Thermodynamic Cycles using.pdf

ThermodynamicCyclesusingCarbonDioxideasWorking

Fluid

CO2transcriticalpowercyclestudy

DoctoralThesisby

YangChen

Stockholm,October,2011

SchoolofIndustrialEngineeringandManagement

DepartmentofEnergyTechnologyDivisionofAppliedThermodynamicsandRefrigeration

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Thermodynamic Cycles using Carbon Dioxide as WorkingFluidCO2transcriticalpowercyclestudyYangChenTritaREFRReport11/03ISSN11020245ISRNKTH/REFR/11/03SEISBN9789175011875DoctoralThesisbyYangChenSchoolofIndustrialEngineeringandManagementDepartmentofEnergyTechnologyDivisionofAppliedThermodynamicsandRefrigerationPrintedbyUniversitetsserviceUSABStockholm,2011YangChen,2011

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Abstract

The interest inutilizing the energy in lowgradeheat sourcesandwaste heat is increasing. There is an abundance of suchheat sources,but theirutilization today is insufficient,mainlyduetothelimitationsoftheconventionalpowercyclesinsuchapplications, such as low efficiency,bulky sizeormoisture attheexpansionoutlet(e.g.problemsforturbineblades).Carbondioxide(CO2)hasbeenwidelyinvestigatedforuseasaworking fluid in refrigerationcycles,because ithasnoozonedepleting potential (ODP) and low globalwarming potential(GWP). It is also inexpensive, nonexplosive, nonflammableandabundantinnature.Atthesametime,CO2hasadvantagesinuseasaworking fluid in lowgradeheat resource recoveryandenergyconversion fromwasteheat,mainlybecause itcancreateabettermatchingtotheheatsourcetemperatureprofilein the supercritical region to reduce the irreversibilityduringthe heating process. Nevertheless, the research in suchapplicationsisverylimited.Thisstudyinvestigatesthepotentialofusingcarbondioxideasa working fluid in power cycles for lowgrade heatsource/wasteheatrecovery. Atthebeginningofthisstudy,basicCO2powercycles,namelycarbon dioxide transcritical power cycle, carbon dioxideBraytoncycleandcarbondioxidecoolingandpowercombinedcycle were simulated and studied to see their potential indifferentapplications (e.g. lowgradeheat sourceapplications,automobile applications and heat and power cogenerationapplications).Fortheapplicationsinautomobileindustries,lowpressuredropontheenginesexhaustgassideiscrucialtonot

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reducingtheenginesperformance.Therefore,aheatexchangerwithlowpressuredroponthesecondaryside(i.e.thegasside)wasalsodesigned,simulatedandtestedwithwaterandengineexhaustgasesattheearlystageofthestudy(Appendix2).The study subsequently focused mainly on carbon dioxidetranscritical power cycle, which has a wide range ofapplications. The performance of the carbon dioxidetranscritical power cycle has been simulated and comparedwiththeothermostcommonlyemployedpowercyclesinlowgrade heat source utilizations, i.e. the Organic Rankin Cycle(ORC). Furthermore, the annual performance of the carbondioxidetranscriticalpowercycleinutilizingthelowgradeheatsource (i.e. solar) has also been simulated and analyzedwithdynamicsimulationinthiswork.Lastbutnot least, thematchingof the temperatureprofiles inthe heat exchangers for CO2 and its influence on the cycleperformance have also been discussed. Second lawthermodynamic analyses of the carbon dioxide transcriticalpowersystemshavebeencompleted.The simulation models have been mainly developed in thesoftwareknownasEngineeringEquationSolver(EES)1forbothcycleanalysesandcomputeraidedheatexchangerdesigns.ThemodelhasalsobeenconnectedtoTRNSYSfordynamicsystemannual performance simulations. In addition, Refprop 7.02isusedforcalculatingtheworkingfluidproperties,andtheCFDtool (COMSOL) 3 has been employed to investigate theparticular phenomena influencing the heat exchangerperformance.

1EngineeringEquationSolver:http://www.fchart.com/ees/ees.shtml2Refprop7.0:http://www.nist.gov/srd/nist23.htm3http://www.comsol.se/

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Publications

Thisthesisisbasedonthefollowingpapers,whichareenclosedattheend.AshortsummaryofeachpapercanalsobefoundinAppendix3.I. Y.Chen,P.Lundqvist,P.Platell

Theoretical Research of Carbon Dioxide Power CycleApplication in Automobile Industry to Reduce VehiclesFuelConsumptionPaperpublishedinAppliedThermalEngineering25(2005),pp20412053

II. Y.Chen,P.Lundqvist,A.Johansson,P.PlatellA comparative studyof theCarbonDioxideTranscriticalPowerCyclecomparedwithanOrganicRankineCyclewithR123asworkingfluidinWasteHeatRecoveryPaperpublishedinAppliedThermalEngineering26(2006),pp21422147

III. Y.Chen,W.Pridasawas,P.Lundqvist

Dynamic Simulation of a SolarDriven Carbon DioxideTranscriticalPowerSystemforSmallScaleCombinedHeatandPowerProductionPaperpublishedinSolarEnergy84(2010),pp11031110

IV. Y.Chen,A.B.Workie,P.LundqvistSecond Law Analysis of a Carbon Dioxide TranscriticalPowerSysteminLowgradeHeatSourceRecoveryPapersubmittedtoAppliedThermalEngineering

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V. Y.Chen,P.LundqvistCarbon dioxide cooling and power combined cycle formobileapplications.Paperpublishedandpresentedat7thIIRGustavLorentzenConference on Natural Working Fluids, Trondheim,Norway,May2831,2006

VI. Y.Chen,P.LundqvistAnalysisofsupercriticalcarbondioxideheatexchangersincoolingprocessPaper published and presented at InternationalRefrigeration andAirConditioningConference atPurdue,USA,July1720,2006.

VII. Y.Chen,P.LundqvistLowgradeHeatSourceUtilizationbyCarbonDioxideTranscriticalPowerCyclePaperpublishedandpresentedatASMEJSMEThermalEngineeringSummerHeatTransferConference,Vancouver,BritishColumbia,Canada,July913,2007

VIII. Y.Chen,P.LundqvistTheoreticalstudyofcarbondioxidedoubleloopsystemPaperpublishedandpresentedatIIRinternalrefrigerationcongress,Beijing,China,August2126,2007.Thispaperhasbeenselectedasakeynotespeechinoneparallelsectionintheconference

IX. Y.Chen,P.Lundqvist,B.PalmAnovelgaswaterheatexchangerwithminichannelsPaperpublishedandpresentedatASMESummerHeatTransferConference,Jacksonville,FloridaUSA,August1014,2008

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X. Y.Chen,P.LundqvistTheCO2transcriticalpowercycleforlowgradeheatrecoverydiscussionontemperatureprofilesinsystemheatexchangersPaperpublishedandpresentedatASMEPowerandICOPEConference,Denver,USA,July1214,2011

Otherreviewedreports

I. Y.Chen

CarbonDioxideTranscriticalPowerCycleDiscussionTritaREFRReport 2005,No. 05/49, ISSN 11020245, ISRNKTH/REFR/R05/49SE.

II. Y.ChenNovelcyclesusingcarbondioxideasworkingfluidLicentiateThesis inEnergyTechnology,Royal Institute ofTechnology,ISSN:11020245,ISRN:KTH/REFR/R06/50SE,ISBN:9171784101,2006

XI. Y.Chen,P.Lundqvist,A.Alves,L.BrachertCO2 heat pumps for the Swedish market Test andanalysisoftheSANYOECOCUTEheatpumpmodifiedforSwedishconditionsEffsys2projectreport2009(http://www.effsys2.se/P3.htm)

XII. Y.Chen,A.B.Workie,P.LundqvistInvestigationonhighpressurepumpsforCO2transcriticalpowercycleinlowgradeheatsourceutilizationCREATIVprojectreport2010

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Acknowledgements

Therearesomanypeople thatIshould like to thank.Withoutall your assistance, support and encouragement, Iwould nothaveachievedthismuch.Firstofall,Iwould like toexpressmysinceregratitude tomysupervisor,ProfessorPerLundqvist.Youopened thedoor formetothisscientificworldandguidedmeallthewaythroughwith your wise ideas, enormous patience, good humor andconstantencouragement.Thanksarealsodueto:Peter Platell and his father Ove Platell, for initiating theinteresting idea, which was the original motivation of thisthesis.Prof.BjrnPalm, foryour supportandhelpwhenever Ihavehadquestions.Youneversaid no tomewhen Ineededhelpandyourhardworkhasalwaysinspiredme.My CO2 colleague,Dr. Samer Sawalha, for all thenice andinterestingdiscussions,nomatter if theywereCO2 related orjustwild.Mr. Henrik hman for being my piethrowing seminaropponentandgivingmesomanyconstructivesuggestions.Dr. Getachew Bekele, for being such a good officemate andsharingall those talks.Dr.WimolsiriPridasawas, for thehelpwith TRNSYSmodels and all the other support.Dr. PrimalFernando, for yourhumor and friendship. IngaDuRietz, for

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having kept everything at the division in order during mystudytime.Special thanks anddeep sorrow alsogo toBennyAndersson,whohadhelpedalotwithmytestrigandpassedawaybeforeIfinishedthisstudy.Itfeelsasifthoselatenightdiscussionswithyouforthetestrigconstructionjusthappenedyesterday.Iwould like to thank the entire faculty at theDepartment ofEnergyTechnologyandallthePhDstudentsattheDivisionofApplied Thermodynamics and Refrigeration (especially,ProfessorEmeritusEricGranryd,GuestProf.TimothyAmeel,Dr.ClaudiMartin,Dr.RaulAnton,Dr.RashidAli,Dr.MarinoGrozdek, Dr. Rahmatollah Khodabandeh, Peter Hill, JosAcua, Dr. Anders Johansson, Dr.Nabil Kassem , Dr.HansJonsson, Dr. ke Melinder, Dr. Jaime Arias, Dr. JoachimClaesson, JanErikNowacki,BennySjberg,SusyMathew,Dr.Wahib Owhaib, Hatef Madani, Maqbool MuhammadMamayun, Jrgen Wallin, Aleh Kliatsko, Stina Gustafsson,Monika Ignatowicz, Sad Jarall, Oxana Samoteeva, RichardFurberg, Cecilia Hgg, Shota Nozadze, Branko Simanic, Dr.Paulina Bohdanowicz), for being such good colleagues. Ourdivisionwasmorelikeabigfamily.I also want to specially thank Bjrn Qvist, Stefan Cartling,GranDalaryd,MikaelWelanderand JrgenPersson foryourconstant support and encouragement, Jrgen Carlsson, forbeinganicegymmateandalltheothercolleagues,foryouaregreat!Moreover, I want to thank all my relatives, friends andespeciallymyparents,XiaomingTianandJiabaoChen,andmygrandparents, Surun Yan and Zairen Tian for your love,supportandconstantcare.

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To my beloved wife Sha Liu for your love, patience,understandingandthesacrifice inorderformetofinalizethisthesis.

