A NUMERICAL STUDY ON MULTI-CHAMBER OSCILLATING WATER COLUMNS

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1 Journl of JSCE, Vol. 3, 93-4, 5 A UMERICAL STUDY O MULTI-CAMBER OSCILLATIG WATER COLUMS Pllv KOIRALA, Shuichi AGATA, Ysuk IMAI 3, Tengen MURAKAMI 4 nd Toshiki SETOGUCI 5 Posdocorl Resercher, Insiue of Ocen Energy, Sg Universiy (onjo Mchi Bnchi, Sg Shi, Sg Ken 84-85, Jpn) E-mil: koirl@ioes.sg-u.c.jp Member of JSCE, Professor, Insiue of Ocen Energy, Sg Universiy (onjo Mchi Bnchi, Sg Shi, Sg Ken 84-85, Jpn) E-mil: ng@ioes.sg-u.c.jp 3 Associe Professor, Insiue of Ocen Energy, Sg Universiy (onjo Mchi Bnchi, Sg Shi, Sg Ken 84-85, Jpn) E-mil: imiy@cc.sg-u.c.jp 4 Assisn Professor, Insiue of Ocen Energy, Sg Universiy (-48, Kubr-z, iro, Ymshiro mchi, Imri Shi, Sg Ken , Jpn) E-mil: murkmi@cc.sg-u.c.jp 5 Professor, Insiue of Ocen Energy, Sg Universiy (onjo Mchi Bnchi, Sg Shi, Sg Ken 84-85, Jpn) E-mil: seoguci@me.sg-u.c.jp A wo-dimensionl frequency-domin numericl nlysis on he primry conversion efficiency of muli-chmber Oscilling Wer Columns (OWCs) is presened. The numericl model is developed by combining he hydrodynmics of he inercion beween he wve nd he OWC nd he hermodynmics of he ir chmbers. The wve-induced force is clculed using he boundry elemen mehod bsed on he velociy poenil heory. The ir flow is sudied using mss nd energy conservion equions nd n equion of se. The ir pressure in he ir chmbers, he reflecion coefficien, nd he primry conversion efficiency of ech of he chmbers, s well s he combined efficiency, re evlued using he boundry inegrl equions. In ddiion, he behvior of hese physicl quniies, long wih he vriions in he nozzle rio, he relive wer deph, he deph of he curin wll, nd he widh of he fron-chmber re invesiged using he clculed resuls. Key Words : velociy poenil, boundry elemen, frequency domin, primry conversion efficiency. ITRODUCTIO Compred o oher wve energy converers (WECs), he simple design, esy insllion nd operion of Oscilling Wer Columns (OWCs) hve mde hem he mos populr mong wve energy conversion echnologies ),),3). In ddiion, OWCs h uilize ir urbines hve very few moving prs nd here re no moving prs in he wer. Severl lrge-scle ess of OWCs hve mply demonsred he relibiliy of les he shorebsed operions ). In generl, OWCs hve one wer chmber nd one ir chmber s shown in Fig.. On he oher hnd, wo-chmber OWCs hve lso been sudied o increse he oupu power by effecive phse conrol of vlves. More recenly, Min-Fu sieh e l. hve proposed new design wih wo djcen chmbers, ech wih urbine nd generor, ligned in he direcion of wve propgion o smooh he oupu power 4). Wih he objecive of enhncing he efficiency nd smoohing he oupu power, he uhors hve invesiged he primry conversion efficiency of OWCs wih muliple chmbers numericlly: wo-chmber OWC wih wo wer chmbers nd wo ir chmbers s shown in Fig., nd wo-chmber OWC wih wo wer chmbers nd one ir chmber s illusred in Fig.3. The numericl resuls re compred wih hose of single-chmber OWC (Fig.). This pper presens 93

