ENCIT2012-155

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Proceedings of ENCIT 2012 14 th Brazilian Congress of Thermal Sciences and EngineeringCopyright 2012 !y "BC# No$em!er 1%&22' 2012' (io de )aneiro' ()' Brazil

NUMERICAL SIMULATION OF SEA WAVE ENERGY CONVERTERSUSING THE OPENFOAM SOFTWARE

Jeferson Avila So !a" #aso !a$f r%&'rLi(r)io An*r( Isol*i" lier)ioisol*i$%+ail&)o+Eli!al*o ,o+in% es *os San-os" eli!al*o$i'es-&)o+&'rUniversidade Federal do Rio Grande FURG, Escola de Engenharia, Av. Itlia, Km 8, S/ , !E" #$%&'(#&&, Rio Grande, RS,)rasil

Ma-e s *as Neves Go+es" +a-e s&%o+es$if.r&e* &'rInstit*to Federal do "aran +IF"R ( R*a Ant-nio !arlos Rodrig*es, '. "aranag*/"R, )rasil.

L i! Al'er-o Oliveira Ro)/a" laoro)/a$%+ail&)o+Universidade Federal do Rio Grande do S*l, 0e1artmento de Engenharia 2ec3nica, "orto Alegre, Rio Grande do S*l, )rasil.

Abstract. In this work OpenFOAM software is used to simulate the generation of regular gravity waves inside a

rectangular tank. Interaction between the generated waves and an oscillating water column (OW ! device" used toconvert wave energy into electrical energy" is also simulated. #he main goal of this work is to develop a numerical

strategy to simulate OW converters using OpenFOAM. Obtained results for the regular wave generation werecompared with analytical solution. Ma$imum errors of %&' were observed between numerical and analytical results

for the wave crest elevation. For the OW device" it was investigated the influence of the lip" distance between thewater mean level and the depth of submergence of the OW " on the mass flow passing through the device s chimney.

)esults showed that for the wave climate tested" an increase in the lip length results into a decrease in the mass flowrate.

Keywords * wave energy" OpenFOAM" +umerical simulation" ,OF

0& INTRO,UCTION

Energ4 generation is a 5e4 iss*e 6or technological develo1ment o6 a co*ntr4. It is needed in all segments o6 theind*str4 and m*st 7e ade *atel4 s*11lied. !*rrentl4, most o6 the energ4 generated in the 9orld is 1rovided 74 nonrene9a7le so*rces li5e coal, 1etrole*m and n*clear 6*el. :hese so*rces can 7e *sed to contin*o*sl4 1rod*ce largeamo*nts o6 energ4 since the4 are not s*7;ect to climatic 6actors, ho9ever the4 are not rene9a7le and highl4 1oll*tant.Alternativel4, h4droelectric so*rces are non 1oll*tant and rene9a7le and have 7een s*ccess6*ll4 *sed 9orld9ide 6oralmost a cent*r4, ho9ever this is a limited reso*rce and not availa7le 6or all co*ntries. Some o6 other non 1oll*tantrene9a7le o1tions are the 9ind, solar and tide +9ave energ4. ation.

)eca*se o6 its long coast and the 6act that most o6 the 1o1*lation lives close to the sea, 9ave energ4 ma4 7e o6 greatinterest to )ra>il. In this conte=t, it is necessar4 to develo1 ne9 technologies ade *atel4 ada1ted to the )ra>ilian seaconditions.

