Heat transfer and pressure drop of supercritical CO2 in brazed plate heat exchangers of the tri-partite gas cooler

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International Journal of Heat and Mass Transfer 178 (2021) 121641

ContentslistsavailableatScienceDirect

International Journal of Heat and Mass Transfer

journalhomepage:www.elsevier.com/locate/hmt

Heat transfer and pressure drop of supercritical CO ₂ in brazed plate heat exchangers of the tri-partite gas cooler

Alireza Zendehboudi

^a^,^†^,^∗

, Zuliang Ye

^a^,^b^,^†^,^∗

, Armin Hafner

^a

, Trond Andresen

^c

, Geir Skaugen

^c

aDepartment of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Kolbjørn Hejes v 1B, 7491 Trondheim, Norway

bSchool of Energy and Power Engineering, Xi’an Jiaotong University, 28 Xianning West Road, 710049 Xi’an, China

cSINTEF Energy Research, Sem Sælands vei 11, 7034 Trondheim, Norway

a rt i c l e i nf o

Article history:

Received 12 March 2021 Revised 22 June 2021 Accepted 23 June 2021 Available online 10 July 2021 Keywords:

Supercritical carbon dioxide Brazed plate heat exchanger Tri-partite gas cooler Heat transfer Pressure drop Correlation

a b s t r a c t

TheheattransfercharacteristicofsupercriticalCO₂isanessentialresearchtopicduetoitssignificantin- fluenceontheperformanceofheatexchangersandsystems.Inthispaper,theheattransferandpressure dropofsupercriticalCO₂ inthe brazedplateheatexchangers areexperimentallyresearched. Theheat exchangersbelongtoatri-partitegascoolerwhichcansimultaneouslyfulfillthedemandsofdomestic hotwaterandspaceheating.TheresultsdemonstratesthatthethermalresistanceintheCO2sideisthe mainfactorthatinfluencesthetotalheattransfer.TheincreaseofCO₂inletpressurecanreducetheheat transfercoefficientsexceptatthehightemperatureregion.Theimprovementofheattransfercoefficient byincreasing theCO2 massflowrate ismore significantinthe spaceheating(SH)and domestic hot water (DHW)preheatinggas coolers,andislowestintheDHWreheatinggas cooler.The influenceof DHWinlettemperatureismoreobviousintheDHWpreheatinggascoolerthatconnectedtothewater inlet.TheinfluenceofwatermassflowrateisdifferentintheDHWandSHoperationmodes.Moreover, theeffects ofCO₂ pressure andmassflowrate onthebuoyancy forcearediscussedandtheinfluence ofbuoyancyforceonheattransferisverified. Theinaccuracyofthecorrelationsfromtheliteratureis provedandthennewcorrelationsareestablished.Themeanabsoluterelativeerrorsofthenewcorrela- tionsare11.61%and12.82%fortheone-passandtwo-passconfigurations,respectively.Furthermore,the frictionalpressuredrop intheheatexchangersislow(upto36.51kPa) andbasicallyincreasesasthe Reynoldsnumberincreases.

ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/)

1. Introduction

According to the Kyoto Protocol,the HFC refrigerants that are extensively used have to be replaced due to their negative im- pactonthegreenhouseeffect[1].Naturalrefrigerantsare considered to be the complete solutionfor the refrigerantreplacement predicament [2]. CO₂ is an excellent candidate due to its non- toxicity, incombustibility,safety,lowcostandenvironmentallybe- nign(ODP=0,GWP=1)[3].Itiswidelyimplementedinrefriger- ation andheatpumpsystems,airconditioningandvariousindus- trialuses[4,5].GiventhatonecharacteristicofCO₂isthelowcrit- icalpressureandtemperature, thetranscriticalcycleisintroduced to solvethe ineﬃciency problemof thesubcriticalcyclenearthe

∗Corresponding authors.

E-mail addresses: alireza.zendehboudi@ntnu.no (A. Zendehboudi), zuliangye@foxmail.com (Z. Ye).

† Equal contribution as joint ﬁrst authors (listed alphabetically).

criticalpoint[6].InthetranscriticalCO₂cycle,theheatabsorption processoccursatthesubcritical pressurewhereas theheatrejec- tionprocesshappensatthesupercritical pressure[5].Forthewa- ter heating applicationthat requires a large temperaturelift, the transcriticalCO₂ cycleshows a specialadvantage compared with thetraditionalrefrigerants[7].Thetemperatureglideofsupercrit- icalCO₂ canreduce theheat transfertemperaturedifference,and decreasetheenergylossandentropygeneration[8,9].

TodemonstratethemeritsoftranscriticalCO₂ heatpumpwaterheater,SaikawaandKoyama[10]studiedthecoeﬃcientofper- formance (COP) upper limit of heat pumpwater heater systems withdifferentrefrigerantsandtheCO₂ systemobtainedthehigh- estvalue.TheperformanceofacommercialCO₂ systemwascom- paredwiththatofasimilarR134asystembyNawazetal.[11],and it wasdiscovered that the CO₂ heat pumpwater heater showed comparable eﬃciency. Regarding the further exploitation of the performance potential of the transcritical CO₂ heat pump water heater,thedesignofseparatedgascoolers fordomestichotwater

https://doi.org/10.1016/j.ijheatmasstransfer.2021.121641

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A. Zendehboudi, Z. Ye, A. Hafner et al. International Journal of Heat and Mass Transfer 178 (2021) 121641

Nomenclature

Symbols

A Heattransferarea[m²] b Corrugationdepthofplate[m]

cp Isobaricspeciﬁcheat[J•(kg•K)⁻¹] cp Averageisobaricspeciﬁcheat[J•(kg•K)⁻¹] D Hydraulicdiameter[m]

G Massﬂux[kg•(m²•s)⁻¹] Gr Grashofnumber[-]

g Gravitationalacceleration[m•s⁻²] h Heattransfercoeﬃcient[W•(m²•K)⁻¹] i Enthalpy[J•kg⁻¹]

k Thermalconductivity[W•(m•K)⁻¹] L Port-to-portlengthofplate[m]

m Massﬂowrate[kg•s⁻¹]

