Hostname: page-component-7c8c6479df-r7xzm Total loading time: 0 Render date: 2024-03-29T00:51:06.377Z Has data issue: false hasContentIssue false

Oscillatory flow regimes around four cylinders in a diamond arrangement

Published online by Cambridge University Press:  02 September 2019

Chengjiao Ren
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, China
Liang Cheng*
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, China School of Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Feifei Tong
Affiliation:
School of Engineering, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia
Chengwang Xiong
Affiliation:
School of Civil Engineering, Hebei University of Technology, Tianjin, 300401, China
Tingguo Chen
Affiliation:
Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian, 116024, China
*
†Email address for correspondence: liang.cheng@uwa.edu.au

Abstract

Oscillatory flow around a cluster of four circular cylinders in a diamond arrangement is investigated using two-dimensional direct numerical simulation over Keulegan–Carpenter numbers (KC) ranging from 4 to 12 and Reynolds numbers (Re) from 40 to 230 at four gap-to-diameter ratios (G) of 0.5, 1, 2 and 4. Three types of flows, namely synchronous, quasi-periodic and desynchronized flows (along with 14 flow regimes) are mapped out in the (G, KC, Re)-parameter space. The observed flow characteristics around four cylinders in a diamond arrangement show a few unique features that are absent in the flow around four cylinders in a square arrangement reported by Tong et al. (J. Fluid Mech., vol. 769, 2015, pp. 298–336). These include (i) the dominance of flow around the cluster-scale structure at $G=0.5$ and 1, (ii) a substantial reduction of regime D flows in the regime maps, (iii) new quasi-periodic (phase trapping) $\text{D}^{\prime }$ (at $G=0.5$ and 1) and period-doubling $\text{A}^{\prime }$ flows (at $G=1$) and most noteworthily (iv) abnormal behaviours at ($G\leqslant 2$) (referred to as holes hereafter) such as the appearance of spatio-temporal synchronized flows in an area surrounded by a single type of synchronized flow in the regime map ($G=0.5$). The mode competition between the cluster-scale and cylinder-scale flows is identified as the key flow mechanism responsible for those unique flow features, with the support of evidence derived from quantitative analysis. Phase dynamics is introduced for the first time in bluff-body flows, to the best knowledge of the authors, to quantitatively interpret the flow response (e.g. quasi-periodic flow features) around the cluster. It is instrumental in revealing the nature of regime $\text{D}^{\prime }$ flows where the cluster-scale flow features are largely synchronized with the forcing of incoming oscillatory flow (phase trapping) but are modulated by localized flow features.

Type
JFM Papers
Copyright
Š 2019 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

