Effects of Reynolds Number on Flow-Mediated Interaction between Two Cylinders
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
This paper studies the interaction between two cylinders of an identical diameter immersed in quiescent fluid. The master cylinder carries out forced vibration, while the adjacent slave cylinder is elastically mounted and has one degree of freedom along the centerline between the two cylinders. In this study, the geometry of the problem is fixed, with an initial gap ratio of the two cylinders of 0.9 and a nondimensional vibration amplitude of the master cylinder of 0.477. In total, 7,480 two-dimensional cases have been simulated to cover the parameter space of the problem, with the Reynolds number ranging from 10 to 150, the structural damping factor of the slave cylinder ranging from 0 to 0.2, the mass ratio of the slave cylinder ranging from 1.5 to 2.5, and the master cylinder’s oscillation frequency ratio ranging from 0.05 to 3.2. Both the resonance amplitude and resonance frequency are found to increase with the Reynolds number. A critical Reynolds number is discovered, beyond which the vibration center of the slave cylinder drifts away from the master cylinder, but below which the vibration center of the slave cylinder approaches the master cylinder. This effect is amplified when the master cylinder vibrates at a higher frequency.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The study was primarily funded by Fuzhou Nuocheng Construction Project Management Ltd. This work has been performed using resources provided by the Cambridge Tier-2 system operated by the University of Cambridge Research Computing Service (http://www.hpc.cam.ac.uk) funded by Engineering and Physical Sciences Research Council (EPSRC) Tier-2 capital grant (EP/P020259/1). The computing at Cirrus is funded by EPSRC Tier-2 Open Access Call. This study used the ARCHER UK National Supercomputing Service (http://www.archer.ac.uk). This study used the Cambridge Service for Data Driven Discovery (https://www.hpc.cam.ac.uk) hosted by the Research Computing Services at the University of Cambridge. We are very grateful for the technical support from the team at the University of Cambridge’s Research Computing Services.
References
Bampalas, N., and J. M. R. Graham. 2008. “Flow-induced forces arising during the impact of two circular cylinders.” J. Fluid Mech. 616: 205–234. https://doi.org/10.1017/S0022112008003856.
Bernitsas, M. M., K. Raghavan, Y. Ben-Simon, and E. M. H. Garcia. 2008. “VIVACE (vortex induced vibration aquatic clean energy): A new concept in generation of clean and renewable energy from fluid flow.” J. Offshore Mech. Arct. Eng. 130 (4): 041101. https://doi.org/10.1115/1.2957913.
Cui, Z., M. Zhao, and B. Teng. 2014. “Vortex-induced vibration of two elastically coupled cylinders in side-by-side arrangement.” J. Fluids Struct. 44 (Jan): 270–291. https://doi.org/10.1016/j.jfluidstructs.2013.11.007.
Dütsch, H., F. Durst, S. Becker, and H. Lienhart. 1998. “Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carpenter numbers.” J. Fluid Mech. 360: 249–271. https://doi.org/10.1017/S002211209800860X.
Elston, J. R., H. M. Blackburn, and J. Sheridan. 2006. “The primary and secondary instabilities of flow generated by an oscillating circular cylinder.” J. Fluid Mech. 550: 359. https://doi.org/10.1017/S0022112005008372.
Elston, J. R., J. Sheridan, and H. M. Blackburn. 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. https://doi.org/10.1016/j.euromechflu.2003.05.002.
Gazzola, M., C. Mimeau, A. A. Tchieu, and P. Koumoutsakos. 2012. “Flow mediated interactions between two cylinders at finite Re numbers.” Phys. Fluids 24 (4): 043103. https://doi.org/10.1063/1.4704195.
Gazzola, M., A. A. Tchieu, D. Alexeev, A. de Brauer, and P. Koumoutsakos. 2016. “Learning to school in the presence of hydrodynamic interactions.” J. Fluid Mech. 789: 726–749. https://doi.org/10.1017/jfm.2015.686.
Gyrya, V., I. S. Aranson, L. V. Berlyand, and D. Karpeev. 2010. “A model of hydrodynamic interaction between swimming bacteria.” Bull. Math. Biol. 72 (1): 148–183. https://doi.org/10.1007/s11538-009-9442-6.
Ishikawa, T., M. P. Simmonds, and T. J. Pedley. 2006. “Hydrodynamic interaction of two swimming model micro-organisms.” J. Fluid Mech. 568: 119. https://doi.org/10.1017/S0022112006002631.
Keulegan, G., and L. Carpenter. 1958. “Forces on cylinders and plates in an oscillating fluid.” J. Res. Nat. Bur. Stand. 60 (5): 423. https://doi.org/10.6028/jres.060.043.