N Number[-]

Nu Nusseltnumber[-]

P Pressure[MPa]

p Corrugationpitchofplate[m]

Pr Prandtlnumber[-]

Pr AveragePrandtlnumber[-]

Q Heattransferrate[W]

Re Reynoldsnumber[-]

T Temperature[°C]

t Thicknessofplate[m]

u Flowvelocity[m•s⁻ ¹] V Volumetricﬂowrate[m³•s⁻¹] W Widthofplate[m]

β

^Chevron^angle^of^plate^[^°]

^p ^Pressure^drop^[kPa]

^T Logarithmicmeantemperaturedifference[K]

μ

^Dynamic^viscosity^[Pa^•^s]

ρ

^Density^[kg^•^m⁻³^]

ρ

¯ ^Average^density^[kg^•^m⁻ ³^]

φ

^Areaenlargementfactor[-]

Abbreviations

COP Coeﬃcientofperformance DHW Domestichotwater GC Gascooler

HT Heattransfer

GWP Globalwarmingpotential ODP Ozonedepletionpotential PD Pressuredrop

SH Spaceheating Subscripts

ave Average

b Bulk

ch Channel

CO2 CO₂ f Frictional g Gravitational

in Inlet

m Mean

meas Measured

mp Manifoldsandports out Outlet

p Plate

port Port tot Total

w Wall

water Water

(DHW)productionandspaceheating(SH)hasattractedattention duetothesuperiorcombinationwiththesupercritical exothermic process [12]. Nekså [13] firstly proposed the systemdesign with twogascoolersthatseparatelyfulfilltheheatingdemandofDHW and SH, and the CO₂ from the discharge of compressor initially flows into the DHW gas cooler. Subsequently, the tri-partite gas coolerdesignwasputforwardbyStene[14]andcouldmatchthe temperatureprofilesofwaterandCO₂ andimprovetheenergyef- ficiencyofcycle.AccordingtotheflowsequenceofCO₂ fromcom- pressordischarge,thethreetube-in-tubeheatexchangerswerede- ployedforDHWreheating,SH,andDHWpreheating.Furthermore, withthetri-partitegascooler,theCO₂systemcanbeveryefficient whentheSHdemandissmallcomparedtotheDHWheatingde- mand[15,16].

In the previous publications about the combination of DHW andSH, the heat exchanger type ofgas cooler is generallytube- in-tube.Comparedtothetube-in-tubetype, thebrazedplateheat exchanger can provide higher heat transfer performance because of the sinusoidal corrugated pattern, which generates an irregu- larflowfieldcoupledwithintenseturbulenceandcontinuousdis- ruption of boundary layers [17]. Moreover, the brazed plate heat exchangerhasa compactsize, operabilityathigherpressure,and lower cost than most other compact heat exchangers [18]. Many studies have been carried out on the heat transfer and pressure dropcharacteristicsinbrazedplateheatexchangers,andthesum- maryreview isshowninTable1. Thestudiedobjects HTandPD denotetheheattransferandpressuredrop,respectively.Itcan be seenthat thesingle-phase,two-phase boiling,two-phaseconden- sation andsupercritical fluid in the brazed plateheat exchanger havebeeninvestigated.However,theinformationaboutsupercrit- icalCO₂ hasnotbeenpublishedyet.Inaddition,theexistingpub- lications on supercritical CO₂ aremostly conductedbasedon the research of flowing in channel or tube [5,19,20]. The buoyancy force is an influentialfactor that affectsthe heat transfer perfor- manceandpressuredrop,dependingonthe operatingconditions andfloworientation [5].Fortheflowingincirculartubes, theef- fect of buoyancyon the heat transfer of supercritical fluids was extensively studied by Liaoand Zhao [21], Bruch etal. [22],Bae etal.[23],Liuetal.[24],KimandKim[25],Zhangetal.[26],and Xuetal.[27].Butmostofthesepublicationsfocused ontubesin the vertical direction, and only Forooghi and Hooman[28] studied theinclinedcircular tube.Regarding the non-circulargeome- tries, onlya few studieshave beenreportedon theheat transfer ofsupercriticalfluidsinconcentricoreccentricannuli[29,30]and rectangular ducts[31].Besides, the buoyancyeffect inplate heat exchangershasbeenrarelystudiedintheliterature[32].Forooghi andHooman[33] numericallyinvestigatedtheeffectofbuoyancy onturbulentconvectionheattransferincorrugatedchannels.They found that if thewall heat flux waskept constant, the Reynolds numbermust be 3–7 timessmaller incorrugated channelscom- paredtoavertical tubesothat thebuoyancycould influencethe heattransfer.

The gas cooler is one of the key components in transcritical CO₂ systems, andthe heattransfer and pressuredrop ofthe gas coolerrequiretobefocused[34],whichcancontributetotheper- formanceimprovementofgascoolerandsystem.Thebrazedplate heat exchanger isa promising technologyfor enhancing theeﬃ- ciencyof transcriticalCO₂ heatpump. Nonetheless, regardingthe application of brazed plate heat exchanger to the tri-partite gas cooler,therelevantstudyisstillintheblankcondition.Toﬁllthe research gap,the experimentsare conducted toanalyze the heat transferandpressuredropofsupercriticalCO₂inthebrazedplate heatexchangersthatconstitutethetri-partitegascoolerofatran- scriticalCO₂ heatpumpwaterheater.Thepurposeofthispaperis toprovidea referenceforsimilarapplications andto proposethe heattransfercorrelationthatcanbeeasilyused.

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A. Zendehboudi, Z. Ye, A. Hafner et al. International Journal of Heat and Mass Transfer 178 (2021) 121641 Table 1

Literature review of the studies on brazed plate heat exchanger.