An, H., Cheng, L. & Zhao, M. 2011 Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number. J. Fluid Mech. 666, 77–103.10.1017/S0022112010003691Google Scholar
Anagnostopoulos, P. & Dikarou, C. 2011 Numerical simulation of viscous oscillatory flow past four cylinders in square arrangement. J. Fluids Struct. 27 (2), 212–232.10.1016/j.jfluidstructs.2010.10.005Google Scholar
Anagnostopoulos, P. & Dikarou, C. 2012 Aperiodic phenomena in planar oscillatory flow past a square arrangement of four cylinders at low pitch ratios. Ocean Engng 52, 91–104.10.1016/j.oceaneng.2012.06.009Google Scholar
Balanov, A., Janson, N., Postnov, D. & Sosnovtseva, O. 2008 Synchronization: from Simple to Complex. Springer Science & Busines Media.Google 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/S0022112096002777Google Scholar
Berbish, N. S. 2011 Heat transfer and flow behavior around four staggered elliptic cylinders in cross flow. Heat Mass Transfer 47 (3), 287–300.10.1007/s00231-010-0719-yGoogle Scholar
Blackburn, H. M. & Sherwin, S. J. 2004 Formulation of a Galerkin spectral element – Fourier method for three-dimensional incompressible flows in cylindrical geometries. J. Comput. Phys. 197 (2), 759–778.10.1016/j.jcp.2004.02.013Google Scholar
Bolis, A.2013 Fourier Spectral/hp Element Method: Investigation of Time-Stepping and Parallelisation Strategies. PhD thesis, Imperial College London.Google Scholar
Burattini, P. & Agrawal, A. 2013 Wake interaction between two side-by-side square cylinders in channel flow. Comput. Fluids 77, 134–142.10.1016/j.compfluid.2013.02.014Google Scholar
Cantwell, C. D., Moxey, D., Comerford, A., Bolis, A., Rocco, G., Mengaldo, G., De Grazia, D., Yakovlev, S., Lombard, J. E., Ekelschot, D. et al. 2015 Nektar++: An open-source spectral/hp element framework. Comput. Phys. Commun. 192, 205–219.10.1016/j.cpc.2015.02.008Google Scholar
Chern, M. J., Kanna, P. R., Lu, Y. J., Cheng, I. C. & Chang, S. C. 2010 A CFD study of the interaction of oscillatory flows with a pair of side-by-side cylinders. J. Fluids Struct. 26 (4), 626–643.10.1016/j.jfluidstructs.2010.03.002Google Scholar
Chern, M. J., Shiu, W. C. & Horng, T. L. 2013 Immersed boundary modeling for interaction of oscillatory flow with cylinder array under effects of flow direction and cylinder arrangement. J. Fluids Struct. 43, 325–346.10.1016/j.jfluidstructs.2013.09.022Google Scholar
Deng, J. & Caulfield, C. P. 2015 Dependence on aspect ratio of symmetry breaking for oscillating foils: implications for flapping flight. J. Fluid Mech. 787, 16–49.10.1017/jfm.2015.661Google Scholar
Dütsch, H., Durst, F., Becker, S. & Lienhart, H. 1998 Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers. J. Fluid Mech. 360 (1998), 249–271.10.1017/S002211209800860XGoogle Scholar
Elston, J. R., Blackburn, H. M. & Sheridan, J. 2006 The primary and secondary instabilities of flow generated by an oscillating circular cylinder. J. Fluid Mech. 550, 359–389.10.1017/S0022112005008372Google Scholar
Elston, J. R., Sheridan, J. & Blackburn, H. M. 2004 Two-dimensional Floquet stability analysis of the flow produced by an oscillating circular cylinder in quiescent fluid. Eur. J. Mech. (B/Fluids) 23 (1), 99–106.10.1016/j.euromechflu.2003.05.002Google Scholar
Guermond, J. & Shen, J. 2003 Velocity-correction projection methods for incompressible flows. SIAM J. Numer. Anal. 41 (1), 112–134.10.1137/S0036142901395400Google Scholar
Honji, H. 2006 Streaked flow around an oscillating circular cylinder. J. Fluid Mech. 107, 509–520.10.1017/S0022112081001894Google Scholar
Kamsanam, W.2014 Development of Experimental Techniques to Investigate the Heat Transfer Processes in Oscillatory Flows. PhD thesis, University of Leicester.10.1016/j.expthermflusci.2014.12.008Google Scholar
Karniadakis, G. E., Israeli, M. & Orszag, S. A. 1991 High-order splitting methods for the incompressible Navier–Stokes equations. J. Comput. Phys. 97 (2), 414–443.10.1016/0021-9991(91)90007-8Google Scholar
Kashinath, K., Li, L. K. B. & Juniper, M. P. 2018 Forced synchronization of periodic and aperiodic thermoacoustic oscillations: lock-in, bifurcations and open-loop control. J. Fluid Mech. 838, 690–714.10.1017/jfm.2017.879Google Scholar
Lam, K., Li, J. Y., Chan, K. T. & So, R. M. C. 2003 Flow pattern and velocity field distribution of cross-flow around four cylinders in a square configuration at a low Reynolds number. J. Fluids Struct. 17 (5), 665–679.10.1016/S0889-9746(03)00005-7Google Scholar
Leontini, J. S., Lo Jacono, D. & Thompson, M. C. 2011 A numerical study of an inline oscillating cylinder in a free stream. J. Fluid Mech. 688, 551–568.10.1017/jfm.2011.403Google Scholar
