Research Papers: Ocean Renewable Energy

Computational Modeling of Rolling Wave-Energy Converters in a Viscous Fluid1

[+] Author and Article Information
Yichen Jiang

Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720
e-mail: yichen.e.jiang@gmail.com

Ronald W. Yeung

American Bureau of Shipping Inaugural
Chair in Ocean Engineering;
Director of Computational Marine Mechanics
Laboratory (CMML),
Department of Mechanical Engineering,
University of California at Berkeley,
Berkeley, CA 94720
e-mail: rwyeung@berkeley.edu

2Corresponding 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 April 20, 2012; final manuscript received August 5, 2015; published online October 12, 2015. Assoc. Editor: Hideyuki Suzuki.

J. Offshore Mech. Arct. Eng 137(6), 061901 (Oct 12, 2015) (9 pages) Paper No: OMAE-12-1039; doi: 10.1115/1.4031277 History: Received April 20, 2012; Revised August 05, 2015

The performance of an asymmetrical rolling cam as an ocean-wave energy extractor was studied experimentally and theoretically in the 70s. Previous inviscid-fluid theory indicated that energy-absorbing efficiency could approach 100% in the absence of real-fluid effects. The way viscosity alters the performance is examined in this paper for two distinctive rolling-cam shapes: a smooth “Eyeball Cam (EC)” with a simple mathematical form and a “Keeled Cam (KC)” with a single sharp-edged keel. Frequency-domain solutions in an inviscid fluid were first sought for as baseline performance metrics. As expected, without viscosity, both shapes, despite their differences, perform exceedingly well in terms of extraction efficiency. The hydrodynamic properties of the two shapes were then examined in a real fluid, using the solution methodology called the free-surface random-vortex method (FSRVM). The added inertia and radiation damping were changed, especially for the KC. With the power-take-off (PTO) damping present, nonlinear time-domain solutions were developed to predict the rolling motion, the effects of PTO damping, and the effects of the cam shapes. For the EC, the coupled motion of sway, heave and roll in waves was investigated to understand how energy extraction was affected.

