Int. J. of Thrmodynamics Vol. 12 (No. 1), pp. 38-43, March 29 ISSN 131-9724 www.icatwb.org/journal.htm Abstract Thrmodynamic Modling of an Ammonia-Watr Absorption Systm Associatd with a Microturbin Janilson Arcanglo Rossa and Edson Bazzo 1* Fdral Univrsity of Santa Catarina, Dpartmnt of Mchanical Enginring, Florianópolis, Brazil E-mail: 1 bazzo@mc.ufsc.br Thrmodynamic modling and Scond Law analysis of a small-scal cognration systm consisting of a 5 rfrigrant ton absorption chillr connctd by a thrmosyphon hat xchangr to a 28 kw natural gas microturbin ar prsntd. Th proposd configuration changs th hat sourc of th absorption chillr, rplacing th original natural gas burning systm. A computational algorithm was programmd to analyz th global fficincy of th combind cooling and powr plant and th cofficint of prformanc of th absorption chillr. Th rsults show th consistncy of th proposd modl and a good prformanc of th cognration systm. Th thrmal fficincy of th combind cooling and powr plant is approximatly 41%, which rprsnts a 67% incras rlativ to a singl natural-gas microturbin. Kywords: Cognration, natural gas microturbin, ammonia-watr absorption chillr, scond law analysis. 1. Introduction Absorption rfrigration can bcom conomically attractiv whn using inxpnsiv hat nrgy at tmpraturs in th rang of 1 to 3ºC. Howvr th absorption rfrigration tchnology has bn constraind to larg commrcial and industrial installations, whr a larg amount of thrmal nrgy is rquird. For cost rasons, th most frquntly usd rfrigration cycl has bn th vaporcomprssion rfrigration cycl. During rcnt yars, th incrasing accssibility to natural gas and th continuously incrasing costs of nrgy hav rcommndd th us of nw tchnologis or th us of high-fficincy quipmnt in cognration systms for powr, stam, hot watr or cold watr gnration. In this nw scnario, absorption chillrs ar proposd hr to b usd also in small-scal plants basd on natural gas microturbins, for powr and cold watr gnration. Rcnt rsults from xprimntal and thortical invstigations (Mdrano t al., 26; Takshita t al., 25; Ruckr t al., 24 and Ruckr t al., 23) hav bn rportd in ordr to confirm th plant opration rliability and to show th high global prformanc of small-scal cognration systms using absorption chillrs. In this work, a thrmodynamic modl is prsntd for a smallscal cognration plant with simultanous production of powr and cold watr. Th small-scal plant consists of a 5 rfrigrant ton (RT) ammonia-watr rfrigration systm connctd to a 28 kw microturbin, both drivn originally by natural gas. Th ammonia-watr cycl was slctd bcaus it dos not crystalliz whn submittd to lvatd tmpraturs, as happns with th watr-libr cycl. Th proposd configuration changs th hat sourc of th chillr, rplacing th natural gas burning systm with a hat xchangr connctd to a microturbin. Th xhaust gas coming from th microturbin, whn ntring th hat xchangr, warms th ammonia-watr solution and drivs th ammonia sparation in th chillr. Th ammonia-watr solution flow btwn th hat xchangr and th gnrator is stablishd by th thrmosyphon ffct. No scondary thrmal fluid was proposd to transfr th rsidual nrgy 38 / Vol. 12 (No. 1) from th xhaust gas to th gnrator. Th thrmodynamic simulation taks into account nvironmntal changs. Th rsults show th rliability and good prformanc of th proposd configuration undr diffrnt oprating conditions. Th corrsponding valus ar usd to analyz th opration paramtrs influnc on th cofficint of prformanc (COP), th microturbin fficincy and spcially on th global fficincy or primary nrgy ratio of th cognration systm. A Scond Law analysis was considrd to quantify th irrvrsibility of ach chillr componnt and also to dtrmin th potntial of ach componnt that contributs to th nrgy savings. 