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Reynolds number effect on the flow past two tandem cylinders

  • Derakhshandeh, Javad Farrokhi (College of Engineering and Technology, American University of the Middle East) ;
  • Alam, Md. Mahbub (Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology (Shenzhen))
  • Received : 2019.11.09
  • Accepted : 2020.01.22
  • Published : 2020.05.25

Abstract

This work investigates Reynolds number Re (= 50 - 200) effects on the flows around a single cylinder and the two tandem (center-to-center spacing L= L/D = 4) cylinders, each of a diameter D. Vorticity structures, Strouhal numbers, and time-mean and fluctuating forces are presented and discussed. For the single cylinder, with increasing Re in the range examined, the vorticity magnitude, Strouhal number and fluctuating lift all monotonically rise but time-mean drag, vortex formation length, and lateral distance between the two rows of vortices all shrink. For the two tandem cylinders, the increase in Re leads to the formation of three distinct flows, namely reattachment flow (50 ≤ Re ≤ 75), transition flow (75 < Re < 100), and coshedding flow (100 ≤ Re ≤ 200). The reattachment flow at Re = 50 is steady. When Re is increased from 75 to 200, the Strouhal number of the two cylinders, jumping from 0.113 to 0.15 in the transition flow regime, swells to 0.188. The two-cylinder flow is more sensitive to Re than the single cylinder flow. Fluctuating lift is greater for the downstream cylinder than the upstream cylinder while time-mean drag is higher for the upstream cylinder than for the other. The time-mean drags of the upstream cylinder and single cylinder behaves similar to each other, both declining with increasing Re.

Keywords

Acknowledgement

The second author wishes to acknowledge the support given by the National Natural Science Foundation of China through Grants 11672096 and 91752112 and by Research Grant Council of Shenzhen Government through grant JCYJ20180306171921088

