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Research Papers: CFD and VIV

Two Tandem Cylinders With Passive Turbulence Control in Flow-Induced Vibration: Relation of Oscillation Patterns to Frequency Response

[+] Author and Article Information
Kai Lan

Marine Renewable Energy Laboratory;
Vortex Hydro Energy,
MRELab,
University of Michigan,
Ann Arbor, MI 48109
e-mail: lankai@umich.edu

Hai Sun

Marine Renewable Energy Laboratory,
University of Michigan,
Ann Arbor, MI 48109-2145;
Harbin Engineering University,
Harbin 150001, China
e-mail: hais@umich.edu

Michael M. Bernitsas

Marine Renewable Energy Laboratory;
Department Naval Architecture and
Marine Engineering,
University of Michigan,
Ann Arbor, MI 48109;
Department Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48108;
CTO Vortex Hydro Energy,
University of Michigan,
Ann Arbor, MI 48109-2145
e-mail: michaelb@umich.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received March 15, 2017; final manuscript received December 13, 2017; published online February 13, 2018. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 140(3), 031803 (Feb 13, 2018) (13 pages) Paper No: OMAE-17-1033; doi: 10.1115/1.4038935 History: Received March 15, 2017; Revised December 13, 2017

Flow-induced vibrations (FIV) are conventionally destructive and should be suppressed. Since 2006, the Marine Renewable Energy Laboratory (MRELab) of the University of Michigan has been studying FIV of multiple cylinders to enhance their response for harnessing hydrokinetic power from ocean, river, and tidal currents. Interactions between multiple cylinders in FIV enable high power-to-volume ratio in a converter consisting of multiple oscillators. This paper investigates experimentally the relation between oscillation patterns and frequency response of two cylinders in tandem. All experiments are conducted in the recirculating channel of the MRELab for 30,000 < Re < 120,000. Phase analysis reveals three dominant patterns of oscillation of two tandem cylinders by calculating the instantaneous phase difference between the two cylinders. This phase difference characterizes each major pattern. Pattern A is characterized by small lead or lag of one cylinder over the other. In pattern B, there is nearly 180 deg out of phase oscillations between the cylinders. In pattern C, the instantaneous phase difference changes continuously from −180 deg to +180 deg. Using frequency spectra and amplitude response, oscillation characteristics of each cylinder are revealed in vortex-induced vibration (VIV) and galloping. Pattern A occurs mostly in galloping when the first cylinder has higher stiffness. Pattern B occurs seldom and typically in the initial VIV branch and transition from VIV to galloping. Pattern C occurs in the upper and lower VIV branches; and in galloping when the lead cylinder has lower stiffness.

