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8-1-1997
Design, development, and performance of a
transient heat transfer resistance fouling monitor
David Gruszczynski
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DESIGN, DEVELOPMENT, AND
PERFORMANCE OF A TRANSIENT HEAT
TRANSFER RESISTANCE FOULING
MONITOR
BY: DAVID W. GRUSZCZYNSKI II
A Thesis Submitted in Partial
Fulfillment of the Requirements
for the
MASTERS OF SCIENCE
in
MECHANICAL ENGINEERING
Approved by:
Professor
s.
Kandlikar
(Thesis Advisor)
Professor
P. Marletkar
Professor
Charles Haines
(Department Head)
DEPARTMENT OF MECHANICAL ENGINEERING
COLLEGE OF ENGINEERING
ROCHESTER INSTITUTE OF TECHNOLOGY
Thesis Reproduction Permission Statement
Title
of Thesis: Design, Development, and Performance Testing of a Transient
Heat Transfer Resistance Fouling Monitor
I,
David W Gruszczynski II, prefer to be contacted each time a request for reproduction is
made. If permission is granted, any reproduction will not be for commercial use or
profit. I can be reached at the following address.
1449 Briarfield Way
Webster, NY 14580
Phone: (716) 265-1930
Acknowledgments
Iwouldliketo expressmygratitudeto Dr. S. Kandlikar
for
hisguidance andadvicethroughout thecourse ofthisproject. The
interactions
withhimwerebothmotivationaland
inspirational,
assuch,they
wereinstrumental in
thecompletion ofthiswork.
Iwould
like
to thankS.Kozak,
myworksupervisor, for allowingmetheflexibleworkhourstocompletethisproject andfor his supportofmyacademic endeavors. I
would alsoliketo thankJ.
Elman,
for his
assistanceinthegeneration ofthesimulatedfouling
film.Finally,
Iwouldlike
to thankmywife,Danae,
for hersupport andunderstandingthrough the
long
and attimes stressfulprocess. Withouthersupportthiswork would notAbstract
Fouling
canbe definedastheformation
ofdepositsonheattransfersurfacesthatimpede heat
transferandincreasetheresistancetofluid flow. Thepresenceoffouling
depositsresultinthelossof equipment efficiency, thelossofequipmentutilization, the
requirement ofadditional capitalexpenditures, and addsthecost ofcleaningtoa process.
Thecostof
fouling
to allindustries using heatexchangers intheUnited Stateswasestimatedtobe 2 x 10+1dollarsper yearin 1995.
Thus,
thecontrol ormitigationoffouling
iscriticaltoallindustrieswhichemploy heattransferequipment.Inthis work,asimplifiedtransientheattransferresistance
fouling
measurementapparatus wasdesignedanda simplified analysis protocol was formulated. The designof
theapparatuswasoptimizedthrough
first
order parametricmodelingandfinite differencemodelingofthesystem.
Asolventevaporationtechniquewas utilizedtodepositafilmofknownthickness
andthermalconductivity insidetheapparatus.
Testing
results, from beforeand afterfouling
deposition,
indicatethat theapparatusandanalysis protocolwere capableofmeasuring
fouling
thermalresistancesof2.6m2K/W. Thismeasurementcapability is
TableofContents
1.0 Introduction 1
2.0 Background 4
2.1 Classificationof
Fouling
Categories
42.2 The
Fouling
Process 62.3
Fouling
Mathematical Models 72.4
Fouling
Measurement Methods/Techniques 102.4.1
Commercially
AvailableFouling
Monitors 152.4.2 Heat Transfer Resistance
Fouling
Monitors 172.5 Objectives ofthePresent Work 20
3.0 Theoretical Analysis 22
3.1 Parametric Evaluation
Utilizing
IdealizedLumpedCapacitance Model 23
3.1.1
Sensitivity
AnalysisTheory
243.1.2
Sensitivity
Analysis Application 253.1.3 Measurement
Capability
Analysis 263.1.4 InfluenceofGeometricandHeatTransferProperties.. 27
3.2 Parametric Evaluation
Utilizing
Finite Difference Analysis 30TableofContents
(Continued)
3.2.2 EffectofApparatus Design andExperimental
Conditionson
Measurement
Capability
423.2.2.1 Effectof
Measurement
Node Position 463.2.2.2 EffectofDevice Volume 48
3.2.2.3 EffectofHeat Load 53
3.2.2.4 EffectofConvective Heat
Transfer Coefficient 55
3.3
Summary
ofParametric Analysis 584.0 Experimental Apparatus andProcedures 61
4.1
Recirculating
FlowLoop
614.2
Fouling
Measurement Apparatus 644.2.1 Heaters andAssociated Equipment 66
4.2.2 ThermocouplesandAssociatedEquipment 68
4.2.3 Data Collection/Computational Equipment 69
4.3 Methodof
Simulating Fouling
intheApparatus 704.4 Data Collection Procedure 73
4.5 Data Analysis- Historical 76
4.6 Data Analysis- Application
80
TableofContents
(Continued)
5.0 Results andDiscussion 85
5.1 ExperimentalDesign 85
5.2 Effectof
Heating
Rate 935.3 Comparison oftheTwo Apparatuses 96
5.4 Fouled Versus CleanApparatus 98
5.5 Comparison ofExperimentaland
TheoreticalTime Constants 107
6.0 Conclusions 109
7.0 Recommendations Ill
8.0 References 112
9.0 Appendices 117
A. Listof
Commercially
AvailableFouling
Monitors [Chenoweth
(1981)]
118B. VariationsoftheThermal Resistance
Fouling
Measurement Technique 120C. Finite Difference Model Results 121
D. Schematics ofWatlow Heaters 122
ListofSymbols
As
issurfacearea(m2)
Bi
is
theBiot Number-ratio ofthe
internal
thermalresistanceofa solidto the
boundary
layerthermalresistance (hLc/k)
Cp
is
thespecificheatat constant pressure(J /
kg
K)
d isthecircularductdiameter
(m)
/"isthefrictionfactor (2 tw
/
pUm2)
h
is
theconvectiveheattransfercoefficient(W/
m2K)
k
is
the thermalconductivity (W /mK)
Lc
isthecharacteristiclength(m)
If
isthe thicknessofthefouling
layer(m)
NuistheaverageNusseltnumber-
dimensionless
temperaturegradient at
thesurface(h d I
k)
PristhePrandtlnumber
-ratio of momentumto thermaldiffusivities
(cp
ju/k= vI a)r,
is
thedifference fromthe truevalueoftheparameterRR
is
thedependentparameter underevaluation,whichisafunction
ofX, Y,
etc.R,,.isthe truevalueofthe
dependent
parameterR
is
the thermalresistanceofthesystem(m2K/
W)
Rf
is
thefouling
heattransferresistance(K /W)
Re
is
theReynoldsnumber-ratio of
inertia
toviscousforces(pUm
d/ jj.)t
is
time(s)
Tistheinstantaneoustemperatureofthemass
(K)
Um
meanflow velocity (m/
s)V
is
thevolume of thelumpedmass(m3)
x,
is
thedifferencefromthetruevalue oftheparameterXX,,.isthetruevalueof an
independent
parametery, isthedifferencefromthe truevalue oftheparameterY
Ya
isthe truevalueof anindependentparameterGreek Symbols
ais the thermal
diffusivity
ofthefluid(m2/ s)<fid isthe
fouling
depositionrate(K/
W sec)0r
is
thefouling
removalrate (K/
W sec)jj. isthedynamic viscosityofthefluid
(
Pa* s =Ns/m2
)
p isthe
density
ofthematerial(kg/m3)
rt isthethermal timeconstant
(sec)
tw isthewall shear stress
(kg
/ m2s)
Subscripts
c clean surface
co convection
f
fouled
surfacei
initial
valuein
inherent
valueT total
heat
transferListofTables
Table 1:
Summary
oftheFouling
Measurement TechniqueAttributes
Table2: Calgon
Fouling
Monitoring
Devices: CalgonCorporation
ProductCatelog
(1996)
Table3: Lumped Capacitance
Sensitivity
Analysis:Geometric
andMaterial PropertiesTable4: Measurement
Capability
Influence Analysis: EffectofTimeandTemperatureMeasurement
Capability
onConvective Heat Transfer CoefficientMeasurement
Resolution,
Ah/h(Convective Heat Transfer Coefficientof1000(W/m2
K))
