0
Research Papers: Ocean Renewable Energy

Nonlinear Piecewise Restoring Force in Hydrokinetic Power Conversion Using Flow-Induced Vibrations of Two Tandem Cylinders

[+] Author and Article Information
Chunhui Ma

Jiangsu Maritime Institute,
Nanjing 210000, China;
Marine Renewable Energy Laboratory,
Department of Naval Architecture and
Marine Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: catch0226@163.com

Hai Sun

College of Aerospace and Civil Engineering,
Harbin Engineering University,
154 Nantong Ave,
Harbin 150001, China;
Marine Renewable Energy Laboratory,
Department of Naval Architecture and
Marine Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: sunhai2009@gmail.com

Marinos M. Bernitsas

Northville High School,
Northville, MI 48168;
Marine Renewable Energy Laboratory,
Department of Naval Architecture and
Marine Engineering,
University of Michigan,
Ann Arbor, MI 48109
e-mail: mbernitsas@gmail.com

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 24, 2017; final manuscript received November 16, 2017; published online January 9, 2018. Assoc. Editor: Celso P. Pesce.

J. Offshore Mech. Arct. Eng 140(4), 041901 (Jan 09, 2018) (17 pages) Paper No: OMAE-17-1043; doi: 10.1115/1.4038584 History: Received March 24, 2017; Revised November 16, 2017

