CREST LEVEL OPTIMIZATION OF THE MULTI LEVEL OVERTOPPING BASED WAVE ENERGY CONVERTER SEAWAVE SLOT-CONE GENERATOR. J. P. Kofoed 1 and E.

Transcription

1 6 th European Wave and Tidal Energy Conference Glagow, UK Augut 29 th - September 2 nd 2005 CREST LEVEL OPTIMIZATION OF THE MULTI LEVEL OVERTOPPING BASED WAVE ENERGY CONVERTER SEAWAVE SLOT-CONE GENERATOR J. P. Kofoed 1 and E. Oaland 2 1 Department of Civil Engineering, Aalborg Univerity, Denmark i5jpk@civil.aau.dk, WAVEenergy AS, Aalgaard, Norway epen.oaland@waveenergy.no, ABSTRACT The paper decribe the optimization of the cret level and geometrical layout of the SSG tructure, focuing on maximizing the obtained potential energy in the overtopping water. During wave tank teting at AAU average overtopping rate into the individual reervoir have been meaured. The initial tet led to an expreion decribing the derivative of the overtopping rate with repect to the vertical ditance. Baed on thi, numerical optimization of the cret level, for a number of combination of wave condition, have been performed. The hereby found optimal cret level have been teted in the wave tank and further optimization of the geometry have been carried out. INTRODUCTION The Seawave Slot-cone Generator (SSG) i a multi level wave energy converter (WEC) baed on the wave overtopping principle, being developed by the Norwegian company WAVEenergy AS (WE). The device i utilizing a total of three reervoir placed on top of each other, in which the potential energy of the incoming wave i tored. The water captured in the reervoir then run through the multi-tage turbine (MST). Uing multiple reervoir reult in a higher overall efficiency, compared to a ingle reervoir tructure. The device i illutrated in figure 1. The SSG i built a a robut concrete tructure with the turbine haft and the gate controlling the water flow a virtually the only moving part of the mechanical ytem. The SSG concept make ue of the innovative patent pending multi-tage turbine alo developed by WE. The MST ha the advantage to utilize different height of water head on a common turbine wheel. The multi-tage technology minimize the number of tart/top equence on the turbine, even if only one reervoir i upplying water to the turbine, reulting in a high degree of utilization. SINTEF Energiforkning AS (SEfAS) and the Norwegian Univerity of Science and Technology (NTNU) ha performed a 3D CFD analyi of the guide vane and the runner, baed on the Euler turbine equation. Thi how an etimated efficiency on the individual tage of the MST of ~90 % with a Figure 1. Illutration of the SSG tructure

2 relative flat efficiency curve. The performance of the MST under imultanou varying condition on the different tage i currently being invetigated. The purpoe of the work decribed in the paper ha been to optimize the cret level and geometrical layout of the SSG tructure in a combination of irregular wave condition, focuing on maximizing the obtained potential energy in the overtopping water. Prototype location Figure 2. Planned prototype location. The work i done a a part of the preparation of the pilot project where a full-cale technical prototype of the SSG breakwater tructure which i planned for intallation on the wet coat of the iland of Kvitøy in an 19 kw/m wave climate, marked in figure 2. The pilot project i part funded by European Commiion FP Energy3. Wave data recording have been carried out from 3. November 2004 to 30. April 2005 in order to determine the wave climate on the tet ite and to give input to deign parameter for the SSG and the turbine. The pilot tructure i planned to be a 10 m wide module, with approx. 200 kw intalled capacity. Model tet have been performed in a wave tank at Aalborg Univerity (AAU). Here average overtopping rate into the individual overtopping reervoir have been meaured. The initial tet provided data allowing for the formulation of an expreion decribing the derivative of the overtopping rate with repect to the vertical ditance. Baed on thi expreion numerical optimization of the cret level for a number of combination of wave condition have been performed. The hereby found optimal cret level have then been teted in the wave tank and further optimization of the geometry will alo be carried out. MODEL TESTS In two round model tet have been performed in the deep water 3-D wave bain at the Hydraulic and Coatal Engineering Laboratory, AAU. The tet have been performed uing a length cale of 1:15 and 1:25, compared to the planned prototype. During thee tet average overtopping rate into the individual reervoir, a well a the wave have been meaured. Setup The model tet etup primarily conit of 3 component, ee figure 3: 1. Leading wall (with a ditance equal to the width of the tet ection, 0.5 m, model cale) wa intalled in front of the tet ection, in order to have well defined 2-D incoming wave. The incoming wave were meaured by three wave gauge placed be between the leading wall (in the hereby etablihed flume) in front of the tet ection. Furthermore, a ingle wave gauge wa deployed outide the flume, allowing for comparion. 2. The tet ection. The teted geometrie are decribed in the following ection. The three reervoir were connected by large dimenion hoe to reervoir tank outide the wave tank. 3. Reervoir tank. Each of the three reervoir in the tet ection ha a reervoir tank which i ued to meaure the amount of overtopping in the individual reervoir. In each reervoir tank a level gauge and a pump wa placed. The level gauge and the pump were connected to a PC programmed to empty the reervoir tank and thereby recording the amount of water overtopping into the individual reervoir. Figure 3. Model tet etup. Prior to the teting the wave gauge, level gauge, volume of reervoir tank and pump capacitie have been calibrated