Table 5: Geometric Parameter Influence Analysis: EffectofSystem Volumeon
Convective Heat Transfer Coefficient Measurement
Resolution,
Ah/h(W/m2K)
Table 6: Geometric Parameter Influence Analysis: EffectofSystem Surface Areaon
Convective Heat Transfer Coefficient Measurement
Resolution,
Ah/h(W/m2K)
Table 7: Geometric Parameter Influence Analysis: EffectofInitial Heat Convective
Heat Transfer CoefficientonConvectiveHeat TransferCoefficient
Measurement
Resolution,
Ah/h(W/m2K)
Table 8: Geometric Parameter Influence Analysis: EffectofMeasured Temperature
DifferenceonConvective HeatTransferCoefficient Measurement
Resolution,
Table 9:
Breakdown
or"Allocation"
of
Nodes for
the12Nodeand45NodeTHERMONET Models
Table 10: Parameter Values
for
theFinite Difference AnalysisTable 1 1: Finite Difference
Analysis:
EffectoftheNumberofNodesandtheIterationTime
Step
SizeTable 12: Parameter Levels fortheEffectofMeasurement Node Radial
Position,
DeviceVolume,
HeatLoad,
andConvective Heat Transfer Coefficient StudiesTable 13: EffectofMeasurement Node Positionon
Fouling
DetectionCapability;
ModelVolume- 0.00 1 9
m3, Heat Load 1 000 W
Table 14: EffectofDevice Volumeon
Fouling
DetectionCapability;
Heat Load 1000WTable 15: EffectofHeat Loadon
Fouling
DetectionCapability;
Device Volume- 0.0019m3,Node Position 1 Data
Table 16: EffectofConvective Heat Transfer Coefficient on
Fouling
DetectionCapability;
Node Position 1 DataTable 17: Experimental
Conditions
Table 18: TimeConstant Data
Table 19: Convective Heat Transfer Coefficients- TestConfigurations 2and
4,
CleanTable 20:
Fouling
Resistance Calculations-Using
ExperimentalConvective HeatTransfer Coefficients
Table 21:
Fouling
ThicknessCalculations
-Using
Experimental Convective HeatListofFigures
Figure 1: Typical
Fouling
Resistance-Time Curves
Figure 2:
Schematic
RepresentationoftheTubularGeometry
Utilizedin
theTransientHeat Transfer
Resistance
Fouling
Measurement
DeviceFigure 3: Cross Sectional ViewoftheTransient
Fouling
Monitor HeatBlock;
FiniteDifference Approach
(THERMONET)
ModelFigure 4:
Schematic
Representationofthe12 Node andthe45 Node THERMONETModels
Figure 5: EffectoftheNumberofNodes andtheIteration Time
Step
ontheFiniteDifference Model Temperature Outputfor Node 2 (locatedatthecenter ofthe
tubular wall); h= 1000W/m2
K;
Q
=500 W(for 240 seconds)
Figure 6: Difference PlotoftheEffectoftheNumberofNodesandtheIteration Time
Step
ontheFinite Difference Model Temperature Outputfor
Node 2 (locatedatthecenter ofthe tubular wall); h= 1000W/m2
K;
Q
=500W (for 240seconds)
Figure 7: EffectofNode PositiononTemperature DifferenceMeasurement
Capability;
Model Volume- 0.0019
m3,Heat Load- 1000
W,
Heat TransferCoefficient
-10000W/m2
K,
Fouled Heat Transfer Resistanceof1 E-5 K m2Figure 8:
Effect
ofDevice VolumeonTemperature Difference MeasurementCapability;
Heat Load-1000
W,
Heat Transfer Coefficient- 1000W/m2
K,
Fouled Heat Transfer Resistanceof1 E-5 K
m2
/
WFigure9: EffectofHeat LoadonTemperature Difference Measurement
Capability;
Model Volume- 0.0019
m3, Heat Transfer Coefficient 10000
W/m2
K,
Fouled Heat Transfer Resistanceof1 E-5 Km2
/
W,
Node Position 1 DataFigure 10: EffectofConvective Heat Transfer CoefficientonTemperature Difference
Measurement
Capability;
Model Volume- 0.0019m\Heat Load - 1000
W,
Fouled Heat Transfer Resistanceof1 E-5 Km2
/
W,
Node Position 1 DataFigure 1 1: Schematic RepresentationoftheTransient Heat Transfer
Fouling
MeasurementSystem ExperimentalApparatus
Figure 12: Detailed SchematicoftheTransientHeat TransferApparatus
Figure 13: Photographs oftheTransient Heat Transfer Apparatus
Figure 14: Reflectometer Measurementof aClean Stainless Steel Surface
Figure 15: Reflectometer
Measurement
of aStainlessSteel Surface ExposedtoaSolutionof 5wt%Polystyrene in Tolulene
Figure 16: Reflectometer
Measurement
of aStainless Steel Surface ExposedtoaSolutionof 10wt%
Polystyrene
in ToluleneFigure 17: Graphical RepresentationoftheWilson Method [Wilson
(1915)]
Figure 18: ThermocoupleRaw Data
from
aTest Configuration 1 Experimental Run: 4.85Figure 19: Temperature Difference Data
for
Test Configuration 1: Apparatus1,
LowHeat,
Resultsfor
DifferentCooling
Water Flow RatesFigure 20: Temperature Difference Data for Test Configuration 2: Apparatus
1,
HighHeat,
Resultsfor DifferentCooling
Water Flow RatesFigure 21: TemperatureDifference Datafor Test Configuration 3: Apparatus
2,
HighHeat,
Results forDifferentCooling
Water Flow RatesFigure 22: ComparisonofTime Constants From Test Configuration 1 andTest
Configuration 2: Low Versus High Heat Load
Figure 23: ComparisonofTimeConstants From Test Configuration 2 andTest
Configuration 3: Apparatus 1 Versus Apparatus 2
Figure24: ComparisonofTimeConstants From Test Configuration 2 andTest
Configuration 4: Clean Versus Fouled Measurements
Figure 25: Wilson PlotofApparatus 1 Data: Fouled Versus Clean
Figure 26: Reflectometer MeasurementoftheStainless Steel End Cap: Indirect
Measurementofthe
Apparatus
Fouling
ThicknessFigure27: ComparisonoftheTheoretical Time Constants
(using
PetukhovandPopovCorrelationandtheLumped Capacitance
Model)
andtheExperimental Time1.0 Introduction
Fouling
canbe definedastheformation
ofdepositsonheat
transfersurfacesthatimpede heattransferandincreasetheresistancetofluid flow. Thepresenceof
fouling
deposits
resultsin
thelossof equipmentefficiency (through increased heatexchangerpowerutilization), the
loss
of equipment utilization(throughprocess shutdownsforcleaning), therequirement of additional capital expenditures(throughthecost of
over-sizing
heat
exchangers), and addsthecost ofcleaningto a process.Thus,
fouling
controlresearch
is
drivenby
its
costtoindustry.
Sohal(1993)
estimatedthecost offouling
intherefinery
industry
alonetobe betweenone andninebillion dollars. Bott(1995)
estimatedthecost of
fouling
forallindustries
using heatexchangersintheUnitedStatestobe 2 x10+1
dollarsperyear. Theseestimatesdonotincludetheincreasedcapitalexpenditures
thatwere requiredinequipmentdesign.
Thus,
thecontrol or mitigation offouling
iscriticaltoall industrieswhichemploy heattransferequipment:thepetroleum
industry,
themilkprocessing
industry,
power,andprocessindustries.Becauseofits
importance
to awide rangeofindustrialapplications,fouling
hasbeenstudiedfor manyyears. Information concerningthe typesof
fouling,
modelsforpredicting
fouling
rates,and methodsfor measuringfouling
is abundantintheopenliterature.
However,
detailed understandingofthe typeoffouling
andthecorrelation oftheactual
fouling
kineticswiththefouling
models canonly beattainedthroughexperimentation.
Thus,
fouling
monitoring
equipmentiscriticalto theunderstanding
ofthe
"fouling
Thepurpose ofthis
investigation
wastodesign, fabricate,
and evaluate afouling
measurementapparatus. Therequirements ofthedevice
included
sensitivityto thinfouling
films,
compact size,and state ofthe artaccuracyandrepeatability. Thetransientheattransferresistancetechniquewas selectedforthedesignofthe
fouling
monitoringdevice.