2. Systm dscription Th small-scal cognration systm consists of a 5 RT Robur gas fird chillr of singl ffct (17.7 kw), connctd to a 28 kw Capston turbin modl C3 LP by a thrmosyphon hat xchangr. Th rsidual nrgy of th xhaust gas is rcovrd for driving th absorption chillr bfor it is dischargd to th nvironmnt. In Figur 1 th schmatic of th cognration systm with four subsystms is shown including th natural gas supply, microturbin, hat rcovry and absorption chillr. Th tchnical spcifications of th natural gas microturbin and th absorption chillr, usd for stting th computational cod, ar shown in Tabl 1. As shown in Figur 1, natural gas is supplid to th microturbin to produc lctricity and hot xhaust gas for th hat xchangr. Th prssur of th supplid natural gas is 15 kpa (1.5 bar) and th tmpratur of th hot xhaust gas is about 26 C. An xisting intrnal ful-gas comprssor incrass th natural gas prssur from 359 to 379 kpa. An xtrnal prssur rgulator is usd to maintain a stady ful prssur at th microturbin inlt in ordr to limit prssur oscillations within ±7 kpa. Th xhaust gas from th microturbin is passd through th proposd thrmosyphon hat xchangr. Th hat is dirctly transfrrd to th ammonia-watr solution. No intrmdiat fluid is usd that would incras th thrmal rsistanc. *Corrsponding Author
Tabl 1. Nominal Tchnical Spcifications of th Microturbin and Absorption Chillr. Microturbin Output powr Efficincy Ful Exhaust gas tmp. Exhaust gas flow rat (SCG*) 28 kw 26% Natural Gas 27 C 17 Nm³/min Absorption Chillr Cooling capacity COP Min. chilld watr tmp. Max. nvironmnt tmp. Nominal air flow rat (SCG*) 17.7 kw.6 +4 C 55 C 1 Nm³/h *Nm3 is m3 at SCG Standard Conditions for Gass (T= C and P=11.325 kpa) A solution of watr and ammonia is usd as th working fluid, whr ammonia is th rfrigrant and watr is th absorbing fluid. In th proposd hat xchangr, th ammonia-watr is hatd to boiling, producing vapor with a strong concntration of ammonia, and as a consqunc, a liquid solution with a wak concntration of ammonia. A thrmosyphon ffct was considrd to provid th circulation of th watr-ammonia solution from th gnrator through th hat xchangr. Th thrmosyphon systm has th advantag of providing dirct hating and avoids th us of an xpnsiv circulation pump. Nvrthlss, for ffctiv opration of th systm th hat xchangr must b positiond blow th absorption chillr to allow th vapor ammonia to rturn to th gnrator. On of th first thrmosyphon applications is a Prkins tub, which uss a two-phas procss to transfr hat from a furnac to a boilr (Dunn, 1997; Ptrson, 1994). Th ammonia vapor flows into th rctifir for purification. Th hot and prssurizd ammonia vapor xiting th rctifir ntrs th air-coold condnsr whr it is coold and condnsd. Th liquid ammonia is thn brought to a lowr prssur ( assumd 1536 kpa) by mans of an initial xpansion valv aftr which it is coold in a pr-coolr. Finally, th liquid ammonia prssur is again rducd by a scond xpansion valv from 1536 kpa to an absolut prssur of 458 kpa and tmpratur of approximatly 2 C. At this condition, th liquid ammonia ntrs th vaporator and producs chilld watr to mt th cooling dmand. A vapor-liquid mixtur of ammonia lavs th vaporator at 4 C, flowing again through th pr-coolr whr it cools th liquid ammonia coming from th air condnsr. Th ammonia vapor ntrs th absorbr and coms into dirct contact and subsqunt dilution with th wak solution coming from th gnrator through a third xpansion valv. Th absorption of ammonia vapor is an xothrmic procss. Th solution flows from th absorbr to a subsqunt sction of th hat xchangr nar th air condnsr for cooling and complt absorption. Th lowr th tmpratur, th highr th ammonia concntration. At this point, th liquid solution with a high concntration of ammonia (strong solution) is pumpd through a coil insid th rctifir and through anothr coil insid th absorbr (GAX systm) back to th gnrator. A hydraulically drivn diaphragm pump is usd to displac th strong solution to th high prssur lvl in th gnrator. 