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References

Blevins, R. D. , 1991, Flow-Induced Vibration, 2nd ed., Vol. 2, Van Nostrand Reinhold, New York, pp. 50–86.
Park, H. , Bernitsas, M. M. , and Kumar, R. A. , 2012, “ Selective Roughness in the Boundary Layer to Suppress Flow-Induced Motions of Circular Cylinder at 30,000< Re< 120,000,” ASME J. Offshore Mech. Arct. Eng., 134(4), p. 041801. [CrossRef]
Strouhal, V. , 1878, “ Über Eine Besondere Art Der Tonerregung,” Annalen Der Phys., 241(10), pp. 216–251. [CrossRef]
Wu, W. , 2011, “ Two-Dimensional RANS Simulation of Flow Induced Motion of Circular Cylinder With Passive Turbulence Control,” Ph.D. dissertation, University of Michigan, Ann Arbor, MI, pp. 68–88.
Sarpkaya, T. , 2004, “ A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations,” J. Fluids Struct., 19(4), pp. 389–447. [CrossRef]
Bearman, P. W. , 1984, “ Vortex Shedding From Oscillating Bluff Bodies,” Annu. Rev. Fluid Mech., 16(1), pp. 195–222. [CrossRef]
Williamson, C. , and Govardhan, R. , 2004, “ Vortex-Induced Vibrations,” Annu. Rev. Fluid Mech., 36, pp. 413–455. [CrossRef]
Zdravkovich, M. M. M. , 1997, “ Flow around Circular Cylinders—Vol. I: Fundamentals,” J. Fluid Mech., 350(1), pp. 377–378.
Bernitsas, M. M. , 2016, “ Harvesting Energy by Flow Included Motions,” Springer Handbook of Ocean Engineering, M. R. Dhanak and N. Xiros , eds., Springer-Verlag, Berlin, Chap. 47. [CrossRef]
Sun, H. , Kim, E. S. , Nowakowski, G. , Mauer, E. , and Bernitsas, M. M. , 2016, “ Effect of Mass-Ratio, Damping, and Stiffness on Optimal Hydrokinetic Energy Conversion of a Single, Rough Cylinder in Flow Induced Motions,” Renewable Energy, 99, pp. 936–959. [CrossRef]
Bernitsas, M. , Raghavan, K. , and Maroulis, D. , 2007, “ Effect of Free Surface on VIV for Energy Harnessing at 8 × 103 < Re < 1.5 × 105,” International Conference on Ocean, Offshore and Arctic Engineering, San Diego, CA, June 10–15.
Bernitsas, M. M. , and Raghavan, K. , 2009, “ Converter of Current, Tide, or Wave Energy,” United States Patent and Trademark Office, Washington, DC, Patent No. 7,493,759 B2.
Bernitsas, M. M. , and Raghavan, K. , 2011, “ Enhancement of Vortex Induced Forces and Motion Through Surface Roughness Control,” The Regents of the University Of Michigan, Ann Arbor, MI, U.S. Patent No. 8,047,232 B2. https://www.google.co.in/patents/US8047232
Park, H. R. , Bernitsas, M. M. , and Chang, C. C. , 2013, “ Robustness of the Map of Passive Turbulence Control to Flow-Induced Motions for a Circular Cylinder at 30,000<Re<120,000,” 31st International Conference on Ocean, Offshore and Arctic Engineering, Nantes, France, June 9–14, Paper No. 10123.
Lee, J. , Xiros, N. , and Bernitsas, M. , 2011, “ Virtual Damper–Spring System for VIV Experiments and Hydrokinetic Energy Conversion,” Ocean Eng., 38(5), pp. 732–747. [CrossRef]
Sun, H. , Kim, E. S. , Bernitsas, M. P. , and Bernitsas, M. M. , 2015, “ Virtual Spring–Damping System for Flow-Induced Motion Experiments,” ASME J. Offshore Mech. Arct. Eng., 137(6), p. 061801. [CrossRef]
Kim, E. S. , and Bernitsas, M. M. , 2016, “ Performance Prediction of Horizontal Hydrokinetic Energy Converter Using Multiple-Cylinder Synergy in Flow Induced Motion,” Appl. Energy, 170, pp. 92–100. [CrossRef]
Kim, E. S. , Bernitsas, M. M. , and Kumar, A. R. , 2013, “ Multicylinder Flow-Induced Motions: Enhancement by Passive Turbulence Control at 28,000< Re<120,000,” ASME J. Offshore Mech. Arct. Eng., 135(2), p. 021802.
Bernitsas, M. M. , Sun, H. , Mauer, E. , and Nowakowski, G. , 2016, “ Synergistic Flow Induced Motion of Two Cylinders Harvesting Marine Hydrokinetic Energy,” Marine Energy Technology Symposium (METS), Washington, DC, Apr. 25–27.
Liflyand, E. , 2012, “ Fourier Transform Versus Hilbert Transform,” J. Math. Sci., 187(1), pp. 49–56. [CrossRef]
Feldman, M. , 2011, “ Hilbert Transform in Vibration Analysis,” Mech. Syst. Signal Process., 25(3), pp. 735–802. [CrossRef]
Selesnick, I. W. , 2001, “ Hilbert Transform Pairs of Wavelet Bases,” IEEE Signal Process. Lett., 8(6), pp. 170–173. [CrossRef]
Purves, S. , 2014, “ Phase and the Hilbert Transform,” Leading Edge, 33(10), pp. 1164–1166. [CrossRef]
Yasir, P. A. , and Ivan, J. S. , 2016, “ Phase Estimation Using Phase Gradients Obtained Through Hilbert Transform,” JOSA A, 33(10), pp. 2010–2019. [CrossRef] [PubMed]
Kak, S. , 2014, “ The Number Theoretic Hilbert Transform,” Circuits, Syst., Signal Process., 33(8), pp. 2539–2548. [CrossRef]
Belov, Y. , Mengestie, T. Y. , and Seip, K. , 2010, “ Unitary Discrete Hilbert Transforms,” J. D'Analyse Mathématique, 112(1), pp. 383–393. [CrossRef]
Chen, S. S. , 1983, “ Instability Mechanisms and Stability Criteria of a Group of Circular Cylinders Subjected to Cross-Flow. Part I: Theory,” ASME J. Vib. Acoust., Stress, Reliab., 105(1), pp. 51–58. [CrossRef]
Tegmark, M. , and Zaldarriaga, M. , 2009, “ Fast Fourier Transform Telescope,” Phys. Rev. D, 79(8), p. 083530. [CrossRef]
Brigham, E. O. , and Morrow, R. , 1967, “ The Fast Fourier Transform,” IEEE Spectrum, 4(12), pp. 63–70. [CrossRef]
Chang, C. C. , and Bernitsas, M. M. , 2011, “ Hydrokinetic Energy Harnessing Using the VIVACE Converter With Passive Turbulence Control,” ASME Paper No. OMAE2011-50290.
Raghavan, K. , and Bernitsas, M. , 2011, “ Experimental Investigation of Reynolds Number Effect on Vortex Induced Vibration of Rigid Circular Cylinder on Elastic Supports,” Ocean Eng., 38(5), pp. 719–731. [CrossRef]
Franzini, G. R. , Gonçalves, R. T. , Meneghini, J. R. , and Fujarra, A. L. C. , 2013, “ One and Two Degrees-of-Freedom Vortex-Induced Vibration Experiments With Yawed Cylinders,” J. Fluids Struct., 42, pp. 401–420. [CrossRef]
Raghavan, K. , Bernitsas, M. M. , and Maroulis, D. , 2009, “ Effect of Bottom Boundary on VIV for Energy Harnessing at 8 × 103 < Re < 1.5 × 105,” ASME J. Offshore Mech. Arct. Eng., 131(3), p. 031102. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

