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Rochester Institute of Technology

RIT Scholar Works

Theses

Thesis/Dissertation Collections

8-1-1997

Design, development, and performance of a

transient heat transfer resistance fouling monitor

David Gruszczynski

Follow this and additional works at:

http://scholarworks.rit.edu/theses

This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please contactritscholarworks@rit.edu.

Recommended Citation

(2)

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

(3)

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

(4)

Acknowledgments

Iwouldliketo expressmygratitudeto Dr. S. Kandlikar

for

hisguidance and

advicethroughout thecourse ofthisproject. The

interactions

withhimwereboth

motivationaland

inspirational,

assuch,

they

were

instrumental in

thecompletion ofthis

work.

Iwould

like

to thankS.

Kozak,

myworksupervisor, for allowingmetheflexible

workhourstocompletethisproject andfor his supportofmyacademic endeavors. I

would alsoliketo thankJ.

Elman,

for his

assistanceinthegeneration ofthesimulated

fouling

film.

Finally,

Iwould

like

to thankmywife,

Danae,

for hersupport andunderstanding

through the

long

and attimes stressfulprocess. Withouthersupportthiswork would not
(5)

Abstract

Fouling

canbe definedasthe

formation

ofdepositsonheattransfersurfacesthat

impede heat

transferandincreasetheresistancetofluid flow. Thepresenceof

fouling

depositsresultinthelossof equipment efficiency, thelossofequipmentutilization, the

requirement ofadditional capitalexpenditures, and addsthecost ofcleaningtoa process.

Thecostof

fouling

to allindustries using heatexchangers intheUnited Stateswas

estimatedtobe 2 x 10+1dollarsper yearin 1995.

Thus,

thecontrol ormitigationof

fouling

iscriticaltoallindustrieswhichemploy heattransferequipment.

Inthis work,asimplifiedtransientheattransferresistance

fouling

measurement

apparatus wasdesignedanda simplified analysis protocol was formulated. The designof

theapparatuswasoptimizedthrough

first

order parametricmodelingandfinite difference

modelingofthesystem.

Asolventevaporationtechniquewas utilizedtodepositafilmofknownthickness

andthermalconductivity insidetheapparatus.

Testing

results, from beforeand after

fouling

deposition,

indicatethat theapparatusandanalysis protocolwere capableof

measuring

fouling

thermalresistancesof2.6m2

K/W. Thismeasurementcapability is

(6)

TableofContents

1.0 Introduction 1

2.0 Background 4

2.1 Classificationof

Fouling

Categories

4

2.2 The

Fouling

Process 6

2.3

Fouling

Mathematical Models 7

2.4

Fouling

Measurement Methods/Techniques 10

2.4.1

Commercially

Available

Fouling

Monitors 15

2.4.2 Heat Transfer Resistance

Fouling

Monitors 17

2.5 Objectives ofthePresent Work 20

3.0 Theoretical Analysis 22

3.1 Parametric Evaluation

Utilizing

IdealizedLumped

Capacitance Model 23

3.1.1

Sensitivity

Analysis

Theory

24

3.1.2

Sensitivity

Analysis Application 25

3.1.3 Measurement

Capability

Analysis 26

3.1.4 InfluenceofGeometricandHeatTransferProperties.. 27

3.2 Parametric Evaluation

Utilizing

Finite Difference Analysis 30
(7)

TableofContents

(Continued)

3.2.2 EffectofApparatus Design andExperimental

Conditionson

Measurement

Capability

42

3.2.2.1 Effectof

Measurement

Node Position 46

3.2.2.2 EffectofDevice Volume 48

3.2.2.3 EffectofHeat Load 53

3.2.2.4 EffectofConvective Heat

Transfer Coefficient 55

3.3

Summary

ofParametric Analysis 58

4.0 Experimental Apparatus andProcedures 61

4.1

Recirculating

Flow

Loop

61

4.2

Fouling

Measurement Apparatus 64

4.2.1 Heaters andAssociated Equipment 66

4.2.2 ThermocouplesandAssociatedEquipment 68

4.2.3 Data Collection/Computational Equipment 69

4.3 Methodof

Simulating Fouling

intheApparatus 70

4.4 Data Collection Procedure 73

4.5 Data Analysis- Historical 76

4.6 Data Analysis- Application

80

(8)

TableofContents

(Continued)

5.0 Results andDiscussion 85

5.1 ExperimentalDesign 85

5.2 Effectof

Heating

Rate 93

5.3 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

Available

Fouling

Monitors [Chenoweth

(1981)]

118

B. VariationsoftheThermal Resistance

Fouling

Measurement Technique 120

C. Finite Difference Model Results 121

D. Schematics ofWatlow Heaters 122

(9)

ListofSymbols

As

issurfacearea

(m2)

Bi

is

theBiot Number

-ratio ofthe

internal

thermalresistanceofa solid

to the

boundary

layerthermalresistance (h

Lc/k)

Cp

is

thespecificheatat constant pressure

(J /

kg

K)

d isthecircularductdiameter

(m)

/"isthefrictionfactor (2 tw

/

pUm2

)

h

is

theconvectiveheattransfercoefficient(W

/

m2

K)

k

is

the thermalconductivity (W /m

K)

Lc

isthecharacteristiclength

(m)

If

isthe thicknessofthe

fouling

layer

(m)

NuistheaverageNusseltnumber-

dimensionless

temperature

gradient at

thesurface(h d I

k)

PristhePrandtlnumber

-ratio of momentumto thermaldiffusivities

(cp

ju/k= vI a)

r,

is

thedifference fromthe truevalueoftheparameterR

R

is

thedependentparameter underevaluation,whichisa

function

of

X, Y,

etc.

R,,.isthe truevalueofthe

dependent

parameter

R

is

the thermalresistanceofthesystem(m2K

/

W)

Rf

is

the

fouling

heattransferresistance(K /

W)

(10)

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 oftheparameterX

X,,.isthetruevalueof an

independent

parameter

y, isthedifferencefromthe truevalue oftheparameterY

Ya

isthe truevalueof anindependentparameter

Greek Symbols

ais the thermal

diffusivity

ofthefluid(m2/ s)

<fid isthe

fouling

depositionrate(K

/

W sec)

0r

is

the

fouling

removalrate (K

/

W sec)

jj. isthedynamic viscosityofthefluid

(

Pa* s =N

s/m2

)

p isthe

density

ofthematerial

(kg/m3)

rt isthethermal timeconstant

(sec)

tw isthewall shear stress

(kg

/ m2

s)

(11)

Subscripts

c clean surface

co convection

f

fouled

surface

i

initial

value

in

inherent

value

T total

heat

transfer
(12)

ListofTables

Table 1:

Summary

ofthe

Fouling

Measurement Technique

Attributes

Table2: Calgon

Fouling

Monitoring

Devices: Calgon

Corporation

Product

Catelog

(1996)

