Modeling and simulation of thermal power plants with thermosyspro a theoretical introduction and a p by Ebook Home

Theoretical

Guide Baligh El Hefni

Visit to download the full and correct content document: https://textbookfull.com/product/modeling-and-simulation-of-thermal-power-plants-wit h-thermosyspro-a-theoretical-introduction-and-a-practical-guide-baligh-el-hefni/

More products digital (pdf, epub, mobi) instant download maybe you interests ...

Modeling Simulation and Control of a Medium Scale Power System 1st Edition Tharangika Bambaravanage

https://textbookfull.com/product/modeling-simulation-and-controlof-a-medium-scale-power-system-1st-edition-tharangikabambaravanage/

Practical Building Energy Modeling with OpenStudio: A Guide for Students and Professionals Team Educohack

https://textbookfull.com/product/practical-building-energymodeling-with-openstudio-a-guide-for-students-and-professionalsteam-educohack/

Healthcare Simulation Research A Practical Guide Debra Nestel

https://textbookfull.com/product/healthcare-simulation-researcha-practical-guide-debra-nestel/

Thermal process modeling proceedings from the 5th

International Conference on Thermal Process Modeling and Computer Simulation 1st Edition B. Lynn Ferguson

https://textbookfull.com/product/thermal-process-modelingproceedings-from-the-5th-international-conference-on-thermalprocess-modeling-and-computer-simulation-1st-edition-b-lynnferguson/

Introduction to Modeling and Simulation with MATLAB and Python 1st Edition Steven I. Gordon

https://textbookfull.com/product/introduction-to-modeling-andsimulation-with-matlab-and-python-1st-edition-steven-i-gordon/

Bayesian Analysis with Python: A practical guide to probabilistic modeling Osvaldo Martin

https://textbookfull.com/product/bayesian-analysis-with-python-apractical-guide-to-probabilistic-modeling-osvaldo-martin/

Managing Biogas Plants: A Practical Guide 1st Edition

Mario Alejandro Rosato

https://textbookfull.com/product/managing-biogas-plants-apractical-guide-1st-edition-mario-alejandro-rosato/

Advances in Power Engineering Part A Advances and Challenges Part A Thermal Hydro and Nuclear Power First Edition Badescu

https://textbookfull.com/product/advances-in-power-engineeringpart-a-advances-and-challenges-part-a-thermal-hydro-and-nuclearpower-first-edition-badescu/

Systems Architecture Modeling with the Arcadia Method A

Practical Guide to Capella 1st Edition Pascal Roques

https://textbookfull.com/product/systems-architecture-modelingwith-the-arcadia-method-a-practical-guide-to-capella-1st-editionpascal-roques/

Baligh El Hefni · Daniel Bouskela

Modeling and Simulation of Thermal Power Plants with

BalighElHefni • DanielBouskela

BalighElHefni EDFR&D

Chatou,France

DanielBouskela EDFR&D

Chatou,France

ISBN978-3-030-05104-4ISBN978-3-030-05105-1(eBook) https://doi.org/10.1007/978-3-030-05105-1

LibraryofCongressControlNumber:2018962771

Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart ofthematerialisconcerned,speciﬁcallytherightsoftranslation,reprinting,reuseofillustrations, recitation,broadcasting,reproductiononmicroﬁlmsorinanyotherphysicalway,andtransmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped.

Theuseofgeneraldescriptivenames,registerednames,trademarks,servicemarks,etc.inthis publicationdoesnotimply,evenintheabsenceofaspeciﬁcstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.

Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthis bookarebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernorthe authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardto jurisdictionalclaimsinpublishedmapsandinstitutionalafﬁliations.

ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland

Preface

Modellingandsimulationisbecominganessentialtooltoassessthebehaviorof largecomplexenergysystemsagainstevermorestringentsafety,availability, environmental,economicandsocietalconstraintspromptedbytheongoingenergy transition.Indeed,thelargenumberofrequirementstobeconsideredandthe complexphysicalinteractionsbetweensystemsandtheirenvironmentcallfor efﬁcientmeansforquantitativeandqualitativeanalysisofthesystemsphysicaland functionalbehavior.

Systemmodelling,alsocalled0D/1Dmodelling,isthedisciplineatthecrossroadsbetweendetailed3Dphysicalmodellingsuchascomputational ﬂuid dynamicsandfunctionalmodellingsuchascontrolsystemdesign.Itaimsatrepresentingthephysicalbehaviorofthewholesystemusing ﬁrstprinciplephysical laws.Theselawsareaveragedinspaceandareclosedwithempiricalcorrelationsin ordertocomputethequantitiesofinteresttotheengineerwhileavoidingunrealistic assumptionsandminimizingcomputationaltime.Physicalmodellingismostoften usedforsimulationwhichconsistsinpredictingthesystem’sbehaviorfromgiven initialconditionsoveragiventimeperiod.Thanksto0D/1Dmodelling,thetime periodscanextendoverseveraltimescales(fromsecondstoyears),andsimulation canusuallybeperformedmuchfasterthanrealtimeonordinarylaptops.This convenienceisespeciallyneededforsimulationoverlongtimeperiods.0D/1D modellingisalsousedforassessingandmonitoringthesystemcurrentstatein combinationwithothertechniquessuchasdataassimilationthataimatusingthe knowledgeembeddedinthemodelstoimprovedataquality.

0D/1Dmodellingcancoverthewholesystemengineeringlifecycle,frompreliminarydesigntocommissioning,operationandmaintenance.Itcanbeusedfor diversetaskssuchastheoptimalsizingofarefuelingcavity,theoptimalplant startupthatconsistsinminimizingstartupdelaywhilemeetingoperationalconstraints,theassessmentofsteamgeneratorcloggingwhiletheplantisinoperation, themonitoringanddiagnosticsofefﬁciencydegradationduetothermallosses, operatorstraining,etc.

Thisbookisaboutthescienceandartofphysicalsystemmodellingappliedto thermalpowerplantswithalibraryofcomponentmodelscalledThermoSysPro whichisusedatEDF(andalsootherorganizations)fortheengineeringofpower plantsatthedesignandoperationphases.Theambitionistoshowhowtomake powerplantmodelsthatprovideconvincingsimulationresults.Tothatend,it containsEDF’slongstandingexperienceinpowerplantmodellingandsimulation. Theequationsusedinthecomponentmodelsarepresentedindetailwiththeir validitydomainsusingmathematicalnotationinatool-independentway.Theyare justi ﬁedwithrespecttofundamentalknowledgeinthermodynamicsandheat transferusinganalyticalderivationsorproofswhennecessary.Foreachcomponent model,asmalltest-casewithsimulationresultsisgiven.Modelsofthermalpower plants(fossilfuel ﬁredandsolar)arepresentedwithresultsofnumericalsimulation andpracticalhintsonhowtobuildthemwiththelibrary.Inaddition,comparison withrealmanufacturerdataisprovidedinthecaseofacombinedcyclepower plant.Someinsightisalsogivenontheinternalstructureofthelibraryforthe interestedreader.

Thewholespaceofthebookisdedicatedtothephysicalandmathematical aspectsofpowerplantmodelling.Althoughtheyareimportant,thenumerical aspectsarenotconsidered.ThisismadepossiblethankstotheModelicatechnology thatemergedattheturnofthetwenty-ﬁrstcenturyandthatisnowfullyoperational inseveralcommercialandopensourcetools.Itallowstotranslateautomatically modelsequationsintoefﬁcientsimulationcode.Therefore,althoughthisbookrelies onModelicatoproducenumericalresults,itisnotanintroductiontomodelingand simulationwithModelica,soitdoesnotpresentthelanguagenordoesitmention theassociatedtechniques.Moreover,thelessonslearnedfromthisbookcanbeused withanykindoftool,notonlyModelicatools.

Thebookisintendedtostudentsandconﬁrmedpractitionersinpowerplant modellingandsimulation.Allmodelspresentedinthebookcanbefoundinthe ThermoSysProlibrarywhichisreleasedunderopensourcelicenseandfreely availabletothepublic.

Chatou,FranceDanielBouskela October2018BalighElHefni

Acknowledgements

FirstthankstothePRISMEdepartmentofEDFLabfortheirsupporttothe accomplishmentofthisbook.

