Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-28T13:02:52.170Z Has data issue: false hasContentIssue false

Wake of two tandem square cylinders

Published online by Cambridge University Press:  14 March 2024

Yu Zhou
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Jingcheng Hao
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
Md. Mahbub Alam*
Affiliation:
Center for Turbulence Control, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China
*
Email address for correspondence: alamm28@yahoo.com

Abstract

The wake of two tandem square cylinders of identical width (d) is experimentally studied, with a view to understanding the dependence of the flow structure, aerodynamics forces and Strouhal number on the centre-to-centre spacing ratio L/d and Reynolds number Re, where L is the distance between the cylinder centres. Extensive measurements are carried out, using hot-wire, particle imaging velocimetry, laser-induced fluorescence flow visualization, surface-oil-flow visualization and surface pressure scanning techniques, for L/d = 1.0 ~ 5.0 and Re ≡ Ud/ν = 2.8 × (103 ~ 104), where U is the free-stream velocity and ν is the kinematic viscosity of the fluid. The flow is classified into four regimes, i.e. the extended-body (L/d ≤ 1.5–2.0), reattachment (1.5–2.0 < L/d < 2.7–3.2), co-shedding (L/d ≥ 3.0–3.4) and transition (2.7 ≤ L/d ≤ 3.3) where both reattachment and co-shedding phenomena may take place. The mean drag and fluctuating drag and lift exhibit distinct features for different flow regimes, which is fully consistent with the proposed flow classification. Comparison is made between this flow and the wake of two tandem circular cylinders, which provides valuable insight into the profound effect of the flow separation point and the presence of sharp corners on the flow development and classification.

Type
JFM Papers
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aasland, T.E., Pettersen, B., Andersson, H.I. & Jiang, F. 2023 Asymmetric cellular bi-stability in the gap between tandem cylinders. J. Fluid Mech. 966, A39.CrossRefGoogle Scholar
Abdelhamid, T., Alam, M.M. & Islam, M. 2021 Heat transfer and flow around cylinder: effect of corner radius and Reynolds number. Intl J. Heat Mass Transfer 171, 121105.CrossRefGoogle Scholar
Alam, M.M. 2014 The aerodynamics of a cylinder submerged in the wake of another. J. Fluids Struct. 51, 393400.CrossRefGoogle Scholar
Alam, M.M., Abdelhamid, T. & Sohankar, A. 2020 Effect of cylinder corner radius and attack angle on heat transfer and flow topology. Intl J. Mech. Sci. 175, 105566.CrossRefGoogle Scholar
Alam, M.M., Rastan, M.R., Wang, L. & Zhou, Y. 2022 Flows around two nonparallel tandem circular cylinders. J. Wind Engng Ind. Aerodyn. 220, 104870.CrossRefGoogle Scholar
Alam, M.M. & Sakamoto, H. 2005 Investigation of Strouhal frequencies of two staggered bluff bodies and detection of multistable flow by wavelets. J. Fluids Struct. 20 (3), 425449.CrossRefGoogle Scholar
Alam, M.M., Sakamoto, H. & Zhou, Y. 2005 Determination of flow configurations and fluid forces acting on two staggered circular cylinders of equal diameter in cross-flow. J. Fluids Struct. 21 (4), 363394.CrossRefGoogle Scholar
Alam, M.M. & Zhou, Y. 2007 Phase lag between vortex shedding from two tandem bluff bodies. J. Fluids Struct. 23 (2), 339347.CrossRefGoogle Scholar
Alam, M.M., Zhou, Y. & Wang, X.W. 2011 The wake of two side-by-side square cylinders. J. Fluid Mech. 669, 432471.CrossRefGoogle Scholar
