Two circular cylinders in cross-flow: A review

Journal of Fluids and Structures

Volumn 26, Issue 6, 2010, Pages 849-899

  Sumner, D ^a  

^a UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

Bluff body; Circular cylinder; Cylinder groups; Vortex shedding; Wake interference

Indexed keywords

AERODYNAMIC FORCE COEFFICIENTS; AERODYNAMIC FORCES; BLUFF BODY; CROSS FLOWS; CYLINDER GROUPS; ENGINEERING APPLICATIONS; GENERAL TRENDS; INTERFERENCE EFFECTS; NUMERICAL STUDIES; REYNOLDS NUMBER EFFECT; STAGGERED CONFIGURATION; TWO CIRCULAR CYLINDERS; WAKE FLOWS; WAKE INTERFERENCE; WAKE STRUCTURES;

AERODYNAMICS; FLOW PATTERNS; REYNOLDS NUMBER; VORTEX SHEDDING; WAKES;

CIRCULAR CYLINDERS;

EID: 77956984934     PISSN: 08899746     EISSN: 10958622     Source Type: Journal    
DOI: 10.1016/j.jfluidstructs.2010.07.001     Document Type: Article

References (166)

1. Agrawal A., Djenidi L., Antonia R.A. Investigation of flow around a pair of side-by-side square cylinders using the lattice Boltzman method. Computers & Fluids 2006, 25:1093-1107.
2. Aiba S., Ota T., Tsuchida H. Heat transfer of tubes closely-spaced in an in-line bank. International Journal of Heat and Mass Transfer 1980, 23:311-319.
3. Aiba S., Tsuchida H., Ota T. Heat transfer around a tube in a bank. Bulletin of the JSME 1980, 23:1163-1170.
4. Aiba S., Tsuchida H., Ota T. Heat transfer around a tube in a bank. Bulletin of the JSME 1981, 24:380-387.
5. Aiba S., Yamazaki Y. An experimental investigation of heat transfer around a tube in a bank. ASME Journal of Heat Transfer 1976, 98:503-508.
6. Akbari M.H., Price S.J. Numerical investigation of flow patterns for staggered cylinder pairs in cross-flow. Journal of Fluids and Structures 2005, 20:533-554.
7. Akosile O.O., Sumner D. Staggered circular cylinders in a uniform planar shear flow. Journal of Fluids and Structures 2003, 18:613-633.
8. Alam M.M., Moriya M., Sakamoto H. Aerodynamic characteristics of two side-by-side circular cylinders and application of wavelet analysis on the switching phenomenon. Journal of Fluids and Structures 2003, 18:325-346.
9. Alam M.M., Moriya M., Takai K., Sakamoto H. Fluctuating fluid forces acting on two circular cylinders in a tandem arrangement at a subcritical Reynolds number. Journal of Wind Engineering and Industrial Aerodynamics 2003, 91:139-154.
10. Alam M.M., Sakamoto H. Investigation of Strouhal frequencies of two staggered bluff bodies and detection of multistable flow by wavelets. Journal of Fluids and Structures 2005, 20:425-449.
11. Alam M.M., Sakamoto H., Zhou Y. Determination of flow configurations and fluid forces acting on two staggered circular cylinders of equal diameter in cross-flow. Journal of Fluids and Structures 2005, 21:363-394.
12. Alam M.M., Zhou Y. Flow around two side-by-side closely spaced circular cylinders. Journal of Fluids and Structures 2007, 23:799-805.
13. Alam M.M., Zhou Y. Phase lag between vortex shedding from two tandem bluff bodies. Journal of Fluids and Structures 2007, 23:339-347.
14. Alam M.M., Zhou Y. Strouhal numbers, forces and flow structures around two tandem cylinders of different diameters. Journal of Fluids and Structures 2008, 24:505-526.
15. Arie M., Kiya M., Moriya M., Mori H. Pressure fluctuations on the surface of two circular cylinders in tandem arrangement. ASME Journal of Fluids Engineering 1983, 105:161-167.
16. Auger J.L., Coutanceau J. Ecoulement transversal de l'air à travers une grille de tubes: Phénomènes associés de vibrations mécaniques et acoustiques. Entropie 1979, 86:13-27. (in French).