Author Year Method Fluid Flow type Studied object Correlation

Focke et al. [35] 1985 Experimental Water Single-phase HT & PD Frictional factor & colburn j-factor

Martin [36] 1996 Theoretical Water Single-phase HT & PD Frictional factor & Nusselt number

Longo [37] 2008 Experimental R134a Two-phase

condensation

HT & PD Frictional pressure drop

Khan et al. [38] 2010 Experimental Water Single-phase HT Nusselt number

Huang et al. [39] 2012 Experimental R134a, R507A, R717, R12 Two-phase boiling HT & PD Frictional factor & Nusselt number

Forooghi and Hooman [40]

2014 Experimental 98%-pure Perﬂuoro-butane Supercritical ﬂuid HT Nusselt number Huang et al. [41] 2015 Experimental Al 2O 3/water & MWCNT/water

nanoﬂuids

Single-phase HT & PD Frictional factor & Nusselt number

Longo et al. [42] 2015 Experimental R236a, R134a, R410A, R600a,

R290a, R1270, R1234yf Two-phase boiling HT Heat transfer coeﬃcient Nilpueng and

Wongwises [43]

2015 Experimental Water Single-phase HT & PD Frictional factor & Nusselt number

Sarraf et al. [44] 2015 Simulation Water Single-phase HT, PD & Flow

structure

Frictional factor & Nusselt number

Amalﬁ and Thome

[ 45 , 46 ] 2016 Experimental R245fa, R236fa Single-phase HT & PD Frictional factor & Nusselt number

Amalﬁ et al. [17] 2016 Experimental R245fa Two-phase boiling HT & PD Frictional factor Barzegarian et al. [18] 2016 Experimental TiO 2/water nanoﬂuid Single-phase HT & PD Not available

Longo et al. [47] 2016 Experimental R1234ze(E) Two-phase boiling HT & PD Frictional pressure drop Desideri et al. [48] 2017 Experimental R245fa, R1233zd Two-phase boiling HT & PD Frictional pressure drop &

heat transfer coeﬃcient Imran et al. [49] 2017 Experimental R245fa Two-phase boiling HT & PD Frictional factor & Nusselt

number

Nilpueng et al. [50] 2018 Experimental Water Single-phase HT & PD Frictional factor & Nusselt number

Pourhoseini et al. [51] 2018 Experimental Silver/water nanoﬂuid Single-phase HT Not available

Shon et al. [52] 2018 Experimental R1233zd(E) Two-phase

condensation

HT & PD Frictional factor & Nusselt number

Miyata et al. [53] 2018 Experimental R134a R1234ze(E) Supercritical ﬂuid HT Not available Longo et al. [54] 2019 Experimental R1234ze(Z), R1233zd(E) Two-phase boiling HT & PD Not available

Lee et al. [55] 2020 Experimental R1234ze(E) Supercritical ﬂuid HT & PD Frictional factor & Nusselt number

Fazeli et al. [56] 2021 Experimental Water, MWCNT-CuO hybrid nanoﬂuid

Single-phase HT & PD Heat transfer coeﬃcient

2. Experimentalsetup 2.1. Systemdescription

To investigate theheat transferperformance in the tri-partite gascooler,atranscriticalCO₂heatpumpwaterheatersystemises- tablished.TheschematicdiagramofthesystemisshowninFig.1. The system consists of the refrigerant circuit, DHW circuit, and SH watercircuit. The refrigerant circuit includes a compressor, a tri-partitegas cooler,ahigh-pressurevalve, anevaporator andan internal heat exchanger. The compressor is a reciprocating type, which hasarated displacementof9.48m³•h ⁻ ¹.The tri-partite gascoolerismadeofthreebrazedplateheatexchangersthatwill beintroducedinthelatterparagraph.Thehigh-pressurevalvecan control the gas coolerpressure, andthe evaporationtemperature canbecontrolledbythebrineinlettemperatureoftheevaporator tofurthercontrolthegascoolerinlettemperature.

The DHW and SH water circuits have water pumps and sev- eral valves.The valves2and4 cancontrol thereturnwaterflow rates atthe DHW and SH outlets andmanipulate the water inlet temperatures(T5forDHWandT8forSH). Thevalves1and2 can control the DHW flowrate, and thevalves 3and 4can reg- ulatetheSHwaterflowrate.Thesystemcanoperateunderthree modes:DHWoperation,SHoperationandDHW+SHoperation.The designing heatingcapacitiesofthe DHW,SHandDHW+SHoper- ation modesare respectively10kW,8kWand10kW,whichcan provide the DHW outlettemperature of70 °C andthe SH water outlettemperatureof35°C.TheDHWpumpisturnedonandthe

Table 2

Geometrical characteristics of the three brazed plate heat exchangers.

Parameter Value

Port-to-port length L (mm) 154.0

Width W (mm) 76.0

Chevron angle β⁽^°) ⁶⁰

Corrugation depth b (mm) 1.38 Corrugation pitch p (mm) 2.7

Thickness t (mm) 0.23

Area enlargement factor φ 1.49

Total number of plates N p GC1: 34 GC2: 50 GC3: 14 Diameter of inlet/outlet port D port(mm) 14

SH pumpis stopped under the DHW operation mode, while the statusofthepumpsisoppositeundertheSHoperationmode.Un- der theDHW+SHoperation mode, bothwater pumpsare turned on.

2.2. Testedbrazedplateheatexchangers

The three brazed plate heat exchangers of the tri-partite gas cooler,whicharerepresentedasGC1,GC2andGC3(DHWreheat- inggascooler,SHgascoolerandDHWpreheatinggascooler),are developedby ALFA LAVAL.The usedAXP14 modelheat exchange plate hasa dimension of 190 mm length by 76 mm width. The detailed characteristics of the brazed plate heat exchangers are showninFig.2andTable2.TheGCshavedifferentfunctions:for theDHWheatingdemand,theinlet tapwaterisﬁrstlypreheated by the GC3, and then the intermediate temperature waterﬂows

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Fig. 1. Schematic diagram of the studied transcritical CO 2heat pump system.

Fig. 2. The schematic of the heat exchange plate [54] .

into the GC1 and is reheated to the required high temperature;

while the GC2 is used for the SH demand which has a moder- atetemperaturelevel.Thesupercriticalandhigh-temperatureCO₂ fromthecompressorsuccessivelyflowsthroughtheGC1,GC2and GC3, andexchangesheatwithwaterinthecounter-flow configu- ration.