Thistechniquewas selectedbased
onitsdocumented
sensitivitytofouling
[Fetkovichetal.
(1977),
Kuzay
andBors(1984)].Toprovideinsight
into
theinfluenceofthegeometric parametersonthefouling
heattransferdetection
limit,
an erroranalysiswasperformed. Becauseofthecomplexityofthesystemofgoverningequations [Fetkovichet al.
(1977)],
afirst
orderapproximationwas performedutilizingthelumpedcapacitanceformula fortransientheat
transfer. Theanalysisdeterminedtheinfluence oftimeandtemperaturemeasurement
detectionlimitson measurement accuracy.
Afinite difference heattransferanalysiscode,THERMONET [Kandlikar
(1993)],
was usedto analyzethe transientheattransfer
in
theproposedfouling
measurementapparatus. A THERMONETmodelsensitivity analysiswas performedexaminingthe
number ofnodes and
iteration
step size. Modelswithdifferentvolumes,heatloads,
andconvective
heat
transfercoefficients were usedtooptimizethe designofthemeasurementdevice for increasedmeasurement sensitivity. Themodelresults were also comparedto
theexperimentaldatato
determine
thepredictivecapabilityofthemodels.Twotransientheattransfer
devices
werefabricated. Bothdevices
were evaluatedcoatingofknownthicknessandthermal
conductivity
wasthenappliedtotheinteriorofone ofthedevices. This devicewasthenre-evaluated. Theresultsoftheexperiments
were analyzed andconclusionsregardingthe
fouling
measurementcapabilityandfeasibility
oftheanalysistechniquewerederived.
Recommendationsfor futureupgradesto thedevicetoincreasemeasurementcapabilityand
improve
operationalaspects were2.0 Background
Thissection will provide an overview ofthecategories of
fouling,
thefouling
process,modelsfor predicting
fouling
rates, and methodsfor measuring fouling. Thereviewwill
focus
onthemethodsformeasuring
fouling
andonlyacursoryreview offouling
categories, thefouling
process,andfouling
modelswillbe
given.2.1 Classification of
Fouling
CategoriesFouling
isanextremelycomplex phenomenon. Fromafundamentalpoint ofview,it may becharacterized as a combinedmomentum,
heat,
and masstransferproblem[HermanandKnudson(1979)].
Fouling
isnotonlydependent
ontheoperatingconditions ofthe process,but is
highly
dependentontheoperating solution. Forthisreason
fouling
takesplaceby
differentmechanisms,atdifferentrates,possessesdifferentcompositions,andpossessesdifferenteffectsonthe overallprocess. Thecategories of
fouling (fouling
mechanisms)andtheenvironments inwhichthey
aredominantaresummarizedbelow.
Precipitation
(Crystallization) Fouling
Crystallizationofdissolvedmaterialinthe
flowing
fluidoccurswheneverthefluid
becomessupersaturated withrespectto the
depositing
material.Precipitation
fouling
canoccurin coolingwatersystems,
desalination
systems,boilers,
geothermalsystems, andParticulate
Fouling
Accumulationof particles
from
fluid containingsuspended solids. Particulatefouling
canoccurintheenergygeneration
industry.
Chemical Reaction
Fouling
Chemicalreactions
taking
place at aheat
transfersurface. Thesolid products ofthereactionaredepositedonthesurface. Chemicalreaction
fouling
canoccurinthepetroleumandfood processing
industry.
Corrosion
Fouling
Chemicalreaction ofcontaminant materials
(including
heat transfersurfaces) withthecirculatingprocess stream. Corrosion
fouling
canbeclassifiedintotwocategories:ex-situ(corrosionproductsform inthe solutionandaredepositedontheheattransfer
surface) or
in-situ
(corrosionproductsformattheheattransfersurface).Biological
Fouling
Developmentof anorganicfilm consistingofmicroorganisms
(microbial bio
fouling)
andtheirproductsontheheattransfer surface, ordepositionand growth of macroorganisms
Solidification
Fouling
Freezing
of a pureliquidorthehigher
meltingconstituents ofa multi-component solutiononto a subcooled surface.
Combination
Fouling
Thistypeof
fouling
takesinto
consideration"realworld"fouling. Most
fouling
thatoccurs onheattransfersurfaces aretheresult oftwo ormore oftheabovedescribed
fouling
types. Intheinitialstageofdepositformation,
one particulartypeoffouling
maypredominate, andthiscan acceleratedeposition
by
othertypesoffouling.2.2 The
Fouling
ProcessInadditionto thecategoryofthe
fouling,
thegeneral sequence of eventsby
whichthe
fouling
takes place,fouling
kinetics,
is ofimportance in understanding fouling.Informationon
fouling
kineticscan provideinsightinto
theinfluenceofsolutionproperties,processequipment, andprocess parameters onthe
fouling
process. Inaddition,informationon
fouling
kinetics
can also provideinsight intotheselectionoftheoreticalmodelsfor
describing
thefouling
process. Theseaspects ofthefouling
process enabletheengineerto generatepreventative measurestomitigateor
delay
fouling.
The
fouling
processcanbe divided in fivesteps[Epstein(1983),
Knudson1. Initiation: Formationor aggregation of
fouling
componentsinthebody
ofthefluid2. Transport: Transportof
fouling
componentsto theheattransfersurface3.
Attachment:
Attachmentorformation
ofthedepositattheheattransfersurface4. Removal: Removalofmaterial
from
theheat
transfersurface(by:dissolution,
erosion orre-entrainment,spalling,orsloughing)
5.Aging: Changes inthephysical or chemicalnature ofthe
fouling
Itis importanttonotethat theseprocesses aredifferent for every
fouling
problemduetothedifferencesinprocessconditions,equipment(surface
finishes,
etc.) andprocesssolutions.
However,
in boththeoilrefineryandthemilkprocessing industries it hasbeen
observedthatproducts with similar composition andprocessingconditions exhibitsimilar
fouling
composition/kinetics.2.3
Fouling
Mathematical ModelsFouling
is
consideredtobe
theresult oftwo simultaneous processes: depositionand re-entrainment. Thenet
fouling
rateorfluxis
thedifferencebetweenthese twoprocesses.
dRt
Vdt T" Tr
Where: dRj/dt isthenet
fouling
ratefy
isthefouling
depositionrate<f>r isthe
fouling
removal rateAmodel ofthis formwasfirstproposed
by
Kem andSeaton (1959). Sincethennumerous
fouling
modelshave been generated, butthey
allfollowtheformproposedby
KernandSeaton (1959).
The
fouling
processcanbestudiedby
examiningchangesintheheattransfercharacteristicsof a process. Changes
in
themeasured convectiveheattransferrepresentthethermalconductivity
due
tofouling
in
thedevice.1 1
//
Rf = = 1 Equation 2
f
hfA,
hrA,
kfA,
Where:
Rf
isthefouling
heattransferresistance(K/W)
hf
isthefouledsurface convectiveheattransfercoefficienthc
isthecleansurface convectiveheattransfercoefficientAs
issurface areak
is
the thermalconductivityIf
isthe thicknessofthefouling
layerThekineticsof
fouling
canbemeasuredby
monitoringfouling
resistance withtime(Rf
versustime). Knudson
(1992)
hasidentified
that thefouling
resistance curvesfollowseveraldistinctmodels;
linear,
falling
rate, asymptotic, and saw-tooth.The
fouling
resistancecurves shownin Figure 1 canbemodeledby
Equation 1 if& 1
I-o: = - 2 o
III
ra >. ro u- < toW O
o
E
c
o
'55
oQ. 0)
Q
O)
3
O
n u
"5.
