Modelling of food transportation systems – a review

　　InternationalJournalofRefrigeration29(2006)947e957

　　http://www.wendangwang.com/locate/ijrefrig

　　ReviewArticle

　　Modellingoffoodtransportationsystemseareview

　　S.J.James*,1,C.James,J.A.Evans

　　FRPERC,UniversityofBristol,ChurchillBuilding,Langford,Bristol,BS405DU,UKReceived1November2005;receivedinrevisedform15March2006;accepted27March2006

　　Availableonline7July2006

　　Abstract

　　In2002,overamillionrefrigeratedroadvehicles,400,000refrigeratedcontainersandmanythousandsofotherformsofrefrigeratedtransportsystemsareusedtodistributechilledandfrozenfoodsthroughouttheworld.Allthesetransportationsystemsareexpectedtomaintainthetemperatureofthefoodwithincloselimitstoensureitsoptimumsafetyandhighqualityshelflife.

　　Increasingly,modellingisbeingusedtoaidthedesignandoptimisationoffoodrefrigerationsystems.Muchofthisefforthasconcentratedonthemodellingofrefrigerationprocessesthatchangethetemperatureofthefoodsuchaschilling,freezingandthawing.Thepurposeofarefrigeratedtransportsystemistomaintainthetemperatureofthefoodandappearstohaveattractedlessattentionfrommodellers.Thispaperreviewstheworkthathasbeencarriedoutspeci?callyonthemodellingoffoodtemperature,microbialgrowthandotherparametersinthetransportationoffood.2006ElsevierLtdandIIR.Allrightsreserved.

　　Keywords:Food;Refrigeratedtransport;Roadtransport;Refrigeratedcontainer;Survey;Modelling

　　lisationdessyste`mesdetransportutilisespourRevuedelamode

　　esalimentaireslesdenre

　　?te;ModelisationMotscles:Produitalimentaire;Transportfrigori?que;Transportroutier;Conteneurfrigori?que;Enque

　　1.Introduction

　　Developmentsinfrozentransportinthelastcentury

　　establishedtheinternationalfoodmarket.In1877,acargo

　　*Correspondingauthor.Fax:441179289314.

　　E-mailaddress:steve.james@bristol.ac.uk(S.J.James).1

　　MemberofIIRCommissionC2.

　　0140-7007/$35.002006ElsevierLtdandIIR.Allrightsreserved.

　　doi:10.1016/j.ijrefrig.2006.03.017

　　offrozenmeatwassentfromBuenosAirestoFrance[1].Thefollowingyear5000frozenmuttoncarcassesweretransportedfromParaguaytoFrance.In1880,theS.S.StrathlevenarrivedinLondonwithacargoof40tonsoffro-zenAustraliabeef,theS.S.Dunedinfollowedin1882withmutton,lambandporkfromNewZealand,andby1910GreatBritainwasimporting600,000tonsoffrozenmeat.However,Dellacasa[2]considersthattherealadvanceandexpansionofrefrigeratedtransportbyseawaslinkedtoshipmentsofbananasin1901.Furtherdevelopmentsin

　　948S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957

　　temperature-controlledtransportationsystemsforchilledproductshaveledtotherapidexpansionofthe‘‘fresh’’foodmarket.TheseatransportationofchilledmeatfromAustralasiatoEuropeanandotherdistantmarkets,androadtransportationofchilledproductsthroughoutEuropeandtheMiddleEastisnowacommonpractice.In2002,itwasstatedthat‘Worldwide,thereareatleast1millionrefrig-eratedroadvehiclesand400,000refrigeratedcontainersinuse.’[3]Theretailvalueoftheproductstransportedwases-timatedtobe1200billionUSdollars.Asrefrigeratedtrans-portationincreasestherehasbeensubstantialinterestinimprovingenergyconsumptionbyreducingvehicleweight,improvinginsulationandchangingdistributionsystems[4].Itisparticularlyimportantthatthefoodisatthecorrecttemperaturebeforeloadingsincetherefrigerationsystemsusedinmosttransportcontainersarenotdesignedtoextractheatfromtheloadbuttomaintainthetemperatureoftheload.Inthelargecontainersusedforlong-distancetranspor-tation,foodtemperaturescanbekeptwithin0.5??Cofthesetpoint.Withthisdegreeoftemperaturecontrol,transpor-tationtimesof8e14weeks(forvacuumpackedmeatsstoredat1.5??C)canbecarriedoutandstillretainasuf?-cientchilledstoragelifeforretaildisplay.

　　Modellinghasbeenusedquiteextensivelyintheareaoflocaldelivery;however,unlikeotherfoodrefrigerationpro-cessestherestofthetransportcoldchainhasnotbeenexten-sivelymodelled.Inthisreview,theuseofmodellinginfoodtransportationtogetherwithinvestigationsthatprovideuse-fuldataforfuturepredictivemodellingarecovered.2.Foodtransportationchain

　　Foodistransportedinmanyformsandbymanymeansfromfarm/harvesttoultimateconsumption.2.1.Airtransportation

　　AirfreightingisincreasinglybeingusedforhighvalueperishableproductsandmeatproductssuchasvenisonandWagyubeef[5].However,foodsdonotnecessarilyhavetofallintothiscategorytomakeairtransportationviablesinceithasbeenshownthat‘‘theintrinsicvalueofanitemhaslittletodowithwhetherornotitcanbene?tfromairshipment,thedecidingfactorisnotpricebutmark-upandpro?t’’[6].Therewasa10e12%increaseperyearinthevolumeofperishablestransportedbyairinthe1990s[7].Althoughairfreightingoffoodsoffersarapidmethodofservingdistantmarkets,therearemanyproblemsbecausetheproductisunprotectedbyrefrigerationformuchofitsjourney.Upto80%ofthetotaljourneytimeismadeupofwaitingonthetarmacandtransporttoandfromtheairport.During?ighttheholdisnormallybetween15and20??C.Perishablecargoisusuallycarriedinstandardcontainers,sometimeswithaninsulatingliningand/ordryicebutisoftenunprotectedonaircraftpallets[2].