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Preface

Ihavebeenthinkingofthismomentforlonguntiltoday,whenIamreallysittinghereandfinalizingthelastpartofmythesis.At thismoment, I am starting to realize howmuch the timeflies.Almosteverykidhasbeenaskedthesamequestion:Whatdoyou want to be when you grown up? The answers werealwaysverysimilarinChinawhenIwasachild:Iwanttobeascientist!andIwasnoexception.However,duringthetimewhenIgrewup,myrealanswerhaschangedmanytimes,sinceIlearnedmoreandmoreabouttheworldandsomanythingshavecaughtmyinterest.Apartfromthoseminorwishes,myfirstdreamwastobecomeapilot.AfterIpassed thefirstselectionexamaftergraduatingfromhighschool,thedreamalmostcametrue,untilmyparentsthought I should still continue to the engineering college, sothatIcouldfollowmyfatherscareerpathandbecomeahotelmanager.Although I followed their advice and entered engineeringcollege,Ichangedmymindaboutfollowingmyfatherscareerpath and instead chose to study abroad. I had beenworkinghardincollegeonmyEnglishandtookalltherequiredexamssuch as GRE, TOEFL, etc. in order to apply for a graduateschool in theU.S.After I finishedall these tests, Iwas facingtwooptions:either towait forabout8months for the startoftheapplicationperiod forUSgraduateschoolsor toapply,asrecommended by a schoolmate, to the Royal Institute ofTechnology inSwedendirectly, since theapplicationdeadline

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wasinApril.Itriedoption2andthatbroughtmetotheEnergyDepartment of the Royal Institute of Technology in Sweden.Here,IspentoneandhalfyearsfinishingmyMastersdegree.Iwas thenplanning touse thestillvalidscores from theGREtesttoapplyforaschoolintheU.S.againinthelastpartofmystudy inSweden,until ImetProf.LundqvistandPeterPlatellfor this interesting topicofusingCO2 to recover energy fromlowgradeheatsourcesandwasteheat.IfeelveryluckythatIdecidedtopursuethistopicandtheyopenedthedoorformetothisreallyinterestingscientificresearchworld!After so many years staying in Sweden, I indeed love thisbeautifulcountry from thebottomofmyheartand Iamveryproud that I have been studying at the Royal Institute ofTechnology.During theseyears, Ihavematuredandmade somany friends here. I always feel life is amazing and I am soluckythatIevengotmarriedtomybeautifulandbelovedwifeinthelastyearofmyPh.D.study!Now,afterthis long,mythesis isfinallysubmittedforaPh.D.degree.YangChen,20111030LatenightinStockholm

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TableofContents

ABSTRACT....................................................................................IIIPUBLICATIONS.............................................................................VACKNOWLEDGEMENTS...........................................................IXPREFACE......................................................................................XIIITABLEOFCONTENTS..............................................................XVLISTOFTABLES......................................................................XVIILISTOFFIGURES......................................................................XIX1 INTRODUCTION....................................................................1

1.1 MOTIVATION .................................................................................. 11.2 OBJECTIVES AND APPROACH .......................................................... 4

2 BACKGROUND.......................................................................72.1 WORKING FLUID COMPARISON ...................................................... 72.2 HISTORY OF CO2 POWER CYCLE .................................................. 112.3 SYSTEM ILLUSTRATION AND CORRESPONDING CYCLE DESCRIPTION ............................................................................................. 12

2.3.1 The CO2 bottoming system and corresponding cycles ............. 122.3.2 The CO2 cooling and power combined system and the corresponding cycle .............................................................................. 15

3 CO2TRANSCRITICALCYCLEAPPLICATIONSANDPERFORMANCESIMULATIONS.............................................19

3.1 BASIC CYCLES AND THE PARAMETERS THAT INFLUENCE THE CYCLE PERFORMANCES ............................................................................. 19

3.1.1 Carbon dioxide transcritical power cycle ............................... 213.1.2 The influences of the cycle working parameters on the CO2 transcritical power cycle performance ................................................. 223.1.3 Carbon dioxide Brayton cycle ................................................. 263.1.4 The influence of the cycle working parameters on the CO2 Brayton cycle performance ................................................................... 263.1.5 Carbon dioxide cooling and power combined cycle ................ 303.1.6 The influence of cycle working parameters on the CO2 cooling and power combined cycle performance .............................................. 31

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3.2 CO2 POWER CYCLE APPLICATIONS AND PERFORMANCE SIMULATIONS ............................................................................................ 33

3.2.1 CO2 double loop system ........................................................... 333.2.2 Solar driven CO2 transcritical power system .......................... 39

3.3 SUMMARY .................................................................................... 484 TEMPERATUREPROFILESINCO2POWERSYSTEMHEATEXCHANGERS..................................................................51

4.1 CP VARIATION AND ITS INFLUENCE ON THE CO2 POWER CYCLE TEMPERATURE PROFILES IN THE HEAT EXCHANGERS ............................... 514.2 COMPARISON BETWEEN A TYPICAL CO2 POWER AND A TYPICAL ORC CYCLE............................................................................................... 584.3 THE IMPORTANCE OF THE TEMPERATURE PROFILE MATCHING .... 594.4 SUMMARY .................................................................................... 61

5 SECONDLAWTHERMODYNAMICANALYSIS.........635.1 EXERGY AND ENTROPY CALCULATIONS ....................................... 645.2 SIMULATION ASSUMPTIONS .......................................................... 665.3 SIMULATION RESULTS AND DISCUSSION ...................................... 675.4 SUMMARY .................................................................................... 74

6 CONCLUSIONANDSUGGESTIONSFORFURTHERWORK..............................................................................................77

6.1 CONCLUSION ................................................................................ 776.2 SUGGESTIONS FOR FURTHER WORK ............................................. 80

7 NOMENCLATURE................................................................838 REFERENCES..........................................................................879 APPENDIX..............................................................................95

9.1 APPENDIX 1 SAFETY GROUP CLASSIFICATIONS (FROM IIR) ...... 959.1.1 Toxicity classification .............................................................. 959.1.2 Flammability classification ..................................................... 95

9.2 APPENDIX 2 HEAT EXCHANGER PROPOSED FOR HEAT RECOVERY IN ENGINE EXHAUST GASES .................................................... 97

9.2.1 Description of the heat exchanger ........................................... 979.2.2 Counter flow compact heat exchanger with laminar flow at the airside 989.2.3 Superiority of laminar flow .................................................... 1009.2.4 Description of the heat exchanger calculation model ........... 1029.2.5 Basic correlations .................................................................. 1049.2.6 Program description .............................................................. 1099.2.7 Example of program operation window ................................ 1149.2.8 Results ................................................................................... 118

9.3 APPENDIX 3 SUMMARY OF ATTACHED PAPERS ...................... 121

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ListofTables

TABLE 2-1PROPERTIES OF DIFFERENT FLUIDS .................................................. 8TABLE 3-1 CARBON DIOXIDE DOUBLE LOOP SYSTEM BASIC OPERATING

CONDITIONS ........................................................................................... 35TABLE 3-2 CARBON DIOXIDE DOUBLE LOOP SYSTEMS PERFORMANCE UNDER

THE BASIC OPERATING CONDITIONS ....................................................... 36TABLE 3-3 SIMULATION PARAMETERS ........................................................... 41TABLE 4-1CARBON DIOXIDE TRANSCRITICAL POWER CYCLE OPERATING

CONDITIONS ........................................................................................... 54TABLE 4-2 HEAT SOURCE (EXHAUST GAS) DATA ............................................ 54

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ListofFigures

FIGURE 1-1 TYPICAL TEMPERATURE RANGE OF DIFFERENT HEAT SOURCES FOR HEAT RECOVERY ...................................................................................... 1

FIGURE 1-2 ILLUSTRATION OF CYCLE REVERSIBILITY ...................................... 3FIGURE 1-3 SCHEMATIC REPRESENTATION CHART OF THE HEAT TRANSFER

BETWEEN THE LOW-GRADE HEAT SOURCE AND WORKING FLUID IN THE MAIN HEAT EXCHANGER: (1A) PURE FLUID; (1B) ZEOTROPIC FLUID MIXTURES; (1C) CARBON DIOXIDE ........................................................... 4

FIGURE 2-1 SCHEMATIC OF THE CARBON DIOXIDE POWER SYSTEM (FOR BOTH BRAYTON CYCLE AND TRANSCRITICAL CYCLE) ..................................... 13

FIGURE 2-2 CARBON DIOXIDE TRANSCRITICAL CYCLE T-S CHART ................. 14FIGURE 2-3 CARBON DIOXIDE BRAYTON CYCLE T-S CHART .......................... 14FIGURE 2-4 CARBON DIOXIDE COOLING AND POWER COMBINED SYSTEM

SCHEMATIC LAYOUT .............................................................................. 15FIGURE 2-5 CARBON DIOXIDE COOLING AND POWER COMBINED CYCLE T-S

CHART ................................................................................................... 16FIGURE 3-1 CARBON DIOXIDE TRANSCRITICAL CYCLE EFFICIENCY VS.

EXPANSION INLET TEMPERATURE AGAINST VARIOUS EXPANSION EFFICIENCIES (FROM EES, BASIC CYCLE WITHOUT IHX) ....................... 23

FIGURE 3-2 CARBON DIOXIDE TRANSCRITICAL CYCLE EFFICIENCY VS. EXPANSION INLET TEMPERATURE AGAINST VARIOUS PUMP EFFICIENCIES (FROM EES, BASIC CYCLE WITHOUT IHX) ............................................. 24

FIGURE 3-3 OPTIMUM GAS HEATER PRESSURE OF A CARBON DIOXIDE TRANSCRITICAL CYCLE (FROM EES, WITHOUT IHX AND WITH A 90% EFFECTIVENESS IHX) ............................................................................ 25

FIGURE 3-4 THE IHX EFFECTIVENESS INFLUENCE ON CARBON DIOXIDE TRANSCRITICAL CYCLE EFFICIENCY (FROM EES) .................................. 25

FIGURE 3-5 CARBON DIOXIDE BRAYTON CYCLE EFFICIENCY VS. EXPANSION INLET TEMPERATURE AGAINST VARIOUS EXPANSION EFFICIENCIES (FROM EES, BASIC CYCLE WITHOUT IHX) ........................................................ 27

FIGURE 3-6 CARBON DIOXIDE BRAYTON CYCLE EFFICIENCY VS. EXPANSION INLET TEMPERATURE AGAINST VARIOUS PUMP EFFICIENCIES (FROM EES, BASIC CYCLE WITHOUT IHX) ................................................................. 27

FIGURE 3-7 OPTIMUM GAS HEATER PRESSURE OF A CARBON DIOXIDE BRAYTON CYCLE (FROM EES, WITHOUT IHX AND WITH A 90% EFFECTIVENESS IHX) ............................................................................ 28

FIGURE 3-8 OPTIMUM GAS COOLER PRESSURE OF A CARBON DIOXIDE BRAYTON CYCLE (FROM EES, WITHOUT IHX AND WITH A 90% EFFECTIVENESS IHX) ............................................................................ 29

FIGURE 3-9 THE INFLUENCE OF IHX EFFECTIVENESS ON CARBON DIOXIDE TRANSCRITICAL CYCLE EFFICIENCY (FROM EES) .................................. 29

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FIGURE 3-10 THE COP OF COOLING PART OF THE COMBINED CYCLE VS. DIFFERENT GAS COOLER PRESSURE ........................................................ 31

FIGURE 3-11 THE COP OF COOLING PART OF THE COMBINED CYCLE VS. DIFFERENT GAS HEATER PRESSURE ........................................................ 32

