Analysis and Comparison of Closed System Based Thermal Cycles Undergoing Different Polytropic Transformations

Transcription

1 Iteratoal Joural of Emergg Egeerg Research ad Techology olume 7, Issue 1, 019, PP 6-7 ISSN (Prt & ISSN (Ole Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos Ramo Ferrero. Garca 1, Jose Carba Carrl 1 Id. Eg. Dept., Eergy & Propulso Dept Uversty of A Corua, ETSNM, Paseo de Roda 51, 15011, A Corua, Spa. *Correspodg Author: Ramo Ferrero. Garca, Id. Eg. Dept Uversty of a Corua, ETSNM, Paseo de Roda 51, 15011, a Corua, Spa ABSTRACT Ths research work deals wth a feasble thermal eergy covertor cosstg of a o-regeeratve thermal cycle, composed by two closed polytropc trasformatos ad two closed sochorc trasformatos whch are mplemeted y meas of a double effect recprocatg cylder whch dffers bascally from the Carot based covetoal thermal cycles that: All cycle processes udergoes closed trasformatos, stead of the covetoal ope processes of the Carot based thermal cycles, I the actve processes of ths cycle (polytropc path fuctos, as heat s beg absorbed or rejected uder load-depedet path fuctos, mechacal work s smultaeously performed, avodg the covetoal uas-adabatc expaso or compresso processes heret to the Carot based eges ad, Durg the load-depedet path fuctos of the closed polytropc processes of ths cycle, mechacal work s also performed by meas of the workg flud cotracto due to heat rejecto. A aalyss of the proposed cycle s carred out for helum workg fluds ad results are compared wth those of a Carot ege operatg uder the same rato of temperatures. Because of the cycle aalyss, t follows that the rato of top to the bottom cycle temperatures has very low depedece o the deal thermal effcecy, but the specfc work. Furthermore, wth the rage of relatve low operatg temperatures, hgh thermal effcecy s acheved, eve exceeds the Carot factor whe t operates wth a thermal workg flud such as helum. Keywords: Carot factor, Closed trasformatos, Load-depedet path fuctos, Polytropc processes, Thermal effcecy. Nomeclature adabatc expaso coeffcet polytropc expaso coeffcet thermal effcecy thermal effcecy of process (-( Cp specfc heat at costat pressure (kj/kg-k Cv v h u p s T o R specfc heat at costat volume(kj/kg-k specfc volume (m /kg specfc work (kj/kg specfc ethalpy (kj/kg specfc teral eergy (kj/kg pressure (bar specfc etropy (kj/kg-k temperature (K heat rejected by the cycle (kj/kg heat suppled to the cycle (kj/kg uversal costat of deal gases (kj/kg-k C CF CR EES GP Acroyms costat value parameter Carot factor = Carot effcecy heat coverso rato Egeerg Euato Solver global warmg potetal NCTC o-carot thermal cycle NORC o-orgac Rake cycle ORC orgac Rake cycle PI polytropc dex Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I

2 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos INTRODUCTION Almost all kow thermal cycles so far rely o the Carot cycle, meag uadrlateral cycles whch deally, heat s absorbed at costat temperature (top temperature ad work s delvered whe temperature decreases from the top temperature to approach the bottom temperature uder a uas etropc trasformato. The power cycles that obey ths model are classfed two ma groups based o the ature of the workg flud: gas power cycles ad vapour power cycle. The dfferece betwee the two groups s that, the frst case, the workg flud s gaseous ad does ot expermet ay phase chage, whle for the secod group, there s a lud-vapour phase chage process of the workg flud wth the cycle. I Fg.1 a smple classfcato of heat ege based cycles s depcted. Some studes regardg trlateral thermal cycles have recetly appeared scetfc lterature. Thus, for stace, a comparso of trlateral NCTCs ad orgac Rake cycles has bee carred out by [1] whch a clear cotrbuto to the thermal