Li, L. K. B. & Juniper, M. P. 2013 Phase trapping and slipping in a forced hydrodynamically self-excited jet. J. Fluid Mech. 735, R5.10.1017/jfm.2013.533Google Scholar
Liu, Y., Li, S., Yi, Q. & Chen, D. 2016 Developments in semi-submersible floating foundations supporting wind turbines: a comprehensive review. Renew. Sustainable Energy Rev. 60, 433–449.10.1016/j.rser.2016.01.109Google Scholar
Morison, J. R., Johnson, J. W. & Schaaf, S. A. 1950 The force exerted by surface waves on piles. J. Petrol. Tech. 2 (05), 149–154.10.2118/950149-GGoogle Scholar
Moskalik, P. & Buchler, J. R. 1990 Resonances and period doubling in the pulsations of stellar models. Astrophys. J. 355 (2), 590–601.10.1086/168792Google Scholar
Nehari, D., Armenio, V. & Ballio, F. 2004 Three-dimensional analysis of the unidirectional oscillatory flow around a circular cylinder at low Keulegan–Carpenter and 𝛽 numbers. J. Fluid Mech. 520, 157–186.10.1017/S002211200400134XGoogle Scholar
Ongoren, A. & Rockwell, D. 1988 Flow structure from an oscillating cylinder. Part 2. Mode competition in the near wake. J. Fluid Mech. 191, 225–245.10.1017/S0022112088001570Google Scholar
Papaioannou, G. V., Yue, D. K. P., Triantafyllou, M. S. & Karniadakis, G. E. 2006 Evidence of holes in the Arnold tongues of flow past two oscillating cylinders. Phys. Rev. Lett. 96 (1), 014501.10.1103/PhysRevLett.96.014501Google Scholar
Perdikaris, P. G., Kaiktsis, L. & Triantafyllou, G. S. 2009 Chaos in a cylinder wake due to forcing at the Strouhal frequency. Phys. Fluids 21 (10), 101705.10.1063/1.3258287Google Scholar
Pikovsky, A., Rosenblum, M. & Kurths, J. 2003 Synchronization: A Universal Concept in Nonlinear Sciences, vol. 2. Cambridge University Press.10.1007/978-94-010-0217-2Google Scholar
Sumer, B. M. & Fredsøe, J. 1997 Hydrodynamics Around Cylindrical Structures, vol. 26. World Scientific.10.1142/3316Google Scholar
Tang, G., Cheng, L., Tong, F., Lu, L. & Zhao, M. 2017 Modes of synchronisation in the wake of a streamwise oscillatory cylinder. J. Fluid Mech. 832, 146–169.10.1017/jfm.2017.655Google Scholar
Tatsuno, M. & Bearman, P. W. 1990 A visual study of the flow around an oscillating circular cylinder at low Keulegan–Carpenter numbers and low Stokes numbers. J. Fluid Mech. 211, 157–182.10.1017/S0022112090001537Google Scholar
Tong, F., Cheng, L., Xiong, C., Draper, S., An, H. & Lou, X. 2017 Flow regimes for a square cross-section cylinder in oscillatory flow. J. Fluid Mech. 813, 85–109.10.1017/jfm.2016.829Google Scholar
Tong, F., Cheng, L., Zhao, M. & An, H. 2015 Oscillatory flow regimes around four cylinders in a square arrangement under small KC and Re conditions. J. Fluid Mech. 769, 298–336.10.1017/jfm.2015.107Google Scholar
Tong, F., Cheng, L., Zhao, M., Zhou, T. & Chen, X. 2014a The vortex shedding around four circular cylinders in an in-line square configuration. Phys. Fluids 26 (2), 024112.10.1063/1.4866593Google Scholar
Tong, F., Cheng, L. & Zhou, T. 2014b Modelling of oscillatory flow around four cylinders in a diamond arrangement. In Presented at Proceedings of the 19th Australasian Fluid Mechanics Conference, AFMC 2014.Google Scholar
Vos, P. E. J., Eskilsson, C., Bolis, A., Chun, S., Kirby, R. M. & Sherwin, S. J. 2011 A generic framework for time-stepping partial differential equations (PDEs): general linear methods, object-oriented implementation and application to fluid problems. Intl J. Comput. Fluid Dyn. 25 (3), 107–125.10.1080/10618562.2011.575368Google Scholar
Williamson, C. H. K. 1985 Sinusoidal flow relative to circular cylinders. J. Fluid Mech. 155, 141–174.10.1017/S0022112085001756Google Scholar
Xiong, C., Cheng, L., Tong, F. & An, H. 2018a Oscillatory flow regimes for a circular cylinder near a plane boundary. J. Fluid Mech. 844, 127–161.10.1017/jfm.2018.164Google Scholar
Xiong, C., Cheng, L., Tong, F. & An, H. 2018b On regime C flow around an oscillating circular cylinder. J. Fluid Mech. 849, 968–1008.10.1017/jfm.2018.436Google Scholar
Yang, K., Cheng, L., An, H., Bassom, A. P. & Zhao, M. 2013 The effect of a piggyback cylinder on the flow characteristics in oscillatory flow. Ocean Engng 62, 45–55.10.1016/j.oceaneng.2013.01.017Google Scholar
Zdravkovich, M. M. 2003 Flow Around Circular Cylinders. Vol. 2: Applications. Oxford Science Publications (Oxford University Press).Google Scholar
Zhao, M. & Cheng, L. 2014 Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers. J. Fluid Mech. 751, 1–37.10.1017/jfm.2014.268Google Scholar