Flow-induced vibrations (FIVs) of two tandem, rigid, circular cylinders with piecewise continuous restoring force are investigated for Reynolds number 24,000 ≤ Re ≤ 120,000 with damping, and restoring force function as parameters. Selective roughness is applied to enhance FIV and increase the hydrokinetic energy captured by the vortex-induced vibration for aquatic clean energy (VIVACE) converter. Experimental results for amplitude response, frequency response, interactions between cylinders, energy harvesting, and efficiency are presented and discussed. All experiments were conducted in the low-turbulence free-surface water (LTFSW) Channel of the MRELab of the University of Michigan. The main conclusions are as follows: (1) the nonlinear-spring converter can harness energy from flows as slow as 0.33 m/s with no upper limit; (2) the nonlinear-spring converter has better performance at initial galloping than its linear-spring counterpart; (3) the FIV response is predominantly periodic for all nonlinear spring functions used; (4) the influence from the upstream cylinder is becoming more dominant as damping increases; (5) optimal power harnessing is achieved by changing the linear viscous damping and tandem spacing L/D; (6) close spacing ratio L/D = 1.57 has a positive impact on the harnessed power in VIV to galloping transition; and (7) the interactions between two cylinders have a positive impact on the upstream cylinder regardless of the spacing and harness damping.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Bearman, P. W. , 1984, “ Vortex Shedding From Oscillating Bluff Bodies,” Annu. Rev. Fluid Mech., 16(1), pp. 195–222. [CrossRef]
Bearman, P. W. , 2011, “ Circular Cylinder Wakes and Vortex-Induced Vibrations,” J. Fluids Struct., 27(5), pp. 648–658. [CrossRef]
Sarpkaya, T. , 2004, “ A Critical Review of the Intrinsic Nature of Vortex-Induced Vibrations,” J. Fluids Struct., 19(4), pp. 389–447. [CrossRef]
Williamson, C. H. K. , and Govardhan, R. , 2004, “ Vortex-Induced Vibrations,” Annu. Rev. Fluid Mech., 36, pp. 413–455. [CrossRef]
Blevins, R. D. , 1990, Flow-Induced Vibration, 2nd ed., Vol. 2, Van Nostrand Reinhold, New York, pp. 50–65.
Bernitsas, M. M. , and Raghavan, K. , 2009, “Converter of Current, Tide, or Wave Energy,” U.S. Patent No. 7,493,759.
Bernitsas, M. M. , and Raghavan, K. , 2011, “Enhancement of Vortex Induced Forces & Motion Through Surface Roughness Control,” The Regents of the University of Michigan, Flint, MI, U.S. Patent No. 8,047,232. https://www.google.ch/patents/US20090250129
Park, H. , Bernitsas, M. M. , and Chang, C. C. , 2013, “Map of Passive Turbulence Control to Flow-Induced Motions for a Circular Cylinder at 30,000< Re< 120,000: Sensitivity to Zone Covering,” ASME Paper No. OMAE2013-10123.
Bernitsas, M. M. , 2016, “ Harvesting Energy by Flow Included Motions,” Springer Handbook of Ocean Engineering, M. R. Dhanak and N. I. Xiros , eds., Springer-Verlag, Berlin, Chap. 47. [CrossRef]
Liao, J. C. , 2007, “ A Review of Fish Swimming Mechanics and Behaviour in Altered Flows,” Philos. Trans. R. Soc. London B: Biol. Sci., 362(1487), pp. 1973–1993. [CrossRef]
Ma, C. , Sun, H. , Nowakowski, G. , Mauer, E. , and Bernitsas, M. M. , 2016, “ Nonlinear Piecewise Restoring Force in Hydrokinetic Power Conversion Using Flow Induced Motions of Single Cylinder,” Ocean Eng., 128, pp. 1–12. [CrossRef]
Zdravkovich, M. M. , 1997, Flow around Circular Cylinders, E. Achenbach , ed., Vol. 1, Oxford University Press, Oxford, UK, pp. 121–162.
Sumner, D. , Heseltine, J. L. , and Dansereau, O. J. P. , 2004, “ Wake Structure of a Finite Circular Cylinder of Small Aspect Ratio,” Exp. Fluids, 37(5), pp. 720–730. [CrossRef]
Chen, S. S. , 1986, “ A Review of Flow-Induced Vibration of Two Circular Cylinders in Crossflow,” ASME J. Pressure Vessel Technol., 108(4), pp. 382–393. [CrossRef]
King, R. , and Jones, R. , 1980, “ Flow-Induced Vibrations of an Anchor Agitator,” Pract. Exper. Flow-Induced Vib., 5(2), pp. 323–332.
Ruscheweyh, H. P. , 1983, “ Aeroelastic Interference Effects Between Slender Structures,” J. Wind Eng. Ind. Aerodyn., 14(1–3), pp. 129–140. [CrossRef]
Bokaian, A. , and Geoola, F. , 1984, “ Wake-Induced Galloping of Two Interfering Circular Cylinders,” J. Fluid Mech., 146, pp. 383–415. [CrossRef]
Laneville, A. , and Brika, D. , 1999, “ The Fluid and Mechanical Coupling Between Two Circular Cylinders in Tandem Arrangement,” J. Fluids Struct., 13(7–8), pp. 967–986. [CrossRef]
Huera-Huarte, F. J. , and Gharib, M. , 2011, “ Flow-Induced Vibrations of a Side-by-Side Arrangement of Two Flexible Circular Cylinders,” J. Fluids Struct., 27(3), pp. 354–366. [CrossRef]
Sun, H. , Ma, C. , Kim, E. S. , Nowakowski, G. , Mauer, E. , and Bernitsas, M. M. , 2017, “ Hydrokinetic Energy Conversion by Two Rough Tandem-Cylinders in Flow Induced Vibrations: Effect of Spacing and Stiffness,” Renewable Energy, 107, pp. 61–80. [CrossRef]
Sun, H. , Kim, E. S. , Bernitsas, P. M. , 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]
Kinaci, O. K. , Lakka, S. , Sun, H. , and Bernitsas, M. M. , 2016, “ Effect of Tip-Flow on Vortex Induced Vibration of Circular Cylinders for Re< 1.2 × 10 5,” Ocean Eng., 117, pp. 130–142. [CrossRef]
Chang, C. C. J. , Kumar, R. A. , and Bernitsas, M. M. , 2011, “ VIV and Galloping of Single Circular Cylinder With Surface Roughness at 3.0× 10 4≤ Re≤ 1.2× 10 5,” Ocean Eng., 38(16), pp. 1713–1732. [CrossRef]
Lee, J. H. , Xiros, N. , and Bernitsas, M. M. , 2011, “ Virtual Damper–Spring System for VIV Experiments and Hydrokinetic Energy Conversion,” Ocean Eng., 38(5), pp. 732–747. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