It is worth mentioning that the brazed plate heat exchangers usedinthisresearchhavetwotypesofinternalconﬁguration:one- pass andtwo-pass,which isshowninFig.3. Fortheone-pass,it

meansthat thewaterandCO₂ flow betweentheinletandoutlet distribution ports without changing the flow direction, and thus thewaterandCO₂respectivelyflowupwardanddownward.While forthetwo-pass,thefluidsintheheatexchangerdeflectonce,and boththewaterandCO₂ flowfirstdownwardandthenupward.In theexperiments,theGC2isalwaysone-pass,andtheGC1andGC3 are tested both with one-pass and two-pass configurations. The testsbasedonthecontrolvariablemethodareconductedwiththe one-passGC2andtwo-passGC1andGC3.Besides,theexperiments withtheone-passGC1andGC3arealsocarriedoutbutthedatais onlyusedforanalyzingthebuoyancyforceandthepressuredrop, andultimatelyfittingtheheattransfercorrelations.

2.3. Measuringdevices

Asforthemeasuringdevices,thelocationsoftheappliedtem- perature,pressureandflowratesensorsaredisplayedinFig.1.The Danfossdatarecordingsoftware(Minilog)isappliedtocollectand processtheoutputfromthesensors.Thetestfacilityunitisacom- prehensivetestrigwithmanypossibilitiesofexperimentalinvesti- gationsinvolvingtestingalargerangeofsystemconfigurationsand conditions.Atthebeginningofeachexperiment,theDanfossdata recordingsoftwareis switchedon,andthen the waterregulating valves are opened. The water circulation pumps and compressor are turned on. All the controllableprocess parameters are set to thedesiredvaluesintheMinilog.Thewaterinlettemperatureand massflowratesofCO₂ andwaterareadjusted manuallybyregu- latingthevalvestosetthe heattransferbetweenwaterandCO₂. During the experiments, the parameters logged into the Minilog arecontinually controlled byfollowing theprofiles plottedinthe

’Measurement/Graph’tag.

Oncethedesiredvaluesarereachedandaftersteady-statecon- ditionsof all parametersare achievedformore than20 min,the valuesarerecordedasasetofsteadydata.Thetime-averagedval- uesofthesteady-stateareusedforthisinvestigation.Thecharac- teristicsofthemeasuringdevicesareshowninTable3.

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Fig. 3. The (a) one-pass and (b) two-pass internal conﬁgurations of the brazed plate heat exchangers.

Fig. 4. Variation of isobaric speciﬁc heat and density of supercritical CO 2with the change of temperature under different pressures.

Table 3

Characteristics of the measuring devices.

Parameter Device Accuracy

CO 2pressure Cerabar PMP71 digital pressure transmitter ±0.25% of span Pressure difference Deltabar PMD75 differential pressure transmitter ±0.25% of span

Temperature PT 1000 ±0.15 °C

DHW ﬂow rate FLR 1000 ±3% of span

CO 2and SH water ﬂow rates Rheonik RHM 08 Coriolis ﬂow meter ±0.1% of reading

3. Datareduction

Inthebrazedheatexchangers,theheattransferrateintheCO₂ side(Q_CO2)canbeexpressedas:

QCO2=mCO2

(

ⁱCO2,in−iCO2,out

)

⁽¹⁾

Where m_CO2 isthe CO₂ massﬂow rate;i_CO2_,in andi_CO2,out are the CO₂ enthalpy at the inletand outletof the heat exchangers.

Theheattransferrateinthewaterside(Q_water)canbedeﬁnedas:

Qwater=mwaterc_p,water

(

^Twater,out−Twater,in

)

⁽²⁾

Where mwater is the watermass ﬂow rate; cp,water is the spe- ciﬁcheat ofwater;Twater,outandT_water,in arethe wateroutletand

inlet temperatures ofthe heat exchangers. According to the heat balance,Q_CO2andQ_wateraretheoreticallysupposedtobeequal.In thepresentresearch,thedeviationsbetweenthesetwoheattrans- ferratesarelessthan5%.ThepropertiesofwaterandCO₂arede- terminedbyusingREFPROP.

The totalheat transfer coeﬃcient (htot) is calculatedbased on the averaged heat transfer rate (Qave), the heat transfer area (A) andtheactualmeantemperaturedifference(^T^):

htot= Qave

A

^T ⁽³⁾

wheretheaveragedheattransferratecanbeexpressedas:

Qave= QCO2+Qwater

2 (4)

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Fig. 5. Total and CO 2heat transfer coeﬃcients versus CO 2mean temperature under different pressures.

The commonly used logarithmic meantemperature difference (LMTD)assumesthatbothfluidshaveconstantspecificheatduring the heat transfer process. As shown in Fig. 4, the physical prop- erties ofsupercriticalCO2 varysignificantly withthe temperature around its pseudo-criticalpoint.Forexample,thespecific heat of CO₂ reaches a maximum value near pseudo-critical temperature for all considered pressures. The peak value of specific heat decreases as the pressure increases and the variations of the spe- cificheatwithtemperaturebecomesrelativelyflatatthetempera- turesawayfromthepseudo-criticalpoint.Thedensityshowssharp downwardtrendwithanincreaseintemperature. Atoneparticu- lar temperature, smalltemperaturevariation causesa sharp drop inthevalues,andthecurvesbecomenearlyverticalforthelower pressures.Therefore,theLMTDmethodisnotvalidfortheexperi- mentalconditionsconductedinthisstudy.

ToobtaintheactualmeantemperaturedifferenceinEq.(3),the UAiscalculatedbasedonitsdeﬁnition:

UA= Atot

0

UdA= Qtot

0

dQ

^T ⁽⁵⁾

ToobtainthenumericallyintegratedresultofEq.(5),theheat transferprocessisequallydividedintoNsegmentswiththesame heattransferrate(

δ

Q).Ineachsegment,thetemperaturedifference isobtainedbasedontheenergybalance.Therefore,theUAcanbe numericallyintegratedas:

UA= N

i=1

δ

^Q

^Ti

(6)

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Fig. 6. Total and CO 2heat transfer coeﬃcients versus CO 2mean temperature under different CO 2mass ﬂow rates.