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Salter, S. H. , 1974, “ Wave Power,” Nature, 249, pp. 720–724. [CrossRef]
Evans, D. V. , 1976, “ A Theory for Wave-Power Absorption by Oscillating Bodies,” J. Fluid Mech., 77(1), pp. 1–25. [CrossRef]
Seah, R. K. M. , and Yeung, R. W. , 2008, “ Vortical-Flow Modelling for Ship Hulls in Forward and Lateral Motion,” 27th Symposium on Naval Hydrodynamics, Seoul, South Korea.
Carmichael, A. D. , 1979, “ An Experimental Study and Engineering Evaluation of the Salter Cam Wave Energy Converter,” Sea Grant Collage Program, Massachusetts Institute of Technology, Cambridge, MA, Technical Report No. MITSG 78-22.
Yeung, R. W. , and Wu, C. F. , 1991, “ Viscous Effects on the Radiation Hydrodynamics of Horizontal Cylinders,” ASME J. Offshore Mech. Arct. Eng., 113(4), pp. 334–343. [CrossRef]
Yeung, R. W. , and Ananthakrishnan, P. , 1992, “ Oscillation of a Floating Body in a Viscous Fluid,” J. Eng. Math., 26(1), pp. 211–230. [CrossRef]
Gentaz, L. , Alessandri, B. , and Delhommeau, G. , 1997, “ Motion Simulation of a Two-Dimensional Body at the Surface of a Viscous Fluid By a Fully Coupled Solver,” 12th International Workshop on Water Waves and Floating Bodies, pp. 85–90.
Downie, M. , Graham, J. , and Zheng, X. , 1990, “ Effect of Viscous Damping on the Response of Floating Bodies,” 18th Symposium on Naval Hydrodynamics, Ann Arbor, MI, pp. 149–155.
Yeung, R. W. , and Jiang, Y. , 2014, “ Shape Effects on Viscous Damping and Motion of Heaving Cylinders,” ASME J. Offshore Mech. Arct. Eng., 136(4), p. 041801. [CrossRef]
Quérard, A. B. G. , Temarel, P. , and Turnock, S. R. , 2009, “ The Hydrodynamics of Ship-Like Sections in Heave, Sway, and Roll Motions Predicted Using an Unsteady Reynolds averaged Navier–Stokes Method,” Proc. Inst. Mech. Eng., Part M, 223(2), pp. 227–238. [CrossRef]
Yeung, R. W. , and Cermelli, C. A. , 1998, “ Vortical Flow Generated by a Plate Rolling in a Free Surface,” Free Surface Flow With Viscosity (Advances in Fluid Mechanics). P. Tyvand, ed., Computational Mechanics Publications, Southampton, UK, Vol. 16, pp. 1–35.
Yeung, R. W. , 2002, “ Fluid Dynamics of Finned Bodies—From VIV to FPSO,” Plenary Paper, The 12th International Offshore and Polar Engineering Conference, Vol. 3, pp. 1–11.
Jiang, Y. , and Yeung, R. W. , 2014, “ Effects of Bilge Keels and Forward Speed On Roll Motion,” 30th Symposium on Naval Hydrodynamics, Tasmania, Australia.
Chorin, A. J. , 1973, “ Numerical Study of Slightly Viscous Flow,” J. Fluid Mech., 57(4), pp. 785–796. [CrossRef]
Yeung, R. W. , Roddier, D. R. , Alessandrini, L. , Gentaz, L. , and Liao, S. W. , 2000, “ On Roll Hydrodynamics of Cylinders Fitted With Bilge Keels,” 23rd Symposium on Naval Hydrodynamics, Val de Reuil, France.
Yeung, R. W. , and Vaidhyanathan, M. , 1994, “ Highly Separated Flows Near a Free Surface,” Proceedings of the International Conference on Hydrodynamics, Wuxi, China.
Israel, M. , and Orszag, S. A. , 1981, “ Approximation of Radiation Boundary Conditions,” J. Comput. Phys., 41(1), pp. 115–135. [CrossRef]
Grosenbaugh, M. A. , and Yeung, R. W. , 1989, “ Nonlinear Free-Surface Flow at a Two-dimensional Bow,” J. Fluid Mech., 209, pp. 57–75. [CrossRef]
Roddier, D. R. , Liao, S.-W. , and Yeung, R. W. , 1999, “ Time-Domain Solution of Freely-Floating Cylinders in a Viscous Fluid,” 9th International Conference of Society of Offshore and Polar Engineers, Brest, France, Vol. 3, pp. 454–462.
Liao, S. , 2000, “ Development and Applications of the Free-Surface Random Vortex Method (FSRVM),” Ph.D. dissertation, University of California, Berkeley.
Wehausen, J. V. , 1971, “ Motion of Floating Bodies,” Annu. Rev. Fluid Mech., 3, pp. 237–268. [CrossRef]
Mynett, A. E. , Serman, D. D. , and Mei, C. C. , 1979, “ Characteristics of Salter's Cam for Extracting Energy From Ocean Waves,” Appl. Ocean Res., 1(1), pp. 13–20. [CrossRef]
Tom, N. , and Yeung, R. W. , 2012, “ Performance Enhancements and Validations of the UC-Berkeley Ocean-Wave Energy Extractor,” Paper No. OMAE2012-83736.


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Fig. 1

EC and KC with radius R=25 cm, reference shape with origin at y = 0

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Fig. 2

EC, KC, and Salter Cams with their center of rotation submerged

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Fig. 3

Computational domain D for a rolling body in waves

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Fig. 5

Optimal ideal efficiency η, calculated from inviscid-fluid models based on potential theory

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Fig. 7

Comparison between the viscous and inviscid hydrodynamic coefficients of the KC

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Fig. 4

The comparison of the cam's efficiency between experiments and FSRVM simulations for the case that the MOI of the Salter Cam, Î=I/(ρR4)=3.56

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Fig. 8

Comparison between the viscous and inviscid hydrodynamic coefficients of the EC

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Fig. 9

Roll amplitude and efficiency of the two cams over a range of extractor damping, B̃g, using viscous-fluid modeling

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Fig. 6

RAO α0/kA, required to achieve the optimum ideal efficiency (inviscid-fluid solution)

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Fig. 10

Visualization of vortex blobs for both cams with the optimum Bg in one 30th period of oscillation (ω̃inc=0.6). a) Eyeball Cam in the first half of 30th period, b) Eyeball Cam in the second half of 30th period, c) Keeled Cam in the first half of 30th period, and d) Keeled Cam in the second half of 30th period

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Fig. 11

Mooring system of the 3DOF model

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Fig. 12

Roll extraction efficiency in 3DOF motion with the effects of mooring cables

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Fig. 13

Time history of sway, heave and roll displacement in five periods



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