Table3: Lumped Capacitance

Sensitivity

Analysis:

Geometric

andMaterial Properties

Table4: Measurement

Capability

Influence Analysis: EffectofTimeandTemperature

Measurement

Capability

onConvective Heat Transfer Coefficient

Measurement

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/m2

K)

Table 6: Geometric Parameter Influence Analysis: EffectofSystem Surface Areaon

Convective Heat Transfer Coefficient Measurement

Resolution,

Ah/h(W/m2

K)

Table 7: Geometric Parameter Influence Analysis: EffectofInitial Heat Convective

Heat Transfer CoefficientonConvectiveHeat TransferCoefficient

Measurement

Resolution,

Ah/h(W/m2

K)

Table 8: Geometric Parameter Influence Analysis: EffectofMeasured Temperature

DifferenceonConvective HeatTransferCoefficient Measurement

Resolution,

(13)

Table 9:

Breakdown

or

"Allocation"

of

Nodes for

the12Nodeand45Node

THERMONET Models

Table 10: Parameter Values

for

theFinite Difference Analysis

Table 1 1: Finite Difference

Analysis:

EffectoftheNumberofNodesandtheIteration

Time

Step

Size

Table 12: Parameter Levels fortheEffectofMeasurement Node Radial

Position,

Device

Volume,

Heat

Load,

andConvective Heat Transfer Coefficient Studies

Table 13: EffectofMeasurement Node Positionon

Fouling

Detection

Capability;

Model

Volume- 0.00 1 9

m3, Heat Load 1 000 W

Table 14: EffectofDevice Volumeon

Fouling

Detection

Capability;

Heat Load 1000W

Table 15: EffectofHeat Loadon

Fouling

Detection

Capability;

Device Volume- 0.0019

m3,Node Position 1 Data

Table 16: EffectofConvective Heat Transfer Coefficient on

Fouling

Detection

Capability;

Node Position 1 Data

Table 17: Experimental

Conditions

Table 18: TimeConstant Data

Table 19: Convective Heat Transfer Coefficients- TestConfigurations 2and

4,

Clean
(14)

Table 20:

Fouling

Resistance Calculations

-Using

ExperimentalConvective Heat

Transfer Coefficients

Table 21:

Fouling

Thickness

Calculations

-Using

Experimental Convective Heat
(15)

ListofFigures

Figure 1: Typical

Fouling

Resistance-Time Curves

Figure 2:

Schematic

RepresentationoftheTubular

Geometry

Utilized

in

theTransient

Heat Transfer

Resistance

Fouling

Measurement

Device

Figure 3: Cross Sectional ViewoftheTransient

Fouling

Monitor Heat

Block;

Finite

Difference Approach

(THERMONET)

Model

Figure 4:

Schematic

Representationofthe12 Node andthe45 Node THERMONET

Models

Figure 5: EffectoftheNumberofNodes andtheIteration Time

Step

ontheFinite

Difference 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 Output

for

Node 2 (located

atthecenter ofthe tubular wall); h= 1000W/m2

K;

Q

=500W (for 240

seconds)

Figure 7: EffectofNode PositiononTemperature DifferenceMeasurement

Capability;

Model Volume- 0.0019

m3,Heat Load- 1000

W,

Heat Transfer

Coefficient

-10000W/m2

K,

Fouled Heat Transfer Resistanceof1 E-5 K m2
(16)

Figure 8:

Effect

ofDevice VolumeonTemperature Difference Measurement

Capability;

Heat Load

-1000

W,

Heat Transfer Coefficient- 1000

W/m2

K,

Fouled Heat Transfer Resistanceof1 E-5 K

m2

/

W

Figure9: 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 Data

Figure 10: EffectofConvective Heat Transfer CoefficientonTemperature Difference

Measurement

Capability;

Model Volume- 0.0019

m\Heat Load - 1000

W,

Fouled Heat Transfer Resistanceof1 E-5 Km2

/

W,

Node Position 1 Data

Figure 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 Exposedtoa

Solutionof 5wt%Polystyrene in Tolulene

Figure 16: Reflectometer

Measurement

of aStainless Steel Surface Exposedtoa

Solutionof 10wt%

Polystyrene

in Tolulene

Figure 17: Graphical RepresentationoftheWilson Method [Wilson

(1915)]

Figure 18: ThermocoupleRaw Data

from

aTest Configuration 1 Experimental Run: 4.85
(17)

Figure 19: Temperature Difference Data

for

Test Configuration 1: Apparatus

1,

Low

Heat,

Results

for

Different

Cooling

Water Flow Rates

Figure 20: Temperature Difference Data for Test Configuration 2: Apparatus

1,

High

Heat,

Resultsfor Different

Cooling

Water Flow Rates

Figure 21: TemperatureDifference Datafor Test Configuration 3: Apparatus

2,

High

Heat,

Results forDifferent

Cooling

Water Flow Rates

Figure 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

Thickness

Figure27: ComparisonoftheTheoretical Time Constants

(using

PetukhovandPopov

CorrelationandtheLumped Capacitance

Model)

andtheExperimental Time
(18)

1.0 Introduction

Fouling

canbe definedasthe

formation

ofdepositson

heat

transfersurfacesthat

impede heattransferandincreasetheresistancetofluid flow. Thepresenceof

fouling

deposits

results

in

thelossof equipmentefficiency (through increased heatexchanger

powerutilization), the

loss

of equipment utilization(throughprocess shutdownsfor

cleaning), therequirement of additional capital expenditures(throughthecost of

over-sizing

heat

exchangers), and addsthecost ofcleaningto a process.

Thus,

fouling

control

research

is

driven

by

its

costto

industry.

Sohal

(1993)

estimatedthecost of

fouling

inthe

refinery

industry

alonetobe betweenone andninebillion dollars. Bott

(1995)

estimated

thecost of

fouling

forall

industries

using heatexchangersintheUnitedStatestobe 2 x

10+1

dollarsperyear. Theseestimatesdonotincludetheincreasedcapitalexpenditures

thatwere requiredinequipmentdesign.

Thus,

thecontrol or mitigation of

fouling

is

criticaltoall industrieswhichemploy heattransferequipment:thepetroleum

industry,

themilkprocessing

industry,

power,andprocessindustries.

Becauseofits

importance

to awide rangeofindustrialapplications,

fouling

has

beenstudiedfor manyyears. Information concerningthe typesof

fouling,

modelsfor

predicting

fouling

rates,and methodsfor measuring

fouling

is abundantintheopen

literature.

However,

detailed understandingofthe typeof

fouling

andthecorrelation of

theactual

fouling

kineticswiththe

fouling

models canonly beattainedthrough

experimentation.