UsingtheUA,theactualmeantemperaturedifference(^T)^can bedetermined:

^T=Qtot

UA (7)

whereQtotisequaltoQaveinthisstudy.

The heattransfer area(A)ofthebrazed plateheatexchangers canbecalculatedas[52]:

A=

φ

^W^L^N^p ⁽⁸⁾

where

φ

îs^theâreaenlargementfactorthatconsiderstheincrease ofarea duetothecorrugation ontheplates;W,LandN_pare the width,port-to-portlengthandnumberoftheheatexchangeplates, respectively.Theareaenlargementfactorisdefinedas:

φ

^≈

(

¹⁺

1+X²+4

1+X²/2

)

^/⁶ ⁽⁹⁾

where X=

π

^b

p (10)

Similarly, due to the change of speciﬁc heat, the CO₂ tem- peraturewouldnonlinearlyvary duringthe heattransfer process.

Therefore,toobtaintheCO₂ temperatureatwhichthethermody- namicpropertiesaredeﬁned, thecommonlyusedconceptofbulk temperature that is the average of inlet andoutlet temperatures [22,57] cannotfulﬁll therequirement.Instead,theconcept ofCO₂ meantemperature(Tm)isadopted:

Tm= N

i=1

T_CO₂_,i

N (11)

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Fig. 7. Total and CO 2heat transfer coeﬃcients versus CO 2mean temperature under different water inlet temperatures.

ThetotalheattransfercoeﬃcientcomprisestheCO₂ andwater side heat transfer coeﬃcientsand the wall thermalresistance. It canbealsoexpressedas:

1 htot = 1

hCO2+ 1 hwater+ t

kw

(12) whereh_CO2andhwater aretheheattransfercoeﬃcientsintheCO₂ andwatersides;t isthethicknessoftheplate;k_w isthethermal conductivity ofthe wall. hwater is calculatedby applyingthe correlation ofHuang etal.[41] becausethe plategeometryandthe rangeofReynoldsnumberaresimilartothoseofthestudiedheat exchangers.

Nuwater=0.2302Re⁰_water^.⁷⁴⁵Pr_water⁰^.⁴ (13)

hwater= Nuwaterkwater

D (14)

Thehydraulicdiameter(D)canbedeﬁnedas:

D=2b

φ

⁽¹⁵⁾

wherebisthecorrugationdepthoftheplate.TheReynoldsnum- ber(Re)canbecalculatedas:

Re=

ρ

^uD

μ

⁽¹⁶⁾

whereuistheflowvelocityoffluidandisdefinedas:

u= V bWNch

(17)

where

ρ

^and

μ

âre^the^densityând^dynamic^viscosityôf^the^fluid;

V isthe volumetricﬂow rate;N_ch isthe numberof thechannels forﬂuid.

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Fig. 8. Total and CO 2heat transfer coeﬃcients and CO 2mean temperature versus water mass ﬂow rates.

The measured pressure drop (^p^meas⁾ ôf ^the ^heat êxchang- ersconsistsofthefrictionalpressuredrop(^pf),thegravitational pressure drop (^pg) andthe pressure dropof themanifolds and ports(^p^mp⁾^[⁴⁸^,⁵⁰^].^Thus,^the^frictional^pressure^drop^can^be^de- finedas:

^pf=

^p^meas−

^p^g−

^p^mp ⁽¹⁸⁾

Thegravitationalpressuredropisdeterminedby:

^p^g⁼^g

ρ

^m^L ⁽¹⁹⁾

where

ρ

^mîs^the^densityât^the^CO2meantemperature.Thepres- suredropofthemanifoldsandportsisdefinedas:

^pmp=1.5G²_port

2

ρ

^m ⁽²⁰⁾

whereGportistheCO₂massﬂuxatthecrosssectionoftheport.

BasedonthemethodproposedbyMoffat[58],theuncertainty analysisisconducted.Theuncertaintiesofhtot,hwater,h_CO2and^pf

are8.16%,4.59%,11.76%and2.73%,respectively.

4. Resultsanddiscussion 4.1. Heattransfer

4.1.1. EffectofCO₂inletpressure

Fig. 5 shows the total and CO₂ side heat transfer coefficients (htot and h_CO2) versus the CO₂ mean temperature under the in- letpressureof9.4MPaand10MPa.Theresultsare obtainedunder theDHW operation mode atCO2 inlettemperature of97°C, CO₂ massflowrateof0.0358kg•s⁻¹,waterinlettemperatureof 13.1 °C and DHWmass flow rate of0.030 - 0.043kg•s ⁻ ¹. The dashedrectanglesindicatethedatagroupsforeachgascoolerthat thedatapointsbelongto.ThedatapointswithdifferentCO₂mean temperaturesare achievedbyadjusting theDHW massflow rate, andthelarger theDHW massflow ratethelower theCO₂ mean temperature.

The averaged htot, hwater and h_CO2 from all data are 1380.2, 6094.1and2035.0 W•(m²•K)⁻¹,which suggeststhat thethermal resistanceattheCO₂ sidebasicallydominatesthetotalheattrans-

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Fig. 9. Heat transfer rates and actual mean temperature differences versus water mass ﬂow rate corresponding to the results of Fig. 8 .

fer. AsshowninFig.5(a),giventhedifferentheatingfunctionsof GC1 andGC3, the corresponding CO₂ mean temperatures are di- vided into two groups. The reheating GC1has higher CO₂ mean temperaturesandlowheattransfercoefficientsduetothelowspe- cific heat in this gas-like supercritical region. Whereas, the pre- heatingGC3showsan operationnearthepseudo-criticaltemperature (42.04°Cfor9.4MPa and45 °C for10MPa). Thedramatic increaseofspecificheatinthevicinityofthepseudo-criticalpoint leads to the higher heat transfer coefficients of GC3. Moreover, withtheincrease ofCO₂ meantemperature,the heattransferco- efficientsincreaseandthendecrease,andthuspeakvaluesappear.

For GC3, atthe pressure of 9.4MPa, thepeak valuesof htot and h_CO2 arehigherthanthoseatthepressureof10MPa.