FIGURE 3-12 DOUBLE LOOP SYSTEM SCHEMATIC SYSTEM LAYOUT ................ 34FIGURE 3-13 DOUBLE LOOP SYSTEM T-S CHART (EES) ................................. 35FIGURE 3-14 BASIC REFRIGERATION SYSTEMS COP AND DOUBLE LOOP

SYSTEMS COP VS. DIFFERENT GAS COOLER PRESSURES AT DIFFERENT GAS HEATER PRESSURES ........................................................................ 37

FIGURE 3-15 DOUBLE LOOP SYSTEMS COP AGAINST DIFFERENT GAS HEATER PRESSURES AT DIFFERENT GAS COOLER PRESSURES AND DIFFERENT EXPANSION INLET TEMPERATURES ........................................................ 38

FIGURE 3-16 DOUBLE LOOP SYSTEMS COP AGAINST DIFFERENT COMPONENTS EFFICIENCIES .................................................................. 39

FIGURE 3-17 SOLAR-POWERED TRANSCRITICAL CARBON DIOXIDE POWER SYSTEM ................................................................................................. 40

FIGURE 3-18 DAILY PERFORMANCE OF SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM DURING A SUMMER DAY IN STOCKHOLM (AT 120 BAR GAS HEATING PRESSURE) ....................................................................... 42

FIGURE 3-19 DAILY PERFORMANCE OF THE SOLAR- DRIVEN CARBON DIOXIDE POWER SYSTEM DURING A SUMMER DAY IN STOCKHOLM (AT 120 BAR GAS HEATER PRESSURE) ......................................................................... 43

FIGURE 3-20 DAILY NET POWER PRODUCTION (KWH/DAY) OF A SOLAR DRIVEN CARBON DIOXIDE POWER SYSTEM IN ONE YEAR (AT 120 BAR GAS HEATING PRESSURE) .............................................................................. 44

FIGURE 3-21 MONTHLY NET POWER PRODUCTION (KWHS) OF THE SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM IN ONE YEAR (AT 120 BAR GAS HEATING PRESSURE) .............................................................................. 44

FIGURE 3-22 DAILY HEAT PRODUCTION (KWHS) OF THE SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM IN ONE YEAR (AT 120 BAR GAS HEATING PRESSURE) .............................................................................. 45

FIGURE 3-23 MONTHLY HEAT (KWHS) OF THE SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM IN ONE YEAR (AT 120 BAR GAS HEATING PRESSURE) ............................................................................................. 45

FIGURE 3-24 DAILY AVERAGE POWER PRODUCTION OF SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM AT DIFFERENT EXPANSION ISENTROPIC EFFICIENCIES ......................................................................................... 46

FIGURE 3-25 DAILY AVERAGE POWER PRODUCTION OF SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM AT DIFFERENT GAS HEATING PRESSURES ........ 47

FIGURE 3-26 SOLAR-DRIVEN CARBON DIOXIDE POWER SYSTEM POWER OUTPUT AND THERMAL EFFICIENCY IMPROVEMENT VS. IHX EFFECTIVENESS (RESULTS CALCULATED FOR THE SAME DAY THAT CHOSEN FOR FIGURE 3-18) ..................................................................................................... 48

FIGURE 4-1 SPECIFIC HEAT OF SUPERCRITICAL CO2 VS. TEMPERATURE AT DIFFERENT PRESSURES ........................................................................... 52

FIGURE 4-2 SPECIFIC HEAT OF AIR VS. TEMPERATURE AT DIFFERENT PRESSURES (NOTE THE SCALE DIFFERENCE FROM FIGURE 4-1) .............. 52

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FIGURE 4-3 SPECIFIC HEAT OF EXHAUST GAS AND EXPANSION OUTLET CARBON DIOXIDE (NOTE THE SCALE DIFFERENCE FROM FIGURE 4-1) .................. 53

FIGURE 4-4 SCHEMATIC LAYOUT OF A BASIC CARBON DIOXIDE CO2 POWER SYSTEM ................................................................................................. 54

FIGURE 4-5 CPH CHART FOR SUPERCRITICAL CO2, EXPANSION OUTLET CARBON DIOXIDE AND HEAT SOURCE FOR THE INTEGRATED TOTAL HEAT EXCHANGER LENGTH ............................................................................. 55

FIGURE 4-6 INTEGRATED HEAT EXCHANGERS T--H CHART OF CARBON DIOXIDE TRANSCRITICAL POWER CYCLE WITH DIFFERENT MASS FLOW RATES OF SUPERCRITICAL CO2 (A): MCO2=0.1 KG/S, M EXHAUST GAS=0.4 KG/S, IHX EFFECTIVENESS=0.9, MHX EFFECTIVENESS =0.9 (B): MCO2=0.2 KG/S, M EXHAUST GAS=0.4 KG/S, IHX EFFECTIVENESS=0.9, MHX EFFECTIVENESS =0.9 ............................................................................. 57

FIGURE 4-7 INTEGRATED HEAT EXCHANGER T-H CHART OF R123 ORC. MR123=0.15 KG/S, M EXHAUST GAS=0.4 KG/S, IHX EFFECTIVENESS =0.9, MHX EFFECTIVENESS =0.9 (THE PROCESS IN THE FIGURE DOES NOT INCLUDE THE SUPERHEATING OF VAPOR) ............................................................. 58

FIGURE 4-8 SCHEMATIC ILLUSTRATION OF A TYPICAL CYCLE CARNOT CYCLE .................................................................................................... 59

FIGURE 4-9 CYCLE EFFICIENCY WITH VARYING HEAT SOURCE TEMPERATURES AND A CONSTANT HEAT SINK TEMPERATURE (293 K) FOR DIFFERENT TEMPERATURE DIFFERENCES IN THE TWO HEAT EXCHANGERS (GAS HEATER AND CONDENSER) ..................................................................... 60

FIGURE 5-1 SCHEMATIC LAYOUT OF THE BASIC CARBON DIOXIDE POWER SYSTEM ................................................................................................. 63

FIGURE 5-2 EXERGY DESTRUCTION VS. CO2 MASS FLOW RATE ...................... 67FIGURE 5-3 ENTROPY GENERATION VS. CO2 MASS FLOW RATE ...................... 67FIGURE 5-4 DISTRIBUTION OF ENTROPY GENERATION VS. CO2 MASS FLOW

RATE ...................................................................................................... 68FIGURE 5-5 EXERGY DESTRUCTION VS. SYSTEM HIGH PRESSURE SIDE PRESSURE

.............................................................................................................. 69FIGURE 5-6 ENTROPY GENERATION VS. SYSTEM HIGH PRESSURE SIDE

PRESSURE .............................................................................................. 69FIGURE 5-7 DISTRIBUTION OF ENTROPY GENERATION VS. SYSTEM HIGH

PRESSURE SIDE PRESSURE ...................................................................... 70FIGURE 5-8 EXERGY DESTRUCTION VS. HEAT SOURCE TEMPERATURE AT THE

GAS HEATER INLET ................................................................................ 71FIGURE 5-9 ENTROPY GENERATION VS. HEAT SOURCE TEMPERATURE AT THE

GAS HEATER INLET ................................................................................ 71FIGURE 5-10 DISTRIBUTION OF ENTROPY GENERATION VS. HEAT SOURCE

TEMPERATURE AT THE GAS HEATER INLET............................................. 72FIGURE 5-11 CO2 POWER CYCLE EXERGY EFFICIENCY AND THE HEAT

EXCHANGERS MIN TEMPERATURE DIFFERENCES VS. CO2 MASS FLOW RATE ...................................................................................................... 73

FIGURE 5-12 CO2 POWER CYCLE EXERGY EFFICIENCY AND THE HEAT EXCHANGERS MIN TEMPERATURE DIFFERENCES VS. SYSTEM HIGH PRESSURE SIDE PRESSURE ...................................................................... 73

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FIGURE 5-13 CO2 POWER CYCLE EXERGY EFFICIENCY AND THE HEAT EXCHANGERS MIN TEMPERATURE DIFFERENCES VS. HEAT SOURCE TEMPERATURE AT GAS HEATER INLET ................................................... 73

FIGURE 9-1 RANOTOR HEAT EXCHANGERS ................................................. 97FIGURE 9-2 RANOTOR HEAT EXCHANGERS ................................................. 98FIGURE 9-3 SCHEMATIC ILLUSTRATION OF A RANOTOR COMPACT HEAT

EXCHANGER ........................................................................................ 100FIGURE 9-4 SCHEMATIC ILLUSTRATION OF THE FLOW SCHEME FOR A

RANOTOR COMPACT HEAT EXCHANGER ........................................... 100FIGURE 9-5 SUPERIORITY OF LAMINAR FLOW HEAT TRANSFER COEFFICIENT VS.

TUBE DIAMETER (SHAH, 1991) ............................................................ 102FIGURE 9-6 HEAT EXCHANGER CALCULATION MODULE, SCHEMATIC 1 ........ 103FIGURE 9-7 ILLUSTRATION OF HEAT EXCHANGER OUTSIDE GAS FLOW (SIDE

VIEW) .................................................................................................. 104FIGURE 9-8 PROGRAM FLOW CHART EVAPORATOR .................................. 110FIGURE 9-9 PROGRAM FLOW CHART GAS COOLER .................................... 112FIGURE 9-10 PROGRAM FLOW CHART GAS HEATER .................................. 114FIGURE 9-11 PROGRAM OPERATION WINDOWCO2 TRANSCRITICAL POWER

CYCLE .................................................................................................. 115FIGURE 9-12 PROGRAM OPERATION WINDOWCO2 COOLING AND POWER

COMBINED CYCLE ................................................................................ 117FIGURE 9-13 CARBON DIOXIDE TRANSCRITICAL REFRIGERATION CYCLE HEAT

EXCHANGER ........................................................................................ 118FIGURE 9-14 CARBON DIOXIDE TRANSCRITICAL POWER CYCLE HEAT

EXCHANGERS ....................................................................................... 119FIGURE 9-15 CARBON DIOXIDE REFRIGERATION AND POWER COMBINED CYCLE

HEAT EXCHANGER ............................................................................... 120

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1 Introduction

1.1 MotivationEnergy security, economic development and environmentprotectionarenotwellbalancedtodayandtheenergydemandisstillcloselyconnected to theeconomicgrowth.At thesametime,fossilfuelsstillplaythedominantroleinenergyresourcesworldwide, accounting for 77% of the increasing energydemand20072030 (IEA,2009).Therefore, theglobaleconomicgrowthhasledtodramaticenvironmentalproblems,suchasairpollutionandclimatechange.Improvingtheenergyefficiencybyutilizingtheenergyinlowgradeheatsource /wasteheatoffersagreatopportunityforasustainable energy future and fewer environmentalproblems.Figure11showssomeexamplesofthemosttypicallowgradeandwasteheatsources.

