Proceedin of te ASME 3 Interntionl Tecnicl Conference nd Exibition on Pckin nd Intertion of Electronic nd Potonic Microytem InterPACK3 July 6-8, 3, Burlinme, CA, USA IPACK3-7395 ANALTIC OPTIMIZATION OF CO EFFECTIVE THERMOELECTRIC GENERATION ON TOP OF RANKINE CCLE Kzuki z Purdue Univerity Wet Lfyette, IN, U.S.A. ee Rui Ko Purdue Univerity Wet Lfyette, IN, U.S.A. Ali Skouri Purdue Univerity Wet Lfyette, IN, U.S.A. ABRACT Termoelectric () enertor ve potentil dvnte of te ide pplicble temperture rne by proper election of mteril. In contrt, tem turbine () Rnkine cycle termodynmic enertor i limited up to more or le 63 o C for te et ource. Unlike typicl te enery recovery ytem, e propoe combined ytem plcin enertor on top of Rnkine cycle enertor. Ti ytem produce n dditionl poer from te me enery ource comprin to tnd-lone tem turbine ytem. Fuel efficiency i eentil bot for te economic efficiency nd te ecoloicl friendline, epecilly for te lobl rmin concern on te crbon dioxide (CO ) emiion. We report our tudy of te overll performnce of te combined ytem it primrily focuin on te dein prmeter of termoelectric enertor. Te tem temperture connectin to individul enertor ive trde-off in te ytem dein. Too muc loer te temperture reduce te performnce nd too muc ier te temperture reduce te temperture difference cro te enertor ence reduce te performnce. Bed on te nlytic modelin, te optimum tem temperture to be deined i found ner t te mximum poer dein of enertor. Ti optimum point cne dependin on te our-of-opertion. It i becue te enery converion efficiency directly connect to te fuel conumption rte. A te reult, pyicl upper-limit temperture of tem for ppered to provide te bet fuel economy. We lo invetited te impct of improvin te fiure-of-merit (ZT) of mteril. A like eneric enine, reduction of terml conductivity i te mot influentil prmeter for improvement. We lo dicu te cot-performnce. Te combined ytem provide te pybck per poer output t te initil nd lo provide te inificntly better enery economy [$/KW]. Nomenclture C: rtio to Crnot efficiency [-] d: tickne [m] F: fill fctor (frctionl re rtio) [-] G: mteril price [$/k] : our of opertion [r] i: electricl current [A] I: initil mteril cot [$] m: electricl reitnce rtio [-] R: electricl reitnce [] S: Seebeck coefficient [V/K] T: temperture [K] : poer output per unit re [W/m ] x: tickne rtio [-] : enery production cot [$/KW] Copyrit 3 by ASME
Z: fiure of merit of mteril [/K] Symbol : terml conductivity [W/mK] : efficiency [-] : denity [k/m 3 ] : electricl conductivity [/.m] : terml reitnce [K/W] Subcript : optimum for mximum poer : mbient c: cold ide f: fuel : interfce : ot ide in: input : ubtrte for module : tem turbine : termoelectric INTRODUCTION Te U.S. enery flo crt [] o tt te enery in ervice i only ~4.7% of te enery input in yer. Ti tudy repreent one pproc for increin fuel efficiency in poer production nd loerin te enery cot [$/kw]. Amon poer enertor, Rnkine cycle tem turbine re idely ued for poer enertion. Stem turbine re lo one of te mot effective mecnicl enine [] due to it reltively imple tructure. Becue it i uin tem, oever, te Rnkine cycle termo dynmic limittion. Te termodynmic converion efficiency i limited by te inlet tem temperture. Te tructurl mteril of turbine, uc tinle teel, temperture-dependent yield limit t te extremely i tem preure. Te Crnot efficiency it 9 K tem temperture nd 3 K mbient temperture i only 67%. Coniderin te relitic irreverible terml contct, te efficiency t te mximum poer output become even loer 4% bed on Curzon nd Alborn [3]. Wit n nlyticl pproc, e ill find te bet opertin point for fuel economy for te termoelectric toppin cycle tem turbine beteen te mximum efficiency nd te efficiency t mximum poer output. COMBINED-SEM CONCEPT Addin termoelectric () poer enertor into te p beteen te dibtic flme temperture nd te tem temperture ill mke dditionl poer output. We ve tudied combined ytem compoed of enertor on top of Rnkine cycle. Te enerte n dditionl mount of poer by uin te lre temperture p beteen te ource temperture nd te tem temperture. Even it pecil dein dedicted for i temperture opertion for turbine [4], te tem temperture i