17. Auger J.L., Coutanceau J. On the complex structure of the downstream flow of cylindrical tube rows at various spacings. Mechanics Research Communications 1978, 5:297-302.
18. Batham J.P. Pressure distributions on circular cylinders at critical Reynolds numbers. Journal of Fluid Mechanics 1973, 57:209-228.
19. Baxendale A.J., Grant I., Barnes F.H. The flow past two cylinders having different diameters. Aeronautical Journal 1985, 125-134.
20. Bearman P.W. The effect of base bleed on the flow behind a two-dimensional model with a blunt trailing edge. The Aeronautical Quarterly 1967, 18:207-224.
21. Bearman P.W., Wadcock A.J. The interaction between a pair of circular cylinders normal to a stream. Journal of Fluid Mechanics 1973, 61:499-511.
22. Bhattacharyya S., Dhinakaran S. Vortex shedding in shear flow past tandem square cylinders in the vicinity of a plane wall. Journal of Fluids and Structures 2008, 24:400-417.
23. Biermann, D., Herrnstein, W.H., 1934. The interference between struts in various combinations. NACA Report No. 468.
24. Bokaian A., Geoola F. Wake displacement as cause of lift force on cylinder pair. ASCE Journal of Engineering Mechanics 1984, 111:92-99.
25. Brun C., Tenchine D., Hopfinger E.J. Role of the shear layer instability in the near wake behaviour of two side-by-side circular cylinders. Experiments in Fluids 2004, 36:334-343.
26. Carmo B.S., Meneghini J.R. Numerical investigation of the flow around two circular cylinders in tandem. Journal of Fluids and Structures 2006, 22:979-988.
27. Carmo B.S., Meneghini J.R., Sherwin S.J. Possible states in the flow around two circular cylinders in tandem with separations in the vicinity of the drag inversion spacing. Physics of Fluids 2010, 22:054101.
28. Carmo B.S., Meneghini J.R., Sherwin S.J. Secondary instabilities in the flow around two circular cylinders in tandem. Journal of Fluid Mechanics 2010, 644:395-431.
29. Chang K.S., Song C.J. Interactive vortex shedding from a pair of circular cylinders in a transverse arrangement. International Journal of Numerical Methods in Fluids 1990, 11:317-329.
30. Chatterjee D., Biswas G., Amiroudine S. Numerical simulation of the flow past row of square cylinders for various separation ratios. Computers & Fluids 2010, 39:49-59.
31. Chen L., Tu J.Y., Yeoh G.H. Numerical simulation of turbulent wake flows behind two side-by-side cylinders. Journal of Fluids and Structures 2003, 18:387-403.
32. Chen S.S. Flow-Induced Vibration of Circular Cylindrical Structures 1987, Hemisphere Publishing Corporation, Washington, DC, USA.
33. Cheng M., Moretti P.M. Experimental study of the flow field downstream of a single tube row. Experimental Thermal and Fluid Science 1988, 1:69-74.
34. Chern M.J., Kanna P.R., Lu Y.J., Cheng I.C., Chang S.C. A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders. Journal of Fluids and Structures 2010, 26:626-643.
35. Cokgor S., Avci I. Forces on partly buried, tandem twin cylinders in waves at low Keulegan-Carpenter numbers. Ocean Engineering 2003, 30:1453-1466.
36. Cokgor S., Avci I. Hydrodynamic forces on partly buried tandem, twin pipelines in current. Ocean Engineering 2001, 28:1349-1360.
37. Cooper, K.R., 1974. Wind tunnel measurements of the steady aerodynamics forces on a smooth circular cylinder immersed in the wake of an identical cylinder. National Research Council of Canada, LTR-LA-119.
38. Coutanceau M., Defaye J. Circular cylinder wake configurations: a flow visualization survey. Applied Mechanics Reviews 1991, 44:255-305.
39. Deng J., Ren A.L., Zou J.F., Shao X.M. Three-dimensional flow around two circular cylinders in tandem arrangement. Fluid Dynamics Research 2006, 38:386-404.
