ANALYSIS OF A COMBINED BRAYTON/RANKINE CYCLE WITH TWO REGENERATORS IN PARALLEL

ANALYSIS OF A COMBINED BRAYTON/RANKINE CYCLE WITH TWO REGENERATORS IN PARALLEL J. T. dos Sntos, T. M. Fgundes, E. D. dos Sntos b, L. A. Isoldi b, nd L. A. O. Roc c Universidde Federl do Rio Grnde do Sul, Escol de Engenri Porto Alegre, RS, Brsil b Universidde Federl de Rio Grnde, Escol de Engenri Rio Grnde, RS, Brsil c Universidde do Vle do Rio dos Sinos, ABSTRACT Tis ork presents configurtion of to regenertors in prllel for poer genertion Bryton/Rnkine cycle ere te output poer is 10 MW. Te orking fluids considered for te Bryton nd Rnkine cycles re ir nd ter, respectively. Te ddition of regenertor it te previous existing cycle of tis kind resulted in te ddition of second-stge turbine in te Rnkine cycle of reet. Te objective of tis modifiction is to increse te terml efficiency of te combined cycle. In order to exmine te efficiency of te ne configurtion, it is performed termodynmic modelling nd numericl simultions for bot cses: regulr Bryton/Rnkine cycle nd te one it te proposed cnges. At te end of te simultions, te to cycles re compred, nd it is seen tt te ne configurtion reces 0.9% iger efficiency. In ddition, te vpor qulity t te exit of te iger turbine is iger, reducing te required mss flo rte in 14%. Progrm de Pós-Grdução em Engenri Mecânic, São Leopoldo, RS, Brsil luizor@unisinos.br Received: My 25, 2017 Revised: June 19, 2017 Accepted: July 20, 2017 Keyords: Bryton/Rnkine cycle, terml efficiency, prllel configurtion, regenertors NOMENCLATURE ṁ mss flo rte, kg/s T temperture, K p pressure, kp x vpor qulity k polytropic coefficient W ork, kj Q et, kj specific entlpy, kj/kg Greek symbols Η efficiency Subscripts c cycle t terml s idel ter ir b pump n-m process n-m X stte X INTRODUCTION In te current Brzilin energetic mtrix, poer-generting cycles, ic trnsform te et resultnt of fossil fuels into electric energy, ply relevnt prt, becuse, even toug te society clims for clener energy production metods, tese cycles present strtegic lterntive supply for te drougt seson. In ddition, tis metod provides lo initil cost nd reltively lo implementtion costs. Witin tis context, seeking for lterntive to improve te efficiency of tese cycles is extremely importnt, not only in n economic point of vie, reducing te fuel consumption, but lso in n mbient-friendly prt, reducing te emission of pollutnts to te tmospere. Considering tis necessity of more efficient use of te energetic resources vilble, tis study ims to model nd numericlly simulte combined Bryton/Rnkine poer genertion cycle it n lterntive configurtion of te et regenertors, dding regenertor in prllel nd second-stge turbine in te combine cycle. Te study of combined Bryton/Rnkine cycle it te use of regenertors s been point of focus for some resercers. Bejn et l. (2012) soed tt te pt to improve te efficiency of regenertor, iming te mximum et trnsfer nd minimum ed loss, s to turn te current prllel cnnel 10 Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17

Sntos, et l. Anlysis of Combined Bryton/Rnkine structure into more complex structures in te form of dendritic cnnels, it te tree sped configurtion being tendency of evolution for tose systems. Cn Gülen e Rub W. Smit (2009) described simple, but very precise metod, to estimte o muc poer cn be extrcted from loer Rnkine cycle given n exergy output by gs turbine (iger Bryton cycle). Te metod is bsed in te Second L of Termodynmics nd, ccording to te utors, considering te tecnicl nd economic restrictions, te model cn deliver te mximum poer tt cn be extrcted by te loer cycle to ny gs turbine by just considering te output exergy. Hbib nd Zubir (1992) exmined te performnce of regenertive/reet Rnkine poer generting plnts troug n exergetic nlysis. His results indicte tt most losses occurred in te boiler nd tt tese losses could be minimized by eting te feeding ter, reducing te irreversibility of te cycle in 18%. Akib et l. (1993) creted tree types of computer softre to clculte te