　　2.2.Seatransportation

　　Historically,itwastheneedtopreservefoodduringseatransportthatleadtothedevelopmentofmechanicalrefrig-erationandthemoderninternationaltradeinfoodstuffs.Recentdevelopmentsintemperaturecontrol,packagingandcontrolledatmosphereshavesubstantiallyincreasedtherangeoffoodsthatcanbetransportedaroundtheworldinachilledcondition.

　　MostInternationalStandardOrganisation(ISO)con-tainersforfoodtransportareeither6or12mlong,holdupto26tonsofproductandcanbe‘insulated’or‘refriger-ated’[8].Therefrigeratedcontainersincorporateinsulationandhaverefrigerationunitsbuiltintotheirstructure.Theunitsoperateelectrically,eitherfromanexternalpowersupplyonboardtheship,dock,orfromageneratoronaroadvehicle.Insulatedcontainersutiliseeitherplugtyperefrigerationunitsormaybeconnecteddirectlytoanair-handlingsysteminaship’sholdoratthedocks.Closetem-peraturecontrolisveryeasilyachievedincontainersthatareplacedininsulatedholdsandconnectedtotheship’srefrig-erationsystem.However,suitablerefrigerationfacilitiesmustbeavailableforanyoverlandsectionsofthejourney.Whenthecontainersarefullyloadedandthecooledairisforceduniformlythroughthespacesbetweencartons,themaximumdifferencebetweendeliveryandreturnaircanbelessthan0.8??C.Theentireproductinacontainercanbemaintainedtowithin1.0??Cofthesetpoint.

　　Refrigeratedcontainersareeasiertotransportoverlandthantheinsulatedtypes,butoftenhavetobecarriedondeckwhenshippedbecauseofproblemsinoperatingtherefrigerationunitswithinclosedholds.Onthedecktheyaresubjectedtomuchhigherambienttemperaturesandconsequentlylargerheatgainswhichmakeitfarmoredif-?culttocontrolproducttemperatures.Containersareoftenstackedontopofeachotherandthoseonthetopofthestackwillbesubjectedtosolarradiation.Theremayalsobeproblemsondocks,oftentheremaynotenoughpowersupplypluginpoints.Itisdif?cultforportstopre-dictaccuratelythearrivalofshipsandthemaximumnum-berofrefrigeratedcontainerstheyneedtocopewithatanyonetime.

　　http://www.wendangwang.comndtransportation

　　Landtransportationsystemsrangefrom12mrefriger-atedcontainersforlongdistanceroad,orrail,movementofbulkchilledorfrozenproducts,tosmallun-insulatedvanssupplyingfoodtolocalretailoutletsorevendirectlytotheconsumer.Someofthe?rstrefrigeratedroadandrailvehiclesforchilledproductswerecooledbyairthatwascirculatedbyfreeorforcedsystems,overlargecon-tainersofice[9].Similarsystemsusingsolidcarbondioxideastherefrigeranthavealsobeenusedforcoolingofthetransportvehicles.However,mostoverlandvehiclesfor

　　S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957949

　　long-distancetransportarenowmechanicallyrefrigerated.Theriseinsupermarkethomedeliveryservices[10],wheretherearerequirementsformixedloadsofproductsthatmayeachrequiredifferentstoragetemperatures,isintroducinganewcomplexitytolocaloverlanddelivery.

　　Therearesubstantialdif?cultiesinmaintainingthetemperatureofrefrigeratedfoodstransportedinsmall-refrigeratedvehiclesthatconductmulti-dropdeliveriestoretailstoresandcaterers.Inasurveycarriedbytheauthorsitwasfoundthatduringanyonedeliveryrun,therefriger-atedproductcanbesubjectedtoasmanyas50dooropen-ings,wherethereisheatingressdirectlyfromoutsideandfrompersonnelenteringtoselectandremoveproducts.Thedesignoftherefrigerationsystemhastoallowforexten-sivedifferencesinloaddistribution,dependingondifferentdeliveryrounds,daysoftheweekandtheremovalofprod-uctsduringadeliveryrun.

　　3.Modellingapproaches

　　Transportationisavariedsubjectanddifferentaspectsmaybeaddressed.Ingeneralmodelsthataddressthepredic-tionofheatandmasstransferduringtransportationcanbedividedintothosethatconsidertheenvironmentwithinthetransportunit(usuallyinregardtotheair?ow)andthosethatconcentrateonthetemperatureoftheproduct.Somemodelscombinetheseaspectsanddealwiththetemporalas-pectsoftransportation:?uctuatingambientconditions,dooropenings,productremoval/loading,etc.Othermodelsspe-ci?callyaddresstheeffectsoftransportationtemperaturesonmicrobialgrowthandit’sin?uenceonfoodsafety.Otheraspectsmayalsobeaddressed.

