Class Note for ECE 449 at UA 2
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Date Created: 02/06/15
A I we 449549 ontinnons System mutualitth The Dymola ThermoBondGraph Library 0 In this lecture we shall introduce a second bondgraph library one designed explicitly to deal with convective ows 0 To this end we shall need to introduce a new type of bonds bonds carrying in parallel three distinct yet inseparable power ows a heat ow a volume ow and a mass ow These new busbonds together with their corresponding bus0juncti0ns enable the modeler to describe convective ows at a high abstraction level 0 The example of a pressure cooker model completes the presentation November 5 2003 start Presentation I we 449549 Glontinnnns System mutualitth Table of Contents Thennobond graph connectors Evaporation and condensation Acausal and causal bonds 0 Simulation of pressure cooker Busjunctions Free convective mass ow 0 Heat exchanger Free convective volume ow 0 Volume work Forced convective volume ow Forced volume ow 0 Water seppentine Resistive field 0 Bio sphere H Pressure cooker Capacitive elds November 5 2003 start Presentation A I we 449549 ontinnons System whalingl The ThermoBond Graph Connectors I 0 We shall need to introduce new thermobond graph connectors to carry the six variables associated With the three ows They are designed as an 11tuple E I henna y M lt1Eu Q m V gagg inwmg J jj Real 5cm quotEntropy ilnwquot Real q quotVolume flawquot 0WS Reel Melee quotMass nowquot Real 5 quotEntropyquot Real v quotValium generabked positions a Real M quotMESSquotv Real a quotDereeqenai Varlahlequot directional voriable d Boolean Exlsb True 1 substance eznsts lndlcatar van The thermobond connector icon is a red dot J November 5 2003 start Presentation I we 449549 Glontinnnns System mutualitth The ACausal ThermoBond Model We eggeegeg ene T979 v 3 4 l J Bquatlon A 1 Sdolq Mdul 391 1 ThBandConZ T ThBondCon1T ThBonannZ p ThBCdeDnl p ThBonann2 g ThEnndConl g TthnannZ Sdnt ThEDndCDnl Sdat TthndCanZ q ThBDndCDnl q ThBDndCunZ Mdot Thmmmmmme ThBDndCDnZ s ThBendCDnis ThBDndConZ v ThEDndCon1V ThBondConZ M ThBondCan1n 5 e TthdecmlExlst ThBDnannZ d 139 November 5 2003 start Presentation A I we 449549 ontinnons System mutualitth The ThermoBond Graph Connectors II 0 Like in the case of the general bondgraph library also the thermobondgraph library offers causal next to acausal bonds input Real T Temperature Input Real D Freesurequot Input Real 5 Glbhs Patentlal quot output Real Sdnt EntrDDV levquot 1 Dutput Real Cl VDlume i luv output Real 14th Mags f law output Real 5 Entrupy output Reel V VDJJAme output Reel M Hess Dutput Real El nlx actlcnal veritablequot output Eunlean Exlst quotTrue 1f substance BXJSESquot v JJ l I F J 394 Declarations of class November 5 2003 start Presentation EAEE I we 449549 Glontinnnns System mutualitth The ThermoBond Graph Connectors 111 g m m any Real T quotTamera A chutqu Real 1 quotPressure mu Reentl g 21th pummelquot input Real Sdot quotEntropy flaw Input Real El quotVolume flowquot input Real Mdnt Mass fitu DutDut Real 5 quotEntrDFY 4 output Real V quotVulumequot Output Real M quotMaSSquot output Real 1 quotDirectlunal vsrlahle Dutiut Boulean Erst quotTrue 1E substance exlsts Either the three efforts or the three ows are treated as input variables All other variables are output variables of the thermobond e and fconnectors November 5 2003 start Presentation ILA 449549 untinuuus y tml momma The Causal ThermoBond Blocks 1 51 Help USIng these connectors causal l El 3 M SIZJAI 