3
characteristic of a
fouling
system wherethedeposition
rateis
constant andtheremovalrate
is
either zeroor constant. The asymptoticfouling
modelischaracteristicof afouling
system wherethedepositionrate
is
constant andtheremoval rateisproportionalto thethicknessofthe
deposit;
orthedeposition
ratedecreases
withdepositthicknessandtheremovalrate remains constant. This behavior
is indicative
ofdepositswhichflakeoffeasily dueto fluid flow (shear forces). The
falling
ratefouling
modelischaracteristic ofafouling
system wherethedeposition
and removal rates are complex functionsofflowrate,
fouling
thickness,
etc. Thesaw-toothfouling
modelischaracteristicof afouling
system wherethe
fouling
periodicallysloughs off orperiodiccleaningis
performed. Thetime segment,denoted
tD,
representsthedelay
timeofthefouling. Thiscan occurduring
thenucleation ofthe
fouling
layerontheprocess surfaceatthemicroscopiclevel.During
this timeno significantlosses
in
heattransferare observed andinsome casestheheattransferresistance
is
decreased dueto theincreased surfaceroughness [Knudson (1992)].2.4
Fouling
MeasurementThe primarygoals ofa
fouling
measurementsystem are:Togainunderstandingofthe
kinetics
offouling
andcleaning;To understandthecorrelation
between
fouling
kineticsand processperformance;To gainunderstandingofthenature ofthe
fouling
deposits;
and,Tothis end,numerousdevices have been
designed for
theexplicitpurposeofmeasuringprocess
fouling.
Thefouling
monitoringdevices have
utilizeddifferentmeasurementmethodsortechniques. A listofthe
different
measurementmethodsalongwith abriefdescriptionoftheprincipleof operation
is included
below.Heat Transfer Resistance Techniques
Heattransferresistancetechniques
involve
thecomparative assessmentofadevices heattransferperformancebeforeand after
fouling
occurs. Thismeasurementtechniquehasbeenutilizedasbothalocalmeasurementparameter(change in heattransferof a specific
location inthedevice [Somerscales et al.
(1986)])
andas a global or overallmeasurementparameter(change
in
heattransferoftheentiredevice
[WebbandKim(1989),
Abu-Zaid(1992)]). Themeasurementtechniquehas beenusedin boththesteadystatemode,
usingtheWilson Technique [Wilson
(1915),
Somerscaleset al.(1986)],
andthe transientmode[Fetkovichet al. (1977)].
Somerscales
et al.(1986)
statedthat thermalresistancesas lowas 1.96 x 10"5to3.56 x 10"5m2
K/Wweremeasuredwith ahigh levelof
confidence
by
thesteadystate,globalmeasurement system. Fetkovichetal.(1977)
andPanchal
(1989)
bothstatedthermalresistancesmeasurementcapabilityof10x 10"5 m2Optical Techniques
Opticaltechniquesuse opticallytransparent sectionsthatenabletheuseof optical sensors
for
themeasurement offouling
[Gallot-Lavallee
et al. (1982)]. The accuracyandprecisionofthis technique
depend
notonlyontheopticalsystem appliedbutontheoptical properties ofthefouling.
Gallot-Lavallee
et al. utilized an optical sensortoqualitatively detecttheamountofmaterial removed
by
a chemicalcleaningsolution(opticalsystem outputvoltage was correlatedto the
fouling
levelin
thechemicalsolution).
RemovableSection Technique
Theremovable sectiontechniqueutilizes removable "witnessplates"
or samplecoupons
placed
in
theprocess flowstream[Roeet al. (1985)]. Thesample coupons canbe
removedfromtheprocessingequipment
for
detailedanalysisofthefouling. Analysistechniquesincludemicroscopic, gravimetric, spectroscopic,andotheranalytical
techniques. Roeetal.
(1985)
statedseveraldisadvantagesto thistechnique,
including:
Intrusivenature ofsampling
technique;
Thesamplemaynot seeexact processconditions
(temperature,
etc.);Sample may betoosmallforphysicalor chemicalassays;and,
Pressure
Drop
TechniqueThepressure
drop
techniqueinvolves
themonitoringoftheinletand outletpressureof anapparatustodetect
increased
resistancetofluid flow
(back pressure) [Roeet al. (1985)].Theresistanceto
fluid
flowis
theresult of adecrease
inthesizeoftheflowpath,hydraulic
diameter,
dueto theaccumulation offouling. Roeet al. stated severaldisadvantagesto this
technique;
themeasurementis
insensitiveuntil acriticalfouling
thicknessisreached, and pressure
drop
is
usually only important fortransferprocesses(i.e.,
fouling
willbeginto affecttheheattransferprocesseslong
beforethepressuremeasurementwilldetectthepresence offouling).
ElectrochemicalTechniques
Electrochemicaltechniques are usedforthedetectionandmonitoringof corrosion
fouling. Several differenttechniques exist[Winters et al. (1993)]:
Zeroresistanceammetry
(ZRA);
Electrochemicalcurrent noise
(ECN);
Electrochemicalpotentialnoise
(EPN);
and,Linearpolarizationresistance
(LPRM).
Wintersetal.
(1993)
statedthatEPNandECNwereparticularlysensitivetocorrosion pitHolographic
Interferometry
Technique
Holographic
interferometry
fouling
measurementtechniqueutilizestwo-wavelengthinterferometry
tomeasuretemperatureand concentration profilessimultaneously incrystalline
fouling
[Seyfried(1990)]. Seyfried
(1990)
utilizedthis technique to observe thedynamicfouling
process,inreal-time.Ultrasonic Technique
Ultrasonic
fouling
measurementtechniqueutilizestransmissionultrasonicstomeasurefouling
[Withers (1993)]. Withers statedthat the techniquewouldbeusefulforthemeasurementof
fouling
deposits inthepipework of continuoushigh-temperatureprocessingplants. Withershasshownthat the techniquewas abletodetecta minimum
thicknessof0.1 mm.
Specialized Methods: Silicon Sensor
Thesiliconsensortechniqueutilizes a siliconchip embeddedintothewallofthe test
surfacetodetectthepresence of
fouling [Stenberg
etal.(1988)]. Withinthesiliconchipaheaterresistorwasusedto setupathermal
boundary
layerwhich wasmeasuredby
atemperaturesensing diode.
Fouling
changedthe thermalboundary
layerproducedby
theheaterresistor, thuschangingthetemperaturemeasured
by
the temperaturesensingdiode.
Stenberg
etal.'s resultsimpliedthat thermalresistances as lowas 0.5 x 10"5m2
K/W
Table 1 summarizesoftheattributesofthe
different
fouling
measurementtechniques.Measurements utilizingtheseprincipals of operationhavebeenemployed in
laboratory,
andindustrialsettings. Theenvironmentdictatesthedesignoftheinstrument.FryerandPritchard
(1987)
proposedfourcriteriaforthedesignof eitheraproduction orlaboratory fouling
monitoringsystem:1. Size Themonitor should
be
of modest size sothatit
canbe
easilyinstalled,
serviced, andreplaced;
2. Cost Becauseit isnot an acceptedpracticetoutilize
fouling
monitorsit is importantthat theinitialcostsbe
low;
3.
Reliability
Themonitor shouldbe robustlyconstructed,requiretheminimummaintenance and provide reproducibledatathatis easyto
interpret;
and,4. Relevance- The
device
shouldcloselymodeltheprocessflowconditions sothat
resultscanberelatedbackto thefull scale process
2.4.1
Commercially
AvailableFouling
MonitorsBecauseofthe
importance
offouling
in industrialoperations, heattransferfouling
monitoring systemshave been
developed
andare nowcommerciallyavailable.Chenoweth
(1981)
providedasummary
offouling
monitoringdevices
thatwerecommerciallyavailablein
1981,
seeAppendix
A. Thefouling
monitor manufacturersTable 1:
Summary
oftheFouling
Measurement Technique AttributesFouling
Measurement Technique1 2 3 4 5 6 7 8
Direct Measurement X X
Indirect Measurement X X X X X X
Local
Fouling
Measurement X X X X X X XGlobal
Fouling
Measurement X X XLaboratory
Technique X X X X X X XProduction Technique X X X
Commercially
Available X X X XTypeof
Fouling
Detected All Most BeOpaqueAll All Corrosion All All All
SizeofEquipment Moderate Moderate Small Small Moderate Large Small Small
CostofEquipment Moderate Unknown Low Low Unknown Unknown Moderate Unknown
Reliability
Excellent Unknown Good Poor Unknown Unknown Unknown Unknown Measurement Resolution Excellent Good Excellent Poor Good Good Poor ExcellentMeasurementCycle Time Good Good Poor Excellent Good Good Excellent Good
Fouling
Measurement Technique Key:1. Heat Transfer Resistance Techniques
2. Optical Techniques
3. RemovableSection Technique
4. Pressure
Drop
Technique5. Electrochemical Technique
6. Holographic
Interferometry
Technique7. Ultrasonic Technique
commercially
availabletoday. Twoofthecompaniesprovidedinformation
onthe"stateoftheart"
commerciallyavailable
devices (attempted
contactswiththeother companieswere unsuccessful).
