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Implementation of ‘chaotic’ advection for viscous fluids in heat exchanger/reactors
Zoé Anxionnaz-Minvielle, Patrice Tochon, Raphael Couturier, Clément Magallon, Félicie Theron, Michel Cabassud, Christophe Gourdon
To cite this version:
Zoé Anxionnaz-Minvielle, Patrice Tochon, Raphael Couturier, Clément Magallon, Félicie Theron, et al.. Implementation of ‘chaotic’ advection for viscous fluids in heat exchanger/reactors.
Chemical Engineering and Processing: Process Intensification, Elsevier, 2016, 113, pp.118-127.
�10.1016/j.cep.2016.07.010�. �hal-01506812�
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To link to this article :
DOI: 10.1016/j.cep.2016.07.010 URL : http://doi.org/10.1016/j.cep.2016.07.010
To cite this version : Anxionnaz-Minvielle, Zoé and Tochon, Patrice
and Couturier, Raphael and Magallon, Clément and Théron, Felicie and Cabassud, Michel and Gourdon, Christophe Implementation of
‘chaotic’ advection for viscous fluids in heat exchanger/reactors.
(2016) Chemical Engineering and Processing: Process Intensification, 113. pp. 118-127. ISSN 0255-2701
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Implementation of ‘ chaotic ’ advection for viscous fl uids in heat exchanger/reactors
Z. Anxionnaz-Minviellea,*,P.Tochona,R.Couturiera,C.Magallona,F. Théronb, M. Cabassudb,C.Gourdonb
aCEA,LITEN,DTBH,17ruedesMartyrs38054Grenoble,France
bUniversityofToulouse,LaboratoiredeGénieChimiqueUMR5503CNRS/INPT/UPS,31432Toulouse,France
Keywords:
Heatexchanger/reactor Chaoticadvection Viscousfluids Continuousmode Processintensification Split-And-Recombinepattern
ABSTRACT
Whenviscousfluidsareinvolved,laminarhydraulicconditionsandheatandmasstransferintensification are conflicting phenomena. A channel geometry based on Split-And-Recombine (SAR) patterns is experimentally investigated. The principle implements the Baker’s transformation and ‘chaotic’ structuresaregeneratedtopromoteheatandmasstransfer.Thisworkassessestheenergyefficiency ofdifferentheatexchanger/reactorsintegratingtheseSARpatterns.
Theheattransfercapacityisassessedandcomparedwiththeenergyconsumptionofeachmock-up.It issensitivetothecoolingmodeandtothenumberofSARpatternsperlengthunitaswell.
Thecontinuousoxidationof sodium thiosulfatewithhydrogenperoxide hasbeenimplemented.
Conversionsupto99%arereachedaccordingtotheutilityfluidtemperatureandtheresidencetime.
Finally,thewholeperformancesoftheSARgeometriesarecomparedtoaplate-typeheatexchanger/
reactorwithacorrugatedpattern.Themoreviscousthefluid,themoretheenergyefficiencyoftheSAR designincreasescomparedtothecorrugateddesignbecauseofthebalancebetweenadvectionand diffusionmechanisms.TheinterestintermsofenergyefficiencyinworkingwithSARheatexchanger/
reactorappearsfromReynoldsnumbersbelow50.
1.Introduction
Among the technologies promoting process intensification [1,2],heat-exchanger/reactor(HEXreactor)isapromisingone[3].
This device combines the benefits of a large heat transfer performanceandaplug-flowregimeallowinganintensiveradial mixing,asaresultofthespecificdesignofprocesschannels[4–9].