effcecy ehacemet has bee reported. Nevertheless, the work preseted ths paper, a dfferet perspectve regardg the covetoal trlateral ad uadrlateral thermal cycles s cosdered. Such characterstc dffereces are depcted Fg.1, whch exhbt some propertes heret to the NCTC, summarsed as: Load reacto drve path fuctos alog the actve stroke of the double effect cylder, Operates uder closed o-regeeratve thermal processes, Performs mechacal work by expasocotracto polytropc path fuctos, ad Thermal effcecy uas-depedet of the cycle temperatures Sce the thermal effcecy of the Carot based ege at very low top temperature teds to zero, t follows that uder such codtos, the proposed cycle could surpass the lmts stated by the Carot statemet. Fg1. Classfcato of commoly thermal cycles (Carot ad o-carot based thermal eges The objectve of the study s to effcetly covert low temperature heat from reewable thermal sources ad heat rejected from varous dustral sources ad coolg systems, whch may clude but s ot lmted to geothermal, ocea thermal ad drect solar thermal sources, heat rejected from Desel coolg systems (ar, lube ol ad jacket water coolers, ad resdual flue gases, as well bottomg steam Rake codesers, to be coverted by meas of the proposed thermal cycle ad plat structure to electrc eergy. The proposed coverso method s based o a dfferet thermodyamc cycle: the o codesg mode trlateral thermal cycle wth or wthout regeerato. The proposed cycle s ot based o the uadrlateral Carot cycle but o the trlateral cycle whch absorbs heat ad performs mechacal work smultaeously betwee states ( ad ( of Fg.. As a coseuece of ths cotrbuto, ths cycle s ot restrcted by the CF costrats. Its maxmum thermal effcecy s flueced ot oly by the rato of the top to bottom temperatures lke, for stace, the cycles aalyss descrbed [], [], but also by some factors such as the characterstcs of the workg fluds ad regeerato capabltes whe regeerato s cosdered. I the low temperature rage, bottomg ORCs costtute aother vable opto, havg show good thermodyamc performace for low top temperature of the bottomg cycles [4], [5] ad [6]. 7 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

3 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos The orgac workg fluds for resdual heat applcatos wth low temperature ORCs due to ther thermal effcecy have gaed mportace for several dfferet applcatos such as: reewable eergy ad low temperature heat recovery [7], ad [8] as the most relevat. The proposed heat coverso procedure s based o a o-covetoal thermodyamc cycle whch dffers from the Carot based cycles that: All cycle trasformatos are performed udergog closed system trasformatos, stead of the covetoal ope trasformatos heret to the Carot based thermal cycles ad I all actve processes of ths cycle, as heat eergy s beg absorbed, udergog a polytropc load-depedet path fucto, mechacal work s smultaeously performed, avodg the covetoal uas-adabatc expaso processes of the Carot based eges. Because of ths cotrbuto, ths cycle s ot restrcted by the CF costrats. Its maxmum thermal effcecy s ot flueced by the rato of the top to bottom temperatures. As coseuece, ths cycle s ot effcet at medum ad hgh temperatures. However, at low temperatures t ca surpass the Carot factor accordg to a recetly publshed work cosstg of a verse Rake cycle proposed by [9], whch the Carot Factor has bee surpassed. The authors showed that the proposed hybrd vapor compresso refrgerato system acheves sgfcatly hgher COP tha a covetoal vapor compresso refrgerato system, ad eve hgher tha the reverse Carot cycle at the same operato codtos. Aalyss of the Some Ideal Thermodyamc Trasformatos I order to focus atteto o the closed thermal processes that could take place such thermal cycles, ths secto deals wth the deal trasformatos terms of