Wave–Structure Interactions of Flexible Bags with Elastic Tendons: Application to Wave Energy Conversion
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147, Issue 1
Abstract
A new type of wave energy device has recently been proposed with the key component being a flexible air-filled bag, which is constructed such that the fabric is encased by an array of tendons. The behavior of the bag in still water under hydrostatic loading and its dynamic response when subjected to hydrodynamic loading in waves were previously analyzed using a numerical model developed with the assumption of inextensible tendons. In the present work, the model is extended to include the effects of tendon elasticity. The behavior of the bag with tendons of various moduli of elasticity is then compared with that of the bag with inextensible tendons. It is found that adding elasticity to the tendons has a similar effect to that of increasing the air volume connected to the bag, that is, it increases the resonance period of the device. Consequently, a bag with elastic tendons can be made even smaller in size than a bag with inextensible tendons in order to match the same target resonance period.
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Acknowledgments
Dr. Thanh Toan Tran from the National Renewable Energy Laboratory (NREL) provided the hydrodynamic coefficients for the dynamic response calculations. A.K. is supported by the Wave Energy Research Centre, jointly funded by The University of Western Australia and the Western Australian Government, via the Department of Primary Industries and Regional Development (DPIRD). Part of this study was conducted while A.K. was with the Department of Civil Engineering, Aalborg University. S.B. and D.F would also like to acknowledge support from Wave Energy Scotland through the project “A feasibility study on Elastomeric-based WECs” (ELASTO).
Notation
The following symbols are used in this paper:
- A
- combined mean cross-sectional area of the tendons;
- An, An+1
- angles (measured in the vertical plane relative to horizontal) at the element endpoints (in the dynamic model, these angles are denoted as An−1, An);
- an−1, an
- angular displacements at the element endpoints (complex);
- BPTO
- power take-off damping;
- C
- power take-off coefficient;
- mean capture width ratio for the wave climate;
- E
- modulus of elasticity of the tendon;
- vertical excitation force on the substructure (complex);
- vertical wave radiation force on the substructure due to a unit normal displacement of node k (complex);
- wave radiation force on the substructure due to a unit heave displacement of the mean geometry (complex);
- vertical hydrodynamic force on the substructure (complex);
- g
- acceleration due to gravity;
- Hn+0.5
- unit step function;
- Hs
- significant wave height;
- h
- arc length of element, including static extension;
- h0
- original length of element before extension;
- i
- imaginary unit;
- mean wave energy transport for the wave climate;
- MB
- mass of the substructure;
- Ms
- mean mass of air in secondary volume;
- m
- increase in air mass in the compressible volume (complex);
- ms
- increase in air mass in the secondary volume (complex);
- N
- number of discretized tendon elements;
- N′
- N + 1;
- nwl
- index of the first node below the waterline;
- P
- mean internal bag pressure relative to atmospheric;
- mean absorbed power;
- mean absorbed power for the entire wave climate;
- Patm
- atmospheric pressure;
- Prob(Hs, Tz)
- long-term probability of occurrence of the sea state;
- p
- pressure increase in the bag (complex);
- wave excitation pressure on node n (complex);
- hydrodynamic pressure on node n (complex);
- wave radiation pressure on node n due to a unit outward normal displacement of node k (complex);
- wave radiation pressure on node n due to a unit heave displacement of the mean geometry (complex);
- ps
- pressure increase in the secondary volume (complex);
- R
- radial coordinate;
- Rwl
- mean waterplane radius;
- rn
- radial displacement of node n (complex);
- S(ω, Hs, Tz)
- wave spectrum for the sea state;
- T
- sum of mean tension in all tendons;
- Te
- wave energy period;
- Tp
- spectral peak period;
- Tz
- mean wave period;
- V
- mean compressible air volume;
- Vs
- secondary air volume;
- v
- increase of bag volume (complex);
- Z
- vertical coordinate;
- zn
- vertical displacement of node n relative to ξ3 (complex);
- γ
- heat capacity ratio;
- δAn
- An+1 − An;
- δRn
- Rn+1 − Rn;
- δZn
- Zn+1 − Zn;
- η
- incident wave amplitude (complex);
- θ
- angular coordinate;
- ξ3
- vertical displacement of substructure (complex);
- ρ
- water density;
- ρair
- mass density of air in the system at the mean pressure P;
- ρn
- radius of curvature of element n;
- τ
- increase in total tendon tension (complex);
- ϕn
- half of the arc sector angle of element n; and
- ω
- wave angular frequency.
