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The wake of two side-by-side square cylinders

Published online by Cambridge University Press:  26 January 2011

Md MAHBUB ALAM ,
Y. ZHOU  and
X. W. WANG
Md MAHBUB ALAM
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria 0002, South Africa
Y. ZHOU*
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
X. W. WANG
Affiliation:
Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Key Laboratory of Manufacture and Test Techniques for Automobile Parts, Chongqing University of Technology, China
*
†Email address for correspondence: [email protected]
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Abstract

Aerodynamic interference between two cylinders involves most of the generic flow features associated with multiple structures, thus providing an excellent model for gaining physical insight into the wake of multiple cylindrical structures. This work aims to provide an experimental systematic study of the flow behind two side-by-side square cylinders. The square cylinder is a representative model for bluff bodies with sharp corners, characterized by a fixed flow separation point, which are distinct from those of continuous curvature with oscillating separation points, typically represented by the circular cylinder. Experiments were performed at a Reynolds number Re of 4.7 × 104 and a cylinder centre-to-centre spacing ratio T/d (d is the cylinder height) of 1.02–6.00. The flow was measured using different techniques, including hot wires, load cell, particle imaging velocimetry and laser-induced fluorescence flow visualization. Four distinct flow regimes and their corresponding T/d ranges are identified for the first time on the basis of the flow structure and the Strouhal number. Physical aspects in each regime, such as interference between shear layers, gap flow deflection and changeover, multiple flow modes, entrainment, recirculation bubble, vortex interactions and formation lengths, are investigated in detail and are connected to the characteristics of the time-averaged and fluctuating fluid forces. The flow displays a marked difference in many facets from that behind two side-by-side circular cylinders, which is linked to their distinct flow separation natures. A crucial role played by the gap flow and its passage geometry in contributing to the observed difference is also unveiled.

JFM classification

Wakes/Jets: Separated flows Wakes/Jets: Vortex streets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 669 , 25 February 2011 , pp. 432 - 471
Copyright
Copyright © Cambridge University Press 2011