mechacal work that could be carred out closed process based NCTCs. I ths way, the fact of troducg the cocept of dsplacemet work udergoes the movemet of the psto a cylder from posto to posto +1, whle volume chages from to +1, causg a amout of (mechacal work doe by the system whch s gve as 1 p d 1 The amout of work doe s gve by the area uder the process ( (+1 show the dagram of Fg.. I order to aalyse the deal closed thermodyamc cases amed at the mechacal work doe, let s cosder the dsplacemet of a psto to ts cylder uder dfferet path fuctos as show Fg., whch udergoes dfferet realsable path fuctos desged as Isobarc process (pressure,costat at costat load, Fg (a Polytropc process ( p = C, wth C, costat, Fg (b Adabatc process ( p = C, wth C, costat, Fg (c Fg. Mechacal work performed uder dfferet thermodyamc processes whe evolvg from state pot ( to state pot (+1, deoted as state pot ( ad state pot ( respectvely. (a, sobarc path-fucto. (b, polytropc path fucto, ad (c, adabatc path fucto. The work doe uder sobarc trasformatos PI=0, Fg. (a The mechacal work delvered uder a sobarc process where =0 s 1 p d p ( 1 1 (1 The work doe uder polytropc trasformatos, PI =, Fg. (b Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I

4 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos The polytropc trasformato obey p p p p C. 1 1 Coseuetly, the pressure at ay termedate pot of the polytropc trasformato s 1 1 x x p p p p ( p The mechacal work delvered uder a polytropc process whe evolvg from a pot ( to pot ( s determed as follows p d p p p d 1 R.( T T 1 ( The mechacal work doe uder adabatc trasformatos, PI=, Fg. (c The mechacal work delvered udergog adabatc path fucto, where =, s determed as follows: The adabatc trasformato obey p p p p C 1 1 Coseuetly, the pressure at ay pot of the adabatc trasformato s 1 1 x x p p p p p (4 here, Q or dq 0 ad the adabatc expoet Cp Cv Sce Q du d 0, the d du Cv dt d wth p p d p C The mechacal work delvered uder a adabatc process whe evolvg from a pot ( to pot ( s determed as follows C d C p p d 1 R.( T T (5 1 Obvously, the sgle deal closed process based trasformatos above descrbed above may be oly useful f they ca be mplemeted to a thermal cycle. I ths purpose, the followg sub-secto deals wth such topc. The Eergy Coverso Rato for Closed Processes The thermal effcecy of a sgle closed thermodyamc trasformato, also called the eergy (coverso rato C R whch s the verse of the heat trasfer rato, s defed as the rato of the work doe to the heat absorbed durg a thermodyamc trasformato. Thus, cosderg trasformato (-( of Fg. (a udergog a sobarc path fucto, for whch PI = 0, accordg to the frst prcple appled to closed processes, t follows that the mechacal work s u (6 The the C R or process effcecy of ths closed reversble trasformato (-( for a sobarc path fucto yelds u u Cv ( T T 1 (7 C R Cp ( T T Cosderg a polytropc path fucto, so that PI =, the, the coverso rato of ths closed reversble trasformato (-( show Fg. (b yelds C R u u 1 Cv ( T T (1 Cv Cp Cv R ( T T Cp Cv Cp Cv Cv ( T T 1 Sce the mechacal work s C p p d 1 u 1 u R.( T T 1 (8 Cosderg a adabatc path fucto, so that PI =, the, the coverso rato of ths closed reversble trasformato (-( show Fg. (c yelds C u u u 1 1 R u (9 Cv ( T T (1 Cv Cp Cv R ( T T Cp Cv Cp Cv Cv ( T T 1 Sce the mechacal work doe s C p p d 1 R.( T T, 1 here, the amout of heat terchaged wth the closed adabatc process (adabatc expaso or cotracto processes durg the trasformato s zero, so that the result acheved by (9 s coheret wth the adabatc trasformato. The reured heat absorbed by the gas to perform a adabatc trasformato must be accouted to the prevous process cosstg of a heatg process wthout performg work. Surprsgly, expressos (7, (8 ad (9 defg the C R, deally exhbt total 9 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