ManythankstoAudreyJardinforfruitfulcommentsandtoBenoîtBridefor providingcombustioncomponentmodels.

ThankstoallThermoSysProenthusiasticusersfortheircommentsandfeedback onthelibrary.

ThankstotheModelicacommunitywhodevelopedtheModelicalanguagethat madeThermoSysPropossible.

ThankstoPeterFritzsonandtheOpenModelicateamfortheirsupportof ThermoSysProintheOpenModelicaopensourceplatform.

Finally,thankstotheEurekaITEAclusterprogramanddedicatedteamfor providingtheinnovativeframeworkthatboostedthedevelopmentofModelicaand ThermoSysPro.

5.2.2ComputingtheVolumeSpeci

6.2TypicalUsageofPowerPlantModels

6.3TheThermoSysProLibrary

6.4HowtoDevelopaPowerPlantModel

6.4.1UsingtheThermoSysProLibrary

6.4.2ConceptualSteps

ﬁculty:FindingtheSteady-State

6.4.4PracticalSteps

6.4.5PracticalHints

6.5DynamicModelofaRealCombinedCyclePowerPlant

6.5.1DescriptionofaCombinedCyclePowerPlant

6.5.2DescriptionofthePhuMyCombinedCyclePower

6.5.3DescriptionoftheModel

6.6DynamicModelofaOnce-ThroughSupercriticalCoal-Fired

6.6.1DescriptionofaOnce-ThroughSupercritical Coal-FiredPowerPlant

6.6.2DescriptionoftheModel

6.7DynamicModelofa1MWeConcentratedSolarPowerPlant (CSP)withaPTSC ................................

6.7.1DescriptionoftheConcentratedSolar

7.2.2Nomenclature

7.2.3GoverningEquations

7.2.4ModelicaComponentModel:

7.2.5Test-Case

8CombustionChamberModeling

8.1CombustionChamberforaGasTurbine

8.1.1ModelingPrinciples

8.1.2Nomenclature

8.1.3GoverningEquations

8.1.4ModelicaComponentModel: GTCombustionChamber

8.1.5Test-Case ................................

8.2CombustionChamberforBoilerFurnace

8.2.1ModelingPrinciples

8.2.2Nomenclature

8.2.3GoverningEquations

9.2.1Nomenclature

9.2.2Assumptions

9.2.3OverallHeatTransferCoef

9.2.4ConvectiveHeatTransferCoef

9.2.5TheLogMeanTemperatureDifferenceMethod

9.2.6TheEffectivenessandtheNumberofTransfer UnitsMethod(NTU)

9.2.7TheUAMethod

9.2.8TheEfﬁ

9.2.9TakingintoAccountPhaseTransitions

9.2.10SimpleHeatExchangers

9.4.2TubeBundleHeatExchanger

9.4.3Shell-SideHeatExchangerModeling

9.5.1Introduction

9.5.2DynamicModelingofaWaterHeater

9.5.3DynamicModelingofaSimpleCondenser

13.8.4ModelicaComponentModel:

17.1.3VolumeComponentsandFlowComponents

17.1.4ConnectingVolumeComponentstoFlow

17.1.5StructureoftheConnectors

17.2.1CurrentSituationwithThermoSysProV3.x

17.2.2FutureDirectionsforThermoSysProV4.x

AbouttheAuthors

Dr.-Ing.BalighElHefni has35yearsofresearch,industryandteachingexperience.Hespecialisedinphysicalmodellingofvarioustypesofpowerplants. In2002,hejoinedEDFResearch&Developmentdivision(R&D).Hecontributed tothedevelopmentofpowerplantsmodelingactivities,withintheEDFandits subsidiaries,thankstotheuseofThermoSysProlibrary(developedbytheauthors). Thishasallowedhimtocollaboratewithmajorindustrialplayers,researchand academicsintheframeworkofmanyEuropeanprojects(DLR,Dassault-Systèmes, Dassault-Aviation,Siemens,IFP,OpenModelica …),inwhichEDF’scontribution wasrecognized.Themainobjectivesoftheseprojectsare:toimprovethemodeling languages,thetools,themethods(statestimation),andtoextendthemodeling domains(multi-modesystems,propertymodeling).Theexperienceinthepower plantmodelinghasallowedhimtodevelopsolidcompetenciesandaspeci ﬁc know-howthathasallowedhimtoexpandouractivitytowardsthedevelopmentof solarpowerplants,andcollaboratewithCENER(Spain),ChineseAcademyof Sciences(China),CEA(France)andotherpartners.Heisinchargeoftraining coursesofthemodellingofpowerplantsandenergysystems,forEDFstaffand partners.HewasalsoinchargeofthesametrainingatEcoleCentraledeParis “EngineeringTrainingSchool”

DanielBouskela graduatedfromEcoleCentraledeParis(France).Heiscurrently SeniorResearcheratEDFResearchandDevelopmentDivisionwherehismain interestsareinthedomainofthemodelingandsimulationofenergysystems.

DanielBouskelaisstronglyinvolvedinEuropeanandFrenchcooperative projects.HewasinparticulartheleaderoftheEuropeanMODRIOproject.Heis theco-authoroftheopensourceThermoSysProModelicalibraryforthemodeling andsimulationofpowerplants.

Chapter1 IntroductiontoModelingandSimulation

Abstract Powerplantmodelingplaysakeyroleinmanypurposes,likeprocess designassessment,theassessment,andpredictionofplantperformance,operating procedureevaluation,controlsystemdesign,andsystemprognosisanddiagnosis. Thepresentchapterintroducesthedisciplineof0D/1Dmodelingappliedtothermal hydraulicsandtheirmainapplicationstoreal-lifesystems:how0D/1Dmodeling relatestothe3Dphysicalequations,whatarethefundamentalassumptions underlying0D/1Dphysicalmodelsandthemainlimitationsofthenumericalsolverscommonlyusedforsuchmodels,whatistherationalefora0D/1Dcomponent modelslibraryandwhatkindsofreal-lifesystemscanbemodeledandsimulated fordifferentpurposes(plantsizing,control,operationandmaintenance,prognosis, diagnosisandmonitoring).Also,inthischapter,manyquestionsareanswered: whatisasystem,whatisamodelandmodeling,whatissimulationandwhyis modelingimportant?

1.1Systems,ComplexSystems,andCyber-Physical Systems

Ausualsystemsengineeringdeﬁnitionofasystemisthatitis “asetofinterrelated partsthatworktogethertoaccomplishacommonpurposeormission” (Cloutier etal. 2015).

Systemsaredecomposedintosubsystemsandobjectsatthelowestlevel.They aredynamicallystructuredusingabstractconceptssuchasmodes,states,events, andtrajectories.Modesrefertothelogicalorfunctionalstatesofthesystem(e.g. started,stopped,closed,open,dysfunctional,undermaintenance),whereasstates refertothephysicalstatesofthesystem(e.g.temperature,mass ﬂowrate,angular velocity).Eventscauseswitchingbetweenmodes.Trajectoriesaretheevolutionin timeofthestates.Systemsinteractwiththeirenvironmentviainputsandoutputs. Theinputsrepresenttheactionoftheenvironmentonthesystem,whereasthe outputsrepresenttheinﬂuenceofthesystemontheenvironment.

B.ElHefniandD.Bouskela, ModelingandSimulationofThermalPowerPlants withThermoSysPro, https://doi.org/10.1007/978-3-030-05105-1_1

Forinstance,acoolingsystemwhosemissionistocoolmachinescanbe decomposedintothreesubsystems:apumpingsystemcomposedofpumpsthat circulateswateraroundtheequipmenttobecooled,afeedwatersystemcomposed ofatankandswitchvalvesthatensuressufﬁcientwaterpressureatthepumping systeminlet,andagroupofheatexchangersthattransfersheattotheenvironment. Agivenpumpcanbeinvariousnormalordysfunctionalmodes:started,stopped, cavitating,broken,etc.Thepumphydraulicstateismostfrequentlydescribedby thepumphead(thevariationofpressurethroughthepump)andthepumpvolumetric ﬂowrate(theamountofliquidvolumethatgoesthroughthepumpcasing pertimeunit).Themechanicalstateofthepumpcanbegivenbytheangular velocityandthetorqueoftheshaft.However,iftheshaftisbrokenintotwoparts, thenthemechanicalstateinvolvestheangularvelocitiesandthetorquesofeachend ofthebrokenshaft.Therefore,thestateofabrokenshafthastwiceasmanystate variablesasanormalone.Thisshowsthatmodeswitchingcancauseacomplete structuralchangeinthesystemdescription.Thetemperatureoftheenvironmentis aninputofthesystem(insuchcaseitisassumedthatthesystemdoesnotchange thetemperatureoftheenvironment),andtheheatreleasedtotheenvironmentisan outputofthesystem.