:here are man4 t41es o6 energ4 converter devices 9hich can 7e classi6ied according to their o1erating 1rinci1al as?+i @scillating

0esign and constr*ction o6 s*ch devices +1rotot41es is *s*all4 a com1le= and highl4 e=1ensive o1eration. In thisconte=t, n*merical sim*lation a11ears as an attractive tool 6or the earl4 stages o6 develo1ment and/or o1timi>ation o6geometr4 and o1erating condition o6 these e *i1ment. @verto11ing and oscillating 9ater col*mn are t9o t41es o6 9aveenerg4 converters that have 7een s*7;ect to n*merical investigations 74 )ra>ilian researchers +Gomes et al., %&CIahn5e at al., %&, 2achado et al., %&BB . In all o6 these 9or5s, the D@F +Dol*me o6 Fl*id method have 7eens*ccess6*ll4 *sed to model sea 9ave movement and its iteration 9ith s*ch devices. All sim*lations have 7een

1er6ormed 9ith F UE : so6t9are 9hich is a general !F0 +!om1*tational Fl*id 04namics code 1rovided 74 A S S+htt1?//999.ans4s.com/ . Alternativel4 to F UE :, @1enF@A2 is an o1en so*rce !F0 code that is also ca1a7le o6sim*late this 5ind o6 1ro7lem. :he main advantage o6 @1enF@A2, i6 com1ared 9ith F UE : 9hich is a 1a4edso6t9are, relies in that 6act that it is a 6ree so6t9are licensed *nder the G U General "*7lic icence+htt1?//999.gn*.org/licenses/g1l.html .

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:he *se o6 @1enF@A2 has constantl4 increased in the last 6e9 4ears. Recentl4 a ne9 version +%.& has 7eenreleased 9ith a n*m7er o6 im1rovements. In the 1artic*lar case o6 modeling 1ro7lems 9ith the D@F method, there are an*m7er o6 9or5s that have s*ccess6*ll4 *sed @1enF@A2 + a7la et al., %&BB, Favero et al., %&B& .

In the 1resent 9or5, a %0 model develo1ed in @1enF@A2 so6t9are is *sed to sim*late n*mericall4 gravit4 9avesgenerated in a rectang*lar tan5. :he sol*tion is 6irst validated 74 direct com1arison 7et9een n*merical and anal4tical

sol*tion 6or reg*lar 9aves and in a 6lo9ing ste1 *sed to model the interaction these 9aves 9ith an @

1& MATHEMATICAL FORMULATION

In 1resent sol*tion, the D@F method + irt and ichols, B#8B is *sed. :he D@F is a m*lti1hase model *sed tosolve 6l*id 6lo9 1ro7lems 9ith t9o or more inviscid 6l*ids. In this 6orm*lation, all 1hases are 9ell de6ined and thevol*me occ*1ied 74 one 1hase can not 7e occ*1ied 74 other 1hases. In the D@F method, a vol*me 6raction 6or each

1hase f i is de6ined s*ch as?i i6 f i H & the cell is em1t4 9ith 6l*id o6 1hase iCii i6 f i & the cell is 6*ll 9ith 6l*id o6 1hase iCiii i6 & J f i J B the cell contains the inter6ace 7et9een 1hase i and one or more other 6l*ids.

For the 1artic*lar case o6 modeling 9ater and air, onl4 t9o 1hases are considered in the 6orm*lation.A single set o6 moment*m and contin*it4 e *ations is a11lied to 7oth 6l*ids, and the vol*me 6raction o6 each 6l*id

in ever4 com1*tational cell +control vol*me is trac5ed thro*gho*t the domain 74 the addition o6 a trans1ort e *ation6or the vol*me 6raction f . :he model is com1osed 74 the contin*it4, vol*me 6raction and moment*m e *ations as6ollo9s?

t

, = 0 +B

f t

f , = 0 +%

, t

, , = p g +'

9here f is the vol*me 6raction o6 resin, - is the densit4 5g/m'

L, the a7sol*te viscosit4 "a sL, t the time sL, V thevelocit4 vector m/sL, g the gravit4 vector m/s %L, the stress tensor "aL and p the 1ress*re "aL.As a single set o6 moment*m and contin*it4 e *ations is *sed 6or 7oth 1hases, average 1ro1erties and need to

7e de6ined. :hese 1ro1erties can 7e a11ro=imated as +Srinivasan et al., %&BB

= f water +( 1 f )air +

= f water +( 1 f )air +A schematic re1resentation o6 the com1*tational domain 9ith the *sed 7o*ndar4 conditions is sho9n in Fig. B.