Thus,

fouling

monitoring

equipmentiscriticalto the

understanding

of

the

"fouling

(19)

Thepurpose ofthis

investigation

wasto

design, fabricate,

and evaluate a

fouling

measurementapparatus. Therequirements ofthedevice

included

sensitivityto thin

fouling

films,

compact size,and state ofthe artaccuracyandrepeatability. Thetransient

heattransferresistancetechniquewas selectedforthedesignofthe

fouling

monitoring

device.

Thistechniquewas selected

based

onits

documented

sensitivityto

fouling

[Fetkovichetal.

(1977),

Kuzay

andBors(1984)].

Toprovideinsight

into

theinfluenceofthegeometric parametersonthe

fouling

heattransferdetection

limit,

an erroranalysiswasperformed. Becauseofthecomplexity

ofthesystemofgoverningequations [Fetkovichet al.

(1977)],

a

first

order

approximationwas performedutilizingthelumpedcapacitanceformula fortransientheat

transfer. Theanalysisdeterminedtheinfluence oftimeandtemperaturemeasurement

detectionlimitson measurement accuracy.

Afinite difference heattransferanalysiscode,THERMONET [Kandlikar

(1993)],

was usedto analyzethe transientheattransfer

in

theproposed

fouling

measurement

apparatus. A THERMONETmodelsensitivity analysiswas performedexaminingthe

number ofnodes and

iteration

step size. Modelswithdifferentvolumes,heat

loads,

and

convective

heat

transfercoefficients were usedtooptimizethe designofthemeasurement

device for increasedmeasurement sensitivity. Themodelresults were also comparedto

theexperimentaldatato

determine

thepredictivecapabilityofthemodels.

Twotransientheattransfer

devices

werefabricated. Both

devices

were evaluated
(20)

coatingofknownthicknessandthermal

conductivity

wasthenappliedtotheinteriorof

one ofthedevices. This devicewasthenre-evaluated. Theresultsoftheexperiments

were analyzed andconclusionsregardingthe

fouling

measurementcapabilityand

feasibility

oftheanalysistechniquewere

derived.

Recommendationsfor futureupgrades

to thedevicetoincreasemeasurementcapabilityand

improve

operationalaspects were
(21)

2.0 Background

Thissection will provide an overview ofthecategories of

fouling,

the

fouling

process,modelsfor predicting

fouling

rates, and methodsfor measuring fouling. The

reviewwill

focus

onthemethodsfor

measuring

fouling

andonlyacursoryreview of

fouling

categories, the

fouling

process,and

fouling

modelswill

be

given.

2.1 Classification of

Fouling

Categories

Fouling

isanextremelycomplex phenomenon. Fromafundamentalpoint of

view,it may becharacterized as a combinedmomentum,

heat,

and masstransferproblem

[HermanandKnudson(1979)].

Fouling

isnotonly

dependent

ontheoperating

conditions ofthe process,but is

highly

dependentontheoperating solution. Forthis

reason

fouling

takesplace

by

differentmechanisms,atdifferentrates,possessesdifferent

compositions,andpossessesdifferenteffectsonthe overallprocess. Thecategories of

fouling (fouling

mechanisms)andtheenvironments inwhich

they

aredominantare

summarizedbelow.

Precipitation

(Crystallization) Fouling

Crystallizationofdissolvedmaterialinthe

flowing

fluidoccurswheneverthe

fluid

becomessupersaturated withrespectto the

depositing

material.

Precipitation

fouling

can

occurin coolingwatersystems,

desalination

systems,

boilers,

geothermalsystems, and
(22)

Particulate

Fouling

Accumulationof particles

from

fluid containingsuspended solids. Particulate

fouling

can

occurintheenergygeneration

industry.

Chemical Reaction

Fouling

Chemicalreactions

taking

place at a

heat

transfersurface. Thesolid products ofthe

reactionaredepositedonthesurface. Chemicalreaction

fouling

canoccurinthe

petroleumandfood processing

industry.

Corrosion

Fouling

Chemicalreaction ofcontaminant materials

(including

heat transfersurfaces) withthe

circulatingprocess stream. Corrosion

fouling

canbeclassifiedintotwocategories:

ex-situ(corrosionproductsform inthe solutionandaredepositedontheheattransfer

surface) or

in-situ

(corrosionproductsformattheheattransfersurface).

Biological

Fouling

Developmentof anorganicfilm consistingofmicroorganisms

(microbial bio

fouling)

and

theirproductsontheheattransfer surface, ordepositionand growth of macroorganisms

(23)

Solidification

Fouling

Freezing

of a pureliquidorthe

higher

meltingconstituents ofa multi-component solution

onto a subcooled surface.

Combination

Fouling

Thistypeof

fouling

takes

into

consideration"realworld"

fouling. Most

fouling

that

occurs onheattransfersurfaces aretheresult oftwo ormore oftheabovedescribed

fouling

types. Intheinitialstageofdeposit

formation,

one particulartypeof

fouling

may

predominate, andthiscan acceleratedeposition

by

othertypesoffouling.

2.2 The

Fouling

Process

Inadditionto thecategoryofthe

fouling,

thegeneral sequence of events

by

which

the

fouling

takes place,

fouling

kinetics,

is ofimportance in understanding fouling.

Informationon

fouling

kineticscan provideinsight

into

theinfluenceofsolution

properties,processequipment, andprocess parameters onthe

fouling

process. In

addition,informationon

fouling

kinetics

can also provideinsight intotheselectionof

theoreticalmodelsfor

describing

the

fouling

process. Theseaspects ofthe

fouling

process enabletheengineerto generatepreventative measurestomitigateor

delay

fouling.

The

fouling

processcanbe divided in fivesteps[Epstein

(1983),

Knudson
(24)

1. Initiation: Formationor aggregation of

fouling

componentsinthe

body

ofthefluid

2. Transport: Transportof

fouling

componentsto theheattransfersurface

3.

Attachment:

Attachmentor

formation

ofthedepositattheheattransfersurface

4. Removal: Removalofmaterial

from

the

heat

transfersurface(by:

dissolution,

erosion orre-entrainment,spalling,orsloughing)

5.Aging: Changes inthephysical or chemicalnature ofthe

fouling

Itis importanttonotethat theseprocesses aredifferent for every

fouling

problemdueto

thedifferencesinprocessconditions,equipment(surface

finishes,

etc.) andprocess

solutions.

However,

in boththeoilrefineryandthemilkprocessing industries it has

been

observedthatproducts with similar composition andprocessingconditions exhibit

similar

fouling

composition/kinetics.