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References

REFERENCES

Achenbach, E. 1968 Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 × 106. J. Fluid Mech. 34, 625–639.CrossRefGoogle Scholar
Agrawal, A., Djenidi, L. & Antonia, R. A. 2006 Investigation of flow around a pair of side-by-side square cylinders using the lattice Boltzmann method. Comput. Fluids 35, 1093–1107.CrossRefGoogle Scholar
Alam, M. M., Moriya, M. & Sakamoto, H. 2003 a Aerodynamic characteristics of two side-by-side circular cylinders and application of wavelet analysis on the switching phenomenon. J. Fluids Struct. 18, 325–346.CrossRefGoogle Scholar
Alam, M. M., Moriya, M., Takai, K. & Sakamoto, H. 2002 Suppression of fluid forces acting on two square cylinders in a tandem arrangement by passive control of flow. J. Fluids Struct. 16, 1073–1092.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), 425–449.CrossRefGoogle Scholar
Alam, M. M., Sakamoto, H. & Moriya, M. 2003 b Reduction of fluid forces acting on a single circular cylinder and two circular cylinders by using tripping rods. J. Fluids Struct. 18, 347–366.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, 363–394.CrossRefGoogle Scholar
Alam, M. M. & Zhou, Y. 2007 a Flow around two side-by-side closely spaced circular cylinders. J. Fluids Struct. 23 (5), 799–805.CrossRefGoogle Scholar
Alam, M. M. & Zhou, Y. 2007 b The turbulent wake of an inclined cylinder with water running. J. Fluid Mech. 589, 261–303.CrossRefGoogle Scholar
Alam, M. M., Zhou, Y., Yang, H. X., Guo, H. & Mi, J. 2010 The ultra-low Reynolds number airfoil wake. Exp. Fluids 48, 81–103.CrossRefGoogle Scholar
Balachandar, S., Mittal, R. & Najjar, F. M. 1997 Properties of the mean recirculation region in the wakes of two-dimensional bluff bodies. J. Fluid Mech. 351, 167–199.CrossRefGoogle Scholar
Batham, J. P. 1973 Pressure distribution on circular cylinders at critical Reynolds numbers. J. Fluid Mech. 57, 209–228.CrossRefGoogle Scholar
Bearman, P. W. & Obajasu, E. D. 1982 An experimental study of pressure fluctuations on fixed and oscillating square section cylinders. J. Fluid Mech. 119, 297–321.CrossRefGoogle Scholar
Bearman, P. W. & Trueman, D. M. 1972 An investigation of the flow around rectangular cylinders. Aeronaut. Q. XXIII (Pt 3), 229–237.CrossRefGoogle Scholar
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinder normal to a stream. J. Fluid Mech. 61, 499–511.CrossRefGoogle Scholar
Biermann, D. & Herrnstein, W. H. Jr 1933 The interference between struts in various combinations. NACA Tech. Rep. 468.Google Scholar
Bloor, S. M. 1964 The transition to turbulence in the wake of a circular cylinder. J. Fluid Mech. 19, 290–309.CrossRefGoogle Scholar
Chern, M., Kanna, R., Lu, Y., Cheng, I. & Chang, S. 2010 A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders. J. Fluids Struct. 26, 626–643.CrossRefGoogle Scholar
Couder, Y. & Basdevant, C. B. 1986 Experimental and numerical study of vortex couples in two-dimensional flows. J. Fluid Mech. 173, 225–251CrossRefGoogle Scholar
Courchesne, J. & Laneville, A. 1982 An experimental evaluation of drag coefficient for two-dimensional rectangular cylinders exposed to grid turbulence. ASME J. Fluids Engng 104, 523–528.CrossRefGoogle Scholar
Farell, C., Carrasquel, S., Guven, O. & Patel, V. C. 1977 Effect of wind tunnel walls on the flow past circular cylinder and cooling tower models. J. Fluids Engng 99, 470–490.CrossRefGoogle Scholar
Franssona, J. H. M., Koniecznyb, P. & Alfredsson, P. H. 2004 Flow around a porous cylinder subject to continuous suction or blowing. J. Fluids Struct. 198, 1031–1048.CrossRefGoogle Scholar
Gerrard, J. H. 1966 The mechanics of the formation region of vortices behind bluff bodies. J. Fluid Mech. 25, 401–413.CrossRefGoogle Scholar
Griffin, O. M. & Ramberg, S. E. 1974 The vortex street wakes of a vibrating cylinders. J. Fluid Mech. 66, 729–738.CrossRefGoogle Scholar
Hori, E. 1959 Experiments on flow around a pair of parallel circular cylinders. In Proceedings of 9th Japan National Congress for Applied Mechanics, paper III-11, pp. 231–234.Google Scholar
Hu, J. C. & Zhou, Y. 2008 Flow structure behind two staggered circular cylinders. Part 1. Downstream evolution and classification. J. Fluid Mech. 607, 51–80.CrossRefGoogle Scholar
