BEM-FDM modeling of water free surface interaction with trapped air in OWC chamber for calculating generated power

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1 I. J. M. Sc. Eg., 3, 77-84, Summe ISSN IAU BEM-FDM modelg of e fee ufce eco h pped OWC chmbe fo clculg geeed poe M. Ghod Hbd Gdue School of Me Scece d Techolog, Scece d Reech Bch, Ilmc Ad Uve, Teh, I Receved 9 Jue ; eved Jul ; cceped 8 Jul ABSTRACT:Fee ufce modelg pl mpo ole ome oce ucue deg, epecll Ocllg We Colum OWC devce. Boud eleme mehod BEM uble mehod fo fee ufce modelg due o mplc, uc olvg, d lo d oge eueme. I h ppe, BEM ued fo fee ufce modelg OWC chmbe d ou of. Le emc d dmc boud codo ee ued fo fee ufce ou of OWC chmbe d ole fom ee ued fo fee ufce he chmbe. Thee boud codo ee deced b fe dffeece mehod FDM. Alo, ome hemodmc elo ee ppled fo pped behvo modelg OWC chmbe. Wve pecfco Chbh ego due o hgh poe ve eeed pogmmg code pu d. The eul ho good geeme h eul of ohe eeche. Alo, cocluded h I e ve hve o good poel fo ue od OWC devce, becue, lle poe bou KW c be eced fom OWC, he be po. Keod: OWC; BEM; FDM; fee ufce modelg INTRODUCTION OWC poe pl e he mo pevle ufce ve eeg bobe he old. Lmpe, Ope, d co l e ome of he fmou OWC model G d Foeo, 7. Oe of he m deg pmee of hee poe pl effcec d eleccl oupu. Thee pmee deped o ube d, cde ve pecfco, OWC ucue, d ec. m eeche hve focued o ube deg pmee Mohmed e l, ; hu, 8; Shml e l, 4; edgo d Smeo, 3; Fg d Auld, 3. Aohe mpo em hch he b of geeed poe fee ufce moo. Fee ufce modelg he mo mpo p of OWC deg, becue, deeme ohe deg pmee. BEM oe of he be mehod fo h modelg due o uc olvg d mplc. I ome eeche, Aud ofe BEM bed h bee ued fo OWC modelg ougl Cu e l, 7. Opmo of OWC poe pl Aoe h bee pefomed co Ild Joe d Cleme, 7.Alo, ome epemel eeche h bee focued o OWC poe pl Thuvem e l, 5. I h ud, boud eleme mehod hch * Coepodg Auho Eml: m.ghod@bu.c. Tel: / F: coupled h fe dffeece mehod ued fo fee ufce modelg h Chbh co ve pecfco pogmmg code pu. Th oe h he hghe ve poe I co le. Fee ufce ve moo OWC chmbe ffec o pped he chmbe d cue o ube p. Thee clculo ee pefomed fo Chbh oe I co le. MATERIALS AND METHODS Seme of poblem I he pee ud, he ve deco umed o be pepedcul o hoele d de ll of OWC poe pl e pllel o hoele. Fg. ho OWC poe pl chemcll. Fg. : he poblem of ve eco h OWC poe pl

2 M. Ghod Hbd A llued Fg., oluo dom hlved due o mme. I h ce, compuo me d CU uge e ocebl educed. Smme ple Fg. : he hlf of oluo dom The dom dvded o hee oe b og mehod fo peveg gul poblem. Fg. 3 ho hee hee oe. No-dmeol euo d boud codo. Nole e ve I h ud, he flud e umed o be vcd d compeble, he flo e ool, d he effec of cpll e goed. Theefoe, poel euo ued goveg euo o-dmeol fom. Alo, fee ufce ole boud codo, gd bod boud codo, d ommefeld f feld boud codo e ued De, 99; Scho, 99. Thee euo o-dmeol fom e belo: he flud A A o he fee ufce A A [ ] A A C h o he boom The o-dmeol pmee e: Zoe Zoe 3 Zoe Fg. 3: hee oe of he poblem 78

