Hostname: page-component-f554764f5-fr72s Total loading time: 0 Render date: 2025-04-18T14:26:38.042Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulations of flow past three circular cylinders in equilateral-triangular arrangements

Published online by Cambridge University Press:  23 March 2020

Weilin Chen Open the ORCID record for Weilin Chen [Opens in a new window] ,
Chunning Ji Open the ORCID record for Chunning Ji [Opens in a new window] ,
Md. Mahbub Alam Open the ORCID record for Md. Mahbub Alam [Opens in a new window] ,
John Williams  and
Dong Xu
Weilin Chen
Affiliation:
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China
Chunning Ji*
Affiliation:
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin300350, China
Md. Mahbub Alam
Affiliation:
Institute for Turbulence-Noise-Vibration Interaction and Control, Harbin Institute of Technology (Shenzhen), Shenzhen, 518055, China
John Williams
Affiliation:
School of Engineering and Material Science, Queen Mary University of London, LondonE1 4NS, UK State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu610065, China
Dong Xu
Affiliation:
State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin300350, China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration, Tianjin University, Tianjin300350, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Flow past three identical circular cylinders is numerically investigated using the immersed boundary method. The cylinders are arranged in an equilateral-triangle configuration with one cylinder placed upstream and the other two side-by-side downstream. The focus is on the effect of the spacing ratio $L/D(=1.0{-}6.0)$, Reynolds number $Re(=50{-}300)$ and three-dimensionality on the flow structures, hydrodynamic forces and Strouhal numbers, where $L$ is the cylinder centre-to-centre spacing and $D$ is the cylinder diameter. The fluid dynamics involved is highly sensitive to both $Re$ and $L/D$, leading to nine distinct flow structures, namely single bluff-body flow, deflected flow, flip-flopping flow, steady symmetric flow, steady asymmetric flow, hybrid flow, anti-phase flow, in-phase flow and fully developed in-phase co-shedding flow. The time-mean drag and lift of each cylinder are more sensitive to $L/D$ than $Re$ while fluctuating forces are less sensitive to $L/D$ than $Re$. The three-dimensionality of the flow affects the development of the wake patterns, changing the $L/D$ ranges of different flow structures. A diagram of flow regimes, together with the contours of hydrodynamic forces, in the $Re-L/D$ space, is given, providing physical insights into the complex interactions of the three cylinders.

JFM classification

Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 891 , 25 May 2020 , A14
Copyright
© The Author(s), 2020. 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.)

Article purchase

Temporarily unavailable

References

Akbari, M. H. & Price, S. J. 2005 Numerical investigation of flow patterns for staggered cylinder pairs in cross-flow. J. Fluids Struct. 20, 533–554.10.1016/j.jfluidstructs.2005.02.005CrossRefGoogle Scholar
Akilli, H., Akar, A. & Karakus, C. 2004 Flow characteristics of circular cylinders arranged side-by-side in shallow water. Flow Meas. Instrum. 15, 187–197.10.1016/j.flowmeasinst.2004.04.003CrossRefGoogle Scholar
Alam, M. M. 2014 The aerodynamics of a cylinder submerged in the wake of another. J. Fluids Struct. 51, 393–400.10.1016/j.jfluidstructs.2014.08.003CrossRefGoogle Scholar