These geometries generate instabilities even in laminar flow regime(50<Re<2000).Howevermostofthestudieshavebeen carriedoutwithinviscidfluidsandtheintensificationofperform- anceswhenthefluidviscosityincreasescomesattheexpenseof pumpingcosts.Processesoffoodindustry,intermediatechemistry likesiliconesorpolymers,... involveviscousfluidsandastudy, carriedoutintheframeoftheindustrialnetworkEUROPIC[10], pointedoutthatheatandmasstransfersinviscousmediaareone ofthemainindustrialconcern.Intheverylaminarflowregime,
precludingturbulenceasamixingmechanism,mixingbydiffusion canbeefficientprovidedthatthecontactareaissufficient.Thiscan beachievedwithsystemsbasedonmulti-laminationmechanism and baker’s transformation [11,12]. These have been proposed especiallyinthecontextofmicrofluidics[13–16].Inmicrofluidic devices,thetypicalchanneldimensionsandflowratesaresolow that all flow is laminar (Re!0.1) and turbulence cannot be achieved.Diffusionisalsotooslowtobeeffectiverequiringtoo longchannellengths.Theimplementationofviscousfluidstreams in HEX reactor and the typical millimetre dimensions of the channel cross-section lead to similarconclusions. However,by applyingaseriesof Baker’stransformationsindedicatedthree- dimensionalmixingelements,namedSplit-And-Recombine(SAR) patterns,therequiredchannellengthcanbereducedexponentially with thenumber of mixing patterns.The involved separation/
stackingmechanismslieontheBaker’stransformationprinciple.
Two fluid streams are combined, split out-of-plane, rotated in oppositedirectionsandrecombinedasillustratedwithFig.1.Then, a 2-strips domainbecomes 2nalternatingstrips afternmixing patterns.
*Correspondingauthor.
E-mailaddress:[email protected](Z. Anxionnaz-Minvielle).
http://dx.doi.org/10.1016/j.cep.2016.07.010
AveryefficientmixingisachievedbydiffusionandSchönfeld etal.[13]evenproposedasanoutlooktousesimilarSARstructures toimproveheattransferinminiheatexchangers.Theinfluenceof chaotic advection on heat transfer has been numerically and experimentallyinvestigated[17–21].Resultsina singlechannel arepromising.
TheinterestofHEXreactorsistheclosecontrolofthereaction temperature.Theveryshortcharacteristiclengthsbetweenboth theprocessandtheutilitystreamsareofparamountimportance.
Withthree-dimensionalSARstructures,characteristicdimensions are quite different from ‘classical’ two-dimensional patterns (plate-typeHEXreactor)andheattransfermightbeaffected.
ThustoinvestigatetherelevanceofimplementingSARpatterns ina HEXreactordevice,performanceindicatorsbesides mixing havetobeassessed.Theyaccountfor heattransferand energy consumption.Theobjectiveistopromoteheatandmasstransfer eveninviscousconditions.
For that purpose, we experimentally characterized three stainlesssteelmock-ups"assembled bydiffusionbonding. Two differentflowpatternsaccordingtothenumberofSARstructures areconsidered.Theirdesignscomefrom[14,15].
For oneofthesegeometries,two coolingsystemshavebeen investigated, external cooling Plates "isothermal wall- and integrated cooling tubes. For each mock-up, the 3mm square cross-sectionchannelsarearound3.5mlong.Then,acasestudyin reactiveconditionsisimplementedwiththecontinuousoxidation ofsodiumthiosulfatewithhydrogenperoxide.Finally,thewhole performancesoftheSARgeometrieshavebeencomparedwiththe onesofacorrugatedpatternplate-typeheatexchanger/reactor[6].
2.Heat-exchangerreactordesignandintegration
2.1.SARpatterns
ThreeSARpatterns,basedonthedesignsof[14,15]havebeen considered. Fig. 2 depicts four patterns of each considered geometry.
The square cross-sections of the channels are 3#3mm2 correspondingtoanequivalenthydraulicdiameterof3mm.The Reynoldsnumberassessmentisbasedonthishydraulicdiameter andonthefluidvelocityattheinletoftheprocesschannel,i.e.
upstreamthefirstfluidstreamseparation.Thisreferenceistaken since the inlet flowrate is a major process parameter for the industrialapplication.
TwochannellengthscanbedefinedintheSARgeometries.We considerthedeveloped length,Ldevand thetotallength,L. The former corresponds tothe distance travelled by a single fluid particle between the inlet and the outlet of the HEX reactor.