Figure11Typicaltemperaturerangeofdifferentheatsourcesforheat

recovery4

4PicturesaretakenfromtheInternetandonlytosymbolizedifferentheatsources

2

The most commonly investigated cycles in lowgrade heatsource andwasteheatutilizations today areOrganicRankineCycles (ORCs) and Kalina cycle (binary fluids and fluidmixtures).The ORC uses an organic working fluid (such as R113 andR123) to generate power (electricity). The working fluid isheated tosaturatedvaporand theexpandingvapor isused todrive an expansionmachine. Themain advantage ofORC isthat for many organic compounds, it is not necessary tosuperheat theworking fluid to avoidmoisture erosion at theturbineoutlet,whichmayresult inhighercycleefficiency.Forthe Kalina cycle, the advantage is that the zeotropic fluidmixturescanmatch theheatsource temperatureprofilebetter,so that better efficiency can be expected. However, thedrawbacks of these cycles are also numerous: for ORC, theworking fluids such as R113 and R123 are expensive, strongclimate gases themselves, and also ozonedepleting. Inaddition, the change of phase for organic compounds duringthe heating process (evaporation) may introduce socalledpinching 5 in the heat exchanger, which producesirreversibility and counteracts the effort to improve the cycleefficiencyfromathermodynamicviewpoint.ForKalinacycles,using fluid mixtures will yield a poorer heat transferperformance than using pure working fluid. Moreover,ammoniawater,which is themost commonly usedworkingfluid in the Kalina cycle, is highly toxic and corrosive (Yan,1991,Thorin,2000).Compared to the working fluids that have beenmentioned,carbon dioxide is a natural working fluid and has manyadvantages: it is inexpensive, nonexplosive and nonflammable.ItalsohaslowGlobalWarmingPotential(GWP=1)andnoOzoneDepletingPotential(ODP).Formanyyears,CO2has been proposed by many scientists as a replacement for5Pinchingisthesmallesttemperaturedifferenceintheheatexchanger

3

syntheticrefrigerantsinrefrigerationfields(Gustav,1992,Peter,1998, Armin, 2000, ManHoe et al., 2004, Tomoichiro, 2005,Samer,2008,Silvia,2011).Theoretically, all the refrigeration cycles can be reversed aspowercycles,asillustratedbelow:

Figure12IllustrationofcyclereversibilityDue to the low critical temperature ofCO2(31.1 C), theCO2heatingprocessinareversedcarbondioxiderefrigerationcycleislikelybelocatedinthesupercriticalregionandthecyclewillthenbe called a carbondioxide transcriticalpower cycle or asupercriticalpower cycle respectively,dependinguponwherethecoolingprocessofCO2islocated.

OneofthemainadvantagesrevealedwhenaCO2refrigerationcycleisrunreverselyasapowercycleisthetemperatureprofileintheheatingprocessofsupercriticalCO2.Figure13illustratesthe temperature profiles of the lowgrade heat source anddifferentworkingfluids intheheatexchangerfortheworkingfluid heating process. As shown in the figure, the carbondioxide temperature profile in the supercritical region canprovide a bettermatch to the heat source temperature glidethanworkingfluidsusedinORCsandKalinacycles.Thus,thesocalled pinching, which commonly occurs for otherworkingfluids,canbeavoidedinsidetheCO2counterflowheatexchanger.This is crucial to reducing the irreversibilityof the

4

cycle and achieving good thermal efficiency, especiallywhenutilizingtheenergyinlowgradeheatsourcesisutilized6.

Figure13Schematicrepresentationchartoftheheattransferbetweenthelowgradeheatsourceandworkingfluidinthemainheatexchanger:(1a)

purefluid;(1b)zeotropicfluidmixtures;(1c)carbondioxide

For the reasons mentioned above, CO2 seems to have greatpotentialforuseasaworkingfluidinpowercyclesinutilizingthe energy in lowgrade heat sources and waste heat. Thisthesisworkwasthereforeproposed.

1.2 ObjectivesandApproachThemainobjectiveofthisprojectistoinvestigatethepotentialoftheproposedCO2cyclesandsystemsinutilizingtheenergyfromlowgradeheatsourcesandwasteheat.Theresearchworkisperformedmainlybycomputeraidedsimulations.Toachieve thegoalof the study, thiswork coversmainly thefollowingaspects:

6The reason for the temperature profilematching being importantwillbeexplainedinmoredetailinchapter4inthisbook.

5

Generalcomputeraidedinvestigationonthepossibilityand potential of the proposed cycles in exploiting theenergyfromlowgradeheatsourcesandwasteheat.

Detailed computeraided studies of selected cycles on

their characteristics, such as the influences ofdifferentworkingparametersonthecycleperformance.

Computeraided dynamic performance simulations of

theselectedcyclesincertainapplications.

Thermodynamic analyses of the proposed cycles andcomparisons between the selected cycles and othercommonlyadoptedcyclesinthesameapplicationfields(i.e. comparisonbetweenCO2 transcriticalpower cycleandatypicalORCcycle).

During the study, the work also involved studies in otherparallelandrelatedtopicssuchascomponentdesignforcertainapplications(i.e. lowairsidepressuredropheatexchangerforrecoveringthewasteheatfromengines).Cycleandsystemmodelsandcomputersimulationsaremainlyperformed with Engineer Equation Solver (EES). TRNSYS isadopted to provide the boundary conditions for dynamicsimulations.Thepropertiesoftheworkingfluidunderdifferentconditions are calculated by Refprop 7.0. Commercial CFDsoftware (COMSOL) has also been used to simulate relevantheat transfer problems and to analyze the air flows in heatexchangerdesigns.

7

2 Background

2.1 WorkingFluidComparisonThere are many thermophysical properties that should beconsideredwhenselectingaproperworkingfluidforutilizingthe energy in lowgrade heat sources and waste heat. Forinstance, the critical temperature and critical pressure willindicatewhetherthecyclewillberunasatranscriticalcycleorasubcriticalcycle,thepossibilityforcondensingandthesystemworkingpressurerespectively; theCpvaluewill influence theshape of the temperature profiles in the system heatexchangers;thespecificvolumeandspecificpowerdensitywillpredict the sizes of the system components for certainapplications; thevalueof/will indicate thepossibilityofmoisture content at the turbine outlet (i.e. the need forsuperheating),etc.Meanwhile, there are also other issues that need to beconsidered,suchasenvironmentalaspects(i.e.GWPandODP),safety,availability,andcost.More than 50 working fluids have been proposed in theliterature,amongwhichthereis,however,nobestfluidthatcanmeet all the criteria. Therefore, certain compromisesmay beneeded to find themost suitableworking fluid for a certainapplication.Table 21 gives theproperties of some typicalworking fluidsthat representdifferent categoriesofworking fluidsproposedintheliterature(waterisusedasareference).

8

Table21Propertiesofdifferentfluids

Fluidname ASHRAENo.

Criticaltemp.(C)

Criticalpress.(Bar)

ASHRAELevelforsafety7

ODP GWP100yr8 dS/dT9

Trifluoromethane R23 26.29 48.3 A1 0 11700 6.49Difluoromethane R32 78.26 57.8 A2 0 580 4.332.2Dichloro1.1.1trifluoroethane R123 183.83 36.6 B1 0.02 93 0.26

Pentafluoroethane R125 66.17 36.2 A1 0 2800 1.08Hydroflorocarbon R134a 101.1 40.7 A1 0 1300 0.39

1.1.1Trifluoroethane R143a 72.86 37.6 A2 0 3900 1.491.1Difluoroethane R152a 113.41 45.2 A2 0 140 1.14Octafluoropropane R218 72.02 26.4 A1 0 7000 0.45

Propane R290 369.8 42.47 A3 0

9

Butane R600 152 37.9 A3 0

10

If one considers toxicity and flammability, working fluid ofASHRAE levelA1 shouldbe the safestone touse.Therefore,workingfluidslikeammoniaandisobutenearenotpreferred.Ifone considers the environmental impacts,working fluidwiththe lowest ozone depleting potential (ODP) and globalwarming potential (GWP) should be selected. Consequently,workingfluids likeTrifluoromethane(R23),Octafluoropropane(R218)andAzeotropicmixture (R500)can thenbeneglected. Ifoneconsidersmoisturesattheexpansionoutlet,workingfluidsthathavenegativevaluesofdS/dT (e.g.Difluoromethane,R32andPentafluoroethane,R125)may lead tomoisturecreationattheturbineoutletwithoutapropersuperheatingandthereforetheyarenotdesired.Moreover,althoughitisreportedthattheKalinacyclecanachievebetterperformance thanconventionalORCs (fluids such as 2.2Dichloro1.1.1trifluoroethane,R123),fluid mixtures often show poorer heat transfer performancethan pureworking fluids. Because of this, fluidmixtures areless desirable, if a transcritical power cycle can be realized.Meanwhile,workingfluidsthathavehighcriticaltemperatureswillhavedifficultybeingutilizedintranscriticalpowercyclesiflowgradeheatsourcesaretobeutilized.Aftertakingalltheseaspects intoaccount,carbondioxideproved tobeapromisingworkingfluidforutilizingtheenergyinlowgradeheatsourcesand waste heat in transcritical power cycles with goodtemperaturematching.Carbondioxidehas thusmanyadvantagesasaworking fluidfor utilizing the energy in lowgrade heat sources andwasteheat.Itisanenvironmentallybenignnaturalworkingfluidandsafe to use. Furthermore, it is abundant in nature and it isavailable at low cost. Moreover, the chemical andthermodynamic properties of carbon dioxide have beenthoroughlystudiedandthereisthereforesufficientknowledgeaboutthem.Compared to otherworking fluids listed inTable 21, carbondioxidehasalowcriticaltemperatureandrelativehighcritical

11

pressure(31.1C/87.98Fand7.38MPa/1070.38psi).Thanksto the low critical temperature, even a lowgradeheat sourcecan give a transcritical cycle whose gliding temperatureprofile can provide a better match to the heat sourcetemperature glide than other working fluids (as mentionedabove).Moreover, since theheatingprocess takesplace in thesupercritical region, some complexity involved in a phasechanging process (e.g. flowmaldistribution) can be avoided.Althoughthehighpressuremayhavecreatedsomechallengesin system component design in the past, this field has fastdeveloped in recent years with faster and faster technicalimprovements.Furthermore,duetoitshighspecificpower,theCO2systemismorecompactthansystemsusingotherworkingfluids. Moreover, the energy in the expansion outlet carbondioxide can be recovered within the cycle through aregenerativeheatexchanger (i.e.a regenerator); thus, thehighworking pressure is helpful in reducing the regenerator sizeand the excellent heat transfer characteristics of CO2 help tominimizetheinfluenceofpressuredroponthecycleefficiency.