2 model is vlided by compring wih he experimenl d of one-chmber OWC by Ojim e l. 6),7). FORMULATIO OF TE UMERICAL MODEL Fig. Definiion skech of one-chmber OWC. The numericl model is developed by combining he hydrodynmics beween he wve nd OWC, nd he hermodynmics of he ir chmber. The fluid force is clculed using he boundry elemen mehod bsed on he velociy poenil heory. Assuming ir o be n idel gs, he ir flow is clculed using n equion of se nd he equions of conservion of mss nd energy. Finlly,, p/w, nd re clculed using he boundry inegrl equions. In his secion, he numericl model for he OWC wih wo wer chmbers nd wo ir chmbers (Fig.) is presened. The numericl model for he OWC shown in Fig.3 cn be obined by simple modificion of his model. () Equions reled o wve moion Assuming he fluid moion o be inviscid, incompressible, nd of smll mpliude, he poenil heory gives he linerized governing equions for he velociy poenil Φ(x,z;) s follows: Fig. Definiion skech of wo-chmber OWC wih wo ir chmbers. Φ= in he fluid () on SF,SF,SF () z g ( p p ) on SF g ( p p ) on SF (4) p g on SF (5) on S, S B (6) Fig.3 Definiion skech of wo-chmber OWC wih one ir chmber. he resuls of D numericl nlysis in frequency domin for he OWCs by g e l. s 5) mehod. The mjor physicl quniies exmined re he primry conversion efficiency, ; he reflecion coefficien, ; nd he ir pressure in he ir-chmbers, p/w ; where he pressure p is nondimensionlized using he specific weigh of wer, w, nd he inciden wve heigh,. The numericl where ζ is he wer surfce elevion; p is he mospheric pressure; p nd p re he dynmic ir pressures in ir chmbers nd, respecively; ρ is he densiy of fluid; g he ccelerion due o grviy; nd ν he uni norml vecor on he body surfce. The exernl free wer surfce, he sebed, he weed surfce of he body, nd he inernl wer surfces in chmber nd chmber re denoed by SF, S, S B, SF, nd SF, respecively. The rificil dmping force due o Ryleigh is denoed by μ in Eqs. nd (4). Combining Eqs.(),, nd (5) nd nd Eqs.(), (4), nd (5), he following equions re obined: 94

3 g on SF (7) z p g on SF (8) z z p g z z on SF (9) The fluid region is divided ino four: region, region, region nd region 3 s shown in Fig.. The wer deph is h in region. Region is he ouer region of he OWC. Regions nd 3 correspond o he fluid region in chmbers nd of he OWC, respecively. The velociy poenil Φ(x,z;) in region is obined s he soluion of Lplce s equion, which sisfies he free surfce nd he boom boundry condiions consn wer deph h s follows: ( xz, ; ) g cosh k( z h) e KRe e cosh kh ikx ikx i () where he firs erm in he righ-hnd side corresponds o he inciden wve, nd he second erm hs he complex consn represening he refleced wve. ζ in Eq.() denoes he mpliude of he inciden wve.the wve number k in he equion is obined by solving he following dispersion relion: gknh kh () The velociy poenil Φ, ir pressure in he ir chmbers p nd p, nd he coordine sysem re non-dimensionlized using wer deph h s g () i p () g Re p e ( xz, ; ) Re ( x, z) e i i () Re p g p e (4) i ( x; ) Re e (5) x z x, z (6) h h These dimensionless erms re used herefer wihou he primes. () The boundry vlue problem The boundry vlue problems for he poenil funcions in region ϕ (), in region ϕ (), nd in region 3 ϕ cn be wrien s ) Region () in he fluid (7) () () on SF (8) () on S,S B (9) () (, ) il il lz e Ke A ( z ) on RS () () il il (, lz) i e Ke R A( z) where b) Region () R cosh ( z ) A( z) cosh h g kh on RS () () () in he fluid ip i c) Region 3 () () on SF (4) on S B (5) in he fluid (6) ip i on SF (7) on S B (8) d) Kinemicl condiions on boundry DC () () (9) () () e) Kinemicl condiions on boundry ED () () Boundry inegrl equions The boundry enclosing he fluid region is divided ino elemens by poins (Fig.4). If we denoe he 95