5 coverso rato (CR for He Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos depedece of the temperature. Ths suggests to us that sce the Carot factor teds to zero as the rato of top to bottom temperatures approaches uty, for low top temperatures, Carot effcecy s lower tha the value of ths C R, sce, as stated before, whe the top temperature approaches the bottom temperature, CF teds towards zero. Thus, thermal cycles that volve trasformatos whch heat s absorbed ad work s developed smultaeously do ot obey the Carot statemet. 1,00 1,000 0,800 0,600 0,400 0,00 0,000-1,5-1 -0,5 0 0,5 1 1,5 polytropc expoet ( CR Cosderg a approach to deal gases such as helum, the correspodg coverso rato defto udergog a sobarc trasformato, for whch PI = 0 yelds C R = 0.4 as show (10, matches the coverso rato represeted Fg. for a PI = 0 C R ( He The coverso rato as fucto of the PI values ragg from -1.5 to 1.5 s depcted Fg.. It s observed that for a PI value of zero, the C R s 0.4, whch matches the value yelded by (10. I the same way, for a PI value of zero whch s the case of a sothermal trasformato, the C R s oe, sce all trasferred heat s coverted to work ad vce-versa, udergog costat teral eergy. The Aalyss of Heatg ad Coolg Processes Udergog Closed System Trasformatos Followg Isobarc Quas-Reversble Path Fuctos A uas-reversble process s depcted the Fg. 4, although all actual processes are rreversble Fg. The coverso rato for dfferet PI values because ature, such spotaeous trasformatos do ot occur. I Fg. 4, t s cosdered a specfc amout of gaseous workg flud eclosed a psto cylder arragemet s cosdered. The weght o the psto fxes the pressure the cylder as heat s added to or extracted from the system. At the tal state (, the workg flud s compressed at supercrtcal pressure p ad temperature T. The reader mght evso that a heat source ad heat sk devces could be used as a heater ad cooler respectvely. The added heat eergy results a crease the temperature of the flud, whle the flud expads at costat pressure, causg the chagg of state from pot ( to a termedate pot lower tha pot (. Cotug wth further addto of heat, the workg flud s coverted from supercrtcal cold flud to supercrtcal ad superheated hot gas. At state (, the trasformato s complete, ad all the cold supercrtcal flud has tured to hot supercrtcal superheated gas at temperature T. Fg4. The process of heatg ad coolg a flud at costat pressure (closed process as a approach to a reversble process, where flud s cofed to a heater ad a cylder, as heat s beg added. Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I

6 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos Assumg that the heatg process was coducted uas-statcally, path (-( s a collecto of eulbrum states followg a sobar (a le of costat pressure. The expermet could be repeated wth lesser or greater weght o the psto (.e., at lower or hgher pressures. he cosderg a approach to a reversble process, the reversble closed system eergy balace appled o the closed system show Fg. 4, whe chagg from pot ( to pot (, udergog sobarc path fuctos t states that u mgz KE (11 Assumg that potetal ad ketc eerges ca be eglected, the (1 ca be stated as u (1 Coseuetly, the suppled heat at costat pressure alog trasformato (-( s also defed as ( u u p ( here, two smultaeous modes of eergy absorpto take place alog process (-(: u -creasg teral eergy u -performg mechacal work p ( p ( (1 system s very dffcult to be realsed durg the occurrece of a thermodyamc process. Thermal systems of the dustral processes do ot atta thermodyamc eulbrum, therefore oly certa assumptos make t ak to a system eulbrum for the sake of aalyss. Quas-statc refers to almost statc, assocated to the slowess of the occurrece of a process. Ths