Whereas the latter corresponds to the sum of every stream branches,i.e.thetotalfluidvolumedividedbythecrosssection.
PatternsSAR-1andSAR-2areverysimilar.Thedifferencestems fromthepatterndimensiononthez-axiswhen fluidstreamis split.IncomparisonwithSAR-2,theSAR-1patternisexpandedto allowtheinsertionofcross-flowcoolingtubes(seeSection2.2).
SAR-3patternislesscomplexthanSAR-1andSAR-2patterns.It makeseasieritsmanufacturing.It includes3bendsperpattern versus6bendsperpatterninbothSAR-1andSAR-2geometries.
2.2.HEXreactorintegrationandmanufacturing
ThethreeSARgeometriesareintegratedinrespectivelythree wholeHEXreactorprototypes.TomanufacturetheHEXreactors, theSARchannelisfirstdividedinseverallayerswhicharethen transposedincorrespondingplatesasdepictedinFig.3.
The HEX reactors are made of one process plate including severalrowsofSARpatternsinseriesandsensorconnectionsat eachendoftherows(seeFig.4b).
ThestratificationstepdepictedinFig.3 isduplicatedonthe platetoobtaintherequirednumberofrows(seeFig.4a).Laser machiningisusedandplatesarethenstackedintoacontainer.The assembling process is based on diffusion bonding (High Nomenclature
A [m2]heatexchangearea
Cp [Jkg"1K"1]thermalcapacity
dh [m]hydraulicdiameter
Fp [kgh"1]processflowrate
Fu [kgh"1]utilityflowrate
L [m]totallengthoftheprocesschannel Ldev [m]developedlengthoftheprocesschannel
n_i [mols"1]initialmolarflowrate
Ploss [W]thermalloss Pth [W]thermalpower Preaction [W]heatofreaction Pe [-]pecletnumber(=RePr) Pr [-]prandtlnumber Re [-]reynoldsnumber T [K]temperature
u [ms"1]fluidvelocity
U [Wm"2K"1]globalheattransfercoefficient
V [m3]volumeoffluid Greekletters
DHr [kJmol"1]enthalpyofreaction
DP [Pa]pressuredrop
e [Wm"3]energydissipationrate
L [-]darcycoefficient
l [Wm"1K"1]thermalconductivity
m [Pas]viscosity
r [kgm"3]density
x [%]conversionrate
Fig.1.Illustrationofa3Dmixingpattern.Top:Cross-sectionillustratingtheBaker’s transformationaftertwoiterations.Bottom:sketchofmixingactionsaftertwo elements[11].
temperatureIsostaticPressing–HIP–assembling,[22]).Thefinal prototypeismadeofstainlesssteel.
Twocoolingconfigurationshavebeenconsidered.Thefirstone assumesisothermalwalltemperature. Theprocessplate(SAR-2 andSAR-3)issandwichedbetweentwocoolingplates.Thesecond cooling configuration involvescross-flow coolingtubes directly integratedthroughtheSARpatterns(SAR-1).Fig.5illustratesSAR- 1andSAR-3integration.
Thefinalprototypesarearound185mmlongand90mmwidth.
ThegeometricalcharacteristicsarelistedinTable1.
2.3.Corrugatedpattern
TheperformancesofthepreviousSARpatternsarecompared withaclassical2Dcorrugatedonewhichdesignisbasedontheone studiedby[5,6].Themanufacturingprocessofthe2DHEXreactor
isthesameandthecoolingsystemisbasedonisothermalwalls (withcoolingplates).Thesquarecross-sectionofthecorrugated channelis2#4mm2andthehydraulicdiameteris2.67mm.The channelis2.2mlongincluding103bends(90$)perlengthunit.The corrugatedchannelisshowninFig.6.
3.Thermalandhydraulicinvestigations
ToassesstheHEXreactorsperformances,thestudiedReynolds number rangesfrom0.1 to10,000.Waterand twosolutions of glycerolintowater(70%w.and90%w.ofglycerol)areused.