1 13 Prcoolr Air-Coold Condnsr 4. Absorption chillr 14 2 Rctifir 1. Natural gas supply P 7 12 Gnrator 4 6 8 18 3 17 5 15 1 9 16 11 Evaporator 2 Absorbr P T 19 Thrmal Powr 3. Hat rcovry 22 2. Microturbin Air Natural Gas Hat Exchangr 21 Elctricity Gnration 24 23 Combustor Exhaust Gas Rcuprator Figur 1. Schmatic Diagram of th Cognration Systm. Int. J. of Thrmodynamics (IJoT) Vol. 12 (No. 1) / 39
3. Thrmodynamic analysis Th principl of mass consrvation and th First and Scond Laws of Thrmodynamics wr applid to ach componnt of th systm for th analysis. Evry componnt was considrd as a control volum, taking into account th hat transfr, work intraction and inlt and outlt strams. Th microturbin was not modld at th sam lvl of dtail as th absorption chillr, sinc it is not th focal point of this work. Th govrning quations for mass consrvation ar: m i m o = (1) mx i i m oxo = (2) whr x i and x o corrspond to th inlt and outlt ammonia mass fractions. Th First Law of Thrmodynamics yilds th nrgy balanc of ach componnt of th whol systm in following form Q W = m oho m ihi (3) and subjctd to th following assumptions: Stady stat opration; Thrmodynamic quilibrium at all points; Output powr qual to 26 kw; Inlt tmpratur of th gnrator: T 6 = 12ºC; Rfrigrant vapor concntration laving th rctifir qual to.99 (point 12); Diffrnc btwn inlt and outlt chilld watr tmpraturs qual to 5 C; Environmntal condition of 25 C; Dad stat of 25 C and 11.325 kpa. Th rfrigrant vapor concntration was st qual to.99 and variations with oprating conditions wr nglctd. Only th rsidual nrgy from th microturbin xhaust gas was considrd as th nrgy sourc of th hat xchangr. A minimum inlt tmpratur of th gnrator of T 6 = 12ºC (s Figur 1) was considrd for th simulation. Th vapor mass flow rat at point 7 was corrlatd to th vapor mass flow rat gnratd insid th hat xchangr. Th COP of th absorption systm is dfind as: Q cool COP = m 21 c p, T 21 T ( rf ) whr Q cool is th cooling load mt by th vaporator (s Figur 1) and th corrsponding dnominator rprsnts th availabl nrgy associatd with th microturbin xhaust gas ntring th hat xchangr. This COP includs th hat xchangr as part of th absorption chillr. As usd in th COP calculation for an absorption chillr using a dirct firing systm, th COP, valuatd in quation (4), is basd on th ffctiv availabl nrgy in th xhaust gas. Th T rf considrd hr is 25 ºC, th sam rfrnc tmpratur for th Lowr Hating Valu (LHV) of th fuls. In fact, for both cass, it is impossibl to cool th gas to th rfrnc tmpratur. (4) Th global fficincy, or primary nrgy ratio, of th combind cooling and powr (CCP) systm is dfind as η W + Q cool CCP = Q ful whr W is th powr output of th microturbin, again th cooling load mt by th vaporator and (5) Q cool is Q ful is th ful nrgy rquird by th microturbin. Th Scond Law of Thrmodynamics was usd for analysis and calculation of th CCP prformanc basd on xrgy. Disrgarding magntic, lctrical, nuclar, and surfac tnsion ffcts, th total xrgy of th systm bcoms th summation of physical and chmical xrgis as ch ph ψ = ψ + ψ (6) Th physical xrgy of a fluid stram is dfind as: ( h h ) T ( s s ) ph ψ = (7) whr h and s ar th nthalpy and th ntropy of th fluid, rspctivly. Th calculation procdur for th chmical xrgy of various substancs basd on standard chmical