DOUBLE PHASE COAXIAL GAS HEATER FOR MOLTEN CARBONATE FUEL CELL

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1 EFAT005 t Intrnatonal Conrnc on at Transr, Flud cancs and Trmodynamcs Caro, Egypt Papr numbr: RF DOUBLE PASE COAXIAL GAS EATER FOR OLTEN CARBONATE FUEL CELL Cotana F, Ross F and Flppon Unvrstà dgl Stud d Pruga Dpartmnto d Inggnra Industral Va G. Durant, 67 Pruga, 065 Italy E-mal: cotana@unpg.t, ross@unpg.t, lppon.unpg@cra.t ABSTRACT An orgnal small sz, modular moltn carbonat ul cll (CFC) as bn patntd (patnt n : PG 00 A 009) by rsarcrs o t Unvrsty o Pruga. T proposd CFC may b convnntly mployd or µcp rsdntal applcatons bcaus o: - g cncy; - long l; - natural gas supplyng. Bcaus o t small sz and compact gomtry o t proposd CFC stack, a partcular systm or natural gas and watr ntroducton s rqurd: natural gas must b atd (stack tmpratur s 650 C) and md wt stam n ordr to attan anodc umdcaton wc s vry mportant to mprov CFC workng l []. In ts work, a doubl lud (watr, natural gas), pas transton at cangr wc s sutabl to stack gomtrcal constrants s proposd and studd; t s composd by two coaal pps. Two drnt solutons av bn analyzd wt drnt stam and ul gas arrangmnts. By ormulatng and solvng an orgnal quatons systm, t gomtrcal conguraton tat mnmzs t cangr dmnson as bn dntd. INTRODUCTION T CFC lctrolyt s a moltn carbonat salt mtur, usually ltum carbonat and potassum carbonat. T lctrolyt s kpt n cramc matr. Cll opratng tmpraturs rang s C. g-tmpratur moltn carbonat ul clls can b d by ydrogn attand by a varty o ydrocarbons usng tr an ntrnal or trnal rormr. CFC can tolrat gr amounts o carbon monod wt rspct to low tmpratur ul clls, wc maks natural gas mor attractv or ts typ o ul cll []. In ts work a doubl lud pas transton at cangr or an orgnal small sz and ntrnal rormr CFC s studd. Bcaus o t pcular CFC stack gomtry watr and gas natural ntroducton must b carrd out by two coaal pps. Pps ar soakd nto unorm tmpratur nvronmnt: CFC anod compartmnt. at cangr am s to: - warm mtan up to 650 C; - vaporz watr; - warm stam up to 650 C; - m gass (mtan and stam) or rormng. By ormulatng and solvng an orgnal quatons systm, t gomtrcal conguraton tat mnmzs t cangr dmnson as bn dntd. TEORETICAL ANALYSIS In ordr to t small sz ul cll dmnsons, t only gomtrcal soluton allowd s a sngl pp wr at cang occurs. A coaal pp soluton s adoptd; t pp s mad up by two sctons: - t rst scton s consttutd by two coaal pps wr luds sparatly, on nsd ntrnal pp and t otr nsd trnal pp; - t scond scton s consttutd by a sngl pp wr two luds, bot n gas pas, ar md. In t rst scton, at s absorbd n part by lud tat s n t trnal annular scton, n part s transmttd to nnr pp lud. Coaal pp caractrstcs ar sktcd n Fg.. 0 mm Outr pp 65 mm mm mm Innr pp Fgur : Coaal pp caractrstcs. Pag o 6

2 Two drnt gas arrangmnts av bn analyzd: - Cas : watr n t outr pp and mtan n t nnr pp; - Cas : mtan n t outr pp and watr n t nnr on. Cas analyss In Fg. t coaal pp scm s sktcd; tr sgmnts may b obsrvd: - sgmnt L, wr watr ats rom room tmpratur (scton 0) up to saturatd lqud condton at 00 C (scton ); - sgmnt L, wr watr pas cang taks plac (scton ); - L sgmnt, wr mtur (C + O) s atd up to 650 C. C Scton 0 L dq Pas cang dq Scton L Pas cang dq dqc Scton Turbulnt/ Lt Fgur : Coaal pp scm. L Ll Scton at balanc as bn ound assumng t ollowng ypotss:. stady stat: lud spd and tmpratur ar