2.2 HistoryofCO2PowerCycleResearchontheCO2powercyclewasfirstproposedbySulzerBros in 1948 and later several countries, such as the SovietUnion, Italy and the United States, became involved in theresearch on such a cycle (Feher, 1962 and 1967, Dekhtiarev,1962;Angelino,1966).However,after thegreat interestduringthe 60ties, research on such cyclesdwindled formany yearsuntil the 1990s,mainlydue to the limited amount of suitableheat sources e.g. nuclear) and limited knowledge of suitablecompact heat exchangers and expansion machines (Dostal,2004).After the 1990s and the development of compact heatexchangers and materials, renewed interest was shown incarbon dioxide power cycles and much research has beencarried out (Dostal, 2004; Chang, 2002). Nevertheless, mostinvestigations have focused on a carbon dioxide power cyclewith anuclear reactor as aheat source, thus a cycleworking

12

withahighgradeheatsource(upto800C)andhighpressuresin both the gas heater and gas cooler (CO2 Brayton cycle).Researchonemployingsuchacyclefor lowgradeheatsourcerecoveryhasbeenrelativelylimited.Inrecentyears,moreandmoreinteresthasbeenshowninCO2transcriticalpowercyclesforutilizingtheenergyinlowgradeheat sources. For instance, Zhang and his colleaguesinvestigatedthepotentialofCO2powercycle inutilizingsolarenergyboththeoreticallyandexperimentally(Zhangetal.,2006and 2007). The author and his colleagues investigated theperformanceofthecarbondioxidepowercycleinutilizinglowgradeheat sourcesand compared itsperformancewithORCs(Chen et al., 2005, 2006 and 2010).Moreover, Cayer and hiscolleagues studied CO2 power system under fixed systemworkingconditionsanddiscussedsystemoptimizations(Cayeret al., 2009). Wang et al. tried to optimize the workingparametersofsupercriticalCO2powercycleunderafixedheatsource condition by using a genetic algorithm and artificialneural network with an assumption that the system heatexchangers will provide sufficient heating /cooling to thedesired cycle working conditions (Wang et al., 2010).Furthermore, Baik et al. compared the power basedperformance betweenCO2 andR124 transcritical power cycle(Baiketal.2011)

2.3 SystemIllustrationandCorrespondingCycleDescription

There are two systems proposed in this study: the carbondioxidebottomingsystemand thecarbondioxidecoolingandpowercombinedsystem.

2.3.1 TheCO2bottomingsystemandcorrespondingcyclesTheCO2bottomingsystemconsistsoffourmainparts,namely:agasheater,a turbine,a condenser (gas cooler),andapump

13

(Figure21).Inthissystem,thecarbondioxideisfirstpumpedto a supercriticalpressure, and thenheated in thegasheater.The heated supercritical carbon dioxide will expand in anexpansionmachine(e.g.aturbine).Thevapordischargedfromthe expansion machine outlet will then be cooled andcondensed in a condenser (gas cooler). An Internal HeatExchanger(IHX,regenerator)canbeaddedtothebasicsystemto optimize the system performance. The importance ofutilizinga regenerator ina carbondioxide transcriticalpowercyclewillbeshowninthelatterpartofthisthesis.

Figure21Schematicofthecarbondioxidepowersystem(forbothBrayton

cycleandtranscriticalcycle)The corresponding cycles of this system are carbon dioxidetranscritical power cycle and carbon dioxide Brayton cyclerespectively. Both cycles consist of four processes, namely:compression (ab), isobaricheat supply (bd), expansion (de),isobaricheatrejection (ea).Theonlydifferencebetween thesetwo cycles iswhether part of the cycle is located in the subcritical region or not. Therefore, both cycles are sometimes

14

related to supercritical cycles in the literature.Both cycles areillustratedintheTSchartsasfollows(Figure22&Figure23).

Figure22CarbondioxidetranscriticalcycleTSchart

Figure23CarbondioxideBraytoncycleTSchart

-1.75 -1.50 -1.25 -1.00 -0.75 -0.50-20

20

60

100

140

180

s [kJ/kg-K]

T [

C]

340 bar

220 bar

160 bar

100 bar

40 bar

0.4 0.6 0.8

0.0

017

0.0

057 0

.01

0.0

19m

3/kg

Carbon Dioxide Transcritical Power Cycle

a

bc

d

e

f

g 60 bar

0.2

-1.5 -1.25 -1 -0.75 -0.5

0

40

80

120

160

200

s [kJ/kg-K]

T [

C]

300 bar 200 bar

150 bar 100 bar

0,2 0,4 0,6 0,8

0,0

017

0,0

057

0,0

1

0,0

34

0,0

63 m

3/kg

Carbon Dioxide Brayton Cycle

a

bc

d

e

f

15

It isworthnoticingfromthefiguresthatcarbondioxideattheexpansionoutletstillholdsaveryhighenergycontent(i.e.hightemperature).Atthesametime,thecycleheatrejectionprocesshas an obvious temperature glide,which enables the carbondioxide power system to produce heat (e.g. hot water) andpower (e.g. electrical energy) at the same time. For the caseswhere power is most sought, the regenerator will be verybeneficialforthecycleefficiency.

2.3.2 TheCO2coolingandpowercombinedsystemandthecorrespondingcycle

The carbon dioxide cooling and power combined system ismainly composed of six parts, namely: an evaporator, acompressor, a gas heater, an expander, a gas cooler, and athrottlingvalve.ThesystemschematiclayoutandtheTSchartofthecorrespondingcycleareshownrespectivelyinFigure24andFigure25.

Figure24Carbondioxidecoolingandpowercombinedsystemschematiclayout

16

Figure25CarbondioxidecoolingandpowercombinedcycleTSchart

The corresponding cycle consists of six processes, namely:compression (cd), isobaric heat supply (df), expansion (fg),isobaric heat rejection (gk), throttling (ka) and isobaric heatapply(ac).Afterabsorbingheatintheevaporator(ab),thecarbondioxidewill be further heated in the IHX I until it becomes slightlysuperheated (bc).The superheated carbondioxidevaporwillthenbecompressedbyacompressortoasupercriticalpressure(cd),wheresupercriticalcarbondioxideabsorbstheheatfirstlyfrom the expansion outlet carbondioxide in IHX II (de) andthen from theheat source inagasheater (ef).After that, thesupercriticalcarbondioxidewillbeexpandedinanexpander(fg)andthencooledbyIHXII(gh),agascooler(hj)andIHXI(jk) in turn. Finally, it flows though a throttling valve andenters theevaporator(ka).Inthepowerpartof thecombinedcycle(dfgi),carbondioxidewillabsorbtheheatfromthelow

-1.50 -1.25 -1.00 -0.75 -0.50 -0.25-50

0

50

100

150

200

250

300

350

400

s [kJ/kg-K]

T [

C]

350 bar

250 bar

100 bar

40 bar 0,2 0,4 0,6 0,8

0,0

017

0,0

057

0,0

1

0,0

19 0

,034

0,0

63 m

3/kg

Carbon Dioxide Cooling and Power Combined Cycle T-S Chart

a b

d

e

f

c

j

g

k

h

i

17

grade heat sources or waste heat and convert it into usefulmechanicalwork.Thecombinedcycle isdesignedtobeemployed inautomobileapplications (i.e. trucks), for which the power part of thecombined cyclewill utilize the energy in the engine exhaustgasestoproducepowerforthecompressorofthecoolingpart.

19

3 CO2TranscriticalCycleApplicationsandPerformanceSimulations

3.1 BasicCyclesandtheParametersthatInfluencetheCyclePerformances

Asmentioned in theprevious chapter, there are three cycles,namelycarbondioxidetranscriticalpowercycle,carbondioxideBraytoncycle,andcarbondioxidecoolingandpowercombinedcycle, which have been proposed in the current study forutilizingtheenergyinlowgradeheatsourcesandwasteheat.Thermodynamically, the larger the temperature differencebetween the cycles heat absorbing temperature and its heatrejectingtemperature,thehigherthecycleefficiency.Fromthisviewpoint, for the same heat absorbing temperature, theCO2transcriticalpower cyclewill achieve a higher efficiency thanthe CO2 Brayton cycle if a low temperature heat sink isavailable. To achieve a satisfactory efficiency from a carbondioxide Brayton cycle, a significantly higher heat sourcetemperatureisneeded.Thecurrentstudymainlyfocusesonthesystems that work with carbon dioxide transcritical powercycles in lowgrade heat source utilization. However, theBraytoncycleandcarbondioxidecoolingandpowercombinedcyclehavealsobeenanalyzed for theirpotential inwasteheatutilization(i.e.theengineswasteheat)bybasiccycleanalyses.Several definitions are needed to analyze the performance oftheproposedcarbondioxidesystems in lowgradeheatsource

20

and waste heat utilization. The cycle thermal efficiency ofcarbondioxidepowercyclescanbedefinedby

Equation31:

)()()(.exp

cd

abed

input

pump

input

netth hh

hhhhQ

WWQW

Equation31

whereQinputistheheatinputtothesystemandWnetisthepowerproductionbythesystem.

The Coefficient of Performance (COP) of the carbon dioxiderefrigerationcycleandtheCOPofthecoolingpartofthecarbondioxide cooling andpower combined cycle canbedefined asEquation32:

basic

cooling

WQ

COP Equation32whereQcoolingis thecoolingcapacityof thecoolingsystemandWbasicistherequiredcompressionworkofthecompressor.One of the originalmotivations of the current studywas toreduce the energy usage of refrigeration / air conditioningsystems by utilizing the energy in lowgrade heat source orwasteheatby carbondioxidepower systems. Inotherwords,theaimwas toemployacarbondioxidepower systemor thepowerpartofthecarbondioxidecoolingandpowercombinedsystem toutilize theenergy in lowgradeheatsourceorwasteheattoproducepower.Theproducedpowerwillbethenusedtopartly,or totally,cover thecompressorpowerdemand inarefrigerationsystemorinthecoolingpartofthecarbondioxidecombinedsystem.Insuchapplications,theCOPofthecoolingsystem can be redefined as Equation 33 , since the powerproducedby theCO2power system or thepowerpart of thecombinedsystemisgainedfreeofchargefromthelowgradeheatsourceorwasteheat.

21

new

cooling

outputbasic

coolingnew W

QWW

QCOP

10 Equation33

where Q cooling is the required cooling capacity, W basic is theoriginal compressionwork of the cooling cycle, andWoutput istheworkoutputfromtheCO2powersystemorthepowerpartofthecombinedsystem, i.e.thefreeenergygainedfromthelowgradeheatsourceorwasteheat.Wnew is theworkneededby the compressor after taking away the energy gained fromlowgradeheatsourceorwasteheat.Although the applications will determine the possibletemperature levels and the capacity aswell as the obtainableefficiencies for the various components, several assumptionsaremade in thischapterbasedon thepublished literatures tobe able to specify the cycle working conditions and gain ageneralpictureofbasiccycleperformance.

3.1.1 CarbondioxidetranscriticalpowercycleFor carbon dioxide transcritical power cycles, the gas heaterpressurecanbeselectedarbitrarily.Anoptimumpressurecanbe found as a functionofother cycleparameters, such as thecondensing pressure and the heat source temperature. If anInternalHeatExchanger(IHX)ispartofthesystem,anoptimalgas heater pressure around 120 bar appears likely for anexpansioninlettemperatureof100C,forinstance(Figure33).Atthesametime,theselectionofthegasheaterpressureneedstoconsider thepractical issues,suchas thematerialdurabilitydurance and safety.Most of the calculations for transcriticalpowercycles in thecurrentstudyhavechosen120bar for theinitialcalculationandtheinfluenceofthegasheaterpressureisanalyzed afterwards. The expansion inlet temperature is, ofcourse, related to the heat source temperature. Furthermore,10Thedefinitionmaybequestionable froma strictly thermodynamicperspectivesincetheCOPmaygotoinfinityifWbasicWoutput=0.

