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.

References

References
1.
Blevins
,
R. D.
,
1991
,
Flow-Induced Vibration
, 2nd ed., Vol.
2
,
Van Nostrand Reinhold
,
New York
, pp.
50
86
.
2.
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
.
3.
Strouhal
,
V.
,
1878
, “
Über Eine Besondere Art Der Tonerregung
,”
Annalen Der Phys.
,
241
(
10
), pp.
216
251
.
4.
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
.
5.
Sarpkaya
,
T.
,
2004
, “
A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations
,”
J. Fluids Struct.
,
19
(
4
), pp.
389
447
.
6.
Bearman
,
P. W.
,
1984
, “
Vortex Shedding From Oscillating Bluff Bodies
,”
Annu. Rev. Fluid Mech.
,
16
(
1
), pp.
195
222
.
7.
Williamson
,
C.
, and
Govardhan
,
R.
,
2004
, “
Vortex-Induced Vibrations
,”
Annu. Rev. Fluid Mech.
,
36
, pp.
413
455
.
8.
Zdravkovich
,
M. M. M.
,
1997
, “
Flow around Circular Cylinders—Vol. I: Fundamentals
,”
J. Fluid Mech.
,
350
(
1
), pp.
377
378
.
9.
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.
10.
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
.
11.
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.
12.
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.
13.
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
14.
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.
15.
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
.
16.
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
.
17.
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
.
18.
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.
19.
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.
20.
Liflyand
,
E.
,
2012
, “
Fourier Transform Versus Hilbert Transform
,”
J. Math. Sci.
,
187
(1), pp.
49
56
.
21.
Feldman
,
M.
,
2011
, “
Hilbert Transform in Vibration Analysis
,”
Mech. Syst. Signal Process.
,
25
(
3
), pp.
735
802
.
22.
Selesnick
,
I. W.
,
2001
, “
Hilbert Transform Pairs of Wavelet Bases
,”
IEEE Signal Process. Lett.
,
8
(
6
), pp.
170
173
.
23.
Purves
,
S.
,
2014
, “
Phase and the Hilbert Transform
,”
Leading Edge
,
33
(
10
), pp.
1164
1166
.
24.
Yasir
,
P. A.
, and
Ivan
,
J. S.
,
2016
, “
Phase Estimation Using Phase Gradients Obtained Through Hilbert Transform
,”
JOSA A
,
33
(
10
), pp.
2010
2019
.
25.
Kak
,
S.
,
2014
, “
The Number Theoretic Hilbert Transform
,”
Circuits, Syst., Signal Process.
,
33
(
8
), pp.
2539
2548
.
26.
Belov
,
Y.
,
Mengestie
,
T. Y.
, and
Seip
,
K.
,
2010
, “
Unitary Discrete Hilbert Transforms
,”
J. D'Analyse Mathématique
,
112
(
1
), pp.
383
393
.
27.
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
.
28.
Tegmark
,
M.
, and
Zaldarriaga
,
M.
,
2009
, “
Fast Fourier Transform Telescope
,”
Phys. Rev. D
,
79
(
8
), p.
083530
.
29.
Brigham
,
E. O.
, and
Morrow
,
R.
,
1967
, “
The Fast Fourier Transform
,”
IEEE Spectrum
,
4
(
12
), pp.
63
70
.
30.
Chang
,
C. C.
, and
Bernitsas
,
M. M.
,
2011
, “
Hydrokinetic Energy Harnessing Using the VIVACE Converter With Passive Turbulence Control
,”
ASME
Paper No. OMAE2011-50290.
31.
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
.
32.
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
.
33.
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
.
You do not currently have access to this content.