termodynmic properties of orking fluids nd evlute te performnce of te combined Bryton/Rnkine cycle. Severl prmeters ere vried in order to nlyze teir effects over te performnce of te combine cycle in poer plnts. According to te utors, te numericl results ere very comptible to te dt of ctive poer plnts. Kliq nd Kusik (2004) pplied te Second L of Termodynmics in combined Bryton/Rnkine cycle it reet of te gs turbine. It s investigted te effects of pressure, temperture, number of reets nd pressure loss. It s noticed tt te combustion cmber ccounted for more tn 50% of te totl exergy loss. In ddition, te efficiency of te cycle nd te mximum output poer ere found in medium pressure nd ere improved significntly en to reet stges ere present. Hoever, for more tn to reet stges, te efficiency nd output poer did not rise significntly. Frnco nd Csros (2004) evluted te fesibility of ig efficiency combined cycles. Te results soed tt it is possible to obtin poer plnts it efficiency iger tn 62%. In order to do tt, it ould be necessry to mke pproprite use of te existing tecnologies, itout te need of iting for ne tecnologicl development of turbines. Albdodim et l. (2004) investigted te performnce of big cycle composed of Bryton, to reverse prllel Bryton nd Rnkine cycle. Te expnsion pressure reltion beteen te to reverse Bryton cycles s vried, considering vlues bove te tmosperic pressure. Results soed tt te best terml efficiencies occurred for iger expnsion pressures, recing vlues of pproximtely 54%. Zng et l. (2012) proposed regenertive Bryton combined it to reverse Bryton cycles in prllel, it te regenertion occurring before te reverse cycles. Troug te nlysis of te First L of Termodynmics, it s found tt te cycle could rec iger terml efficiency en compred to tt of common cycle, but it loer specific ork. Te optiml efficiency found for tis system s of 51.2%. Gomez et l. (2014) presented poer genertion plnt in ic closed Bryton cycled s combined in prllel it vpor Rnkine cycle, exploiting te cold exergy vilble due to te regsifiction process of liquid nturl gs. Te cold exergy s used to bring te elium used in te Bryton cycle to cryogenic tempertures in te compressor entrnce nd to generte electricl poer troug direct expnsion. Energetic nd exergetic nlysis soed tt it is possible to obtin ig poer efficiency in te poer plnt, given te rigt conditions. Considering tis necessity of more efficient usge of te vilble energetic resources, tis study proposed n lterntive configurtion of et regenertors in combined Bryton/Rnkine cycle, ere regenertor in prllel is dded to te system long it second stge turbine. In order to nlyze te performnce of tis ne configurtion, termodynmic modelling nd numericl simultions ere performed for to cses: regulr Bryton/Rnkine cycle nd noter one it te proposed modifictions. At te end of te simultions, te results obtined for bot cycles re compred. COMBINED BRAYTON/RANKINE CYCLE WITH REGENERATORS IN PARALLEL In tis ork, ne configurtion for te Bryton/Rnkine cycle s proposed. Te objective s to increse te efficiency by inserting n extr regenertor nd second stge turbine, using te concept of reet for te Rnkine cycle. It s proposed tt tis extr regenertor ould be in prllel it te previous existing, s illustrted in Fig. 1. In tis cse, te ot ir output from te gs turbine (in red in Fig. 1) ould be divided in to strems t te sme temperture: te first pssing troug regenertor 1 nd being used to et te vpor input for te first stge turbine. Tis flo s clled ṁ 4. Te second flo s used to reet te vpor output from te first stge turbine troug regenertor 2. Tis flo s clled ṁ 4b. In order to equte te cycle mtemticlly, te folloing ypotesis ere considered: Stedy-stte system; Air modelled s n idel gs it polytropic coefficient k = 1.4; no ed nd et losses; no cnges in kinetic nd potentil energies; Pumps, compressors, turbines nd regenertors re dibtic. In te formultion of te mtemticl model of te different components of te cycle, it s used te Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17 11