s the basc assumpto for attag ear eulbrum of a system. It s cosdered that the chage state occurs at a ftely slow pace, thus cosumg very log tme for completo of the process. Thus, uas-statc processes are cosdered to rema thermodyamc eulbrum. A paradgmatc example of a uasstatc process s depcted Fg. 4, cosstg of a cofed flud whch s heated ad cooled at costat pressure to a cylder. To expla the behavour of the processes carred out durg a cycle whch heat s absorbed, a fracto of the absorbed heat s coverted to mechacal work ad the rest s rejected, let us cosder the locatg of a workg flud (gas a sgle effect cylder wth a certa load kept o the psto, as show Fg. 5(a. The gas at state pot ( attas the eulbrum codtos defed by p,, T, s ad u. After a certa amout of heat s added to the gas, t s foud that the psto becomes dsplaced, reachg state pot ( show Fg. 4(b, so that the state pot codtos are p,, T, s ad u. he dealg wth sobarc closed process aalyss, thermodyamc eulbrum of a The amout of heat trasferred to the system at costat pressure to evolve from state ( to state ( (sobarc expaso s defed as h C T u u u p ( P (14 The chage state from ( to ( s sgfcat. Alog ths process a amout of mechacal work s performed, whch s uatfed as p dv p ( (15 Cotug wth the cycle evolutos, the amout of heat trasferred from the system to the heat sk at costat pressure (sobarc compresso to evolve from state ( to state ( s defed as h CPT u u u p ( (16 ( The chage state from ( to ( s smlar to the prevous. Alog ths process, mechacal work was performed o the sobarc compresso process, whch s uatfed as (17 p dv p ( Fg. 4(c ad Fg. 4(g depct the p- ad T-s dagrams showg the seres of ftesmal state chages alog the sobarc expaso occurrg betwee states (-(, ad sobarc compresso (- 1 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

7 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos ( completg a cycle. The et work performed durg the cycle accordg to the frst prcple must satsfy - =0. Fg5. Quas-statc process: A successo of termedate eulbrum states at costat pressure whe addg or extractg heat to ad from a cylder. THE ANALYSIS OF CLOSED SYSTEM BASED SINGLE EFFECT THERMAL CYCLES UNDERGOING ISOBARIC PATH FUNCTIONS The aalyss of a cycle udergog et mechacal work s uder aalyss. Thus, wth regard to the thermal effcecy of the closed trasformato based cycle, t wll be demostrated that the thermal effcecy depeds largely o the adabatc expaso coeffcet, whle the specfc work depeds o the cycle temperatures. The aalyses of the closed system based cycle are depcted Fg. 6. Fg6. A thermal cycle composed of closed system trasformatos. (a, a trlateral NCTC cosstg of a cylder that absorbs heat, delverg work smultaeously alog trasformato (-( ad rejectg heat durg trasformato (-(1. (b, the T-s dagram of the trlateral NCTC. At costat load, the pressure s costat whch results the heatg process udergog a sobarc path fucto. Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

8 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos Cosderg a cycle composed of closed system based trasformatos of sgle effect (that s, loaded oly alog trasformato (-( ad uloaded alog trasformato (-(1. Ths cycle s charactersed by ts ablty to perform useful mechacal work whle smultaeously absorbg heat. Therefore, assumg the trlateral NCTC composed of closed system trasformatos as show Fg. 4 (a ad Fg. 5 (b t follows that the suppled heat from a exteral power source s u Cv( T T R ( T u u p ( v T Cp ( T The rejected heat to the heat sk s o u v T 1 1 u u1 p1 T sce p ( v v Thus the thermal effcecy s o 1 1 u Cv ( T T1 1 ( T T1 1 1 Cp ( T T ( T T o (18 ( v v1 Cv ( T 1 u u1 u p ( v v (19 (0 From (10 t follows that as T creases, due to the creasg of pressure rato, the thermal effcecy decreases accordgly. From (7 t follows also that the maxmum theoretcal thermal effcecy s acheved whe T approaches T 1 sce Lm T T1 ( Lm T T1 1 ( T T ( T T (1 Assumg a approach to deal gasses such as helum, the maxmum achevable effcecy s approached as 1 1 for helum He as workg flud, ad for ay temperature T > T > T1 Cosderg ow the same cycle composed of closed system trasformatos, as show Fg. 7 (a ad Fg. 7 (b, where trasformato (- (4 correspods to the process of system uloadg (whch s a setropc expaso or cotracto, t follows that the suppled heat from a exteral power source s u u u p ( v v ( Cv( T T R ( T T Cp ( T T The rejected heat to the heat sk s o where u u u p ( v 1 ( v ( T p v v R ( T ad 41 0, sce alog ths trasformato, the cylder s uloaded. Thus, the thermal effcecy s o 1 o Cv ( T4 T1 1 ( T4 T1 1 1 Cp ( T T ( T T (4 cosstg of a cylder that absorbs heat alog states (-(, smultaeously delverg mechacal work, ad rejectg heat alog the trasformato (4-(1. (b, the T-s dagram of the uadrlateral cycle. At costat load, the pressure s costat so that the heatg process udergoes a sobarc path fucto. Accordg to the results of both aalysed cycles, a mportat amout of heat suppled to cycle s rejected as o. Aother thermal ege structure, composed of closed system based trasformatos for whch the coolg phase s carred out by smultaeously performg useful mechacal work s possble. The topc aalysed the ext secto deals wth such cocept. Fg7. A thermal cycle composed of closed systems trasformatos. (a, the uadrlateral cycle Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

9 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos Closed System Based Double Effect Thermal Cycle Aalyss uder Isobarc Path Fuctos I order to apply a techue o closed system based trasformatos whch the coolg phase the heat rejecto phase s carred out by smultaeous performg useful mechacal work, the thermal cycle depcted Fg. 8 s aalysed. The uadrlateral cycle depcted wth Fg. 8 cossts of a cylder that absorbs heat The suppled heat from a exteral power source s betwee state pots ( ad (, performg mechacal work. Also, t rejects heat alog trasformato (5-(6 whle delverg smultaeously mechacal work. The trasformatos carred out are show T-s ad v- dagrams 8(b ad 8(c. At costat load, the pressure s costat so that the heatg ad coolg processes udergo sobarc path fuctos whle trasformatos (-(4 ad (6- ( are setropc path fuctos. u u u p ( v (5 v The rejected heat to the heat sk s o u u u p ( v 6 ( v Thus the thermal effcecy s u o o (7 u u u p p ( v ( v v v T T T T Fg8. Closed system based double effect thermal cycle. (a, the structure of a sgle effect psto- cylder ege. (b, the T-s dagram of the uadrlateral cycle. (c, p- dagram of the uadrlateral cycle. Oce a thermal cycle udergog sobarc actve processes has bee descrbed, the ext secto deals wth a case study appled to a thermal cycle udergog actve closed polytropc path fuctos. A CASE STUDY I ths secto a case study dealg wth a NCTC cosstg of a closed systems based thermal cycle s descrbed ad aalysed wth the help of Fg 9. It s based o a double effect cylder whch drves a crakshaft as the mechacal power coverter. The double effect cylder operates wth the selected workg flud whch s heated ad cooled by meas of a exteral heat source ad heat sk. Cycle modellg s carred out wth data extracted from [7], accordg to the selected workg fluds, usg the computatoal tool EES, (Egeerg Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I