3 Figure 4. Illutration of parameter decribing the teted geometrie. Teted geometrie A total of 17 different geometrie have been teted, 10 in the firt round and 7 in the econd. The principal layout of the teted geometrie i illutrated in figure 4. The firt 10 geometrie have been teted uing a length cale of 1:15 and a water depth of 6.0 m, correponding to the local water depth at the deployment ite (tet A1-E2). The tructure wa in thee tet placed directly on a horizontal eabed. All 10 geometrie had cret level of 2.25, 3.30 and 4.65 m for reervoir 1, 2 and 3, repectively, except for the lat two tet (E, E2) where the cret level of the lowet reervoir wa changed to 1.5 m. The angle α of the front lope wa changed from 19 to 35 through the firt round. After the firt round of tet it wa found that placing the tructure directly on a horiontal eabed did not repreent the reality well, a the rocky horeline at the ite wa een from chart to be rather teep. Thi wa taken into account in the econd round of teting where the water depth wa increaed to 25 m, and a 1:2 lope leading up to the tructure wa ued (tet F1-F7). In order to accommodate thi in the wave bain, and to facilitate handling of the large quantitie of overtopping water, the length cale wa et at 1:25 in the econd round of teting. During thee tet cret level of 1.5, 3.0 and 5.0 m for reervoir 1, 2 and 3, repectively, wa ued, except for the firt geometry (F1), where the cret level of reervoir 2 and 3 were 2.5 and 4.0 m, repectively. Wave condition Baed on wave data from DNMI and Torethaugen (1990) the offhore wave climate near the deployment ite wa eimated to a given in table 1. Thee wave condition were ued a target in the generation of the irregular wave in the model tet. In the firt round of teting wave condition 1-5 were ued. However, due to the relatively low water level, quit evere wave breaking occurred in wave condition 3-5. In the econd round of teting wave condition 1-7 were applied and here only limited wave breaking occurred and only in the larget wave condition. The available wave power averaged with probability over thee 6 wave condition i P wave 31.7 kw/m. Thee wave condition cover 86.5 % of the time. Of the remaining 13.5 %, 12.6 % correpond to wave condition with H < 1 m and 0.6 % correpond to wave condition with H > 7 m. Table 1 Wave condition a applied in model tet. Wave condition H [m] Tp [] Te [] Pwave [kw/m] Probability [%] RESULTS AND DISCUSSION Firt round Baed on the reult of the firt round of model tet it wa found, for the wave condition given in table 1, that the cret level ued here wa probably not the optimal one. Thi wa indicated by the fact that ignificantly larger efficiencie wa optained for geometry E, which ha a lower cret level for the lowet reervoir, than in the other geometrie. In order to enable optimization of cret level for the three reervoir, data from geometry D and E (which are identical in etup, except for a change in cret level) wa ued to determine the empirical coefficient A, B and C in the expreion by Kofoed (2002) dq dz z Rc,1 B + C H H Q' Ae (1) gh where Q i the dimenionle derivative of the overtopping rate with repect to the vertical ditance z. By non-linear regreion analyi the coefficient A, B and C ha been found to be 0.197, and