Alam, M. M. 2016 Lift forces induced by the phase lag between the vortex sheddings from two tandem bluff bodies. J. Fluids Struct. 65, 217–237.10.1016/j.jfluidstructs.2016.05.008CrossRefGoogle Scholar
Alam, M. M. & Meyer, J. P. 2013 Global aerodynamic instability of twin cylinders in cross flow. J. Fluids Struct. 41, 135–145.10.1016/j.jfluidstructs.2013.03.007CrossRefGoogle Scholar
Alam, M. M., Moriya, M. & Sakamoto, H. 2003a Aerodynamic characteristics of two side-by-side circular cylinders and application of wavelet analysis on the switching phenomenon. J. Fluids Struct. 18, 325–346.10.1016/j.jfluidstructs.2003.07.005CrossRefGoogle Scholar
Alam, M. M., Moriya, M., Takai, K. & Sakamoto, H. 2003b Fluctuating fluid forces acting on two circular cylinders in a tandem arrangement at a subcritical Reynolds number. J. Wind Engng Ind. Aerodyn. 91, 139–154.10.1016/S0167-6105(02)00341-0CrossRefGoogle 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), 425–449.10.1016/j.jfluidstructs.2004.11.003CrossRefGoogle Scholar
Alam, M. M. & Zhou, Y. 2007 Phase lag between vortex sheddings from two tandem bluff bodies. J. Fluids Struct. 23, 339–347.10.1016/j.jfluidstructs.2006.11.003CrossRefGoogle Scholar
Alam, M. M., Zhou, Y. & Wang, X. W. 2011 The wake of two side-by-side square cylinders. J. Fluid Mech. 669, 432–471.10.1017/S0022112010005288CrossRefGoogle Scholar
Bansal, M. S. & Yarusevych, S. 2017 Experimental study of flow through a cluster of three equally spaced cylinders. Exp. Therm. Fluid Sci. 80, 203–217.Google Scholar
Bao, Y., Zhou, D. & Huang, C. 2010 Numerical simulation of flow over three circular cylinders in equilateral arrangements at low Reynolds number by a second-order characteristic-based split finite element method. Comput. Fluids 39 (5), 882–899.10.1016/j.compfluid.2010.01.002CrossRefGoogle Scholar
Bao, Y., Zhou, D. & Tu, J. 2013 Flow characteristics of two in-phase oscillating cylinders in side-by-side arrangement. Comput. Fluids 71, 124–145.10.1016/j.compfluid.2012.10.013CrossRefGoogle Scholar
Barkley, D. & Henderson, R. D. 1996 Three-dimensional floquet stability analysis of the wake of a circular cylinder. J. Fluid Mech. 322, 215–241.10.1017/S0022112096002777CrossRefGoogle Scholar
Bearman, P. W. & Wadcock, A. J. 1973 The interaction between a pair of circular cylinders normal to a stream. J. Fluid Mech. 61, 499–511.10.1017/S0022112073000832CrossRefGoogle Scholar
Behara, S. & Mittal, S. 2010 Wake transition in flow past a circular cylinder. Phys. Fluids 22, 114104.10.1063/1.3500692CrossRefGoogle Scholar
Berger, E. & Wille, R. 1972 Periodic flow phenomena. Annu. Rev. Fluid Mech. 4, 313–340.10.1146/annurev.fl.04.010172.001525CrossRefGoogle Scholar
Brede, M., Eckelmann, H. & Rockwell, D. 1996 On secondary vortices in the cylinder wake. Phys. Fluids 8, 2117–2124.10.1063/1.868986CrossRefGoogle Scholar
Carini, M., Auteri, F. & Giannetti, F. 2015 Centre-manifold reduction of bifurcating flows. J. Fluid Mech. 767, 109–145.10.1017/jfm.2015.3CrossRefGoogle Scholar
Carini, M., Giannetti, F. & Auteri, F. 2014a First instability and structural sensitivity of the flow past two side-by-side cylinders. J. Fluid Mech. 749, 627–648.10.1017/jfm.2014.230CrossRefGoogle Scholar
Carini, M., Giannetti, F. & Auteri, F. 2014b On the origin of the flip–flop instability of two side-by-side cylinder wakes. J. Fluid Mech. 742, 552–576.CrossRefGoogle Scholar
Carmo, B. S., Meneghini, J. R. & Sherwin, S. J. 2010 Possible states in the flow around two circular cylinders in tandem with separations in the vicinity of the drag inversion spacing. Phys. Fluids 22 (5), 054101.CrossRefGoogle Scholar
