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1、Thermal Calculations OverviewContentsConduction,convection and radiationStream coefficientsOverall coefficientAverage values for whole exchangerHow TASC worksTASC modesQ=U A THeat flowHeat goes from hot to cold byConductionConvectionRadiationConductionHeat transfer rate predicted bywhere w is the th
2、ermal conductivity of the wallMetal wall(say)ThotTcoldywTypical values of thermal conductivityConvection(with conduction)In the modelthe bulk and wall temps.are the samethe slope at the wall is the sameThe heat flux is given byorRealityTbulkTw“Film”modelStream heat transfer coefficient is the stream
3、 coefficient sometimes referred to as the film coefficient-typical valuesFluidState W/m2.KWaterSingle Phase5000-7500WaterBoiling 5Bar3000-10000Steam Condensing 1 Bar10000-15000OrganicSingle Phase 0.5-2.5 cp750-1500OrganicBoiling 0.5-2.5 cp1000-3500OrganicCondensing 0.5-2.5 cp1500-4000Gas1 Bar80-125G
4、as10 Bar250-400RadiationTransfer of heat between objects without the use of an intermediate fluid Stefan-Boltzmanns Law:Heat transfer Q=A(T4-To4)Stefan-Boltzmann constant 5.67 x 10-8 W/(m2 K4)When designing shell and tube heat exchangers radiation is not normally consideredOverall coefficient-UWe ha
5、ve thermal resistances in serieswhereThotTcoldFoulingWe must add the resistances due to the fouling(often called fouling factors)ThotTcoldTypical fouling resistanceFluid streamr m2K/WSea water below 50oC0.0001Treated cooling water below 50oC0.0002Treated cooling water above 50oC0.0003Untreated water
6、0.0005-0.0008Fuel oil0.0008Crude oil0.0003-0.0010Refrigerant liquid0.0002Steam(oil free)0.0001Compressed air0.0003Natural gas0.0002Overall coefficient for tubeU defined on the basis of the area of the outside of the tubeMust correct for smaller inside area,hencewheredidoLocal and mean values“Overall
7、”means from the hot side to the cold side including all resistancesHowever it is still at a particular point in the exchanger:i.e.it is localHence you can have a local,overall coefficientLOCALLYFOR WHOLE EXCHANGERIntegrating over the exchanger areaLocal equationRearrangingand integratingdQdATotal ar
8、ea ATDefinitions of mean valuesFrom previous slidesComparing the two sidesMean stream coefficientsWhen required,these should be averaged as followsAlternative formSpecial case where Ts are linear with QTypical of single-phase duties(with constant specific heats)Parallel flow-usually counter currentE
9、qn.integrates to give log.mean temperature difference-LMTDTaTbQTemperatureDerivation of LMTDThe definition of MTDChanging variablesIntegratingRe-arrangingWhen the temp.lines are not straightDivide into straight-line zones and calc.LMTD for each zone.ThenQTemp.23451Calculating mean overall coefficien
10、tDivide into zones over which U does not vary greatly(usually same zones as for MTD calc.)Take U for zone as(Ua+Ub)/2 where Ua and Ub are the values at the ends of the zoneCalculate the area of each zone fromA=Q/UTLMHence for whole exchangerMultipass exchangersFor single-phase duties,theoretical cor
11、rection factors,FT,have been derivedFT values are less than 1Do not design for FT less than 0.8QTemp.T1T2t1t2Note:modern software does not use these chartsbut does the detailed integrationTypical FT correction factor curves T,t=Shell/tube side 1,2=inlet/outletFT problemsTASC does not use these corre
12、ction factorsIt uses a rigorous step-by-step calculationHowever,you should note that the curves are steep for low FT,making the design sensitive to process conditionsHow TASC handles 2 passesWe have for the two passesdhI=+UI(T-tI)dA/2dhII=-UII(T-tII)dA/2DividingHintout,houtAdAtin,hinHinATemp.TtIItIM
13、ean tube-site temperatureWe can average the temperatures between the passesThe two pass exchanger then appears like a one-pass exchangerHence use existing zone methodATemp.TtIItItavMore than 2 passesGuess inter-pass temp.Integrate to back end of exchangerTemps.must meet at back endRefine guess till
14、they doThen calc.tube-side average temp.as beforeATemp.Must guesstemp.hereto start calc.Lines mustmeet hereZoning in TASCTASC uses intelligent methods to divide the exchanger into the required zones with well-chosen boundariestIITtIEnthalpy TempCross-flow calculationTASC includes similar rigorous me
15、thods for solving cross-flow exchangers(TEMA X type)CHECKING:the basic TASC calc.Starting pointfully specified geometry,hence the Aactual knownthe required heat duty,Qreqthe process inlet and outlet conditions(implicit in above)the allowable pressure drops on the two sides,pallowMain results of calc
16、ulationthe calculated heat transfer area to do the duty,Acalcthe calculated stream pressure drops,pcalcThe CHECKING resultsArea ratio,Aactual/Acalc The pressure drop ratio for each stream,pcalc/pallowDetailed performance information including the“resistance diagram”Shell SideTube SideStreamFoulingWa
17、llResistance diagram(continued)Also shows the area attributable to each resistanceand the distribution of temperatures from hot to cold streamShell SideTube SideHeat transfer areaTemperatureTsTtTw“CHECKING”or“RATING”Some people software companies use the word RATING where we say CHECKINGThey are the
18、 same thingCHECKING is answering the questionswill this exchanger handle the specified dutyand how much under or over-surface does it haveSIMULATIONFor exchanger with fully specified geometryCalculates the outlet conditions of the two streams from their inlet conditionsTherefore answers the question
19、,“How will this exchanger perform?”SetSetGeometry setCalc.Calc.DESIGNSetRequired duty(inlet and outlet conditions)Maximum allowable pressure dropSome other optional and practical constraintsCalculates-what is the best exchanger geometry to achieve the duty?You have CHECKING type results for the best
20、 and alternative designsTHERMOSIPHONOften spelt THERMOSYPHONHandles the natural-circulation calculations in reboilersSteamCondensateLiquidTwo-phaseLiquidSurfaceTHERMOSYPHON(cont.)User fully specifies reboiler geometry including the inlet and outlet pipingUser specifies the pressure in the column,the
21、 height of the liquid in the column,and the inlet and outlet condition of the heating fluidTASC calculates the actual duty Q and the cold stream flowrate due to natural circulation driven by the liquid head in the columnTASC also calculates the hot stream flow-rate to meet specified outlet condition
22、sNote:Fixed flow option also availableComments on modesCHECKINGQuick and easy to use butResults may not be very accurate if the exchanger is greatly under/over surfacedSIMULATIONResults are a true prediction of the exchangers performance(especially pressure drop)butCan take a longer time to runPrope
23、rties must be specified over full temperature range otherwise program may fail to convergeMore commentsDESIGNCalculations not necessarily as accurate as CHECKING or SIMULATIONMost problems with DESIGN are caused by pressure drop constraintsMany engineers use DESIGN only to find a“ball park”design an
24、d refine it using CHECKING modeSummary of modesFour calculation modes:DESIGN-what exchanger will perform the specified duty?CHECKING(RATING)-will this exchanger perform the specified duty?SIMULATION-what duty will this exchanger perform?THERMOSYPHON-a Simulation of a thermosyphon reboiler and inlet/outlet pipework