Althoughthereisnowidelyaccepteddeﬁ nitionofacomplexsystem,wewill considerascomplexsystemsthesystemscomposedofnumeroustightlyinteracting subsystems.Cyber-physicalsystemsarecomplexsystemshavingsoftwareand physicalsubsystemsintightinteractionordeeplyintertwined.Goodexamplesof cyber-physicalsystemsarepowerplants,cars,planes,powergrids,etc. Cyber-physicalsystemsexhibit emerging behaviorsthatarenotnecessarilyforeseenatdesigntimeandthatappearatoperationtimeduetothemultipleinteractions (thewholeismorethanthesumofitsparts).Oneofthemainchallengesofphysical modelingandsimulationistobeabletopredictemergingbehaviors.However,the objectiveofthisbookisnottoshowhowtodothat,buttoprovidethefundamental knowledgeintermsofphysicalequationsforthethermalhydraulicpartsofthe systemsthatarenecessaryforthisgoalinparticular,andmoregenerallyforany otherpurposerequiringtheunderstandingofthephysicalbehaviorofthesystem.

1.2WhatisSystemModeling?

Generallyspeaking,modelingistheprocessofrepresentingaparticularconcept, physicalphenomenon,orreal-worldobjectusingabstractnotationsincludingbut notlimitedtomathematicalsymbols.Inthisbook,modelingisreferredtoas derivingfromphysicallawsavalidsetofmathematicalequationsthatdescribethe system physicalbehavior inordertoassessquantitativelyhowthesystemperforms itsdutiesaccordingtosomeprescribedmission,e.g.,toverifywhetherapower plantcomplieswithoperatingrulesduringstart-uporshutdown.Otherwaysof modelingcomplexsystemssuchasstatediagramsorotherkindsofschemas,in particularforthepurposeofexpressingrequirements,assumptions,or logical

behavior,arenotconsideredhere.However,suchmodelsarenecessaryforthe designofcontrolsystemsandcanbeconsideredastheenvironmentofthephysical system(i.e.,theyinteractwiththephysicalsystemviainputsandoutputs).Also, stochasticmodelsarenotexplicitlydealtwith,butrandomnesscanbeintroduced intophysicalmodelsbyreplacingscalarvariableswithdistributionsinthephysical equationsandusingMonteCarlosimulationstocomputetheresponseofthesystem touncertainties.

Physicalmodelingisnotlimitedtoassessingthedynamicbehaviorofthesystem.Itcanalsobeusedtocomputeisolatedoperatingpoints.Thisiscalled static modeling,asopposedto dynamicmodeling thataimsatcomputingsystemstrajectories.Staticmodelingismainlyusedforsystemsizingandoptimizationat designtime,whiledynamicmodelingisoftenusedforsystemcontroldesignand optimizationatoperationtime.Systemdiagnosismayusestaticordynamicmodelingdependingonthephenomenatobeexplored.

1.3WhatisSimulation?

Simulationisanexperimentconductedonamodel.Asmathematicalmodelsare consideredhere,simulationsarenumericalexperimentsconductedwitha computer-executableversionofthemodel,whichisusuallyobtainedbycompiling withacompilerthemodelexpressedinacomputerlanguageintoamachineexecutablecode.Thecomputerlanguageusedformodelingiscalledamodeling language.Thechallengefortheuseristhentowritethemodel’sequationsinthe modelinglanguage.

Thereareroughlytwokindsofmodelinglanguages:imperativelanguagesand equationallanguages.ImperativelanguagessuchasFortran,C,C++,Java,Python, etc.areusedforimperativeprogramming,whichconsistsinwritingexplicitlythe algorithmsthatcomputethemodel’sequations.Thisrequiresasigni ﬁcanteffort fromtheuserwhomusttranslatemanuallytheequationsthatexpressmathematical relationsintosequenceofcomputinginstructionsthatcomputesthenumerical solutionoftheequations.Itismoreconvenienttoperformthistedioustaskautomaticallybyusinganequationallanguagethatletstheuserexpressthemodel’s equationsdirectlyinequationalform,hence,withverylittletransformationofthe originalequationsaswrittenonpaper.Modelicaisanequationallanguage. Modelicacompilerstranslateequationalmodelsintoimperativeprograms,which areinturncompiledwithregularcompilers(C,C++,Fortran,etc.)toproduce executablecode.Modelicahasbeenusedinthisbooktowriteandverifymodels equations.

Experimentswiththesamemodeldifferaccordingtothenumericalvalues providedtotheinputsofthemodelandtotheinitialvaluesofthestatevariables, whicharealsocalledinputsinthesequel.Thosevaluesmustbephysicallyconsistentinordertoprovidecorrectresults.Consistencycannotbeobtainedusingthe model’sequationsbecausetheunknownsarecomputedusingtheinputsasknown

variables.Inotherwords,theknownvariablesarenotconstrainedbythemodel’s equations.Soalthough,fromanumericalpointofview,anyinputcanproduce numericalresults,anyinputcannotproduce valid numericalresults.Therefore, consistencyoftheinputsmustbeachievedbyothermeanssuchasdataassimilation,forinstance,whichisthescienceofproducingthebestestimateoftheinitial stateofasystembycombininginformationfromobservationsofthatsystem(e.g. viasensors)withanappropriatemodelofthesystem(i.e.,themodelathandtobe initialized),seeSwinbanketal.(2003).Thistechniquewhichusescontinuous optimizationalgorithmsissuccessfullyusedinmeteorologyandcanbeappliedto anyphysicalsystemprovidedithasonlycontinuousinputstobeassimilated(this excludestheassimilationoflogicalinputssuchastheon–offpositionofaswitch). Anothertechnique,whichisusedinthisbook,istocomputetheinputsfromthe knowledgeofthenominaloperatingpointusinginversecomputationonsquare systemsofequations(i.e.,havingasmanyunknownsasequations).Thedrawback ofthistechniqueisthatonehastomakeachoicebetweenredundantinformationin ordertoobtainasquaresystem(e.g.,iftwovalvepositionsinﬂuenceasinglestate, onehastomakeachoicebetweenthetwovalvepositions).Thistechniqueisused inthisbookasitismorereadilyavailablewithexistingmodelingandsimulation toolsthanoptimizationtechniques.

Tosummarize,asimulationrunconsistsessentiallyinsolvinganinitialvalue problem,i.e.,adifferential-algebraicequationwithcorrectinitialvaluesforthestate variablesandcorrectvaluesfortheinputs.Inputswith ﬁxedvaluesallalonga simulationrunareoftencalledparameters.Thiswillbelookedatinmoredetailin thesequel.

1.4Whatis0D/1DModeling?

Physicalequationsarefunctionsofspaceandtime.3Dmodelsinvolvethethree spacecoordinates.However,whendealingwithspaceandtime,itisoftendesirable toreducethenumberofspacecoordinatestospeed-upthecomputationoftrajectoriesasthefullmodel’sequationsmustbecomputedateachtimestep.Reducing thedimensionalityoftheproblembygoingfromthreespacecoordinatesdownto oneorevenzerospacecoordinatesiscalled0D/1Dmodelingasopposedto3D modeling.Thisisobtainedbyexploitingthegeometricalpropertiesofthemodel suchasthecylindricalsymmetryofapipe.Inthesequel,thisdiscussionisrestricted tothermalhydraulicsystemswhicharethescopeofthisbook.