limited to < 65 o C, ile te ier temperture of opertionl mteril i round 3-5 K [5]. We ten optimize te interfcil temperture for let enery cot. Te enertor received more ttention n enine for te et recovery, for ic te temperture rne i quite imilr to tt of tem turbine. Ti olid tte device i lo knon moderte performnce device due to te lo efficiency of tody termoelectric mteril nd te intrinic terml reitnce tt diipte te et enery lo. Tu only pce/eit limited ppliction, uc veicle exut et recovery [6][7][8], been evily invetited o fr, even tou, te olid-tte termoelectric enery converion i clble to ier temperture. Ti crcteritic become n dvnte ic oter tecnoloie could not ccommodte. Te module cn be deined for optimum reult by cnin te element tickne to mtc te externl terml reitnce reported in our previou ork [9]. A et flo concentrtion inide of te module by mkin te fill fctor mller, yield muc le mteril m necery for te me poer output per unit re fr it mintin te internl terml reitnce mtc to te um of externl terml reitnce []. We lo tudied te terml nd electricl pritic impct [] for te optiml dein. A fill fctor of pproximtely % o inificnt reduction of mteril m it reonbly mller pritic impct. Te optimum dein in ti tudy tke into ccount bot te initil cot to build te combined ytem nd te runnin cot of te fuel. Knole nd Lee [] recently tudied combined ytem it toppin cycle on ier temperture Bryton cycle turbine. In teir report, efficiency t mximum poer output dicued. Tey point out tt ltou termoelectric enertor toppin cycle ennce efficiency of Bryton for lo temperture turbine, efficiency cnnot exceed i temperture turbine. Tey uet tt uin toppin cycle i limited to ce en pce or price for i temperture turbine cnnot be jutified. To conider te full enery cot, e optimized te dein prmeter for fuel economy nd tu e cn point out te broder dvnte of toppin cycle tem turbine function of opertion time nd fuel cot. Copyrit 3 by ASME
MODEL DEVELOPEMENT Te terml circuit model of te nd Rnkine cycle combined ytem i on in Fi.. We umed te et flux q in i not limited to pecific rne nd te ource temperture T nd te terml round temperture T (room temperture) re fixed. More pecificlly, T i te dibtic flme temperture of te fuel. T i te interfcil temperture beteen te to enine. Te poer output from te i extrcted t te externl electricl lod R L in n electricl circuit connected to te element. Due to te Seebeck effect creted by te temperture difference beteen T nd T c, te electricl current j oe trou te element nd connected R L. Te poer output from i decribed function of te dein prmeter d, ic i te tickne of termoelement nd directly connected to bot te terml nd electricl performnce. We ly ume et flo nd ytem dein per unit re in te nlyi. Rj SjT Rj SjT c q in T T T c c T q in R L (- )q in T S (- )q in S Fiure : Terml netork model of te combined ytem it on top (left nd ide of dirm) of te (rit nd ide). Left ide o te prt nd Te electricl circuit of i djcent to te terml reitnce of element (in drk block reion). At te ection, te externl terml reitnce nd c re umed to be ymmetric. Ti i convenient for implifyin te eqution. Alo, te poer output i inenitive to ymmetric terml contct it ot nd cold reervoir over rne everl time te rtio beteen te to terml reitnce. Accordin to [9], te temperture reltion i decribed function of le tickne T T c T T d m d d d d c T () ere, d i te element tickne, d i te optimum tickne for te mximum poer output. m i te electricl reitnce rtio of te lod reitnce int te internl reitnce. T nd T c re te ot ide nd te cold ide temperture of te termoelement, repectively. Accordin to terml nd electricl impednce mtcin, d m () ile, c nd m ZT (4) Z T i dimenionle fiure-of-merit of termoelectric mteril ile T tnd for men opertin temperture cro te le nd Z contin mteril propertie, i.e. terml conductivity, electricl conductivity, nd Seebeck coefficient S, in reltion Z=S / Poer output per unit re i found for T nd T c, m Z T Tc (6) m d Ten te efficiency i found q in m ZT Tc m d T T To invetite enerl trend, e mke core umption tt (T - T ) nd (T c - T ) re pproximtely equl. Ten Eq. (6) nd (7) cn be reritten, Z m d / d d / d Z d d T T m d d T T (9) Tee re function of te dimenionle tickne d/d it iven condition, T, nd T. An extremely tin termoelement enerte nerly zero output nd te extremely tick termoelement lo enerte nerly zero output ccordin to Eq. (8). (7) (8) 3 Copyrit 3 by ASME
Te enery production cot for te termoelectric ection [$/kw] i clculted follo. I f () ere, i our of opertion, f i te cot of potentil cemicl enery of te fuel in unit of $/kw, nd I i te initil mteril cot to build te ytem, iven by I dfg d G () ere, ubcript tnd for te ubtrte of termoelectric module, i denity, F i fill fctor, nd G i te mteril mrket unit price [$/k]. Het ink re not included in ti prt of te model, ince tey re lredy included in te Rnkine cycle unit. We my replce tem it modified verion but do not expect different price, tu e did not double count te et ink in Eq. (). Te firt term of te rit nd ide of Eq. () i te pyoff for one time initil invetment of te enertor nd involve poer output performnce. Ti initil cot i mortized over te opertin our. Te econd term i te opertin cot tt directly depend on te fuel cot nd te enery converion efficiency. Terefore, tere mut be te lobl optimum in beteen te mximum efficiency nd te mximum poer output. A Eq. (8) nd (9) o, tee re titly relted. Subtitutin Eq. (8), (9), nd () into Eq. (), te enery production cot i found function of le tickne, d. For te furter implifiction, e ume te rtio of te element tickne nd te ubtrte tickne d/d i contnt. Replcin d/d it x, te enery production cot become, FG cg m dx ZT T OPTIMIZATION m x f T Zx T () By tkin te derivtive of Eq. (),, e find te x vlue of x tt ill minimize. Te olution i found Eq. (3) ic i te only rel formul mon te poible tree olution. x X (3) 3 X ile ivin te mcro prmeter X, X 3 A (4) 3 3 A 7A B 3 3 4 5 7A B 4A B it inin A nd B, FG cg m d m A, B Z T T Z T T f (5) Te Rnkine cycle in ti ork conider impler model, ic i compried of n idel enine nd te irreverible terml contct for te ot ide S nd te cold ide S, repectively. Te efficiency reltive to termodynmic limit (Crnot efficiency) of te Rnkine cycle i umed to cne by te flo rte of tem independent of te tem temperture. Te ork enerted by te turbine i conidered electricl poer. Te efficiency of te turbine include te mecnicl efficiency nd te converion efficiency from dynmic enery to electricity. It i reonble to ume tt te efficiency follo te Crnot efficiency it coefficient C, C. W i C C T T _ mx _ mx f (6) T Subtitutin into Eq. (6), T T A D B C T C T C (7) (8) E (9) ere te locl vrible A, B, C, D, nd E re, A C D f, B T i, E T T C, C T, T T T C () Similr to te termoelectric enine, e find te efficiency. Te olution i found, AE BD AE BD BCD E AE BD CD E / C () 4 Copyrit 3 by ASME
ANALSIS Te folloin i et of prmeter ued for te nlyi. Adibtic flme temperture i T = 5 [K] from [3] nd te mbient temperture i T =3 [K] Performnce fctor of te ytem re: Terml reitnce nd c =. [K/W] Terml reitnce in Stem Turbine ytem (et ink) S = S : peudo defined [K/W] Rnkine cycle tem turbine. At te very beinnin, te enery production cot i ier ince it i dominted by te initil invetment of enertor. A te opertin our incree, te minimum enery production cot decree. Te efficiency t ti minimum cot rdully ift increin te opertin our. A loner our of opertion tend to yield te dein to mtc ier efficiency, ile te ytem produce poer loer tn te mximum potentil. beline mteril propertie, referred te mteril ZT i unity in te lter dicuion: Terml conductivity =.5 [W/mK] Electricl conductivity = 5 [/.m] Seebeck coefficient S = x -4 [V/K] Denity = 8 [k/m 3 ] Fill fctor = % (frctionl re covere) performnce contnt C i umed 6%. Cot fctor common for te mteril re: mteril price 5 [$/k] mcine cot 7 [$/kw] bed on [4] Fuel cot.8[$/kw] We umed te termoelectric mteril bed on typicl BiTe3 for mteril propertie nd te cot nd extrpolted te electricl propertie it fixin terml conductivity to mtc to te tretin opertin temperture. Te fuel cot bove i clculted bed on te mrket price of oline nd nturl ell te clorific vlue of te fuel from [5]. Interetinly te price for clorific vlue imilr for oline nd LPG. Ti cot vlue i lo te bottom line (minimum) for te electricity upply cot. A fr burnin fuel, te electricity cot cnnot