正版新书]核工程基本原理俞冀阳9787302490876

1 Fundamentals of Mathematics and Physics
1.1 Calculus
1.1.1 Differential and Derivative
1.1.2 Integral
1.1.3 Laplace Operator
1.2 Units
1.2.1 Unit Systems
1.2.2 Conversion of Units
1.. Graphics of Physical ntity
Exercises
2 Thermodynamics
2.1 Thermodynamic Properties
2.2 Energy
2.2.1 HeandWrk
2.2.2 Energy and Power
. System and Process
2.4 Phase Change
2.5 Property Diagrams
2.5.1 PressureTemperature (pT) Diagram
2.5.2 PressureSpecific Volume (pv) Diagram
2.5.3 PressureEnthalpy (ph) Diagram
2.5.4 EnthalpyTemperature (hT) Diagram
2.5.5 TemperatureEntropy (Ts) Diagram
2.5.6 EnthalpyEntropy (hs)Diagram or Mollier Diagram
2.6 The FirsLwf Thermodynamics
2.6.1 Rankine Cycle
2.6.2 Utilization of the FirsLwf Thermodynamics in Nuclear Power Plant
2.7 The Second Law of Thermodynamics
2.7.1 Entropy
2.7.2 Carnots Principle
2.8 Power Plant Components
2.8.1 Turbine Efficiency
2.8.2 Pump efficiency
2.8.3 Ideal and Real Cycle
2.9 Ideal Gas Law
Exercises
3 Heat Transfer
3.1 Heat Transfer Terminology
3.2 Heat Conduction
3.2.1 Fouriers Law of Conduction.
3.2.2 Rectangular
3.. Equivalent Resistance
3.2.4 Cylindrical
3.3 Convective Heat Transfer
3.3.1 Convective Heat Transfer Coefficient
3.3.2 Overall Heat Transfer Coefficient
3.4 Radiant Heat Transfer
3.4.1 Thermal Radiation
3.4.2 Black Body Radiation
3.4.3 Radiation Configuration Factor

1FundamentalsofMathematicsandPhysicsInengineeringfield,somepracticalproblemscannotbeadequatelysolvedusingarithmeticandalgebraonly.Advancedmathematicaltoolssuchascalculusandintegralareneededtounderstandphysicalprocessusedinnuclearengineering.1.1CalculusArithmeticinvolvesthefixedvaluesofnumbers.Algebrainvolvesbothliteralandarithmetiubers,whichstillhasfixedvaluesinagivencalculationalthoughtheliteralnumbersinalgebraicproblemscanchangeduringcalculation.Heresomeexamplesaregiven.Whenaweightisdroppedandallowedtofallfreely,itsvelocitychangescontinually.Theelectriccurrentinanalternatingcurrentcircuitchangescontinually.Bothofthesequantitieshaveadifferentvalueatsuccessiveinstantsoftime.Physicalsystemsthatinvolvequantitiesthatchangecontinuallyarecalleddynamicsystems.Thesolutionofproblemswhichinvolvingdynamicsystemsoftenneeddifferentmathematicaltechniquesfromarithmeticandalgebra.Calculusinvolvesallthesamemathematicaltechniquesinvolvedinarithmeticandalgebra,suchasaddition,subtraction,multiplication,division,equations,andfunctions,butitalsoinvolvesseveralothertechniques.Thesetechniquesarenotdifficulttounderstandbecausetheycanbedevelopedusingfamiliarphysicalsystems,buttheydoinvolvenewideasandterminology.Therearemanydynamicsystemsencounteredinnuclearengineeringfield.Thedecayofradioactivematerials,thesruofareactor,andthepowerchangeofaturbinegeneratorallinvolvequantitieschangewithtime.Ananalysisofthesedynamicsystemsinvolvescalculus.Calculusisthemosthelpfultoolstounderstandcertainofthebasicideasandterminologywhichisinvolvedinnuclearfacilityfield,thoughdetailedunderstandingofcalculusisnotrequiredfortheoraioalaspect.Theseideasandterminologyareencounteredfrequently,andabriefintroductiontothebasicideasandterminologyofthemathematicsofdynamicsystemsisdiscussedinthischapter.1.1.1DifferentialandDerivativeInmathematics,differentialisatooltodescribethelocalcharacteristicofafunctionusinglineartechniques.Supposeafunctionisdefinedinaregion.x0andx0+Δxaretwopoints(value)inthisregion.Thentheincrementalchangeofthefunctioncanbeexpressedas1:Δy=f(x0+Δx)－f(x0)(11)Usinglocallineartechnique,itcanbeexpressedas:Δy=A·Δx+o(Δx)(12)where,AisaconstantnumberindependentwithΔx,o(Δx)isahigherorderinfinitxfromx=x1tox=x2.Thiscanbevisualizedastakingtheproductoftheinstantaneousforce,F,andtheincrementalchangeinpositiondxateachpointbetweenx1andx2,andsummingalloftheseproducts.Example15:Givethephysicalinterpretationofthefollowingequationrelatingtheamountofradioactivematerialpresentingasafunctionoftheelapsedtime,t,andthedecayconstant,λ.