2.3

Fouling

Mathematical Models

Fouling

is

consideredto

be

theresult oftwo simultaneous processes: deposition

and re-entrainment. Thenet

fouling

rateorflux

is

thedifferencebetweenthese two

processes.

dRt

V

dt T" Tr

Where: dRj/dt isthenet

fouling

rate

fy

isthe

fouling

depositionrate

<f>r isthe

fouling

removal rate
(25)

Amodel ofthis formwasfirstproposed

by

Kem andSeaton (1959). Sincethen

numerous

fouling

modelshave been generated, but

they

allfollowtheformproposed

by

KernandSeaton (1959).

The

fouling

processcanbestudied

by

examiningchangesintheheattransfer

characteristicsof a process. Changes

in

themeasured convectiveheattransferrepresent

thethermalconductivity

due

to

fouling

in

thedevice.

1 1

//

Rf = = 1 Equation 2

f

hfA,

hrA,

kfA,

Where:

Rf

isthe

fouling

heattransferresistance(K/

W)

hf

isthefouledsurface convectiveheattransfercoefficient

hc

isthecleansurface convectiveheattransfercoefficient

As

issurface area

k

is

the thermalconductivity

If

isthe thicknessofthe

fouling

layer

Thekineticsof

fouling

canbemeasured

by

monitoring

fouling

resistance withtime

(Rf

versustime). Knudson

(1992)

has

identified

that the

fouling

resistance curvesfollow

severaldistinctmodels;

linear,

falling

rate, asymptotic, and saw-tooth.

The

fouling

resistancecurves shownin Figure 1 canbemodeled

by

Equation 1 if
(26)

& 1

I-o: = - 2 o

III

ra >. ro u- < to

W O

o

E

c

o

'55

o

Q. 0)

Q

O)

3

O

n u

"5.

3

(27)

characteristic of a

fouling

system wherethe

deposition

rate

is

constant andtheremoval

rate

is

either zeroor constant. The asymptotic

fouling

modelischaracteristicof a

fouling

system wherethedepositionrate

is

constant andtheremoval rateisproportionalto the

thicknessofthe

deposit;

orthe

deposition

rate

decreases

withdepositthicknessandthe

removalrate remains constant. This behavior

is indicative

ofdepositswhichflakeoff

easily dueto fluid flow (shear forces). The

falling

rate

fouling

modelischaracteristic ofa

fouling

system wherethe

deposition

and removal rates are complex functionsofflow

rate,

fouling

thickness,

etc. Thesaw-tooth

fouling

modelischaracteristicof a

fouling

system wherethe

fouling

periodicallysloughs off orperiodiccleaning

is

performed. The

time segment,denoted

tD,

representsthe

delay

timeofthefouling. Thiscan occur

during

thenucleation ofthe

fouling

layerontheprocess surfaceatthemicroscopiclevel.

During

this timeno significantlosses

in

heattransferare observed andinsome casestheheat

transferresistance

is

decreased dueto theincreased surfaceroughness [Knudson (1992)].

2.4

Fouling

Measurement

The primarygoals ofa

fouling

measurementsystem are:

Togainunderstandingofthe

kinetics

of

fouling

andcleaning;

To understandthecorrelation

between

fouling

kineticsand processperformance;

To gainunderstandingofthenature ofthe

fouling

deposits;

and,
(28)

Tothis end,numerousdevices have been

designed for

theexplicitpurposeofmeasuring

process

fouling.

The

fouling

monitoring

devices have

utilizeddifferentmeasurement

methodsortechniques. A listofthe

different

measurementmethodsalongwith abrief

descriptionoftheprincipleof operation

is included

below.

Heat Transfer Resistance Techniques

Heattransferresistancetechniques

involve

thecomparative assessmentofadevices heat

transferperformancebeforeand after

fouling

occurs. Thismeasurementtechniquehas

beenutilizedasbothalocalmeasurementparameter(change in heattransferof a specific

location inthedevice [Somerscales et al.

(1986)])

andas a global or overallmeasurement

parameter(change

in

heattransferoftheentire

device

[WebbandKim

(1989),

Abu-Zaid(1992)]). Themeasurementtechniquehas beenusedin boththesteadystatemode,

usingtheWilson Technique [Wilson

(1915),

Somerscaleset al.

(1986)],

andthe transient

mode[Fetkovichet al. (1977)].

Somerscales

et al.

(1986)

statedthat thermalresistances

as lowas 1.96 x 10"5to3.56 x 10"5m2

K/Wweremeasuredwith ahigh levelof

confidence

by

thesteadystate,globalmeasurement system. Fetkovichetal.

(1977)

and

Panchal

(1989)

bothstatedthermalresistancesmeasurementcapabilityof10x 10"5 m2
(29)

Optical Techniques

Opticaltechniquesuse opticallytransparent sectionsthatenabletheuseof optical sensors

for

themeasurement of

fouling

[Gallot-Lavallee

et al. (1982)]. The accuracyand

precisionofthis technique

depend

notonlyontheopticalsystem appliedbutonthe

optical properties ofthefouling.

Gallot-Lavallee

et al. utilized an optical sensorto

qualitatively detecttheamountofmaterial removed

by

a chemicalcleaningsolution

(opticalsystem outputvoltage was correlatedto the

fouling

level

in

thechemical

solution).

RemovableSection Technique

Theremovable sectiontechniqueutilizes removable "witnessplates"

or samplecoupons

placed

in

theprocess flowstream[Roeet al. (1985)]. Thesample coupons can

be

removedfromtheprocessingequipment

for

detailedanalysisofthefouling. Analysis

techniquesincludemicroscopic, gravimetric, spectroscopic,andotheranalytical

techniques. Roeetal.

(1985)

statedseveraldisadvantagesto this

technique,

including:

Intrusivenature ofsampling

technique;

Thesamplemaynot seeexact processconditions

(temperature,

etc.);

Sample may betoosmallforphysicalor chemicalassays;and,

(30)

Pressure

Drop

Technique

Thepressure

drop

technique

involves

themonitoringoftheinletand outletpressureof an

apparatustodetect

increased

resistanceto

fluid flow

(back pressure) [Roeet al. (1985)].

Theresistanceto

fluid

flow

is

theresult of a

decrease

inthesizeoftheflowpath,

hydraulic

diameter,

dueto theaccumulation offouling. Roeet al. stated several

disadvantagesto this

technique;

themeasurement

is

insensitiveuntil acritical

fouling

thicknessisreached, and pressure

drop

is

usually only important fortransferprocesses

(i.e.,

fouling

willbeginto affecttheheattransferprocesses

long

beforethepressure

measurementwilldetectthepresence 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 pit
(31)

Holographic

Interferometry

Technique

Holographic

interferometry

fouling

measurementtechniqueutilizestwo-wavelength

interferometry

tomeasuretemperatureand concentration profilessimultaneously in

crystalline

fouling

[Seyfried

(1990)]. Seyfried

(1990)

utilizedthis technique to observe thedynamic

fouling

process,inreal-time.