constant n ac pont;. lud tmpratur s unorm along ac scton;. nvronmntal tmpratur s unorm and constant;. dnsty ρ, spcc at C P and lud conductvty ar tmpratur ndpndnt; 5. pps matral s omognous and sotropous; 6. no cmcal ractons occur; 7. tn pp walls; 8. radatv at transr rat s nglgbl. T nntsmal at lu transmttd rom watr to gas troug nnr pp wall s gvn by: ( T T ) r d dq O C π () Smlarly, at transmttd by outr nvronmnt to watr troug outr pp wall s: ( T T ) r d dq O π () dq s partally absorbd by O (dq ) and partally absorbd by mtan (dq C ). In L scton drntal at lus ar rspctvly: dq CP m dt dq () C m dt () C PC C C In L sgmnt t drntal at lu rat absorbd by mtan s gvn by (), wl t at lu absorbd by watr s: q m r (5) For ypotss ) along L and L sgmnts t ollowng dntts ar consdrd: dq dq + dq (6) dq dqc (7) In L sgmnt, bot luds tmpraturs vary; substtutng (), (), () and () nto q. (6) and (7), t ollowngs rst ordr drntal quatons ar obtand: dt C π r (8) ( T -TC) d CP C mc dt π r π r ( T -T ) ( T -TC) d CP m CP m Gvn wall transmttancs and and pps raduss r, r, T () and T C () can b obtand by solvng (8). L lngt s calculatd by mposng watr tmpratur T 00 C n Scton. In L only mtan tmpratur s dpndnt wl watr tmpratur s constant bcaus o pas cang. T nrgy balanc bcom: ( T TC ) r d CPC mc dtc π (9) solvng prvous prsson wt rspct to T C (): π r - CPC mc TC ( ) T O - ( T O -TC / L ) (0) wr trms T C/L s gvn by q. (8) soluton. To calculat L lngt at balanc (6) as bn mployd: T T )π r d m r + ( T T ) π r d () ( C Substtutng T C () nto () and ntgratng btwn scton ( 0) and ( L ) an quaton wt an only unknown (L ) as bn obtand: L L r πr O O C / L ( ) ( ) C P C m C T -T d+ T -T π r m r π () L as bn numrcally ound. In L sgmnt, t at lu dq tat s transrrd troug pp wall causs mtur tmpratur growng. dq and dq ar gvn by: Pag o 6

3 dq ( T -T ) π r d () dq C m dt () P Snc ypotss ): dq dq (5) By (), () and (5) a drntal quaton s obtand. Equaton soluton s: ln π r ( T T ) K (6) C m + P K s calculatd by mposng t ollowngs constrants: - mtur tmpratur at L nal scton s t sam as L nput scton tmpratur; - mtur tmpratur at L nal scton s 650 C. Transmttanc calculaton Tanks to 7) ypotss, t transmttanc o t outr pp wall along L sgmnt s gvn by: s (7) Flud moton caractrstc as bn dntd by mans o Graso (Gr) and Raylg (Ra) admnsonal numbrs. T convcton cocnt as bn obtand by mans o Curcll-Cu quaton [] Ra Nu Pr (8) For, Nusslt numbr as bn calculatd by Cn- awkns-solbrg quaton or lamnar lud moton nsd annular sctons []: dq d Tm Nu.0 R Pr µ Gz L d µ Tp 0.05 (9) In q. (9) an arbtrary valu o L as bn ntroducd as rst attmpt valu. Ultmat L as bn dtrmnd by mans o an tratv procss wc gvs: L 0. 0 m (0) By 7) ypotss, t transmttanc o t outr pp wall or L sgmnt s gvn by: s C () In ordr to dtrmn, wall tmpratur o t nnr pp as bn assumd as t avrag valu o watr tmpratur along L sgmnt (T P 57 C). For C, Nu as bn ound by mans o Sdr-Tat quaton or lamnar lud moton []: Nu 0. µ Tm.86 Gz Gz µ Tp () In L sgmnt t transmttanc o outr pp wall s gvn by: s () s supposd to b t sam as or L. In t annular scton, watr moton s turbulnt nar outr wall bcaus o bolng. In ordr to dtrmn and, Bromly quaton as bn usd, obtanng t convcton cocnt or lm vaporaton []. λvs.06 µ vsd ( ρ ρ ) ls q ρ vsg m ( T T ) p vs () wr T m s watr bolng tmpratur and T p, s consdrd t trnal tmpratur. Innr pp wall transmttanc s gvn by: s λ C (5) C as bn obtand by () assumng, as rst attmpt valu, an arbtrary L. Ultmat L as bn dtrmnd by mans o an tratv procss wc gvs: L m (6) Pag o 6