4 is one. ence he ol number of source poins m in () () () () () Eq.(34) is ( ). b) Region Fig.4 Definiion of poenil funcion on boundries. cener nd he lengh of ech elemen by j=(ξ j,η j ) nd S j (j=~), respecively, relionships beween he poenils on he boundry ( ( j, j ) nd heir norml derivives ()( j ( j, j) re given by Green s heorem s where F ) Region Fmj Emj (33) j F E for region mj mj mj E for regions nd 3 mj mj mj E E mj mj log Rmjds s s j j log Rmjds mj j m j m R () () () () () () () mj mj mj j j F E F () 3 j () () () () Fmj 3 Emj 3 () () 4 5 () () () () () () mj 4 mj 4 mj 5 j j F E F () 6 () () R mj mj j K F i E () 6 j e il A( kz ) () () il Fmj i E mj e A( kzj ) j (34) The number of source poin m on he boundry SR () j () () () Fmj Emj i () () 3 () 4 j j F () () mj () () () () Fmj 3 Emj 3 () () () 5 6 () () () Fmj 4 i E mj p j j (35) The ol number of source poins m in Eq.(35) () () () () () () is ( ). c) Region 3 j Fmj Emj i j 3 j F mj Fmj 3 Emj Fmj 4 i E mj p j j (36) The ol number of source poins m in Eq.(36) is ( ) (4) Thermodynmics in ir chmbers The equions presened in his secion re pplicble o boh chmbers. Therefore, subscrips nd denoing he respecive chmbers re dropped here nd will be reinroduced ler. Assuming ir s perfec gs, he equion of se, he equion of coninuiy, nd he equion of conservion of energy re given s 7) p RT (37) d dm ( V) (38) d d 96

5 dv d p V dm p Cv CpTe d d R d (39) where ρ is he mss densiy of ir in he chmber, R he gs consn of ir, T he emperure in he ir chmber, T e he bsolue emperure of ir, T e =T for ouflow nd T e =T for inflow, V he volume of ir in he ir chmber, C v he specific he consn volume, nd C p (=C v +R) he specific he consn pressure, dm /d is he re of he mss of he ir ouflow (or inflow) hrough he nozzle on he ceiling of he ir chmber nd is expressed by dm d C C A C T T (4) e d s W P where C d is he coefficien of conrcion, C s he coefficien of velociy, nd T he bsolue emperure of ir in open ir. The re of he wer chmber sill wer level is denoed by A W =l c W where l c is he lengh of he ir chmber (equl o he ol lengh of OWC, B in Figs.~3) nd W he widh. The nozzle rio ε is defined s he rio of he re of he nozzle opening A n o A W. ρ e is he mss densiy of ir, ρ e = ρ for ouflow nd ρ e = ρ for inflow. ρ is he mss densiy of mospheric ir. In his pper, kgw nd Ueki mehod 8) is used in which he pressure nd he verge wer surfce elevion in he ir chmber is given bsed on Eqs.(37)~(4) nd by linerizing he nonliner erm in Eq.(4). We consider he cse of ouflow firs. The following equion is obined by using Eq.(37) in Eq. (38): i p() p ps() p Repˆ se i V () V Reve ˆ () ˆ i T T ReTse (44) where p ˆ, s ˆ nd Tˆ re complex mpliudes respecively. Subsiuing Eq.(44) ino Eq.(4) nd Eq.(43) s i nd compring he coefficien of e we obin pˆ ˆ s T p T vˆ i pˆ s i Re i e Re i e V p CCA d s W CT p Tˆ i Re e V T (45) (46) where γ(=c p /C v ) is he specific he rio. The nonliner erm in Eq.(46) is linerized s follows: where ˆ ˆ Re T i T i e Re e T T / / (47) Tˆ cos cos d (48) T d pv dm d RT d (4) We obin he following equion fer subsiuing Eq.(47) in Eq.(46) Elimining dm /d in Eq.(39) using Eq.(4) leds o dt R dp T d C p d p Eq.(43) is obined from Eqs.(37), (39), nd (4). (4) Cp dv Cv dp CpCCA d s W Cp TT (43) V d p d V We ssume he mgniude of he vriions in p, V nd T re smll enough so h hey cn be wrien s where ˆ ˆ ˆ i v i ps T V p T ˆ T / T CC d saw CT p V / cos cos d / (49) (5) From Eq. (45) nd Eq.(49) we obin 97