be loer tn ti vlue,.8$/kw. i) Toppin Te initil (=) mximum poer output i found t d=d [9]. A ticker le (d >> d ) led lrer efficiency but loer poer output ince te ticker le inificntly limit te vilble et flo for te temperture contrint. A increin te opertion our, te optimum dimenionle tickne incree. It i becue te ier efficiency i required for loerin te overll enery cot. ii) Stem turbine Fi. o te enery production cot function of te opertin efficiency it vryin te our of opertion of Enery cot [$/kw] 3.5% 6% 3%,, >>,. % % % 3% 4% Efficiency Fiure : Enery cot v. opertin efficiency of. T =8 K RESULT AND DISCUSSION i) Poer output Fi. 3 o reult of combined ytem. Te poer output optimized for minimum enery cot i on function of te interfce temperture T. Te totl poer output nd it prt nd te prt re lo on. By te poer output int te our of opertion nlyi, te prt it te mximum t pproximtely - our of opertion nd litly decree te our of opertion incree detiled in [6]. Te optimum tickne of te le become ticker te interfce temperture incree. It ive inificnt impct on poer output by ddin on top of it compre to lone. Te et flo comin into te prt i limited by te temperture contrint nd le tickne. Te reltion bove ive pek poer output for te combined ytem. Te mximum poer output i oberved t 78 K for te dein of, our opertion ile te mximum of prt i found t 974 K itout ivin ny prcticl limittion. Te optimum tem temperture 78 K i quite i, but it i vilble for uperet tem turbine. Coniderin te reult of 5 Copyrit 3 by ASME
toppin Bryton cycle [] uet tt our reult could cover te rne from tem turbine to te trnitionl reion to Bryton cycle. Poer output [kw/m ] 3 5 5 5 @ 78K + prt @ 974K prt lone 3 8 3 8 Interfce temperture [K] Fiure 3: Optimum poer output for te loet enery cot function of interfce temperture t, our of opertion. ii) Efficiency Fi. 4 o te efficiency of te enery production function of interfce temperture T. Te combined ytem i optimized for loet enery cot t, our of opertion. Te trde-off reltion beteen nd ive ytem crcteritic, ic incree efficiency by increin temperture nd it rdully turte in ier temperture for beline ZT=. A increin te fiure-ofmerit (ZT) of te mteril, te mximum efficiency of prt inificntly incree. Ti impct i muc more tn t te mximum poer optimum. Tere i no optimum interfce temperture for ZT= for ti ce. A ZT incree to ZT=, te optimum interfce temperture i oberved nd te temperture ift to loer ZT furter incree. We lo invetited te impct of cnin te mteril propertie (ee Eq. 5) of te fiure-ofmerit (ZT) individully. Te impct of decrein terml conductivity (olid curve) i more influentil tn increin poer fctor (ded curve). Te impct of eiter electricl conductivity or Seebeck coefficient re exctly te me. It i lo upported by Eq. () it creful invetition. If T i cloe te mbient temperture, te enery production cot [$/kw] inificntly cne. A efficiency curve incree T incree in Fi.4, te enery cot decree T incree. At 454K of temperture nd 5% of efficiency, cro over point i oberved beteen -lone nd -lone for, our of opertion. In erlier our, te cro over temperture i found in ier rne. iii) Enery production cot Te firt term of te Eq. () depend on te opertion our. Te enery cot i dominted by te firt term durin te mll initil our nd exponentilly decy opertion run loner our. If ny improvement employed for ZT, increin fiure-of-merit reduce te enery cot expected. In prticulr, decrein terml conductivity drmticlly loer te enery cot in te erly opertion te firt term (x+) mke n impct. For loner time opertion, te econd term doe not mke inificnt difference beteen cnin terml conductivity nd cnin electricl conductivity or Seebeck coefficient. Totl cot in certin opertion our i on in Fi 5. Te minimum enery cot for prticulr our-of-opertion i found. It i coincidence tt te optimum dein temperture T i found ner te mximum lloble tem temperture for prcticl. Te bottom ded curve in Fi. 5 o te minimum enery cot if te combined ytem could operte for infinity our. Efficiency 6% 5% 4% 3% % % +(ZT=5) +(ZT=) + lone lone % 3 8 3 8 Interfce temperture [K] Fiure 4: Efficiency function of interfce temperture for ZT= beline nd te nd totl efficiency for ZT=5 nd ZT= re lo on. Ded curve correpond to te cne in poer fctor nd olid curve correpond to te cne in terml conductivity for ZT improvement. Dot on te + curve indicte te pek efficiencie, ic re (34 K, 43 K) nd (85 K, 94 K) for of ZT= nd ZT=5 by cnin (poer fctor, or terml conductivity), repectively. 6 Copyrit 3 by ASME