Thermalhydraulicsistheapplicationof fluiddynamicsforheatandmass transferinenergysystemssuchaspowerplants.Phenomenastudiedincludeconvection,conduction,radiation,phasechange,single-phase(liquidorvapor), two-phase(liquidandvapor),andmulti-phase flows(forexamplewater/steamwith air).Themostcommon fluidsusedinpowerplantsarewater/steamand fluegases, butother fluidscanbeusedaswellsuchasmoltensalt.

1.4Whatis0D/1DModeling?5

Thedynamicphysicalbehaviorofthermalhydraulicsystemsisdescribedwith partialderivativeequations(PDEs)thatexpressthethreefundamentalconservation lawsofmass(1.1),momentum(1.2),andenergy(1.3).

whereD=Dt standsforthematerialderivative(thattakesintoaccountthe fluid motion), V isthe fluidvolume, q isthe fluiddensity, ~ v isthe fluidvelocity, ~ f arethe externalvolumeandsurfaceforcesactinguponthe fluid(suchaspressureand friction), u isthe fluidinternalenergy, Q and W are,respectively,theamountof heatandworkreceivedbythe fluidperunittime.

Theseequationsareclosedbyclosurelaws(fluidcorrelations)thatcompute unknownquantitiesfoundin ~ f suchaspressurelossorheatexchangecoefficientsas functionsofthepressure P andthetemperature T ofthe fluid.Stateequationsare usedtocompute q and u withrespectto P and T.

The0D/1Dmodelingapproachconsistsinaveragingphysicalquantitiesoverthe cross-sectionalarea A perpendiculartothemain ﬂowdirection x,thenalongthe main ﬂowdirection x:

where Dx isalengthincrementand V ¼ A Dx. Inpractice,thismethodconsistsin:

1.Dividingthesystemintocontrolvolumes V ¼ A Dx alongthemain ﬂow direction;

2.Averagingthephysicalquantitiesusing(1.4)forallindividualcontrolvolumes;

3.Connectingthecontrolvolumesalongthemain ﬂowdirectiontoaccountforthe variationofthephysicalquantitiesalongthatdirectioninstepscorrespondingto thelengths Dx ofthecontrolvolumes.

Dx isadaptedtothestudyathand.It,therefore,canbesmallorlargewithout limitation. Dx isequaltozeroforcomponentsconsideredasasingularitiessuchas valves.Itislargeforlongpipesorlargevesselswhennoinformationisneeded regardingthedistributionofphysicalquantitiesalongthecomponentlength.One

mustnotethatthechoiceof Dx doesnotinduceanyapproximationinitselfas computedquantitiesareconsideredasaveragedquantitiesover V ¼ A Dx,butthe larger Dx,thelowertheresolutionofthecomputationinspace.

0D/1Dmodelinggivestheabilitytochoosethespaceresolutionofrealistic modelsdescribedfrom ﬁ rstprinciplephysics.It,therefore,allowstoadjustthe spaceresolutioninordertocomputelargetransientsforcomplexsystemsfor engineeringstudiesthatoftenrequiresimulationspeedordersofmagnitudefaster thanrealtime.Therefore,themainbeneﬁtofthismethodistoallowtherealistic modelingandsimulationofcomplexsystemsoverlargetransients.

Astheonlydifferentialvariableleftin0D/1Dmodelsisdt ,0D/1Dmodelsare setsofdifferential-algebraicequations(DAEs):

where C isacoefficientmatrix, x isthestatevectorofthesystem, _ x isthetime derivativeof x (nottobeconfoundedwiththelengthincrement Dx above), p are fixedparameters(suchas fi xedboundaryconditions),and u areinputsofthesystem (suchasvariableboundaryconditions).Notethat x maycontaintimederivatives.

If C isinvertible,then(1.5)canbetransformedintoanordinarydifferential equation(ODE)andintegratedwithstandardODEnumericalsolvers:

If C isnotinvertible,then(1.5)isatrueDAEthatcannotbetransformedintoan ODEanditsresolutionismoreproblematic.

If C isnotinvertiblebecauseitcontainsrowsequaltozero,then(1.5)canbe writtenasthefollowingDAE:

where a arethealgebraicvariables,i.e.,thevariablesfrom x in(1.5)withzero coefficientsfor _ x,coefficientmatrix D iscoefficientmatrix C withouttherowsand columnscorrespondingtothealgebraicvariables a,and x aretheremainingdifferentialvariables,i.e.,thevariablesfrom x in(1.5)withnonzerocoefficientsfor x. Equation(1.7b)isafrequentcasethatappearswhendynamicsareneglected. ItcanbesolvedwithnumericalsolversthatcombinetheresolutionofODEswith algebraicequations.Ifthesizeof x isequaltozero,then(1.7a,b)boilsdownto (1.7b)andthemodelispurelystatic.Thiscaseisfrequentlyencounteredinsizing problems.Off-the-shelfModelicatoolssolve(1.7a,b)althoughtheyallowto expresstheproblemas(1.5).If C isnotinvertible,thenadivisionbyzerooccursat simulationtime.

If C containspredicates(i.e.,Booleanconditions)thatdependonelementsof x, andifthepredicatesaresuchthat C isnotinvertibleatsomeinstants t,thenthe systemmaybeconsideredasaseriesofcommutingDAEssuchas(1.7a,b)with

1.4Whatis0D/1DModeling?7

varyingstructure(i.e.,varyingsizesfor x, a, p, and u)fromoneDAEtotheother. Suchsystemsarecalledmulti-modesystems.Thereiscurrentlynoindustrialtool abletosolvesuchsystemsalthoughaprototypewasdevelopedintheframeworkof theITEA2MODRIOproject(2012–2016);(Elmqvistetal. 2014;Bouskela 2016), andthedevelopmentofanindustrialtoolisongoingintheframeworkoftheFUI ModeliScaleproject(startedin2018).

1.5Whatisa0D/1DThermalHydraulicComponent ModelsLibrary?

WhenusingDAEssuchas(1.5)torepresentthefundamentalequationsofthermal hydraulics,integrationof(1.1)–(1.3)mustbeperformedoverthevariouscomponentvolumesconsideredinthesystemmodel(pipes,valves,pumps,heat exchangers,turbines,etc.).Thevariouswaysofchoosingtheappropriateclosure lawsandofperformingtheintegrationoverthevariouscomponentvolumes commonlyfoundinthesystemstobemodeledresultinthedifferent0D/1D componentmodelsthatpopulatethelibrary.

Therefore,alibrarycomponentmodelisaDAEsuchas(1.5)thatdependson inputs u andparameters p.Theparametersaresetaccordingtotheproblemathand. Theyusuallyrepresentquantitiesthataregivenasdesigners’ assumptionsoras measuredquantitiesonthesystemoronitsenvironment.Theinputsaregivenas testscenariosorasoutputsfromneighboringcomponents.Thelattercaseisknown as connecting themodelcomponenttoitsneighboringcomponents.Thewayto performsuchconnectionshasastronginﬂuenceonthestructureofthecomponent models.Thewaytoorganizethecomponentmodelsinthelibraryinordertobe abletocomposeafullmodelbyinterconnectingthemisreferredtoasthe structure ofthelibrary inthesequel.

Inorderforlibrarycomponentmodelstobefullyreusable,i.e.,tobeusedinany modelwithoutmodi ﬁcation,theyshouldexhibitthefollowinggoodproperties: 1.Beacausal; 2.Beproperlyparameterized.

Beingacausalmeansthatwhenwrittenas(1.7a,b),theDAEmaybesolvedin anyofthevariables x, _ x, a, p, or u.Thisisneededbecausetheoutputsofone componentmodelaretheinputsofitsconnectedones,andtherefore,theknownor unknownstatusofthevariablesdependsonthewaythecomponentmodelsare

connectedtogethertoformthefullmodel.Theprocessofassigningthisstatustoall variablesinthemodelisknownas causalityanalysis1 andisperformedautomaticallybyModelicatools.

Beproperlyparameterizedmeansthatapropersetofparametersshouldbe deﬁnedinordertoaccountformostpossibleusagesofthecomponentmodel,while keepingthesizeofthesetassmallaspossible.

1.6Whatare0D/1DModelsUsefulfor?