40. Eastop T.D., Turner J.R. Air flow around three cylinders at various pitch-to-diameter ratios for both a longitudinal and transverse arrangement. Transactions of the Institution of Chemical Engineers 1982, 60:359-363.
41. Edamoto K., Kawahara M. Finite element analysis of two- and three-dimensional flows around square columns in tandem arrangement. International Journal for Numerical Methods in Fluids 1998, 28:95-112.
42. Farrant T., Tan M., Price W.G. A cell boundary element method applied to laminar vortex-shedding from arrays of cylinders in various arrangements. Journal of Fluids and Structures 2000, 14:375-402.
43. Gerrard J.H. The wakes of cylindrical bluff bodies at low Reynolds number. Philosophical Transactions of the Royal Society of London A 1978, 288:351-382.
44. Gu Z.F., Sun T.F. On interference between two circular cylinders in staggered arrangement at high subcritical Reynolds numbers. Journal of Wind Engineering and Industrial Aerodynamics 1999, 80:287-309.
45. Gu Z.F., Sun T.F., He D.X., Zhang L.L. Two circular cylinders in high-turbulence flow at supercritical Reynolds number. Journal of Wind Engineering and Industrial Aerodynamics 1993, 49:379-388.
46. Hanson R., Mohany A., Ziada S. Flow-excited acoustic resonance of two side-by-side cylinders in cross-flow. Journal of Fluids and Structures 2009, 25:80-94.
47. Hetz A.A., Dhaubhadel M.N., Telionis D.P. Vortex shedding over five in-line cylinders. Journal of Fluids and Structures 1991, 5:243-257.
48. Hiwada M., Taguchi T., Mabuchi I., Kumada M. Fluid flow and heat transfer around two circular cylinders of different diameters in cross-flow. Bulletin of the JSME 1979, 22:715-723.
49. Hiwada M., Mabuchi I., Yanagihara H. Fluid flow and heat transfer around two circular cylinders. Bulletin of the JSME 1982, 25:1737-1745.
50. Hori, E., 1959. Experiments on flow around a pair of parallel circular cylinders. In: Proceedings of the Ninth Japan National Congress for Applied Mechanics, Paper III-11, pp. 231-234.
51. Hu J.C., Zhou Y. Flow structure behind two staggered cylinders, Part I: downstream evolution and classification. Journal of Fluid Mechanics 2008, 607:51-80.
52. Hu J.C., Zhou Y. Flow structure behind two staggered cylinders, Part II: heat and momentum transport. Journal of Fluid Mechanics 2008, 607:81-107.
53. Huhe-Aode, Tatsuno M., Taneda S. Visual studies of wake structure behind two cylinders in tandem arrangement. Reports of Research Institute for Applied Mechanics (Kyushu University, Japan) 1985, 32(99):1-20.
54. Igarashi T. Characteristics of the flow around two circular cylinders arranged in tandem (1st report). Bulletin of the JSME 1981, 24:323-331.
55. Igarashi T. Characteristics of a flow around two circular cylinders of different diameters arranged in tandem. Bulletin of the JSME 1982, 25:349-357.
56. Igarashi T. Characteristics of the flow around two circular cylinders arranged in tandem (second report, unique flow phenomenon at small spacing). Bulletin of the JSME 1984, 27:2380-2387.
57. Igarashi T. Characteristics of the flow around four circular cylinders arranged in-line. Bulletin of the JSME 1986, 29(249):751-757.
58. Igarashi T., Suzuki K. Characteristics of the flow around three circular cylinders arranged in-line. Bulletin of the JSME 1984, 27:2397-2404.
59. Ishigai S., Nishikawa E. Experimental study of structure of gas flow in tube banks with tube axes normal to flow (Part II, On the structure of gas flow in single-column, single-row, and double-row tube banks). Bulletin of the JSME 1975, 18:528-535.
60. Ishigai S., Nishikawa E., Nishimura K, Cho K. Experimental study of structure of gas flow in tube banks with tube axes normal to flow (Part I, Kármán vortex flow from two tubes at various spacings). Bulletin of the JSME 1972, 15:949-956.