Hu, J. C., Zhou, Y. & Dalton, C. 2006 Effects of the corner radius on the near wake of a square prism. Exp. Fluids 40, 106–118.CrossRefGoogle Scholar
Huang, J. F., Zhou, Y. & Zhou, T. M. 2006 Three-dimensional wake structure measurement using a modified PIV technique. Exp. Fluids 40, 884–896.CrossRefGoogle Scholar
Igarashi, T. 1978 Flow characteristics around a circular cylinder with a slot. Bull. JSME 21 (154), 656–664.CrossRefGoogle Scholar
Ishigai, S., Nishikawa, E., Nishimura, E. & Cho, K. 1972 Experimental study of structure of gas flow in tube banks axes normal to flow. Bull. Japan Soc. Mech. Eng. 15, 949–956.CrossRefGoogle Scholar
Jendrzejczyk, J. A. & Chen, S. S. 1982 Fluid forces on two circular cylinders in liquid crossflow. ASME PVP 63, 31–44.Google Scholar
Kamemoto, K. 1976 Formation and interaction of two parallel vortex streets. Bull. Japan Soc. Mech. Eng. 19, 283–290.CrossRefGoogle Scholar
Kim, H. J. & Durbin, P. A. 1988 Investigation of the flow between a pair of circular cylinders in the flopping regime. J. Fluid Mech. 196, 431–448.CrossRefGoogle Scholar
Kiya, M., Arie, M., Tamura, H. & Mori, H. 1980 Vortex shedding from two circular cylinders in staggered arrangement. ASME J. Fluids Engng 102, 166–173.CrossRefGoogle Scholar
Knisely, C. W. 1990 Strouhal numbers of rectangular cylinders at incidence: a review and new data. J. Fluids Struct. 4, 370–393.CrossRefGoogle Scholar
Kolávř, V., Lyn, D. A. & Rodi, W 1997 Ensemble-averaged measurements in the turbulent near wake of two side-by-side square cylinders. J. Fluid Mech. 346, 201–237.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 Wind Effects on Buildings (&) Structure, Heathrow, UK, K75–363 (ed. Eator, K. J.), 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, 263–282.CrossRefGoogle Scholar
Lesage, F. & Gartshore, I. S. 1987 A method of reducing drag and fluctuating side force on bluff bodies. J. Wind Engng Indust. Aerodyn. 25, 229–245.CrossRefGoogle Scholar
Meneghini, J. R., Saltara, F., Siquira, C. L. R. & Ferrari, J. A. 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. J. Fluids Struct. 15, 327–350.CrossRefGoogle Scholar
Moretti, P. 1993 Flow-induced vibration in arrays of cylinders. Annu. Rev. Fluid Mech. 25, 99–114.CrossRefGoogle Scholar
Nakagawa, S., Nitta, K. & Senda, M. 1999 An experimental study on unsteady turbulent near wake of a rectangular cylinder in channel flow. Exp. Fluids 27, 284–294.CrossRefGoogle Scholar
Nakaguchi, H., Hasimoto, K. & Muto, S. 1968 An experimental study of aerodynamic drag on rectangular cylinders. J. Japan Soc. Aeronaut. Space Sci. 16, 1–5.Google Scholar
Nakamura, Y. & Tomonari, Y. 1976 The effect of turbulence on the drag of rectangular prisms. J. Japan Soc. Aeronaut. Space Sci. 19 (44), 81–86.Google Scholar
Noda, H. & Nakayama, A. 2003 Free-stream turbulence effects on the instantaneous pressure and forces on cylinders of rectangular cross section. Exp. Fluids 34, 332–344.CrossRefGoogle Scholar
Norberg, C. 1993 Flow around rectangular cylinders: pressure forces and wake frequencies. J. Wind Engng Indust. Aerodyn. 49, 187–196.CrossRefGoogle Scholar
Novak, J. 1974 Strouhal number of a quadrangular prism, angle iron and two circular cylinders arranged in tandem. Acta Tech. CSAV 19 (3), 361–373.Google Scholar
Ohya, Y. 1994 Note on a discontinuous change in wake pattern for a rectangular cylinder. J. Fluids Struct. 8, 325–330.CrossRefGoogle Scholar
Okajima, A. 1982 Strouhal number of rectangular cylinders. J. Fluid Mech. 123, 379–398.CrossRefGoogle Scholar
Oudheusden, B. W., Scarano, F., Hinsberg, N. P. V. & Roosenboom, E. W. M. 2008 Quantitative visualization of the flow around a square-section cylinder at incidence. J. Wind Engng Indust. Aerodyn. 96, 913–922.CrossRefGoogle Scholar
Paranthoen, P., Browne, L. W. B., Masson, S. L., Dumouchel, F. & Lecordier, J. C. 1999 Characteristics of the near wake of a cylinder at low Reynolds numbers. Eur. J. Mech. B/Fluids 18, 659–674.CrossRefGoogle Scholar
Ramberg, S. E. 1983 The effects of yaw and finite length upon the vortex wakes of stationary and vibrating circular cylinders. J. Fluid Mech. 128, 81–107.CrossRefGoogle Scholar
Rao, Y. Ni, Y., & Liu, C. 2008 Flow effect around two square cylinders arranged side-by-side using lattice Boltzmann method. Intl J. Mod. Phys. C 19, 1683–1694.CrossRefGoogle Scholar