4 0.408, repectively. For comparion the coefficient A, B and C wa found by Kofoed (2002) to be 0.37, -4.5 and 3.5, repectively, for model tet with reervoir without front mounted. Baed on the equation above overtopping rate for individual reervoir can be etimated uing q n ( z z ) 1, 2 z2 z1 gh 3 gh A e B z2 dq dz z1 Ae R c,1 C H B dz z H e e R c,1 C H z2 B H dz e z1 B H (2) where z 1 and z 2 denote the lower and upper vertical boundary of the reervoir, repectively. Generally, z 1 R c,n and z 2 R c,n+1 i ued, n being the reervoir number. However, for the top reervoir z 2 i in principle infinite, but ha here been et at 10 m (full cale). The optimal cret level of the three reervoir wa then found by uing eq. (2) in a numerical optimization. Here, the overall hydraulic efficiency, defined a the ratio ΣP total Prob / ΣP wave Prob (i.e. the ratio between the potential power in the overtopping water at the time the water overtop the cret, and the available power in the incoming wave) for the conidered wave condition wa ued a optimization parameter. Thi optimization gave 1.5, 3.0 and 5.0 m a optimal cret level for reervoir 1, 2 and 3, reulting in an overall hydraulic efficiency of 44.0 % for the conidered wave condition given in table 1. qn, calc D_Q1 D_Q3 E_Q2 Calc. data D_Q2 E_Q1 E_Q qn, mea Figure 5. Comparion of calculated and meaured data. The black x repreent data point found in the optimization of the cret level. Second round Baed on the above the econd round of model tet were planned. All but one of the geometrie ued in thee tet, were with cret level a given above. The purpoe of the econd round of tet were to check the reult of the numerical optimization and to further optimize the geometry by teting change in the geometrie other than the cret level. The reult of the econd round of tet are given in table 2. Here the reult of the econd round of model tet are preented in term of full cale overtopping rate (q n, n indicating the reervoir number) and hydraulic power in each of the three reervoir (P n, n, found a the overtopping rate time the cret level of the reervoir time the acceleration of gravity), and the total overtopping rate (q total, the um of q n ) and total hydraulic power (P total, the um of P n ) and efficiency (defined a the ratio between P total and P wave ) for the individual tet. From here it i een that an overall hydraulic efficiency over wave condition 1-7 of 51.8 % ha been achieved for geometry F7, which i conidered the optimal for the given wave condition. Thi i ignificantly higher than the reult of the numerical optimization baed on the reult of the firt round of model tet. The reaon for thi i conidered primarely to be the change in water depth from firt to econd round, together with the fact that the geometrical change, other than the cret level, teted in the econd round have optimized the tructure ignificantly. Furthermore, eq. (2), ued in the numerical optimization, wa baed on a relatively mall data et, i.e. ome uncertainty mut be expected. The increae in performance i alo illutrated in figure 6 where the reult for geometry F7 are compared to eq. (2). qn, calc qn, mea F7_q1 F7_q2 F7_q3 Figure 6. Comparion of eq. (2) (traight line) and meaured data for geometry F