61. Ishigai, S., Nishikawa, E., Yagi, E., 1973. Structure of gas flow and vibration in tube banks with tube axes normal to flow. In: Proceedings of the International Symposium on Marine Engineering, Tokyo, Japan, pp. 1-5-2-1-15-33.
62. Jendrzejcyk, J.A, Chen, S.S., 1986. Fluid forces on two circular cylinders in crossflow. In: Proceedings of the Flow-Induced Vibration 1986, PVP-vol. 104, ASME, New York, pp. 1-13.
63. Jester W., Kallinderis Y. Numerical study of incompressible flow about fixed cylinder pairs. Journal of Fluids and Structures 2003, 17:561-577.
64. Kamemoto K. Formation and interaction of two parallel vortex streets. Bulletin of the JSME 1976, 19:283-290.
65. Kim H.J., Durbin P.A. Investigation of the flow between a pair of circular cylinders in the flopping regime. Journal of Fluid Mechanics 1988, 196:431-448.
66. Kitagawa T., Ohta H. Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number. Journal of Fluids and Structures 2008, 24:680-699.
67. Kiya M., Arie M, Tamura H., Mori H. Vortex shedding from two circular cylinders in staggered arrangement. ASME Journal of Fluids Engineering 1980, 102:166-173.
68. Kiya M., Mochizuki O., Ido Y., Suzuki T., Arai T. Flip-flopping flow around two bluff bodies in tandem arrangement. Proceedings of IUTAM Symposium, September 7-11, 1992 Göttingen, Germany 1992, 15-18. Springer-Verlag, Berlin. H. Eckelmann, J.M.R. Graham, P. Huerre, P.A. Monkewitz (Eds.).
69. Ko N.W.M., Wong P.T.Y., Leung R.C.K. Interaction of flow structures within bistable flow behind two circular cylinders of different diameters. Experimental Thermal and Fluid Science 1996, 12:33-44.
70. Kolář V., Lyn D.A., Rodi W. Ensemble-averaged measurements in the turbulent near wake of two side-by-side square cylinders. Journal of Fluid Mechanics 1997, 346:201-237.
71. Kondo N. Numerical simulation of aerodynamic characteristics of two rectangular cylinders in side-by-side arrangement. International Journal of Computational Fluid Dynamics 2004, 18:367-379.
72. Kostic G., Oka S.N. Fluid flow and heat transfer with two cylinders in cross-flow. International Journal of Heat and Mass Transfer 1972, 15:279-299.
73. Kumada M., Hiwada M., Ito M., Mabuchi I. Wake interference between three circular cylinders arranged side-by-side normal to a flow. Transactions of the JSME 1984, 50:1699-1707. (in Japanese).
74. Kumar S.R., Sharma A., Agrawal A. Simulation of flow around a row of square cylinders. Journal of Fluid Mechanics 2008, 606:369-397.
75. Kwon, S.H., Park, J., Ha, D.D., Lee, Y.H., 1996. Experimental study of flow fields around cylinder arrays using PIV. In: Proceedings of the Sixth International Offshore and Polar Engineering Conference, vol. III, Los Angeles, USA, May 26-31, 1996, pp. 145-150.
76. Lam K.M., Wong P.T.Y., Ko N.W.M. Interaction of flows behind two circular cylinders of different diameters in side-by-side arrangement. Experimental Thermal and Fluid Science 1993, 7:189-201.
77. Lee D.S., Ha M.Y., Yoon H.S., Balachandar S. A numerical study on the flow patterns of two oscillating cylinders. Journal of Fluids and Structures 2009, 25:263-283.
78. Lee K., Yang K.S., Yoon D.H. Flow-induced forces on two circular cylinders in proximity. Computers & Fluids 2009, 38:111-120.
79. Lee T., Basu S. Nonintrusive measurements of the boundary layer developing on a single and two circular cylinders. Experiments in Fluids 1997, 23:187-192.
80. Lee, T., Panagakos, A., 1997. Investigation of boundary layer behaviour on single and tandem cylinders. In: Proceedings of the Fourth International Symposium on Fluid-Structure Interactions, Aeroelasticity, Flow-Induced Vibration & Noise, Dallas, USA, vol. 1, ASME, New York, pp. 103-112.
