Exergy Analysis of a Combined Power and Ejector Refrigeration Cycle

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1 Exrgy Analysis of a Combind Powr and Ejctor Rfrigration Cycl Hyung Jong Ko, Ba Duck Park, and Kyoung Hoon Kim Abstract Assssmnt of xrgtical prformanc of a combind organic Rankin cycl and jctor rfrigration cycl is carrid out for th ffctiv rcovry of low-tmpratur wast hat. Effcts of th turbin inlt and outlt prssur, and turbin inlt and condnsr tmpratur ar paramtrically invstigatd on th xrgy dstruction (anrgy) ratio of ach componnt of systm and xrgy fficincy of th combind cycl. Rsults show that injctor and condnsr hav scond highst anrgy aftr th boilr and sourc xhaust. Th xrgy fficiny can hav pak valus with rspct to turbin inlt prssur, whil it dcrass monotonically with turbin outlt prssur and condnsr tmpratur. Kywords anrgy, cognration, jctor rfrigration cycl, xrgy fficincy, organic Rankin cycl. I. INTRODUCTION HERE has bn an incrasing intrst in th mthods to Tffctivly convrt th low-tmpratur wast hat into usful forms of nrgy. Th wast hat which is mrly dischargd du to th lack of ffctiv convrsion mthod contributs to th thrmal pollution and nvironmntal problm [1]. Th organic Rankin cycl (ORC) has bn considrd as on of th most fasibl mthods to achiv high fficincy in rcovring low-tmpratur wast hat [2]. Among othr studis, [3], [4] and [5] carrid out th rviws on th stat of th art of rsarch in nrgy convrsion from low-grad nrgy sourcs. Vlz t al. [6] conductd a comparativ study of working fluids for ORC oprating at low tmpratur. Schustr t al. [7] prsntd a stat of th art of ORC applications such as gothrmal powr plants, biomass fird combind hat and powr plants, solar dsalination plants, wast hat rcovry and micro cognration of hat and powr. Wang t al. [8] proposd a thortical thrmal fficincy modl basd on an idal ORC to analyz th influnc of working fluid proprtis. On of th advantags of jctor rfrigration cycl (ERC) is its comparativly simpl structur, which is th rsult of rplacing th comprssor of convntional rfrigration cycl by Hyung Jong Ko is with th Dpartmnt of Mchanical Enginring, Kumoh National Institut of Tchnology, Gumi, Gyongbuk 7-701, Kora (-mail: kohj@kumoh.ac.kr). Ba Duck Park is a graduat studnt for MS dgr in th Dpartmnt of Mchanical Enginring, Kumoh National Institut of Tchnology, Gumi, Gyongbuk 7-701, Kora (-mail: dduk_jjang@navr.com). Kyoung Hoon Kim is with th Dpartmnt of Mchanical Enginring, Kumoh National Institut of Tchnology, Gumi, Gyongbuk 7-701, Kora (phon: ; fax: ; -mail: khkim@kumoh.ac.kr). Corrsponding author. jctor with no moving parts. In addition ERC can b drivn by low-grad nrgy sourcs using organic fluid as working fluid. ERC can b usd for th cognration of powr and rfrigration by combining it with various powr cycls. Dai t al. [9] proposd a novl combind powr and rfrigration cycl, in which a turbin is addd btwn boilr and jctor of ERC. An xrgy analysis and a paramtric analysis of th combind cycl using R123 as working fluid wr prformd to guid th thrmodynamic improvmnt of this cycl and to valuat th ffcts of th ky paramtrs on th cycl prformanc. This combind cycl was invstigatd by Zhng and Wng [] for th working fluid of R5fa without considring th xrgy loss of th hat addition procss. Th modifid vrsion of th combind cycl of [9] was studid by Wang t al. [11] for th sam fluid, in which only a part of vapor was xtractd from th turbin in th midst of xpansion to th jctor. This modifid vrsion was also analyzd by Habibzadh t al. [12] for diffrnt working fluid. For improving th prformanc of a thrmodynamic cycl, xrgy analysis is rgardd as an appropriat tool sinc it can locat and stimat th wast and loss of usful nrgy of a cycl [13]. In this study an assssmnt of xrgtical prformanc of a combind powr and jctor rfrigration cycl which has bn invstigatd by [9], [] is carrid out for th ffctiv utilization of low-tmpratur wast hat with R5fa as working fluid. Th ffcts of th systm paramtrs including th turbin inlt tmpratur and prssur ar invstigatd paramtrically on th anrgy ratio in ach componnt of systm and th xrgy fficincis of cycl. II. SYSTEM ANALYSIS Th systm considrd in this study is an organic Rankin cycl combind with an jctor rfrigration cycl and is shown schmatically in Fig. 1. Th systm consists of a pump, boilr, turbin, jctor, condnsr, xpansion valv, and vaporator. Th working fluid of th combind cycl is R5fa and its thrmodynamic proprtis ar calculatd by th Patl-Tja quation of stat [14], []. Th basic data of th working fluid ndd whn applying th Patl-Tja quation ar listd in TABLE 1, whr M, T cr, P cr and ω ar molcular wight, critical tmpratur, critical prssur, and acntric factor, rspctivly [16]. Th combind cycl is drivn by th snsibl hat supplid by a low-tmpratur hat sourc. Both th sourc fluid and th coolant for th condnsr ar considrd as watr. In this study th following assumptions ar usd for th 6

2 Hat sourc 2 1 Pump Boilr Turbin Condnsr Ejctor 9 Evaporator Expansion valv Fig. 1 Schmatic diagram of th systm. convninc of analysis [9], [17]. 1) Th working fluid ntrs th turbin as suprhatd vapor, and lavs th condnsr and vaporator as saturatd liquid and saturatd vapor, rspctivly. 2) Th tmpratur diffrnc btwn th hot and cold strams in th boilr and condnsr is highr than th pinch point tmpratur diffrnc. 3) Prssur drop and hat loss in th systm ar ngligibl. 4) Th pump and turbin hav constant isntropic fficincy. 5) Th flow in th jctor is on-dimnsional and th mixing of primary and scondary flows occurs at constant prssur. Th ffcts of irrvrsibility at th nozzl, mixing, and diffusr sctions can b takn into account by using thir fficincis. Using ths assumptions and rfrring to Fig. 1 th thrmodynamic stats at 1 to 9 ar dtrmind for givn condnsr and vaporator tmpraturs. In this procdur th xit stat 4 and ntrainmnt ratio of th jctor ar dtrmind itrativly from th consrvation quations of mass, momntum, and nrgy. Th ratios of mass flow rat of working fluid and coolant fluid to that of sourc fluid, m s, ar dtrmind from th nrgy balanc and pinch point condition. Not that th mass flow rat in th condnsr is qual to th sum of thos in th turbin and vaporator. m = m + m (1) cd t Th ratio, r /t = m /m t, is calld th ntrainmnt ratio of jctor. Th rats of hat input, nt work production and rfrigration output ar calculatd from W nt in mt ( h 2 h 1 ) [( h3 h2 ) ( h1 h6 )] m ( ) Q =, (2) = Wt Wp = m, (3) t Q = h 9 h 8. (4) Th spcific xrgy and th rats of xrgy input to th systm, loss du to th xhaust of sourc fluid, and xrgy 8 TABLE I: BASIC DATA FOR THE WORKING FLUID Substanc M (kg/kmol) T cr (K) P cr (bar) ω R5fa output