22

considering the availability of the low temperature water inrealityandthelimitationofthecyclescriticaltemperature(31.1C),thecondenserpressureissetto60bar,whichcorrespondsto approximately 22 C condensing temperature. The pumpefficiencyisassumedtobe0.8,basedonTadanoetal.sresearchonCO2hermetic compressors (Tadano etal.,2000),due to thefactthatresearchonCO2pumpsisrelativelylimitedcomparedtotheresearchonCO2compressors.Atthesametime,itiswellknown that a pumps efficiency is normally higher than acompressors,mainlyduetothesmallervolumechangeduringthe pumping process than during the compressing process,and,moreover,Tadanoetal.sresearchwasdoneundersimilarworking conditions. Different expansion efficiencies rangingfrom70%(conservativevalveusedintheearlierstudies)to85%(inthelateststudies)havebeenusedinthisstudy.Sincethereisvery limitedresearchonCO2expanders in the lowgradeheatsourceutilization field, the efficiencyvaluesare chosenbasedon the research on carbon dioxide expansion machines intranscriticalrefrigerationcycles,wheretheyareusedtoreplacethethrottlingvalveinordertoincreasethecycleCOP(Nickletal.,2003;Zhaetal.,2003;Huffetal.,2003).Inaddition,theIHXseffectiveness is assumed to be 90% according to Boewe et al.(Boeweetal.2001).

3.1.2 TheinfluencesofthecycleworkingparametersontheCO2transcriticalpowercycleperformance

Therearemany factors thatmay influence theperformanceofCO2 transcriticalpowercycles,suchas theeffectivenessof theIHX, the heat source temperature, aswell as the compressorandexpandersspecifications.Byplottingtheexpansion inlettemperaturevs.cycleefficiencyforagivenpumpefficiencywithvariousexpansionefficiencies,and by plotting the expansion inlet temperature vs. cycleefficiency foragivenexpansionefficiencywithvariouspumpefficiencies (Figure31&Figure32), it is found that thecycle

23

efficiencywill be improved by increasing the expansion inlettemperature.However,afterasharp increaseatthebeginning,the efficiency slope becomes flat if one further increases theexpansion inlet temperature to the high temperature region11.These figures also illustrate that the efficiencies of expansionunitswillhavemorecrucialimpactonthecycleefficiencythantheefficienciesofcompressionunits.

Figure31Carbondioxidetranscriticalcycleefficiencyvs.expansioninlettemperatureagainstvariousexpansionefficiencies(fromEES,basiccycle

withoutIHX)

11Thisresultisbasedonthegivengasheaterpressure,whichisinthelower pressure region compared with the carbon dioxide Braytoncycle.Inthecurrentresearchinutilizingthelowgradeheatsourcebytranscritical power cycle, only relatively lower gas pressure isconsidered,fortheconsiderationofsystemsafety,etc.

100 150 200 250 3000.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

T expan. inlet [C]

eff.

80% pump eff. 90% expan. eff.80% pump eff. 90% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 70% expan. eff.80% pump eff. 70% expan. eff.80% pump eff. 60% expan. eff.80% pump eff. 60% expan. eff.

120 bar gas heater pressure 60 bar condensing pressure

24

Figure32Carbondioxidetranscriticalcycleefficiencyvs.expansioninlettemperatureagainstvariouspumpefficiencies(fromEES,basiccyclewithout

IHX)

Furthermore, the influenceof thecyclegasheaterpressureonthecycleefficiencyofacarbondioxidetranscriticalpowercyclewithout IHX andwith a 90% effectiveness12IHX are plottedrespectively fordifferentexpansion inlet temperatures (Figure33). It isshown that there isanoptimumgasheaterpressurefor a certain expansion inlet temperature and condensingtemperature.At a certain condensing pressure, the lower theexpansioninlettemperature,thelowertheoptimumgasheaterpressure. Moreover, the cycle with an IHX has a loweroptimumgasheaterpressure thana cyclewithout IHXunderthesameworkingconditions.

12

icTihTicTocTessEffectiven

..

,,)(

100 140 180 220 260 300

0.06

0.07

0.08

0.09

0.1

T expan. inlet [C]

th90% pump eff. 80% expan. eff.90% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.70% pump eff. 80% expan. eff.70% pump eff. 80% expan. eff.60% pump eff. 80% expan. eff.60% pump eff. 80% expan. eff.

120 bar gas heater pressure 60 bar condensing pressure

25

Figure33Optimumgasheaterpressureofacarbondioxidetranscriticalcycle(fromEES,withoutIHXandwitha90%effectivenessIHX)

As mentioned in the previous section, the carbon dioxidetranscritical power benefits strongly from internal heatregeneration. Therefore, the IHX (regenerator) will have acrucial influence on the cycle performance. The influence ofIHXonthecycleefficiencyhasbeenplottedinFigure34.

Figure34TheIHXeffectivenessinfluenceoncarbondioxidetranscriticalcycleefficiency(fromEES)

75 110 145 180 215 2500.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Gas heater pressure (Bar)

th

Condensing pressure 60 bar; Condensing temperature 22 C

120C expansion inlet temp.120C expansion inlet temp.140C expansion inlet temp.140C expansion inlet temp.

80 C expansion inlet temp.80 C expansion inlet temp.100 C expansion inlet temp.100 C expansion inlet temp.

120C expansion inlet temp. IHX120C expansion inlet temp. IHX140C expansion inlet temp. IHX140C expansion inlet temp. IHX

100 C expansion inlet temp. IHX100 C expansion inlet temp. IHX80 C expansion inlet temp. IHX80 C expansion inlet temp. IHX

0 0.2 0.4 0.6 0.8 10.07

0.08

0.09

0.1

0.11

0.12

IHX effectiveness

th,H

X

100 C expansion inlet temp.100 C expansion inlet temp.120 C expansion inlet temp.120 C expansion inlet temp.140 C expansion inlet temp.140 C expansion inlet temp.

120 bar gas heater pressure60 bar condensing pressure

26

3.1.3 CarbondioxideBraytoncycleWhen the cycleworks as a Brayton cycle, the heat rejectionprocess will take place in the supercritical region and thecondenser will, therefore, be called a gas cooler. The sameefficiencies as those chosen for the pump and the expansionmachine for carbon dioxide transcritical power cycles areadopted for the compressor and the expansion machine forcarbondioxideBraytoncyclesasinitialanalysisconditions(i.e.75%forthecompressorand7585%fortheexpansionmachine).Thegasheaterpressureandgascoolerpressureareassumedtobe200barand100barrespectivelyfortheinitialcycleanalysisand the influences of different gas cooler and gas heaterpressuresarealsoanalyzedseparately.

3.1.4 TheinfluenceofthecycleworkingparametersontheCO2Braytoncycleperformance

Unlikethecarbondioxidetranscriticalpowercycle,thecarbondioxideBraytoncycleliescompletelyinthesupercriticalregion.Forthisreason,boththegasheaterpressureandthegascoolerpressure will influence the cycle performance besides theinfluence by the effectiveness of the IHX, the heat sourcetemperatureandthecompressorandexpandersspecifications,etc.Byplottingtheexpansion inlettemperaturevs.cycleefficiencyforagivenpumpefficiencywithvariousexpansionefficiencies,and by plotting the expansion inlet temperature vs. cycleefficiency foragivenexpansionefficiencywithvariouspumpefficiencies (Figure35&Figure36), it is found that thecycleefficiencywill be improved by increasing the expansion inlettemperature.Moreover,theimprovementsofthecyclethermalefficiencyarelessobviousinthehighertemperatureregions.Ingeneral, the Brayton cycle achieves lower thermal efficiencythan the transcriticalpower cycle at the same expansion inlettemperature.Furthermore,itcanbenoticedthattheefficiencies

27

ofexpansionunitswillhavemorecrucial impacton the cycleefficiencythantheefficienciesofcompressionunits.

Figure35CarbondioxideBraytoncycleefficiencyvs.expansioninlettemperatureagainstvariousexpansionefficiencies(fromEES,basiccycle

withoutIHX)

Figure36CarbondioxideBraytoncycleefficiencyvs.expansioninlettemperatureagainstvariouspumpefficiencies(fromEES,basiccyclewithout

IHX)

100 140 180 220 260 3000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

T expan. inlet [C]

th

80% pump eff. 60% expan. eff.80% pump eff. 60% expan. eff.80% pump eff. 70% expan. eff.80% pump eff. 70% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 90% expan. eff.80% pump eff. 90% expan. eff.200 bar gas heater pressure

80 bar condensing pressure 35 C gas cooler outlet temperature

100 140 180 220 260 3000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

T expan. inlet [C]

th

60% pump eff. 80% expan. eff.60% pump eff. 80% expan. eff.70% pump eff. 80% expan. eff.70% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.80% pump eff. 80% expan. eff.90% pump eff. 80% expan. eff.90% pump eff. 80% expan. eff.

200 bar gas heater pressure80 bar condensing pressure 35 C gas cooler outlet temperature

28

Furthermore, the influenceof thecyclegasheaterpressureonthe cycleefficiencyofa carbondioxideBrayton cyclewithoutIHXandwitha90%effectivenessIHXrespectivelyareplottedfor different expansion inlet temperatures (Figure 37). It isshown that there is an optimum gas heater pressure for acertain cycleworking condition.Moreover, the cyclewith anIHX has a lower optimum gas heater pressure than a cyclewithoutIHXunderthesameworkingconditions.

Figure37OptimumgasheaterpressureofacarbondioxideBraytoncycle(fromEES,withoutIHXandwitha90%effectivenessIHX)

Besidestheoptimumgasheaterpressure,theBraytoncyclealsohasanoptimumgascoolerpressureforacertaincycleworkingconditionwhichisshowninFigure38.

100 120 140 160 180 200 220 240 260 2800

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16


th

200 C expansion inlet temp.

200 C expansion inlet temp. IHX





225 C expansion inlet temp.225 C expansion inlet temp. IHX

Gas cooler pressure 80bar, gas cooler outlet temp. 35 C

29

Figure38OptimumgascoolerpressureofacarbondioxideBraytoncycle

(fromEES,withoutIHXandwitha90%effectivenessIHX)

Furthermore,theinfluenceoftheIHX(regenerator)onthecyclethermalefficiencyhasalsobeenplottedinFigure39.Asshownin thefigure, theeffectivenessof theIHXhascritical influenceonthecyclethermalefficiencyaswell.

Figure39TheinfluenceofIHXeffectivenessoncarbondioxidetranscriticalcycleefficiency(fromEES)

75 80 85 90 95 1000.02

0.04

0.06

0.08

0.1

0.12

0.14


th


150 C expansion inlet temp.175 C expansion inlet temp.


Gas cooler pressure 80bar, gas cooler outlet temp. 35 C

150 C expansion inlet temp. IHX150 C expansion inlet temp. IHX175 C expansion inlet temp. IHX175 C expansion inlet temp. IHX200 C expansion inlet temp. IHX200 C expansion inlet temp. IHX225 C expansion inlet temp. IHX225 C expansion inlet temp. IHX

0 0.2 0.4 0.6 0.8 10.04

0.05

0.06

0.07

0.08

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0.1

0.11

0.12

0.13

IHX effectiveness

th,H

X

150 C expansion inlet temp.150 C expansion inlet temp.175 C expansion inlet temp.175 C expansion inlet temp.200 C expansion inlet temp.200 C expansion inlet temp.