Calgon'
sproductline
included four
monitoringdevices
thatfocusedoncorrosiondetection
andtwomonitoring devicesthatfocused
onthedetectionofgenericfouling.Thedevicenames and abrief descriptionoftheprinciple ofoperation areincluded
in
Table2.
BridgerScientific offeredanupdatedversionoftheirDATS 1200
fouling
monitor. Theupdateddesignutilizesthesame
theory
of operation astheDATS 1200device,
overallheattransferresistancetechnique,
applied asasteadystate measurement.NeitherCalgonnorBridgerScientificoffered a
fouling
monitorthatutilizesthe transientheattransferresistance measurementtechnique. This may bearesult ofthesimplicityof
theanalysistechniquesforthesteadystatedevices.
2.4.2 Heat Transfer Resistance
Fouling
MonitorsBecauseofthemeasurementaccuracyanddetailed documentationofthe
measurement
theory,
heattransferresistancemeasurementtechniquesareby
farthedominantmethodfor measuring
fouling.
Withinthisvery broadmeasurementtechniquecategory, thereare twotheoriesof application- transientand
steadystate. Inthe transient
Table 2: Calgon
Fouling Monitoring
Devices:Calgon
Corporation
ProductCatalog
(1996)
DeviceName PrincipleofOperation
Coupon Removable Section Technique- Gravimetric Analysis
CORRATER Electrochemical Technique- LinearPolarization-Resistance
CORROSOMETER Electrochemical Technique- Electrical Resistance (Zero
Resistance
Anemometry)
CDTU Removable SectionandVisualization Techniques- Observation
andAnalysisofCorrosion Under Heat Transfer Conditions
DDM Heat Transfer Resistance Technique
-Steady
State,
OverallMeasurement Technique - Off-line Accelerated
Fouling
Test DeviceTest Heat
Exchanger
HeatTransfer Resistance Technique
-Steady
State,
OverallMeasurement Technique- Off-line Real-Time
monitored. Inthesteadystatemethod, thewalltemperature
is
monitored whileaconstant
heat
flux isapplied.HermanandKnudson
(1979)
provided an overview ofthedifferentheat
transferresistance
fouling
measurement apparatusesthathave
been developed (see Appendix B).Theoverview
included
theforms ofheating,
the systemgeometry, applicationtechnique(transient andsteadystate),andthe
distinguishing
featuresofthedevices.Heating
techniques that
have
beenemployedin heattransferfouling
monitors include indirectelectrical,
thermoelectric,
direct
electrical,sensibleheating
offluids,
condensingvapor,andelectrically heatedwiresand coils. System geometriesthathave beenemployedin
heattransfer
fouling
monitors includeannular, circular, and complex. Inadditiontotheoperational and configuration
differences,
HermanandKnudson'
s summary
(1979)
(Appendix
B),
also noteswhetherthemeasurement was local(applying
to thefouling
at aspecificpointintheprocessequipment)or overall
(applying
to thefouling
oftheentireapparatus). Localmeasurements givereliable results for bothsmall
fouling
resistancesandlowheat fluxes [Fischeret al. (1975)].
However,
this techniquecanleadtofluctuating
resultsparticularly incaseswherethefouling builds-up
andperiodicallybreaks free fromthesurface
(e.g.,
sedimentationfouling
- saw-toothfouling
pattern).Fetkovichetal.,
(1977)
andPanchal(1989)
statedthatthermalresistances aslowas 10x 10"5 m2
K/Wcouldbemeasuredaccurately
by
thetransient, local
measurementDirectmeasurement oftemperature
differential
by
athermopileandtheaccuracyoftimemeasurements gives greater measurementprecision; and,
Insensitivity
tocalibration- exceptfortheflow
meter.The complexityofthis techniquelies inthemethodfor
determining
therelationshipbetween
theheat
transferresistance andthe timeconstant. Fetkovich(1976)
andKuzay
etal.
(1982)
utilizedan analyticalapproximationto theexact solutionfortheanalysis ofexperimentaldata.
Kuzay
et al.(1982)
also modeledthe transientheattransfersystemusingthe finite differencetechniqueand comparedtheresults ofthemodelto the
experimentalresults.
2.5 Objectives ofthePresent Work
Theobjectivesto this studywere:
1. To
identify
theexistingfouling
measurementtechniquesand comparetheirfouling
detectioncapabilities;
2. Tounderstandtheinfluenceofprocessandgeometric parameters onthemeasurement
sensitivityof aselectedmeasurement
technique;
3. To designandfabricatea prototype
fouling
monitorutilizingoptimizeddesignconditions;
4. Totesttheprototype
fouling
monitor anddetermineitsmeasurementcapability; and,5. Tocomparethemeasurementcapabilityoftheprototype
fouling
monitor withfouling
Therequirements ofthe
device included:
sensitivitytothinfouling
films,
stateoftheartaccuracyandrepeatability,and compactdimensions. Thetransientheattransfer
resistances measurementtechniquewasselected foruseinthisstudy basedon
its
3.0
Theoretical
AnalysisFouling
analysisby
the transientheat
transferresistancemethodhas beenemployedinnumerous studies
[Fetkovich
(1977),
Panchal(1989),
Meyeretal(1981),
Meyeretal.
(1982),
Kuzay
(1980),
Owens (1986)].
Themost commondesignutilizedwasthe"Carnegie-Mellon"Ocean Thermal
Energy
Conversion(OTEC)
design[Fetkovich (1977)]. The geometryofthe
device
wastubular,
withheatbeing
appliedtotheoutersurfaceandthecoolingwater
flowing
inside
(fouling
surface).Fouling
wasmonitored
by
measuringtherateofheattransferfromatube walltothecoolingsolutionflowing
inside.
Variationsonthisdesign
were utilizedby
otherinvestigators [Owens(1986)],
butthesamegeometryand measurement concepts were used. Meyeret al.'s(1981)
studyutilizedthe transient techniquewith adifferentgeometry, arectangularflowpath.Basedonthe
dominance
ofthe tubulargeometryin
pasttransientheatfouling
monitorsandits in-situapplicability, the tubulargeometrywas selectedforthisstudy.
Atheoreticalanalysis ofthe transientheattransferresistance measurement
techniquewasperformedto
determine
the effect of process anddesignvariables onmeasurement capability. Theprocess variables examinedincludedthe temperatureand
timemeasurementcapability, the
heat load
appliedto thedeviceandtheconvectiveheattransfercoefficient. The
design
variables examinedweretheinside
and outsidediameter(volume)
ofthecylindricalapparatus. Thetimeandtemperaturemeasurementconvective
heat
transfer coefficient,andthedevice geometrywere evaluatedby
finite
difference
modelinganalysis.3.1 Parametric Evaluation
Utilizing
Lumped Capacitance ModelTo gain
insight
into
theeffectsofmeasurement capabilities ontheprecision of atransient thermalresistance
fouling
monitor, anerroranalysis oruncertaintyestimationwas performed. Becauseofthecomplexityofthegoverningequations intheexact
analytical solution [Fetkovichetal.
(1977)],
theuncertaintyestimation was performedutilizinga
first
order approximationto theanalytical solution. Thefirst
orderapproximationused wasthelumpedcapacitanceheattransfer
formulation.
The
lumped
capacitanceheattransfergoverningequationis
shownin
Equation3.pVc T.-T
t = - In-i
-Equation 3
H
T-Tn
Where: tistime
p isthe
density
ofthematerialVisthevolume ofthematerial
cp isthespecific
heat
at constant pressureTisthetemperature
Ti
istheinitialtemperatureofthematerialEquation 3
is
rearrangedinto
aform
equatingthemeasurement andgeometric parametersto theconvectiveheattransfercoefficient.
pVc T-T
h =
'-^
In-*=-Equation 4
tA. T-T M
3.1.1
Sensitivity
AnalysisTheory
Schenck
(1979)
provided a comprehensive overview ofthetheory
ofuncertaintyanalysisinexperimentation. Schenckoutlinedtwogenericformulations fortheerror and
uncertaintyanalysis ofaresult: thedeviationoftheresultfromthe truevalue andthe percent error. Thedeviation quantitycanbeusedtopredicttheinfluenceof an
independentparameter measurementcapabilityon adependentparameter.