81. Le Gal P., Chauve M.P., Lima R., Rezende J. Coupled wakes behind two circular cylinders. Physical Review A 1990, 41:4566-4569.
82. Le Gal P., Peschard I., Chauve M.P., Takeda Y. Collective behaviour of wakes downstream a row of cylinders. Physics of Fluids 1996, 8:2097-2106.
83. Li H., Sumner D. Vortex shedding from two finite circular cylinders in a staggered configuration. Journal of Fluids and Structures 2009, 25:479-505.
84. Li J., Chambarel A., Donneaud M., Martin R. Numerical study of laminar flow past one and two circular cylinders. Computers & Fluids 1991, 19:155-170.
85. Lin J.C., Yang Y., Rockwell D. Flow past two cylinders in tandem: instantaneous and averaged flow structure. Journal of Fluids and Structures 2002, 16:1059-1071.
86. Liu C.H., Chen J.M. Observations of hysteresis in flow around two square cylinders in a tandem arrangement. Journal of Wind Engineering and Industrial Aerodynamics 2002, 90:1019-1050.
87. Liu, Y., Cui, Z.X., 2006. Two side-by-side cantilevered cylinders in a cross flow. In: Proceedings of PVP2006-ICPVT-11, 2006 ASME Pressure Vessels and Piping Division Conference, July 23-27, 2006, Vancouver, Canada, Paper No. PVP2006-ICPVT-11-93894, 9 pp.
88. Ljungkrona, L., 1992. Characteristics of mean and fluctuating surface pressure distributions on tubes in tandem arrangement and in-line tube bundles. Ph.D. Thesis, Department of Thermodynamics and Fluid Dynamics, Chalmers University of Technology, Göteborg, Sweden.
89. Ljungkrona L., Norberg C., Sundén B. Free-stream turbulence and tube spacing effects on surface pressure fluctuations for two tubes in an in-line arrangement. Journal of Fluids and Structures 1991, 5:701-727.
90. Ljungkrona L., Sundén B. Flow visualization and surface pressure measurement on two tubes in an inline arrangement. Experimental Thermal and Fluid Science 1993, 6:15-27.
91. Luo S.C., Gan T.L., Chew Y.T. Uniform flow past one (or two in tandem) finite length circular cylinders. Journal of Wind Engineering and Industrial Aerodynamics 1996, 59:69-93.
92. Mahir N., Rockwell D. Vortex formation from a forced system of two cylinders, Part I: tandem arrangement. Journal of Fluids and Structures 1996, 10:473-489.
93. Mahir N., Rockwell D. Vortex formation from a forced system of two cylinders, Part II: side-by-side arrangement. Journal of Fluids and Structures 1996, 10:491-500.
94. Meneghini J.R., Saltara F., Siqueira C.L.R., Ferrari J.A. Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. Journal of Fluids and Structures 2001, 15:327-350.
95. Miau J.J., Wang H.B., Chou J.H. Flopping phenomenon of flow behind two plates placed side-by-side normal to the flow direction. Fluid Dynamics Research 1996, 17:311-328.
96. Mittal S., Kumar V., Raghuvanshi A. Unsteady incompressible flows past two cylinders in tandem and staggered arrangements. International Journal for Numerical Methods in Fluids 1997, 25:1315-1344.
97. Mohany A., Ziada S. Effect of acoustic resonance on the dynamic lift forces acting on two tandem cylinders in cross-flow. Journal of Fluids and Structures 2009, 25:461-478.
98. Mohany A., Ziada S. Flow-excited acoustic resonance of two tandem cylinders in cross-flow. Journal of Fluids and Structures 2005, 21:103-119.
99. Moriya M., Sakamoto H. Fluctuating fluid forces acting on a downstream circular cylinder in the staggered arrangement. Transactions of the JSME 1985, 51:2098-2104. (in Japanese).
100. Moriya M., Sakamoto H. Effect of a vibrating upstream cylinder on a stationary downstream cylinder. ASME Journal of Fluids Engineering 1986, 108:180-184.
101. Morkovin, M.V., 1964. Flow around circular cylinder-a kaleidoscope of challenging fluid phenomena. In: Hansen, A.G. (Ed.), Proceedings of the Symposium on Fully Separated Flows, ASME Fluids Engineering Division Conference, Philadelphia, USA, May 18-20, 1964, pp. 102-118.