1 therrno bond blocks can be defined 0 The fconnector is used at the side of the causality stroke 0 The econnector is used at the other TPQ side 3 e 0 The causal therrnobondgraph connectors are only used in the SdOtvq Mdot quot context of the therrnobond blocks Everywhere else the acausal therrnobondgraph connectors are to be used l November 5 2003 Start Presentation cm 449549 Ginn nunns System Muslim The BusOJunction n1 The junctions can now be programmed Let us look at a busOjunction with three bond attachments 39 7 r m 5 liqen lMl mayquot Real v3 quotValuingquot Real m3 quotMassquot Banlean Exist3 quotTrue 11 substance Existsquot LIVE ThEnndCunl 1 ThEcdecml p ThEcdecml g ThECndCle d ThEundCcml SdDL ThEcdecm dThEcdecm1 q ThEcdecml daeThEundCcui Mam ThEundCunl 5 ThEcdecml v m1 ThEcdecml n Exlst1 ThEcdecml Exlst 1392 ThEDndCcmZ r ThEundCunZ p ThEDndCCInZ g ThEDndCcmZ d ThEnndCCmZ Sdut ThEDndCCInZ dThEundCcm2 q ThEDndCunZ daerhnundcgnz 1mm ThECdecmZ s ThEcdeCmZ v ThECndCCmZ n 2 ThEundC nZ Exist ThEcdecIn r ThEcdecln3 p ThEDndCCIn3 g ThEDndCun daerhnundcgna Sam ThECdecmS dThEldeDn3 q ThEDndCun3 dThEcdecm3 Mam ThEDndCcm s ThEundCun v ThECdecIn u Exlst3 ThEundC nS Exist m a E u Wu H u u m at s uuumumuuur uuuNuNuuu A new 449549 Giuntinuunx system mmml Special BusOJunctions I 4 9210510 miter ololn val rm em wwsww mm HIE f quot Extends Intetf ea OnEO J equarxon l a s Sdct r u Easiest Exxst quotTrue 1f substance exlstzsquot Real 2 quotElcmdgraphl effart lilac n Real 2 quotElnndgraphl flawquot LlJ I m mu DEFIKltU1ED mm 15 maanchm T ThEIDndC nl p ThEundCclnl g c TthndCclnl detTthlndCanl Sdut EUndC nl daerhnundcgnl q t 7 ThEnndCunl dThBundCcn1 Ham ThECIndCclnl 5 ThElundCunl v maanchm M x15 ThBCIndCCuLl Exxst DaleanOutPartl Slgnal1 Exlst Handcunl a Bunann1 a eBanacUm f Boolean signal connector Thermoebond Regular bond connector connector u uuununuuun 4 Lt November 5 2003 Start Presentation I was 449549 Luminous System manual Special BusOJunctions II am Mmmmklm o T P November 5 2003 Start Presentation AL e 449549 ontinuuu 5p tw1 nheling The Heat Exchanger November 5 2003 Start Presentation A c c 449549 outinuuu system nomad The ThermoBond Heat Exchange Element J Heat is only exchanged if both substances to the left nd to ilg the right exist A o 70 The conductance is split in two Hali39 goes to the left half to the right Conversion from ther mo bonds to regular bonds The speci c Ihermal conductance l is imported inlo the model as a modulating signal November 5 2003 Start Presentation Eh I we 449549 Summons system mmml The Volume Work November 5 2003 Start Presentation 1A5 I it 449549 un nuonx System mammal The Pressure Volume Exchange Element l 777 m IiIllsw 1 u A Jam name PVE mNV G1 We pick up the two pressures The difference between the two pressures causes a volume ow The surplus power is split in two to be converted into additional entropy The generated entropy is delivered back to the thermal ports November 5 2003 Start Presentation A I we 449549 Giantinnons System whalingl Forced Volume Flow I W7 anal ntm eeggng Extends Interfaces TutFart Reel q quotFereea Vulume flawquot Eeeleen sq True 1e lew rum Prlmarv t eeeenaeryquot Reel Sref quotReference Entr pvquot Reel quotReference Vslume Reel quotReference Meeequot Reel rhcl DEnsltV e quotSpeelne Entr pvquot Reel Tref quotReference temperaturequot Reel 5am quotEntrapy belenee can he negeuve Reel Delta quotPressure 11 feral ACEquot Eeeleen Exlst l x Vre z Mref Ree l mSF A quotTrue 1 there ls e rlewquot n2g Equat 1 cm CI InFurcl elenelrll 