Thepurposeof0D/1Dmodelsisnottodiscoverorstudynewphysicalphenomena, buttounderstandthephysicalbehaviorofsystemsusingthestandardlawsof physicscomplementedwithphysicalcorrelationsforvariousengineeringpurposes atdesign,commissioning,oroperationtime.Tothatend,itisonlynecessaryto monitorasmallnumberofsignificantvariablescalledthe variablesofinterest.This iswhythespaceaveragingoperationstoreducethedimensionalityoftheproblem from3to1or0areacceptable,providedthatuncertaintymarginsarecorrectly computedtotakeintoaccountrequirementsrelatedtosafetylimitsforinstance. Thisallowsfastcomputationofthesystembehaviorallalongitstrajectoryintime. Intheveryearlyphasesofsystemdesign,oneisgenerallyconcernedwiththe logicalbehaviorofthesysteminordertoverifythatthesystemwillcorrectly performitsmissionsfromafunctionalstandpoint.Thephysicalaspectsarenotvery importantatthisstage.However,atthedetaileddesignphase,whenfunctionsmust beimplementedintophysicalpiecesofequipment,itbecomesimportanttoevaluate differentimplementationalternativesquantitativelyinordertomakesurethatthe system’srequirements,inparticularthoseinvolvingreal-timephysicalconstraints suchassafety,aresatis fiedwhileavoidingoversizing(aslackofprecisequantitativeassessmentmostoftenresultsinexcessiveoperationalmargins),oversizing leadinginturntodelaysandovercosts.Thiscanbeachievedusing0D/1Dmodels, inparticularstaticmodelsforthesizingofnominaloperatingpoints,anddynamic modelsforthedesign,verifi cation,andvalidationofcontrolsystems. Atcommissiontime,0D/1Dmodelscanbeusedtopreparetheacceptancetests.

1Theword causality in causalityanalysis shouldnotbeconfoundedwiththeword causality in physicalcausality whichmeansthatcausesalwaysprecedetheireffects.However,thereisa relationshipbetweenthetwonotions.Theobjectiveofcausalityanalysisistoassigneach unknownvariabletoauniqueequationthatcomputesthisvariableandviceversa.Statederivatives areassignedinthemostobviouswaytoequationssuchas(1.7a).Suchassignmentsareconformantwithphysicalcausalityasstatederivatives(predictors)arethuscomputedfromthestatepast values.However,algebraicvariablesareassignedtoequationssuchas(1.7b)whosephysical causalitiesarelostasalgebraicequationsareobtainedbyneglectingthedynamicsofthesystem thatforcethephysicalcausalities.Theresultoftheanalysismay,thus,notreﬂectthephysical causalityoftherealsystemforthealgebraicvariables.Thisiswhyalgebraicvariablesshouldnot beusedinamodelwhencausalitiesareimportant,suchasthefeedbackloopofacontrolsystem.

1.6Whatare0D/1DModelsUsefulfor?9

Fig.1.1 Using0D/1Dmodelsfromsystemdesigntosystemoperation.(Source MODRIOproject,withpermissionfromtheauthor:AudreyJardin)

Atoperationtime,0D/1Dmodelsareusefultopredicttheshort-termbehaviorof thesystemtomaketherightoperationdecision,forinstance,tooptimizeplant start-upswhilecomplyingwithequipmentoperationalconstraints.Operatorscanbe trainedfortheconductofdifﬁculttransients(i.e.,transientsthatarerarelyperformedandaresubjecttotightsafetyconstraints)using0D/1Dmodels.0D/1D modelscanalsobeusedincombinationwithplantonsitemeasurementstomonitor andassesstheplantperformancedegradationssuchaswearorclogginginorderto providekeyeconomicperformanceindicatorsfortheplantandanticipateon maintenanceactionsinordertoreduceplantshutdownformaintenanceandcorrelativelyincreaseplantavailability.

Beyondindividualpowerplants,thereisagrowingneedtoassessthecollective behaviorofenergynetworkswhensubmittedtoperturbationssuchaschangesin regulatory,economic,orweatherconditions,andhowwellthepowersystemcan adapttodynamicandchangingconditions,see,e.g.,EPRI(2016).Thegrowthin variablegenerationsuchassolar(photovoltaicandthermodynamic)andwindisa strongdriverfortheuseof0D/1Dforlarge-scaleenergysystems.Thisnewneed promptedthelaunchoftheModeliScaleprojectthataimsatupscalingModelicato verylargemulti-modephysicalsystems.

Figure 1.1 presentsthedifferentstagesofthesystemslifecycle,fromdesignto operation,where0D/1Dmodelsareuseful.

References

BouskelaD(2016)Multi-modephysicalmodellingofadrumboiler,complexadaptivesystems. ProcComputSci95:516–523

CloutierR,BaldwinC,BoneMA(2015)Systemsengineeringsimpliﬁed.CRCPress,Taylor& Francis

ElmqvistH,MattssonSE,OtterM(2014)Modelicaextensionsformulti-modeDAEsystems.In: Proceedingsofthe10thinternationalModelicaconference

EPRI(2016)ElectricPowerSystemFlexibility,challengesandopportunity.Availablefrom https://www.epri.com/#/pages/product/3002007374/?lang=en MODRIOproject(2012–1016),ITEA211004MODRIO.Availablefrom https://github.com/ modelica/modrio and https://www.modelica.org/external-projects/modrio

SwinbankR,ShutyaevV,LahozWA(2003)Dataassimilationfortheearthsystem.In:SeriesIV: earthendenvironmentalsciences,vol26.Kluwer

Chapter2 IntroductiontoThermodynamics andHeatTransfer

Abstract Thermodynamicsisthesciencethatdealswiththeexchangeofenergyin theformofheatandworkandwiththedifferentstates(solid,liquid,gas,etc.)and properties(density,viscosity,thermalconductivity,etc.)ofsubstancesthatare relatedtoenergyandtemperature.Thermodynamicsisformalizedintothreebasic laws,the firstlawbeingtheconservationofenergy,andthesecondandthirdlaws beingrelatedtothenotionofentropyandiscompletedbythethreemainlawsfor heattransfer:radiation,convection,andconduction.Inthischapter,weintroduce firstthepropertiesofsubstances(density,pressure,andtemperature),energy, enthalpy,andentropy,thentheconceptofstatevariables,thedifferenttypesof thermodynamicsystems,the firstandsecondthermodynamiclaws,thethermodynamicscycles(idealandactualBraytoncycles,idealandactualRankinecycles), theidealgaslaw,andthethreeheattransferprocesses(radiation,convection,and conduction).Itisshownwhythesedifferentnotionsareessentialinorderto computethecompletethermal-hydraulicstateofthesystem,whichisthemain challengeof0D/1Dmodelingandsimulationforthat field.

2.1WhatAreThermodynamicsandThermalHydraulics?

Thermodynamicscanbedeﬁ nedintwoways:thescienceofheatandthermal machinesorthescienceoflargesystems(i.e.,composedofmanyparticles)in equilibrium.Inthisbook,thetwoaspectswillbeconsideredbecausepowerplants arethermalmachinesthatproducemechanicalenergyusingheatandmasstransfer. Asthermalmachines,theyaresubjectedtothermodynamiccycles(cf.Sect. 2.9), andastheyuse ﬂuidstotransferenergyfromthereactortotheturbine,theyare subjectedtothelawsofthermalhydraulicswhichisthecombinationofhydraulics withthermodynamics.

Thetwomainconceptsinthermodynamicsareheatandtemperature.Thesetwo quantitiesaredefinedandusedintwowaysthatreflectthetwoaspectsofthermodynamics:viatheeffi ciencyofthermalmachinesandviastatistics(averages) overvolumescontaininglargenumbersofparticles.Thesequantitiesaregoverned

B.ElHefniandD.Bouskela, ModelingandSimulationofThermalPowerPlants withThermoSysPro, https://doi.org/10.1007/978-3-030-05105-1_2

bythe ﬁrstandsecondlawsofthermodynamics.Heatandtemperaturearerelated viatheconceptofentropy,withthefundamentalformula:

wheredS isthevariationofentropyofthesystemthatreceives dQrev amountof heatenergyduringareversibleprocessattemperature T. Thetwoadditionalconceptsusedforhydraulicsaretheconservationofmass andtheconservationofmomentum.