102. Moretti P.M., Cheng M. Instability of flow through tube rows. ASME Journal of Fluids Engineering 1987, 109:197-198.
103. Ng C.W., Ko N.W.M. Flow interaction behind two circular cylinders of equal diameter-a numerical study. Journal of Wind Engineering and Industrial Aerodynamics 1995, 54-55:277-287.
104. Nishimura T. Flow across tube banks. Encyclopedia of Fluid Mechanics-Flow Phenomena and Measurement 1986, vol. 1:763-785. Gulf Publishing Company, Houston, USA.
105. Nishimura T., Ohori Y., Kawamura Y. Flow pattern and rate of mass transfer around two cylinders in tandem. International Chemical Engineering 1986, 26:123-129.
106. Nishiyama H., Ota T., Matsuno T. Heat transfer and flow around elliptic cylinders in tandem arrangement. JSME International Journal Series II 1988, 31:410-419.
107. Norberg C. An experimental investigation of the flow around a circular cylinder: influence of aspect ratio. Journal of Fluid Mechanics 1994, 258:287-316.
108. Ohya Y.O., Okajima A., Hayashi M. Wake interference and vortex shedding. Encyclopedia of Fluid Mechanics-Aerodynamics and Compressible Flow 1989, vol. 8:322-389. Gulf Publishing Company, Houston, USA.
109. Okajima A. Flows around two tandem circular cylinders at very high Reynolds numbers. Bulletin of the JSME 1979, 22:504-511.
110. Ota T., Nishiyama H. Flow around two elliptic cylinders in tandem arrangement. ASME Journal of Fluids Engineering 1986, 108:98-103.
111. Ota T., Nishiyama H., Kominami J., Sato K. Heat transfer from two elliptic cylinders in tandem arrangement. ASME Journal of Heat Transfer 1986, 108:525-531.
112. Ozono, S., Oda, J., Yoshida, Y., Wakasugi, Y., 2001. Critical nature of the base pressure of the upstream circular cylinder in two staggered ones in cross-flow. In: Theoretical and Applied Mechanics, vol. 50, Proceedings of the 50th Japan National Congress on Theoretical and Applied Mechanics, January 23-25, 2001, Tokyo, pp. 335-340.
113. Palau-Salvador G., Stoesser T., Rodi W. LES of the flow around two cylinders in tandem. Journal of Fluids and Structures 2008, 24:1304-1312.
114. Papaioannou G.V., Yue D.K.P., Triantafyllou M.S., Karniadakis G.E. On the effect of spacing on the vortex-induced vibrations of two tandem cylinders. Journal of Fluids and Structures 2008, 24:833-854.
115. Papaioannou G.V., Yue D.K.P., Triantafyllou M.S., Karniadakis G.E. Three-dimensionality effects in flow around two tandem cylinders. Journal of Fluid Mechanics 2006, 558:387-413.
116. Park C.W., Lee S.J. Flow structure around two finite circular cylinders located in an atmospheric boundary layer: side-by-side arrangement. Journal of Fluids and Structures 2003, 17:1043-1058.
117. Peschard I., Le Gal P. Coupled wakes of cylinders. Physical Review Letters 1996, 77:3122-3125.
118. Prasanth T.K., Mittal S. Flow-induced oscillation of two circular cylinders in tandem arrangement at low Re. Journal of Fluids and Structures 2009, 25:1029-1048.
119. Prasanth T.K., Mittal S. Vortex-induced vibration of two circular cylinders at low Reynolds number. Journal of Fluids and Structures 2009, 25:731-741.
120. Price S.J. The origin and nature of the lift force on the leeward of two bluff bodies. The Aeronautical Quarterly 1976, 27:154-168.
121. Price S.J., Païdoussis M.P. The aerodynamic forces acting on groups of two and three circular cylinders when subject to a cross-flow. Journal of Wind Engineering and Industrial Aerodynamics 1984, 17:329-347.