39 11 q 12 ql Sq q gt u Sref e 1 sq than 51 elee 52 Vref e 1i sq than v1 elee v2 Mref e if sq than M1 elee M2 EDndCcnl e eBendCenl dBundCDn1 f at T1 e T2x5dclt1 121 e p25l gl 7 92Hdut1 131 7 p2 ea and Exlstl er en sq end 15813122 November 5 2003 A Dederemuns at Class I we 449549 Glontinnnns System whalingl A Forced Volume Flow II represent eg a pump or a compressor because i discussed later in this lecture The model presented here cannot yet be used to t doesn t consider the power needed to move the uid around 0 The model is acceptable to describe small mass movements such as pressure equilibrations between the bulk and a mathematical boundary layer An improved forced volume flow model shall be November 5 2003 Start Presentation one 449549 continuous system mnamgl The Resistive Field Ilm generated emrum 1g is reimeneu in me 1 dire ton m llu III 1 0 WI Due to the potsugialmE differences in the P O Proportional mas we puteu alsp and heat quot0W5 3quot additional entropy ESE 2 caused by the forced being 33 th volume now my 5 mSF O Forced volume ow November 5 2003 Start Presentation ttlit 449549 aluminum System Whaling I Pressure Equilibration With Constant Volume 0 Sometimes it is useful to allow a mass ow to take place While the volume doesn t change remember the gas cartridge z 1L 3 Pressure equlllbratlon causes a 3 2 volume ow to occur Bl A ow sensor element measures 39 the volume ow taking place fez 5 F1 M at w 7 A counter volume ow of equal size is forced November 5 2003 Start Presentation A I we 449549 ontinnons System mmml The Pressure Cooker I November 5 2003 Start Presentation I we 449549 Glontinnnns System mutualingl The Pressure Cooker II November 5 2003 Start Presentation 10 RM EF IHVE H39E Vapor r vel PVE k F PVE e z SE V lass 39 957 CF39TML IO a 0 rFIIjEI39E lee EL a HEIae gt v V53 mu Q w if w r HE S was Exammng 391 WE e 5 5 a he CF H E 57 glue C 7139 C i C r 1 lt m 390 o quotI 613 O l O a I 449549 Stuntman System mowing I Let us look at the capacitive field for air Linear ca acitive eld derg C I By integration derg 1quot e C g Nonlinear capacitive eld der 1quot 11 22 Capacitive Fields galg aj extends Interfaces paeerveOmepert a parameter Real 5 81010184 quotEnttclpv 1t uCI arrquot parameter Real v 33112221 quotValuing rt nCI altquot parameter Real K quotMax 1f nCI sir parameter Real epel and Heat eagaertv at arr at constant pressurequot parameter Real REI 2372 Gas eeeetamu parameter Real EpSEU puns wSmallest maee dretrnpurehable rm zere parameter Reeleam f1 tialse quotTrue 1 tretrtreue Values are usedquot parameter Real Tit 293 53 quotFretrtreue temperature re nD arr parameter Real piflcl m1 Fretrtreus preeeure 1f me arrquot Real lert quotMass at arr Real Silnt Entrqu er a Real 77an Vulume et a1 Real v quotHeat eapaerty e arr at Gnstant volume Real v quotSpeclil vulumequot Real e 39Specliu entropy Real lag quotNatural legarrtlrm at Speclill vulumequot a f equatrem r derler Mm 3E3 rat 5e32 derg q nt gt epeu rt pare them ventneat elee n artneat Madellca Hath luglViintHixntL else MD elee vn November 5 2003 elee 5p Declarations DI class 11 15 449549 hummus system mnheliml Evaporation and Condensation I The models describing evaporation and condensation are constructed by interpolation from steam tables a 415 Saturation Dsnz pressures 53mm am T2 Saturation vol 5 S 55175 Entllalpy tamper E November 5 2003 E A 5931 449549 untinuoux System mowing Evaporation and Condensation II a il equatma DSaLl u pSatz u VSaLl u VSatZ u T2 parameter Real Re mm H a 11 Real psatiliq