∫N1N0dNN=-λt(115)Solution:Thephysicalmeaningofthisequationcanbestatedintermsofasummation.Thenegativeoftheproductofthedecayconstant,λ,andtheelapsedtime,t,equalstheintegralofdN/NfromN=N0toN=N1.ThisintegralcanbevisualizedastakingthequotientoftheincrementalchangeinN,dividedbythevalueofNateachpointbetweenN0andN1,andsummingallofthesequotients.1.1.3LaplaceOperatorTheLaplaceoperator2isusefulinnuclearengineeringtoexpressconservationofneutron,mass,momentumorenergy.Forndimensionalspace,theLaplaceoperatorisatwoorderdifferentialoperator.Itisthedivergenceofgradientofafunction.InrectangularplanecoordinatesystemshownasFigure14,theLaplaceoperatorhasexpressionasshowninEquation(116).2u=·(u)=2ux2+2uy2+2uz2(116)wherethegradientoperatorisdefinedas:=xi+yj+zk(117)IncylindricalcoordinatesystemshownasFigure15,thetransformofcoordinatesare:r=x2+y2,θ=arctanyx,z=z(118)Figure14RectangularPlaneCoordinateSystemFigure15CylindricalCoordinateSystemDopartialderivativeofcoordinates,weget:rx=xr=cosθ(119a)ry=yr=sinθ(119b)θx=－sinθr(119c)θy=cosθr(119d)Thus,wehave:ux=urrx+uθθx=cosθur－sinθruθ(120a)uy=urry+uθθy=sinθur+cosθruθ(120b)Finally,weget:2ux2=cosθr－sinθrθcosθur－sinθruθ=cos2θ2ur2+sin2θrur－2rsinθcosθ2urθ+sin2θr22uθ2+2sinθcosθr2uθ(121)2uy2=sinθr+cosθrθsinθur+cosθruθ=sin2θ2ur2+cos2θrur+2rsinθcosθ2urθ+cos2θr22uθ2－2sinθcosθr2uθ(122)2uz2=2uz2(1)Makeanarrangement,itbecomes:2ux2+2uy2+2uz2=2ur2+1rur+1r22uθ2+2uz2(124)Figure16SphericalCoordinateSystemThus,theLaplaceoperatorincylindricalcoordinatesystemisexpressedasEquation(125).2=1rrrr+1r22θ2+2z2(125)ForsphericalcoordinatesystemshownasFigure16,onecangettheexpressionofEquation(126).Weleaveitasahomeworkforyoutoderive.2=1r2rr2r+1r2sinθθsinθθ+1r2sinθ22(126)1.2UnitsAnumberaloneisnotsufficienttodescribeaphysicalquantity.Forexample,tosaythat“apipemustbe4longtofit”hasnomeaningunlessaunitofmeasurementforlengthisalsospecified.Byaddingunitstothenumber,itbecomesclear,“apipemustbe4meterslongtofit.”Theunitdefinesthemagnitudeofameasurement.Ifwehaveameasurementoenth,theunitusedtodescribethelengthcouldbeameterorkilometer,eachofwhichdescribesadifferentmagnitudeoenth.Theimportanceofspecifyingtheunitsofameasurementforanumberusedtodescribeaphysicalquantityisdoublyemphasizedwhenitisnotedthatthesamephysicalquantitymaybemeasuredusingavarietyofdifferentunits.Forexample,lengthmaybemeasuredinmeters,inches,miles,furlongs,fathoms,kilometers,oravarietyofotherunits.Unitsofmeasurementhavebeenestablishedforusewitheachofthefundamentaldimensionsmentionedpreviously.Thefollowingsectiondescribestheunitsystemsinusetodayandprovidesexamplesofunitsthatareusedineachsystem.1.2.1UnitSystemsTherearetwounitsystemsinnuclearengineeringfieldatthepresenttime,EnglishunitsandInternationalSystemofUnits(SI)3.Insomecountries,theEnglishsystemiscurrentlyused.Unitsystemconsistsofvariousunitsforeachofthefundamentaldimensionsormeasurements.ThebasicunitsofSIareshowninTable11.ItisalsocalledasMKSsystem.Table11theBasicUnitsoftheInternationalSystemofUnitsntitySymbolofntityNameSymbolofUnitLengthLMetermMassmKilogramkgTimetSecondsCurrentΙAmpereATemperatureTKelvinKntityofmassn(v)MolemolLuminousintensityI(Iv)CandelacdOtherquantitiescanbeexpressedasthebasicunits.TheyarecalledasderivedquantitiesandsomeofthemareshowninTable12.Table12SomeofDerivedntitiesUsedinNuclearEngineeringntitySymbolofntitySymbolofUnitRelationshipwiththeBasicUnitsEnergyEJkg·m2·s-2ForceFNkg·m·s-2PowerPWkg·m2·s-3ChargeCC·soltageVVkg·m2·s-3·A-1ResistanceRΩkg·m2·s-3·A-2CapacityCFkg-1·m-2·s4·A2InductanceLHkg·m2·s-2·A-2FrequencyfHzs-1MagneticFluxFWbkg·m2·s-2·A-1MagneticFluxDensityBTkg·s-2·A-1TheMKSsystemsaremuchsimplertousethantheEnglishsystembecausetheyuseadecimalbasedsysteminwhichprefixesareusedtodenotepowersoften.Forexample,onekilometeris1000meters,andonecentimeterisoneonehundredthofameter.TheEnglishsystemhasoddunitsofconversion.Forexample,amileis5280feet,andaninchisonetwelfthofafoot.TheprefixesusedinMKSsystemarelistedinTable13.Table13PrefixesofMKSSystemSymbolPrefixPowersofTenyyoct0-24zzept0-21aatt0-18ffemt0-15ppic0-12nnan0-9μmicr0-6mmilli10-3kkil03Mmega106Ggiga109Ttera1012Ppeta1015Eexa1018Zzetta1021Yyotta10241.2.2ConversionofUnitsToconvertfromonemeasurementunittoanothermeasurementunit(forexample,toconvert5feettometers),onecanusetheappropriateequivalentrelationshipfromtheconversionTable144.Table14RelationshiptoConvertUnitsLength1inch=25.4mm1fot=2inches=0.3048m1yard=3feet=0.9144m1mile=1760yards=1.609km1nauticalmile=1852mArea1squareinch=6.45squarecentimeter1squarefot=44squareinch=9.29squaredecimeter1squareyard=9squarefoot=0.836squaremeter1acre=4840squareyard=0.405hectare1squaremile=640acre=259hectareVolume1cubicinch=16.4cubiccentimeter1cubicfot=728cubicinch=0.0283cubicmeter1cubicyard=27cubicfoot=0.765cubicmeterMass1pound=16ounce=0.4536kgesmallofΔx.Wecallthefunctiony=f(x)isderivablenearthepointofx0andA·Δxiscalledasthedifferentialofthefunctiony=f(x)atpointx0correspondingtoΔx(theincrementalchangeofargumentx).Itisdenotedasdy.Theincrementalchangeofargumentxisthedifferentialofx.Itisdenotedasdx.Soweget:dy=Adx(13)Hereweuseanexampleinphysicstoexplaintheconceptofdifferential.Oneofthemostcommonlyencounteredmathematicalapplicationsofthedynamicsystemistherelationshipofpositionandtimeofamovingobject.Figure11representsanobjectmovinginastraightlinefroitionP1topositionP2.ThedistancetPfromafixedreferencepoint,pointO,alongthelineoftravelisrepresentedbyS1;thedistancetoP2frompointObyS2.Figure11MotionBetweenTwoPointsIfthetimerecordedbyatimer,whentheobjectisaitionP1ist1,andifthetimewhentheobjectisaitionP2ist2,thentheaveragevelocityoftheobjectbetweenpointsP1andP2equalsthedistancetraveled,dividedbythetimeelapsedasEquation(14).vav=S2－S1t2－t1(14)IfpositionsP1andP2arereallyclose,thedistancetraveledandtheelapsedtimearesmall.ThesymbolΔisusedtodenotechangesinquantities.Thus,theaveragevelocitywhenpositionsP1andP2areclosetogethercanbewrittenasEquation(15).vav=ΔSΔt=S2－S1t2－t1(15)Althoughtheaveragevelocityisoftenanimportantquantity,inmanycasesitisnecessarytoknowthevelocityatagiveninstantoftime.Thisvelocity,calledtheinstantaneousvelocity,isnotthesameastheaveragevelocity,unlessthevelocityisnotchangingwithtime.Thegraphofdisplacement（S）versustime（t）inFigure12willhelptodescribetheconceptofthederivative.Figure12DisplacementvsTimeUsingEquation(14)wefindtheaveragevelocityfrmStoS2is(S2-S1)/(t2-t1).IfweconnectthepointsS1andS2byastraightline,itdoesnotaccuratelyreflecttheslopeofthecurvedlinethroughalthotsbetweenS1andS2.Similarly,ifwelookattheaveragevelocitybetweentimet2andt3(asmallerperiod),weseethestraightlineconnectingS2andS3morecloselyfollowsthecurvedline.Assumingthetimebetweent3andt4islessthanthatbetweent2andt3,thestraightlineconnectingS3andS4verycloselyapproximatesthecurvedlinebetweenS3andS4.Aswefurtherdecreasingthetimeintervalbetweensuccessivepoints,theΔS/Δtwillbeclosetotheslopeofthedisplacementcurve.AsΔt→0,ΔS/Δtapproachestheinstantaneousvelocity.Theexpressionforthederiate(nthiscasetheslopeofthedisplacementcurve)canbewrittenasEquation(16).Inwords,thisexpressionwouldbe“thederivativeofSwithrespecttotime(t)isthelimitofΔS/ΔsΔaproaches0.”v=limΔt→0ΔSΔt(16)ThesymbolsdSanddtarenotproductsofdandS,orofdandt,asinalgebra.Theyarepronounced“deeess”and“deetee”,respectively.Andyoualsohavetonoticethattheletter“d”iswritteninnormalstylewhiletheletter“S”and“t”areallwritteninitalicstyle.Theseexpressionsandthequantitiestheyrepresentarecalleddifferentials.v=dSdt=limΔt→0ΔSΔt(17)Thus,dSisthedifferentialofSanddtisthedifferentialoft.Theseexpressionsrepresentincrementalchanges,wheredSrepresentsanincrementalchangeindistanceS,anddtrepresentsanincrementalchangeintimet.ThecombinedexpressiondS/dtiscalledaderiate;tisthederivativeofSwithrespecttot.Insimplestterms,aderivativeexpressestherateofchangeofonequantitywithrespecttoanother.Thus,dS/dtistherateofchangeofdistancewithrespecttotime.ReferringtoFigure12,thederivativedS/dtistheinstantaneousvelocityatanychosenpointalongthecurve.Thisvalueofinstantaneousvelocityisnumericallyequaltotheslopeofthecurveatthechosenpoint.Whiletheequationforinstantaneousvelocity,v=dS/dt,mayseemlikeacomplicatedexpression,itisafamiliarrelationship.Instantaneousvelocityispreciselythevaluegivenbythespeedometerofamovingcar.Thus,thespeedometergivesthevalueoftherateofchangeofdistancewithrespecttotime;itgivesthederivativeofSwithrespecttot;i.e.,itgivesthevalueofdS/dt.Theideasofdifferentialsandderivativesarefundamentaltotheapplicationofmathematicstodynamicsystems.Theyareusednotonlytoexpressrelationshipsamongdistancetraveled,elapsedtimeandvelocity,butalsotoexpressrelationshipsamongmanydifferentphysicalquantities.Oneofthemostimportantpartsofunderstandingtheseideasishavingaphysicalinterpretationoftheirmeaning.Forexample,whenarelationshipiswrittenusingadifferentialoraderivative,thephysicalmeaningintermsofincrementalchangesorratesofchangeshouldbereadilyunderstood.Whenexpressionsarewrittenusingdeltas,theycanbeunderstoodintermsofchanges.Thus,theexpressionΔT,whereTisthesymbolfortemperature,representsachangeintemperature.Aspreviouslydiscussed,alowercasedelta,d,isusedtorepresentverysmallchanges.Thus,dTrepresentsaverysmallchangeintemperature.Thefractionalchangeinaphysicalquantityisthechangedividedbythevalueofthequantity.Thus,dTisanincrementalchangeintemperature,anddT/Tisafractionalchangeintemperature.Whenexpressionsarewrittenasderivatives,theycanbeunderstoodintermsofratesofchange.Thus,dT/dtistherateofchangeoftemperaturewithrespecttotime.Example11:InterprettheexpressionΔv/v,andwriteitintermsofadifferential.Solution:Δv/vexpressesthefractionalchangeofvelocity.Itisthechangeinvelocitydividedbythevelocity.ItcanbewrittenasadifferentialwhenΔvistakenasanincrementalchange.