2.2ThermodynamicProcesses

Athermodynamicprocessisachangeinthesystemstatefromaninitialstatein equilibriumtoa ﬁ nalstateinequilibrium.Whentheinitialand ﬁnalstatesarethe same,theprocessiscalleda cycle

A reversibleprocess isaprocessinwhichthesystemisinequilibriumateach step.Thiscorrespondstoanidealinﬁnitelyslowtransformationofthesystem whereeachstepoftheprocessisasystemstate.

An irreversibleprocess isaprocessthatisnotreversible.Thiscorrespondsto realprocesseswherechangesbetweentheinitialand ﬁnalstatesoccuroutof equilibrium.

2.3PropertiesofSubstances

Propertiesofsubstancesarequantitiessuchasmass,temperature,volume,and pressure.Propertiesareusedtodeﬁ nethecurrentphysicalstateofasubstance. Thermodynamicpropertiesaredividedintotwogeneralclasses:intensiveand extensiveproperties.

Anintensivepropertyisindependentofthemassofthesubstance.Temperature, pressure,speci ﬁcvolume,anddensityareexamplesofintensiveproperties. Thevalueofanextensivepropertyisdirectlyproportionaltothemassofthe substance.Theinternalenergyortheenthalpyisanexampleofextensiveproperties.Massandvolumearealsoextensiveproperties.

Thus,ifaquantityofmatterinagivenstateisdividedintotwoequalpartsin mass,eachpartwillhavethesamevalueoftheintensivepropertyastheoriginal andhalfthevalueoftheextensiveproperty.

Relationshipsbetweenpropertiesareexpressedintheformequationswhichare calledequationsofstate.Themostfamousstateequationistheidealgaslawthat relatesthepressure,volume,andtemperatureofanidealgas(cf.Sect. 2.10).

Another random document with no related content on Scribd:

[1444] Seward (04) p. 31.

[1445] Hollick and Jeffrey (09) p 24

[1446] Raciborski (94) A. Pl. . figs. 1, 2; Zeiller (002) p. 98.

[1447] v 5950

[1448] Fontaine (89) Pls. . .

[1449] Solms-Laubach (91) A. p. 141.

[1450] Schimper (69) A p 472

[1451] Kurr (45) Pl. . fig. 1.

[1452] Seward (04) p 30

[1453] Saporta (73) A.

[1454] Schenk (67) A.

[1455] Salfeld (07) p 192

[1456] Seward (04) p. 34, fig. 2, Pl. .

[1457] Salfeld (09).

[1458] Schenk (76) Pl fig 7

[1459] Salfeld (09) p. 34.

[1460] Zigno (56) A

[1461] Solms-Laubach (91) A. p. 114.

[1462] Nathorst (78).

[1463] Saporta (73) A p 352

[1464] Nathorst (78) p. 122.

[1465] Zeiller (03) p 52

[1466] Leckenby (64) A. Pl. . fig. 1; Seward (04) p. 36.

[1467] Schenk (87).

[1468] Zeiller (03) Pls –

[1469] Zigno (56) A. Pls. . .

[1470] Seward (00) p. 170.

[1471] Brongniart (28) A p 49

[1472] Seward (00) p. 171.

[1473] Saporta (73) A p 368

[1474] Krasser (95).

[1475] Saporta (73) A. Pl. .

[1476] Brongniart (28) A p 60

[1477] Kidston (012) p. 196.

[1478] Potonié (93) A Pl

[1479] Kidston (89) p. 409.

[1480] Zeiller (06) Pls – ; (002) p 100, fig 73

[1481] Weiss, C. E. (70).

[1482] Zeiller (06) p. 90.

[1483] Lesquereux (80) A p 131; Weiss (70)

[1484] Weiss (69) p. 37.

[1485] Grand’Eury (77) A Pl A

[1486] Renault and Zeiller (88) A. p. 219.

[1487] Stur (84).

[1488] Grand’Eury (77) A Pl

[1489] Grand’Eury (08).

[1490] Renault and Zeiller (88) A Pl

[1491] Weiss, C. E. (69); Goeppert (64) A.; Potonié (93) A, (04); Lesquereux (80) A., p. 124; White (99) p. 125.

[1492] Seward (08) p. 97, Pl. .

[1493] Brongniart, in Murchison, Verneuil, and Keyserling (45) Pl A

[1494] Weiss, C. E. (70) p. 871.

[1495] Brongniart (49) A p 24

[1496] Grand’Eury (06).

[1497] Weiss (69) Pls. . .

[1498] Potonié (93) A Pl figs 1, 2

[1499] Weber and Sterzel (96) p. 99.

[1500] Zeiller (90) p. 84.

[1501] Zeiller (983).

[1502] For figures of this and other species, see Potonié (07).

[1503] For synonymy, see Zeiller (90) p 87 and Potonié (07) p 2

[1504] Schuster (08) Pl. . fig. 7.

[1505] Weiss, C. E. (70).

[1506] Schlotheim (20) A p 406

[1507] Renault and Zeiller (88) A. Pl. XIX.

[1508] White (052) p 388

[1509] Forbes (53) p. 43.

[1510] Baily (59) p 75

[1511] Schimper (69) A. p. 473.

[1512] Dawson (71) A p 48; (82)

[1513] Kidston (912) p. 30, Pl. .; (06) p. 434.

[1514] Baily (75) Pl. .

[1515] Carruthers (722) Pl

[1516] Dawson (71) A.

[1517] Smith and White (05) p 39

[1518] Lesquereux (80) A.

[1519] Crépin (74).

[1520] Nathorst (02)

[1521] Schmalhausen (94).

[1522] Nathorst (04)

[1523] Krasser (00) Pl. . figs. 3–7.

[1524] Zeiller (032) p. 27.

[1525] Stur (75) A Pls

[1526] Kidston (882).

[1527] Grand’Eury (08)

[1528] Brongniart (22) A.

[1529] Kidston (052)

[1530] Renault (76).

[1531] Grand’Eury (08).

[1532] White (99) p 128

[1533] Grand’Eury (77) A. p. 122.

[1534] Zeiller (90) Pl. . fig. 6.

[1535] Potonié (99) p 113

[1536] Renault (82) A. Vol. .; Zeiller (90) p. 139.

[1537] Grand’Eury (77) A p 105

[1538] Brongniart (22) A. Pl. . fig. 6. For synonymy, see Kidston (03) p. 773; Zeiller (88) A. p. 261.

[1539] For synonymy, see Kidston (88) p. 354.

[1540] Scheuchzer (1723) A p 129, Pl fig 3

[1541] Lhywd (1760) A. Pl. . fig. 190.

[1542] Lesquereux (79) A Pl

[1543] Fontaine and White (80) p. 47.

[1544] Bunbury (47) Pl

[1545] Kidston (94) p 357; (03) p 806

[1546] White (99) p. 132.

[1547] Zeiller (88) A p 251

[1548] See Vol. . p. 45.

[1549] Zalessky (07) Pl. . fig. 5.

[1550] Zeiller (88) A p 251

[1551] Renault and Zeiller (88) A. p. 251, Pl. .

[1552] Brongniart (28) A p 51

[1553] Lindley and Hutton (33) A. p. 28.

[1554] Lesquereux (66) A.

[1555] Roehl (69)

[1556] Seward (88).

[1557] Potonié (99) p. 153 (note).

[1558] Gutbier (35)

[1559] Presl, in Sternberg (38) A.

[1560] Grand’Eury (04)

[1561] Zeiller (90) Pl. . fig. 9.

[1562] Zeiller (99) p. 46.

[1563] Bunbury (47) A p 427

[1564] Lyell (45) A. Vol. . p. 202.

[1565] Lesquereux (80) A p 146

[1566] Sternberg (26) A.

[1567] Grand’Eury (04).

[1568] Grand’Eury (90) A

[1569] Zeiller (90) Pl. . fig. 6, A.

[1570] Stur (83).

[1571] Scott (07) p 206; Scott and Maslen (06) p 112

[1572] Grand’Eury (04).