Ultrasonic Technique

Ultrasonic

fouling

measurementtechniqueutilizestransmissionultrasonicstomeasure

fouling

[Withers (1993)]. Withers statedthat the techniquewouldbeusefulforthe

measurementof

fouling

deposits inthepipework of continuoushigh-temperature

processingplants. Withershasshownthat the techniquewas abletodetecta minimum

thicknessof0.1 mm.

Specialized Methods: Silicon Sensor

Thesiliconsensortechniqueutilizes a siliconchip embeddedintothewallofthe test

surfacetodetectthepresence of

fouling [Stenberg

etal.(1988)]. Withinthesiliconchip

aheaterresistorwasusedto setupathermal

boundary

layerwhich wasmeasured

by

a

temperaturesensing diode.

Fouling

changedthe thermal

boundary

layerproduced

by

the

heaterresistor, thuschangingthetemperaturemeasured

by

the temperaturesensing

diode.

Stenberg

etal.'s resultsimpliedthat thermalresistances as lowas 0.5 x 10"5

m2

K/W

(32)

Table 1 summarizesoftheattributesofthe

different

fouling

measurementtechniques.

Measurements utilizingtheseprincipals of operationhavebeenemployed in

laboratory,

andindustrialsettings. Theenvironmentdictatesthedesignoftheinstrument.

FryerandPritchard

(1987)

proposedfourcriteriaforthedesignof eitheraproduction or

laboratory fouling

monitoringsystem:

1. Size Themonitor should

be

of modest size sothat

it

can

be

easily

installed,

serviced, andreplaced;

2. Cost Becauseit isnot an acceptedpracticetoutilize

fouling

monitorsit is important

that theinitialcostsbe

low;

3.

Reliability

Themonitor shouldbe robustlyconstructed,requiretheminimum

maintenance and provide reproducibledatathatis easyto

interpret;

and,

4. Relevance- The

device

shouldcloselymodeltheprocessflowconditions sothat

resultscanberelatedbackto thefull scale process

2.4.1

Commercially

Available

Fouling

Monitors

Becauseofthe

importance

of

fouling

in industrialoperations, heattransfer

fouling

monitoring systemshave been

developed

andare nowcommerciallyavailable.

Chenoweth

(1981)

provideda

summary

of

fouling

monitoring

devices

thatwere

commerciallyavailablein

1981,

see

Appendix

A. The

fouling

monitor manufacturers
(33)

Table 1:

Summary

ofthe

Fouling

Measurement Technique Attributes

Fouling

Measurement Technique

1 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 X

Global

Fouling

Measurement X X X

Laboratory

Technique X X X X X X X

Production Technique X X X

Commercially

Available X X X X

Typeof

Fouling

Detected All Most BeOpaque

All 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 Excellent

MeasurementCycle 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

Technique

5. Electrochemical Technique

6. Holographic

Interferometry

Technique

7. Ultrasonic Technique

(34)

commercially

availabletoday. Twoofthecompaniesprovided

information

onthe"state

oftheart"

commerciallyavailable

devices (attempted

contactswiththeother companies

were unsuccessful).

Calgon'

sproductline

included four

monitoring

devices

thatfocusedoncorrosion

detection

andtwomonitoring devicesthat

focused

onthedetectionofgenericfouling.

Thedevicenames and abrief descriptionoftheprinciple ofoperation areincluded

in

Table2.

BridgerScientific offeredanupdatedversionoftheirDATS 1200

fouling

monitor. Theupdateddesignutilizesthesame

theory

of operation astheDATS 1200

device,

overallheattransferresistance

technique,

applied asasteadystate measurement.

NeitherCalgonnorBridgerScientificoffered a

fouling

monitorthatutilizesthe transient

heattransferresistance measurementtechnique. This may bearesult ofthesimplicityof

theanalysistechniquesforthesteadystatedevices.

2.4.2 Heat Transfer Resistance

Fouling

Monitors

Becauseofthemeasurementaccuracyanddetailed documentationofthe

measurement

theory,

heattransferresistancemeasurementtechniquesare

by

farthe

dominantmethodfor measuring

fouling.

Withinthisvery broadmeasurementtechnique

category, thereare twotheoriesof application- transientand

steadystate. Inthe transient

(35)

Table 2: Calgon

Fouling Monitoring

Devices:

Calgon

Corporation

Product

Catalog

(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,

Overall

Measurement Technique - Off-line Accelerated

Fouling

Test Device

Test Heat

Exchanger

HeatTransfer Resistance Technique

-Steady

State,

Overall

Measurement Technique- Off-line Real-Time

(36)

monitored. Inthesteadystatemethod, thewalltemperature

is

monitored whilea

constant

heat

flux isapplied.

HermanandKnudson

(1979)

provided an overview ofthedifferent

heat

transfer

resistance

fouling

measurement apparatusesthat

have

been developed (see Appendix B).

Theoverview

included

theforms of

heating,

the systemgeometry, applicationtechnique

(transient andsteadystate),andthe

distinguishing

featuresofthedevices.

Heating

techniques that

have

beenemployedin heattransfer

fouling

monitors include indirect

electrical,

thermoelectric,

direct

electrical,sensible

heating

of

fluids,

condensingvapor,

andelectrically heatedwiresand coils. System geometriesthathave beenemployedin

heattransfer

fouling

monitors includeannular, circular, and complex. Inadditiontothe

operational and configuration

differences,

Hermanand

Knudson'

s summary

(1979)

(Appendix

B),

also noteswhetherthemeasurement was local

(applying

to the

fouling

at a

specificpointintheprocessequipment)or overall

(applying

to the

fouling

oftheentire

apparatus). Localmeasurements givereliable results for bothsmall

fouling

resistances

andlowheat fluxes [Fischeret al. (1975)].

However,

this techniquecanleadto

fluctuating

resultsparticularly incaseswherethe

fouling builds-up

andperiodically

breaks free fromthesurface

(e.g.,

sedimentation

fouling

- saw-tooth

fouling

pattern).

Fetkovichetal.,

(1977)

andPanchal

(1989)

statedthatthermalresistances aslow

as 10x 10"5 m2

K/Wcouldbemeasuredaccurately

by

the

transient, local

measurement
(37)

Directmeasurement oftemperature

differential

by

athermopileandtheaccuracyof

timemeasurements gives greater measurementprecision; and,

Insensitivity

tocalibration- exceptforthe

flow

meter.

The complexityofthis techniquelies inthemethodfor

determining

therelationship

between

the

heat

transferresistance andthe timeconstant. Fetkovich

(1976)

and

Kuzay

etal.

(1982)

utilizedan analyticalapproximationto theexact solutionfortheanalysis of

experimentaldata.

Kuzay

et al.

(1982)

also modeledthe transientheattransfersystem

usingthe finite differencetechniqueand comparedtheresults ofthemodelto the

experimentalresults.