The deviation quantity
formulation
utilizedthefirst
two termsof aTaylorseriesexpansion[Schenck (1979)].
R +k =f(Xlr+
K+...)+[(
)
* ! 1 +(
),
,r yx^+...
tr \ J\ tr tr ^flC**
\\
dfj
1!Where: Risthe
dependent
parameterunder evaluationRfr
is
the truevalue ofthedependentparameterr
is
thedifference from
Rfr
x, isthe
difference from
the truevalue ofthe parameter,X,,.X,,.
is
the truevalue of anindependent
parametery,
is
thedifference from
the truevalue ofthe parameter,Y,,.Ya
is
thetrue value of anindependent
parameterThe
first
termintheTaylorseries expansion(f(Xtr
+Yfr
+...)
)is
thedefinitionofR;r
Thus,
thefirsttermonbothsides ofEquation 5drops fromtheformulationleaving
thedifferenceordeviationterms.
,cR, k ,dR, A .
r
r, =
(
)
Ajc+(
)
vAy+.... Equation 61
ax y 3Y x
Equation6 canbeusedtocalculatetheeffectofoneparameteron another.
3.1.2
Sensitivity
Analysis
ApplicationThesensitivityanalysis equation was appliedto the
lumped
capacitancegoverning equation, Equation4. The resultingsensitivityanalysis
formulation is
shownAh= At+ AT Equation 7
dt r dTt
Where:
oh
isthepartial
derivative
oftheconvectiveheattransfer,
ordt t
3i -pVc T-T
=-V-^ln(^-^) Equation8
aT
t2A.T-T'
oh
is
thepartialderivative
ofthe convectiveheattransfer,
ordT,
gh -pVcn T-T
=-!E-c!fs-)m Equation9
cTt
tA,
Tt-Tj
Equation 7
is
theformulation fordetennining
theeffect of one parameter onanother,i.e.
theeffect oftimeandtemperaturemeasurementcapabilityon convectiveheattransfer
measurement capability. Equations 8and9aredefinitionsofthederivativesgivenin
Equation7.
3.1.3 Measurement
Capability
AnalysisEquations
7, 8,
and9were utilizedtoanalyzetheinfluenceof measurementcapabilityonconvectiveheattransferdetection limits. Thegeometric system evaluated
wasthatof atubular geometrywithfluid
flowing
through thecenter. Thelumped
volume, surfacearea, andthermodynamicproperties ofthematerial. Theseparameters
were calculatedforthetubulargeometryand utilizedintheanalysis. Figure 2
is
aschematicrepresentationofthe tubularapparatus. Theportionoftheapparatus
being
modeled
is
identified in Figure 2. Thegeometric and materialpropertyvalues usedin
theanalysisaregivenin Table 3.
Threelevelsoftemperaturemeasurement andtimemeasurementcapabilitywere
evaluated. Theresultsoftheconvective
heat
transfermeasurementresolution analysisare givenin Table 4. Theresults
in
Table 4 are given as a ratio ofthechangein
convectiveheattransfer to the
initial
convectiveheattransfer coefficient,Ah/h(h= 1000W/m2
K).
Evaluationofdata
in
Table 4revealsaone-to-one correlationbetweenthetemperaturemeasurementcapabilityandtheconvectiveheattransfercoefficientdetection
capability (fortherange evaluated). Inaddition, thedata
in
Table 4revealsthat thereislittletono effect oftimemeasurementcapabilityontheconvectiveheattransfer
coefficientdetection capability (fortherangeevaluated).
3.1.4 Influenceof
Geometric
andHeatTransfer PropertiesSensitivity
analysis was also performedtoevaluatetheinfluence
ofthegeometric(volume andsurfacearea)and
heat
transferproperties(convectiveheat
transfercoefficient,measuredtemperature
difference)
absolute values.Variations
of each0) o > 0) O C1 a> % E E O = Q) W On iss 3 O) = o a> *. o o c o w 5 w JS c * 0) i_ w a> 0) *-c w Q. C o re
*
o ^ re re a> E I^
c u a> (0 "55 c w S h-ii c o o N .* o o .Q t-CD 4* CO *j o c .C 0 T3 a> c tfc: =63
2 0 1 o 0 > U 0 C T3 0 0 -C 0 M-*- oCN 0 I~
CO < E E o CD -C 0 1 *1 f-0 si CNJ r--o
o o2 "Da, o o OT
n C 3
o CO0 O o o < 0 0 E 0 o ro .9? a> Q. C ^ t
JcT ^ ,7 ro
O o oo
ai CO CO -Q
i_ i
0 a) ro ro 0 03
Table 3: Lumped Capacitance
Sensitivity
Analysis: GeometricandMaterialProperties
GeometricorMaterial
Property
Valueusedin Lumped CapacitanceSensitivity
AnalysisConvective Heat
Transfer,
h 1000W/m2KOutside Radiusof
Device,
r0 0.03175mInside Radiusof
Device,
rf 0.0079375mLengthof
Device,
L 0.1524mVolumeof
Device,
V 0.0004524m3
InnerSurface
Area,
A^
0.007601 m2Specific Heat
(316
SS),
cp
468J/kg
KDensity
(316SS),
p 8238kg/m3Applied Temperature
Difference,
Ts
-TM
10 KMeasured Temperature
Difference,
T-T^
1.37 KTime,
t 456.39 secondsTable 4: Measurement
Capability
InfluenceAnalysis: EffectofTimeandTemperature Measurement
Capability
onConvective Heat TransferCoefficientMeasurement
Resolution,
Ah/h (Convective Heat Transfer Coefficientof1000(W/m2
K))
Temperature Measurement
Capability ( K)
0.1 0.01 0.001
Time 0.01 0.006906 0.0007104
0.00009075
Measurement 0.001 0.006887 0.0006906
0.00007104
Tables
5 through8 forvolume,surfacearea,convectiveheattransfer,
and measuredtemperature
difference,
respectively.Theanalysisrevealedthat thevolume
(Table
5),
surface area(Table6),
andconvectiveheattransfercoefficient(Table
7)
parametersdidnotsignificantlyinfluence
the finalconvectiveheattransfer coefficient measurementcapability.
However,
themeasuredtemperaturedifference did havean effect
(Table
8). Largermeasuredtemperaturedifferencesresulted
in
anincreased
sensitivityto theconvectiveheat
transfercoefficient measurement.
Thefactthat the volume,surfacearea,and convective
heat
transfercoefficientdidnothaveaninfluenceonthefinalconvectiveheattransfer coefficient measurement was
notintuitive. These factorsshouldhave hadan
impact.
Thisresultisbelieved
tobearesult oftheover-simplification ofthe transientheattransfersystem
by
thelumpedcapacitance analysis.
Thus,
thefinite difference
modelingapproach was pursuedtoattaininformationonthe
influence
oftheseparameters.3.2 ParametricEvaluation
Utilizing
FiniteDifference AnalysisThelumpedcapacitance analysis
did
notyieldinformationonthecriticaldesign
parameters ofthedevice.
