Thermal-Systems-with-Simscape3e

Copyright©2014.TheMcGraw-HillCompanies,Inc.SystemDynamics,ThirdEditionWilliamJ.PalmIIIUsingSimscapeTMforModelingThermalSystems:DynamicsofaQuenchingProcessPowerPointslidestoaccompany1Theseslidesareintendedtobeusedwiththeauthor’stext,SystemDynamics,3/e,publishedbyMcGraw-Hill©2014.AcknowledgmentsTheauthorwishestoacknowledgethesupportofMcGraw-Hillforhostingtheseslides,andTheMathWorks,Inc.,whosuppliedthesoftware.NaomiFernandes,Dr.GeraldBrusher,andSteveMillerofMathWorksprovidedmuchassistance.Dr.Brusher’scontributionsformedthebasisformanyoftheSimscapemodelspresentedhere.MATLAB®,Simulink®,andSimscape™areregisteredtrademarksandtrademarksofTheMathWorks,Inc.andareusedwithpermission.2TheequationsandmathsymbolsintheseslideswerecreatedwiththenewequationeditorinPowerPoint2010,andthusmaterialcontainingtheseelementswillappearasgraphicswhenviewedinanearlierversion.Simscape™extendsthecapabilitiesofSimulink®byprovidingtoolsformodelingandsimulationofmulti-domainphysicalsystems,suchasthosewithmechanical,thermal,hydraulic,andelectricalcomponents.Inthispresentation,wewillshowyouhowtoutilizeSimscapetoconstructmodelsofthermalprocesses.Onesuchprocessisquenching,whoserepresentationisshownbelow.Wewillstartwithasimplemodel,inwhichweassumethatthebathtemperatureTbremainsconstant.Thedifferentialequationmodelofthiscaseissimpleenoughtobesolvedanalytically,sowecanusethesolutiontocheckourSimscapemodel.ThenwewillconsiderthecasewhereTbcanvarywithtime.3Example1:QuenchingwithConstantBathTemperature:(Example7.8.1inSystemDynamics,3/e)Hardnessandotherpropertiesofmetalcanbeimprovedbytherapidcoolingthatoccursduringquenching,aprocessinwhichaheatedobjectisplacedintoaliquidbath(seethefigure).Consideraleadcubewithasidelengthofd=20mm.Thecubeisimmersedinanoilbathforwhichh=200W/(m2·°C).Theoiltemperatureis𝑇𝑏.AsshowninExample7.8.1,accordingtotheBiotcriterion,wemaytreatthecubeasalumpedparametersystemwithasingleuniformtemperature,denotedT.Wewilluse1.134×104kg/𝑚3forthedensityofleadand129J/kg·Kforthespecificheat.WewanttodevelopasimulationmodeltopredictthetemperatureTasafunctionoftime,foragivenconstantbathtemperature𝑇𝑏.4Thethermalcapacitanceofthecubeiscomputedas𝐶=𝑚𝑐𝑝=𝜌𝑉𝑐𝑝=1.134×1040.023129=11.7J/K.ThethermalresistanceRisduetoconvection,andis𝑅=1ℎ𝐴=12006(0.02)2=2.08K∙s/J.Applyingconservationofthermalenergy,weobtainthemodel𝐶𝑑𝑇𝑑𝑡=1𝑅𝑇𝑏−𝑇Substitutingthegivenvaluesanrearranginggives24.4𝑑𝑇𝑑𝑡+𝑇=𝑇𝑏If𝑇𝑏isconstant,themodelshowsthatthesteadystatecubetemperatureTwillequal𝑇𝑏asexpected.Thetimeconstantis24.4s.Ifthebathislargeenoughsothatthecube’senergydoesnotappreciablyaffectthebathtemperature𝑇𝑏,thenwhenthecubeisdroppedintothebath,thetemperature𝑇𝑏actslikeastepinput.Thecube’stemperaturewillreachthetemperature𝑇𝑏inapproximately4τ=98s.56NowletusbuildaSimscapemodel.Wewillneedthefollowing:1.amodelofthethermalmass,2.amodeloftheconvectiveresistance,3.areferencetemperature,4.asourcetemperaturetospecify𝑇𝑏,and5.awaytomeasurethecubetemperatureT.ThefollowingthreeblocksareavailableintheSimscapeFoundationLibraryThermalThermalElementslibrary.1.TheThermalMassblock.2.TheConvectiveHeatTransferblock.3.TheThermalReferenceblock.TheIdealTemperatureSourceblockisintheSimscapeFoundationLibraryThermalThermalSourceslibrary.TheIdealTemperatureSensorblockisintheSimscapeFoundationLibraryThermalThermalSensorslibrary.Selectandplacetheseblocksasshownonthenextslide.7Wewilldiscusstheseblocksinmoredetailinthenextfewslides.8ThermalMassBlock:StudytheBlockParametersdialogbox,whichshowsthedefinitionoftheblock.Theblockrequiresthreeparameters.Typeintheirsymbolsasshown.Theserepresentthecubemassm,thespecificheat𝑐𝑝,andtheinitialcubetemperature𝑇0.Notetheunits,whosedefaultvaluesarethesameasoursforthisexample.NotethattheunitsofthespecificheatareselectedasJ/kg/KwhiletheinitialtemperaturehasunitsofC.ThisisreasonablebecauseDK=DC.Moreover,Simscapeinternallyaccountsfordifferencesinunitsandmakesthenecessaryconversions.9ThermalReferenceBlock:ItsBlockParametersdialogboxshowsthedefinitionoftheblock.Itrequiresnoparameters.10ConvectiveHeatTransferBlock:Thismodelstheconvectiveresistance.StudyitsBlockParametersdialogbox,whichshowsthedefinitionoftheblock.Itrequirestwoparameters.Typeintheirsymbolsasshown.TheserepresentthecubesurfaceareaAandtheheattransfercoefficienth.Notetheunits,whosedefaultvaluesarethesameasoursforthisexample.Again,wearemakinguseofthefactthatDK=DC.11IdealTemperatureSourceBlock:ItsBlockParametersdialogboxshowsthedefinitionoftheblock.Itrequiresnoparameters.12IdealTemperatureSensorBlock:ItsBlockParametersdialogboxshowsthedefinitionoftheblock.Itrequiresnoparameters.13NowinsertandconnectthePS-SimulinkConverterblock,whichisintheSimscapeUtilitieslibrary.Connectitsinputtotheloweroutputport(T)ofthetemperaturesensorasshownbelow.ThisportprovidesameasurementofthebathtemperatureT.TheBportisconnectedtheThermalReferenceblock.DatafromaSimscapemodelcanbefurthermanipulatedinSimulink.WewilluseSimulinktoconvertthetemperaturedatatodegreesC.InsertaSumblockandtheScope.The“KtodegC”blockissimplya