Saturatlu Real pSatigas quotSaturatlcu gait 2 1332 Real VSabillq quotSaturatm m z we y Real V5atgas quotSaturatlm as a 32 y39 Real hhcul quotEnthalpy e Hbmu V Real Vgas quotGas valume 39 eai gael Part1el gas in pgas pzavzwgae EB 01 libml u 1i pSac7hq lt p1 and Exxstl then Reepl pSalilzlq else n Real Mcond Meend 1f vSatagae gt P955 and Exlstz then Rcp5atgas e was elee u Boolean Ed 39 Hdatl mzml Mamid Real Daltanot nautz Mdutl Boolean Exlst quotTrue 1 5 a1 a Mbnlli l ac hu a MeenaaeVSatJas Real Mref quotReference ma qz q1 Real 31 Mass fractlnnquot d udetl gt a Real Sdtmlisux Deltaodm 91 e gzmmatl m 7 pthl Real Sth27aux Exist m and Exxstl or not Ed and EXISCZ Real Vsteam Maxmum vol me if d then m else 142 Real humi Relatlve humi x1 at East than MdnLIMrei elee n Real hum2 Relatlve humi Sdatz anx if EXJSLZ than Sdutl DellanDL T1 T2Sdut1T1 ElSB Sdntl Sdotliaux lf Exlstl than SdaLZ DelLanDt T1 T2Ednt2l 2 ElSB SdDLQ Sdcltl 1f fd than x39li39Sl 1 bbDili MthlTl else Sdutl aux SEICWZ 1f Ed then Sdot2aux else 814152 hbolllthDKZTZ A bit messy Vsteam 1p2p53tigas was huml pgespSa a humZ 1 vzvSteaa November 5 2003 A I we 449549 ontinnons System mutualitth Simulation of Pressure Cooker We are now ready to compile and simulate the model I In All Wateri T AM T A m CCellxgzPublicationsEthGzaphsICEEH1chng 400 e translacel lodelquotPrassuzecnokexPtassuratuuketquot remleem started 3 2E mm muss when mlm em 1min seals em 2221 ememes fauna 135 parameter hound Valuables Euund 350 6413 3113 valuables mm 2251 remalnlntj me dEpenden Variables nmhee 340 32n 3007 2am t i u ADDU sum 1 2E4 1 BEA 25A November 5 2003 start Presentation I we 449549 Glontinnnns System mutualitth Simulation Results I Temverulums zen a Heating is suf ciently slow that the temperature values of the different media are essentially indistinguishable The heat exchangers have a smaller time constant than the heating During the cooling phase the picture is very different When cold Water is poured over the pressure cooker air and steam in the small boundary layer cool down almost instantly Air and steam in the bulk cool down more slowly and the liquid Water cools down last November 5 2003 start Presentation l3 A I we 449549 ontinnons System mutualitth Simulation Results II Pressuu The pressure values are essentially 7 WWW indistinguishable throughout the 7 in enquot We 539 s1mulation During the heating phase the pressures rise first do to rising temperature After about 150 seconds the liquid Water begins to boil after Which the pressure rises faster because more steam is produced Water vapor occupies more space at the same r temperature than liquid Water The difference between boundary layer and bulk pressure values in 09 gt33 mm WW 0WD 95 the cooling phase is a numerical artifact Passmmm Mo November 5 2003 start Presentation I we 449549 Glontinnnns System mutualitth Simulation Results 111 W quot2quot The relative humidity decreases at first because the saturation 9 pressure rises With temperature an ie more humidity can be stored l at higher temperatures 75 ml As boiling begins the humidity 5 rises sharply since additional 23 50 vapor is produced 9 In the cooling phase the humidity 20 quickly goes into saturation and stays there because the only Way 20 to ever get out of saturation again to w t Would be by reheating the Water Marin 4 m 541 V J 5411 2 11 255 Meg November 5 2003 start Presentation A I we 449549 Giantinnons System mutualitth Simulation Results IV 55me The mass fraction de nes the m Hiawwm percentage of Water Ivapor contained in