associatd with rfrigration ar writtn as T0 ( s 0 ) { Ts T0 T0 ln( Ts / T0 )} { T T T ln( T T )} = h h0 s, (5) Ein = msc, (6) ps Exh = msc ps xh 0 0 xh /, (7) 0 E = Q ( T 0 T ) / T. (8) cs cs Hr h, s, and c ps man th spcific nthalpy, ntropy, and isobaric spcific hat. Th subscript 0 rfrs to th nvironmnt stat, and T s, T xh and T cs ar th tmpraturs of th sourc inlt, sourc xhaust and coold spac, rspctivly. Th rat of xrgy dstruction or anrgy of adiabatic systm can b calculatd from th diffrnc of th rat of xrgy input and output. At th boilr, for xampl, ( ) Db = Ein Exh + mt 1 2. (9) Th anrgy ratio of ach componnt is dfind as th ratio of its anrgy to xrgy input by th sourc fluid givn in (6).. Two kinds of xprssions for th xrgy fficincy of th cycl dfind by η 2 a = ( W nt + E) / E, () in η = ( W + E ) /( E E ), (11) 2b nt in xh Ar considrd; on is basd on th xrgy input, th othr nt xrgy dlivrd to th systm through th boilr. η 2a rprsnts an stimation of xrgy fficincy by assuming that xrgy of th xhaust sourc is mrly dischargd to nvironmnt. On th contrary η 2b is an optimistic stimation with a hop that th xrgy of xhaust can b fully rcovrd. Not that two fficincis ar qual if th sourc xhaust tmpratur is qual to that of nvironmnt. III. RESULTS AND DISCUSSIONS In this study th xrgtical prformanc of th combind powr and jctor rfrigration cycl using R5fa as working fluid is invstigatd for th varying paramtr valus. Watr is considrd as sourc fluid with inlt tmpratur of 0 o C. Th inlt and outlt prssur of turbin ar varid from 5 to bar and from 3 to 4 bar, rspctivly, whil th turbin inlt and condnsr tmpratur ranging from to o C and from to o C ar considrd. Othr basic data for analysis ar summarizd as follows. Coolant tmpratur: o C, nvironmnt tmpratur: o C, vaporator tmpratur: - o C, tmpratur of coold spac: -5 o C, pinch point tmpratur diffrnc: o C, isntropic fficincy of pump: 0.7, isntropic fficincy of turbin: 0.85, nozzl fficincy: 0.95, mixing fficincy: 0.95, diffusr fficincy:

3 Anrgy ratio of sourc xhaust (%) Anrgy ratio of turbin (%) Fig. 2 Dpndnc of anrgy ratio of sourc xhaust on turbin inlt prssur and tmpratur. Fig. 2 shows th dpndnc of anrgy ratio of sourc xhaust on turbin inlt prssur (TIP) and turbin inlt tmpratur (TIT), which is th portion of xrgy lost by discharging to th nvironmnt. Th rang of TIP is rstrictd such that th working fluid ntrs th turbin as a suprhatd vapor. Th anrgy ratio of sourc xhaust almost linarly incrass with TIP for fixd TIT. Although th diffrnc is not larg, anrgy ratio of sourc xhaust is highr for highr TIT with th sam TIP. Fig. 3 shows th dpndnc of anrgy ratio of boilr on TIP for various TITs. Th anrgy ratio of boilr is comparabl in magnitud with that of sourc xhaust but it xhibits an opposit bhavior. It is smallr for highr TIP or highr TIT. Roughly spaking th sum of anrgy ratios of sourc xhaust and boilr is about 50%. In othr words half of th xrgy input by th sourc is dstroyd or lost during th vapor gnration procss. Fig. 4 Dpndnc of anrgy ratio of turbin on turbin inlt prssur and tmpratur. Th anrgy ratio of turbin is plottd as a function TIP for various TITs in Fig. 4. It incrass with TIP for fixd TIT and rachs a pak valu and thn dcrass. Evn though th ratio is lss than 5% ovr th rang considrd, mor xrgy is dstroyd in th turbin as th TIT is