Fig. B ( !om1*tational domain 6or the 9ave tan5 sim*lation

In Fig. B, a rectang*lar tan5 9ith dimension * d is initiall4 hal6(6illed 9ith 9ater. :he inlet section is de6ined atthe lo9er 1art o6 the le6t 9all +dotted line 9here a transient 1rescri7ed velocit4 7o*ndar4 condition is *sed to ind*cethe 9ave generation +E s. + M and +8 . :he other 7o*ndar4 conditions are? 1rescri7ed 1ress*re e *al to >ero +ga*ge atthe sections re1resented 9ith a dashed line in Fig. B, no(sli1 condition at the 7ottom and right 9alls and 6or the @

1ro7lem +Fig. , no(sli1 condition at the cham7er and chimne4 9alls.:he second order Sto5es 9ave theor4, 1resented 74 0ean and 0alr4m1le +B##B , is *sed to eval*ate the velocit4

1ro6ile at the inlet section. A schematic re1resentation o6 the 9ave 9ith its characteristic 1arameters is sho9n in Fig. %.

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In this theor4, the 6ree(s*r6ace o6 9ater + is e=1ressed as

= A cos k $ t +$

9here A is the 9ave am1lit*de mL, k % /l is the 9ave n*m7er m(B

L, = 2 / # is the ang*lar 6re *enc4 s(B

L,# the9ave 1eriod sL, l the 9ave length mL and t the time sL.

:he velocit4 in the $ and / directions, res1ectivel4, are e=1ressed as

u= A g k cosh k / k h

cosh k h cos k $ t

3

4 A2 k

cosh 2 k h / sinh

4k h

cos [2 k $ t ] +M

w= A g k senh k / k hcosh k h

sen k $ t 3

4 A2 k

sinh 2 k h / sinh

4k h

sin [2 k $ t ] +8

9here g #.8B m/sN is the gravit4 acceleration.

Fig. % (

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Fig. ' ( *merical and anal4tical sol*tion com1arison + $ %& m

6&lip INFLUENCE TO THE OWC ,EVICE PERFORMANCE

:he 1ro7lem geometr4 is sho9n in Fig. . !*rrent sol*tion is similar to the 9ave tan5 sim*lation 1resented insection ' 9ith the di66erence that an @

Inlet+all

+all

"ir

,+C cham!er

"ir Inlet-o.tlet

' m %./ m

$ m

&./ m

&./ m

&.&/ mChimney

+all/ip

Fig. ( !om1*tational domain 6or the @

:he lip in6l*ence to the @

2ass 6lo9 rate is eval*ated at the air inlet/o*tlet section o6 the chimne4 +Fig. . :he mass 6lo9 rate as a 6*nction o6time 6or di66erent lip lengths is sho9n in Fig. .

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Fig. ( ip in6l*ence on mass 6lo9 rate

In Fig. , 1ositive 6lo9 rate indicates that the air is leaving the cham7er thro*gh the chimne4 9hile negative 6lo9rate indicates that the air is entering the cham7er. In this anal4sis, the cham7er vol*me a7ove 9ater level is 5e1tconstant, ho9ever the s*7merged vol*me increases 9ith the increasing o6 the lip . For this 1artic*lar case, as sho9 inFig. , the e66ect o6 increasing the lip res*lts in decreasing the 6lo9 rate thro*gh the chimne4, 9hat is an *ndesired

7ehavior.:he total mass + mtotal o6 air 1assing thro*gh the chimne4 s inlet/o*tlet section d*ring the 8s sim*lation is acco*nted

74

mtotal = t +B&9here is the air densit4 5g/m L, is the vol*metric 6lo9 rate m /sL, and t the n*merical sol*tion time ste1 sL.