5 Table 2. Reult of the econd round of model tet, given in term of full cale overtopping rate and hydraulic power in the three reervoir, and the total power and efficiency for the individual tet. For each geometry the overall efficiency i alo given (for F1-6 the efficiency (eff.) i baed on wave condition 1-2, 3-4 and 5-6, for F7 the efficiency baed on all 6 wave condition (eff. all) i alo given). Geometry Wave cond. q1 [m^3//m] q2 [m^3//m] q3 [m^3//m] qtotal [m^3//m P1 [kw/m] P2 [kw/m] P3 [kw/m] Ptotal [kw/m] eff. [ - ] F eff F eff F eff F eff F eff F eff F eff eff,all It i een that the incerae in performance i due to coniderably larger meaured overtopping rate for reervoir 1 and 3 compared to the expreion baed on the previou model tet. For reervoir 2 the expreion eem to predict the overtopping rate very well. Wave direction and tructure orientation After the econd round of model teting had been performed, a tudy of the wave condition at the prototype location by Kofoed & Guinot (2005) wa concluded. Thi tudy include information about wave direction and change in wave condition due to the bathymetry in the area, and thu give the near hore wave condition. Thee are given in table 3. The available wave power averaged with probability over thee 6 wave condition for the near hore prototype location i P wave 18.1 kw/m. By inter- and extrapolation of the model tet reult for geometry F7, overtopping rate and hydraulic power production, have been etimated for all the relevant wave condition and direction. The etimated overtopping rate are given in figure 7 together with original model tet data. The extrapolation of the overtopping data to wave condition ignificantly higher than the one teted, i obviouly relatively uncertain. However, a it i een from figure 7 the overtopping rate into reervoir 1 and 2 ha been etimated to be cloe to maximum in the larget of the teted wave condition. Table 3. Near hore wave condition in term of ignificant wave height, peak period, direction and probability of occurrence, Kofoed & Guinot (2005). The available wave power in the individual wave condition i alo given, a well a the overall average. Wave condition Sum Tp [] H [m] NW Dir [deg.] Prob 9.9% 8.7% 5.4% 2.7% 1.1% 0.5% 28.4% Pwave [kw/m] Pwave*Prob H [m] W Dir [deg.] Prob 4.8% 4.2% 2.6% 1.3% 0.6% 0.2% 13.7% Pwave [kw/m] Pwave*Prob H [m] SW Dir [deg.] Prob 7.5% 6.5% 4.0% 2.0% 0.9% 0.4% 21.3% Pwave [kw/m] Pwave*Prob H [m] S Dir [deg.] Prob 8.1% 7.1% 4.4% 2.2% 0.9% 0.4% 23.1% Pwave [kw/m] Pwave*Prob Sum Prob 30.3% 26.5% 16.4% 8.3% 3.5% 1.5% 86.5% Pwave*Prob The reaoning behind thi etimate i that the ize of the gap between reervoir 1-2 and 2-3 (controlled by the orthogonal ditance between the reervoir front) are etting an upper limit to the overtopping rate into reervoir 1 and 2. The tendency that the overtopping rate are reaching a maximum value i alo een in the data, epecially for reervoir 1. For reervoir 3 there i no uch upper limit for the overtopping rate, a there i no tructure above it. In the extrapolation it i therefore aumed that the

6 increaing tendency for the overtopping rate i continued. q [m^3//m] q1, F7 q2, F7 q3, F H [m] Figure 7. Model tet reult for geometry F7 (full marker), together with inter- and extrapolated data correponding to near hore prototype location wave condition (open marker). Baed on thee etimated data the overall average hydraulic efficiency at the prototype location i 50.9 % for near hore wave condition correponding to the offhore wave condition 1-7 a given in table 3. Thi correpond to an overall average hydraulic power production of 9.2 kw/m. However, in thee data the effect of orientation of the tructure ha not been taken into account, ie. it i aumed the tructure i facing directly toward the incoming wave, regardle of wave direction. A factor accounting for oblique wave attack on ingle reervoir geometrie i uggeted by Van der Meer & Janen (1995) γ β β (3) where β i the difference between wave direction and orientation of the tructure, meaured in degree, for overtopping rate. γ β i ued by dividing the relative cret freeboard R with it. Eq. (3) i not directly applicable to multi level geometrie, but in lack of alternative a correction factor λ β i defined a λ β 0.2e e Rc, n H γ β Rc, n 2.6 H e R 2.6 c, n 1 1 H γ β 0.2 (4) Thi correction factor ha been calculated baed on the wave data in table 4 and multiplied onto the etimated overtopping rate (given in figure 7). By thi procedure it i found that the overall average hydraulic efficiency at the prototype location for a tructure facing due wet (270 ) i 41.4 % for near hore wave condition correponding to the offhore wave condition 1 7, a given in table 4. Thi correpond to an overall average hydraulic power production of 7.5 kw/m. The optimal orientation of the tructure ha been found by maximizing the overall hydraulic efficiency by changing the orientation. The optimal orientation i found to be in the range. The correction factor given in eq. (3) ha been derived from model tet with 2-D wave and hore protection tructure (breakwater and dike), and not a multi level tructure with a relatively mall width a the SSG tructure. Thu, there i a coniderable uncertainty in uing it for the current purpoe and 3-D tet with more detailed modelling of forehore and tructure i needed in order to include refraction/diffraction effect around the tructure. Comparion to exiting overtopping expreion A a check of the meaured overtopping rate the total overtopping rate in all three reervoir have been ummed for the individual tet and made nondimenional a uggeted by Van der Meer & Janen (1995) Q where 2.6R 0.2e (5) q Q i the non-dimenional λ gh overtopping rate. π ( R) 0.4in for R < 0.75 λ 1 for R 0.75 account for low relative cret freeboard, a uggeted by Kofoed (2002). R i the relative cret freeboard, R c /H. Here et at R c,1 /H. The reult hereof are generally in line with eq. (5), a illutrated in figure 8, and thu agree with well etablihed data from the literature. Q [ - ] Firt round Second round Eq. (5) R [ - ] Figure 8. Non-dimenional overtopping rate a a function of the non-dimenional cret freeboard