the airsteam mixture Until the Water begins to boil the mass fraction is constant It then rises rapidly until it reaches a new equilibrium Where evaporation and condensation balance out mm mm m During the cooling phase the boundary layer cools down quickly and can no longer hold the Water vapor contained Some falls out as Water Whereas other steam gets pushed into the bulk a m mo 530 mm temporarily increasing the mass fraction there even further November 5 2003 start Presentation I we 449549 Glontinnnns System mutualitth Free Convective Mass Flow 0 We are now ready to discuss free convective mass ow such as mass ow occurring in a segment of a pipe 0 The convective mass ow occurs because more mass is pushed in from one end pushing the mass currently inside the pipe segment out by the other end 0 To this end we need to introduce some more models November 5 2003 start Presentation 15 A I we 449549 ontinnons System mutualitth The Forced Flow Source 0 This model describes an element of the regular bond graph library r i 4121 maa gwy equatlun f1 s eiasii e242 A l Luvquot November 5 2003 start Presentation Ah I we 449549 Glontinnnns System mutualitth Density and Specific Entropy I t srl eet 33 t SF39AT 1 Si a C th Cth Cth Cth fi q o o o 0 q 1amp5 q T T T I l xo Ea Iliad0 All 0quot As mentioned some lectures ago we shall need modulated ow sources as introduced one slide ago that are modulated by the specific entropy andor the specific mass ie the density November 5 2003 start Presentation l6 A cm 449549 Glan nnous pstem mmm Density and Speci c Entropy II 0 These models are created as blocks a r 5151 gagga nP rLl slgnsl 2 1 nFanl signal 3 1 Volume ow Corresponding mass ow Vx1 2 November 5 2003 Start Presentation Z L lam 449549 Giontinnous 51mm mnam The State Sensor 0 Many elements that are related to substances require state information This is generated by a specialized theImObond the socalled state sensor element AWE ll vlFIOIVl Al lHl Tp9 3 equatian d OutPDrt1slgnal1 eThBDndCanl s OutPartl signal2 eThEnndCDn1V OntPDrtl Slgnal3 eThEmnann1M EamlaanOutPDrtl signal1 eThBondConl Exist n u u Scionq Mdot SVM E if l November 5 2003 Start Presentation l7 A me 449549 Ginntinunus system Muslim Free Convective Volume Flow 0 We are now ready to describe the free convective volume ow IW39 n Ol ll Iv2mm x hdmu November 5 2003 Start Presentation A3 em 449549 hummus 93mm muslin J E quot Volume ow November 5 2003 Start Presentation 18 I ma 449549 Gluntinuuus System mnamgl sz SwZ a8wv 1lt D me l aggt8w The volume flow is modeled as a Wave equation With friction The friction is in parallel with the inertial The parallel connection Was simpli ed using the diamond rule The ow is measured using a flow sensor element The additional entropy generated by friction is reintroduced in the downWind direction ie in the direction of the flow Switch elements are used to determine the reintroduction point Nonlinear flow sources are used to model the parallel thermal and mass flows These are computed by converting the volume flows to consistent entropy and mass flows November 5 2003 Start Presentation I am 449549 Ginn nuons 91mm mammal m a wv ue 1 0 ae1 w5w State sensor elements are used to determine the current values of volume entropy and mass Upwind state information is being used to convert the volume flow into consistent entropy and mass flows Since entropy doesn t need to be preserved the nonlinear flow source is inserted directly into the thermal branch Since mass flow must be preserved the nonlinear ow source