References

  1. Alam, M.M. (2014), "The aerodynamics of a cylinder submerged in the wake of another", J. Flu. Struct., 51, 393-400, https://doi.org/10.1016/j.jfluidstructs.2014.08.003.
  2. Alam, M.M. (2016), "Lift forces induced by phase lag between the vortex sheddings from two tandem bluff bodies", J. Flu. Struct., 65, 217-237. https://doi.org/10.1016/j.jfluidstructs.2016.05.008.
  3. Alam, M.M. and Sakamoto, H. (2005), "Investigation of Strouhal frequencies of two staggered bluff bodies and detection of multi stable flow by wavelets", J. Flu. Struct., 20(3), 425-449. https://doi.org/10.1016/j.jfluidstructs.2004.11.003.
  4. Alam, M.M. and Zhou, Y. (2007), "Phase lag between vortex shedding from two tandem bluff bodies", J. Flu. Struct., 23, 339-347. https://doi.org/10.1016/j.jfluidstructs.2006.11.003.
  5. Alam, M.M. and Zhou, Y. (2008), "Alternative drag coefficient in the wake of an isolated bluff body", J. Phys. Rev., 78, 036320, https://doi.org/10.1103/PhysRevE.78.036320.
  6. Alam, M.M., Moriya, M. Takai, K. and Sakamoto, H. (2003), "Fluctuating fluid forces acting on two circular cylinders in a tandem arrangement at a subcritical Reynolds number", J. Wind Eng. Ind. Aerod., 91, 139-154. https://doi.org/10.1016/S0167-6105(02)00341-0.
  7. Alam, M.M., Sakamoto, H. and Zhou, Y. (2005), "Determination of flow configurations and fluid forces acting on two staggered circular cylinders of equal diameter in cross-Flow", J. Flu. Struct., 21, 363-394. https://doi.org/10.1016/j.jfluidstructs.2005.07.009.
  8. Alam, M.M., Sakamoto, H. and Zhou, Y. (2006), "Effect of a T-shaped plate on reduction in fluid force on two tandem cylinders in a cross-flow", J. Wind Eng. Ind. Aerod., 94, 525-551. https://doi.org/10.1016/j.jweia.2006.01.018.
  9. Alam, Md. M., Zheng, Q., Derakhshandeh, J.F., Rehman, S., Ji, C. and Zafar F. (2018), "On forces and phase lags between vortex sheddings from three tandem cylinders", Int. J. Heat Flu.Flow", 69, 117-135. https://doi.org/10.1016/j.ijheatfluidflow.2017.12.012.
  10. Assi, G., Bearman, P. and Meneghini, J. (2010), "On the wake-induced vibration of tandem circular cylinders: The vortex interaction excitation mechanism", J. Fluid Mech., 661(1), 365-401. https://doi.org/10.1017/S0022112010003095.
  11. Carmo, B.S. and Meneghini, J.R. (2006), "Numerical investigation of the flow around two circular cylinders in tandem", J. Flu. Struct., 22, 979-988. https://doi.org/10.1016/j.jfluidstructs.2006.04.016.
  12. Carmo, B.S., Meneghini, J.R. and Sherwin, S. (2010), "Secondary instabilities in the flow around two circular cylinders in tandem", J. Flu. Mech., 644, 395-431, https://doi.org/10.1017/S0022112009992473.
  13. Dehkordi, B.G., Moghaddam, H.S. and Jafari, H.H. (2011), "Numerical simulation of flow over two circular cylinders in tandem arrangement", J. Hydrodyn., 23(1), 114-126. 10.1016/S1001-6058(10)60095-9.
  14. Derakhshandeh, J.F. (2015), "Harnessing hydro-kinetic energy from Vortex-Induced Vibration (VIV)", Master Thesis, Adelaide University, Australia. http://hdl.handle.net/2440/119460.
  15. Derakhshandeh, J.F. and Alam, M.M. (2019), "A review of bluff body wakes", Ocean Eng., 182, 475-488. https://doi.org/10.1016/j.oceaneng.2019.04.093.
  16. Derakhshandeh, J.F., Arjomandi, M., Dally, B. and Cazzolato, B. (2014a), "The effect of arrangements of two circular cylinders on the maximum efficiency of vortex- induced vibration power using a Scale-Adaptive Simulation model", J. Flu. Struct., 49, 654-666. https://doi.org/10.1016/j.jfluidstructs.2014.06.005.
  17. Derakhshandeh, J.F., Arjomandi, M., Dally, B. and Cazzolato, B. (2014b), "Effect of a rigid wall on the vortex induced vibration of two staggered cylinders", J. Renew. Sustain. Energy Rev., 6, 033114. https://doi.org/10.1063/1.4879275.
  18. Derakhshandeh, J.F., Arjomandi, M., Dally, B. and Cazzolato, B. (2016), "Flow induced vibration of an elastically mounted airfoil under the influence of oncoming vortices", J. Exp. Therm. Fluid Sci., 74, 58-72. https://doi.org/10.1016/j.expthermflusci.2015.12.003.
  19. Igarashi, T. (1981), "Characteristics of the flow around two circular cylinders arranged in tandem", I. JSME Int. J. Series B., 24, 323-333. https://doi.org/10.1299/jsme1958.24.323.
  20. Igarashi, T. (1984), "Characteristics of the flow around two circular cylinders arranged in tandem: 2nd report, unique phenomenon at small spacing", Bull. JSME, 27(233), 2380-2387. https://doi.org/10.1299/jsme1958.27.2380.