Fig. 5(b) displays the results under the DHW+SH operation mode at CO₂ inlet temperature of 80 °C, CO₂ mass flow rate of 0.040kg•s ⁻ ¹,DHW inlettemperatureof12.8°C,SH waterinlet temperatureof30°C,SHwatermassflowrateof0.1917kg•s ⁻ ¹ and DHW mass flow rateof 0.0167 - 0.0417kg•s ⁻ ¹. The heat

transfercoefficientsintheGC1andGC3show anincreasingtrend with the decrease of CO₂ mean temperature. The reason is that thedecreaseofCO₂meantemperatureisattributedtotheincrease ofDHWmassflow rate,andtheassociatedincreasing waterflow velocity enhances the water side heat transfer coefficient, which improvesthe total heattransfer coefficient. Besides,the variation ofthermodynamicpropertiesintheliquid-likesupercriticalregion isalso smallandaccordinglyhasan unimportant impact onGC3 under DHW+SH operation. As for GC2, the CO₂ mean temperatures are closeto the pseudo-criticaltemperature(Tpc= 34.63 °C forP=8MPaandT_pc=40°CforP=9MPa),andthepressuresig- nificantlyinfluencesthethermodynamicpropertiesincludingspe- cificheatandthermalconductivity.Forbothhtot andh_CO2 inGC2, the maximumvalues at8 MPa are greater than those at9 MPa.

Inaddition,withtheincrease ofpressure,the temperaturecorre- spondingtothemaximalheattransfercoeﬃcientinGC2increases becauseofrisingpseudo-criticaltemperature.

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A. Zendehboudi, Z. Ye, A. Hafner et al. International Journal of Heat and Mass Transfer 178 (2021) 121641 Table 4

The effects of parameters on the averaged Reynolds number and heat transfer coeﬃcients.

Variable Item Condition DHW operation Condition DHW + SH operation

GC1 GC3 GC1 GC2 GC3

CO 2pressure ( P in) Re m 9.4 MPa 3672.9 4979.8 8 MPa 4389.2 941.1 3855.6

10 MPa 3474.8 4350.9 9 MPa 4007.7 678.2 3320.8

Variation −5.4% −12.6% Variation −8.7% −27.9% −13.9%

h tot,ave 9.4 MPa 941.4 2058.7 8 MPa 859.6 1755.4 1594.5

10 MPa 977.8 1870.5 9 MPa 909.1 1187.4 1416.0

Variation 3.9% −9.1% Variation 5.8% −32.4% −11.2%

h CO2,ave 9.4 MPa 1163.5 2860.4 8 MPa 1097.5 2429.2 2173.8

10 MPa 1220.5 2521.1 9 MPa 1187.1 1465.9 1876.2

Variation 4.9% −11.9% Variation 8.2% −39.7% −13.7%

CO 2mass ﬂow rate ( m c) Re m 0.036 kg ^•s ⁻¹ 3474.8 4350.9 0.028 kg ^•s ⁻¹ 2758.8 420.4 2277.3 0.040 kg •s ⁻¹ 3977.2 5343.6 0.040 kg •s ⁻¹ 4007.7 678.2 3320.8 Variation 14.5% 22.8% Variation 45.3% 61.3% 45.8%

h tot,ave 0.036 kg •s ⁻¹ 977.8 1870.5 0.028 kg •s ⁻¹ 827.9 721.5 1132.1

0.040 kg •s ⁻¹ 1003.5 2154.9 0.040 kg •s ⁻¹ 909.1 1187.4 1416.0 Variation 2.6% 15.2% Variation 9.8% 64.6% 25.1%

h CO2,ave 0.036 kg •s ⁻¹ 1220.5 2521.1 0.028 kg •s ⁻¹ 1072.6 818.1 1429.0

0.040 kg ^•s ⁻¹ 1245.7 2999.2 0.040 kg ^•s ⁻¹ 1187.1 1465.9 1876.2 Variation 2.1% 19.0% Variation 10.7% 79.2% 31.3%

DHW inlet temperature ( T5 ) Re m 13.1 °C 3672.9 4979.8 12.8 °C 4007.7 678.2 3320.8 16 °C 3615.8 5553.3 17.8 °C 4032.2 711.4 3462.5 Variation −1.6% 11.5% Variation 0.6% 4.9% 4.3%

h tot,ave 13.1 °C 941.4 2058.7 12.8 °C 909.1 1187.4 1416.0

16 °C 886.5 2160.8 17.8 °C 812.9 1227.4 1327.7

Variation −5.8% 5.0% Variation −10.6% 3.4% −6.2%

h CO2,ave 13.1 °C 1163.5 2860.4 12.8 °C 1187.1 1465.9 1876.2

16 °C 1077.4 3022.7 17.8 °C 1051.3 1523.1 1759.2 Variation −7.4% 5.7% Variation −11.4% 3.9% −6.2%

Theimpactofpressureontheheattransfercoefficientisdueto thevariationsofCO₂thermodynamicpropertiescausedbychang- ingpressure.Thevariationsbecomemoredramaticwhenthepres- sureisclosertothecriticalpressure.AsseenfromFig.5,thevari- ationtrendoftheheattransfercoefficientissimilartothatofspe- cific heat under different operating pressures. The trend demon- stratesthat theheattransfercoefficientsare higherin theliquid- like region forlower pressures, while the values for lower pressure are lower in the gas-like region. The peak value of specific heat increases significantly near the critical point by decreasing operatingpressure;therefore,theheattransfercoefficienttendsto liftsharply inthisregionandthe heattransferis thebestat the pseudo-criticalpoint.

Toshowtheinfluenceofparametersquantitively,theresultsare summarizedinTable4.Re_m,h_tot,aveandh_CO2,avearetheaveragesof theCO₂ Reynoldsnumberandtheheattransfercoefficientsbased on thedatapointsinFig.5,Fig.6andFig.7.Thecomparisons ig- noretheinfluenceofCO₂meantemperatureandonlyfocusonthe numericalvalues.Withtheresultatthelowervalueofvariablesas thereferencevalue,thevariationsaredetermined.FromTable4,it can be observed thatwith theincrease ofpressure, theaveraged heat transfer coefficientsdecrease exceptinthe GC1, andthere- ductions reach up to 32.4%and 39.7% forhtot,ave andh_CO2,ave, respectively.

