandem arrangement, Journal of Mechanical Science and Technology, 22 (2008) 397–407.

    Article  Google Scholar 

  13. A. Lankadasu and S. Vengadesan, Interference effect of two equal-sized square cylinders in tandem arrangement: With planar shear flow, International Journal for Numerical Methods in Fluids, 57 (2007) 1005–1021.

    Article  MATH  Google Scholar 

  14. A. Sohankar, A numerical investigation of the flow over a pair of identical square cylinders in a tandem arrangement, International Journal for Numerical Methods in Fluids, 70 (2011) 1244–1257.

    Article  MathSciNet  Google Scholar 

  15. P. P. Patil and S. Tiwari, Numerical investigation of laminar unsteady wakes behind two inline square cylinders confined in a channel, Engineering Applications of Computational Fluid Mechanics, 3 (2009) 369–385.

    Article  Google Scholar 

  16. 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 (2001) 327–350.

    Article  Google Scholar 

  17. D. B. Ghadiri, M. H. Sarvghad and J. H. Houri, Numerical simulation of flow over two circular cylinders in tandem arrangement, Journal of Hydrodynamics, 23 (2011) 114–126.

    Article  Google Scholar 

  18. A. Sohankar, A LES study of the flow interference between tandem square cylinder pairs, Theoratical and Computational Fluid Dynamics, 28 (2014) 531–548.

    Article  Google Scholar 

  19. O. Inoue, M. Mori and N. Hatakeyama, Aeolian tones radiated from flow past two square cylinders in tandem, Physics of Fluids, 18 (2006) 1–15.

    Google Scholar 

  20. C. K. Vikram, Y. T. Krishne, H. V. Ravindra and C. J. Gangadara, Manu, Numerical simulation of two dimensional unsteady flow past two square cylinders, International Journal of Technology And Engineering System, 2 (2011) 355–360.

    Google Scholar 

  21. T. Igarashi and K. Suzuki, Characteristics of the flow around three circular cylinders arranged in line, Bulletin of JSME, 27 (1984) 2397–2404.

    Article  Google Scholar 

  22. 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 

  23. A. R. Vasel-Be-Hagh, D. Ting and R. Carriveau, Correlating flow pattern with force coefficients in air flow past a tandem unit of three circular cylinders, International Journal of Fluid Mechanics Research, 40 (2013) 235–253.

    Article  Google Scholar 

  24. S. U. Islam, W. S. Abbasi, H. Rahman and R. Naheed, Numerical investigation of wake modes for flow past three tandem cylinders using the multi-relaxation-time lattice Boltzmann method for different gap spacings, Journal of the Brazilian Society of Mechanical Sciences and Engineering, DOI 10.1007/s40430-014-0282-4.

  25. Y. Bao, Q. Wu and D. Zhou, Numerical investigation of flow around an inline square cylinder array with different spacing ratios, Computers & Fluids, 55 (2012) 118–131.

    Article  MathSciNet  MATH  Google Scholar 

  26. C. M. Sewatkar, R. Patel, A. Sharma and A. Agrawal, Flow around six in-line square cylinders, Journal of Fluid Mechanics, 710 (2012) 195–233.

    Article  MATH  Google Scholar 

  27. S. Chen and G. Doolen, Lattice Boltzmann method for fluid flows, Annual Review of Fluid Mechanics, 30 (1998) 329-364.

    Article  MathSciNet  Google Scholar 

  28. P. Lallemand and L. S. Luo, Theory of the lattice Boltzmann method: Acoustic and thermal properties in two and three dimensions, Physical Review E, 68 3 (2003) 036706.

    Article  MathSciNet  Google Scholar 

  29. G. M. Kremer, An introduction to the Boltzmann equation and transport processes in gases, Springer (2010).

    Book  MATH  Google Scholar 

  30. Z. Guo, H. Liu, L. Luo and K. Xu, Comparative study of the LBE and GKS methods for 2D near incompressible laminar flows, Journal of Computational Physics, 227 (2008) 4955–4976.

    Article  MathSciNet  MATH  Google Scholar 

  31. D. Yu, M. Renwei, L. S. Luo and S. Wei, Viscous flow computations with the method of lattice Boltzmann equation, Progress in Aerospace Sciences, 39 (2003) 329–367.

    Article  Google Scholar 

  32. A. Okajima, Strouhal numbers of rectangular cylinders, Journal of Fluid Mechanics, 123 (1982) 379–398.

    Article  Google Scholar 

  33. C. Norberg, Flow around rectangular cylinders: Pressure forces and wake frequencies, Journal of Wind Engineering and Industrial Aerodynamics, 49 (1993) 187–196.

    Article  Google Scholar 

  34. A. S. Abograis and A. E. Alshayji, Reduction of fluid forces on a square cylinder in a laminar flow using passive control methods, COMSOL Conference, Boston, USA (2013).

    Google Scholar 

  35. W. S. Abbasi, S. Ul. Islam, S. C. Saha, Y. T. Gu and C. Y. Zhou, Effect of Reynolds numbers on flow past four square cylinders in an in-line square configuration for different gap spacings, Journal of Mechanical Science and Technology, 28 2 (2014) 539–552.

    Article  Google Scholar 

  36. H. R. Kim, M. Ha, H. S. Yoon and S. W. Son, Dynamic behavior of a droplet on a moving wall, Journal of Mechanical Science and Technology, 28 5 (2014) 1709–1720.

    Article  Google Scholar 

  37. J. Bang and W. Yoon, Stochastic analysis of a collection process of submission particles on a single fiber accounting for the changes in flow field due to particle collection, Journal of Mechanical Science and Technology, 28 9 (2014) 3719–3732.

    Article  Google Scholar 

  38. N. Jeong, Rarefied gas flow simulation with TMAC in the slip and the transition flow regime using the lattice Boltzmann method, Journal of Mechanical Science and Technology, 28 11 (2014) 4705–4715.

    Article  Google Scholar 

  39. S. Ul. Islam, H. Rahman, W. S. Abbasi, U. Noreen and A. Khan, Suppression of fluid force on flow past a square cylinder with a detached flat plate at low Reynolds number for various spacing ratios, Journal of Mechanical Science and Technology, 28 12 (2014) 4969–4978.

    Article  Google Scholar 

  40. M. Jourabian and M. Farhadi, Melting of nanoparticlesenhanced phase change material (NEPCM) in vertical semicircle enclosure: numerical study, Journal of Mechanical Science and Technology, 29 9 (2015) 3819–3830.

    Article  Google Scholar 

  41. S. Ul. Islam, C. Y. Zhou, A. Shah and P. Xie, Numerical simulation of flow past rectangular cylinders with different aspect ratios using the incompressible lattice Boltzmann method, Journal of Mechanical Science and Technology, 26 4 (2012) 1027–1041.

    Article  Google Scholar 

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Correspondence to Shams-ul-Islam.

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Shams-ul-Islam is currently a assistant professor in Mathematics Department COMSATS Institute of Information, Technology, Islamabad. He received his Ph.D. in 2010. His research interests include, fluid structure interaction, drag reduction of bluff body and heat and mass transfer.

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Manzoor, R., Shams-ul-Islam, Abbasi, W. et al. Variation of wake patterns and force coefficients of the flow past square bodies aligned inline. J Mech Sci Technol 30, 1691–1704 (2016). https://doi.org/10.1007/s12206-016-0325-0

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  • DOI: https://doi.org/10.1007/s12206-016-0325-0

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