6 pˆ s i vˆ p i ( ) V (5) Eq.(5) is vlid for he cse of inflow s well. The volume of ir in he ir chmber is expressed s V V dxdy (5) SW (5) Primry conversion efficiency The equions presened in his secion re pplicble o boh he chmbers nd herefore subscrips nd denoing chmber nd chmber re dropped. The ol efficiency of he sysem is obined by dding he conribuions from he individul chmbers. The wve power of he inciden wve E W is expressed s where S W is he wer surfce in he ir chmber sill wer level. Subsiuing Eq.(5) in Eq.(5) nd compring wih he second equion of Eq.(44), we obin where E W g W (59) 4 f ( kh) vˆ dxdy (53) S W f( kh) cosh kh kh sinhkh (6) From Eqs.(5), (53), nd pˆ s g p we obin s p ic dx / l (54) s E c l W where l W is he wer line long x-xis in he ir chmber nd C E p gh D i ( ) (55) where D is he heigh of he ir chmber. Eqs.~(4) cn be used o express he complex mpliude of he free wer surfce ζ s ii p s (56) Finlly, by subsiuing Eq.(56) ino Eq.(54) nd discreizing,we obin he following for chmbers nd, respecively, where he corresponding subscrips hve been reinroduced: () CE () s ( ice) l c j p i x (57) j CE s ( ice) l c j p i x (58) j ere, l c nd l c re he lenghs of he bck nd he fron ir chmbers. For he OWCs under considerion (Figs.~3), l c =b c. The bsorbed power by OWC, E ir, cn be wrien s E p () Q() (6) ir where Q() is he ir ouflow (or inflow) re hrough he nozzle of he ir chmbers nd he overhed br denoes ime verge over period. Q() cn be wrien s Q () CCA C T T d s W P Tˆ i CCA d s W CT P Re e T Finlly, E ir cn be wrien s where E g p p ir Re s s CCA d s W p CT p (6) (63) (64) The serisk mrk in Eq.(63) denoes he complex conjuge. The primry conversion efficiency cn now be wrien s E ir (65) EW 98

7 3. VALIDATIO OF TE UMERICAL MODEL Owing o he lck of experimenl d for wo-chmber OWCs, he vlidion of he proposed numericl model ws done using he experimenl d of one-chmber OWC by Ojim e l. 6) The numericl model proposed in secion ws modified nd pplied o he one-chmber OWC (Fig.). The specificions of he OWC used in he numericl clculion is given in Tble. The vlues for C d nd C s re obined from Ojim e l. 6) The primry conversion efficiency, he reflecion coefficien, nd he ir pressure hve been ploed for vrious vlues of he nozzle rio, ε, nd he deph-o-wvelengh rio, h/λ. Figure 5 shows h for given wve period, increses wih he nozzle rio, peks nd hen decreses gin. Tble Specificions of OWC used for vlidion. Iems Vlues Lengh of OWC (B=l c ).4m Wer deph (h).6m Curin wll deph (d c ).m eigh of ir chmber (D ).4m γ T=.5s (cm) EXP. CAL h=6cm d c =cm B=4cm D =4cm... () T=.5s h=6cm d c =cm B=4cm D =4cm (cm) EXP. CAL. 4.5~ ~. 4. ~ ~. 3.7~5.4.. h/ () ε=/ h=6cm d c =cm B=4cm D =4cm (cm) EXP. CAL.. 4.5~5.9 9.~. 4. ~ ~... h/.3.4 (b) ε=/ Fig.6 Reflecion coefficien vs h/λ..8.6 p/w.4.. h/..3.4 () ε=/ (cm) EXP. CAL. 4.5~5.9 9.~. 4. ~ ~. 3.7~5.4 h=6cm d c =cm B =4cm D =4cm..8 T=3.s (cm) EXP. CAL...8 p/w (cm) EXP. CAL. 4.5~5.9 9.~. 4. ~ ~..6.4 h=6cm d c =cm B=4cm D =4cm.... (b) T=3.s Fig.5 Primry conversion efficiency vs nozzle rio..4 h=6cm d c =cm B =4cm D =4cm. h/..3 (b) ε=/3 Fig.7 Air pressure vs h/λ. 99