122. Price S.J., Païdoussis M.P., Krishnamoorthy S. Cross-flow past a pair of nearly in-line cylinders with the upstream cylinder subjected to a transverse harmonic oscillation. Journal of Fluids and Structures 2007, 23:39-57.
123. Quadflieg H. Vortex-induced loads on a pair of cylinders in incompressible flow at high Reynolds numbers. Forschung im Ingenieurwesen 1977, 43:9-18. (in German).
124. Sarode R.S., Gai S.L., Ramesh C.K. Flow around circular- and square-section models of finite height in a turbulent shear flow. Journal of Wind Engineering and Industrial Aerodynamics 1981, 8:223-230.
125. Sharman B., Lien F.S., Davidson L., Norberg C. Numerical prediction of low Reynolds number flows over two tandem circular cylinders. International Journal for Numerical Methods in Fluids 2005, 47:423-447.
126. Singha S., Sinhamahapatra K.P. High-resolution numerical simulation of low Reynolds number incompressible flow about two cylinders in tandem. ASME Journal of Fluids Engineering 2010, 132:011101. (10 pp).
127. Spivack H.M. Vortex frequency and flow pattern in the wake of two parallel cylinders at varied spacing normal to an air stream. Journal of the Aeronautical Sciences 1946, 13:289-297.
128. Sumer B.M., Fredsøe J. Hydrodynamics around Cylindrical Structures 1997, World Scientific, London.
129. Sumner D. Closely spaced circular cylinders in cross-flow and a universal wake number. ASME Journal of Fluids Engineering 2004, 126:245-249.
130. Sumner D., Price S.J., Païdoussis M.P. Flow-pattern identification for two staggered circular cylinders in cross-flow. Journal of Fluid Mechanics 2000, 411:263-303.
131. Sumner D., Price S.J., Païdoussis M.P. Tandem cylinders in impulsively started flow. Journal of Fluids and Structures 1999, 13:955-965.
132. Sumner D., Price S.J., Païdoussis M.P. Investigation of impulsively started flow around side-by-side circular cylinders: application of particle image velocimetry. Journal of Fluids and Structures 1997, 11:597-615.
133. Sumner D., Richards M.D. Some vortex-shedding characteristics of the staggered configuration of circular cylinders. Journal of Fluids and Structures 2003, 17:345-350.
134. Sumner D., Richards M.D., Akosile O.O. Two staggered circular cylinders of equal diameter in cross-flow. Journal of Fluids and Structures 2005, 20:255-276.
135. Sumner D., Schenstead A.J. Moderately and widely spaced circular cylinders in cross-flow and a universal wake number. ASME Journal of Fluids Engineering 2006, 128:1122-1125.
136. Sumner D., Wong S.S.T., Price S.J., Païdoussis M.P. Fluid behaviour of side-by-side circular cylinders in steady cross-flow. Journal of Fluids and Structures 1999, 13:309-338.
137. Sun T.F., Gu Z.F., He D.X., Zhang L.L. Fluctuating pressure on two circular cylinders at high Reynolds numbers. Journal of Wind Engineering and Industrial Aerodynamics 1992, 41-44:577-588.
138. Suzuki, N., Sato, H., Iuchi, M., Yamamoto, S., 1971. Aerodynamic forces acting on circular cylinders arranged in a longitudinal row. In: Wind Effects on Buildings and Structures, International Wind Conference, Tokyo, Part II, pp. 20-1-20-10.
139. Taniguchi S., Sakamoto H., Arie M. Interference between two circular cylinders of finite height vertically immersed in a turbulent boundary layer. ASME Journal of Fluids Engineering 1982, 104:529-536.
140. Ting D.S.K., Wang D.J., Price S.J., Païdoussis M.P. An experimental study on the fluidelastic forces for two staggered circular cylinders in cross-flow. Journal of Fluids and Structures 1998, 12:259-294.
141. Wang X.W., Zhang H.J., Zhou Y., Tu J.Y. Flow visualization behind three cylinders of equal and unequal spacing. Journal of Flow Visualization & Image Processing 2002, 9:139-151.
142. Wang Z.J., Zhou Y., Li H. Flow-visualization of a two side-by-side cylinder wake. Journal of Flow Visualization & Image Processing 2002, 9:123-138.