References
Babarit, A. 2015. “A database of capture width ratio of wave energy converters.” Renewable Energy 80: 610–628. https://doi.org/10.1016/j.renene.2015.02.049.
Babarit, A., and G. Delhommeau. 2015. “Theoretical and numerical aspects of the open source BEM solver NEMOH.” In Proc., 11th European Wave and Tidal Energy Conf. Nantes, France. https://ewtec.org/.
Cathey, H. 2009. “The NASA super pressure balloon – A path to flight.” Adv. Space Res. 44 (1): 23–38. https://doi.org/10.1016/j.asr.2009.02.013.
Chaplin, J., F. Farley, D. Greaves, M. Hann, A. Kurniawan, and M. Cox. 2015a. “Numerical and experimental investigation of wave energy devices with inflated bags.” In Proc., 11th European Wave and Tidal Energy Conf. Nantes, France. https://ewtec.org/.
Chaplin, J. R., F. Farley, A. Kurniawan, D. Greaves, and M. Hann. 2015b. “Forced heaving motion of a floating air-filled bag.” In Proc., 30th Int. Workshop on Water Waves and Floating Bodies, 29–32. Bristol, UK. http://iwwwfb.org/.
Falnes, J. 1999. “Wave-energy conversion through relative motion between two single-mode oscillating bodies.” J. Offshore Mech. Arct. Eng. 121 (1): 32–38. https://doi.org/10.1115/1.2829552.
Farley, F. J. M. 2018. “The underwater resonant airbag: A new wave energy converter.” Proc. R. Soc. London, Ser. A 474: 20170192.
Flanagan, D. T., and R. C. Hopkins. 1993. Advanced underwater lift device. Rep. No. 185709. Washington, DC: NASA.
Kurniawan, A., J. R. Chaplin, D. M. Greaves, and M. Hann. 2017a. “Wave energy absorption by a floating air bag.” J. Fluid Mech. 812: 294–320. https://doi.org/10.1017/jfm.2016.811.
Kurniawan, A., J. R. Chaplin, M. R. Hann, D. M. Greaves, and F. J. M. Farley. 2017b. “Wave energy absorption by a submerged air bag connected to a rigid float.” Proc. R. Soc. London, Ser. A 473: 20160861. https://doi.org/10.1098/rspa.2016.0861.
Kurniawan, A., and D. Greaves. 2016. “Wave power absorption by a submerged balloon fixed to the sea bed.” IET Renewable Power Gener. 10: 1461–1467. https://doi.org/10.1049/iet-rpg.2016.0044.
Kurniawan, A., D. Greaves, and J. Chaplin. 2014. “Wave energy devices with compressible volumes.” Proc. R. Soc. London, Ser. A 470: 20140559. https://doi.org/10.1098/rspa.2014.0559.
Nielsen, K., and T. Pontes. 2010. Annex II Task 1.1 Generic and site-related wave energy data. Rep. No. T02-1.1. OES IA.
Pimm, A. J., S. D. Garvey, and M. de Jong. 2014. “Design and testing of energy bags for underwater compressed air energy storage.” Energy 66: 496–508. https://doi.org/10.1016/j.energy.2013.12.010.
Price, A. A. E., C. J. Dent, and A. R. Wallace. 2009. “On the capture width of wave energy converters.” Appl. Ocean Res. 31 (4): 251–259. https://doi.org/10.1016/j.apor.2010.04.001.
Taylor, G. I. 1963. “On the shapes of parachutes.” The scientific papers of G. I. Taylor, edited by G. K. Batchelor, 26–37. Cambridge: Cambridge University Press. (Original work published 1919).
Thompson, J. M. T. 1983. “Complex dynamics of compliant off-shore structures.” Proc. R. Soc. London, Ser. A 387 (1793): 407–427. https://doi.org/10.1098/rspa.1983.0067.
Tucker, M. J., and E. G. Pitt. 2001. Waves in ocean engineering. Ocean Engineering Series 5. Amsterdam, Netherlands: Elsevier.
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Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 147 • Issue 1 • January 2021
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Feb 26, 2020
Accepted: Jun 15, 2020
Published online: Sep 23, 2020
Published in print: Jan 1, 2021
Discussion open until: Feb 23, 2021
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