raisd. Dpndncs of anrgy ratio of jctor on TIP and TIT, and turbin outlt prssur (TOP) and condnsr tmpratur ar shown in Fig. 5 and Fig. 6, rspctivly. Lik in th boilr, anrgy ratio of jctor dcrass as TIP or TIT is raisd. This bhavior is idntical to th bhavior that highr thrmal fficincy rsults for highr TIP or TIT. As sn in Fig. 6, th anrgy ratio of jctor for TIP of bar and TIT of o C incrass almost linarly with TOP and is highr for lowr condnsr tmpratur. This bhavior is a rsult of mass ffct sinc th anrgy ratio of jctor is proportional to th ntrainmnt ratio of th jctor. For fixd Anrgy ratio of boilr (%) Anrgy ratio of injctor (%) Fig. 3 Dpndnc of anrgy ratio of boilr on turbin inlt prssur and tmpratur. Fig. 5 Dpndnc of anrgy ratio of injctor on turbin inlt prssur and tmpratur. 8

4 19 18 Anrgy ratio of injctor (%) Exrgy fficincis (%) η 2a η 2b Turbin outlt prssur (bar) Fig. 6 Dpndnc of anrgy ratio of injctor on turbin outlt prssur and condnsr tmpratur. TIP and TIT, th ntrainmnt ratio of jctor shows a narly linarly incrasing bhavior with rspct to TOP and is highr for low condnsr tmpraturs [17]. Fig. 7 shows th dpndnc of anrgy ratio of condnsr on TOP and condnsr tmpratur for TIP of bar and TIT of o C. As for injctor for fixd turbin conditions, anrgy ratio of condnsr incrass almost linarly with incrasing TOP. This is bcaus th ratio of mass rat of condnsr to sourc fluid xhibits such bhavior. By contrast, anrgy ratio of condnsr is highr for highr condnsr tmpratur sinc th irrvrsibility incrass with th tmpratur diffrnc in th hat xchang procss. Rcall that th coolant tmpratur is hld constant at o C. Finally th variations of two kinds of xrgy fficincis dfind in () and (11) ar shown in Fig. 8 with rspct to TIP and TIT, and in Fig. 9 with rspct to TOP and condnsr Fig. 8 Variation of xrgy fficincis with rspct to turbin inlt prssur and tmpratur. tmpratur, rspctivly. Th fficincy η 2a rprsnts th xrgy fficincy of th cycl basd on th xrgy input of sourc fluid. In this cas th xrgy of th sourc xhaust is considrd as a loss. Whil th fficincy η 2b is basd on th xrgy actually dlivrd to th systm by th sourc fluid. Th lattr is intrinsically highr than th formr and th diffrnc bcoms largr as th anrgy ratio of sourc xhaust gts highr. Thrfor thir diffrnc magnifis with incrasing TIP, whil it rmains almost unchangd with rspct to TOP or condnsr tmpratur. η 2a has pak valus at som TIPs for ach TIT. Though η 2b is monotonically incrasing in th considrd rang of TIP, it is also xpctd to hav pak valus if th sourc tmpratur is furthr raisd. Both η 2a and η 2b for fixd turbin inlt conditions dcras with incrasing TOP bcaus th anrgy of jctor and condnsr xhibit th similar bhavior. Thy ar lowr for Anrgy ratio of condnsr (%) Turbin outlt prssur (bar) Exrgy fficincis (%) 18 η 2a η 2b Turbin outlt prssur (bar) Fig. 7 Dpndnc of anrgy ratio of condnsr on turbin outlt prssur and condnsr tmpratur. Fig. 9 Variation of xrgy fficincis with rspct to turbin outlt prssur and condnsr tmpratur. 9