Sntos, et l. Anlysis of Combined Bryton/Rnkine pproc similr to Morn nd Spiro (2002). In tis pproc, te volumes of control re defined s ell s te energy nd mss blnce for ec process of te cycle, ic re: Process 1-2: Isentropic compression troug te compressor. Process 2-3: Het input by te eting/combustor et trnsfer. Process 3-4: Isentropic expnsion troug te turbine. Process 4-5: Het rejection troug te cooling et excnger. Process 6-7: Het input troug regenertor 1. Process 7-10: Isentropic expnsion troug te first stge turbine. Process 10-11: Het input troug regenertor 2. Process 11-8: Isentropic expnsion troug te second stge turbine. Process 8-9: Het rejection troug te condenser. Process 9-6: Isentropic compression troug te pump. ddition, η c is te isentropic efficiency of te process. It is importnt to mention t tis time tt specific poer, entlpy nd et per unit mss re given in kj/kg, for ll te times tese properties re mentioned. For process 2-3, te et per unit mss delivered to te ir Q 2 3 3 2 (3) ere 3 is te specific entlpy of te stndrd ir leving te combustor. For te gs turbine, process 3-4, te poer per unit mss generted in te turbine, given, 4s nd 4 te entlpies of ir in te exit of te turbine, for idel nd rel cses, respectively, given in nd η t te isentropic efficiency of te turbine. W t 3 4 (4) 3 4 (5) 3 In te cooling et excnger, represented by te process 4-5, te et per unit mss tt is removed from te fluid, in kj/kg, is given by 4s Q si 4 5 (6) Figure 1. Illustrtion of te proposed Bryton/Rnkine cycle it regenertors in prllel. Te ork generted in te compressor in te process 1-2 is presented s W c 2 1 m (1) nd correction to rel cse, ere irreversibility is considered, cn be obtined s c 2s 1 2 1 (2) ere Ẇc/ṁ te poer per unit mss consumed by te compressor 1 nd 2 te entlpies of ir t te inlet nd outlet of te compressor nd 2s te specific entlpy t te compressor outlet to te idel cse. In ere 5 is te specific entlpy tt leves te combustor, in kj/kg. Te volumes of control of te regenertors of te combined cycle ere estblised, it process 4-5 in te ir prt nd processes 6-7 nd 10-11 for te ter prt. By pplying mss nd energy blnces, te ir mss flo rtes tt pss troug regenertors 1 nd 2, respectively, re obtined s 4 5 4 7 6 4 5 4b 11 10 m m m4b (7) (8) 4 (9) ere ṁ is te mss flo rte of ter, 5 is te specific entlpy tt leves te combustor, 7 nd 11 re te specific entlpies of sturted vpor tt leve ec of te regenertors. For te process 6-9, Eq. (7) te poer per unit mss consumed by te pump, in kj/kg for n idel 12 Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17

Sntos, et l. Anlysis of Combined Bryton/Rnkine cse is given s W b 6 9 nd te correction to rel cse is (10) For te condenser (process 8-9), te et per unit mss bsorbed by te condenser cn be derived s Q 8 9 8 9 (18) 6 s 9 b (11) 6 9 Here, 9 is te specific entlpy of te sturted liquid in te inlet of te pump nd 6s nd 6 re te specific entlpies of te compressed liquid tt leves te pump, in kj/kg, for te idel nd rel cses, respectively. For te regenertors, processes 6-7 nd 10-11, te et per unit mss delivered to te fluid is, respectively, s Q Q 6 7 1011 7 11 6 10 (12) (13) ere 7 nd 11 re te specific entlpies of sturted vpor tt leves ec of te regenertors. For equting purposes, it is considered tt te vpor genertor is inside te control volume of te regenertor. In te first stge vpor turbine, disregrding te losses, it is possible to obtin te poer per unit mss generted by te turbine s W 7 10 (14) Te rel entlpy of te outlet flo cn be obtined if te isentropic efficiency of te turbine is knon, troug 7 10 t (15) 7 10s Here, Ẇ 10 nd 10s re te specific entlpies of te vpor t te outlet of te turbine, for rel nd idel cses, respectively. Te sme cn be considered for te second stge turbine, W b 8 11 (16) 8 11 tb (17) 8 11 ere 9 is te specific entlpy of te vpor t te exit of te condenser. Troug te poer blnce in te tree cycles, Bryton, Rnkine nd Combined cycle, te ork from te Bryton cycle (W ), te Rnkine cycle (W ) nd te totl ork (W t ) cn be