2.5 Objectives ofthePresent Work

Theobjectivesto this studywere:

1. To

identify

theexisting

fouling

measurementtechniquesand comparetheir

fouling

detectioncapabilities;

2. Tounderstandtheinfluenceofprocessandgeometric parameters onthemeasurement

sensitivityof aselectedmeasurement

technique;

3. To designandfabricatea prototype

fouling

monitorutilizingoptimizeddesign

conditions;

4. Totesttheprototype

fouling

monitor anddetermineitsmeasurementcapability; and,

5. Tocomparethemeasurementcapabilityoftheprototype

fouling

monitor with

fouling

(38)

Therequirements ofthe

device included:

sensitivitytothin

fouling

films,

stateof

theartaccuracyandrepeatability,and compactdimensions. Thetransientheattransfer

resistances measurementtechniquewasselected foruseinthisstudy basedon

its

(39)

3.0

Theoretical

Analysis

Fouling

analysis

by

the transient

heat

transferresistancemethodhas been

employedinnumerous studies

[Fetkovich

(1977),

Panchal

(1989),

Meyeretal

(1981),

Meyeretal.

(1982),

Kuzay

(1980),

Owens (1986)].

Themost commondesignutilized

wasthe"Carnegie-Mellon"Ocean Thermal

Energy

Conversion

(OTEC)

design

[Fetkovich (1977)]. The geometryofthe

device

was

tubular,

withheat

being

appliedto

theoutersurfaceandthecoolingwater

flowing

inside

(fouling

surface).

Fouling

was

monitored

by

measuringtherateofheattransferfromatube walltothecoolingsolution

flowing

inside.

Variationsonthis

design

were utilized

by

otherinvestigators [Owens

(1986)],

butthesamegeometryand measurement concepts were used. Meyeret al.'s

(1981)

studyutilizedthe transient techniquewith adifferentgeometry, arectangularflow

path.Basedonthe

dominance

ofthe tubulargeometry

in

pasttransientheat

fouling

monitorsandits in-situapplicability, the tubulargeometrywas selectedforthisstudy.

Atheoreticalanalysis ofthe transientheattransferresistance measurement

techniquewasperformedto

determine

the effect of process anddesignvariables on

measurement capability. Theprocess variables examinedincludedthe temperatureand

timemeasurementcapability, the

heat load

appliedto thedeviceandtheconvectiveheat

transfercoefficient. The

design

variables examinedwerethe

inside

and outsidediameter

(volume)

ofthecylindricalapparatus. Thetimeandtemperaturemeasurement
(40)

convective

heat

transfer coefficient,andthedevice geometrywere evaluated

by

finite

difference

modelinganalysis.

3.1 Parametric Evaluation

Utilizing

Lumped Capacitance Model

To gain

insight

into

theeffectsofmeasurement capabilities ontheprecision of a

transient thermalresistance

fouling

monitor, anerroranalysis oruncertaintyestimation

was performed. Becauseofthecomplexityofthegoverningequations intheexact

analytical solution [Fetkovichetal.

(1977)],

theuncertaintyestimation was performed

utilizinga

first

order approximationto theanalytical solution. The

first

order

approximationused wasthelumpedcapacitanceheattransfer

formulation.

The

lumped

capacitanceheattransfergoverningequation

is

shown

in

Equation3.

pVc T.-T

t = - In-i

-Equation 3

H

T-Tn

Where: tistime

p isthe

density

ofthematerial

Visthevolume ofthematerial

cp isthespecific

heat

at constant pressure

Tisthetemperature

Ti

istheinitialtemperatureofthematerial
(41)

Equation 3

is

rearranged

into

a

form

equatingthemeasurement andgeometric parameters

to theconvectiveheattransfercoefficient.

pVc T-T

h =

'-^

In-*

=-Equation 4

tA. T-T M

3.1.1

Sensitivity

Analysis

Theory

Schenck

(1979)

provided a comprehensive overview ofthe

theory

ofuncertainty

analysisinexperimentation. Schenckoutlinedtwogenericformulations fortheerror and

uncertaintyanalysis ofaresult: thedeviationoftheresultfromthe truevalue andthe percent error. Thedeviation quantitycanbeusedtopredicttheinfluenceof an

independentparameter measurementcapabilityon adependentparameter.

The deviation quantity

formulation

utilizedthe

first

two termsof aTaylorseries

expansion[Schenck (1979)].

R +k =f(Xlr+

K+...)+[(

)

* ! 1 +

(

),

,r yx

^+...

tr \ J\ tr tr ^flC**

\\

dfj

1!
(42)

Where: Risthe

dependent

parameterunder evaluation

Rfr

is

the truevalue ofthedependentparameter

r

is

the

difference from

Rfr

x, isthe

difference from

the truevalue ofthe parameter,X,,.

X,,.

is

the truevalue of an

independent

parameter

y,

is

the

difference from

the truevalue ofthe parameter,Y,,.

Ya

is

thetrue value of an

independent

parameter

The

first

termintheTaylorseries expansion

(f(Xtr

+

Yfr

+

...)

)is

thedefinitionof

R;r

Thus,

thefirsttermonbothsides ofEquation 5drops fromtheformulation

leaving

the

differenceordeviationterms.

,cR, k ,dR, A .

r

r, =

(

)

Ajc+

(

)

vAy+.... Equation 6

1

ax y 3Y x

Equation6 canbeusedtocalculatetheeffectofoneparameteron another.

3.1.2

Sensitivity

Analysis

Application

Thesensitivityanalysis equation was appliedto the

lumped

capacitance

governing equation, Equation4. The resultingsensitivityanalysis

formulation is

shown
(43)

Ah= At+ AT Equation 7

dt r dTt

Where:

oh

isthepartial

derivative

oftheconvectiveheat

transfer,

or

dt t

3i -pVc T-T

=-V-^ln(^-^) Equation8

aT

t2A.

T-T'

oh

is

thepartial

derivative

ofthe convectiveheat

transfer,

or

dT,

gh -pVcn T-T

=-!E-c!fs-)m Equation9

cTt

tA,

Tt-Tj

Equation 7

is

theformulation for

detennining

theeffect of one parameter onanother,

i.e.

theeffect oftimeandtemperaturemeasurementcapabilityon convectiveheattransfer

measurement capability. Equations 8and9aredefinitionsofthederivativesgivenin

Equation7.

3.1.3 Measurement

Capability

Analysis

Equations

7, 8,

and9were utilizedtoanalyzetheinfluenceof measurement

capabilityonconvectiveheattransferdetection limits. Thegeometric system evaluated

wasthatof atubular geometrywithfluid

flowing

through thecenter. The

lumped

(44)

volume, surfacearea, andthermodynamicproperties ofthematerial. Theseparameters

were calculatedforthetubulargeometryand utilizedintheanalysis. Figure 2

is

a

schematicrepresentationofthe tubularapparatus. Theportionoftheapparatus

being

modeled

is

identified in Figure 2. Thegeometric and materialpropertyvalues used

in

the

analysisaregivenin Table 3.