Chen, W., Ji, C., Wang, R., Xu, D. & Campbell, J. 2015a Flow-induced vibrations of two side-by-side circular cylinders: Asymmetric vibration, symmetry hysteresis and near-wake patterns. Ocean Engng 110, 244–257.CrossRefGoogle Scholar
Chen, W., Ji, C., Williams, J., Xu, D., Yang, L. & Cui, Y. 2018 Vortex-induced vibrations of three tandem cylinders in laminar cross-flow: Vibration response and galloping mechanism. J. Fluids Struct. 78, 215–238.CrossRefGoogle Scholar
Chen, W., Ji, C. & Xu, D. 2019 Vortex-induced vibrations of two side-by-side circular cylinders with two degrees of freedom in laminar cross-flow. Comput. Fluids 193, 104288.CrossRefGoogle Scholar
Chen, W., Ji, C., Xu, W., Liu, S. & Campbell, J. 2015b Response and wake patterns of two side-by-side elastically supported circular cylinders in uniform laminar cross-flow. J. Fluids Struct. 55, 218–236.CrossRefGoogle Scholar
Dadmarzi, F. H., Narasimhamurthy, V. D., Andersson, H. I. & Pettersen, B. 2018 Turbulent wake behind side-by-side flat plates: computational study of interference effects. J. Fluid Mech. 855, 1040–1073.CrossRefGoogle Scholar
Esfahani, J. A. & Vasel-Be-Hagh, A. R. 2010 A Lattice Boltzmann simulation of cross-flow around four cylinders in a square arrangement. In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, ESDA2010, Istanbul, Turkey.Google Scholar
Esfahani, J. A. & Vasel-Be-Hagh, A. R. 2013 A numerical study on shear layer behaviour in flow over a square unit of four cylinders at Reynolds number of 200 using the LB method. Prog. Comput. Fluid Dyn. 13 (2), 103–119.CrossRefGoogle Scholar
Étienne, S. & Pelletier, D. 2012 The low Reynolds number limit of vortex-induced vibrations. J. Fluids Struct. 31, 18–29.CrossRefGoogle Scholar
Farge, M. 1992 Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech. 24, 395–458.CrossRefGoogle Scholar
Gao, Y., Qu, X., Zhao, M. & Wang, L. 2019 Three-dimensional numerical simulation on flow past three circular cylinders in an equilateral-triangular arrangement. Ocean Engng 189, 106375.CrossRefGoogle Scholar
Han, Z., Zhou, D. & Tu, J. 2013 Laminar flow patterns around three side-by-side arranged circular cylinders using semi-implicit three-step Taylor-characteristic-based-split (3-TCBS) algorithm. Eng. Appl. Comput. Fluids Mech. 7 (1), 1–12.Google Scholar
Harichandan, A. B. & Roy, A. 2010 Numerical investigation of low Reynolds number flow past two and three circular cylinders using unstructured grid CFR scheme. Intl J. Heat Fluid Flow 31 (2), 154–171.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Igarashi, T. 1981 Characteristics of the flow around two circular cylinders arranged in tandem: 1st report. Bull. JSME 24, 323–331.CrossRefGoogle Scholar
Igarashi, T. & Suzuki, K. 1984 Characteristics of the flow around three circular cylinders. Bull. JSME 27, 2397–2404.CrossRefGoogle Scholar
Ji, C., Munjiza, A. & Williams, J. J. R. 2012 A novel iterative direct-forcing immersed boundary method and its finite volume applications. J. Comput. Phys. 231 (4), 1797–1821.CrossRefGoogle Scholar
Jiang, H. & Cheng, L. 2017 Strouhal–Reynolds number relationship for flow past a circular cylinder. J. Fluid Mech. 832, 170–188.CrossRefGoogle Scholar
Jiang, H., Cheng, L., Draper, S., An, H. & Tong, F. 2016a Three-dimensional direct numerical simulation of wake transitions of a circular cylinder. J. Fluid Mech. 801, 353–391.CrossRefGoogle Scholar