5 highr condnsr tmpraturs bcaus of th largr tmpratur diffrnc in th condnsr. IV. CONCLUSIONS An assssmnt of xgtical prformanc of a combind powr and jctor rfrigration cycl is carrid out for th ffctiv rcovry of low-tmpratur wast hat. Th cycl uss R5fa as working fluid and watr at 0 o C as sourc fluid. Th ffcts of turbin conditions and condnsr tmpratur on th xrgy dstruction ratio of systm componnt and cycl xrgy fficincy ar invstigatd. Rsults show that th biggst xrgy dstruction occurs in th hat addition procss and has an almost 50% of th total xrgy dstruction of th cycl. Th rsult that th xrgy fficincy can hav pak valus with rspct to turbin inlt prssur may b a usful guid to th cycl opration for th ffctiv rcovry of low tmpratur wast hat. A furthr study of th ffcts of systm paramtrs such as th sourc tmpratur and vaporator tmpratur and th slction of working fluid on th xrgtical prformanc of th combind cycl is rquird. [12] A. Habibzadh, M. M. Rashidi, and N. Galanis, Analysis of a combind powr and jctor-rfrigration cycl using low tmpratur hat, Enrgy Convs. Mgmt., vol. 65, pp , 13. [13] A. Bjan, Advancd nginring thrmodynamics; 3rd d., Nw Jrsy: John Wily & Sons, 06. [14] T. Yang, G. J. Chn, and T. M. Guo, Extnsion of th Wong-Sandlr mixing rul to th thr-paramtr Patl-Tja quation of stat: Application up to th nar-critical rgion, Chm. Eng. J., vol. 67, pp , [] K. H. Kim, and C. H. Han, Analysis of transcritical organic Rankin cycls for low-grad hat convrsion, Adv. Sci. Ltt., vol. 8, pp , 12. [16] C. L. Yaws, Chmical proprtis handbook, McGraw- Hill, [17] H. J. Ko, and K. H. Kim, Thrmodynamic prformanc of a combind powr and jctor rfrigration cycl, WASET, vol. 79, pp , 13. ACKNOWLEDGMENT This rsarch was supportd by Basic Scinc Rsarch Program through th National Rsarch Foundation of Kora (NRF) fundd by th Ministry of Education, Scinc and Tchnology (No ). REFERENCES [1] T. C. Hung, T. Y. Shai, and S. K. Wang, A rviw of organic Rankin cycls (ORCs) for th rcovry of low-grad wast hat, Enrgy, vol., pp , [2] P. J. Mago, L. M. Chamra, K. Srinivasan, and C. Somayaji, An xamination of rgnrativ organic Rankin cycls using dry fluids, App. Thrm. Eng., vol., pp , 08. [3] N. T. Raj, S. Iniyan, and R. Goic, A rviw of rnwabl nrgy basd cognration tchnologis, Rnw. Sustain. Enrgy Rv., vol., pp , 11. [4] B. F. Tchanch, Gr. Lambrinos, A. Frangoudakis, and G. Papadakis, Low-grad hat convrsion into powr using organic Rankin cycls - A rviw of various applications, Rnw. Sustain. Enrgy Rv., vol., pp , 11. [5] H. Chn, D. Y. Goswami, and E. Stfanakos, A rviw of thrmodynamic cycls and working fluids for th convrsion of low-grad hat, Rnw. Sustain. Enrgy Rv., vol. 14, pp ,. [6] F. Vlz, J. J. Sgovia, M. C. Martin, G. Antolin, F. Chjn, and A. Quijano, Comparativ study of working fluids for a Rankin cycl oprating at low tmpratur, Ful Proc. Tch., vol. 3, pp , 12. [7] A. Schustr, S. Karllas, and H. Splithoff, Enrgtic and conomic invstigation of innovativ Organic Rankin Cycl applications, Appl. Thrm. Eng., vol. 29, pp , 08. [8] D. Wang, X. Ling, H. Png, L. Liu, and L. Tao, Efficincy and optimal prformanc valuation of organic Rankin cycl for low grad wast hat powr, Enrgy, vol. 50, pp , 13. [9] Y. Dai, J. Wang, and L. Gao, Exrgy analysis, paramtric analysis and optimization for a novl combind powr and jctor rfrigration cycl, Appl. Thrm. Eng., vol., pp , 09. [] B. Zhng, and Y. W. Wng, A combind powr and jctor rfrigration cycl for low tmpratur hat sourcs, Sol. Enrgy, vol. 84, pp ,. [11] J. Wang, Y. Dai, and Z. Sun, A thortical study on a novl combind powr and jctor rfrigration cycl, Int. J. Rfrig., vol. 32, pp ,