Skip to main content
SpringerLink
Log in

Strouhal numbers in the wake of two inline cylinders

  • Original
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

The dominant vortex frequencies f s in the wake of two tandem circular cylinders of identical diameter d have been measured simultaneously using two hot wires placed behind each cylinder. Measurements were conducted over the Reynolds number Re (≡U ∞ d/ν, where U ∞ and ν are the free-stream velocity and the kinematic viscosity of fluid, respectively) =800–4.2×104 and the cylinder centre-to-centre spacing L/d=1–15. The Strouhal number St (≡f s d/U ∞) exhibits a strong dependence on L/d and Re. For L/d<(L/d)c, which is a critical value and ranges between 3.5 and 5, there is no vortex street formed in the gap between the cylinders, and St measured behind the downstream cylinder drops rapidly for increasing L/d. For L/d>(L/d)c, co-shedding occurs, that is, vortices are shed from the upstream as well as the downstream cylinder, and their frequencies are found to be identical. St climbs with increasing L/d, approaching a constant between 0.18 and 0.22 for L/d>10. The St–Re relationship is classified into four categories, based on their behaviours, which are associated with distinct flow physics—category 1: for 1≤L/d<2, the shear layers separated from the upstream cylinder roll up behind the downstream cylinder; category 2: for 2≤L/d≤3, there is a transition from the shear layer rollup behind to reattachment on the downstream cylinder; category 3: for 3<L/d≤5, transition from the reattachment to co-shedding regime occurs at a critical Reynolds number; and category 4: the flow for L/d>5 is characterized by co-shedding only. The present measurements reconfirm the previous observation of a bi-stable flow at the transition from the reattachment to co-shedding regime. It is found for the first time that another bi-stable flow occurs at the transition from category 1 to 2, that is, the stable reattachment co-exists with the stable rollup (behind the downstream cylinder) of shear layers separating from the upstream cylinder, resulting in two distinct vortex-shedding frequencies even at the same Re and L/d. The St behaviour is further discussed along with flow visualization using the laser-induced fluorescence technique.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5a, b
Fig. 6a–d
Fig. 7
Fig. 8a, b
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Arie M, Kiya M, Moriya M, Mori H (1983) Pressure fluctuations on the surface at two circular cylinders in tandem arrangement. J Fluid Eng 105:161–167

    Google Scholar 

  • Armstrong BJ, Barnes FH, Grant I (1987) A comparison of the structure of the wake behind a circular cylinder in a steady flow with that in a perturbed flow. Phys Fluids 30:19–26

    Article  Google Scholar 

  • Bauer AB (1961) Vortex shedding from thin flat plates parallel to the free stream. J Aeronaut Sci 28:340–341

    Google Scholar 

  • Bearman PW (1984) Vortex shedding from oscillating bluff bodies. Ann Rev Fluid Mech 16:195–222

    Article  Google Scholar 

  • Bloor MS (1964) The transition to turbulence in the wake of a circular cylinder. J Fluid Mech 19:290–304

    Google Scholar 

  • Bloor MS, Gerrard JH (1966) Measurements on turbulent vortices in a circular cylinder. Proc R Soc A 294:319–342

    Google Scholar 

  • Chang K, Song C (1990) Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement. Int J Num Meth Fluids 11:317–329

    Google Scholar 

  • Gerrard JH (1966) The mechanics of the formation region of vortices behind bluff bodies. J Fluid Mech 25:401–413

    Google Scholar 

  • Hori E (1959) Experiments on flow around a pair of parallel circular cylinders. In: Proceedings of the 9th Japan National Congress for Applied Mechanics, Tokyo, pp 231–234

  • Huhe-Aode H, Tatsuno M, Taneda S (1985) Visual studies of wake structure behind two cylinders in tandem arrangement. Rep Res Inst Appl Mech Kyushu Univ 32(99):1–20

    Google Scholar 

  • Igarashi T (1981) Characteristics of the flow around two circular cylinders arranged in tandem, 1st report. Bull JSME B24(188):323–331

    Google Scholar 

  • Igarashi T (1984) Characteristics of the flow around two circular cylinders arranged in tandem, 2nd report. Bull JSME B27(233):2380–2387

    Google Scholar 

  • Ishigai S, Nishikawa E, Nishimura K, Cho K (1972) Experimental study on structure of gas flow in tube banks with tube axes normal to flow (Part 1, Karman vortex flow around two tubes at various spacings). Bull JSME 5(86):949–956

    Google Scholar 

  • Jester W, Kallinderis Y (2003) Numerical study of incompressible flow about fixed cylinder pairs. J Fluids Struct 17:561–577

    Article  Google Scholar 

  • Lai WC, Zhou Y, So RMC, Wang T (2003) Interference between stationary and vibrating cylinder wakes. Phys Fluids 15:1687–1695

    Article  CAS  Google Scholar 

  • Lin J-C, Yang Y, Rockwell D (2002) Flow past two cylinders in tandem: instantaneous and averaged flow structure. J Fluids Struct 16:1059–1071

    Article  Google Scholar 

  • Liu C-H, Chen JM (2002) Observations of hysteresis in flow around two square cylinders in a tandem arrangement. J Wind Eng Ind Aerodyn 90:1019–1050