xrgy valus has bn widly discussd in Szargut at al. (1988). For th watr-ammonia solution considrd hr, th chmical xrgy of th flows was approximatd using th following xprssion: ψ ( 1 x) ch x = + (8) M ch, NH3 ch, H2O NH M 3 H2O whr ch, NH3 and ch, H2O ar th chmical xrgis of ammonia and watr, rspctivly, as givn by Ahrndts (198). Th chmical xrgy unit is kj/kmol. Th xrgy dstroyd in ach componnt was calculatd as T X ds = miψi moψo + Q 1 W T (9) whr th first two trms of th right hand sid ar th inlt and outlt xrgy strams of th control volum. Th third trm is associatd with th xrgy of hat transfrrd from th sourc at tmpratur T. Th last trm is th xrgy of th mchanical work. Th total dstroyd xrgy of th absorption systm is th sum of dstroyd xrgis for ach componnt: Total k ds ds (1) X = X Th Scond Law fficincy of th systm is masurd by th xrgy fficincy, dfind as th ratio of th usful xrgy producd by th systm to th ful xrgy supplid to th systm. Thrfor, th xrgy fficincy of th cognration systm is th sum of th lctricity nrgy gnratd by th microturbin and th xrgy incras of th chilld watr in th vaporator dividd by th corrsponding xrgy of th hat sourc: ε CCP W = ( ψ ψ ) + m m ψ 2 2 19 ful ful (11) 4 / Vol. 12 (No. 1) Int. Cntr for Applid Thrmodynamics (ICAT)
whrψ ful is th ful xrgy, assumd to b qual to th LHV of th natural gas obtaind from th natural gas supplir company - SCGas. Th calculations wr carrid out using th softwar EES with th NH 3 -H 2 O library. Th proprty routins in th NH 3 -H 2 O library usd th corrlation dscribd by Ibrahim and Klin (1993). 4. Rsults and discussion As assumd bfor, for an output powr qual to 26 kw, th rsults concrning th prformanc and xrgy dstruction ar givn in Tabls 2 and 3, rspctivly. Othr input data includ th nvironmntal conditions, natural gas lowr hating valu, hat xchangr ffctivnss, and chilld watr flow rat, inlt and outlt tmpraturs. Th valus of prssur, tmpratur, nthalpy, ntropy, mass concntration, mass flow rat, and xrgy of th solution wr calculatd. Th oprating conditions of th whol systm ar shown in Tabl 4. Tabl 2. Prformanc Rsults. Cognration plant Symbol Valu Global fficincy η CCP 41.9 % Exrgy fficincy 25 % Microturbin Efficincy η MT 25.1 % Natural gas (SCG) m ful 1.45 Nm³/h Cooling systm Cofficint of prformanc COP.27 As shown in Tabl 2, th COP was calculatd as.27, which is at last 5% smallr than th nominal COP for th dirct firing systm. It is important to mphasiz th availabl nrgy associatd with th xhaust gas ntring th hat xchangr and th corrsponding tmpratur rfrnc, as dfind by Eq. 4. Th xrgy fficincy of th plant and th CCP global fficincy wr stimatd as approximatly 25 and 42%, rspctivly. Tabl 3. Exrgy Dstruction. Componnt X ds [kw] Microturbin 41.29 Absorption chillr 37.5 Hat xchangr/gnrator 27.87 Absorbr 3.65 Expansion valvs 1.75 Prcoolr 1.53 Air Condnsr 1.15 Rctifir 1.2 Evaporator.49 Hydraulic Pump.4 Th largst irrvrsibilitis ar associatd with th ful combustion for th microturbin and th hat xchangr/gnrator for th absorption chillr. As xpctd, th ful burning in th microturbin causs vry larg irrvrsibilitis. In th cas of th absorption chillr, a larg amount of thrmal nrgy is rquird in th hat xchangr/gnrator to driv th sparation of ammonia from th strong solution. Th xrgy dstruction in th absorbr taks into account all th irrvrsibilitis rlatd to th absorbr itslf and th subsqunt sction of th hat xchangr, placd clos to th air condnsr. Th othr componnts prsntd rlativly low xrgy dstructions. As sn in Tabl 3, th microturbin has th gratst xrgy dstruction followd by th hat xchangr as a consqunc of th hat xchanging or corrsponding ammonia-watr sparation. Furthr analysis is now focusd on