3 I. J. M. Sc. Eg., 3, 77-84, Summe g ; C C g ω ω g A g ; A ρ g V ; V ; 3 L Lg L K K ρ 3 L g I hch ^ g fo llug odmeol fom of ech pmee. Alo,,, d e compoe of Ce coode, d,,, F,, V,, L, g, A,, d K e ve umbe, me, gul feuec, poel fuco, peue, volume, ve mplude, ve legh, gvol cceleo, mmum mplude, volume flo e, d ube lo coeffce, epecvel. Whe e ve e ecoueed o obcle, poel fuco F geeed hch upepoo of hee poel fuco cued b cde ve, ceed ve, d ded ve Fle, 4. Theefoe, he follog euo e ued fo he poblem of h ppe. Â coh π ẑ ĥ. e ω coh π ĥ, π ω 3 The bove euo e ppled fo oe, ccodg o Fg. 3. Thee euo e mll ued fo oe d.. Tpped fomulo Aohe p of he poblem he modelg of he volume ecloed he OWC chmbe bove he e fee ufce. The peue he chmbe e vble fo hch e euo ece. Th peue ec o he hdodmc poblem hough he dmcl fee-ufce codo E.. Hdodmc d eodmc e heefoe ogl coupled. Fg. 4 ho chemc ve of OWC chmbe h pped pmee o. Fg. 4: cheme of OWC chmbe B codeg Fg.4, he follog euo e obed b ug hdodmc d hemodmc pcple Joe d Cleme, 7. 4 K K Whee,, d e flo e fom ube, mophee peue, d gge peue of pped, epecvel. ρ ρ V γ ε 5 K V ρ V I hch, g, V, e,, d ρ e he o of he cpce.4 fo, volume of pped, co umbe he flo d he flo ou, vble de, d mophee de, epecvel. I umed h he poce eopc. Hece: γ γ ρ ρ 6 Fom euo 4 d 5, e hve: & / γ γ ε / γ KV / γ V& V Th euo coupled h dmc boud codo E. d peue clculed ech me ep. I h euo, de h bee elmed. Theefoe, c be el coupled h hdodmc euo. Alo, he follog euo e eeded o complee clculo. vd d B B d B V & We fee ufce Tpped V Tube

4 8 BEM-FDM modelg of e fee ufce eco h pped V V V 9 The fl fom of peue euo follo: / / / V K V γ γ γ ε γ & Numecl modelg udlel mehe geeed o boude of hee oe. Fg. 5 ho mehe o he geome of oluo dom. Alo, Fg. 6 ho hoe hee oe cloe o ech ohe. Fg. 6: udlel mehe o hole of oluo dom I ode o olve he Lplce euo h ll boud codo, he Gee fuco ued d he goveg euo c be fomed o he boud egl euo ho Kdel, : Ψ Ψ d p p p ],, [ π α Whee 4π Ψ I hch p ouce po d Y fudmel oluo. Dchle d Neum ue of boude ee obed b dceg egl euo boud eleme mehod. The me mchg d he hpe of fee ufce ech me ep eue dceg d olvg he emc d dmc boud codo of fee ufce. The fe dffeece mehod eleced fo dceg he fee ufce boud codo. The hpe of fee ufce of e modfed b ple epolo ech me ep. Kemc boud codo o commo ufce of ol d e dceed belo: / / ] [ 3 / / ] [ 4 I hch, upe cp ho h d h me ep. ] [ b b c c b Fg. 5: udlel mehe o ufce of hee oe 5

5 I. J. M. Sc. Eg., 3, 77-84, Summe b b γ ρgl / γ ε / γ K V V / γ 6 7 Co pmee, b, c,, d b ee oduced euo 3 o 6, e beee eo d. If hee pmee e eul o, he oluo ll be full mplc; hoeve, f he e eul o eo, he oluo ll be full eplc. Dffee ue of hee pmee deeme he egh of dffee mplc d eplc em euo. Fo lohg D ecgul coe he opmum u of, b d c e.7,.5 d.5, epecvel Abbpou d Ghod,. I h ud, b, b, d c e eul o.5, me Abbpou d Ghod eech. Bu d e eleced.3 fo bl of umecl compuo. Fo el gul po, lcl ego ued ed of Gu ego. Th cued covegece me mchg Abbpou d Ghod,. RESULTS AND DISCUSSION Befoe peeg eul, he pogmmg code hould be vefed. Theefoe, OWC poe pl Aoe ld co l, ougl hch h bee modeled b Joe d Cleme Joe d Cleme, 7, modeled g pee eech. The eul ho good geeme h Joe d Cleme eul. Fg. 7 ho he geome pecfco of he meoed poblem. Fee Sufce eue of ee Reech Fg. 8 llue compo beee eul of h ud d Joe d Cleme ud. I h poblem, ve mplude d peod e m d, epecvel. [] Fg. 8: Compo of fee ufce peue eul of pee ud h Joe d Cleme ud m Alo, cpue dh pmee ε m comped h Joe d Cleme eul. I h m m h 7.8 m OWC chmbe We fee ufce Wve deco hoc.5 m h7.8 m Sebed Fg. 7: Scheme of OWC poe pl ued Joe d Cleme eech 8

6 M. Ghod Hbd fomulo, m poe pg fom ube d m me cde poe pe mee of ve ce. Fg. 9 ho h compo. I OWC devce, peue dffeece beee de d oude he chmbe ll cue he ube o p. The de peue vo e cued b e colum ocllo. Thu, peue clculo ech me ep mpo pmee o ob he elecc poe geeed b OWC. Vo of peue OWC chmbe hve bee llued Fg.. I h fgue, me beg fom 5 ll oe peod, becue, fee ufce ocllo becme ed e fe 5. Fg. 9: Cpue dh of co l OWC veu ve peod ve mplude.78m Tble ho ve pecfco of Chbh ego. Thee ue e mmum ue fo degg he o codo MO, 7. Thee m ueo fo degg OWC poe pl. Ho much elecc poe pecfed OWC poe pl c poduce? Fo h pupoe, hdodmc d eodmc clculo fom cde ve o ube ehu hve bee doe b BEM-FDM model, pee eech. Fg. : A peue OWC chmbe oe peod Clculg poe he fl pupoe of h ud. Fg. ho o-dmeol eou Tble : Icde ve pecfco u o OWC chmbe mee ue decpo Nodm.. mee ue A m.475 Wve mplude Â.39 T ec 4.7 eod T.57 h m 5 We deph L m 34. Wve legh L ĥ.439 ec.5 Tme ep.537 X fo m 75 F feld X behd m Behd ll dce X f m Legh of fee ufce he chmbe K 9.4 Lo coeffce of ube degee 75 Agle beee fee ufce d OWC fo ll.93 X fo.585 X behd.9 X f.865 K