143. Wardlaw, R.L., Cooper, K.R., 1973. A wind tunnel investigation of the steady aerodynamic forces on smooth and stranded twin bundled power conductors for the Aluminum Company of America. National Research Council of Canada, LTR-LA-117.
144. Williamson C.H.K. Vortex dynamics in the cylinder wake. Annual Review of Fluid Mechanics 1996, 28:477-539.
145. Williamson C.H.K. Evolution of a single wake behind a pair of bluff bodies. Journal of Fluid Mechanics 1985, 159:1-18.
146. Wood C.J. Visualization of an incompressible wake with base bleed. Journal of Fluid Mechanics 1967, 29:259-272.
147. Wu J., Welch L.W., Wels M.C., Sheridan J., Walker G.J. Spanwise wake structures of a circular cylinder and two circular cylinders in tandem. Experimental Thermal and Fluid Science 1994, 9:299-308.
148. Xu G., Zhou Y. Strouhal numbers in the wake of two inline cylinders. Experiments in Fluids 2004, 37:248-256.
149. Xu S.J., Zhou Y., So R.M.C. Reynolds number effects on the flow structure behind two side-by-side cylinders. Physics of Fluids 2003, 15:1214-1219.
150. Yen S.C., San K.C., Chuang T.H. Interactions of tandem square cylinders at low Reynolds numbers. Experimental Thermal and Fluid Science 2008, 32:927-938.
151. Zdravkovich M.M. Flow around Circular Cylinders, vol. 1: Fundamentals 1997, Oxford University Press, Oxford, UK.
152. Zdravkovich M.M. Flow Around Circular Cylinders, vol. 2: Applications 2003, Oxford University Press, Oxford, UK.
153. Zdravkovich M.M. Interstitial flow field and fluid forces. Technology for the 90s: A Decade of Progress 1993, 594-658. ASME, New York, USA. M.K. Au-Yang (Ed.).
154. Zdravkovich M.M. Flow induced oscillations of two interfering circular cylinders in cross flow. Journal of Sound and Vibration 1985, 101:511-521.
155. Zdravkovich M.M. The effects of interference between circular cylinders in cross flow. Journal of Fluids and Structures 1987, 1:239-261.
156. Zdravkovich M.M. Review of flow interference between two circular cylinders in various arrangements. ASME Journal of Fluids Engineering 1977, 99:618-633.
157. Zdravkovich M.M., Pridden D.L. Interference between two circular cylinders; series of unexpected discontinuities. Journal of Industrial Aerodynamics 1977, 2:255-270.
158. Zdravkovich M.M., Stonebanks K.L. Intrinsically nonuniform and metastable flow in and behind tube arrays. Journal of Fluids and Structures 1990, 4:305-319.
159. Zhang H., Melbourne W.H. Interference between two circular cylinders in tandem in turbulent flow. Journal of Wind Engineering and Industrial Aerodynamics 1992, 41-44:589-600.
160. Zhang H.J., Zhou Y. Effect of unequal cylinder spacing on vortex streets behind three side-by-side cylinders. Physics of Fluids 2001, 13:3675-3686.
161. Zhou Y. Vortical structures behind three side-by-side cylinders. Experiments in Fluids 2003, 34:68-76.
162. Zhou Y., Feng S.X., Alam M.M., Bai H.L. Reynolds number effect on the wake of two staggered cylinders. Physics of Fluids 2009, 21:125105.
163. Zhou Y., So R.M.C., Liu M.H., Zhang H.J. Complex turbulent wakes generated by two and three side-by-side cylinders. International Journal of Heat and Fluid Flow 2000, 21:125-133.
164. Zhou Y., Wang Z.J., So R.M.C., Xu S.J., Jin W. Free vibrations of two side-by-side cylinders in a cross flow. Journal of Fluid Mechanics 2001, 443:197-229.
165. Zhou Y., Yiu M.W. Flow structure, momentum and heat transport in a two-tandem-cylinder wake. Journal of Fluid Mechanics 2006, 548:17-48.
166. Zhou Y., Zhang H.J., Yiu M.W. The turbulent wake of two side-by-side circular cylinders. Journal of Fluid Mechanics 2002, 458:303-332.