obtined, respectively, by W W W W (19) t b c W W W (20) W t b W W (21) Te idel terml efficiency, tcc, is defined s te totl liquid ork produced by determined poer cycle divided by te externl et tt is delivered to it. Applying tis definition to te combined cycle, te objective function, is obtined: tcc METHODOLOGY W t Q 2 3 (22) Te metodology used in tis ork s termodynmic modelling coupled it numericl simultion nd compring te results obtined for to systems: bencmrk cse, ere regulr combined Bryton/Rnkine cycle nd second cse bsed in te cycle illustrted in Figure 1. Te equtions for bot cses re prcticlly te sme, prt from te bencmrk cse only ving one regenertor nd turbine. Tus, Eqs. (10), (13), (14), (16), (17) nd (18) re suppressed. In order to ve strict comprison beteen bot cses, te input dt for bot ve to be te sme, given tt cnge in te termodynmic properties or te efficiencies of te cycles ould led to disprities in te comprison, tus nullifying te results. Te lgebric system of non-liner equtions ere solved using te softre Interctive Termodynmics (IT) nd te termodynmic properties of te fluids involved in te process, stndrd ir nd ter, ere obtined it te softre s dtbse. In te present ork, ll equtions ere solved it residul error belo 10-13, tus it is possible to Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17 13

Sntos, et l. Anlysis of Combined Bryton/Rnkine ffirm tt te numericl error did not influence te results obtined. Opposite to te numericl results, te ypotesis used in te modelling for tis ork migt ve more influence over eventul devition of te results obtined ere. Hoever, tis is not going to be nlyzed in tis ork. Te termodynmic properties, s ell s te efficiency of te cycle components re son in Tble 1. As previously mentioned, te sme vlues ere considered for bot systems in suc y tt te only points it degree of freedom in te cycle it to regenertors ere in points 10 nd 11, te exct points ere te cycles re different. Tble 1. Termodynmic properties, efficiencies nd totl poer for te bencmrk cse (regulr cycle). Prmeter Vlue T 1 300 p 1 100 T 3 1,400 p 3 1,200 p 4 100 T 5 480 p 5 100 T 7 673 p 7 8,000 p 8 8 p 9 8 Ẇ t 100,000 ɳ c 0.84 ɳ t 0.88 ɳ t 0.9 ɳ b 0.8 Hoever, te post-reet temperture, T 11, s considered to be te sme 673 K, te sme temperture s T 7 (te temperture of te fluid leving te regenertor for te bencmrk cse). Tis s necessry in order to consider tt te regenertor from bot cses ould ve te sme cpcity. After tese considertions, te only termodynmic property from te system tt remined free to nlyze its influence in te proposed system s te pressure from point 10, te intermedite pressure beteen te to stges of te turbine. It is importnt to reiterte tt te pressure from points 10 nd 11 re considered te sme. By modeling te cycle it regenertors in prllel, te pressure in point 10 s cnged from 400 to 1500 kp, it intervls of 100 kp. Wit tis, te responses of te cycle for tis rnge of pressure ere obtined. Tese vlues ere compred to te one obtined in te bencmrk cse. In ddition, it is importnt to restte tt tis pressure rnge s cosen becuse te vpor qulity of te fluid t te first stge turbine of te lo cycle lys remined in te sturtion region. Pressure vlues bove 1500 kp (supereted vpor) ere lso nlyzed. Hoever, since te efficiency of te system did not increse considerbly nd te vpor qulity of te fluid t te exit of te second stge decrese bruptly, it vlues belo 90%, tese results ere suppressed from tis text. ANALYSIS AND RESULTS Using te previously described metodology nd model, ll interest prmeters ere obtined for te studied cycles. Tese prmeters re: efficiency, mss flo rtes, turbines poers, outlet vpor turbine vpor qulities nd externl et delivered to te system. Te results obtined for te relevnt prmeters to te bencmrk cse re son in Tb. 2. Tble 2. Relevnt prmeters obtined for te bencmrk cse. Prmeter Vlue ṁ 239.8 ṁ 30.44 η tcc 0.4939 Q 202,500 23 Ẇ Ẇ 6.89E+04 3.11E+04 x 8 0.8034 Te results obtined for te cycle it regenertors in prllel cn be seen troug te grps of Figs. 2-6. tcc Figure 2. Effect of te pressure of point 10 over te idel terml efficiency of te cycle it to regenertors in prllel. Looking t Fig. 2, it is seen tt s te pressure of point 10 increses, tere is n increse of terml efficiency in te combined cycle, strting it 49.46% for 400 kp pressure nd recing 49.84% for 1500 kp. In ddition, by compring te results from Fig. 2 to te bencmrk cse, it is seen tt te proposed cycle reces iger efficiencies, it terml efficiency incresing up to 0.45%. Looking 14 Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17