th prdiction of systm fficincis for diffrnt chilld watr tmpraturs. Figur 2 shows th influnc of diffrnt chilld watr tmpraturs on th COP and xrgy fficincy. Th highr th vaporator tmpratur, th highr th chilld systm s COP. This is bcaus th solution concntration diffrnc incrass and th solution mass flow rat is rducd. So th hat transfrrd from th xhaust gas to th ammonia-watr solution dcrass and th COP incrass. As dfind in this work, th COP includs th hat xchangr as part of th absorption chillr and it is rfrncd to th ffctiv availabl nrgy in th xhaust gas, considring T rf qual to 25ºC. Considring th actual hat rmovd from th microturbin xhaust gas and for th chilld watr tmpratur qual to 5ºC, th COP bcoms.52. On th othr hand, th CCP xrgy fficincy dcrass slightly with incrasing outlt chilld watr tmpraturs. Th xrgy fficincy dcrass bcaus th xrgy of th chilld watr dcrass with incrasing outlt tmpratur sinc th chilld watr is at a tmpratur lss than th dad stat s tmpratur. COP.32.28.24 COP 28 26 24.2 22 4 8 12 Chilld watr [ºC] [%] Figur 2. Th Effct of Chilld Watr Tmpratur on th COP and CCP Exrgy Efficincy. Th gnral rsults of th whol systm for th tmpratur, mass fraction of ammonia, prssur, nthalpy, mass flow rat and xrgy obtaind from th thrmodynamic simulation ar shown in Tabl 4. Figur 3 shows th variation of th CCP global fficincy, microturbin fficincy and CCP xrgy fficincy with th plant s powr output. As can b sn from th figur, th highr th output powr, th highr th CCP global fficincy, th microturbin fficincy, and xrgy fficincy. A maximum global fficincy of approximatly 42% was found for 25 kw output, which rprsnts a 67% fficincy incras rlativ to a singl microturbin powr plant. Int. J. of Thrmodynamics (IJoT) Vol. 12 (No. 1) / 41
Tabl 4. Gnral Rsults Obtaind from th Thrmodynamic Simulation. Point Tmpratur x P h m ψ [ C] [% NH 3 ] [kpa] [kj/kg] [kg/s] [kj/kg] 1 4..471 458 91..1392 939 2 4.2.471 1538 92.7.1392 9391 3 51.4.471 1538 145..1392 9394 4 88.1.471 1538 358.4.1392 9424 5 12.3.396 1538 394.5.134 7945 6 12..396 1538 666.2.134 86 7 115..92 1538 195..26 18676 8 76.1.525 1538 286.1.31 1493 9 12.3.396 1538 394.5.1217 7945 1 68.5.396 458 394.5.1217 7931 11 52.5.471 458 33.6.1392 945 12 76.1.99 1538 1751..175 227 13 4..99 1538 522.1.175 19956 14 39.9.99 1536 522.1.175 19956 15 11.4.99 1536 385..175 19956 16 2..99 458 385..175 19953 17 4..99 458 1448..175 19866 18 13..99 458 1585..175 19857 19 12.2-2 51.5.8452 1.279 2 7.2-2 3.5.8452 2.411 21 251. - 12 528..2797 195.8 22 126.8-11 41.3.2797 73.4 23 25. - 11 -.21 49661 24 25. - 11 -.2775 49.96 η MT and η CCP [%] 4 3 2 1 η MT η CCP 5 1 15 2 25 Elctric powr [kw] 4 3 2 1 [%] Figur 3. Variation of th Microturbin Efficincy, Global Efficincy and Exrgy fficincy with Microturbin Powr Output. Th microturbin fficincy dcrass with incrasing nvironmntal tmpratur. As a consqunc, th xrgy fficincy and th global fficincy prsntd a small dclin. In fact, thr is no significant chang in th xrgy dstruction in th microturbin and in th chilld systm. 5. Conclusions Th absorption chillr connctd by a thrmosyphon hat xchangr to a microturbin was analyzd as a tchnically rliabl altrnativ for chilld watr and powr gnration. Th rsults show th consistncy and usability of th proposd thrmodynamic modl. A CCP global fficincy up to 42% was found, which rprsnts a 67% fficincy incras rlativ to a singl microturbin powr plant. Th COP was calculatd to b approximatly.27 (for a chilld watr tmpratur of 5ºC), which is at last 5% smallr than th nominal COP for th dirct firing systm. As dfind bfor, th COP is rfrncd to th ffctiv availabl nrgy in th xhaust gas ( T rf = 25ºC). For a COP rfrncd to th ral hat supplid