Reinhold, T. A., Tieleman, H. W. & Maker, F. J. 1977 Interaction of square prisms in two flow fields. J. Indust. Aerodyn. 2, 223–241.CrossRefGoogle Scholar
Roshko, A. 1993 Perspectives on bluff body aerodynamics. J. Wind Engng Indust. Aerodyn. 49, 79–100.CrossRefGoogle Scholar
Roshko, A. 1954 On the drag and shedding frequency of two-dimensional bluff bodies. NACA Tech. Note 3169.Google Scholar
Sakamoto, H. & Haniu, H. 1988 Effect of free stream turbulence on characteristics of fluctuating forces acting on two square prisms in tandem arrangement. ASME J. Fluids Engng 110, 140–146.CrossRefGoogle Scholar
Sakamoto, H., Haniu, H. & Obata, Y. 1987 Fluctuating forces acting on two square prisms in a tandem arrangement. J. Wind Engng Indust. Aerodyn. 26, 85–103.CrossRefGoogle Scholar
Sakamoto, H. & Oiwake, S. 1984 Fluctuating forces on a rectangular prism and a circular cylinder placed vertically in a turbulent boundary layer. ASME J. Fluids Engng 106, 160–166.CrossRefGoogle Scholar
Shames, I. H. 2003 Mechanics of Fluids, 4th edn. McGraw-Hill.Google Scholar
Spivack, H. M. 1946 Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacing normal to an air stream. J. Aeronaut. Sci. 13, 289–301.CrossRefGoogle Scholar
Sumner, D., Wong, S. S. T., Price, S. J. & Paidoussis, M. P. 1999 Fluid behavior of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309–339.CrossRefGoogle Scholar
Surry, D. 1972 Some effects of intense turbulent on the aerodynamic of a circular cylinder at subcritical Reynolds number. J. Fluid Mech. 52 (Pt 2), 543–563.CrossRefGoogle Scholar
Szepessy, S. & Bearman, P. W. 1992 Aspect ratio and end plate effects on vortex shedding from a circular cylinder. J. Fluid Mech. 234, 191–217.CrossRefGoogle Scholar
Tamura, T. & Miyagi, T. 1999 The effect of turbulence on aerodynamic forces on a square cylinder with various corner shapes. J. Wind Engng Indust. Aerodyn. 83, 135–145.CrossRefGoogle Scholar
Thomas, O. G. & Kraus, K. A. 1964 Interaction of vortex streets. J. Appl. Phys. 365, 3458–3459.CrossRefGoogle Scholar
Venugopal, V., Varyani, K. S. & Barltrop, N. D. P. 2006 Wave force coefficients for horizontally submerged rectangular cylinders. Ocean Engng 33, 1669–1704.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, 481–494.CrossRefGoogle Scholar
Wang, H. F. & Zhou, Y. 2009 The finite-length square cylinder near wake. J. Fluid Mech. 638, 453–490.CrossRefGoogle Scholar
Wang, Z. J. & Zhou, Y. 2005 Vortex interaction in a two side-by-side cylinder near-wake. Intl J. Heat Fluid Flow 26, 362–377.CrossRefGoogle Scholar
Wei, T. & Smith, C. R. 1986 Secondary vortices in the wake of circular cylinders. J. Fluid Mech. 169, 513–533.CrossRefGoogle Scholar
West, G. S. & Apelt, C. J. 1982 The effect of tunnel blockage and aspect ratio on mean flow past a circular cylinder with Reynolds number between 104 to 105. J. Fluid Mech. 14, 361–377.CrossRefGoogle Scholar
West, G. S. & Apelt, C. J. 1993 Measurements of fluctuating pressures and forces on a circular cylinder in the Reynolds number range 104 to 2.5 × 105. J. Fluids Struct. 7, 227–244.CrossRefGoogle Scholar
West, G. S. & Apelt, C. J. 1997 Fluctuating lift and drag forces on finite lengths of a circular cylinder in the subcritical Reynolds number range. J. Fluids Struct. 11, 135–158.CrossRefGoogle Scholar
Williamson, C. H. K. 1996 Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–526.CrossRefGoogle Scholar
Xu, S. J., Zhou, Y. & So, R. M. C. 2003 Reynolds number effects on the flow structure behind two side-by-side cylinders. Phys. Fluids 15, 1214–1219.CrossRefGoogle Scholar
Zdravkovich, M. M. 1977 Review of flow interference between two circular cylinders in various arrangements. ASME J. Fluids Engng 199, 618–633.CrossRefGoogle Scholar
Zdravkovich, M. M. & Pridden, D. L. 1977 Interference between two circular cylinders; series of unexpected discontinuities. J. Indust. Aerodyn. 2, 255–270.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, 125105, 14pp.CrossRefGoogle Scholar
Zhou, Y., Wang, Z. J., So, R. M. C., Xu, S. J. & Jin, W. 2001 Free vibrations of two side-by-side cylinders in a cross-flow. J. Fluid Mech. 443, 197–229.CrossRefGoogle Scholar
Zhou, Y., Zhang, H. J. & Yiu, M. W. 2002 The turbulent wake of two side-by-side circular cylinders. J. Fluid Mech. 458, 303–332.CrossRefGoogle Scholar