　　Long-distancetransportsystems,whetherbylandorsea,maybeconsideredsimplymobilerefrigeratedcoldstoresandsharemostofthesameprocessesandmecha-nismsthatoccurinstaticfacilities.Therefore,someofthemodellingapproachesappliedforcoldstorescanbeconsideredrelevanttotransportsystemswithlittlechangebeingrequiredtotheinherentmodel.Suchsystemspassthroughawiderangeofclimaticconditions,andtheeffectofheattransferbetweentheoutsideairandthetransportcontainer’swalls,solarradiation,andairin?ltrationfromambientintothevehiclecavityareparticularlyimportant.Oneimportantdifferencebetweencoldstoresandrefriger-atedtransportsystemsarethattransportcontainersarenotstaticandconditionsareaffectedbyvehiclespeedandorientationinrelationtofactorssuchasthesun.Inlocaldelivery,apartfromtheproblemsalreadymentioned,thereisalsointensifyingdemandfromlegislationandretailersforlowerdeliverytemperatures,andheightenedpressureon?eetoperatorstoimprovetemperaturecontrol.Thecomputational?uiddynamics(CFD)techniquesthathavebeenusedtomodelair?owincoldstores[11e13],andthroughcold-storedoorways[14e17]couldequallybeappliedtotransportsystems.

　　4.Modellingofheatandmasstransferduringtransport

　　Ingeneralmodelsthataddressthepredictionofheatandmasstransferduringtransportationcanbedividedintothosethatconsidertheenvironmentwithinthetransportunit(usuallytodowiththeair?ow)andthosethatconcentrateonthetemperatureoftheproduct.Somemodelscombinetheseaspectsanddealwiththetemporalaspectsoftranspor-tation:?uctuatingambientconditions,dooropenings,productremoval/loading,etc.

　　4.1.Modelsoftheenvironmentinrefrigeratedtransportunits

　　Inthe1990s,whenmodellingrefrigeratedtransport,Cominietal.[18]statethattheyusedasanalternativetothecontinuousanalysisofcoupledvelocityandtemperature?elds,theaverage?uidvelocitiesandtheconvectiveheattransfercoef?cientsestimatedbystandardengineeringpro-cedures.Thevalueswerethenusedasinputdataina?niteelementcodethatcalculatedthedetailedtemperaturedistri-butionsinthesolidandthebulktemperaturevariationsinthe?uid.Todemonstrateitsuse,asimplisticcargodistributioncasewasusedwherethewidthsofallthe?owpassagesandtheairvelocitiesinthe?owpassageswereallassumedtobethesame.Constantvalueswereusedforthethermalproper-tiesoftheproductandtheairinthevehicle.Inpreliminarycalculations,itwasshownthatheatexchangesthroughtheroofand?oorofthecontainerhadanegligibleeffectontheairtemperatureinthecontainer.Thiswasduetothehighaircirculationrate(approximately0.7ms1)intheup-perandlowerplenum.Ifthecontainerwasloadedwithwarmproduct(20??C),thatdidnotgenerateinternalheat,itwaspredictedthatafter24hthecentretemperatureoftheproductwouldbeabove15??Cwhentheairinthecon-tainerwascirculatedat5??C,0.7ms1.Ifthecargogener-atesheatthetemperaturewouldbeabove17??Cafter24h.AnintegraledifferentialealgebraicsolverwasusedbyNorwegianUniversityofScienceandTechnologytodevelopamodeltosimulatetheeffectofpalletloadingontheairdistributioninreeferholds(shippingcontainers)underdifferentconditions[19].Thismodeldidnottakeintoconsiderationtheheattransferfromwalls,packaging,ceilingand?oor.

　　CFDhasbeenusedtoinvestigatetheoptimisationofairdistributioninrefrigeratedvehiclesinordertodecreasethetemperaturevariationwithintheloadspace[20,21].Ithasadditionallybeenusedtocharacterisetheair?owgeneratedbyawalljetwithinalongandemptyslot-ventilatedenclo-sure[22],adesignstatedtobeextensivelyusedinrefriger-atedtransport.Experimentswerecarriedoutonascalemodel(1:3.3)ofatrailer.Inthestudy,asecond-momentclo-sure,theReynoldsstressmodel(RSM)andtwo-equationturbulencemodels:thestandardk-epsilonandarenormaliza-tiongroup(RNG),weretested,contrastedandcompared

　　950S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957

　　withexperimentaldata.ItwasdemonstratedthatonlytheRSMmodelenableddetectionofthepresenceandthelocal-isationofseparated?owandcorrectlypredictedair?owpat-ternsrelatedtoprimaryandsecondaryrecirculation.Theworkwasextendedtolookattheeffectofairdistributionwithandwithoutairductsontemperaturedifferencethroughoutthecargo[21,23].Airductsremovedtheareasofstagnantairintherearpartoftheloadwhilstreducingairmovementatthefront.Thepredictionsshowedthatairductswouldreducethemaximumairtemperaturefrom16to20??Candreducetheoveralltemperaturedifferencefrom12to8??C.

　　Tsoetal.[24]usedacommercialCFDprogramtomodeltheeffectofdooropeningsonairtemperaturewithinarefrig-eratedtruck.Theycarriedoutaseriesofexperimentstostudytheeffectofdooropeningswithunprotecteddoors,withaircurtainsandwithplasticstripcurtains.Twominutesafterthedoorwasopenedtheaverageairtemperaturewasstatedtohaverisenfrom10to14,7and8??C,respectivelyfortheunprotected,aircurtainandplasticstripsituations.TheCFDsimulationsgenerallyoverestimatedthetempera-turerisebybetween3and4??C.Thedifferencewasbelievedtobeduetotheeffectofcondensingwatervapourintheex-perimentalsituation.