Jiang, H., Cheng, L., Tong, F., Draper, S. & An, H. 2016b Stable state of mode a for flow past a circular cylinder. Phys. Fluids 28, 104103.CrossRefGoogle Scholar
Kang, S. 2003 Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Phys. Fluids 15 (9), 2486–2498.CrossRefGoogle Scholar
Kang, S. 2004 Numerical study on laminar flow over three side-by-side cylinders. KSME Int. J. 18 (10), 1869–1879.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
Kumar, B. & Mittal, S. 2006 Prediction of the critical Reynolds number for flow past a circular cylinder. Comput. Meth. Appl. Mech. Engng 195, 6046–6058.CrossRefGoogle Scholar
Lam, K. & Cheung, W. C. 1988 Phenomena of vortex shedding and flow interference of three cylinders in different equilateral arrangements. J. Fluid Mech. 196, 1–26.CrossRefGoogle Scholar
Lam, K., Li, J. Y. & So, R. M. C. 2003 Force coefficients and Strouhal numbers of four cylinders in cross flow. J. Fluids Struct. 18, 305–324.CrossRefGoogle Scholar
Lee, D. S., Ha, M. Y., Yoon, H. S. & Balachandar, S. 2009 A numerical study on the flow patterns of two oscillating cylinders. J. Fluids Struct. 25 (2), 263–283.CrossRefGoogle Scholar
Li, Y., Zhang, R., Shock, R. & Chen, H. 2009 Prediction of vortex shedding from a circular cylinder using a volumetric Lattice-Boltzmann boundary approach. Eur. Phys. J. 171 (1), 91–97.Google 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), 1019–1050.CrossRefGoogle Scholar
Liu, K., Ma, D., Sun, D. & Yin, X. 2007 Wake patterns of flow past a pair of circular cylinders in side-by-side arrangements at low Reynolds numbers. J. Hydrodyn. B 19 (6), 690–697.CrossRefGoogle Scholar
Ljungkrona, L., Norberg, C. H. & 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 (6), 701–727.CrossRefGoogle Scholar
Mittal, S. 2005 Excitation of shear layer instability in flow past a cylinder at low Reynolds number. Intl J. Numer. Meth. Fluids 49 (10), 1147–1167.CrossRefGoogle Scholar
Mittal, R. & Balakandar, S. 1995 Generation of streamwise vortical structures in bluff body wakes. Phys. Rev. Lett. 75, 1300–1303.CrossRefGoogle ScholarPubMed
Miller, G. D. & Williamson, C. H. K. 1994 Control of three-dimensional phase dynamics in a cylinder wake. Exp. Fluids 18 (1–2), 26–35.CrossRefGoogle Scholar
Mizushima, J. & Ino, Y. 2008 Stability of flows past a pair of circular cylinders in a side-by-side arrangement. J. Fluid Mech. 595, 491–507.CrossRefGoogle Scholar
Papaioannou, G. V., Yue, D. K. P., Triantafyllou, M. S. & Karniadakis, G. E. 2006 Three-dimensionality effects in flow around two tandem cylinders. J. Fluid Mech. 558, 387–413.CrossRefGoogle Scholar
Park, J., Kwon, K. & Choi, H. 1998 Numerical solutions of flow past a circular cylinder at Reynolds numbers up to 160. KSME Int. J. 12 (6), 1200–1205.CrossRefGoogle Scholar
de Paula, A. V., Endres, L. A. M. & Möller, S. V. 2013 Experimental study of the bistability in the wake behind three cylinders in triangular arrangement. J. Braz. Soc. Mech. Sci. Engng 35 (2), 163–176.CrossRefGoogle Scholar
Persillon, H. & Braza, M. 1998 Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation. J. Fluid Mech. 365, 23–88.CrossRefGoogle Scholar
Peskin, C. S. 1972 Flow patterns around heart valves: a numerical method. J. Comput. Phys. 10 (2), 252–271.CrossRefGoogle Scholar
Posdziech, O. & Grundmann, R. 2001 Numerical simulation of the flow around an infinitely long circular cylinder in the transition regime. Theor. Comput. Fluid Dyn. 15 (2), 121–141.Google Scholar