4.1.2. EffectofCO₂massﬂowrate

Fig. 6(a) showsthe results under DHW operation mode with differentCO₂massflowratesatCO₂inletpressureof10MPa,CO₂ inlettemperatureof97°C,DHWinlettemperatureof13.1°C,and DHWmassflowrateof0.030-0.043kg•s⁻¹.Itcanbeobserved thattheincreaseofCO₂massflowrateleadstotheincreaseofhtot

andh_CO2.ThehigherCO₂massﬂowrategeneratestheincreaseof the Reynolds number and the diffusion rate, andthen enhances theheattransfercoeﬃcients.

Fig.6(b)showstheresultsunderDHW+SHoperationmode at CO₂inletpressureof9MPa,CO₂ inlettemperatureof80°C,DHW inlettemperatureof12.8°C,SHwaterinlettemperatureof30°C,

and SH water mass flow rate of 0.1917 kg•s ⁻ ¹. Increasing the CO₂ massflowratesignificantlyimprovestheheattransfercoeffi- cients.ItcanbefoundfromTable4thattheinfluenceofCO₂mass flowrateisthelargest.Inall conditions,the averagedheattrans- fer coefficients are enhanced with the increase of the CO₂ mass flowrate.UndertheDHWandDHW+SHoperationmodes,theen- hancement ofheat transfer coefficientsin the GC1 is the lowest whilethe improvementis muchmore significantin theGC2and GC3.

4.1.3. Effectofwaterinlettemperature

Fig.7(a) depictstheheat transfercoefficientsunder DHWop- eration mode withdifferent DHW inlet temperatureatCO₂ inlet pressureof9.4MPa,CO₂inlettemperatureof97°C,andCO₂mass flow rate of 0.0358 kg•s ⁻ ¹. As shown, no significant influence ofthewaterinlettemperaturecanbefoundintheresultsofGC1.

However,becausethewaterinletisdirectlylinkedtoGC3,thein- ﬂuence ismoreobvious andtheheat transfercoeﬃcientsare in- creasedbytheincreaseofDHWinlettemperature.

Fig.7(b)showstheresultsundertheDHW+SHoperationmode at CO₂ inlet pressure of 9 MPa, CO₂ inlet temperatureof 80 °C, CO₂ massflowrateof0.040kg•s⁻ ¹,SHwaterinlettemperature of30 °C, andSH water massflow rate of0.1917 kg•s ⁻ ¹. Simi- larly,theeffectofwaterinlettemperatureislargerwhentheheat exchangerisclosetothewaterinlet.Theincreaseoftemperature from12.8°Cto17.8°Cresultsinanignorableimpactontheheat transfercoefficientsinthehightemperaturestate.Comparedwith theCO₂ pressureandmassflowrate, thewaterinlettemperature hasarelativelysmalleffect.FromTable4,thevariationscausedby increaseofDHWwaterinlettemperaturearealllowerthan12%.

4.1.4. Effectofwatermassﬂowrate

Fig.8showstheeffectsofDHWandSHwatermassflowrates on theheat transfer coefficients, andthevariations ofCO₂ mean temperatures with the change of water mass flow rates are de- picted aswell. Forthe DHWoperation inFig. 8(a),the CO₂ inlet pressure,CO₂ inlettemperature,CO₂ massflowrateandDHWin-

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Fig. 10. The buoyancy forces in the three GCs.

let temperature are 9.4 MPa, 97 °C, 0.0358 kg•s ⁻ ¹ and16 °C, respectively.AstheDHWmassflowrateincreases,theheattrans- fer coefficientsofGC1andGC3increase,andtheCO₂ meantemperature decreases. The CO₂ mean temperature in GC3 is closer to the pseudo-critical point, which leads to larger heat transfer coefficients. Fig. 8(b) presents the situation under the SH operation mode at CO₂ inlet pressure of 9 MPa, CO₂ inlet tempera- tureof76 °CandCO₂ massflowrateof0.040kg•s ⁻ ¹.TheCO₂ meantemperaturesarenearlyconstantwiththechangeofSHwa- ter mass flow rate. It can be seen that when the SH waterinlet temperatureis25°C,theheattransfercoefficientsarehigherthan thoseat35°C,whichresultsfromthehigherspecific heatcaused by thelowerCO₂ meantemperature. DifferentfromtheDHWop- eration mode,the increaseofSH watermassflow rateunderthe SHoperationmodeconducestothedecreasingtrendofheattrans- fercoefficients.Thisdiscrepancyisattributedtothedifferentvari- ationsof heattransfer rateandtemperature differenceunderthe DHWandSHoperationmodes.

Fig.9displaystheresultsrelatedtotheconditionsinFig.8.As canbeseeninFig.9(a),theheattransferratesofGC1andGC3rise withtheincrease ofDHWmassflow rate.However,thetempera- turedifferencesshowdifferenttrends.The increaseofDHWmass flowrateslightlyaffects^T^for^GC1^but^resultsⁱⁿ^the^decreaseôf ^T^for^GC3.Âccording^toÊq.⁽³⁾^,^the^total^heat^transfer^coefficients ofGC1andGC3areenhanced.

Based on Eq. (3), the decreasing trend of heat transfer coefficients under SH operation mode can be explained as well. In Fig. 9(b), with the increase of SH water mass flow rate, the actual mean temperature difference presents the increasing trend, buttheincrease of^Tât^the^SH^waterînlettemperatureof35°C is relatively small. In addition, the change of heat transfer rates ismarginal.Thus,thereductionofheattransfercoefficientsisthe consequence of the increase of actual mean temperature difference.

4.1.5. Effectofbuoyancyforce

According to the literature, the heat transfer performance of thesupercriticalCO₂ isalsosignificantlyaffectedbythebuoyance force in some conditions [59]. Based on the effects of buoyancy force on theflow andheat transfer, theflow ofsupercritical CO2

canbe dividedintoforcedandmixedconvections[60].Thebuoy- ancyforce hasanimportantinﬂuenceon theheattransferinthe

mixed convection, while in the forced convection, the inﬂuence is negligible. The large densitygradient caused by a large radial temperaturegradientisanessentialconditionwherethebuoyancy forcecanaffecttheheattransfer.