7 I. J. M. Sc. Eg., 3, 77-84, Summe poe hch clculed oe peod. Alo, h poe clculed b dmeo hch e oduced h ppe. Fg. ho poe epec o me. Fg. : No-dmeol poe epec o o-dmeol me oe peod Fg. : A poe epec o me oe peod A eul, he vege cpue dh d poe oe peod e 4.748m d.87 KW, epecvel, b codeg ple cuve fg fo clculed d. I ohe od, uul OWC poe pl he be poo of I e fom cde ve poe po of ve c geee bou KW. CONCLUSION Accodg o ome old eeche, bou 5% of pped poe OWC chmbe c cove o elecc poe Cu e l, 998. I he e fe e, ell ube mpoved d he effcece ceed o 65% ome ce edgo d Smeo, 3; Fg d Auld, 3. I eech, he effcec of ell ube ouced beee 7% d 8% Flco, 4. Afe h, uppe effcec h o bee epoed ll o. If e code mmum effcec fo ell ube 8% he mo opmc e, OWC poe pl c poduce bou 9.5 KW elecc poe. I eem h o covee d ffodble fo I e. Thu, e hould ech fo ohe fo ecg e ve eeg. Sce OWC poe pl e he mo uul d commecl ufce ve eeg covee he old, ug ll be cluded ome dvge. A uggeo, ug pbolc de ll bede OWC chmbe c mpove OWC fo pplg I. REFERENCES Abbpou, M.; Ghod Hbd, M.,. Compg he lohg pheome D ecgul coe h d hou poou medum ug eplc ole BEM-FDM. J. of Sce Ic, Tco B: Mechcl Egeeg, 7, 93-. Abbpou, M.; Ghod, M. H.,. Deg of e cheme o dce he dom of pplcbl of e gul ppoch D BEM. Egeeg Al h Boud Eleme., 35, Cu, J. M. B..; Smeo, A. J. N. A., 7. Se e chceo of he e e of offhoe ve eeg pl. Oce Egeeg., 34, Cu, R.; Whe, T. J. T.; Se T.., 998, Aeodmc coveo of oce poe fom ve o e. Eeg Cove. Mgm., 396-8, De R. G.; Dlmple R. A., 99. We ve mechc fo egee d ce. Wold Scefc., 3 d edo. Flc o A.F., 4. Sochc modelg ve poe-eupme opmo: mmum eeg poduco veu mmum pof. Oce Egeeg, 3, Fle, J., 4. Oce ve d ocllg em: Le eco cludg ve-eeg eco. Cmbdge Uve e. Fg, T.; Auld, D., 3. Model Teg of Vble-ch Aeodmc Tube. oc. 3h I. Offhoe d ol Eg. Cof, ISOE, G M.; Foeo., 7. Reeble eouce d eeble eeg, globl chllege. Tlo & Fc Goup. Joe, C.; Cleme A. H., 7. A me-dom umecl mulo fo ocllg e colum ve poe pl. Reeble Eeg, 3, Kdel J. T.,. Boud eleme: heo d pplco. edo, Eleve Scece Ld. Mohmed, M. H.; Jg, G.; p, E.; Théve, D.,. Mul-objecve opmo of he fol hpe of Well ube ued fo ve eeg coveo. Eeg., 36, edg o, J.; Smeo, A., 3. Ovell-effcec opmo OWC devce. Appled Oce Reech, No. 5, MO, 7. I e ve modelg- The ve fo he 99 o 3 - Om Se d e Gulf, o d Me Og., f Ed., Vol.. 83

8 BEM-FDM modelg of e fee ufce eco h pped hu, V.A., 8. The ube pl effcec: Mmum effcec ed d he he of dvdul ge. Appled Theml Egeeg., 8, Scho S. H., 99. Egh e of Sommefeld do codo. Ho Mhemc. 94, Shml, N.; Jlhl,.; Sm, A. K.; Rvd, M., 4. Wve poeed delo em. Eeg., 9, Thuvem, K.; Neelm, S.; So, M., 5. Nobeg ve foce o muleo ocllg e colum ve poe co bee, J. of We, o, Col d Oce egeeg, 3, Ho o ce h cle: Hvd le Ghod Hbd, M.,. BEM-FDM modelg of e fee ufce eco h pped OWC chmbe fo clculg geeed poe. I. J. M. Sc. Eg., 3,