　　4.2.Modelsofheatandmasstransferinfoodsandpackagesduringtransport

　　Rushbrook[25,26]developedasimpleone-dimensionalmodeltorepresentheat?owintocartonsofchilledmeatinastandardmechanicallyrefrigeratedcontainer.Hethenusedittodeterminetheeffectofvarioustypesofcontrolsystemsandmeasurementpositionsonreturnair,deliveryairandmeatsurfacetemperatures.Althoughtheauthorstatedthatthemodelwaslimited,hethoughtitasusefulinpredictingthat:(1)On/offactionwouldbeimprovedifthetemperaturesensormeasuredtheairoffthecartonstackinsteadofthereturnair.Itwouldreduceovercoolingoftheproductandtemperaturecycling,(2)Proportionalcontrolontherefrigerationcapacitywasmorestableandgaveanimprovedresponseoveron/offaction,(3)Temperaturecon-trolwasverysensitivetochangesinsystemparameters.Meffertadvocatesthatastraightforwardmechanistic-analyticalmodelforthedistributionoftemperatureswithinacargocantakeaccountofallthemostimportantin?uences.Hedevelopedasimplemodelforasteadystateconditionin1976[27]thatwasfurtherdeveloped[28e31]andrelatesthetemperaturedropacrosstheaircoolerinarefrigeratedcontainerwiththerangeofcargotemperatures.In1998,herecommendedthatthemethodbeappliedtoreefercon-tainersandvehicles,storageroomsandretailcabinets[32].MourehandDerens[33]usedCFDtomodeltemperaturerisesinpalletloadsoffrozenfoodduringdistribution.Theyspeci?callylookedatthetimesduringloading,unloadingandtemporarystoragewhenthepalletswouldbeinanam-bientabove0??C.Experimentswerecarriedoutwithpallets

　　offrozen?shblocksinashadedloadingbay(4??C,80%RH)andanopenbay(22??C,50%RH).Themodeltookintoaccountconductiveandradiativeheattransferintothesurfaceofthepalletbutignoredcondensation.Aswouldbeexpected?shinthetopcornersofthepalletshowedthelargesttemperaturerise.Intheshadedbaythepredictedtem-peratureriseafter25mininthecornerwas2.7??Ccomparedwithanaverageof2.5??Cexperimentally.Intheexposedbaythecorresponding?gureswere6.4and6??C.Astheau-thorspointout,underEuropeanquick-frozenfoodregula-tionsthe?shmustbedistributedat18??Corlowerwithbriefupward?uctuationofnomorethan3??Callowedwithindistribution.Inthecaseoftheopenloadingbaytheinitialtemperatureofthe?shwouldhavetobebelow25??Ctokeepitwithintheregulations.

　　Therearestagesintransportationwherefoodisnotinarefrigeratedenvironment,i.e.,inloadingbays,insuper-marketsbeforeloadingintoretaildisplays,domestictrans-portationfromshoptohome,etc.Thetransportofhighlyperishableproductsbyairisalsoofteninunrefrigeratedcon-tainers,orincontainerspassivelycooledbywaterordryice.Duringtheseprocessestheuseofinsulationcansubstan-tiallyreduceanytemperatureriseinthefood.

　　Thepresenceofaninsulatingcoveronpalletscanaidthedeliveryofthermo-sensitivefood[34].Studiesshowedthatthepresenceofthecoverincreasedthetimetakenfortem-peraturerisefrom12to24??Cfrom1.5to5.5hinthecornerofthepallet.Tenmillimetreintotheloadthetimewasincreasedfromapproximately2toover8h.

　　Insulationhasasubstantialeffectonthetemperatureriseinthefoodsupplieddirectlytoconsumersbypost.Directsupplyisagrowingmarketbroughtaboutbythepopularityofwed-basedshopping.Stubbsetal.[35]developedanumericalmodelforthelengthoftimeafoodstuffpackedinanexpandedpolystyreneboxwithagelcoolantcouldremainbelow8or5??C.ThemodelwasbasedonaTLM(transmissionlinematrix)techniqueandisnotdescribedindetail.Aswouldbeexpectedifthecoldgellinedthetop,sidesandbaseoftheboxthetimeforthefoodtoreach5or8??Cwassubstantiallylongerthanwithgelatthesidesandtoporjustthetop(Table1).Assumingthattheproductwouldbedeliveredwithin24hofpostingthiswastheonly

　　Table1

　　Timeforwarmestpredictedpointtoriseabove5and8??Cunderthreepackagingcon?gurations[35]AmbientTime(h)to8??CTime(h)to5??C(??C)incon?gurationincon?gurationABCABC15232525204241325252.520122430

　　1.5

　　15.5

　　24

　　1

　　1

　　22

　　A,refrigerantpacksattop;B,packsattopandsides;C,packsattop,sidesandbottom.

　　S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957951

　　con?gurationthatwouldmaintaintheproductbelow8??Cinambientsupto30??Candbelow5??Cinambientsupto25??C.