Armstrong, B.J., Barnes, F.H. & 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 (1), 19.CrossRefGoogle Scholar
Bai, H. & Alam, M.M. 2018 Dependence of square cylinder wake on Reynolds number. Phys. Fluids 30 (1), 15102.CrossRefGoogle Scholar
Bauer, A.B. 1961 Vortex shedding from thin flat plates parallel to the free stream. J. Aerosp. Sci. 28 (4), 340341.CrossRefGoogle Scholar
Bearman, P.W. & Trueman, D.M. 1972 An investigation of the flow around rectangular cylinders. Aeronaut. Q. 23 (3), 229237.CrossRefGoogle Scholar
Bloor, M.S. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19 (2), 290.CrossRefGoogle Scholar
Chen, J.G., Zhou, Y., Zhou, T.M. & Antonia, R.A. 2016 Three-dimensional vorticity, momentum and heat transport in a turbulent cylinder wake. J. Fluid Mech. 809, 135167.CrossRefGoogle Scholar
Choi, C.B., Jang, Y.J. & Yang, K.S. 2012 Secondary instability in the near-wake past two tandem square cylinders. Phys. Fluids 24 (2), 024102.CrossRefGoogle Scholar
Derakhshandeh, J.F. & Alam, M.M. 2019 A review of bluff body wakes. Ocean Engng 182, 475488.CrossRefGoogle Scholar
Du, X., Xu, Q., Dong, H. & Chen, L. 2022 Physical mechanisms behind the extreme wind pressures on two tandem square cylinders. J. Wind Eng. Ind. Aerodyn. 231, 105249.CrossRefGoogle Scholar
Farhadi, M., Sedighi, K. & Mohsenzadeh Korayem, A. 2010 Effect of wall proximity on forced convection in a plane channel with a built-in triangular cylinder. Intl J. Therm. Sci. 49 (6), 10101018.CrossRefGoogle Scholar
Gerrard, J.H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25 (2), 401413.CrossRefGoogle Scholar
Grandemange, M., Gohlke, M. & Cadot, O. 2013 Turbulent wake past a three-dimensional blunt body. Part 1. Global modes and bi-stability. J. Fluid Mech. 722, 5184.CrossRefGoogle Scholar
Griffin, O.M. & Ramberg, S.E. 1974 The vortex-street wakes of vibrating cylinders. J. Fluid Mech. 66 (3), 553576.CrossRefGoogle Scholar
Haffner, Y., Borée, J., Spohn, A. & Castelain, T. 2020 Mechanics of bluff body drag reduction during transient near-wake reversals. J. Fluid Mech. 894, A14.CrossRefGoogle Scholar
Hasan, M. 1989 The near wake structure of a square cylinder. Intl J. Heat Fluid Flow 10 (4), 339348.CrossRefGoogle Scholar
Igarashi, T. 1981 Characteristics of the flow around two circular cylinders arranged in tandem: 1st report. Bull. JSME 24 (188), 323331.CrossRefGoogle Scholar
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), 23802387.CrossRefGoogle Scholar
Jester, W. & Kallinderis, Y. 2003 Numerical study of incompressible flow about fixed cylinder pairs. J. Fluids Struct. 17 (4), 561577.CrossRefGoogle Scholar
Kim, M.K., Kim, D.K., Yoon, S.H. & Lee, D.H. 2008 Measurements of the flow fields around two square cylinders in a tandem arrangement. J. Mech. Sci. Technol. 22 (2), 397407.CrossRefGoogle Scholar
Laneville, A., Gartshore, I.S. & Parkinson, G.V. 1975 An explanation of some effects of turbulence on bluff bodies. In Proceedings of the Fourth International Conference on Wind Effects on Buildings & Structure, Heathrow, UK, K75–363 (ed. K.J. Eator), pp. 333–341. Cambridge University Press.Google Scholar
Lee, B.E. 1975 The effect of turbulence on the surface pressure field of a square prism. J. Fluid Mech. 69 (2), 263282.CrossRefGoogle Scholar
Lee, T. & Basu, S. 1997 Nonintrusive measurements of the boundary layer developing on a single and two circular cylinders. Exp. Fluids 23 (3), 187192.CrossRefGoogle Scholar
Lin, J.-C., Yang, Y. & Rockwell, D. 2002 Flow past two cylinders in tandem: instantaneous and averaged flow structure. J. Fluids Struct. 16 (8), 10591071.CrossRefGoogle Scholar