Ren et al. supplementary movie 1

Evolutions of streaklines for a typical regime F′ flow at (G, KC, Re) = (2, 8, 120).

Download Ren et al. supplementary movie 1(Video)
Video 14.4 MB

Ren et al. supplementary movie 2

Evolutions of streaklines for a typical regime C′ flow at (G, KC, Re) = (1, 11, 110).

Download Ren et al. supplementary movie 2(Video)
Video 16.3 MB

Ren et al. supplementary movie 3

Evolutions of streaklines for a typical regime A′ flow at (G, KC, Re) = (1, 6, 180).

Download Ren et al. supplementary movie 3(Video)
Video 14.4 MB

Ren et al. supplementary movie 4

Evolutions of streaklines for a typical regime D1′ flow at (G, KC, Re) = (2, 11, 80).

Download Ren et al. supplementary movie 4(Video)
Video 18.5 MB

Ren et al. supplementary movie 5

Evolutions of streaklines for a typical regime D2′ flow at (G, KC, Re) = (2, 11, 90).

Download Ren et al. supplementary movie 5(Video)
Video 16.6 MB

Ren et al. supplementary movie 6

Evolutions of streaklines for a typical regime D3′ flow at (G, KC, Re) = (2, 10, 100).

Download Ren et al. supplementary movie 6(Video)
Video 16.7 MB

Ren et al. supplementary movie 7

Evolutions of streaklines for a typical regime T flow at (G, KC, Re) = (2, 10, 80).

Download Ren et al. supplementary movie 7(Video)
Video 18.8 MB

Ren et al. supplementary movie 8

Evolutions of streaklines for a typical regime N flow at (G, KC, Re) = (1, 12, 120).

Download Ren et al. supplementary movie 8(Video)
Video 18.4 MB