8 Tble Specificions for he nlysis of wo-chmber OWC. Iems Vlues Tol lengh of OWC (B=l c ).4m Lengh of bck ir chmber (lc ).m Lengh of fron ir chmber (b c =lc ).m Opening heigh of he bck chmber (d ).m Opening heigh of he fron chmber (d ).m Wer deph (h).6m Curin wll deph (d c ).m eigh of ir chmbers (D ).4m γ.45 Figure 6 shows h for given nozzle rio, decreses wih he relive deph, reches minimum, nd hen increses gin wih furher increse of he relive deph. As shown in Fig.7, he ir pressure increses wih he relive deph firs, reches mximum vlue, nd decreses gin wih furher increse of he relive deph. I is found from Figs.5~7 h he numericl resuls re in good greemen wih he experimen resuls for,, nd p/w. 4. UMERICAL AALYSIS () Primry conversion efficiency, ir pressure nd reflecion coefficien of wo-chmber OWC wih wo ir chmbers The vriions in he primry conversion efficiency, he reflecion coefficien, nd he pek ir pressure for he wo-chmber OWC shown in Fig. re nlyzed using he numericl model presened in secion. The specificions of he device under considerion is given in Tble. The vlues for C d nd C s re obined from Ojim e l. 6) Ech of he chmbers of he wo-chmber OWC conribues o he overll efficiency of he OWC. The ol efficiency is esimed s he sum of hese conribuions. The combined efficiency is beween 6 o 9 percen nd is lrger for shor wve periods s shown in Figs.8()~(d). In hese figures, Chr nd Chr denoe he bck chmber nd he fron chmber, respecively. The conribuion of chmber is much greer hn h of chmber for shor wve periods nd decreses wih he increse of he period. For T=.5s nd.5s, is highes for nozzle rio slighly greer hn /. For T=.s i is grees ε=/ nd for longer wve periods i is highes smller vlues of he nozzle rio.the pek ir pressures in he ir chmbers ploed gins h/λ rio re shown in Figs.9()~(d). The pressures in chmber nd pek differen vlues of h/λ. In generl, he pressure increses wih incresing h/λ, peks nd hen decreses gin. The reflecion coefficien is..8.6 T=.5s h=6cm d c =cm d =cm =cm B=4cm D =4cm Tol Chr Chr (cm) T=.5s () T=.5s Tol Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm T=.s (b) T=.5s Tol Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm T=.5s (c) T=.s Tol Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm... (d) T=.5s Fig. 8 Primry conversion efficiency vs nozzle rio.

9 .3. p/w. Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm. h/.4 () ε=/5.8.6 p/w.4.. h/.4 (e) ε=/3 Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm.4.3 p/w.. Chr Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm. h/ p/w..6.4 p/w. (b) ε=/5 Chr Chr (cm). h/.4 (c) ε=/ Chr. h/.4 (d) ε=/ h=6cm d c =cm d =cm =cm B=4cm D =4cm Chr (cm) h=6cm d c =cm d =cm =cm B=4cm D =4cm Fig. 9 Air pressure vs h/λ. ploed gins h/λ for vrious vlues of he nozzle rio s shown in Figs.()~(d). For nozzle rio /, he minimum vlue of is less hn.4. For nozzle rios / nd /3, hs he smlles mgniude for he relive deph rio of bou.5 o.. () Effec of curin wll deph nd fron chmber widh in wo-chmber OWC In his secion, he effecs of he vriions in he curin wll deph, d c, nd he fron chmber widh, b c, on, p/w, nd re invesiged. The wve heigh nd he nozzle rio in he clculion re.cm nd /, respecively. Figure shows h he primry conversion efficiency of chmber is independen of d c /h for ll wve periods. In he cse of chmber, for T=.5s nd.5s, he primry conversion efficiency decreses wih d c /h. This effec is more pronounced for T=.5s. owever, for longer wve periods here is sligh increse wih d c /h. Figure