Liu, C.-H. & Chen, J.M. 2002 Observations of hysteresis in flow around two square cylinders in a tandem arrangement. J. Wind Engng Ind. Aerodyn. 90 (9), 10191050.CrossRefGoogle Scholar
Ljungkrona, L., Norberg, C. & Sundén, 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 (6), 701727.CrossRefGoogle Scholar
Mondal, M. & Alam, M.M. 2023 Blockage effect on wakes of various bluff bodies: a review of confined flow. Ocean Engng 268, 115592.CrossRefGoogle Scholar
Monkewitz, P.A. & Nguyen, L.N. 1987 Absolute instability in the near-wake of two-dimensional bluff bodies. J. Fluids Struct. 1 (2), 165184.CrossRefGoogle Scholar
Nakaguchi, H., Hasimot, K. & Muto, S. 1968 An experimental study of aerodynamic drag on rectangular cylinders. J. Japan Soc. Aeronaut. Space Sci. 16, 15.Google Scholar
Ng, Z.Y., Vo, T., Hussam, W.K. & Sheard, G.J. 2016 Two-dimensional wake dynamics behind cylinders with triangular cross-section under incidence angle variation. J. Fluids Struct. 63, 302324.CrossRefGoogle Scholar
Norberg, C. 1993 Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Engng Ind. Aerodyn. 49 (1–3), 187196.CrossRefGoogle Scholar
Norberg, C. 1994 An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. J. Fluid Mech. 258, 287316.CrossRefGoogle Scholar
Okajima, A. 1982 Strouhal numbers of rectangular cylinders. J. Fluid Mech. 123, 379398.CrossRefGoogle Scholar
Ota, T., Nishiyama, H., Kominami, J. & Sato, K. 1986 Heat transfer from two elliptic cylinders in tandem arrangement. J. Heat Transfer 108 (3), 525531.CrossRefGoogle Scholar
Otsuki, Y., Washizu, K., Tomizawa, H. & Ohya, A. 1974 A note on the aeroelastic instability of a prismatic bar with square section. J. Sound Vib. 34 (2), 233248.CrossRefGoogle Scholar
Prasad, A. & Williamson, C.H.K. 1997 The instability of the shear layer separating from a bluff body. J. Fluid Mech. 333, 375402.CrossRefGoogle Scholar
Rastan, M.R. & Alam, M.M. 2021 Transition of wake flows past two circular or square cylinders in tandem. Phys. Fluids 33, 081705.CrossRefGoogle Scholar
Reinhold, T.A., Tieleman, H.W. & Maher, F.J. 1977 Interaction of square prisms in two flow fields. J. Wind Engng Ind. Aerodyn. 2 (3), 223241.CrossRefGoogle Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Ind. Aerodyn. 49 (1–3), 79100.CrossRefGoogle Scholar
Sakamoto, H. & Haniu, H. 1988 Effect of free-stream turbulence on characteristics of fluctuating forces acting on two square prisms in tandem arrangement. J. Fluids Engng. 110 (2), 140146.CrossRefGoogle Scholar
Sakamoto, H., Hainu, H. & Obata, Y. 1987 Fluctuating forces acting on two square prisms in a tandem arrangement. J. Wind Engng Ind. Aerodyn. 26 (1), 85103.CrossRefGoogle Scholar
Shang, J., Zhou, Q., Alam, M.M., Liao, H. & Cao, S. 2019 Numerical studies of the flow structure and aerodynamic forces on two tandem square cylinders with different chamfered-corner ratios. Phys. Fluids 31 (7), 075102.CrossRefGoogle Scholar
Shi, X., Alam, M. & Bai, H. 2020 a Wakes of elliptical cylinders at low Reynolds number. Intl J. Heat Fluid Flow 82, 108553.CrossRefGoogle Scholar
Shi, X., Alam, M.M., Bai, H. & Wang, H. 2020 b The effect of Reynolds number on the elliptical cylinder wake. Wind Struct. 30 (5), 525.Google Scholar
Shi, X., Bai, H., Alam, M.M., Ji, C. & Zhu, H. 2023 Wake of wavy elliptic cylinder at a low Reynolds number: wavelength effect. J. Fluid Mech. 969, A22.CrossRefGoogle Scholar
