SECOND ORDER DRIFT FORCES ON "OFFSHORE" WAVE ENERGY CONVERTERS. Luca Martinelli, Alberto Lamberti, Piero Ruol DISTART Università di Bologna

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1 2nd order Presented drift at forces the COMSOL on Off-shore Conference 2009 Milan Wave Energy Converters L. Martinelli et al. SECOND ORDER DRIFT FORCES ON "OFFSHORE" WAVE ENERGY CONVERTERS Luca Martinelli, Alberto Lamberti, Piero Ruol DISTART Università di Bologna IMAGE Università Milan , di Padova October 16

2 Milan , October 16 Layout Introduction on Wave Energy Converters Potential Classification Examples Laboratory tests Motivations for this study 2nd order Peculiarities of the application Conclusions

3 Wave Energy

4 REWEC3 Boccotti et al. Ocean Engineering GWh/y/Km of breakwater Ponza Cost: 7% more than traditional vertical brkw HYDRAULIC EFFICIENCY % Comune di Leni Messina, isola di Salina Eolie Several sound possibilities of installation e.g. Porto Gioia Tauro

5 Milan , October 16 Sea Breath Artist s s impression of placement in an array structure Multi Absorbing Oscillating Water Column MAWEC

6 Sea Breath

7 Concept The circle of air feeds a turbine Wave direction Milan , October 16 Inventor: Luigi Rubino Patent n.: PCT/IB2009/ Priority:PR2008A Luigirubino@hotmail.com

8 Physical model tests New tests planned, aiming at R&D Padova University, Italy

9 OE Buoy

10 Record of mooring force

11 CONTENUTI MOTIVAZIONI OBIETTIVI POTENZIALITÀ TIPOLOGIE ESEMPI ANCORAGGI CONCLUSIONI Objectives Present a procedure for evaluating 2nd order drift forces on floating bodies, often the most important t loading component for mooring design, in case of high waves propagating in relatively shallow water depths.

12 Irrotational flow around floating body 2 =0 = I + S +V H Channel+ Effect of fixed FB + Effect of movements = O 3 = O 3 O X X X X V i i S I V Milan , October 16 i i S W V

13 Milan , October 16 Regular wave - phasor variables Ax,t=ax cos 1 t+ 1 x= + Re[x 1 ei 1 t] Peculiarity of the method is how to compute the product of two phasor variables

14 Milan , October 16 Ax,t=ax cos 1 t+ 1 x= + Re[x 1 ei 1 t] Bx,t=bx cos 2t+ 2 2 x= + Re[x 1 ei 2 t] A*B= Re[0.5 ei t+0.5 C S ei D t] where S = and D = w whf wlf And we can differentiate in time the unknown potential!

15 Incident 1st order potential I I Re ihg cosh k y 2 coshkd d i e t kx

16 Milan , October 16 Domain equation 2 =0 2 =0 in

17 2.1 Surface boundary conditon -n = 2 /g S in S s, s and radiated, e.g / [ ] n w, z 1 1 / g [ w i / g], zz, z, z 1 D slf slf g

18 2.1 Radiation condition -n = i k in I already satisfy this

19 Condition at body -n = - n I in B and 0 so that: I + S n=0 for 1st and second order terms, except: t s n X V 1 1 N 1 n

20 1 wave incident Incident+ scattered Wave 2nd Hfreq Total potential fixed body ZOOMED VIEW:

21 2 waves incident Incident+ scattered Wave 2nd Total potential fixed body: small & high wave hight

22 1st Order Force Force on FB = integral of 1st order pressure Exciting force =fixed structure + force due to radiation for unit vel in phase with acceleration i.e. added mass or relative to propagating waves i.e. damping e F v i n d f i I n d v H y 0 S y 0 i - 2 M++i+gW +i+gw =F e v

23 2n Order Drift Force F So 2 1 R wl g ndl dl X n ds MX w, t d, t nds So t

24 Application to a box 1 2D box, Comsol F 2 / g Sphere, Pinkster 1980 I -1 II III I+II+III k L b

25 Conclusive remarks From years 90 the research on WECs has heen very active about 20 devices at sea; The resource is abundant for the European needs, being of order TWh/y; Floating WEC 3rd generation have a low visual and environmental impact; Wave Energy is uncorrelated to solar and more persistent than wind energy, since it averages the wind in time and space. Wave energy is therefore complementary to other renewables;

26 CONTENUTI MOTIVAZIONI OBIETTIVI POTENZIALITÀ TIPOLOGIE ESEMPI ANCORAGGI CONCLUSIONI Conclusive remarks Italian climate is mild. It is therefore very suited to R&D, thanks to the many periods of calm weather; The only economical structures are those that couple WEC to other functions: REWEC3, Univ. di Catania; Coastal defence, Univ. of Bologna and Padova; The note shows how to approach the problem of finding 2nd order forces: All 5 terms forming the second order drift force are described first with reference to a single regular wave and then with reference to a sum of waves; An application was presented, showing reasonable results, in quantitative agreement with asymptotic behaviors.

27 Milan , October 16 This work is funded by CORES "Components for Ocean Renewable Energy Structures" FP7 project. Wave Dragon in scale 1:4,5 - Nissum Bredning DK, 2003