Sntos, et l. Anlysis of Combined Bryton/Rnkine in oter perspective, tis mens tt if te bencmrk cse is turned into cycle it regenertors in prllel, its efficiency ould increse by rougly 1%. Te results son in Figure 3 revels tt, for te proposed cycle, loer mss flo rte of ir s obtined, especilly for pressure vlues round 1500 kp for point 10. Furtermore, for poer plnt ctive for more tn 20 yers, gret mount of fuel could be sved, tus te importnce of tis result s big impct economiclly. Figure 3. Vrition of te mss flo rtes of te orking fluids regrding te pressure of point 10, for te proposed cycle. By looking t Figure 3, it is possible to notice tt, s pressure p 10 increses, te mss flo rte of ir tt goes troug regenertor 1 lso incresed, ile reducing te mss flo rte tt goes troug regenertor 2. Tis result is compreensible, since s te intermedite pressure beteen te to stges turbine (p 10 ) increses, less energy is needed in te second regenertor in order to cnge te orking fluid up to te properties considered in point 11. It is possible to notice tt te exceeding energy tt did not pss troug te second regenertor is utilized minly in te first regenertor, ere mss flo rte of compressed liquid (incresing it te increse of p 10 ) s to be trnsformed into supereted vpor. Still regrding te results in Figure 3, it is seen tt te mss flo rte of vpor increses stedily it te increse of p 10. Hoever, en compred to te bencmrk cse, even for te igest vlue of p 10 studied, tis mss flo rte s reduced significntly for te ne cycle, being, t te orst cse, 14.3% loer tn te mss flo rte for te bencmrk cse. Tis reduction brings benefit of ving more compct instlltions. By nlyzing te results Figure 3, combined it Fig 4, it is seen tt te reduction of te totl mss flo rte s consequence of te reduction of te externl et given to te cycle, s expected. Tis result is son in Figure 4. If it is considered tt te rte of mixture for combustion (r nd fuel) re te sme for bot cses, tis decrese of 0.9% found for te totl ir flo nd for te et delivered to te cycle ould ccount for n equl reduction for te fuel consumption. Figure 4. Cnge in te externl et given to te cycle in function of te pressure on point 10 for te studied cycle. By looking t Figure 5, it is seen tt te resulting vpor qulities for te proposed cycle ere more dequte tn te bencmrk cse. Tis improvement s expected, since it s dded n extr regenertor, nd consequently ne reet process to te system. X Figure 5. Results for te vpor qulity t te exit of te turbines for different vlues of pressure on point 10. Tere is n increse in te vpor qulity, going from 80.34% of te bencmrk cse, for minimum of 91.51% for te proposed cycle. Tis ould men loer er of te vpor turbines, since tey re projected to ork minly it vpor, being dmged by liquid fluids. Finlly, te net mount of ork produced for te turbines of te system ere nlyzed. Results re son in Figure 6. Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17 15