10 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos Euato Solver, where the used data belogs to REFPROP, refereced as [10]. Fg9. Recprocatg double effect cylder, heated ad cooled by meas of a heat source ad heat sk dervg from a crakshaft. The Aalyss of the Quadrlateral NTTC Udergog Closed Polytrophc Path Fuctos Performg the aalyss of the NCTC udergog polytropc deal processes alog the cylder stroke s a tedous task that could be approached oly whe subjected to serous costrats mposed by the heret rreversbltes assocated to ay real thermal cycle. The cases that could yeld acceptable deal thermal effcecy are beg cosdered, are those udergog polytropc path fuctos. Fg. 9 depcts the schematc double effect cylder wth sgle heat exchagers used as heaters ad coolers. The double effect cylder s subjected to polytropc path fuctos uder the correspodg mechacal load to satsfy the aalysed path fuctos. The ecessary codto to esure a polytropc path fucto of PI = alog the cylder stroke reures that the psto load reactg agast the force exerted by the cylder pressure at ay pot of the cylder stroke follows the path defed by p p 1 1 (8 Sce, a polytropc path fucto obeys p p1 1 C (9 here, the varable force exerted o the psto s a fucto of the psto posto alog the full psto stroke, gve by p1 1 F p A A, wth F beg the force ad A the cross-sectoal area of the psto. Table 1 shows the heat flow drecto, the actvty of the path fucto, the path fucto type, the polytropc dex followed by the path fucto of both sdes of the double effect cylder. As show Table 1, the polytropc dex s dfferet depedg o the drecto of the heat flow. Thus, the value selected for the PI = = at trasto (-( correspods to the expaso of the workg flud, whle the PI = = at trasto (4-(1 correspods to the cotracto of the workg flud. Both PI values have bee chose to optmse the thermal effcecy of the cycle. That s, the thermal effcecy s the maxmum achevable wth helum as the workg flud. Table1. The heat flow drecto for the NCTC composed of two sochorc ad two polytropc trasformatos wth = , ad = -1,675. Cylder sde A Cylder sde B (-(+1 heat work process PI (-(+1 heat work process PI (1-( o Isochorc (-(4 o o Isochorc (-( yes polytropc (4-(1 o yes polytropc (-(4 o o Isochorc (1-( o Isochorc (4-(1 o yes polytropc (-( yes polytropc The data used the cycle composed of two polytropc trasformatos ad two sochorc trasformatos s show Table, for both sdes of the cylder. The preseted data has bee used to calculate the thermal effcecy ad the specfc work. As ca be observed that both 5 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019

11 eff Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos the top ad bottom temperatures are abormally uadrlateral Carot based thermal cycles. low (0 K-90 K comparso wth Table. The double effect cylder performg mechacal work uder two sochorc ad two polytropc legs, showg for each state pot ( the correspodg temperature, pressure, specfc volume, the etropy ad the teral eergy. State T(K p (kpa Cylder sde A v (m/kg s (kj/kg.k u (kj/kg State T((K Cylder sde B v( (m/kg p( (kpa s( (kj/kg- K u( (kj/kg 1A B A B A B A B The correspodg p- dagram for helum s show Fg. 10. Sce both sdes A ad B of the cylder operate uder a symmetrc profle wth respect to the parameters show Tables 1 ad, oly the p- dagram of sde A s depcted A However, the specfc work s learly depedet o the top temperature. 0,7 0,6 0,5 0,4 0, w [kj/kg] pa[] A 1A 94 6, 6,4 6,6 6,8 7 7, A[] Fg10. The p- dagram of the NTTC operatg wth the data of Tables 1 ad, wth helum as the workg flud. DISCUSSION OF RESULTS The aalysed cycle operatg wth Table data yelds the results show Fg. 11, where the deal thermal effcecy ad specfc work for helum s show. Accordg to the obtaed results, as coseuece of the aalyss carred out, the uusually hgh thermal effcecy acheved at low temperatures t s truly remarkable, from a theoretc perspectve. At such low top temperatures the Carot factor s also low, so that the acheved thermal effcecy may be eve hgher tha the Carot factor at the same temperatures. th regard to Fg. 11, t s oteworthy observg the thermal effcecy profle accordg to the above temperature rage, t s hghlghted that the slope teds to be caceled as a result of ts low depedece o the temperature. 