is inserted under a ljunction in the mass flow branch November 5 2003 Start Presentation 19 AL i It 449549 Summons system whalingi The Gibbs equation can be written as or more conveniently as Thus the change of the internal energy can be written as 9mm In a segment of pipe both the heat and the internal energy are conserved thus Hence November 5 2003 Start Presentation A i 2039 449549 Gluntinuons system alumni Forced Convective Volume Flow 0 We are now ready to describe the forced convective mass ow mums November 5 2003 Start Presentation 20 y I am 449549 Summons system mammal The Water serpentine I Wm OWMWOWW L Plslou 7 mechanics 1hne Rm m November 5 2003 Start Presentation Aquot I ma 449549 Ginntinnous System whalinggl The Water Serpentine II 0 The pump forces a ow thereby creating a higher pressure at the out ow while creating a lower pressure at the in ow Mass is transported through the pump with the volume Since the mass is getting condensed it occupies less space Thus there is surplus volume that gets used to nance the mass transport in the Gibbs equation 0 In the pipe segments the pressure is gradually reduced again thus each pipe segment has a higher pressure at the in ow than at the out ow The mass thus expands and the volume consumed in the pump is gradually given back so that the overall volume in the water serpentine is being preserved November 5 2003 Start Presentation i3 l we 449549 continuous 5111mm gnawing The Water serpentine III Wm CH We are now ready to simulate this Wm lt CH system an as V D 1 0 wet VF he 0 1 lt LL 7 m m 11mm amlnlmmn 5 l lgt s m TF W Pxnf manuals 21112 and ms smug n LVL t Tl m fl 1 I39mA B E T 7 License number m 39 m V e m CEelllexE1 EE449BondL1b o r VF me o a mammary Sezpentiz mquot Translanlon scam w E E Calais and 3551 Scalar Equations a 2 R2 ables found 0 O I ZI 1 W W I ha mm dEpendenn vazlables Not bad 7 I m November 5 2003 Start Presentation A I 6136 449549 Continuous 5113am mmml Comparison With Biosphere II In the Biosphere II model only the sensible and latent heat were modeled The mass ows were not considered Consequently you never know in the Biosphere II model how much water is available where It is always assumed that the pond never dries out and that the plants always have enough water to be able to evaporate in accordance with their temperature and saturation pressure In the case of the pressure cooker model both the mass ows and the heat ows were modeled and simulated Consequently the case is caught where all the water has evaporated while the airsteam mixture is still not fully saturated November 5 2003 Start Presentation 22 A we 449549 ontinnons System whalingl References I 0 Cellier FE and J Greifeneder 2003 Object oriented modeling of convective ows using the Dvmola thermo bond graph librarV Proc ICBGM 03 Intl Conference on Bond Graph Modeling and Simulation Orlando FL pp 198 7 204 Greifeneder J and FE Cellier 2001 Modeling multi element systems using bond graphs Proc ESS OI European Simulation Symposium Marseille France pp 758 7 766 Bruck D H Elmqvist H Olsson and SE Mattsson 2002 Dvmola for Multi Engineering Modeling and Simulation Proc 2quotd International Modelica Conterence pp 5 5 1 8 November 5 2003 Start Presentation ltIJEIgt we 449549 Glontinnnns System whalingl References II Cellier FE 2001 The Dvmola BondGraph Library Cellier FE 2001 The Dvmola ThermoBond Graph Library Cellier FE 2002 The Dymola Pressure C ookerModel Cellier FE 2002 The Dvmola Water Serpentine Model November 5 2003 Start Presentation ltnrgt 23