:he amo*nt o6 air 1assing thro*gh the chimne4 d*ring the 8s sim*lation is sho9 in sho9n Fig. B. :his 6ig*re sho9san almost linear +inversel4 relationshi1 7et9een the l ip and the mass 1assing thro*gh the chimne4.

0 01 0 02 0 0 0 04 0 0 0 03 0 0 0 0% 0 05 0 100 000

0 00

0 010

0 01

0 020

0 02

Lip (m)

M a s s

( k g

)

Fig. $ ( 2ass o6 air 1assing tho*ght the chimne4 d*ring the 8 s sim*lation 1eriod

7& CONCLUSIONS@1enF@A2 so6t9are, 9hich is and o1en so*rce !F0 1ac5age, has 7een *sed to sim*late an @

9ave climate 9as arti6iciall4 generated 74 im1osing a 1rescri7ed velocit4 7o*ndar4 condition to the le6t 9all o6 thedomain. Sol*tion 9as 6irst validated in a sim1le 9ave tan5 sim*lation 9here the anal4tical 9ater level is com1ared 9ithn*merical res*lts and then *sed to investigate the in6l*ence o6 the lip to the mass 6lo9 rate 1assing thro*gh the device schimne4.

It 9as o7served that increasing the lip , the mass 6lo9 1assing thro*gh the chimne4 +entering or leaving thecham7er is red*ced. Since the energ4 that can 7e e=tracted 6rom the air is 1ro1ortional to the vol*metric 6lo9 rate,res*lts 1resented in Fig. $ indicates that the lip 1arameter is an im1ortant varia7le to 7e controlled.

8& AC3NOWLE,GMENTS

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:he a*thors than5 the F*ndaT o de Am1aro V "es *isa do Estado do Rio Grande do SU +FA"ERGS and the!onselho acional de 0esenvolvimento !ientW6ico e :ecnolXgico +! " 6or the 6inancial s*11ort.

9& REFERENCES

)aha;, A.S., %&BB. YGenerating electricit4 6rom the oceansY. Rene9a7le Z S*staina7le Energ4 Revie9s, Dol. B , o. M, 11. ''##(' B$.

!lement, A., 2c!*llen, "., Falcao, A., Fiorentino, A., Gardner, F., ammarl*nd, K., emonis, G., e9is, :., ielsen,K., "etroncini, S., "ontes, 2., Schild, "., S;ostrom, )., Sorensen, . and :hor1e, :., %&&%. Yo, .S.2. and [asa5, ., %&B&. YDiscoelastic 6l*id anal4sis in internal and in 6rees*r6ace 6lo9s *sing the so6t9are @1enF@A2Y. !om1*ters Z !hemical Engineering, Dol. ' , o. B%, SI, 11. B#8 (B##'.

Gomes, 2. ., Isoldi, .A., @linto, !.R.@., Rocha, .A.@. and So*>a, [.A.. %&. Y *merical sim*lation and lengtho1timi>ation o6 the 9ater col*mn oscillating deviceY. In "roceedings o6 the '&th I7erian( atin(American !ongresson !om1*tational 2ethods in Engineering ( !I A2!E. ArmaT o dos )\>ios, R[, )ra>il.

a7la, F., 2arschall, ., inrichsen, @., 0ietsche, ., [asa5, . and Favero, [. ., %&BB. Y *merical sim*lation o6viscoelastic t9o(1hase 6lo9s *sing o1enF@A2 +R Y. !hemical Engineering Science, Dol. $$, o. %%, 11. 8M(

#$.irt, !.ar, A.[. and Saito, K., %&BB. Y2odeling the disintegration o6 mod*lated li *id ;ets *sing vol*me(o6(6l*id +D@F methodolog4Y. A11lied 2athematical 2odeling, Dol. ' , o. 8, 11. 'MB&('M'&.

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ENCIT2012-155