Therefore,
afinite
element analysis wasperformedtogenerateinput
ongeometricdesignandheat
transferconditions. A commerciallyavailablefinitedifferencesoftwarepackage,
THERMONET
[Kandlikar(1993)],
was usedtostudytheTable 5: Geometric Parameter Influence Analysis: EffectofSystem Volumeon
Convective Heat Transfer Coefficient Measurement
Resolution,
Ah/h (W/m2K)
Convective Heat Transfer Measurement
Resolution,
Ah/h(W/m2K)
System 0.00016
Volume 0.00041
(m3)
0.001850.000693
0.000691
0.000689
Table6: Geometric Parameter Influence Analysis: EffectofSystem Surface Area
onConvective HeatTransfer Coefficient Measurement
Resolution,
Afi/h (W/mK)
Convective Heat TransferMeasurement
Resolution,
Ah/h (W/m2K)
System 0.0047
Surface 0.0076
Area (m3
)
0.02430.00069
0.000691
Table 7: Geometric Parameter Influence Analysis: EffectofInitial HeatConvective
Heat Transfer Coefficienton
Convective
Heat Transfer Coefficient MeasurementResolution,
Ah/h(W/m2K)
Convective
Heat Transfer MeasurementResolution,
Ah/h (W/m2K)
InitialConvective 100
Heat Transfer 1000
Coefficient(W/m2K
)
100000.000689
0.000691
0.00071
Table 8: Geometric Parameter Influence Analysis: EffectofMeasured
Temperature DifferenceonConvective Heat Transfer Coefficient
Measurement
Resolution,
Ah/h (W/m2K)
Convective HeatTransfer
Measurement
Resolution,
Ah/h(W/m2K)
No.ofTime Constants 1
(40%)
0.01175(%
Difference Between 2(86%)
0.000691detection
capability. See Figure 3for
a schematicrepresentationoftheheattransfersystem
being
modeled. Isothermalfluidflows
through thecenterofthedevice,
heatis
appliedto theoutsidediameterofthetubularshaped
device,
theheat load is
removed(turned
off)andthe temperatureinthecylindricaldevice ismeasured withtime.The
finite difference
models generatedtakeinto
consideration allthreedimensionsofthetubular geometry. Theangular
dimension
ofthe tubulargeometrywastakenintoconsiderationthrough the volume, conduction,and convection parameters of
themodel. Heatconduction
in
theangulardimensionwas considered negligible. Theaxial
dimension
ofthe tubulargeometrywastakeninto
considerationthrough thevolumeofthemodel. Heatconductionintheaxialdimensionwas considered negligible. The
resultingmodel appearstobeonedimensional (see Figure
3),
however,
thevolumevalues used
in
themodeltakeintoconsiderationtheangular and axialdimensions
ofthedevice.
3.2.1 EffectofModel Node andIterationTime
Step
A studywas performedto
determine
theeffectofthenumber of nodes andtheiterationtimestepsize onthe
THERMONET
modeloutput. TwoTHERMONET
modelsofthecylindricalmeasurement system werecreatedtoperformthis study;a 12node
model and a45 nodemodel. Two
iteration
timesteps wereevaluatedfor
eachmodel; 1and 10seconds forthe 12nodemodel,and2 and10secondsforthe45node model.
o 0 *J u 'E o o 5 2 O)
P
c UJ z "5 O o LU 2 *- 0 c UJ .2 X c re o o u re **- a o < 5 0 0 O c > 0 ^_ L_ re .2? c it o b s u 0 0 (0 'E (A E (A O it? o uoco CO L. o 0 L. *-3 re O) 0 en to c i/> 0 "5 c o
is
LL co c 0 0 CO c O) CD c 1-c 0 0 .c CO ' 0 M o a. 0 0 a: w 1- o 00 'c
o 0 o
2 co 2
0
Di n
C -i
j= c
(-C 0 ^
0 0 0 0
to > 0 .5 0 -1' CO -CO 0 "-1 C/J CO 1_ 0
R CO0 c 'ro
3 o
D
Figure4: SchematicRepresentationofthe 12 Node
andthe45Node THERMONETModels
12 Node Model
1 Node
Representing
AirGap
BetweenStainlessSteel Tube
andOuter Shell
10
Equally
Spaced NodesRepresenting
theStainless Steel TubeoftheTransient
Fouling
Monitor45 Node Model
1 NodeRepresenting Air
Gap
Between Stainless Steel TubeandOuterShell
43
Equally
Spaced NodesRepresenting
the Stainless SteelTubedivided into
severaldistinctsectionsrepresenting
theflowing
solution, thewallofthe testdevice,
andtheairsurroundingthe testdevice
(laboratory
environment). The breakdownofthenumber of nodes
representing
each section ofthedeviceis
shownin
Table9.Thegeometry,materials ofconstruction,
initial
conditions,andheatload for bothmodels werethesame. The
detailed
model conditions are givenin
Table 10.Thetemperatureoutput ofthe
four
models were examinedfortrends. Thenode attheposition
in
thecenter ofthe testdevice
wall,for
eachmodel,was selectedasthecomparison
datum
point. Thecenter nodetemperatureoutputdatafrom
thefourmodelsare givenin Table 11. Allmodel results were comparedtotheresults ofthe45 node,2
second
iteration
stepmodel1. Thedifference betweenthemodel output andthe45node,2 second
iteration
stepmodel are also givenin
Table 11. Theaveragedifference between
each model andthe45node,2second
iteration
stepmodelis
givenin
thelast
row ofTable 11.
Themodeltemperatureoutputdataand modelcomparisonresults
(Table
11)
areshowngraphically in Figures 5and
6,
respectively. Figure 5 clearlyshowsthatallmodelsproducethesamegeneraltemperature trends. Thisresult was expected. Theplot
ofthedifferenceevaluationresults, Figure
6,
showstwogeneraldeviation
patterns. The12nodemodels(both 1 and 10second
iteration
timesteps)exhibitlarge deviations
earlyin
the temperaturetransient, corresponding
to the time that theheatload
was appliedin
themodel. The45nodemodel shows arandomly
fluctuating
difference
pattern.Table 9: Breakdownor"Allocation" ofNodes forthe 12 Nodeand45 Node
THERMONET
ModelsModel Section 12 Node
Model
45 Node
Model
Flowing
Solution 1 1WallofTest Device 10 43
Air
Surrounding
TestDevice
1 1
Table 10: Parameter Values fortheFinite Difference Analysis
Input Parameter Valueusedin THERMONET Analysis
Convective Heat
Transfer,
h 1000W/m2 KOutside Radiusof
Cylinder,
r0 0.03175mInsideRadiusof
Cylinder,
rs 0.0079375mLengthof
Cylinder,
L 0.1524mVolumeof
Cylinder,
V 0.0004524m3Inner Surface
Area,
A,
0.007601 m2Heat
Load,
H 500 W for 240secondsMaterialofConstruction 316 Stainlesssteel
Table 11: FiniteDifferenceAnalysis: EffectoftheNumberofNodesandthe
Iteration Time
Step
Size;
Model OutputTemperature,
Degrees CTime
(sec)
45 NodeModel,
2 sec. Iteration TimeStep
(45/2Model)
45 NodeModel,
10 sec. Iteration TimeStep
(45/10Model)
12 NodeModel,
1 sec. Iteration TimeStep
(12/1Model)
12 NodeModel,
10 sec. Iteration TimeStep
(12/10Model)
Difference Evaluation Results Between 45/2 Model and45/10 Model Difference Evaluation Results Between 45/2 Model and12/1 Model Difference Evaluation Results Between 45/2 Model and12/10 Model 0 30.0000 30.0000 30.0000 30.0000 0.0000 0.0000 0.0000 10 30.0026 30.0213 30.0042 30.0320 0.0187 0.0017 0.029520 30.0352 30.0920 30.0506 30.1260 0.0568 0.0154 0.0907 30 30.1406 30.2300 30.1828 30.2955 0.0895 0.0422 0.1550 40 30.3355 30.4419 30.4094 30.5407 0.1064 0.0739 0.2052 50 30.6138 30.7222 30.7190 30.8540 0.1085 0.1052 0.2402 60 30.9609 31.0628 31.0954 31.2253 0.1019 0.1345 0.2644
70 31.3633 31.4535 31.5241 31.6444 0.0902 0.1608 0.2812 80 31.8095 31.8836 31.9935 32.1026 0.0741 0.1840 0.2931 90 32.2897 32.3479 32.4948 32.5921 0.0582 0.2050 0.3023 100 32.7965 32.8382 33.0209 33.1068 0.0417 0.2244 0.3103 110 33.3240 33.3510 33.5667 33.6417 0.0269 0.2427 0.3176 120 33.8688 33.8820 34.1280 34.1927 0.0132 0.2592 0.3239
130 34.4275 34.4283 34.7015 34.7567 0.0008 0.2741 0.3292 140 34.9978 34.9872 35.2846 35.3308 0.0106 0.2868 0.3330 150 35.5784 35.5556 35.8751 35.9129 0.0228 0.2967 0.3345 160 36.1679 36.1324 36.4711 36.5012 0.0355 0.3032 0.3333 170 36.7648 36.7166 37.0714 37.0943 0.0482 0.3066 0.3294 180 37.3672 37.3071 37.6746 37.6908 0.0601 0.3074 0.3235 190 37.9730 37.9031 38.2798 38.2896 0.0700 0.3067 0.3166 200 38.5800 38.5034 38.8860 38.8900 0.0766 0.3060 0.3100 210 39.1873 39.1073 39.4926 39.4912 0.0800 0.3053 0.3039 220 39.7935 39.7142 40.0990 40.0926 0.0793 0.3055 0.2991 230 40.3984 40.3224 40.7046 40.6935 0.0760 0.3063 0.2952 240 41.0016 40.9302 41.3091 41.2936 0.0715 0.3074 0.2920 250 41.6002 41.5127 41.9078 41.8605 0.0875 0.3076 0.2603 260 42.1654 42.0452 42.4625 42.3639 0.1202 0.2972 0.1986 270 42.6542 42.5067 42.9294 42.7899 0.1475 0.2752 0.1357 280 43.0505 42.8901 43.2996 43.1382 0.1604 0.2491 0.0878 290 43.3607 43.2022 43.5843 43.4162 0.1585 0.2236 0.0555 300 43.5991 43.4515 43.7996 43.6338 0.1476 0.2005 0.0347 310 43.7796 43.6444 43.9599 43.8009 0.1352 0.1802 0.0213 320 43.9142 43.7920 44.0765 43.9264 0.1222 0.1623 0.0122
330 44.0120 43.9021 44.1585 44.0178 0.1099 0.1465 0.0058 340 44.0802 43.9816 44.2126 44.0811 0.0986 0.1324 0.0009
Table 11:
Continued....