Koch, D. L., and G. Subramanian. 2011. “Collective hydrodynamics of swimming microorganisms: Living fluids.” Ann. Rev. Fluid Mech. 43 (1): 637–659. https://doi.org/10.1146/annurev-fluid-121108-145434.
Lamb, H. 1932. Hydrodynamics. 6th ed. Cambridge, UK: Cambridge University Press.
Liao, J. C. 2003. “Fish exploiting vortices decrease muscle activity.” Science 302 (5650): 1566–1569. https://doi.org/10.1126/science.1088295.
Lin, Z., D. Liang, and M. Zhao. 2016. “Numerical study of the interaction between two immersed cylinders.” Accessed September 8, 2019. http://www.ichd2016.nl/onlineproc/proceedings/display_manuscript/55.htm.
Lin, Z., D. Liang, and M. Zhao. 2017. “Interaction between two vibrating cylinders immersed in fluid.” Accessed September 8, 2019. https://www.onepetro.org/conference-paper/ISOPE-I-17-093.
Lin, Z., D. Liang, and M. Zhao. 2018a. “Effects of damping on flow-mediated interaction between two cylinders.” J. Fluids Eng. 140 (9): 91106–91112. https://doi.org/10.1115/1.4039712.
Lin, Z., D. Liang, and M. Zhao. 2018b. “Flow-mediated interaction between a vibrating cylinder and an elastically-mounted cylinder.” Ocean Eng. 158 (Jun): 389–402. https://doi.org/10.1016/j.oceaneng.2018.04.019.
Lu, L., M. M. Liu, B. Teng, Z. D. Cui, G. Q. Tang, M. Zhao, and L. Cheng. 2014. “Numerical investigation of fluid flow past circular cylinder with multiple control rods at low Reynolds number.” J. Fluids Struct. 48 (Jul): 235–259. https://doi.org/10.1016/j.jfluidstructs.2014.03.006.
Metzger, B., M. Nicolas, and É. Guazzelli. 2007. “Falling clouds of particles in viscous fluids.” J. Fluid Mech. 580: 283–301. https://doi.org/10.1017/S0022112007005381.
Morison, J., J. Johnson, and S. Schaaf. 1950. “The force exerted by surface waves on piles.” J. Pet. Technol. 2 (5): 149–154. https://doi.org/10.2118/950149-G.
Nair, S., and E. Kanso. 2007. “Hydrodynamically coupled rigid bodies.” J. Fluid Mech. 592: 393–411. https://doi.org/10.1017/S002211200700849X.
Riffell, J. A., and R. K. Zimmer. 2007. “Sex and flow: The consequences of fluid shear for sperm-egg interactions.” J. Exp. Biol. 210 (20): 3644–3660. https://doi.org/10.1242/jeb.008516.
Sarpkaya, T. 1977. “In-line and transverse forces on smooth and sand-roughened cylinders in oscillatory flow at high Reynolds numbers.” J. Ship Res. 21 (4): 200–216.
Tatsuno, M., and P. W. Bearman. 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. https://doi.org/10.1017/S0022112090001537.
Tong, F., L. Cheng, M. Zhao, T. Zhou, and X. B. Chen. 2014. “The vortex shedding around four circular cylinders in an in-line square configuration.” Phys. Fluids 26 (2): 024112. https://doi.org/10.1063/1.4866593.
Van Rees, W. M., G. Novati, and P. Koumoutsakos. 2015. “Self-propulsion of a counter-rotating cylinder pair in a viscous fluid.” Phys. Fluids 27 (6): 063102. https://doi.org/10.1063/1.4922314.
Voth, G. A., B. Bigger, M. R. Buckley, W. Losert, M. P. Brenner, H. A. Stone, J. P. Gollub, and J. P. Gollub. 2002. “Ordered clusters and dynamical states of particles in a vibrated fluid.” Phys. Rev. Lett. 88 (23): 2343011–2343014. https://doi.org/10.1103/PhysRevLett.88.234301.
Weihs, D. 2004. “The hydrodynamics of dolphin drafting.” J. Biol. 3 (2): 8–8.16. https://doi.org/10.1186/jbiol2.
Williamson, C. H. K. 1985. “Sinusoidal flow relative to circular cylinders.” J. Fluid Mech. 155: 141–174. https://doi.org/10.1017/S0022112085001756.
Zhao, M., J. M. Murphy, and K. Kwok. 2016. “Numerical simulation of vortex-induced vibration of two rigidly connected cylinders in side-by-side and tandem arrangements using Rans model.” J. Fluids Eng. 138 (2): 21102. https://doi.org/10.1115/1.4031257.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Aug 20, 2018
Accepted: Mar 25, 2019
Published online: Sep 30, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 29, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.