Threelevelsoftemperaturemeasurement andtimemeasurementcapabilitywere

evaluated. Theresultsoftheconvective

heat

transfermeasurementresolution analysis

are givenin Table 4. Theresults

in

Table 4 are given as a ratio ofthechange

in

convectiveheattransfer to the

initial

convectiveheattransfer coefficient,Ah/h(h= 1000

W/m2

K).

Evaluationofdata

in

Table 4revealsaone-to-one correlationbetweenthe

temperaturemeasurementcapabilityandtheconvectiveheattransfercoefficientdetection

capability (fortherange evaluated). Inaddition, thedata

in

Table 4revealsthat thereis

littletono effect oftimemeasurementcapabilityontheconvectiveheattransfer

coefficientdetection capability (fortherangeevaluated).

3.1.4 Influenceof

Geometric

andHeatTransfer Properties

Sensitivity

analysis was also performedtoevaluatethe

influence

ofthegeometric

(volume andsurfacearea)and

heat

transferproperties(convective

heat

transfer

coefficient,measuredtemperature

difference)

absolute values.

Variations

of each
(45)

0) 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: =6

3

2 0 1 o 0 > U 0 C T3 0 0 -C 0 M-*- o

CN 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

(46)

Table 3: Lumped Capacitance

Sensitivity

Analysis: GeometricandMaterial

Properties

GeometricorMaterial

Property

Valueusedin Lumped Capacitance

Sensitivity

Analysis

Convective Heat

Transfer,

h 1000W/m2K

Outside Radiusof

Device,

r0 0.03175m

Inside Radiusof

Device,

rf 0.0079375m

Lengthof

Device,

L 0.1524m

Volumeof

Device,

V 0.0004524

m3

InnerSurface

Area,

A^

0.007601 m2

Specific Heat

(316

SS),

cp

468

J/kg

K

Density

(316

SS),

p 8238kg/m3

Applied Temperature

Difference,

Ts

-TM

10 K

Measured Temperature

Difference,

T

-T^

1.37 K

Time,

t 456.39 seconds

Table 4: Measurement

Capability

InfluenceAnalysis: EffectofTimeand

Temperature Measurement

Capability

onConvective Heat TransferCoefficient

Measurement

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

(47)

Tables

5 through8 forvolume,surfacearea,convectiveheat

transfer,

and measured

temperature

difference,

respectively.

Theanalysisrevealedthat thevolume

(Table

5),

surface area(Table

6),

and

convectiveheattransfercoefficient(Table

7)

parametersdidnotsignificantly

influence

the finalconvectiveheattransfer coefficient measurementcapability.

However,

the

measuredtemperaturedifference did havean effect

(Table

8). Largermeasured

temperaturedifferencesresulted

in

an

increased

sensitivityto theconvective

heat

transfer

coefficient measurement.

Thefactthat the volume,surfacearea,and convective

heat

transfercoefficientdid

nothaveaninfluenceonthefinalconvectiveheattransfer coefficient measurement was

notintuitive. These factorsshouldhave hadan

impact.

Thisresultis

believed

tobea

result oftheover-simplification ofthe transientheattransfersystem

by

thelumped

capacitance analysis.

Thus,

the

finite difference

modelingapproach was pursuedtoattain

informationonthe

influence

oftheseparameters.

3.2 ParametricEvaluation

Utilizing

FiniteDifference Analysis

Thelumpedcapacitance analysis

did

notyieldinformationonthecritical

design

parameters ofthedevice.

Therefore,

a

finite

element analysis wasperformedtogenerate

input

ongeometricdesignand

heat

transferconditions. A commerciallyavailablefinite

differencesoftwarepackage,

THERMONET

[Kandlikar

(1993)],

was usedtostudythe
(48)

Table 5: Geometric Parameter Influence Analysis: EffectofSystem Volumeon

Convective Heat Transfer Coefficient Measurement

Resolution,

Ah/h (W/m2

K)

Convective Heat Transfer Measurement

Resolution,

Ah/h

(W/m2K)

System 0.00016

Volume 0.00041

(m3)

0.00185

0.000693

0.000691

0.000689

Table6: Geometric Parameter Influence Analysis: EffectofSystem Surface Area

onConvective HeatTransfer Coefficient Measurement

Resolution,

Afi/h (W/m

K)

Convective Heat TransferMeasurement

Resolution,

Ah/h (W/m2

K)

System 0.0047

Surface 0.0076

Area (m3

)

0.0243

0.00069

0.000691

(49)

Table 7: Geometric Parameter Influence Analysis: EffectofInitial HeatConvective

Heat Transfer Coefficienton

Convective

Heat Transfer Coefficient Measurement

Resolution,

Ah/h(W/m2

K)

Convective

Heat Transfer Measurement

Resolution,

Ah/h (W/m2

K)

InitialConvective 100

Heat Transfer 1000

Coefficient(W/m2K

)

10000

0.000689

0.000691

0.00071

Table 8: Geometric Parameter Influence Analysis: EffectofMeasured

Temperature DifferenceonConvective Heat Transfer Coefficient

Measurement

Resolution,

Ah/h (W/m2

K)

Convective HeatTransfer

Measurement

Resolution,

Ah/h

(W/m2K)

No.ofTime Constants 1

(40%)

0.01175

(%

Difference Between 2

(86%)

0.000691
(50)

detection

capability. See Figure 3

for

a schematicrepresentationoftheheattransfer

system

being

modeled. Isothermalfluid

flows

through thecenterofthe

device,

heat

is

appliedto theoutsidediameterofthetubularshaped

device,

the

heat load is

removed

(turned

off)andthe temperatureinthecylindricaldevice ismeasured withtime.

The

finite difference

models generatedtake

into

consideration allthree

dimensionsofthetubular geometry. Theangular

dimension

ofthe tubulargeometrywas

takenintoconsiderationthrough the volume, conduction,and convection parameters of

themodel. Heatconduction

in

theangulardimensionwas considered negligible. The

axial

dimension

ofthe tubulargeometrywastaken

into

considerationthrough thevolume

ofthemodel. Heatconductionintheaxialdimensionwas considered negligible. The

resultingmodel appearstobeonedimensional (see Figure

3),

however,

thevolume

values used

in

themodeltakeintoconsiderationtheangular and axial

dimensions

ofthe

device.