4 Along L sgmnt two drnt typs o can b obsrvd: turbulnt n t ntal part corrspondng to luds mng, lamnar n t nal part. sgmnt lngt as bn calculatd mposng: m (7) R 000 π d µ tur vscosty (µ 000 ) as bn dtrmnd by q. (7). Gvn µ 000 and gass molar racton, mtur tmpratur as bn calculatd by mans o Kys quaton by an tratv procss []: µ a0 T a + 0 T a T (8) Gvn T 000, t lamnar sgmnt lngt (L l ) s gvn by [5]: C Pl m T T Ll ln l π r T T m (9) T not lamnar sgmnt lngt (L t ) as bn calculatd by mans o t prvous quaton, consdrng bot turbulnt and lamnar condton: C ln T T Pt m L t t π r T T wr t s gvn by: t s t m (0) () s attand by Curcll-Cu quaton. t as bn calculatd twc: A) on lamnar condtons by q. (); B) on not lamnar condtons by q. () []. Nu ( ) ( Lt d T T ) p 0.0 R m 0.8 Pr 0. () at cangr lngt s gvn by () bot on A) and B) condtons du to t small drnc btwn Nu obtand rspctvly by A) and B). Ltot L + L + Ll + Lt. 7 m () Cas analyss In Fg. t coaal pp scm s sktcd. T problm soluton s attand by t sam mtod as cas ; coaal pp at cangr s agan composd by tr sgmnts: L, L and L (s cas ). C C Scton 0 L dq dq Scton L Pas cang dq dqc Scton Fgur : Coaal pp scm. L Scton T nntsmal at lu transmttd by outr nvronmnt to mtan troug outr pp wall s gvn by: dq ( T T ) π r d () C wl t at transmttd rom gas to watr troug nnr pp wall s: dq ( TC T ) π r d (5) Enrgy absorbd by luds along L and L sgmnts ar gvn rspctvly by (), () and (5), wl quatons (6) and (7) bcom: dq dqc dq (6) dq dq (7) By substtutng quatons (), (), () and (5) nto (6) and (7), t ollowngs rst ordr drntal quatons ar obtand: dt π r (8) ( TC T ) d CP m dtc π r π r ( T TC) ( TC T ) d CP C mc CP C mc Solvng (8) wt rspct to T () and T C (), t ollowng L lngt as bn attand: L 0. 9 m (9) Along L only mtan tmpratur s dpndnt wl watr tmpratur s constant. L lngt as bn calculatd by t sam mtod as cas. Pag o 6

5 Transmttanc calculaton Tanks to ypotss 7) t transmttanc o t outr pp wall along L s gvn by: s C (0) wr s calculatd by Curcll-Cu quaton. tan moton caractrstc along L sgmnt as bn ndvduatd by mans o R. C as bn obtand by mans o Cn- awkns-solbrg quaton. By 7) ypotss, t transmttanc o t nnr pp wall s gvn by: C s () s (6) wr s gvn by Curcll-Cu quaton. To calculat ausn quaton as bn mployd. T L lngt as bn obtand by mans o cas mtod: L. m (7) In ts cas lud moton s lamnar all along L sgmnt and at cangr lngt rsults: L tot L + L + L. m (8) Gass arrangmnt o cas dtrmns: - at cangr lngt longr tan cas ; - mtur moton along L s lamnar and gass mng s nbtd. For C q. (9) as bn mployd; wall tmpratur T p as bn assumd as t avrag valu o t watr tmpratur along L. as bn calculatd by mans o ausn quaton: Gz Nu Gz µ T µ T m p 0. () In L sgmnt, transmttanc o t outr pp wall s gvn by: s C () wr and C av bn calculatd rspctvly by mans o Curcll-Cu and Cn-awkns-Solbrg quatons. Transmttanc o t nnr pp wall s: s C λ () To calculat C quaton (9) as bn mployd. as bn obtand by mans Bromly quaton assumng lm bolng nsd t nnr pp. For L lngt t ollowng valu as bn ound: L. 90 m (5) In L sgmnt, transmttanc o t pp wall s gvn by: NOENCLATURE C PC mtan spcc at along L sgmnt (J/kgK) C P watr spcc at along L sgmnt (J/kgK) C PC mtan spcc at (J/kgK) C P watr spcc at (J/kgK) C P mtur spcc at (J/kgK) C Pl