[1573] For synonymy, see Kidston (03) p 772: Zeiller (88) A

[1574] Scheuchzer (1723) A. Pl. . fig. 4.

[1575] Kidston (94) p 245

[1576] For synonymy, see Kidston (94) p. 596; (03) p. 806; White (99) p. 117.

[1577] Grand’Eury (04)

[1578] Kidston (94) p. 245.

[1579] Brongniart (28) A. p. 59.

[1580] page 494

[1581] Kidston (94) p. 596.

[1582] Grand’Eury (05)

[1583] Potonié (922); (93) p. 54.

[1584] For synonymy, see Kidston (88) p. 366.

[1585] Zeiller (90) p 45; Potonié (93) A p 57

[1586] Germar (44) Pls. . .

[1587] Kidston (88) p 366

[1588] Stur (83).

[1589] Renault and Zeiller (88) A. p. 196.

[1590] Potonié (93) A p 48

[1591] Zeiller (002) p. 88.

[1592] page 397

[1593] Renault and Zeiller (88) A. p. 178, Pls. .–. Ante, p. 419.

[1594] Potonié (02).

[1595] Schimper (69) A p 688

CAMBRIDGE: PRINTED

JOHN CLAY, M.A.

AT THE UNIVERSITY PRESS.

CAMBRIDGE BIOLOGICAL SERIES

General Editor, A. E. S, M.A., F.R.S., Master of Christ’s College.

A Text-Book of Zoogeography. By F E. B, M. A., F.R.S., Prosector of the Zoological Society of London. Crown 8vo. With 5 maps. 6s.

The Elements of Botany. By F D, Sc.D., M.B., F.R.S., Fellow of Christ’s College. Second edition. Crown 8vo. With 94 illustrations. 4s. 6d.

Journal of Education. A noteworthy addition to our botanical literature.

Practical Physiology of Plants. By F D, Sc.D., F.R.S., and E. H A, M.A. Crown 8vo. With 45 illustrations. Third edition. 4s. 6d.

Nature. The authors are much to be congratulated on their work, which fills a serious gap in the botanical literature of this country.

Morphology and Anthropology. By W. L. H. D, M.A., M.D., Fellow and Lecturer of Jesus College, University Lecturer in Physical Anthropology. Demy 8vo. With 333 illustrations. 15s. net. Athenæum. Mr Duckworth has managed to produce in his “Morphology and Anthropology” just such a text-book as students have long been asking for.... It is no easy task to have undertaken such a work and the author is to be congratulated on the success which has attended his efforts. The volume can be confidently recommended to all whose studies lead them in this direction.

Lectures on the History of Physiology during the Sixteenth, Seventeenth and Eighteenth Centuries. By Sir M. F, K.C.B.,

M.D., D.C.L. Demy 8vo. With a frontispiece. 9s.

Nature. There is no more fascinating chapter in the history of science than that which deals with physiology, but a concise and at the same time compendious account of the early history of the subject has never before been presented to the English reader. Physiologists therefore owe a debt of gratitude to Sir Michael Foster for supplying a want which was widely felt.... No higher praise can be given to the book than to say that it is worthy of the reputation of its author.

The Soluble Ferments and Fermentation.

By J. R G, Sc.D., F.R.S., Professor of Botany to the Pharmaceutical Society of Great Britain. Second edition. Demy 8vo. 12s.

Nature. It is not necessary to recommend the perusal of the book to all interested in the subject since it is indispensable to them, and we will merely conclude by congratulating the Cambridge University Press on having added to their admirable series of Natural Science Manuals an eminently successful work on so important and difficult a theme, and the author on having written a treatise cleverly conceived, industriously and ably worked out, and on the whole, well written.

A Treatise on the British Freshwater Algæ.

By G. S. W, M.A., A.R.C.S., F.L.S., Lecturer in Botany in the University of Birmingham. Demy 8vo. With a frontispiece and 166 illustrations. 10s. 6d. net.

Nature. Its aim is stated as “to give the student a concise account of the structure, habits and life-histories of Freshwater Algæ, and also to enable him to place within the prescribed limits of a genus any Algæ he may find in the freshwater of the British Islands.” To do this within the limits of an octavo volume of less than 400 pages, in which are numerous illustrations, is a task possible of accomplishment only by one very familiar with the subject and skilled in concise expression; but that it has been successfully done will, we think, be the verdict after testing the book thoroughly.... Prof. West’s treatment of his subject is instructive and stimulating.

A Manual and Dictionary of the Flowering Plants and Ferns. By J. C. W, M.A., Sc.D., Director of the Royal Botanic Gardens, Ceylon. Third edition. Crown 8vo. 10s. 6d.

Field. Taking this handy volume and a local flora, the traveller or student may do an enormous amount of practical field work without any other botanical literature whatever.... The result is a work that ought to be included in every library of botany and horticulture or agriculture, and it is certainly one that the nomadic botanist cannot afford to leave at home.... We have used the original edition of this work since its publication, and have found it to be one of the most useful and comprehensive works on plants ever produced.

Athenæum. The whole is well abreast of modern research, and a thoroughly business-like volume, lucid though compact.

Agriculture in the Tropics. An elementary Treatise. By J. C. W, M.A., Sc.D. Demy 8vo. With 25 plates. 7s. 6d. net.

Palæontology—Invertebrate. By H W, M.A., F.G.S., University Lecturer in Palæozoology. Crown 8vo. Fourth edition. With 151 illustrations. 6s.

Outlines of Vertebrate Palæontology for students of Zoology. By A S W, M.A., F.R.S., Keeper of the Department of Geology in the British Museum. Demy 8vo. With 228 illustrations. 14s.

Athenæum. The author is to be congratulated on having produced a work of exceptional value, dealing with a difficult subject in a thoroughly sound manner.

CAMBRIDGE UNIVERSITY PRESS

London: FETTER LANE, E.C. C. F. CLAY,

Edinburgh: 100, PRINCES STREET ALSO

London: H. K. LEWIS, 136, GOWER STREET, W.C.

Transcriber’s Notes:

Blank pages have been removed.

Obvious typographical errors have been silently corrected

Odd-numbered page headings are entered at approximate locations as sidenotes in ITALICS ALL CAPS, except where repeated, or duplicated in headings.

Headings and table of contents have been modified to be more consistent

* END OF THE PROJECT GUTENBERG EBOOK FOSSIL PLANTS, VOL. 2: A TEXT-BOOK FOR STUDENTS OF BOTANY AND GEOLOGY *

Updated editions will replace the previous one—the old editions will be renamed.

Creating the works from print editions not protected by U.S. copyright law means that no one owns a United States copyright in these works, so the Foundation (and you!) can copy and distribute it in the United States without permission and without paying copyright royalties. Special rules, set forth in the General Terms of Use part of this license, apply to copying and distributing Project Gutenberg™ electronic works to protect the PROJECT GUTENBERG™ concept and trademark. Project Gutenberg is a registered trademark, and may not be used if you charge for an eBook, except by following the terms of the trademark license, including paying royalties for use of the Project Gutenberg trademark. If you do not charge anything for copies of this eBook, complying with the trademark license is very easy. You may use this eBook for nearly any purpose such as creation of derivative works, reports, performances and research. Project Gutenberg eBooks may be modified and printed and given away—you may do practically ANYTHING in the United States with eBooks not protected by U.S. copyright law. Redistribution is subject to the trademark license, especially commercial redistribution.