　　Simplenumericalmodelshavebeenusedtoidentifytherelativeimportanceofdifferentfactorsintheairfreightofperishableproducts[5].Thisshowedclearlythatsomeformofinsulationwasrequiredaroundtheproducts,andtheprecoolingoftheproductsbeforetransportationwases-sential,whiledryicewasunnecessary.Interestinglystudiescarriedoutin1972ontheairfreightingofchilledlambfoundthatinsulatedboxescouldmaintainthelambtemper-aturebelow4.5??Cfor24hifitwasinitiallyloadedatbelow0.5??C[36].AmosandBollen[37]developedasimplemodeltoevaluatetheeffectofpalletwrappingonthequalityofasparagusduringairtransport.Coveringpalletswithinsu-latedblanketsincreasedtheshelflifeby0.5e0.7days,whiletheuseofaeutecticblanketincreasedshelflifeby2e3days.Finitedifferencemodelshavealsobeendevelopedtopredicttemperaturesinpalletsofperishableproductsduringairtransport[38],lookingateffectofhandlingofthepalletsonthegroundduringloadingaswellasintheair.4.3.ModelsofrefrigerationperformanceduringtransportJollyetal.[39]developedamodeltosimulatethesteadystateperformanceofacontainerrefrigerationsystem.Sub-modelswerecreatedonthekeycomponents:compressor,evaporator,condenser,andthermostaticexpansionvalve.Thesesub-modelswerethencoupledbyappropriatemassandenergytransferrelationstoformthefullmodel.Themodelwasshowntobewithina10%agreementofexper-imentallymeasureddatafromcoolingcapacitytestsconductedona2.2mfull-scalecontainerhousedinatemperature-controlledenvironmentaltestchamber.Suchamodelisusefullookingattheperformanceofdifferentrefrigerantsinsuchsystems,butbeinginsteadystatecannotshowtheeffectofdynamicallychangingexternalambientconditions.

　　http://www.wendangwang.combinedmodels

　　Asoftwaremodelcalled‘Censor’hasbeendevelopedtoestimatecargotemperaturesinrefrigeratedcontainersduringnormalandabnormaloperations[40].Athree-dimensional?niteelementanalysisisusedtopredictthechangeintemperatureatspeci?cpositionswithinthecon-tainerwhensubjectedtovaryingcontrolregimesandambi-entconditions.Dataisrequiredonthecon?gurationoftheload;theinitialtemperatureoftheloadanddifferentpartsofthecontainersstructure;thethicknessandU-valuesofthestructure;dimensionsofairspacesandtotalair?ow.Fur-therdataisrequiredonthedefrostinterval;thetypeofreeferunitused;poweronandofftimes;ambientconditionsandonthetypesoffood(17differenttypesoffoodcanbeselected).Fixedortime-varyingambienttemperaturescanbeenteredortemperaturesfromvesseldecklogsormetof?cerecordscanbestoredaslookup?les.Thesoftwarewillsimulatetwocontrolmodeseithermodulatedoron/offreturnairandallowforvaryingeffectsofsolarheatonthesidesandroof.Thelinearairspeedatanypointinthecontaineriscal-culatedfromthevolumeair?http://www.wendangwang.comingthevalueofthelocalairvelocitytheairtosurfaceheattransfercoef?cientiscalculated.Thesoftwareassumesade?nedair?owpatternwithintheloadspace.ThreeversionsofCensorareavailabletosimulate:(1)blockstowagewith300discretenodesar-rangedin12rowsof55nodesperrow;(2)200pallet/battenstoragewith375nodesin5groupsof3rowsof55nodestosimulate5rowsofpallets;and(3)400pallet/battenstoragewith750nodesin10groupsof3rowsof5http://www.wendangwang.comparisonandvalidationtestswerecarriedoutagainstpublisheddataonfrozenher-rings.Dataonthepredictederrorcomparedwiththepub-lisheddataisprovidedfortheminimum,meanandmaximumtemperaturesatdifferenttimesduringthesimula-tionforfour?xedambientconditionsandavaryingambient.Forthe?xedambientconditionsthemaximumerrorof3.9??Coccurredinthemaximumtemperaturepredictedafter20hinanambientof19.6??http://www.wendangwang.comrgererrorsupto5.5??Cwerereportedinthe?uctuatingambienttemperaturecase.Oneofthelargestandmostsystematicattemptstopredictthetemperatureoffoodsduringmulti-dropdeliverieshasbeentheCoolVanprogramintheUK[41e44].Threemaintypesofrefrigerationsystemwereidenti?ed;aconventionaldieseldrivenunit,ahydraulicdriveunitandaeutecticsys-tem.Dataonvan’sperformanceincommercialoperationwereobtainedduringsevenseparatedeliverytripswithtwomajorfoodcompanies.Thenatestrigconsistingofaninsulatedvanbodythatcouldhavedifferentrefrigerationsystemsattachedtoitandaninterchangeabledoorcon?gu-rationwasconstructed.Experimentswerecarriedouttomeasuretheheatingressduringdooropeningsandtheeffectsofinsulatedplasticstripsinthedoorway.In?ltrationofheatandmoisturethroughthevanbodywasquanti?ed.Thevehicleairisatthecentreoftheheattransfer,actingasaheattransportbetweenallsurfacesinthevehicle(Fig.1).Attheendoftheprogramdevelopment,thecompletemodelwasveri?edagainstmeasureddatafromarealdeliv-eryround.Loggeddataincludedvehiclespeed,ambienttemperature,whetherthesunwasshining,thedirectionoftravel,timesthatthedoorswereopenedandclosed,amountoftimespentinsidethevehiclebytheoperatorandtheamountoffoodremovedateachstop.Theprogrammewasfoundtobeabletopredictthemeantemperatureofthefoodinthevehiclewithanaccuracybetterthan1??Catanytimethroughoutthejourney.However,foodtempera-tureswithinthevehicleactuallyvariedbymorethan5??Catanyonetime,duetotheuneventemperaturedistributionwithinthevehicle.Theheatextractedbytherefrigerationsystemduringthejourneyisshownplottedagainstthethick-nessofinsulationinFig.2.Onlyasmallthicknessofinsu-lationgreatlyreducestheamountofheattobeextracted,