3.1.Pressuredrop
3.1.1.Experimentalset-upandprocedure
Pressuredropsaremeasuredwithadifferentialpressuresensor betweentheinletandtheoutletoftheHEXreactors.Tocovera widerangeof Reynoldsnumber,distilled water,ethylene glycol andtwosolutionsofglycerolareused(70%w.and90%w.).The tests are implemented in isothermalconditions and the mean physico-chemicalpropertiesofthefluidsarelistedinTable2.Since thetemperatureismeasuredduringthepressuredropmeasure- ments,boththeviscosityandthedensityareassessedattheexact testtemperature.
FrompressuredropmeasurementstheDarcycoefficient,L,is assessedaccordingtothefollowingexpression:
L¼ 2&DP&dh
r&Ldev&u2 ð1Þ
AndtheReynoldsnumberisdefinedas:
Re ¼r&u&dh
m ð2Þ
whereLdevisthedevelopedlengthoftheprocesschannel,anduthe processfluidvelocity.TheSARgeometriesaredesignedsuchasthe pressuredropsineachfluidbranchareequal.Moreover,sincea fluid particle flows successively through the inlet zone (flow velocity, u), a split branch (flow velocity, u/2), a stream Fig.2.SARpatterns.ThereddottedlinesdelimitoneSARpattern.(Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderisreferredtothewebversionof thisarticle.)
Fig.3. StratificationoftheSAR-2patternforthemanufacturingprocess.
Fig.4.ManufacturingstepsforSAR-2prototype–(a)Plateslaser-machining,(b)Stacking.
recombinationzone(flowvelocity,u),asplitbranch(flowvelocity, u/2),... Wedecidedtoconsiderthedevelopedlengthtoassess theDarcycoefficientintheSARgeometries.
3.1.2.Resultsanddiscussion
Fig. 7 showstheevolution of theDarcycoefficientwiththe ReynoldsnumberinboththeSARandthecorrugatedchannels.
Nomajordiscontinuityisobservedbetweentheglycerol0.7w.
curve(Reynoldsnumberfrom5to90)andtheglycerol0.9w.one
(Reynoldsnumberfrom0.1to3).Whateverthegeometry,alinear sharpdecreaseisobservedasforstraighttubes(L)64/Re)inthe laminarflowregime.Aweakdecreaseoftheslopecanbenoticed onFig.7whereasReynoldsnumberisfarbelowtheclassicalflow regime transition around Re=2300 for straight channel. To illustrate this low Reynolds number flow regime transition, Fig.8showstheevolutionoftheDarcycoefficientintheSAR-1 channelonawiderReynoldsnumberrange.
AsobservedinFig.7,thelinearsharpdecreaseismeasuredfor Reynoldsnumberrangingfrom10toaround100.Above100,the transitionalzoneseemstoappearandfinallyamoderateslopeis observedforhigherReynoldsnumbers.Thesetrendsaresimilarto straightchannelsexceptthatthetransitionalzoneinourgeometry isaroundRe=100ratherthanRe=2300.Flowinstabilitiesabove these Reynolds number may certainly promote turbulence-like vortices. This is interestingto promote heat and mass transfer intensificationwhileworkingwithlowReynoldsnumbers.Similar trendshavebeenobservedbyTheronetal.[6]inthecorrugated channel.
InthelowReynoldsnumberzone,Fig.7showsdiscrepancies betweentheSARpatterns.LossesintheSAR-3geometryarehigher thaninSAR-1andSAR-2geometries(uptox2).Thismaybedueto thenumberofpatternsperdevelopedlengthunitwhichisaround 50%higherinSAR-3thaninSAR-1and2(39.5vs25patterns/Ldev).
Thefluidundergoesahighernumberofsplittingandrecombina- tionwhichproduceslosses.Moreover,theratiobetweenthelength ofthebrancheswherethefluidflowswithavelocityu/2andthe Table1
GeometricalcharacteristicsofSARHEXreactors.