Sntos, et l. Anlysis of Combined Bryton/Rnkine By nlyzing Figure 6, it s noticed tt te poer generted by te gs turbine s reduced. But, since te system efficiency incresed, tese results s lredy expected, becuse ll te et coming into te system from externl sources do so troug te iger cycle. In ddition, since te termodynmic properties of te ir ere fixed, smller mount of ir nd, tus, loer poer is generted by it. reducing te er of te vpor turbines, becuse te vpor qulity t te exit of te turbines s iger. In tis cse, te turbines could ork in system it less liquid. As te min disdvntges of pplying te cycle proposed in tis ork in poer genertion plnt re: te introduction of second stge turbine, coupled it utomtion systems tt ould control te ir flos nd possible increse in te ir nd vpor piping. It is lso son in tis ork tt te usge of regenertors in prllel is good lterntive to increse te terml efficiency of poer plnts. Hoever, n exergetic nd economic nlysis ould be required to nlyze, in ider form, if te ppliction of te proposed system is dvntgeous. Tese nlyses re going to be ddressed in future orks. ACKNOWLEDGEMENTS Figure 6. Influence of pressure p 10 over te liquid poer of te turbines for te proposed cycle. It is lso noticed tt te turbines of te Rnkine cycle mde up for te poer reduction in te gs turbine. Tis is minly due to te second stge turbine, ere te poer produced incresed s te pressure level incresed. Tis result s lso expected, since by incresing p 10 it is lso reduced te energy removed from te orking fluid in te first stge turbine nd, consequently, incresed te mount of energy vilble to be extrcted by te second stge turbine. CONCLUSIONS Troug te present study, it is concluded tt te ppliction of regenertors in prllel in combined Bryton/Rnkine cycles cn ccount for severl benefits. Te min dvntge is te improvement of te cycle efficiency, ic ould reduce significntly te energy consumption, resulting in less fuel consumption ile lso reducing te pollution tt comes from te combustion of fossil fuels. In ddition, te vpor mss flo rte is reduced in 14.3%. Tis opens te possibility of ving more compct nd ceper systems, since every component in te cycle could be reduced, for given poer demnd. On te oter nd, for te sme instlltion, more poer could be extrcted from te cycle. Te utiliztion of n extr regenertor benefited te reeting process of te Rnkine cycle. Tis proposition soed to be interesting in te spect of Te utors tnk te Conselo Ncionl de Desenvolvimento Científico e Tecnológico (CNPq) nd te Comissão de Aperfeiçomento de Pessol de Nível Superior (CAPES) for te finncil support, s ell s te universities UFRGS nd FURG tt elped in te mking of tis ork. REFERENCES Albdodim M. A., Agne B., nd Alktii A, 2004, Exmintion of te Performnce Envelope of Combined Rnkine, Bryton nd To Prllel Inverse Bryton Cycles, Journl of Poer nd Energy, Vol. 218, pp. 377-385. Bejn, A., Lorente, S., nd Kng, D., 2012, Constructl Design of Regenertors, Interntionl Journl of Energy Reserc, Vol. 37, pp 1509-1518. Cn Gülen S., nd Smit, R. W., 2009, Second L Efficiency of te Rnkine Bottoming Cycle of Combined Cycle Poer Plnt, Journl of Engineering for Gs Turbines nd Poer, Vol. 132, pp. 1017-1-27. Frnco, A., nd Csros, C., 2004, Termoeconomic Evlution of te Fesibility of Higly Efficient Combined Cycle Poer Plnts, Energy, Vol. 29, pp. 1963-1982. Gómez, M. R., Grci, R. F., Gómez, R. R., nd Cril, J. C., 2014, Termodynmic Anlysis of Bryton Cycle nd Rnkine Cycle Arrnged in Series Exploiting te Cold Exergy of LNG (Liquefied Nturl Gs), Energy, Vol. 66, pp. 927-937. Hbib M. A., nd Zubir S. M., 1992, Second- L-Bsed Termodynmic Anlysis of Regenertive-Reet Rnkine-Cycle Poer Plnts, Energy, Vol. 17, pp. 295-301. Kliq A., nd Kusik S. C., 2004, Second- L Bsed Termodynmis Anlysis of Bryton/Rnkine Combined Poer Cycle it Reet, Applied Energy, Vol. 78, pp. 179-197. 16 Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17

Sntos, et l. Anlysis of Combined Bryton/Rnkine Mssi, A., Emd A., nd Mso, T., 1993, A Study of Hig-Accurcy Clcultions of Combined Bryton/Rnkine Cycles for Poer Genertion, JSME Interntionl Journl, Serie B, Vol. 36, No. 1, pp. 178-183. Morn, M. J., nd Spiro, H., 2002, Fundmentls of Engineering Termodynmics, 4t ed., Jon Wiley & Sons. Zng Z., Cen L., nd Sun F., 2012, Energy Performnce Optimiztion of Combined Bryton nd To Prllel Inverse Bryton Cycles it Regenertion before te Inverse Cycles, Scienti Irnic, Trnsctions B: Mecnicl Engineering 19, pp. 1279-1287. Engenri Térmic (Terml Engineering), Vol. 16 No. 2 December 2017 p. 10-17 17