　　952

　　S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957

　　Fig.1.Diagramofthemathematicalmodelused

　　inCoolvanshow-ingthe?owsofheatandjourneyinformation.

　　theamountdecreasingwiththereciprocalofthethicknessofinsulation.Inallcasesthevanandfoodtemperaturesweremaintainedatlessthan5??C.Theheatextractedfromapoorlysealedvanwas86%morethanfromawell-sealedvan.However,in?ltrationduringthetimethatthedoorisclosedisarelativelysmallproportionofthetotalrefrigerationload.Inavehicle,?ttedwithanominal2kWcoolingsystem,thestateofthesealsdidnotcausethetem-peratureofthefoodtoincreasetomorethan5??Cduringthe

　　No food

　　1 Tonne food

　　21.81.61.41.210.80.60.40.20Thickness (mm)

　　Fig.2.Heatextractedbyrefrigerationplantduringasimulatedjourneywithdifferentinsulation

　　thicknesses.

　　5min, No strip curtain5min, Strip curtain10min, No strip curtain

　　10min, Strip curtain

　　1.41.2

　　10.80.60.40.2

　　0Number of stops

　　Fig.3.Therateofheatextractfromthevan,averagedovertheperiodswhenthevehicleismoving,asafunctionofthenumberofstopsthevanmakes.

　　journey.Theheatextractedfromaclosedvanisverysmall(Fig.3)however,dooropeningsgreatlyincreasetheheatload.Theheatextractedbytherefrigerationsystemisfourtimesgreaterifthefoodisloadedat7??Cthanifitisloadedat0??C(Fig.4).Asthelengthofthejourneygetsshorterwhilethenumberofdropsremainsthesametheheatenter-ingthevanduringthestopsmustbeextractedinshortertimeintervalsbetweeneachstop.Therateofheatextractionthereforevariesinverselywiththelengthofthejourney(Fig.5).Itiseasiertomaintainfoodtemperaturesonlongjourneysthanwhentherearealargenumberofstopswithlittletimespentintravellingbetweeneachstop.5.ModellingofmicrobialgrowthduringtransportThemainpurposeofmaintaininggoodtemperaturecontrolduringrefrigeratedtransportistodecreasethe

　　6050403020100Food temperature at loading (C)

　　Fig.4.Theheatextractedbytherefrigerationplantduringthestan-dardjourneywhenthefoodisloadedatdifferentinitialtemperatures.

　　S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957

　　953

　　21.81.61.41.210.80.60.40.20Length of journey (miles)

　　Fig.5.Therateofheatextractfromthevanaveragedovertheperiodswhenthevehicleismovingasthelengthofthejourneydecreases.

　　rateofmicrobialgrowthandhencemaintainingthesafetyandeatingqualityofthefood.Therearemanymicrobialgrowthmodelsthatcouldbeappliedtomodellingthegrowthofmicroorganismsinfoodduringtransport[45e47],suchasthefreelyavailablePathogenModellingProgram(http://www.wendangwang.comda.gov/Services/docs.htm).However,relativelyfewstudiesappeartohavebeenpublishedspe-ci?callyonthissubject.Evenfewerofthesehavelookedatthefullyintegratedapproachofcombiningdynamicmi-crobialgrowthmodellingwithheatandmasstransfermodelsthatcanmodelthecharacteristicsofafooddistri-butionsystem.

　　AsimplecombinedheattransferandmicrobialgrowthmodelwasdevelopedbyAlmonacid-MerinoandTorres[48]toevaluatetheeffectsoftemperatureabuseduringdis-tribution.However,the?nitedifferenceheattransfermodelforheattransferinrectangularcontainerswasnotspeci?-callydesignedtomodeltransportconditionsonlytopredicttheeffectofexternaltemperature?uctuationsonproducttemperatures.

　　Otherstudieshaveintegratedmicrobialgrowthmodelswithrecordedtemperaturedata.GillandPhilips[49]mea-suredthetemperatureindeeptissuesandthesurfacesofbeefsidestransportedbyrailandbeefhindquarterstrans-portedbyroadfromwesternNorthAmericatomarketsintheeastofthecontinent.Threebatchesweremonitoredineachofthetenrailconsignmentsfromoneplant,andineachofthe?veroadconsignmentsfromeachoftwootherplants.Thesurfacetemperaturehistorieswereintegratedwithrespecttoamodeldescribingthedependencyontem-peratureoftherateofgrowthofpsychrotrophicpseudomo-nads.Productwastransportedforperiodsrangingfromabout4toabout7days.Calculatedproliferationsrangedfrom8to21generations.The?ndingsindicatethatinwell-managedrefrigeratedrailwaywagons,thestoragelifeofhangingbeefcanapproachthepossiblemaximum.How-ever,therefrigerationcapabilitiesofroadtrailerscannot

　　compensateforthedeleteriouseffectsonstoragelifeofthecurrentpracticeofloadingwarmcarcasses.