SAR-1 SAR-2 SAR-3
Coolingconfiguration cross-flowcoolingtubes Coolingplates(isothermalwall) Coolingplates(isothermalwall)
Cross-section(mm2) 3#3
Hydraulicdiameter(mm) 3
Developedlength,Ldev(m) 1.9 1.7 2.1
Totallength,L(m) 3.4 2.8 3.4
Totalvolume(mL) 28.3 24.7 28.5
Numberofrowsinseries 4 4 7
Numberofpatternsperrow 12 12 12
Numberofpatternsperunitofdevelopedlength 25 29 39.5
Fig.6.PhotographofthecorrugatedchannelbeforeHIPassembling.
Table2
Physico-chemicalpropertiesofthefluidsusedforpressuredropmeasurements.
Fluid Densityr(kgm"3) Viscositym(Pas) FlowrateFp(kgh"1) Reynolds,Re
Water"Glycerol(70%weightglyc.) 1030 0.018 1.4–18.0 5.3–110.9
Water"Glycerol(90%weightglyc.) 1015 0.210 0.3–7.1 0.1–3.3
Water"Ethyleneglycol(98%weighteth.Glyc.) 1110 0.010 1.0–27.5 9.0–316.0
Fig.5. CADviewsofSAR-1(aandb)andSAR-3(c)HEXreactors.(a)ZoomofthecrossingbetweenthecoolingtubesandtheSAR-1channel.(b)Thecross-flowcoolingtubesin SAR-1HEXreactoraredepictedinred.
developed length is lower in SAR-3 than in SAR-1 and 2. The pressuredropisdirectlyproportionaltothesquareofthevelocity andthisalsogeneratesadditionallossesinSAR-3pattern.
TheslightdiscrepancybetweenSAR-1andSAR-2curvesmight beexplained aswellsince SAR-1 geometryhasbeenexpanded compared withSAR-2.ThismeansthatthelengthofoneSAR-1 patternisslightlyhigherthantheoneoftheSAR-2pattern,i.e.the fluidundergoesalittlebitlesssplittingandrecombinationperunit ofdevelopedlength(29vs25patterns/Ldev).
Finally,the corrugated channel generateshigher losses than SARgeometriesinthelowReynoldsnumberrange(Re<100).The chaoticstructuresseemtogeneratemoderatelossescomparedto theturbulent-likestructuresofthecorrugatedgeometry.
3.2.Thermalcharacterization
3.2.1.Experimentalset-upandprocedure
The HEXreactorsareequippedwithtemperaturesensorsto characterizethetemperatureprofilesversustheflowregime.The temperatureismeasuredbetweentheinletandoutletofeachrow
(seeFigs.4and5).Eitheracounter-currentflow(SAR-2,SAR-3)ora cross-flow(SAR-1,corrugatedchannel)patternisimplementedfor the cooling stream. The intermediate temperature probes are required to locate the temperature pinch and to avoid under- estimatingtheheattransfercapacity.
Tocharacterizethethermal behaviouroftheHEXreactors,a heat transfer capacity, or thermal intensification factor, UA/V
(kWK"1m"3),isassessed.Uistheglobalheattransfercoefficient
(Wm"2K"1),Aistheheatexchangerarea(m2)andVisthevolume
offluid(m3).
InboththeSARpatternsandthe2Dcorrugatedgeometry,the heatexchangeareacanbedefinedaccordingtovariousreferences.
Itcanrepresentthedevelopedheatexchangeareaofthe4facesof thechannel,or aprojected area(i.e.assumingnoheattransfer limitations in the process plate material). The 3-dimensions characteristic of the SAR structures add an extra level of complexityand theresultsinterms of heattransfer coefficient (and the resultant Nusselt number) depends on the chosen reference.It mayleadtointerpretationmistakeswhentheHEX reactorsarecompared.
Fig.7.DarcycoefficientvsReynoldsnumber(glycerol70%andglycerol90%at25$C).
Fig.8.EvolutionoftheDarcycoefficientvsReynoldsnumberintheSAR-1channel(Waterandethyleneglycol"25$C).