START: FULL LICENSE

THE FULL PROJECT GUTENBERG LICENSE

PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free distribution of electronic works, by using or distributing this work (or any other work associated in any way with the phrase “Project Gutenberg”), you agree to comply with all the terms of the Full Project Gutenberg™ License available with this file or online at www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing Project Gutenberg™ electronic works

1.A. By reading or using any part of this Project Gutenberg™ electronic work, you indicate that you have read, understand, agree to and accept all the terms of this license and intellectual property (trademark/copyright) agreement. If you do not agree to abide by all the terms of this agreement, you must cease using and return or destroy all copies of Project Gutenberg™ electronic works in your possession. If you paid a fee for obtaining a copy of or access to a Project Gutenberg™ electronic work and you do not agree to be bound by the terms of this agreement, you may obtain a refund from the person or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be used on or associated in any way with an electronic work by people who agree to be bound by the terms of this agreement. There are a few things that you can do with most Project Gutenberg™ electronic works even without complying with the full terms of this agreement. See paragraph 1.C below. There are a lot of things you can do with Project Gutenberg™ electronic works if you follow the terms of this agreement and help preserve free future access to Project Gutenberg™ electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the Foundation” or PGLAF), owns a compilation copyright in the collection of Project Gutenberg™ electronic works. Nearly all the individual works in the collection are in the public domain in the United States. If an individual work is unprotected by copyright law in the United States and you are located in the United States, we do not claim a right to prevent you from copying, distributing, performing, displaying or creating derivative works based on the work as long as all references to Project Gutenberg are removed. Of course, we hope that you will support the Project Gutenberg™ mission of promoting free access to electronic works by freely sharing Project Gutenberg™ works in compliance with the terms of this agreement for keeping the Project Gutenberg™ name associated with the work. You can easily comply with the terms of this agreement by keeping this work in the same format with its attached full Project Gutenberg™ License when you share it without charge with others.

1.D. The copyright laws of the place where you are located also govern what you can do with this work. Copyright laws in most countries are in a constant state of change. If you are outside the United States, check the laws of your country in addition to the terms of this agreement before downloading, copying, displaying, performing, distributing or creating derivative works based on this work or any other Project Gutenberg™ work. The Foundation makes no representations concerning the copyright status of any work in any country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other immediate access to, the full Project Gutenberg™ License must appear prominently whenever any copy of a Project Gutenberg™ work (any work on which the phrase “Project Gutenberg” appears, or with which the phrase “Project Gutenberg” is associated) is accessed, displayed, performed, viewed, copied or distributed:

This eBook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook.

1.E.2. If an individual Project Gutenberg™ electronic work is derived from texts not protected by U.S. copyright law (does not contain a notice indicating that it is posted with permission of the copyright holder), the work can be copied and distributed to anyone in the United States without paying any fees or charges. If you are redistributing or providing access to a work with the phrase “Project Gutenberg” associated with or appearing on the work, you must comply either with the requirements of paragraphs 1.E.1 through 1.E.7 or obtain permission for the use of the work and the Project Gutenberg™ trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg™ electronic work is posted with the permission of the copyright holder, your use and distribution must comply with both paragraphs 1.E.1 through 1.E.7 and any additional terms imposed by the copyright holder. Additional terms will be linked to the Project Gutenberg™ License for all works posted with the permission of the copyright holder found at the beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg™ License terms from this work, or any files containing a part of this work or any other work associated with Project Gutenberg™.

1.E.5. Do not copy, display, perform, distribute or redistribute this electronic work, or any part of this electronic work, without prominently displaying the sentence set forth in paragraph 1.E.1 with active links or immediate access to the full terms of the Project Gutenberg™ License.

1.E.6. You may convert to and distribute this work in any binary, compressed, marked up, nonproprietary or proprietary form, including any word processing or hypertext form. However, if you provide access to or distribute copies of a Project Gutenberg™ work in a format other than “Plain Vanilla ASCII” or other format used in the official version posted on the official Project Gutenberg™ website (www.gutenberg.org), you must, at no additional cost, fee or expense to the user, provide a copy, a means of exporting a copy, or a means of obtaining a copy upon request, of the work in its original “Plain Vanilla ASCII” or other form. Any alternate format must include the full Project Gutenberg™ License as specified in paragraph 1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying, performing, copying or distributing any Project Gutenberg™ works unless you comply with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing access to or distributing Project Gutenberg™ electronic works provided that:

• You pay a royalty fee of 20% of the gross profits you derive from the use of Project Gutenberg™ works calculated using the method you already use to calculate your applicable taxes. The fee is owed to the owner of the Project Gutenberg™ trademark, but he has agreed to donate royalties under this paragraph to the Project Gutenberg Literary Archive Foundation. Royalty payments must be paid within 60 days following each date on which you prepare (or are legally required to prepare) your periodic tax returns. Royalty payments should be clearly marked as such and sent to the Project Gutenberg Literary Archive Foundation at the address specified in Section 4, “Information about donations to the Project Gutenberg Literary Archive Foundation.”

• You provide a full refund of any money paid by a user who notifies you in writing (or by e-mail) within 30 days of receipt that s/he does not agree to the terms of the full Project

Gutenberg™ License. You must require such a user to return or destroy all copies of the works possessed in a physical medium and discontinue all use of and all access to other copies of Project Gutenberg™ works.

• You provide, in accordance with paragraph 1.F.3, a full refund of any money paid for a work or a replacement copy, if a defect in the electronic work is discovered and reported to you within 90 days of receipt of the work.

• You comply with all other terms of this agreement for free distribution of Project Gutenberg™ works.

1.E.9. If you wish to charge a fee or distribute a Project Gutenberg™ electronic work or group of works on different terms than are set forth in this agreement, you must obtain permission in writing from the Project Gutenberg Literary Archive Foundation, the manager of the Project Gutenberg™ trademark. Contact the Foundation as set forth in Section 3 below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable effort to identify, do copyright research on, transcribe and proofread works not protected by U.S. copyright law in creating the Project Gutenberg™ collection. Despite these efforts, Project Gutenberg™ electronic works, and the medium on which they may be stored, may contain “Defects,” such as, but not limited to, incomplete, inaccurate or corrupt data, transcription errors, a copyright or other intellectual property infringement, a defective or damaged disk or other medium, a computer virus, or computer codes that damage or cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right of Replacement or Refund” described in paragraph 1.F.3, the Project Gutenberg Literary Archive Foundation, the owner of the Project Gutenberg™ trademark, and any other party distributing a Project Gutenberg™ electronic work under this

agreement, disclaim all liability to you for damages, costs and expenses, including legal fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a defect in this electronic work within 90 days of receiving it, you can receive a refund of the money (if any) you paid for it by sending a written explanation to the person you received the work from. If you received the work on a physical medium, you must return the medium with your written explanation. The person or entity that provided you with the defective work may elect to provide a replacement copy in lieu of a refund. If you received the work electronically, the person or entity providing it to you may choose to give you a second opportunity to receive the work electronically in lieu of a refund. If the second copy is also defective, you may demand a refund in writing without further opportunities to fix the problem.

1.F.4. Except for the limited right of replacement or refund set forth in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied warranties or the exclusion or limitation of certain types of damages. If any disclaimer or limitation set forth in this agreement violates the law of the state applicable to this agreement, the agreement shall be interpreted to make the maximum disclaimer or limitation permitted

by the applicable state law. The invalidity or unenforceability of any provision of this agreement shall not void the remaining provisions.

1.F.6.

INDEMNITY

- You agree to indemnify and hold the Foundation, the trademark owner, any agent or employee of the Foundation, anyone providing copies of Project Gutenberg™ electronic works in accordance with this agreement, and any volunteers associated with the production, promotion and distribution of Project Gutenberg™ electronic works, harmless from all liability, costs and expenses, including legal fees, that arise directly or indirectly from any of the following which you do or cause to occur: (a) distribution of this or any Project Gutenberg™ work, (b) alteration, modification, or additions or deletions to any Project Gutenberg™ work, and (c) any Defect you cause.

Section 2. Information about the Mission of Project Gutenberg™

Project Gutenberg™ is synonymous with the free distribution of electronic works in formats readable by the widest variety of computers including obsolete, old, middle-aged and new computers. It exists because of the efforts of hundreds of volunteers and donations from people in all walks of life.

Volunteers and financial support to provide volunteers with the assistance they need are critical to reaching Project Gutenberg™’s goals and ensuring that the Project Gutenberg™ collection will remain freely available for generations to come. In 2001, the Project Gutenberg Literary Archive Foundation was created to provide a secure and permanent future for Project Gutenberg™ and future generations. To learn more about the Project Gutenberg Literary Archive Foundation and how your efforts and donations can help, see Sections 3 and 4 and the Foundation information page at www.gutenberg.org.

Modeling and simulation of thermal power plants with thermosyspro a theoretical introduction and a p