　　Thesafetyofthechillchainisnowbeingassessedusinganapproachbasedonactualriskevaluationatimportantpointsofthechillchaininordertopromoteproductstothenextstageofdistribution[50].TheevaluationcalledtheSafetyMonitoringandAssuranceSystem(SMAS)isbasedonaproduct’stimeetemperaturehistory,variationinitscharacteristics(e.g.aw,pH,etc.),andtheuseofpredic-tivemodelsforthegrowthoffoodpathogens.Itisclaimedthatthisapproachgivesprioritytoproductsinsuchawaythatriskatconsumptiontimeisminimized.TwodecisionpointsareusedtoapplytheSMASapproach.Atthe?rstdecisionpoint,themaindistributioncentre,productsaresenttoeitherthelocalmarketoradistantexportmarketbasedonproduct’srisk.Atthesecondpoint,productsaredividedintothreegroupsforsuccessivestockingofdisplaycabinets.Theproductswiththehighestriskbeingused?rst.

　　Analternativemethodistheshelflifedecisionsystem(SLDS)[51].Thisisachillchainmanagementtoolthatisclaimedtoproduceanoptimiseddistributionofqualityatconsumptiontime.Itintegrateskineticmodelsoffoodspoil-age,dataoninitialqualityandcontinuousmeasurementoftheproduct’stemperaturehistoryusingatimetemperatureintegrator(TTI).Ateachstageofthechillchainstock,rota-tionisbasedona‘leastshelfliferemaining?rstout’princi-pleratherthanthestandard‘?rstin?rstout’(FIFO).UsingtheSLDSsystemwithanexported?shproductwasclaimedinoneexampletoreducetheprobabilityofunacceptable?shatconsumptionfrom20%withFIFOtolessthan1%withtheSLDS.TTIhavebeenusedformanydistributionandtransportapplicationsandtheiruseandhistoryinmodellingdescribedindetailbyTaoukis[52].

　　Thesafetyofthemulti-temperaturesmallvansusedforhomedeliverieshasbeeninvestigatedbyEstrada-FloresandTanner[53].Recordedtemperaturehistorieswereinte-gratedwithmathematicalmodelstopredictthegrowthofpseudomonadsandEscherichiacoli.Theirresultsshowedthatproducttemperaturesweresuchthatpseudomonadscouldgrow,butthatlessthanhalfthetemperaturesmeasuredweresuitableforthegrowthofE.coli.Thethermalbehaviourofthefoodproductsinsidethevanwasstronglyin?uencedbytheloadingperiod.TheauthorshighlightedtherequirementforTTIstobecoupledwithmodelsthatdescribethedynamicbehaviourofspoilageandpathogenicbacteria.

　　AsimilarapproachwasadoptedbyJamesandEvans[54]lookingatthedomestictransportfromthesupermarkettothehome.Temperaturehistorieswererecordedinstrumen-tallyandintegratedwithmathematicalmicrobialgrowthpredictionmodels.Thisworkshowedtheimportanceofacoolboxintransportingtherefrigeratedproductshome.Ambienttemperaturesaroundun-insulatedproductsrapidlyrosetoapproaching40??Cduringa1hcarjourneytheoret-icallyresultinginupto1.8generationsingrowthinbacterial

　　numbers.

　　954S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957

　　6.OthertransportfactorsthathavebeenmodelledAlthoughthemainmodellingemphasishasbeenontem-peraturecontrolotherfactorshavealsobeenmodelled.Forinstance,theperceptionofroadcongestionandproblemsofslowaveragespeedsareofconcerntooperatorsofrefrig-eratedvehicles[55].Approximately1200managersofalltypesoftruckingcompaniesoperatinginCaliforniawerecontacted.Morethan80%ofthesemanagersconsidertraf?ccongestiononfreewaysandsurfacestreetstobeeithera‘‘somewhatserious’’or‘‘criticallyserious’’problemfortheirbusiness.Astructuralequationsmodel(SEM)wases-timatedonthesedatatodeterminehow?veaspectsofthecongestionproblemdifferacrosssectorsofthetruckingindustry.The?veaspectswereslowaveragespeeds,unreli-abletraveltimes,increaseddriverfrustrationandmorale,higherfuelandmaintenancecosts,andhighercostsofaccidentsandinsurance.Themodelalsosimultaneouslyestimateshowthese?veaspectscombinetopredicttheperceivedoverallmagnitudeoftheproblem.

　　ChatzidakisandChatzidakis[56]statethatsomeofthealternativesproposedforcheckingtheenergyef?ciencyofin-serviceandsecondhandrefrigeratedtransportequipmentareincompleteandcangiveincorrectresults.Consequently,thereisanincreaseinenergyconsumptionandenvironmen-talpollution.ModellinghasbeenusedtoinvestigatetheperformanceofchambersdevelopedtotestsystemsfortransportingperishablefoodstuffsinaccordancewiththeUnitedNationsATPagreement[57].Usingatransient?nitedifferencemodel,asimulationwasdevelopedforamodernATPtestchamberandatypicalrefrigeratedvehicletobetested.Thesameauthorsalsomodelledtheisothermaltanksthatarewidelyusedforthetransportofperishableliquidfoodstuffslikemilk,wine,juice,etc.[58].Theystatethat‘‘testingofamulti-compartmentisothermaltankpresentsspecialdif?cultiesincomparisontothetestingofarefriger-atedtruckbecauseofthenumberofcompartmentsthathavetobemeasured’’.