from th hat xchangr to th gnrator, th COP is.52. Th COP incrass with incrasing chilld watr tmpratur. Th xrgy fficincy of th plant was stimatd to b approximatly 25%. Th xrgy fficincy dcrass slightly with incrasing nvironmnt tmpratur. A mor snsitiv influnc on th xrgy fficincy has bn obsrvd for output powr variation than for th variation of th oprational paramtrs of th chillr. Th xrgy dstruction was calculatd for vry componnt of th systm. Th microturbin prsntd th highst rat of xrgy dstruction (approximatly 41 kw). In th chillr, th hat xchangr was th componnt with th highst rat of xrgy dstruction. Nomnclatur COP Cofficint of prformanc c Constant prssur spcific hat of xhaust p, gas [kj/kg.k] Watr standard chmical xrgy [kj/kmol] ch, H2O Ammonia standard chmical xrgy ch, NH3 [kj/kmol] 42 / Vol. 12 (No. 1) Int. Cntr for Applid Thrmodynamics (ICAT)
h LHV M m Q Enthalpy [kj/kg] Low hating valu [kj/kg] Molcular mass [kg/kmol] Mass flow rat [kg/s] Hat transfr rat [kw] Q cool Thrmal load from th vaporator [kw] Q ful Hat supply by ful [kw] s Spcific ntropy [kj/kg.k] T Tmpratur [K] W Powr [kw] X ds Exrgy dstruction [kw] x Mass fraction of ammonia Grk Lttrs ε Exrgy fficincy [%] ψ Exrgy [kj/kg] η Enrgy fficincy [%] Subscripts ac Absorption chillr systm CCP Combind cooling and powr Elctric H2O Watr i Inlt MT Microturbin NH 3 Ammonia o Outlt Environmnt condition Suprscripts Carnot Carnot ch Chmical ful Ful k Componnt ph Physical Acknowldgmnts Th authors thank th FINEP (Rsarch and Projcts Financing), th CNPq (National Council for Scintific and Tchnological Dvlopmnt) and th companis Ptrobras, TBG and SCGás, for th financial support grantd to this rsarch. Rfrncs Ahrndts, J., 198, Rfrnc Stats, Enrgy, Vol.5, pp. 667-677. Dunn, P. D., Ray, D. A., 1997, Hat Pip, Prgamon Prss, 4 th Edition. Klin, S. A., Álvaro, F. L., 23, EES-Enginring Equation Solvr. Vrsion 7.413-3D, F-Chart Softwar, Madson, WI. Kotas, T. J., 1995, Th Exrgy Mthod of Thrmal Plant Analysis, Krigr Publishing Company: Malabar. Ibrahim, O. M., Klin, S. A., 1993, "Thrmodynamic Proprtis of Ammonia-Watr Mixturs," ASHRAE Transactions Papr CH-93-21. Mdrano, M., Mauzy, J., McDonll, V., Samulsn, S. and Bor, D., 26, Thortical Analysis of a Novl Intgratd Enrgy Systm Formd by a Microturbin and an Exhaust Fird Singl-Doubl Effct Absorption Chillr, Int. J. of Thrmodynamics, Vol. 9, No.1, pp. 29-36. Rossa, J. A. and Bazzo, E., 26, Thrmodynamic Modling and Scond Law for an Ammonia-Watr Absorption Systm Associatd to a Microturbin, Procdings of ECOS 26 18th Intrnational Confrnc on Efficincy, Cost, Optimization, Simulation and Environmntal Impact of Enrgy Systms - Aghia Plagia, ISBN 96-87584-1-6, Vol 2, pp 651-658; Grc. Ptrson, G. P., 1994, Hat Pips Modling, Tsting and Applications. John Wily & Sons, Nw York. Ruckr, C. P. R., Bazzo, E. Jonsson M. R., Karlsson, S. J., 23, Exrgy Analysis of a Compact Microturbin- Absorption Chillr Cognration Systm, Procdings of COBEM 23, São Paulo, Brazil. Ruckr, C. P. R., Bazzo, E., 24, Exrgoconomic Optimization of a Small Scal Cognration Systm using th Exrgy Cost Thory. Procdings of ECOS 24 16th Intrnational Confrnc on Efficincy, Costs, Optimization, Simulation and Environmntal Impact of Enrgy and Procss Systms; ISBN-968-489-27-3, Vol. II, pp. 619-628; Guanajuato, vol. II, pp. 619-628. Szargut, J., Morris, F. R., Stward, F. R., 1988, Exrgy Analisis of Thrmal, Chmical, and Mtalurgical Procsss, Hmisphr Publishing Corporation: Nw York. Takshita, K., Amano Y., Hashizum, T., 25, Exprimntal Study of advancd Cognration Systm with Ammonia-Watr Mixtur cycl at Bottoming, Enrgy, Vol.3, pp.247-26. Int. J. of Thrmodynamics (IJoT) Vol. 12 (No. 1) / 43