FIV regions with small overlap between VIV and galloping; K = 400 N/m, ζ = 0.12 [20]

Grahic Jump Location
Fig. 2

FIV regions with overlap of VIV and galloping; K = 600 N/, ζ = 0.04 [20]

Grahic Jump Location
Fig. 3

(a) Piecewise nonlinear stiffness, (b) harnessed power, (c) amplitude, and (d) frequency responses for nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; corresponding damping ratios to K1 of ζharness = 0.13, 0.26, 0.39, 0.53; mass ratio m* = 1.343; nonlinear piecewise function y0/D = 2.0, 2.5, and 3.0 [11]

Grahic Jump Location
Fig. 4

(a) One VIVACE converter with Vck mounted in the LTFSW channel and (b) design details

Grahic Jump Location
Fig. 5

Nonlinear piecewise stiffness functions

Grahic Jump Location
Fig. 6

Passive turbulence control (PTC)-cylinder oscillatory response for nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; function y0/D = 2.5, at L/D = 1.57

Grahic Jump Location
Fig. 7

PTC-cylinder oscillatory response for nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; function y0/D = 2.5, at L/D = 2.01

Grahic Jump Location
Fig. 8

PTC-cylinder oscillatory response for nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; function y0/D = 2.5, at L/D = 2.57

Grahic Jump Location
Fig. 9

PTC-cylinder oscillatory response for nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; the corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; function y0/D = 2.5, at L/D = 4.01

Grahic Jump Location
Fig. 10

Harnessed power (a) and the efficiency (b) of PTC-cylinder, nonlinear restoring force: K1 = 200 N/m, K2 = 1000 N/m; four harness damping values charness; corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; m* = 1.343; piecewise linear function y0/D = 2.5, at L/D = 1.57

Grahic Jump Location
Fig. 11

(a) Harnessed power and (b) efficiency of PTC-cylinder. Parameters: spring stiffness K1 = 200 N/m, K2 = 1000 N/m; four harnessing damping values charness; corresponding damping ratio to K1,ζharness = 0.13, 0.26, 0.39, 0.53; m* = 1.343; piecewise linear function y0/D = 2.5, at L/D = 2.01.

Grahic Jump Location
Fig. 12

Harnessed power (a) and efficiency (b) of PTC-cylinder, nonlinear restoring force K1 = 200 N/m and K2 = 1000 N/m; four harness damping values charness; the corresponding damping ratio to K1, ζ = 0.13, 0.26, 0.39, 0.53; m* = 1.343; piecewise linear function y0/D = 2.5, at L/D = 2.57

Grahic Jump Location
Fig. 13

Harnessed power (a) and efficiency (b) of PTC-cylinder, nonlinear restoring force K1 = 200 N/m, K2 = 1000 N/m; four harness damping values charness; corresponding damping ratio to K1,ζ = 0.13, 0.26, 0.39, 0.53; m*=1.343; piecewise linear function y0/D = 2.5, at L/D = 4.01

Grahic Jump Location
Fig. 14

Instantaneous power, time history, and frequency spectrum for (a) L/D = 1.57, (b) 2.01, (c) 2.57, and (d) 4.01 at U = 0.47 m/s, charness = 20 Ns/m

Grahic Jump Location
Fig. 15

Instantaneous power, time history, and frequency spectrum of L/D = 1.57(a), 2.01(b), 2.57(c), and 4.01(d) at U = 0.71 m/s, charness = 20 Ns/m

Grahic Jump Location
Fig. 16

Instantaneous power, time history, and frequency spectrum of L/D = 1.57(a), 2.01(b), 2.57(c), and 4.01(d) at U = 1.07 m/s, charness = 20 Ns/m

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In