　　Tobeabletomakepredictionsoftheperformanceofarefrigeratedvehicle,informationisrequiredonitsoverallheattransfercoef?cientthroughthecontainer.Thiscanbemeasuredexperimentallybutisalongprocesstaking3daystotestavehicleinthelaboratory[59].Morerapidmethodshavebeenused,using?nitedifferencemethodsas-sumingasteadystate[60],ormorecomplexmethodsthatdonotneglecttheunsteadytemperaturedistributionintheinsu-latingmaterial,buttakelonger(8e11h)[59].Heattrans-missionthroughthestructureoftheholdsofshipshasalsobeenmodelled,takingintoaccountthegeometricalcom-plexityofthestructure[61].

　　Ingeneralmodelsaremathematicallybased.However,http://www.wendangwang.comingaphysicalsimulationofthevibrationslikelyinatransportationoperation,denHerog-Meischke[62]foundthatmeatwithalowintrinsicwater-holdingcapacitywasmoresensitive,i.e.dripincreased,

　　thanmeatwithahighintrinsicwater-holdingcapacity.However,theauthorsstatethattheeffectoftransportwasnotsuf?cienttogiveincreaseddriplossinlargemeatblocks.Vibrationduringthetransportationoffreshfruitandvegetablesisthoughttobemoreimportantthanim-pactsasasourceofdamage[63].Itwasfoundthatforsomefrequenciesbetween5and30Hz,thetopboxofastackvibratedconsiderablymorethanthemiddleandbottomboxes.Accelerationlevelsintrailers?ttedwithair-ridesuspensionsystemsweretypically60%ofthatwithsteel-springsuspension.

　　Modelshavealsobeendevelopedtostudytheeffectofmovingcargoesonvehiclestability.Articulatedvehiclesareoftenusedinthetransportofoscillatingcargoesforex-amplerefrigeratedvehiclesforthetransportofmeat.Cargomovementswithinarticulatedvehiclespresentthegreatestpotentialriskofroadaccidents.Mantriota[64]developedamathematicalmodelforthedynamicstudyofarticulatedvehiclescarryingsuspendedcargoesthatareassumedtobeidenticalanduniformlydistributed.Amathematicalmodelofthearticulatedvehiclewasdevelopedthat,incom-parisonwiththecaseofa?xedcargo,hasonlytwofurtherdegreesoffreedom.Thismodelidenti?edarangeofcriticalspeedsandfrequencies.

　　Thermodynamicmodelshavealsobeenusedtoaidthedevelopmentofalternativerefrigerationsystemsforroadtransportation.Spenceetal.[65]usedasimplemodeltohelpintheinitialdevelopmentofanair-cyclerefrigerationunit.Theunitdevelopedwasofthesamephysicalsizeandpowerastheconventionalunitbutinitsunoptimisedstateitconsumedfarmorepower.Furtheranalysis[66]demon-stratedthattheair-cyclesystemcouldpotentiallymatchtheoverallfuelconsumptionoftheconventionalrefrigera-tionunitwhileofferingotherbene?tsassociatedwithare-frigerantfreesystem.Equationshavealsobeendeveloped[67]toshowthattherecanbeconsiderabledifferencesintherefrigerationperformanceofnominallysimilartransportrefrigerationunitswhenvehiclesenginesareidling,i.e.whenthevehiclesaremovingslowlyorstationary.

　　7.Thefuture

　　Incomparisonwiththemodellingofotherrefrigerationprocesses,suchaschillingandfreezing,refrigeratedtrans-porthasreceivedfarlesscoverage.Thismaybebecauseitisconsideredtobesimilartocoldstorageandthusarela-tivelystaticcondition.Thisisashamesinceinrealityitisacomplexinteractivesystem.Tobeabletopredictaccurateheattransfer,andthustemperatures,infoodproductsinarefrigeratedtransportcontaineramodelneedstoinclude:??Heattransferbetweentheoutsideairandthecontainerwalls.

　　??Solarradiationontheoutsidesurfacesofthecontainerwalls,includingradiationre?ectedbytheground.

　　S.J.Jamesetal./InternationalJournalofRefrigeration29(2006)947e957955

　　??Conductionthroughthewalls.

　　??Heattransferbetweenthecontainerwallsandtherefrigeratedair.

　　??Heattransferbetweenthecontainer?ttingsandtherefrigeratedair.

　　??Heattransferbetweenthefoodandtherefrigeratedair.??Conductionwithinthefood.

　　??Airin?ltrationfromambientintothecontainer’scav-ity:eitherthroughdooropeningswhenthedoorisopenforfoodunloadingorthroughanygapsaroundthedoorandinthecontainer’sstructurewhenthedoorisclosed.Thelatterisrelatedtoexternalairspeed(vehiclespeed)ifthecontainerisonamovingvehiclewhenthedoorisclosed.

　　??Heatremovedfromtheairbytherefrigerationsystem.Thesedifferentaspectsrequiredifferentapproaches.Therearealsofactorsthatcanchangesubstantiallywithtimeduetoweatherconditions,timeofday,andmovementofthevehicleorshipthroughdifferentclimaticzones.Amodelshouldthereforebeabletomodelthedynamiceffectofthesechangesonthetemperatureofthefoodbeingtrans-portedandtheenergythathastobeextractedbytherefrig-erationsystem.Ideally,sincetheideaistopreservefoodthisshouldalsobelinkedtodynamicmicrobialgrowthmodels.Asofyet,nosinglecomputerprogramhasbeendevelopedthatcombinesallofthesedifferentaspects.

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