4A 0, eff [He] w [He] CF 0, T max [K] Fg11. The thermal effcecy ad specfc work of the NCTC, operatg wth helum as the workg flud together wth Table data, uder polytropc path fuctos. CONCLUSIONS The proposed NCTC has bee studed for helum as the workg flud, although ay other gas wth acceptable characterstcs would be useful sce effcecy s a fucto whch strogly depeds o the polytropc dexes. Accordg to the characterstcs of the proposed NCTC, ew expressos for the deal thermal effcecy have bee acheved ad aalysed. The performace results of the NCTC have bee compared wth the results obtaed for the Carot cycle, operatg betwee both the same rage ad rato of temperatures. The most relevat cocluso volves: The cycle processes of the NCTC, whch s structured uder closed system based trasformatos ad, The thermal effcecy of the cycle whch exceeds the Carot effcecy uder approprate operatg codtos. The maxmum thermal effcecy s a fucto of the polytropc dex, regardless 00 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I

12 Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos of the pressure ratos ad operatg temperatures. The cycle ca operate at a very low temperature, eve rederg hgh thermal effcecy comparso wth that of the Carot factor. The reaso for ths obeys the fact that a cycle, polytropc heat absorpto ad smultaeous coverso to mechacal work ad resdual heat, take place smultaeously alog a cycle trasformato. Furthermore, thermal losses due to setropc effcecy are avoded f reversble trasformatos ca be approached. As revealed the results, the deal thermal effcecy s sgfcatly creased comparso wth the covetoal ORCs uder feasble codtos. Fally, a overall cocluso cocers the fact that a ew famly of effcet thermal power plats at low temperatures, whch are ot restrcted by the Carot factor, s possble. REFERENCES [1] Joha Fscher, Comparso of trlateral cycles ad orgac Rake cycles, Eergy, 6 ( , ;. [] S.C. Kaushk,.SvaRedd, S.K.Tyag, Eergy ad exergy aalyses of thermal power plats: A revew, Reewable ad Sustaable Eergy Revews, 15 ( [] Jg L, Gag Pe, Yuzhu L, Dogyue ag, Je J, Eergetc ad exergetc vestgato of a orgac Rake cycle at dfferet heat source temperatures, Eergy, 8 ( [4] Yamamoto T, Furuhata T, Ara N, Mor K, Desg ad testg of the Orgac Rake Cycle, Eergy, 6 ( [5] Doghog e, Xuesheg Lu, Zhe Lu, Jamg Gu. Performace aalyss ad optmzato of Orgac Rake Cycle (ORC for waste heat recovery, Eergy Coverso ad Maagemet, 48 ( [6] agar.r., Zamfrescu C.,. Dcer I., Thermodyamc performace assessmet of a ammoa water Rake cycle for power ad heat producto, Eergy Coverso ad Maagemet, 51( [7] Saleh B, Koglbauer G, edlad M, Fscher J, orkg fluds for low temperature Orgac Rake Cycles, Eergy, (7 ( [8] Hug T, aste heat recovery of Orgac Rake Cycle usg dry fluds, Eergy Coverso ad Maagemet, 4 ( [9] Xaohu She, Yoggao Y, Xaosog Zhag, Thermodyamc aalyss of a ovel eergyeffcet refrgerato system subcooled by lud desccat dehumdfcato ad evaporato, Eergy Coverso ad Maagemet 78 ( [10] E.. Lemmo, M. L. Huber ad M. O. Mc Lde. NIST Referece Flud Thermodyamc ad Trasport Propertes - REFPROP erso 8.0, User's Gude, NIST 007, Boulder, Colorado. Ctato: Ramo Ferrero. Garca, Jose Carba Carrl, Aalyss ad Comparso of Closed System Based Thermal Cycles Udergog Dfferet Polytropc Trasformatos, Iteratoal Joural of Emergg Egeerg Research ad Techology, 7(1, pp.6-7 Copyrght: 019 Ramo Ferrero. Garca. Ths s a ope-access artcle dstrbuted uder the terms of the Creatve Commos Attrbuto Lcese, whch permts urestrcted use, dstrbuto, ad reproducto ay medum, provded the orgal author ad source are credted. 7 Iteratoal Joural of Emergg Egeerg Research ad Techology 7 I1 019