shows h he reflecion coefficien increses wih d c /h for T=.5s nd.5s nd decreses for T=.s,.5s nd 3.s. Figure 3 shows h no significn effec of d c /h on he ir pressure in chmber is noed. In chmber, for T=.5s nd.5s, he ir pressure decreses wih d c /h, nd for T=.s,.5s, nd 3.s, i increses by smll moun. Figures 4~6 show he effec of he vriions in b c /h on vrious physicl quniies. Figure 4 shows h for T=.5 s nd.5s, increses wih he increse of b c /h. For hese shorer wve periods, chmber is more significn hn chmber. For longer wve periods, decreses slighly wih b c /h. As for, i decreses wih b c /h for T=.5s nd.5s, nd increses slighly for oher wve periods (Fig.5). From Fig.6, i is found h for chmber, he pressure increses wih b c /h for T=.5s nd.5s, nd decreses slighly for oher

10 ..8.6 h=6cm d c =cm d =cm =cm B=4cm D =4cm (cm) h/..3 () ε=/5.4. (cm) h/..3 (e) ε=/3 h=6cm d c =cm d =cm =cm B=4cm D =4cm. h=6cm d c =cm d =cm =cm B=4cm D =4cm (cm) Fig. Reflecion coefficien vs h/λ h=6cm d =cm =cm B=4cm D =4cm Tol Chr Chr T(s) h/..3 (b) ε=/5 =.cm..4 d.6.8 C /h. h=6cm d c =cm d =cm =cm B=4cm D =4cm (cm) h/ (cm) (c) ε=/ h=6cm d c =cm d =cm =cm B=4cm D =4cm. h/..3 (d) ε=/ Fig. Primry conversion efficiency vs d c /h...5 =.cm h=6cm d =cm =cm B=4cm D =4cm T(S) d C /h.6.9 Fig. Reflecion coefficien vs d c /h. wve periods. For chmber, he ir pressure decreses wih b c /h for T=.5s nd.5s, nd increses slighly for oher wve periods. Comprison beween one-chmber OWC, wo-chmber OWC wih wo ir chmbers nd wo-chmber OWC wih one ir chmber The primry conversion efficiency, he reflecion coefficien, nd he pek ir pressure re compued for one-chmber OWC, wo-chmber OWC wih wo

11 .8.6 p/w.4 h=6cm d =cm b c =cm B=4cm D =4cm Chr Chr T(s) =.cm One-chmber OWC Two-chmber OWC wih one ir-chmber Two-chmber OWC wih wo ir-chmbers.4.. d C /h = 5. cm B Fig.3 Air pressure vs d c /h. Fig.7 Primry conversion efficiency vs λ/b..5. =.cm Tol Chr Chr T(s) One-chmber OWC Two-chmber OWC wih one ir-chmber Two-chmber OWC wih wo ir-chmbers.6.5 h=6cm d C =cm d =cm B=4cm D =4cm. /h = 5. cm B Fig.4 Primry conversion efficiency vs b c /h. Fig.8 Reflecion coefficien vs λ/b...5 =.cm h=6cm d =cm d C =cm B=4cm D =4cm p/w.6 One-chmber OWC Two-chmber OWC wih one ir-chmber (Two-chmber OWC wih wo ir-chmbers) Chmber Chmber T(S) /h = 5. cm B Fig.5 Reflecion coefficien vs b c /h..8.6 p/w.4. h=6cm d C =cm d =cm B=4cm D =4cm Chr Chr T(s) =.cm. /h.4.6 Fig.6 Air pressure vs b c /h. Fig.9 Air pressure in he ir chmber vs λ/b. ir chmbers nd wo-chmber OWC wih one ir chmber nd ploed gins λ/b rio where B is he ol lengh of he OWC. The dimensions of he device in he clculion re he sme s in Tble for one-chmber OWC nd Tble for wo-chmber OWC wih wo ir chmbers. The dimensions of he wo-chmber OWC wih one ir chmber re lso he sme s hose given in Tble. owever, in his cse, here is only one ir chmber wih one nozzle s shown in Fig.3. The wve heigh ws 5cm nd he nozzle rio ws / in he clculion. The primry conversion efficiency increses wih λ/b, reches mximum, nd decreses gin for he one-chmber OWC nd wo-chmber OWC wih wo 3