(a) Two cylinder oscillators in the LTFSW channel and (b) schematic of experiment system

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Fig. 2

Pattern A: In phase. Set 2 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m, U = 0.3946 m/s. (a) Instantaneous phase difference history, (b) PDF of phase difference, and (c) Time history of two cylinders (5–20 s).

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Fig. 3

Pattern B: Out of phase. Set 2 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m, U = 0.9946 m/s. (a) Instantaneous phase difference history, (b) PDF of phase difference, and (c) time history of two cylinders (5–20 s).

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Fig. 4

Pattern C: Alternating phase. Set 2 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m, U = 0.6346 m/s. (a) Instantaneous phase difference history, (b) PDF of phase difference, and (c) time history of two cylinders (5–20 s).

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Fig. 5

FFT results of Set 1 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 400 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 6

FFT results of Set 1 ζ1 = 0.14, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 400 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 7

FFT results of Set 1 ζ1 = 0.26, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 400 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 8

FFT results of Set 2 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 9

FFT results of Set 2 ζ1 = 0.14, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 10

FFT results of Set 2 ζ1 = 0.26, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

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Fig. 11

FFT results of Set 3 ζ1 = 0.02, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 800 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 12

FFT results of Set 3 ζ1 = 0.14, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 800 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

Grahic Jump Location
Fig. 13

FFT results of Set 3 ζ1 = 0.26, ζ2 = 0.14, m* = 1.343, L/D = 2.57, K1 = 800 N/m, K2 = 600 N/m. (a) Upstream cylinder FFT and (b) downstream cylinder FFT and phase map.

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Fig. 14

FFT results of single cylinder at K = 600 N/m, ζ = 0.14, and m* = 1.685

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Fig. 15

FFT results of downstream cylinder behind stationary upstream cylinder at K2 = 600 N/m, ζ2 = 0.14, m* = 1.685, and L/D = 2.57

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Fig. 16

Amplitude response ratio of two cylinders in tandem for three sets: (a) Set 1 upstream amplitude response at various damping ratios ζ1, m* = 1.343, L/D = 2.57, K1 = 400 N/m, K2 = 600 N/m. (b) Set 1 downstream amplitude response at various damping ratios ζ1, m* = 1.343, L/D = 2.57, K1 = 400 N/m, K2 = 600 N/m. (c) Set 2 upstream amplitude response at various damping ratios ζ1, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m. (d) Set 2 downstream amplitude response at various damping ratioes ζ1, m* = 1.343, L/D = 2.57, K1 = 600 N/m, K2 = 600 N/m. (e) Set 3 upstream amplitude response at various damping ratios ζ1, m* = 1.343, L/D = 2.57, K1 = 800 N/m, K2 = 600 N/m. (f) Set 3 downstream amplitude response at various damping ratios ζ1, m* = 1.343, L/D = 2.57, K1 = 800 N/m, K2 = 600 N/m.

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