Qu, L., Norberg, C., Davidson, L., Peng, S. & Wang, F. 2013 Quantitative numerical analysis of flow past a circular cylinder at Reynolds number between 50 and 200. J. Fluids Struct. 39, 347–370.CrossRefGoogle Scholar
Rigoni, A.2015 Linear stability analysis of the asymmetric base flow of two cylinders in side-by-side arrangement. MSc thesis, Polytechnic University of Milan.Google Scholar
Sayers, A. T. 1990 Vortex shedding from groups of three and four equispaced cylinders situated in a cross flow. J. Wind Engng Ind. Aerodyn. 34 (2), 213–221.CrossRefGoogle Scholar
Sen, S., Mittal, S. & Biswas, G. 2009 Steady separated flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 620, 89–119.CrossRefGoogle Scholar
Sumner, D. 2010 Two circular cylinders in cross-flow: a review. J. Fluids Struct. 26 (6), 849–899.CrossRefGoogle Scholar
Sumner, D., Wong, S. S. T., Price, S. J. & Paidoussis, M. P. 1999 Fluid behaviour of side-by-side circular cylinders in steady cross-flow. J. Fluids Struct. 13, 309–338.CrossRefGoogle Scholar
Supradeepan, K. & Roy, A. 2014 Characterisation and analysis of flow over two side by side cylinders for different gaps at low Reynolds number: a numerical approach. Phys. Fluids 26 (6), 063602.CrossRefGoogle Scholar
Tatsuno, M., Amamoto, H. & Ishi-i, K. 1998 Effects of interference among three equidistantly arranged cylinders in a uniform flow. Fluid Dyn. Res. 22 (5), 297.CrossRefGoogle Scholar
Tong, F., Cheng, L. & Zhao, M. 2015 Numerical simulations of steady flow past two cylinders in staggered arrangements. J. Fluid Mech. 765, 114–149.CrossRefGoogle Scholar
Wieselsberger, E. 1921 Neuere Feststellungen uber die Gesetze des Flussigkeits und Luftwiderstand. Physik. Z. 22, 321.Google Scholar
Williamson, C. H. K. 1985 Evolution of a single wake behind a pair of bluff bodies. J. Fluid Mech. 159, 1–18.CrossRefGoogle Scholar
Williamson, C. H. K. 1989 Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. J. Fluid Mech. 206, 579–627.CrossRefGoogle Scholar
Williamson, C. H. K. 1996a Three-dimensional wake transition. J. Fluid Mech. 328, 345–407.CrossRefGoogle Scholar
Williamson, C. H. K. 1996b Vortex dynamics in the cylinder wake. Annu. Rev. Fluid Mech. 28, 477–539.CrossRefGoogle Scholar
Wood, C. J. 1967 Visualization of incompressible wake with base bleed. J. Fluid Mech. 29 (2), 259–272.CrossRefGoogle Scholar
Yang, S., Yan, W., Wu, J., Tu, C. & Luo, D. 2016 Numerical investigation of vortex suppression regions for three staggered circular cylinders. Eur. J. Mech. (B/Fluids) 55, 207–214.CrossRefGoogle Scholar
Zdravkovich, M. M. 1977 Review of flow interference between two circular cylinders in various arrangements. Trans. ASME J. Fluids Engng 90, 618–633.CrossRefGoogle Scholar
Zdravkovich, M. M. 1987 The effects of flow interference between two circular cylinders in various arrangements. J. Fluids Struct. 1, 239–261.CrossRefGoogle Scholar
Zdravkovich, M. M. 1997 Flow Around Circular Cylinders. Oxford University Press.Google Scholar
Zhao, M., Cheng, L. & An, H. 2012 Numerical investigation of vortex-induced vibration of a circular cylinder in transverse direction in oscillatory flow. Ocean Engng 41, 39–52.CrossRefGoogle Scholar
Zhao, M., Thapa, J., Cheng, L. & Zhou, T. 2013 Three-dimensional transition of vortex shedding flow around a circular cylinder at right and oblique attacks. Phys. Fluids 25, 014105.CrossRefGoogle Scholar
Zheng, S., Zhang, W. & Lv, X. 2016 Numerical simulation of cross-flow around three equal diameter cylinders in an equilateral-triangular configuration at low Reynolds numbers. Comput. Fluids 130, 94–108.CrossRefGoogle Scholar