mtur spcc at or lamnar (J/kgK) C Pt watr spcc at or turbulnt (J/kgK) d pp damtr (m) dq at lu transmttd troug outr pp wall (W) dq at lu transmttd troug nnr pp wall (W) dq at lu transmttd troug outr pp wall along L sgmnt (W) dq C at lu absorbd by mtan (W) dq at lu absorbd by watr (W) dq at lu absorbd by mtur (W) dr watr vaporzaton at (J/kg) dt C mtan tmpratur gradnt (K) dt watr tmpratur gradnt (K) d nntsmal sgmnt (m) Gz Gratz numbr (admnsonal) C mtan-nnr pp convcton cocnt along L (W/m K) watr-outr pp convcton cocnt along L (W/m K) watr-nnr pp convcton cocnt along L (W/m K) C mtan-nnr pp convcton cocnt along L (W/m K) watr-outr pp convcton cocnt along L (W/m K) watr-nnr pp convcton cocnt along L (W/m K) Pag 5 o 6

6 t mtur-outr pp convcton cocnt along L (W/m K) C mtan convcton cocnt (W/m K) outsd lud convcton cocnt (W/m K) watr convcton cocnt (W/m K) outr pp transmttanc (W/m K) nnr pp transmttanc (W/m K) outr pp transmttanc along L (W/m K) nnr pp transmttanc along L (W/m K) outr pp transmttanc along L (W/m K) nnr pp transmttanc along L (W/m K) outr pp transmttanc along L (W/m K) l outr pp transmttanc along L or lamnar (W/m K) t outr pp transmttanc along L or not lamnar (W/m K) K ntgraton constant (admnsonal) L L lngt (m) L L lngt (m) L t not lamnar sgmnt lngt (m) L l lamnar sgmnt lngt (m) m C mtan mass rat (kg/s) m watr mass rat (kg/s) m mtur mass rat (kg/s) Nu Nusslt numbr (admnsonal) Pr Prandtl numbr (admnsonal) r pp radus (m) r at o vaporzaton (J/kg) R Rynolds numbr (admnsonal) s pp tcknss (m) T 000 mtur tmpratur wn R s 000 (K) T C mtan tmpratur (K) T nvronmnt tmpratur (K) T watr tmpratur (K) T watr bolng pont (K) T m bulk tmpratur (K) T mtur tmpratur (K) T mtur tmpratur at Scton (K) T mtur tmpratur at Scton (K) lud tmpratur nar pp wall (K) T P CONCLUSION In ts papr a gas at cangr or an orgnal CFC as bn studd. Bcaus o t anodc compartmnt pcular gomtry t only at cangr conguraton allowd s a col sap sngl pp. T pp s mad up o two sctons. In t rst scton, t col s consttutd by two coaal pps: on or ac lud. r t mtan s warmd up to 00 C wl t watr s warmd up to 00 C and tn vaporzd. In t scond scton t col s consttutd by a sngl pp. T two luds ar md and warmd up to rormng procss tmpratur (650 C). T arrangmnt wt watr n t outr pp and mtan n t nnr pp as bn ound to b t on tat mnmzs t cangr dmnsons: t pp lngt s qual to.7 mtrs, wl t scton occupd by t concntrc pps s 0.70 mtrs long. Furtrmor, suc a conguraton sows a not lamnar transton rgon wr gas mng s nancd. T rsults av bn acvd by proposng and solvng nw at transr drntal quatons wc may also b usul or many otr applcatons. REFERENCES [] EG&G Tcncal Srvcs, Inc., Novmbr 00, Ful Cll andbook, U. S. Dpartmnt o Enrgy, Oc o Fossl Enrgy, Natonal Enrgy Tcnology Laboratory, organtown, Wst Vrgna. [] W.. Rosnow, J. P. artntt, E. N. Ganc, 985, andbook o at Transr Fundamntals, c Graw ll, Nw York. [] F. Krt, 97, Prncpls o at Transr, Dun, Donnlly Publsng Corporaton, Nw York. [] Vargatk, Y. K. Vnogradov, V. S. Yargn, 996, andbook o Pyscal Proprts o Lqud and Gass, Bgll ous, Nw York. [5]. Sclctng, 987, Boundary Layr Tory, c Graw ll, Nw York. Grk Lttrs λ trmal conductvty (W/mK) µ 7 mtur vscosty at T m (Ns/m ) µ 9 mtur vscosty at T m (Ns/m ) µ 000 mtur vscosty at T m (Ns/m ) µ Tm lud vscosty at T m (Ns/m ) µ Tp lud vscosty at T P (Ns/m ) Subscrpts outr q quvalnt nsd/nnr Pag 6 o 6