Sobczyk, J., Wodziak, W., Gnatowska, R., Stempka, J. & Niegodajew, P. 2018 Impact of the downstream cylinder displacement speed on the hysteresis limits in a flow around two rectangular objects in tandem – PIV study of the process. J. Wind Engng Ind. Aerodyn. 179, 184189.CrossRefGoogle Scholar
Sohankar, A. 2014 A LES study of the flow interference between tandem square cylinder pairs. Theor. Comput. Fluid Dyn. 28 (5), 531548.CrossRefGoogle Scholar
Sumner, D. 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26 (6), 849899.CrossRefGoogle Scholar
Surry, D. 1972 Some effects of intense turbulence on the aerodynamics of a circular cylinder at subcritical Reynolds number. J. Fluid Mech. 52 (3), 543563.CrossRefGoogle Scholar
Vickery, B.J. 1966 Fluctuating lift and drag on a long cylinder of square cross-section in a smooth and in a turbulent stream. J. Fluid Mech. 25 (3), 481494.CrossRefGoogle Scholar
Wang, L., Alam, M.M. & Zhou, Y. 2018 Two tandem cylinders of different diameters in cross-flow: effect of an upstream cylinder on wake dynamics. J. Fluid Mech. 836, 542.CrossRefGoogle Scholar
West, G.S. & Apelt, C.J. 1982 The effects of tunnel blockage and aspect ratio on the mean flow past a circular cylinder with Reynolds numbers between 104 and 105. J. Fluid Mech. 114 (1), 361.CrossRefGoogle Scholar
Williamson, C. & Brown, G.L. 1998 A series in 1/√Re to represent the Strouhal–Reynolds number relationship of the cylinder wake. J. Fluids Struct. 12 (8), 10731085.CrossRefGoogle Scholar
Xu, G. & Zhou, Y. 2004 Strouhal numbers in the wake of two inline cylinders. Exp. Fluids 37 (2), 248256.CrossRefGoogle Scholar
Xu, S.J., Zhang, W.G., Gan, L., Li, M.G. & Zhou, Y. 2017 Experimental study of flow around polygonal cylinders. J. Fluid Mech. 812, 251278.CrossRefGoogle Scholar
Yen, S.C., San, K.C. & Chuang, T.H. 2008 Interactions of tandem square cylinders at low Reynolds numbers. Exp. Therm. Fluid Sci. 32 (4), 927938.CrossRefGoogle Scholar
Younis, M.Y., Alam, M.M. & Zhou, Y. 2016 Flow around two non-parallel tandem cylinders. Phys. Fluids 28, 125106.CrossRefGoogle Scholar
Zdravkovich, M.M. 1977 Review of flow interference between two circular cylinders in various arrangements. J. Fluids Engng 99 (4), 618633.CrossRefGoogle Scholar
Zdravkovich, M.M. 1987 The effects of interference between circular cylinders in cross flow. J. Fluids Struct. 1 (2), 239261.CrossRefGoogle Scholar
Zdravkovich, M.M. 1997 Flow Around Circular Cylinders, Vol I: Fundamentals. Oxford University Press.CrossRefGoogle Scholar
Zhao, X., Cheng, D., Zhang, D. & Hu, Z. 2016 Numerical study of low-Reynolds-number flow past two tandem square cylinders with varying incident angles of the downstream one using a CIP-based model. Ocean Engng 121, 414421.CrossRefGoogle Scholar
Zhou, Y. & Alam, M.M. 2016 Wake of two interacting circular cylinders: a review. Intl J. Heat Fluid Flow 62, 510537.CrossRefGoogle Scholar
Zhou, Y., Du, C., Mi, J. & Wang, X.W. 2012 Turbulent round jet control using two steady minijets. AIAA J. 50 (3), 736740.CrossRefGoogle Scholar
Zhou, Y., Feng, S.X., Alam, M.M. & Bai, H.L. 2009 Reynolds number effect on the wake of two staggered cylinders. Phys. Fluids 21 (12), 125105.CrossRefGoogle Scholar
Zhou, Y. & Yiu, M.W. 2006 Flow structure, momentum and heat transport in a two-tandem-cylinder wake. J. Fluid Mech. 548 (1), 17.CrossRefGoogle Scholar
Zhou, Y. & Zhang, B.F. 2021 Recent advances in wake dynamics and active drag reduction of simplified automotive bodies. Appl. Mech. Rev. 73, 060801.Google Scholar
Zhou, Y., Zhang, H.J. & Yiu, M.W. 2002 The turbulent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303332.CrossRefGoogle Scholar