120 bar gas heater pressure80 bar gas cooler pressure35 C gas cooler outlet temperature

30

3.1.5 CarbondioxidecoolingandpowercombinedcycleTheauthor isnotawareofany similar cycle suggested in theliterature. Therefore, there is no reference cycle operatingcondition available for carbon dioxide cooling and powercombinedcycle.For the cooling part of the combined cycle, the workingconditionsare selectedaccording to themost commonlyusedworking conditions in other research and inCO2 automobileA/C prototype testing (Kim et al., 2004). The evaporationpressure isset to40barand theevaporation temperaturewillbe 5.3 C accordingly.As it ismentioned frequently in otherresearch,thereisanoptimumgascoolerpressureforthecarbondioxidetranscriticalrefrigerationcycle(PetterssenandAarlien,1998,Kauf1999).Fortheheatrejectionpressure,Liaoandhiscolleagues(Liaoetal.,2000) proposed a correlation to predict the optimum heatrejectionpressureintermsofevaporationtemperatureandthegascoolersoutlettemperature,whichisexpressedbyEquation34

)34.9381.0()0157.0778.2( eceopt tttp Equation34The gas cooler pressure is then set to 85 bar, which is theoptimumgascoolerpressurecalculatedbythisequation,basedon the assumed evaporation temperature and the 35C gascooleroutlettemperature.Moreover, an IHX is included in the system to secure a 5Ksuperheat at the evaporator outlet as a fixed value to ensurethere isnomoistureat the compressor inlet.Furthermore, thecompressors isentropic efficiency is assumed to be 75%according to the research done by Rozhentsev and Wang(RozhentsevandWang,2001).

31

For thepowerpart, thegasheaterpressure is selected to 200bar.Thegascoolerpressure(85bars)andthegascooleroutlettemperature (35 C) are the same as for the cooling part.Furthermore, the compression and expansion efficiencies areassumed according to the cycle operating conditions listedabove.Moreover, the combined cycle is designedmainly forautomobile (i.e. truck) applications, and thus the expansioninlettemperatureisassumedtobe350C,basedonthefactthatengine exhaust gas can have a temperature of 500C at theexhaustgasmanifold.

3.1.6 TheinfluenceofcycleworkingparametersontheCO2coolingandpowercombinedcycleperformance

ThecoolingpartCOPof thecombinedcycle isplottedagainstdifferent gas cooler pressures, while keeping other cycleworkingconditionsconstant(Figure310).

Figure310TheCOPofcoolingpartofthecombinedcyclevs.differentgascoolerpressure

From the figure, one can see that at the optimum gas coolerpressure, the improvement of the cooling cycles COP is

70 80 90 100 110 1201

1.5

2

2.5

3

3.5

4

4.5

5

Pgascooler (bar)

CO

P

COPnew (200 bar gas heater pressure)

COP basic (without power part)COP basic (without power part)

COPnew (140bar gas heater pressure)COPnew (140bar gas heater pressure)

COPnew (250bar gas heater pressure)COPnew (250bar gas heater pressure)

32

tremendous (e.g.around40%asmentionedabove in thebasiccycle analysis) and the enhancement of COP is different fordifferentgasheaterpressures.Keepingtheoptimumgascoolerpressureconstant,theCOPofthe combined cycles cooling part is plotted against differentgasheaterpressuresfordifferentexpansioninlettemperatures

Figure311TheCOPofcoolingpartofthecombinedcyclevs.differentgasheaterpressure

Theresultsshowthatthere isanoptimumgasheaterpressurefor the combined cyclesnewCOP for certain expansion inlettemperatures (i.e. the gas heater pressure for combined cyclepowerparttoachievethehighestWoutputforacertainexpansioninlet temp.). Furthermore, the optimum gas heater pressureincreaseswithincreasingexpansioninlettemperature.

100 120 140 160 180 200 2202.8

3

3.2

3.4

3.6

3.8

4

4.2

4.4

4.6

4.8

5

Pgasheater

CO

PCOP new (300C expan. inlet temp.)COP new (300C expan. inlet temp.)

COPbasic without powerpartCOPbasic without powerpart

COP new (350C expan. inlet temp.)COP new (350C expan. inlet temp.)

COP new (325C expan. inlet temp.)COP new (325C expan. inlet temp.)

33

3.2 CO2PowerCycleApplicationsandPerformanceSimulations

3.2.1 CO2doubleloopsystemOneof theCO2power cycle applicationsbeing studied in thecurrent work is what the author calls the CO2 double loopsystem.TheschematicsystemlayoutandthecorrespondingTSchartareshownasfollows(Figure312andFigure313).As shown in Figure 312, aCO2 double system contains twoparts: the power part (upper part) and the refrigeration part(lowerpart).Thepowerpartiscomposedoffivemainparts:apump,agasheater,anexpansionmachine,agascooler,andaninternalheatexchanger.The refrigerationpartconsistsof fourmainparts:acompressor,agascooler,anexpansionvalve,andanevaporator.Furthermore,an internalheatexchanger isalsoincluded in the system to ensure the refrigerant vapor isslightly superheated (i.e. 5C superheat) before it enters thecompressor.Inthecurrentanalyses,thesystememploysCO2asaworkingmedia forbothpartsandadopts theadvantagesofboth the CO2 power subsystem and CO2 refrigerationsubsystem.

34

Figure312DoubleloopsystemschematicsystemlayoutThe corresponding CO2 power cycle can be a transcriticalpowercycleoraCO2Braytonpowercycle,dependinguponthecondensing media temperature. For the system proposed inFigure 312, one gas cooler for both systems is adopted forsystem simplicity. Thus, the corresponding power cycle is aCO2 Brayton cycle and the cooling part is aCO2 transcriticalrefrigerationcycle(Figure313).

35

Figure313DoubleloopsystemTSchart(EES)Basedon theassumptionsofsystemworkingconditions listedin Table 31, the CO2 double loop system performance iscalculatedand theresults (Table32)show that ifa lowgradeheat source such as solar thermal orwaste heat is used, theproposed double loop system can improve the COP of theparallelrunningCO2refrigerationsystemby34%.Table31Carbondioxidedoubleloopsystembasicoperatingconditions

SimulationParameters Value UnitEvaporatorpressure 40 barEvaporationtemperature 5.3 CRefrigerantmassflow 0.08 Kg/sSuperheatafterevaporator 5(fixedvalue) KGascoolerpressure 83 barGascooleroutlettemperature 3513 C13This temperature is the temperature before the IHX.The real gascooler outlet temperature is the temperature after providing 5Csuperheatatevaporatoroutlet(I.e.33Cinthecurrentcase).

-1.75 -1.50 -1.25 -1.00 -0.75 -0.50-25

0

25

50

75

100

125

150

s [kJ/kg-K]

T [

C]

40 bar 60 bar

80 bar

120 bar

140 bar

0.2 0.4 0.6 0.8

0.0

017

0.0

057

0.0

1

0.0

19 0

.034

m3/

kg

Carbon Dioxide

ab

c

d

e

f

a' b'c'

d'

e'f'

36

Gasheaterpressure 120 barExpansioninlettemperature 120 CCompressionefficiency 75% Expansionefficiency 85% Pumpefficiency 80% PowerpartIHXeffectiveness 0.9 Cooling water inlettemperature

15 C

Coolingwatermassflowrate 0.15 Kg/sTable32Carbondioxidedoubleloopsystemsperformanceunderthebasicoperatingconditions

PerformanceParameters Value UnitDouble loop power part thermalefficiency(withoutIHX)

4.8%

Double loop power part thermalefficiency(withIHX)

7.5%

BasicrefrigerationsystemCOP 3.1 DoubleloopsystemCOP14double 4.1 Wateroutlettemperature 60.8 CSystemcoolingcapacity 9.8 kWPowerofhotwaterproduction 25.1 kWTheinfluenceofthegascoolerpressureinthepowerpartofthedoubleloopsystemontheCOPofthedoubleloopsystemhasalsobeen investigatedandthesimulationresultsareshown inFigure314.

14COPdouble=COPnewandisdefinedasEquation33

37

Figure314BasicrefrigerationsystemsCOPanddoubleloopsystemsCOPvs.differentgascoolerpressuresatdifferentgasheaterpressures

Itmaybenoticed thatwith thecontributionfrom thesystemspower part, the proposed double loop system can achieve amuchhigherCOP than the basic carbondioxide refrigerationsystem. For a certain system working condition, there is anoptimumpowersubsystemgascoolerpressure,whichenablesamaximumCOPforthedoubleloopsystem.Furthermore, the influence of the power subsystems gasheater pressure and the expansion inlet temperature (heatsource temperature) were also studied and the results areshowninFigure315.

75 80 85 90 95 100

2.4

2.8

3.2

3.6

4

4.4

CO

PCOPdouble at 140 bar GH pressureCOPdouble at 140 bar GH pressureBasic COPBasic COP

COPdouble at 120 bar GH pressureCOPdouble at 120 bar GH pressureCOPdouble at 110 bar GH pressureCOPdouble at 110 bar GH pressure

COPdouble at 130 bar GH pressureCOPdouble at 130 bar GH pressure

Power subsystem's gas cooler pressure (Bar)

38

Figure315DoubleloopsystemsCOPagainstdifferentgasheaterpressuresatdifferentgascoolerpressuresanddifferentexpansioninlettemperatures

Itcanbeseenfromthefigurethatforacertainexpansioninlettemperature and a certain gas cooler pressure, there is anoptimum gas heater pressure, which enables the maximumCOP.The influences of the compressor, expansion machine andpumps isentropic efficiencies on the double loop systemperformanceareshowninFigure316.Theresultsindicatethatthe compressor has amore critical influence on the systemsCOPthanthepumpandtheexpansionmachine.

At 110 C expansion inle temperature

2

2.5

3

3.5

4

4.5

5

90 110 130 150 170 190 210Gas heater pressure (bar)

CO

P do

uble


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5

90 110 130 150 170 190 210Gas heater pressure (bar)

CO

P do

uble


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4

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5

90 110 130 150 170 190 210

Gas heater pressure (bar)

CO

P do

uble

80 bar gas cooler pressure82 bar gas cooler pressure84 bar gas cooler pressure86 bar gas cooler pressure


2

2.5

3

3.5

4

4.5

5

90 110 130 150 170 190 210

Gas heater pressure (bar)

CO

P do

uble

39

Figure316DoubleloopsystemsCOPagainstdifferentcomponentsefficiencies

3.2.2 SolardrivenCO2transcriticalpowersystemAnotherinterestingapplicationofCO2powercycleistoutilizesolarenergyforheatandpowercoproduction(i.e.asocalledsolardrivenCO2Rankinecycle).The basic solardriven carbon dioxide transcritical powersystem consists of four main components, namely: a solarcollector, an expansion machine, a condenser, and a pump(Figure317).

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0.55 0.65 0.75 0.85 0.95Isentropic efficiency

CO

P

COP_double with diff. pump eff.COP with diff. pump eff.COP_double with diff. compressor eff.COP with diff. compressor eff.COP_double with diff. expansion eff.COP with diff. expansion eff.

40

Figure317Solarpoweredtranscriticalcarbondioxidepowersystem

Thedynamicperformanceofasmallscalesolardrivencarbondioxide power system has been analyzed by the dynamicsimulation toolTRNSYS 16 (Klein, 2004) and theEngineeringEquationSolver(EES)(Klein,2004)usingcosolvingtechnique.The thermodynamicmodel of the transcritical carbondioxidepowersubsystemisdevelopedinEES,whilethesolarcollectorandthesystemboundaryconditionsaresimulated inTRNSYS16.AcontrollerthatsensesthetemperatureoftheCO2atthesolarcollectoroutletisalsoaddedtothesystemtocontrolthesystemworkunder threemodes,dependingupon the temperatureofCO2atthesolarcollectoroutlet:

When the temperatureof theCO2at thesolarcollectoroutlet ishigher than80C, thesystemwillworkunderthepowermode.ThecontrollerwillthendirecttheCO2from the solar collector to the expansion machine toproducepowerandthecondenser inthepowersystemwillproduceheat(hotwater)atthesametime.Theflowrateofthecoolingwatertothecondenserisassumedtobe360kg/h(0.1kg/s).