    Article  Google Scholar 

  • Ljungkrona L, Norberg C, Sunden B (1991) Free-stream turbulence and tube spacing effects on surface pressure fluctuations for two tubes in an in-line arrangement. J Fluids Struct 5:701–727

    Google Scholar 

  • Mittal S, Kumar V, Raghuvanshi A (1997) Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. Int J Num Meth Fluids 25:1315–1344

    Article  CAS  Google Scholar 

  • Monkewitz P, Nguyen LN (1987) Absolute instability in the near wake of two-dimensional bluff bodies. J Fluids Struct 1:165–184

    Google Scholar 

  • Moriya M, Sakamoto H (1986) Effect of a vibrating upstream cylinder on a stationary downstream cylinder. J Fluids Eng 108:180–184

    CAS  Google Scholar 

  • Norberg C (1994) An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J Fluid Mech 258:287–316

    CAS  Google Scholar 

  • Norberg C (1998) LDV-measurements in the near wake of a circular cylinder. In: Williamson CHK, Bearman PW (eds) Advances in understanding of bluff body wakes and flow-induced vibration (FEDSM98–5202). ASME, New York, pp 1–12

  • Novak J (1974) Strouhal number of a square prism, angle iron and two circular cylinders arranged in tandem (in English). Acta Tech Czech Acad Sci 3:361–373

    Google Scholar 

  • Ohya Y, Okajima A, Hayashi M (1989) Wake interference and vortex shedding. In: Cheremisinoff NP (ed) Encyclopedia of Fluid Mechanics. Gulf, Houston, pp 323–389

  • Oka S, Kostic ZG, Sikmanovic S (1972) Investigation of the heat transfer processes in tube banks in cross flow. In: International Seminar on Recent developments in heat exchangers, Trogir, Yugoslavia (preprint)

  • Okajima A (1979) Flows around two tandem circular cylinders at very high Reynolds numbers. Bull JSME 22:504–511

    Google Scholar 

  • Prasad A, Williamson CHK (1997) The instability of the shear layer separating from a bluff body. J Fluid Mech 333:375–402

    Article  Google Scholar 

  • Roshko A (1955) On the wake and drag of bluff bodies. J Aeronaut Sci 22:124–132

    Google Scholar 

  • Sakamoto H, Haniu H (1988) Aerodynamic forces acting on two square prisms placed vertically in a turbulent boundary layer. J Wind Eng Ind Aerodyn 31:41–66.

    Article  Google Scholar 

  • Schlichting H (1979) Boundary-layer theory. McGraw-Hill, New York, p 32

  • Slaouti A, Stansby PK (1992) Flow around two circular cylinders by the random-vortex method. J Fluids Struct 6:641–670

    Article  Google Scholar 

  • So RMC, Zhou Y, Liu MH (2000) Free vibrations of an elastic cylinder in a cross flow and their effects on the near wake. Exp Fluids 29:130–144

    Article  Google Scholar 

  • Tanida Y, Okajima A, Watanabe Y (1973) Stability of a circular cylinder oscillating in uniform flow or in a wake. J Fluid Mech 61:769–784

    Google Scholar 

  • Williamson CHK, Brown GL (1998) A series in 1/Re 1/2 to represent the Strouhal–Reynolds number relationship of the cylinder wake. J Fluids Struct 12:1073–1085

    Article  Google Scholar 

  • Wu J, Welch LW, Welsh MC, Sheridan J, Walker GJ (1994) Spanwise wake structures of a circular cylinder and two circular cylinders in tandem. Exp Thermal Fluid Sci 9:299–308

    Article  Google Scholar 

  • Xu SJ, Zhou Y, So RMC (2002) Flow structure behind a streamwise oscillating cylinder. In: Proceedings of the Conference on Bluff body wakes and vortex-induced vibrations, 17–20 December 2002, Fort Douglas, Queensland, Australia, pp 183–186

  • Zdravkovich MM (1977) Review of flow interference between two circular cylinders in various arrangements. J Fluids Eng 99:618–631

    Google Scholar 

  • Zdravkovich MM (1985) Flow induced oscillations of two interfering circular cylinders. J Sound Vibrat 101:511–521

    Google Scholar 

  • Zdravkovich, M.M. 1987 The effects of interference between circular cylinders in cross flow. J Fluids Struct 1:239–261

    Google Scholar 

  • Zhou Y, Wang ZJ, So RMC, Xu SJ, Jin W (2001) Free vibrations of two side-by-side cylinders in a cross flow. J Fluid Mech 443:197–229

    Article  Google Scholar 

  • Zhou Y, Zhang HJ, Yiu MW (2002) The turbulent wake of two side-by-side circular cylinders. J Fluid Mech 458:303–332

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors wish to acknowledge support given to them by the Central Research Grant of The Hong Kong Polytechnic University through Grant G-YW74.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    G. Xu & Y. Zhou

Authors
  1. G. Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. Zhou.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Xu, G., Zhou, Y. Strouhal numbers in the wake of two inline cylinders. Exp Fluids 37, 248–256 (2004). https://doi.org/10.1007/s00348-004-0808-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00348-004-0808-0

Keywords

Search

Navigation