12 ir chmbers s shown in Fig.7. owever, for he OWC wih wo chmbers nd one ir chmber, shows wo peks ining lowes vlue λ/b=8. The reflecion coefficien shows similr rend where he wo-chmber OWC wih one ir chmber hs double roughs s shown in Fig.8. This resul is consisen wih he resul for. The vriions in ir pressure in he ir chmber s ploed in Fig.9 lso show wo peks nd rough for he OWC wih wo chmbers nd single ir chmber. The pek pressure for his OWC is greer hn h for he one-chmber OWC for lrger vlues of λ/b. The resul of our nlysis suggess h he wo-chmber OWC wih wo ir chmbers nd one-chmber OWC wih one ir chmber provide more smooh power oupu compred o he wo-chmber OWC wih one ir chmber. In ddiion, he pek vlue of of wo-chmber OWC wih wo ir chmbers is higher hn h of one-chmber OWC. ence, from he viewpoin of mximizing he power oupu, he wo-chmber OWC wih wo ir chmbers is more dvngeous. 5. COCLUSIOS This sudy invesiged wo-chmber OWCs using wo-dimensionl numericl mehod bsed on he velociy poenil heory in frequency domin. Clculions were mde for hree physicl quniies: primry conversion efficiency, ir pressure, nd reflecion coefficien. Comprison wih one-chmber OWC wih he sme physicl dimensions showed h primry conversion efficiency,, for he wo-chmber OWC wih wo ir chmbers ws slighly greer for longer wve periods. I ws lso observed h fron chmber ws more effecive shorer wve periods. As for he nozzle re rio, he vlue of ε for which he primry conversion efficiency is highes lies in he viciniy of /, nd he exc vlues differ depending on he inciden period. In he cse of he wo-chmber OWC wih one ir chmber, showed wo peks when ploed gins he wvelengh-o-lengh of OWC rio, λ/b. Though he pek vlues were lmos equl o he double chmber OWC wih wo ir chmbers, ws very smll round λ/b=8. The effec of nondimensionlized curin wll deph nd fron chmber widh, d c /h nd b c /h, respecively, on he hree physicl quniies ws sudied. o significn chnge ws found in he vlue of of he fron chmber wih he increse of d c /h. In he cse of he bck chmber, decresed wih he increse of d c /h for T=.5s nd.5s, nd incresed for oher wve periods. The ol lso showed similr behvior. For he cse of he widh of he fron chmber, he ol incresed wih he incresing vlue of b c /h for T=.5s nd.5s, nd decresed for oher periods. As expeced, for he fron chmber decresed rpidly wih b c /h nd vice vers for he bck chmber. REFERECES ) Cruz, J.: Ocen Wve Energy, Springer, 8. ) eh, T. V.: A review of oscilling wer columns, Philosophicl Trnscions of he Royl Sociey A, Vol.37, pp.35 45,. 3) Flnes, J., Oledl, G., Budl, K. nd Lillebekken, P. M.: Simulion sudies of double oscilling wer column, Inernionl Workshop on Wer Wves nd Floing Bodies, pp , ) sieh, M. F., Lin, I.., Dorell, D. G. nd sieh, M. J.: Developmen of wve energy converer using wo chmber oscilling wer column, The IEEE Trnscions on Susinble Energy, Vol. 3, Issue 3, pp ,. 5) g, S., Toyo, K., Imi, Y., Seoguchi, T. nd Mmun, M. A..: umericl nlysis on primry conversion efficiency of floing OWC-ype wve energy converer, Proceedings of he Tweny-firs Inernionl Offshore nd Polr Engineering Conference, pp ,. 6) Ojim, R., God, Y. nd Suzumur, S.: Anlysis of efficiency of pneumic-ype wve power exrcors uilizing cisson brekwers, Repor of he Por nd rbour Reserch Insiue, Vol., o.3, pp. 5-58, 983. (in Jpnese) 7) Tkhshi, S., Ojim, R. nd Suzumur, S.: Air power pneumic-ype wve power exrcors due o irregulr wve cions, Repor of he Por nd rbour Reserch Insiue, Vol.4, o., pp.3-4,989. 8) kgw,. nd Ueki, K.: Sudy on bsorbed wve power by ir chmbers inslled in brekwer, Journl of he Jpn Sociey of vl Archiecs nd Ocen Engineers, o. 5, pp. 55-6, 7. (Received Sepember 6, 4) 4