7 baed on the cret level of the lowet reervoir. The traight line repreent eq. (5). CONCLUSION The optimization of the cret level and geometrical layout of the SSG tructure ha been decribed. Baed on the initial tet the expreion from Kofoed (2002) ha been updated to include geometrie with front mounted on the individual reervoir. Uing thi updated expreion the cret level have been optimized to fit the prevailing wave condition at the prototype location. Further model tet have been performed leading to further optimization of the geometry of the tructure. After taking into account the effect of wave direction and tructure orientation it ha been found that for the optimized tructure the overall average hydraulic efficiency at the prototype location for a tructure facing due wet (270 ) i 41.4 % for near hore wave condition correponding to offhore wave condition 1-7. Thi correpond to an overall average hydraulic power production of 7.5 kw/m. However, the wave direction and tructure heading ha been taken into account uing a correction factor derived from model tet with 2-D wave and hore protection tructure (breakwater and dike), and not a multi level tructure with a relatively mall width. Thu, there i a coniderable uncertainty in uing it for the current purpoe and 3-D tet with more detailed modeling of forehore and tructure i needed in order to include refraction/diffraction effect around the tructure. Further teting of a 3-D model of the tructure in oblique and 3-D wave condition are cheduled for thi autumn. Thee tet will alo include meaurement of local and global force on the tructure to enable a reliable tructural deign. NOMENCLATURE A, B, C Regreion coefficient [ - ]. dq/dz Derivative of the overtopping rate with repect to the vertical ditance z [m 3 //m/m]. g Gravitational acceleration, 9.82 m/ 2 H Significant wave height [m]. P n Hydraulic power pr. width of n th reervoir [kw/m], calculated a qr c g. P total Sum of P n over all reervoir [kw/m]. P wave Available wave power [kw/m], 2 ρg 2 calculated a Pwave Te H 64π q Overtopping rate pr. width [m 3 //m]. Q Non-dimenional overtopping rate [ - ]. Q Dimenionle derivative of the overtopping rate with repect to z [ - ]. q n Overtopping rate pr. width of n th reervoir [m 3 //m]. q total Sum of q n over all reervoir [m 3 //m]. R Relative cret freeboard [ - ]. R c Cret freeboard [m] R c,n Cret level of n th reervoir [m]. T e Wave energy period [], here etimated a T p /1.15. T p Wave peak period []. z Vertical ditance [m]. α Angle of front lope [ ]. β Wave direction, 0 head-on [ ]. γ β Factor accounting for oblique wave attack [ - ]. λ Factor accounting for low R [ - ]. λ β Correction factor derived from γ β for multiplication onto q n [ - ]. REFERENCES Kofoed J. P. (2002): Wave Overtopping of Marine Structure Utilization of Wave Energy. Ph. D. Thei, defended January 17, 2003 at Aalborg Univerity. Hydraulic & Coatal Engineering Laboratory, Department of Civil Engineering, Aalborg Univerity, December, Kofoed, J. P.: Model teting of the wave energy converter Seawave Slot-Cone Generator. Hydraulic and Coatal Engineering No. 18, ISSN: , Dep. of Civil Eng., Aalborg Univerity, April Kofoed, J. P. and Guinot, F.: Study of Wave Condition at Kvitøy Prototype Location of Seawave Slot-Cone Generator. Hydraulic and Coatal Engineering No. 25, ISSN: , Dep. of Civil Eng., Aalborg Univerity, June Kofoed, J. P.: Experimental Hydraulic Optimization of the Wave Energy Converter Seawave Slot- Cone Generator. Hydraulic and Coatal Engineering No. 26, ISSN: , Dep. of Civil Eng., Aalborg Univerity, June Torethaugen, K. (1990): Bølgedata for vurdering av bølgekraft, SINTEF NHL-report No. STF60- A90120, , ISBN Nr Van der Meer, J. W. and Janen, J. P. F. M. (1995): Wave run-up and wave overtopping at dike. Technical report, Tak Committee Report, ASCE

8