Time(sec)
45 NodeModel,
2 sec. Iteration TimeStep
(45/2Model)
45 NodeModel,
10 sec. Iteration TimeStep
(45/10Model)
12 NodeModel,
1 sec. Iteration TimeStep
(12/1Model)
12 NodeModel,
10 sec. Iteration TimeStep
(12/10Model)
Difference Evaluation Results Between 45/2 Model and45/10 Model Difference Evaluation Results Between 45/2 Model and 12/1 Model Difference Evaluation Results Between 45/2Model and12/10 Model360 44.1483 44.0691 44.2568 44.1424 0.0792 0.1085 0.0059
370 44.1560 44.0843 44.2543 44.1476 0.0716 0.0983 0.0084
380 44.1500 44.0842 44.2391 44.1396 0.0658 0.0891 0.0104
390 44.1327 44.0743 44.2133 44.1205 0.0584 0.0807 0.0122
400 44.1058 44.0556 44.1788 44.0921 0.0502 0.0730 0.0137
410 44.0710 44.0270 44.1369 44.0559 0.0440 0.0659 0.0151
420 44.0294 43.9936 44.0889 44.0131 0.0358 0.0595 0.0163
430 43.9822 43.9543 44.0357 43.9648 0.0279 0.0535 0.0174
440 43.9302 43.9087 43.9783 43.9119 0.0215 0.0481 0.0184
450 43.8742 43.8581 43.9173 43.8550 0.0161 0.0431 0.0192
460 43.8149 43.8040 43.8534 43.7948 0.0109 0.0385 0.0201
470 43.7529 43.7455 43.7871 43.7320 0.0074 0.0342 0.0209
480 43.6886 43.6845 43.7187 43.6668 0.0041 0.0301 0.0218
490 43.6225 43.6209 43.6488 43.5998 0.0015 0.0263 0.0227
500 43.5549 43.5560 43.5776 43.5312 0.0011 0.0226 0.0238
510 43.4861 43.4900 43.5053 43.4613 0.0039 0.0191 0.0249
520 43.4163 43.4233 43.4322 43.3904 0.0070 0.0159 0.0259
530 43.3455 43.3557 43.3584 43.3187 0.0101 0.0129 0.0269
540 43.2741 43.2886 43.2842 43.2463 0.0145 0.0102 0.0278
550 43.2022 43.2209 43.2097 43.1735 0.0186 0.0075 0.0288
560 43.1301 43.1531 43.1350 43.1003 0.0231 0.0050 0.0298
570 43.0576 43.0848 43.0602 43.0268 0.0271 0.0025 0.0308
580 42.9851 43.0162 42.9853 42.9533 0.0311 0.0002 0.0319
590 42.9127 42.9470 42.9105 42.8796 0.0343 0.0021 0.0330
600 42.8402 42.8786 42.8358 42.8060 0.0384 0.0044 0.0342
Average
Difference
Values
a o o
5
0 II o 6" <M < E o o o II e> = .c c5i5
W 3 0) I-E -5T |_ -"D gS
.2 _ o
h a) a S <
0 0) o
Sot
2 i_
-c o
** +* .j:
D *; -'
C > -o > J2 o o i_ CM E o 3 Z z ._ ** 3 o .ro u it 0 UJ -io SS a 0 = E
g
u-I-o O o o o o o o o
o O o o o o o o o
o O o o o o o o o
o O o o o o o o o
CD * tN o oo CD * <N o
* * * * to CO CO CO CO
=
it
ro => JS .q </) 3 0 H E : -C H **5
o .2 .-*2 ro t- c ro a) - O ro w o c o *. oc o -n ro (0 (0 0 o *t M u O
55
N3
o o
z ._ II
a 6"
o a-CM
+ -n <
E
1
o o o - So 2- II
*O t0 E -0 0 O "O C O 2 S
s
Qg
1_ <o ro a> := =?
O) u- 'E o oSi Si 25
T >* T> TI T3
c C C
ro ro CO a) <i> a>
u n T3
C) C) o :> > ^
CM CM CM in in in >* * <t
c c c
< 0) <u < m CD
?. J
<i> <i) CO CD m m
R R
c c c
(1) (1) 0>"=T <1) a) fe CD a) <l> JD -o S= o *= n *= o
OS Q5 Q^
(0 D c o o 0) JO 0) E
Theaveragedifference betweenthe45 Nodemodelwitha2second
iteration
stepand a 10seconditeration stepwas0.057
K;
andtheaveragedifferences betweenthe45Nodemodel witha2 second
iteration
stepandthe 12 Nodemodel with 1 and 10seconditeration
steps were0.139 and0.131K,
respectively. Theaveragedifferenceresultsindicate
thatboththenumberof nodes andtheiteration
timestepeffecttheaccuracyofthemodeloutputresults.
The THERMONETmodelwasusedto
determine
thechangein
performanceofthedevicewithchangingprocess and geometric parameters. Sincethe trendsexhibitedin
all models werethe same, themodel which utilizedtheshortest"runtime"
or computer
analysistimewas usedtoperformthegeometric parameters and
heat
loadanalysis.Thus,
forexecution of geometricand processconditionanalysistheTHERMONETmodel with
thesmallest number of nodesandthelargest iterationtimestepwere used
(i.e.,
the 12nodemodel with a 10second
iteration
timestep).3.2.2 EffectofApparatus DesignandExperimental Conditions on
Measurement
Capability
The 12 Node 10second
iteration
stepmodel wasusedto evaluatethefouling
detection abilityoftheproposed measurementdevicewithchangesto the
device
volumeandheat load. Theanalysis was performed
by
generating twofinitedifference
modelswiththe
different device
volumes(same
surfacearea,i.e.,
insidediameter)
andexecutingtemperatureoutput atthreenode
locations (different
radial locationswithintheheat
transferapparatus)were examinedto
determine
theeffect ofmeasurementnoderadiallocation.
Evaluationswereperformedtoexaminetheeffect ofthevolumeofthetestdevice (outside
diameter
ofthereferenceblock
andheaterblocks),
theamountofheataddedto the test
device,
andtheabsolute value oftheconvectiveheattransfercoefficient2. Thefactor levelsevaluated
in
thestudyare givenin Table 12.Theanalysis was conducted
by
comparingmodel results with and without asimulatedfouling.
Fouling
wassimulatedinthemodelby
executingmodel runswithconvective
heat
transfervaluesthatvariedfrom
theabsolute values outlinedin Table 12(i.e.,
simulatingtheincreased
thermalresistance ofthefouling
layer).By
comparingthemodel resultsfromthe"clean"device
(h,,)
to thoseofthef