Enery production cot [$/kw] ACKNOWLEDGMENTS lone Ti ork upported by te Center of Enery Efficient Mteril, one of te Enery Frontier Reerc Center (EFRC) of Te Office of Science, U.S. Deprtment of Enery. lone + (3 r) REFERENCES [] Lrence Livermore Ntionl Lbortory, Enery flo crt Etimted Enery Ue in : 97.3 Qud, ttp://flocrt.llnl.ov/, (). [] C. A. Pron, Te Stem Turbine, Cmbride Univerity Pre, (9). [3] F. Curzon nd B. Alborn, Efficiency of Crnot enine t mximum poer output, Americn Journl of Pyic. Vol. 43, Iue, pp., (975). [4] S. Imno, E. Sito, J. Iki, M. Kitmur, HIGHMPERATURE EAM TURBINE POWER PLANT, US Ptent Appliction 8579. [5] D. M. Roe, ed., Termoelectric Hndbook Mcro to Nno, CRC Pre, (6). [6] J. W. Firbnk, Veiculr Termoelectric: A Ne Green Tecnoloy, Proceedin of te nd Termoelectric Appliction Workop, () [7] Q. E. Huin, D. R. Brim, nd C. W. Mrnville, Termoelectric Exut Het Recovery for Hybrid Veicle, SAE Interntionl Journl of Enine, vol., no., pp. 3-4, (9). [8] J. W. LGrndeur, L. E. Bell, nd D. T. Crne, Recent Prore in Termoelectric Poer Genertion Sytem for Commercil Appliction, MRS Proceedin, Vol. 35, (). [9] K. z nd A. Skouri, Optimiztion of poer nd efficiency of termoelectric device it ymmetric terml contct, Journl of Applied Pyic, Vol., 459, (). [] K. z nd A. Skouri, Optimizin Cot-efficiency Trdeoff in te Dein of Termoelectric Poer Genertor, Environmentl Science nd Tecnoloy - Journl of Americn Cemicl Society, Vol. 45, Iue 7, pp. 7548 7553, (). [] K. z nd A. Skouri, Cot-effective te et recovery uin termoelectric ytem, Invited Feture Pper, Journl of Mteril Reerc, Vol. 7, pp. -6, (). [] C. B. Knole nd H. Lee, Optimized orkin condition for termoelectric enertor toppin cycle for turbine, Journl of Applied Pyic, Vol., 7355 (8pe), (). [3] A. Vn Mren, D. S. Tun, nd L. R H. De Goey, Meurement of Flme Temperture nd Adibtic Burnin Velocity of Metne/Air Mixture, Combution Science nd Tecnoloy, Vol. 96, Iue 4-6, pp. 37-344, (994). [4]. ou-on nd S. Fen-rui, Termoeconomic Cot Modelin of Mrine G Turbine Genertin Unit, Proceedin of IEEE Indutril Enineerin nd Enineerin Mnement (IEEM), pp. 4-8, (). [5] H. Buer, ed., Automotive Hndbook 4t Edition, Robert Boc GmbH, pp. 38 39, (996). [6] K. z,. R. Ko, nd A. Skouri, Optimiztion of termoelectric toppin combined tem turbine cycle for enery economy, Applied Enery, Vol. 9, pp. -9, (3). + (4 r) + (5 r) + ( ). 3 8 3 8 Interfce temperture T [K] Fiure 5: Enery production cot of te combined ytem it lone nd lone int tem temperture T. Dotted curve o our, olid curve o +4 our, nd broken curve o +5 our of opertion. Te bottom ded curve o te minimum cot. CONCLUSIONS We dicued te combined poer enertion ytem it on top of Rnkine cycle, ile te mteril re vilble in opertion t up to round 5K te iet temperture. We developed eneric model nd nlyzed enery economy. Te optimum dein/opertion for te loet enery cot bot for nd re nlyticlly found. Te dvnte of te combined ytem demontrted ile bot ly minimize te pybck of initil cot. Te optimum blnce of te dein/opertion point beteen te mximum poer nd te mximum efficiency depend on te our-of-opertion. Anoter fctor for optimizin te ytem i te interfce temperture beteen te to enertor. A ier interfce temperture loer te enery cot, but tere i prcticl temperture limittion by tructurl mteril concern of turbine. Improvin termoelectric fiure-of-merit (ZT) i noter key to incree poer output nd efficiency. We lo invetited te impct of cnin termoelectric propertie nd oed te different impct of poer fctor nd terml conductivity for te me ZT. Te bet blnce beteen te loet fuel conumption nd te mximum poer output i found t round 8K for interfce temperture for, our of opertion. In ummry, te combined ytem ennce te enery economy by effectively reuin lre mount of et loe tt ould oterie occur in tndlone Rnkine cycle tem turbine.. 7 Copyrit 3 by ASME