Forthe in-tubeﬂowing, whenthe followingequation issatis- ﬁed,thebuoyancyforce cannotbe ignoredintheheattransferof supercriticalCO₂ [61]:

Gr/Re²^.⁷>10⁻⁵ (21)

WhereGristheGrashofnumberandcanbedeﬁnedinthispa- peras:

Gr=

( ρ

w−

ρ

^m

) ρ

^m^gD³

μ

²m

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Wheregistheaccelerationofgravityand

ρ

¯^w ^is^the^density^at theaveragedwalltemperature[62]:

ρ

¯^w⁼ Tm

Tw

ρ

^dT

Tm−Tw

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However,becauseofthecomplexgeometryinthebrazedplate heat exchanger, this criterion cannot be applied. Moreover, the work considering the buoyancy effect in plateheat exchanger is rare[32],andwithourbestknowledge,thereisnopublicationthat suggeststhecriterionforbuoyancyeffectinplateheatexchanger.

Fig.10showsthebuoyancyforcesinthethreeGCs.Thelargest buoyancyforceexistsintheGC2,whichhasthemaximumnumber oftheheat exchangeplates andaccordinglythe largestflowarea andthe lowest CO₂ flow velocity.The GC1has moreplates than GC3andthustheCO₂ flowvelocitycould belowerinGC1,which issupposed toresultinthehigherbuoyancyforce effect.Butthe buoyancy forcesin GC1 and GC3are at a similar level. It is be- causethehightemperatureandlowdensityinGC1counteractthe influenceofplatenumberontheflowvelocity.

To further investigate the buoyancy force, the effects of CO₂ pressure andCO₂ mass ﬂow are shownin Fig.11. The resultsin Fig.11are obtainedunder theconditions ofFig.5 andFig.6. As Fig.11(a)shows, theinﬂuence ofpressureon thebuoyancyforce isdifferentaccordingtothetemperature. Obviously,thebuoyancy force declineswiththe lower pressurewhen theCO₂ meantemperature is high in the GC1. On the contrary, when the temperature is relatively low in the GC3, the buoyancy force is slightly improvedbythedecreaseofpressure.IntheGC2,bothtwotypes

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Fig. 11. The effects of CO 2inlet pressure and CO 2mass ﬂow rate on the buoyancy force.

ofeffectsofpressureoccur.Incomparison,theeffectofCO₂mass flowrateisconsistentatalltemperatures.ThelowertheCO₂mass flow rate the higher the buoyancy force because of the smaller flowvelocityandweakerturbulence.

To investigatethe effect ofbuoyancy force on the heat transfer,theNusseltnumberversusGr/Re^2.7 isshowninFig.12.There- sultsinFig.12arealsoobtainedundertheconditionsofFig.5and Fig. 6. Except the GC3 at 8 MPa under the DHW+SH operation mode, the Nusselt number generally shows an increasing trend withtheincreaseofbuoyancyforce.Therefore,thebuoyancyforce has an inﬂuence onthe heat transfer ofsupercritical CO₂ in this research, which wouldbe considered inthefollowing correlation development.

4.2. Heattransfercorrelationdevelopment

Inthepreviouspublications,thein-tubeheattransferofsuper- criticalCO₂ during thecooling andheatingprocess has beenex- tensively studied [5]. However, the research on the supercritical heat transfer of CO₂ inthe brazed plateheat exchanger has not beenreportedyet.Theheattransfercoefficientofsupercriticalflu- idsisdifficultto bepredictedaccuratelyduetothe drasticvaria- tionof thermodynamicsproperties[63].Moreover, thevalidity of publishedcorrelationsislimitedbytheexperimentaldata,andthe availabilityisreliableonlywithinacertainrange.

Fig.13showsthecomparisonofexperimentalNusseltnumbers and the calculated results based on the correlations from Bruch et al. [22], Liu et al. [57], Forooghi and Hooman [40], Lee et al.

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Fig. 12. The effect of buoyancy force on the Nusselt number.

[55] andKhanetal.[38].Table5showsthefivecorrelationsused forcomparisonandtheirapplicationconditions.Amongthesefive correlations, two are for supercritical CO₂ in-tube flow, two are forsupercriticalfluidsinplateheat exchanger,andone isforsin- gle phase fluid in plate heat exchanger. The application ranges of Reynoldsnumber (ormass flux)of thesecorrelationspartially overlapthevaluesinourresearch.

It can be discovered that thepredictions ofBruch et al.’sand Liu etal.’scorrelations arebasically lower thanthe experimental values,andtherearemassivedatapointswheretherelativeerror islowerthan−60%oreven−90%.Itindicatesthatthecorrelations established basedontheresearchofin-tubeﬂoware notsuitable forthesituationinthebrazed plateheat exchanger.Thecomplex geometry ofplateenhancesthe heat transfer performance. Many prediction points based on the correlations from Lee et al. and

Khanetal.haveanerrorlargerthan90%.Themeanabsoluterela- tiveerrorsofthecorrelationsfromBruchetal.,Liuetal.,Forooghi and Hooman, Lee et al. and Khan et al. are 71.6%, 67.9%, 41.1%, 495.3%and138.1%,respectively.ThecorrelationfromForooghiand Hoomanshowsthebestaccuracybutisstillnotsatisfactory.There- fore,thespecializedcorrelationsarenecessarytodescribetheheat transferofsupercriticalCO₂ inthebrazedplateheatexchanger.

Consideringtheinﬂuenceofthermodynamicspropertiesatthe CO₂ meantemperatureandthewalltemperatureandtheeffectof buoyance force, the correlationsare proposed basedon the least squaremethodaccordingtothebelowexpression[62]:

Nu=a1Re^a_m²Pr^a_m³

ρ

^w

ρ

m

a4

cp

c_p,m

a5

Gr Re²_m^.⁷

a6

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Heat transfer and pressure drop of supercritical CO2 in brazed plate heat exchangers of the tri-partite gas cooler

International Journal of Heat and Mass Transfer