  21. Kadota, A., Aragao, R. and Suzuki, K. (2007), "Visualization of flow pattern around two-in-tandem cylinders", J. Appl. Mech., 10, 667-674. https://doi.org/10.2208/journalam.10.667.
  22. Liu, C., Zheng, X. and Sung, C.H. (1998), "Preconditioned multigrid methods for unsteady incompressible flows", J. Comput. Phys., 139(1), 35-57. https://doi.org/10.1006/jcph.1997.5859.
  23. Ljungkrona, L. and Sunden, B. (1993), "Flow visualization and surface pressure measurement on two tubes in an inline arrangement", Exp. Therm. Flu. Sci., 6(1), 15-27. https://doi.org/10.1016/0894-1777(93)90037-J.
  24. Ljungkrona, L., Norberg, C.H. and Sunden, B. (1991), "Free-stream turbulence and tube spacing effects on surface pressure fluctuations for two tubes in an in-line arrangements", J. Flu. Struct., 5(6), 701-727. https://doi.org/10.1016/0889-9746(91)90364-U.
  25. Mahir, N. and Altac, Z. (2008), "Numerical investigation of convection heat transfer in unsteady flow past two cylinders in tandem arrangements", Int. J. Heat Flu. Flow, 29, 1309-1318. https://doi.org/10.1016/j.ijheatfluidflow.2008.05.001.
  26. Meneghini, J.R., Saltara, F., Siqueira, C.L.R. and Ferrari Jr, J.A. (2001), "Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements", J. Flu. Struct., 15(2), 327-350. https://doi.org/10.1006/jfls.2000.0343.
  27. Mittal, S., Kumar, V. and Raghuvanshi, A. (1997), "Unsteady incompressible flows past two cylinders. in tandem and staggered arrangements", Int. J. Numer. Meth. Flu., 25, 1315. https://doi.org/10.1002/(SICI)10970363(19971215)25:11<1315::AID-FLD617>3.0.CO;2-P.
  28. Papaioannou, G.V., Yue, D., Triantafyllou, M. and Karniadakis, G. (2006), "Three-dimensionally effects in flow around two tandem cylinders", J. Fluid Mech. 558, 387-413. https://doi.org/10.1017/S0022112006000139.
  29. Qin, B., Alam, M.M. and Zhou, Y. (2017), "Two tandem cylinders of different diameters in cross-flow: Flow-induced vibration", J. Flu. Mech., 829, 621-658. https://doi.org/10.1017/jfm.2017.510.
  30. Saha, A.K., Biswas, G. and Muralidhar, K., (2003). "Three-dimensional study of flow past a square cylinder at low Reynolds numbers", Int. J. Heat Flu. Flow, 24(1), 54-66. https://doi.org/10.1016/S0142-727X(02)00208-4
  31. Sarkar, S. and Sarkar, S. (2010), "Vortex dynamics of a cylinder wake in proximity to a wall", J. Flu. Struct., 26(1), 19-40. https://doi.org/10.1016/j.jfluidstructs.2009.08.003.
  32. Singha, S. and Sinhamahapatra, K.P. (2010), "High-resolution numerical simulation of low Reynolds number incompressible flow about two cylinders in tandem", J. Flu. Eng., 132(1), 011101. https://doi.org/10.1115/1.4000649
  33. Sumner, D. (2010), "Two circular cylinders in cross-flow: A review", J. Flu. Struct., 26, 849-899, https://doi.org/10.1016/j.jfluidstructs.2010.07.001.
  34. Williamson, C.H.K. (1996a), "Vortex dynamics in the cylinder wake," Annual Rev. Flu. Mech., 28, 477-539. https://doi.org/10.1146/annurev.fl.28.010196.002401.
  35. Williamson, C.H.K. (1996b), "Three-dimensional wake transition", J. Flu. Mech., 328-345. https://doi.org/10.1017/S0022112096008750.
  36. Zdravkovich, M. (1977), "Review of flow interference between two circular cylinders in various arrangements", ASME, J. Flu. Eng., 99, 618-633, https://doi.org/10.1115/1.3448871.
  37. Zdravkovich, M. (1997), "Flow Around Circular Cylinders", 1. Oxford University Press Inc., New York, U.S.A.
  38. Zdravkovich, M.M. and Pridden, D.L. (1977), "Interference between two circular cylinders; series of unexpected discontinuities", J. Wind Eng. Ind. Aerod., 2, 255-270. https://doi.org/10.1016/0167-6105(77)90026-5.
  39. Zheng, Q. and Alam, M.M. (2017), "Intrinsic features of flow past three square prisms in side-by-side arrangement", J. Fluid Mech., 826, 996-1033. https://doi:10.1017/jfm.2017.378.
  40. Zhou, Q., Alam, M.M., Cao, S., Liao, H. and Li, M. (2019), "Numerical study of wake and aerodynamic forces on two tandem circular cylinders at Re=103", Phys. Flu., 31(4), 04510. https://doi.org/10.1063/1.5087221.
  41. Zhou, Y. and Alam, M.M. (2016), "Wake of two interacting circular cylinders: a review", Int. J. Heat Flu. Flow, 62, 510-537. https://doi.org/10.1016/j.ijheatfluidflow.2016.08.008.

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