Δv/vmaybewrittenasdv/vintermsofadifferential.Example12:GivethephysicalinterpretationofthefollowingequationrelatingtheworkWdonewhenaforceFmovesabodythroughadistancex.Solution:dW=Fdx.ThisequationincludesthedifferentialsdWanddxwhichcanbeinterpretedintermsofincrementalchanges.Theincrementalamountofworkdoneequalstheforceappliemtpliedbytheincrementaldistancemoved.Example13:Givethephysicalinterpretationofthefollowingequationrelatingtheforce,F,aplidoaobject,itsmassm,itsinstantaneousvelocityvandtimet.F=mdvdt(18)Solution:Thisequationincludesthederivativedv/dt;thederivativeofthevelocitywithrespecttotime.Itistherateofchangeofvelocitywithrespecttotime.Theforceaplidoaobjectequalsthemassoftheobjectmultipliedbytherateofchangeofvelocitywithrespecttotime.Equation(18)istheNewton’ssecondlaw.Itcanbeexpressedasthesecondderivativeofdistance.F=mdvdt=md2Sdt2(19)Toextendtheconceptofderivativetomultipleargumentsfunction,partialderiatesintroduced.Foramultiargumentsfunctionf,it’spartialderivativedefinedasEquation(110).fxx=x0y=y0z=z0=limΔx→0f(x0+Δx,y0,z0)－f(x0,y0,z0)Δx(110)1.1.2IntegralDifferentialsandderivativesaroseinphysicalsystemswhensmallchangesinonequantitywereconsidered.Forexample,therelationshipbetweenpositionandtimeforamovingobjectledtothedefinitionoftheinstantaneousvelocity,asthederivativeofthedistancetraveledwithrespecttotime,dS/dt.Inmanyphysicalsystems,ratesofchangearemeasureddirectly.Solvingproblems,whenthisisthecase,involvesanotheraspectofthemathematicsofdynamicsystems;namelyintegralandsummations.Figure13isagraphoftheinstantaneousvelocityofanobjectasafunctionofelapsedtime.Thisisthetypeofgraph,whichcouldbegeneratedifthereadingofthespeedometerofacarwasrecordedasafunctionoftime.Figure13GraphofVelocityvsTimeAtanygiveninstantoftime,thevelocityoftheobjectcanbedeterminedbyreferringtoFigure13.However,ifthedistancetraveledinacertainintervaloftimeistobedetermined,somenewtechniquesmustbeused.LetusconsiderthevelocitychangesbetweentimestAandtB.Thefirstapproachistodividethetimeintervalintothreeshortintervals(Δt1,Δt2,Δt3)andtoassumethatthevelocityisconstantduringeachoftheseintervals.DuringtimeintervalΔt1,thevelocityisassumedconstantatanaveragevelocityv1;duringtheintervalΔt2,thevelocityisassumedconstantatanaveragevelocityv2;duringtimeintervalΔt3,thevelocityisassumedconstantatanaveragevelocityv3.Thenthetotaldistancetraveledisapproximatelythesumoftheproductsofthevelocityandtheelapsedtimeovereachofthethreeintervals.Equation(111)approximatesthedistancetraveledduringthetimeintervalfromtAtotBandrepresentstheapproximateareaunderthevelocitycurveduringthissametimeinterval.S=v1Δt1+v2Δt+vΔt=∑3i=1viΔti(111)Thistypeofexpressioniscalledasummation.Asummationindicatesthesumofaseriesofsimilarquantities.TheuppercaseGreeklettersigma,∑,isusedtoindicateasummation.Generalizedsubscriptsareusedtosimplifywritingsummations.Forexample,thesummationgiveninEquation(111)wouldbewritteninthefollowingmanner:S=∑∞i=1viΔti(112)Thenumberbelowthesummationsignindicatesthevalueofiinthefirsttermofthesummation;thenumberabovethesummationsignindicatesthevalueofiinthelasttermofthesummation.Thesummationthatresultsfromdividingthetimeintervalintothreesmallerintervals,asshowninFigure13,onlyapproximatesthedistancetraveled.However,ifthetimeintervalisdividedintoincrementalintervals,anexactanswercanbeobtained.Whenthisisdone,thedistancetraveledwouldbewrittenasasummationwithanindefinitenumberofterms.S=∑∞i=1viΔti=∫tAtBvdt(113)Example14:Givethephysicalinterpretationofthefollowingequationrelatingthework,W,donewhenaforce,F,movesaboyfopositionx1tox2.W=∫xAxBFdx(114)Solution:Thephysicalmeaningofthisequationcanbestatedintermsofasummation.ThetotalamountofworkdoneequalstheintegralofFd