3.2.1 EffectofModel Node andIterationTime

Step

A studywas performedto

determine

theeffectofthenumber of nodes andthe

iterationtimestepsize onthe

THERMONET

modeloutput. Two

THERMONET

models

ofthecylindricalmeasurement system werecreatedtoperformthis study;a 12node

model and a45 nodemodel. Two

iteration

timesteps wereevaluated

for

eachmodel; 1

and 10seconds forthe 12nodemodel,and2 and10secondsforthe45node model.

(51)

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 uo

co 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 0

0 '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

(52)

Figure4: SchematicRepresentationofthe 12 Node

andthe45Node THERMONETModels

12 Node Model

1 Node

Representing

Air

Gap

Between

StainlessSteel Tube

andOuter Shell

10

Equally

Spaced Nodes

Representing

theStainless Steel Tube

oftheTransient

Fouling

Monitor

45 Node Model

1 NodeRepresenting Air

Gap

Between Stainless Steel Tube

andOuterShell

43

Equally

Spaced Nodes

Representing

the Stainless SteelTube
(53)

divided into

severaldistinctsections

representing

the

flowing

solution, thewallofthe test

device,

andtheairsurroundingthe test

device

(laboratory

environment). The breakdown

ofthenumber of nodes

representing

each section ofthedevice

is

shown

in

Table9.

Thegeometry,materials ofconstruction,

initial

conditions,andheatload for both

models werethesame. The

detailed

model conditions are given

in

Table 10.

Thetemperatureoutput ofthe

four

models were examinedfortrends. Thenode at

theposition

in

thecenter ofthe test

device

wall,

for

eachmodel,was selectedasthe

comparison

datum

point. Thecenter nodetemperatureoutputdata

from

thefourmodels

are givenin Table 11. Allmodel results were comparedtotheresults ofthe45 node,2

second

iteration

stepmodel1. Thedifference betweenthemodel output andthe45node,

2 second

iteration

stepmodel are also given

in

Table 11. Theaverage

difference between

each model andthe45node,2second

iteration

stepmodel

is

given

in

the

last

row of

Table 11.

Themodeltemperatureoutputdataand modelcomparisonresults

(Table

1

1)

are

showngraphically in Figures 5and

6,

respectively. Figure 5 clearlyshowsthatall

modelsproducethesamegeneraltemperature trends. Thisresult was expected. Theplot

ofthedifferenceevaluationresults, Figure

6,

showstwogeneral

deviation

patterns. The

12nodemodels(both 1 and 10second

iteration

timesteps)exhibit

large deviations

early

in

the temperature

transient, corresponding

to the time that theheat

load

was applied

in

themodel. The45nodemodel shows arandomly

fluctuating

difference

pattern.
(54)

Table 9: Breakdownor"Allocation" ofNodes forthe 12 Nodeand45 Node

THERMONET

Models

Model Section 12 Node

Model

45 Node

Model

Flowing

Solution 1 1

WallofTest Device 10 43

Air

Surrounding

Test

Device

1 1

Table 10: Parameter Values fortheFinite Difference Analysis

Input Parameter Valueusedin THERMONET Analysis

Convective Heat

Transfer,

h 1000W/m2 K

Outside Radiusof

Cylinder,

r0 0.03175m

InsideRadiusof

Cylinder,

rs 0.0079375m

Lengthof

Cylinder,

L 0.1524m

Volumeof

Cylinder,

V 0.0004524m3

Inner Surface

Area,

A,

0.007601 m2

Heat

Load,

H 500 W for 240seconds

MaterialofConstruction 316 Stainlesssteel

(55)

Table 11: FiniteDifferenceAnalysis: EffectoftheNumberofNodesandthe

Iteration Time

Step

Size;

Model Output

Temperature,

Degrees C

Time

(sec)

45 Node

Model,

2 sec. Iteration Time

Step

(45/2

Model)

45 Node

Model,

10 sec. Iteration Time

Step

(45/10

Model)

12 Node

Model,

1 sec. Iteration Time

Step

(12/1

Model)

12 Node

Model,

10 sec. Iteration Time

Step

(12/10

Model)

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 0.0295

20 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

(56)

Table 11:

Continued....

Time

(sec)

45 Node

Model,

2 sec. Iteration Time

Step

(45/2

Model)

45 Node

Model,

10 sec. Iteration Time

Step

(45/10

Model)

12 Node

Model,

1 sec. Iteration Time

Step

(12/1

Model)

12 Node

Model,

10 sec. Iteration Time

Step

(12/10

Model)

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 Model

360 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

(57)

a o o

5

0 II o 6" <M < E o o o II e> = .c c5

i5

W 3 0) I-E -5T |_ -"D g

S

.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

(58)

=

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 *. o

c o -n ro (0 (0 0 o *t M u O

55

N

3

o o

z ._ II

a 6"

o a-CM

+ -n <

E

1

o o o - S

o 2- II

*O t0 E -0 0 O "O C O 2 S

s

Q

g

1_ <o ro a> := =

?

O) u- 'E o o

Si 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

(59)

Theaveragedifference betweenthe45 Nodemodelwitha2second

iteration

step

and a 10seconditeration stepwas0.057

K;

andtheaveragedifferences betweenthe45

Nodemodel witha2 second

iteration

stepandthe 12 Nodemodel with 1 and 10second

iteration

steps were0.139 and0.131

K,

respectively. Theaveragedifferenceresults

indicate

thatboththenumberof nodes andthe

iteration

timestepeffecttheaccuracyof

themodeloutputresults.

The THERMONETmodelwasusedto

determine

thechange

in

performanceof

thedevicewithchangingprocess 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 12

nodemodel with a 10second

iteration

timestep).

3.2.2 EffectofApparatus DesignandExperimental Conditions on

Measurement

Capability

The 12 Node 10second

iteration

stepmodel wasusedto evaluatethe

fouling

detection abilityoftheproposed measurementdevicewithchangesto the

device

volume

andheat load. Theanalysis was performed

by

generating twofinite

difference

models

withthe

different device

volumes

(same

surfacearea,

i.e.,

inside

diameter)

andexecuting
(60)

temperatureoutput atthreenode

locations (different

radial locationswithinthe

heat

transferapparatus)were examinedto

determine

theeffect ofmeasurementnoderadial

location.

Evaluationswereperformedtoexaminetheeffect ofthevolumeofthetest

device (outside

diameter

ofthereference

block

andheater

blocks),

theamountofheat

addedto the test

device,

andtheabsolute value oftheconvectiveheattransfer

coefficient2. Thefactor levelsevaluated

in

thestudyare givenin Table 12.

Theanalysis was conducted

by

comparingmodel results with and without a

simulatedfouling.

Fouling

wassimulatedinthemodel

by

executingmodel runswith

convective

heat

transfervaluesthatvaried

from

theabsolute values outlinedin Table 12

(i.e.,

simulatingthe

increased

thermalresistance ofthe

fouling

layer).

By

comparingthe

model resultsfromthe"clean"device

(h,,)

to thoseofthef

References

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