41

When the temperatureof theCO2at thesolarcollectoroutlet is between 35C and 70C, the controller willcontrol the threewayvalveat thesolarcollectoroutlettobypass theexpansionmachine.CO2will thenbe ledto the condenser directly to produce heat (hotwater)andthewaterflowratetothecondenserwillbereducedto180kg/h(0.05kg/s).

When the temperatureof theCO2at thesolarcollectoroutlet is lower than35C, thecontrollerwillswitchoffthe pump and the entire systemwill be stopped untilthetemperatureoftheCO2ishigherthan35Cagain.

Based on the simulation parameters listed in Table 33, theannualdynamic systemperformancehasbeen simulatedwithSwedish climate.METEONORM v5.0 (2006)was adopted forgeneratingthehourlyweatherdata.Table33SimulationParametersSimulationParameters

Descriptions

ClimaticData Weather data is generated byMETEONORM v5.0. TRNSYS TYPE109reads the weather data from weatherdata files and recalculates the solarradiationatdifferentwallorientations.

Location:Stockholm,SwedenSolarCollectorSubsystemCollector TRNSYS model type 71 is used for

modeling the evacuated tube solarcollector.Collectorangle:30Collectordirection:SouthCollectortype:EvacuatedTube(ETC)sc=0.81.5((TiTa)/G)

PowerCycleSubsystemTRNSYS model TYPE66 calls the

42

externalmodelwhichisbuiltinEES.WorkingMedium:Carbondioxide

CO2massflow:180kg/h Cooling water mass flow: 360kg/h

(under power mode). 180kg/h (underheatingmode).Inlettemperature:15C

Pump Pumpefficiency:0.8Turbine Turbineefficiency:0.85Gasheater The basic system gas heater pressure

(solar collector pressure) is selected as120bar

Condenser Condenser pressure is 60 bar,corresponding to the temperatureof22C,andwith80%efficiency

The systemperformance forpowerandhotwaterproductionrespectively on a typical Swedish summer day (July 15th) areshown in Figure 318 and Figure 319.Due to the controller,whichensuresthesystemoperatesonlywhenthesupercriticalcarbon dioxide temperature at the solar collector outlet ishigherthan80C,thesystemoperatesfrom8to17duringthisday.

Figure318DailyperformanceofsolardrivencarbondioxidepowersystemduringasummerdayinStockholm(at120bargasheatingpressure)

0.020.040.060.080.0100.0120.0140.0160.0180.0

0.0

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2.5

7 9 11 13 15 17

Power

(kW)

Time

W_exp

W_pump

Tempe

rature

(C)

43

Figure319DailyperformanceofthesolardrivencarbondioxidepowersystemduringasummerdayinStockholm(at120bargasheaterpressure)As shown in the figures, the temperature of the supercriticalcarbondioxide varieswith time andhas apeak value (about170 C)around13:00,when the systemnetpowerproductionalsoreaches itsmaximum (about1.5kW).Theaveragesystemthermal efficiencyduring the systemworkingperiod is about9%andtheaveragepowerproductionisconsequentlyabout1.2kW. Besides the period when the system is working underpowermode,thesystemalsoworksundertheheatingmodeinthe earlymorning (6:00 to 8:00).The sudden changeofwatertemperature(around8:00) isduetotheshiftbetweendifferentworkingmodesand thedifference incoolingwater flow ratesin differentworkingmodes. This can be further adjusted byoptimizing the coolingwater flow rates in differentworkingmodes.Duringthesystemworkingperiod,thesystemreachesitspeakcapacityaround13:00and itspeakcapacity isaround12kW.Figure 320 to Figure 323 show the daily and monthlyperformanceof the solardrivencarbondioxidepower systemforpowerandhotwaterproductionsforanentireyear.

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Q_w

ater

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Q_water T_w_out

T_w_in T_co2

Tempe

rature

(C)

44

Figure320Dailynetpowerproduction(kWh/day)ofasolardrivencarbon

dioxidepowersysteminoneyear(at120bargasheatingpressure)

Figure321Monthlynetpowerproduction(kWhs)ofthesolardrivencarbondioxidepowersysteminoneyear(at120bargasheatingpressure)

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Net

power

prod

uction

(kWh/mon

th)

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Figure322Dailyheatproduction(kWhs)ofthesolardrivencarbondioxide

powersysteminoneyear(at120bargasheatingpressure)

Figure323Monthlyheat(kWhs)ofthesolardrivencarbondioxidepower

systeminoneyear(at120bargasheatingpressure)Onecansee thatforSwedishclimateconditions, theproposedsystem canwork fromMarch to September and reachesboththemaximum power andmaximum hotwater production inJune. Over the whole year, the maximum daily powerproductionisabout12kWhandthemaximummonthlypower

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46

productionisabout215kWh.Furthermore,theannualaveragethermal efficiency for power production is 8%. For the hotwater production, the maximum daily thermal energyproduction is about 112 kWh and the maximum monthlythermalenergyproductionisabout2320kWh.Figure 324 and Figure 325 show the influences of theexpansion machines isentropic efficiency and gas heatingpressureon thepowerproduction systemperformance. Itcanbe seen from the figures that the efficiency of the expansionmachinewillhaveagreat influenceon thepowerproductionsystemperformance.Furthermore,foracertainexpansioninlettemperature, there is an optimum gas heating pressure.However,theselectionofthegasheatingpressureshouldalsoconsider the material of the solar collector and the annualtemperaturechangeofsupercriticalCO2attheexpansioninlet.

Figure324Dailyaveragepowerproductionofsolardrivencarbondioxide

powersystematdifferentexpansionisentropicefficiencies

0

0.2

0.4

0.6

0.8

1

1.2

1.4

50% 55% 60% 65% 70% 75% 80% 85%

Avarage

Power

Prod

uction

(kW)

IsentropicExpansionefficiency

47

Figure325Dailyaveragepowerproductionofsolardrivencarbondioxide

powersystematdifferentgasheatingpressuresBydefiningtherelativethermalefficiencyimprovementforthesystembyEquation35,theinfluenceofIHXseffectivenessonsystem power output and the relative thermal efficiencyimprovementscanbeplotted(Figure326).TheresultsindicatethatthesystemthermalefficiencycanbeincreasedbyinsertinganIHX,andthemaximumincreaseofthermalefficiencywithathermodynamicallyidealIHXcanreachabout50%.

withoutIHX

withoutIHXIHX

timprovemen efficiency Thermal Equation35

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

W_pump W_exp. W_net

Power

(kW)

80bargasheatingpressure100bargasheatingpressure120bargasheatingpressure140bargasheatingpressure160bargasheatingpressure

48

Figure326Solardrivencarbondioxidepowersystempoweroutputandthermalefficiencyimprovementvs.IHXeffectiveness(resultscalculatedfor

thesamedaythatchosenforFigure318)A simple economic analysiswas also conducted to show theeconomic aspects of the solardrivenCO2 power system. Thesimulation resultsshow that thesimulatedsystemwillhaveapaybacktimearound12years,whichcanbefurthershortenedif thesystem isundermassproductionorbeingused inahotclimateregion,wheremuchhighersolarenergyisavailable.

3.3 SummaryIn this chapter, the basic working conditions of the threeproposedcarbondioxidepowercycles,namelycarbondioxidetranscritical power cycle, carbon dioxide Brayton cycle andcarbon dioxide cooling and power combined cycle, arespecified.Toutilizetheenergyinlowgradeheatsources(i.e.heatsourcewithlowavailabletemperatures),acarbondioxidetranscriticalpowercyclewillbemorepreferabledue to itshigher thermal

1.141.161.181.201.221.241.261.281.301.321.34

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

0 0.2 0.4 0.6 0.8 1

Ave

rage

pow

er o

utpu

t (kW

)

Ther

mal

effi

cien

cy im

prov

emen

t

IHX effectiveness

Average power output

Thermal efficiency improvement

49

efficiencythanthecarbondioxideBraytoncyclewiththesameheat sink condition.When utilizing the energy inwaste heat(e.g.engineexhaustgasses),acarbondioxideBraytoncycleandcarbon dioxide cooling and power combined cyclewill be ofinterest.The simulation results of basic cycle performances show thatthe carbon dioxide transcritical power cycle has an optimumgasheaterpressure foracertaincycleworkingcondition.Theefficiencyofexpansionunitswillhavemorecrucial impactonthe cycle efficiency than the efficiencies of compressionunits.Due to the characterof the cycle, an InternalHeatExchanger(regenerator) is very crucial to improving the cycleperformance,ifpowerissought.For the carbon dioxide Brayton cycle and the power part ofcarbondioxidecoolingandpowercombinedcycle,thereisbothan optimum gas heater pressure and an optimum gas coolerpressureforacertaincycleworkingcondition.Fortheapplicationsofcarbondioxidepowersystems:A carbon dioxide double loop system is proposed and itsperformance has been simulated. The results show that byutilizing the energy in a lowgradeheat source, theproposedcarbon dioxide double loop system can improve the coolingCOPofacarbondioxidecoolingsystemby34%.Fortheproposedcarbondioxidecoolingandpowercombinedsystems, theCOP of the basic carbon dioxide cooling systemcanbeimprovedby40%byutilizingtheenergyintheexhaustgasoftruckengines.TheperformanceofasolardrivencarbondioxidepowersystemintheSwedishclimatehasbeensimulatedindetailbydynamicsimulations.

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ThedailysimulationresultsforatypicalSwedishsummerday(15th of July) show that the system can achieve 8% averagethermal efficiency and 1.2 kW average power productionsduring the system working period. At the same time, thesystemcanproduceheat (hotwater)withanaveragecapacityofabout10kW.Theaverage temperatureof theproducedhotwater is about 40 C, which can be further increased bydecreasing the water flow rate or by system modification.Annually, the system achieves both maximum powerproductionandmaximum thermalenergyproduction in June.Themaximum daily power production is about 12 kWh andmaximummonthly power production is about 215 kWh.Themaximumdaily thermal energyproduction is about 110kWhandthemaximummonthlythermalenergyproductionisabout2300kWh.A simple economic analysis is also conducted to show theeconomic aspects of the solardrivenCO2 power system. Thesimulation resultsshow that thesimulatedsystemwillhaveapaybacktimearound12years,whichcanbefurthershortenedifthesystemisundermassproductionorbeingusedinthehotclimateregion,wheremuchhighersolarenergyisavailable.

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4 TemperatureProfilesinCO2PowerSystemHeatExchangers

4.1 CpVariationandItsInfluenceontheCO2PowerCycleTemperatureProfilesintheHeatExchangers

Asmentioned inprevious chapters, carbondioxidehasa lowcriticaltemperature(31.1C),whichallowsthecarbondioxidepower cycle towork eitherasa transcriticalpower cycleor aBraytoncycledependingupo

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