DETEFMINATION OF THERMAL CONDUCTIVITY OF WCOVERY BOILER CHAR BED MATERIALS

Hanieh Nikfarman

A thesis submitted in conformity with the requirernents for the degree of Master of Applied Science

Graduate Department of Chernical Engineering and Applied Chemistry University of Toronto

O Copyright by Hanieh Nikfarman 2ûû1

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DETERMINATION OF THERMAL CONDUCTIVITY OF

RECOVERY BOILER CHAR BED MATERIALS

Master of Applied Science 2001

Hanieh Nikfarman

Department of Chernical Engineering and Applied Chemistry

University of Toronto

ABSTRACT

Heat tnnskr within a char k d of ri recovery boiler used in pulp and paper mills is important in

determining the cooling rate of a char bed following an emergency shutdown. The rate of heat transfer

drprnds on the thermal conductivitirs of frozen smelt and char. but thrre is little reliablc data availablr on

these thermal properties.

An experimental appantus was thus built to measure the thermal conductivity of various char

samplss made in the laboritory and collected from operriting rrcovery boiters. under normal opention

and following an emergency shutdown procedure. The reliribility of the apparatus and merisurement

method was tirst verified usincg firebricks with known thermal conductivity values and a numericd

simulation.

The thermal conductivity of char bed materials with different porosity and structure was found to

be constant up to 500°C. and then increase Iinearly with the temperature. Based on the data. rt two-part

correlation is recommended to predict the effective thermal conductivity of char bed materials with

V ~ ~ O U S porosity (between 55% and 80%) and structure:

For T I 500°C kff ( W/rn°C) = 0.2 1

Fat T > 500°C kff (W/m°C) = 0.0035 T (OC) - 1.54.

ACKNOWLEDGEMENTS

1 wish to thank my supervisors, Professors Masahiro Kawaji and Honghi Tran for al1 their

guidance, inputs and help during this project. Thank you for making this project an

exciting experience.

1 would like to thank Dr. Vladimir Agranat for helping me with the simulation software.

Also, great appreciation is extended to Dr. Alex Goffman, and Dr. Saied Kochesfahani

for their valuable suggestions and also their help during the field experiments. Special

thanks to Mr. Alarick Tavares for making the field experiments possible.

The financial support of American Forest and Paper Association and the following

members of the "lmproving Recovery Boiler Performance, Emission and Safety"

research consortium is acknowledged: Alstom Power, Andritz-Ahlstrom Corporation,

Aracruz Cellulose S.A., Babcock & Wilcox Company, Boise Cascade Corporation,

Bowater Inc., Clyde-Bergemann Inc., Daishowa-Manibeni International Ltd., Domtar

Inc., Domtar Eddy Specialty Papers, Georgia-Pacific Corporation, International Paper

Company, Irving Pulp & Paper Limited, Kvaerner Pulping Technologies, Potlatch

Corporation, Stora Enso Research AB, Votorantim Cellulose e Paper, Westvaco

Corporation, Weyerhaeuser Paper Company, and Willamette Industries Inc..

Finaliy, 1 would like to thank my family, specially rny dear mother, for their endless

support and encouragement during this project. 1 owe this to you.

TABLE OF CONTENTS

ABSTRACT

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

NOMENCLATURE

CHAPTER 1 INTRODUCTION

1.1 Objectives

CHAPTER 2 LITERATURE REVIEW

2.1 Recovery Boiler Design and Operation

2.1.1 Lower Furnace Construction

2.1.2 Char bed Characteristics

2.2 Smelt- Water Explosion

2.3 Normal shutdown vs. Emergency Shutdown Procedure (ESP)

2.3.1 Char Bed Cooling

2.4 Accelerated char bed cooling

2.5 Measurement of thermal properties of char bed materials

2.6 Arthur D. Little Inc. (ADL) Report

2.6.1 Instrumentation Used

2.6.1.1 Temperatrire Meusurement Probes

ii

iii

iv

viii

ix

xi

2.6-12 Bal1 Hecrr-Flow Probe 2 1

2.6.1.3 Bed SaniplNig Tubes 23

2.6.2 Mill Visits 23

2.7 Effect of temperature on thermal conductivity of porous 24 materials

2.8 Experimental evaluation of the effective thermal conductivity of 25 packed beds at high temperatures

CHAPTER 3 EXPEIUMENTAL APPAFWTUS AND PROCEDURE 29

3.1 Apparatus 29

Cover

Heatino Unit

Test Chamber

Coohg Unit

insulritino Walls

Steel Case

Thennocoupies

Data Ac~uisition

3.2 Calibration

3.3 Char Sarnples

3.3.1 Sarnples tkom Mill A

3.3.1.1 Mill A - I

3.3.1.2 Mill A-2

3.3.1.3 Mill A-3

Mil 1 A -4

Laboratorv-made sarnples -

Lu&- 1

k b - 2

Sample From Mill B

hldl B- 1

3.4 Density Measurement

3.5 Porosity Measurement

3.6 Experirnental Procedure

3.7 Data Processing

3.8 Numerical Simulation

3.5.1 Description of the simulation mode1

3.8.2 Geometrv of the comoutational domain

3.5.3 Heat transfer equations

3.8.4 Boundarv and initial conditions

3.8.5 Simulations

CHAPTER 4 RESULTS AND DISCUSSION

4.1 Calibration of the measurement system

4.2 Porosity and Density

4.3 Laboratory Samples

4.3.1 Lab- 1

3.3.2 Lab-2

4.4 Mill Samples

4.4.1 bIiIl A- 1 and Mill A-2

4.4.2 Mill A-3

4.3.3 Mill A 4

4.4.4 Mill B

4.5 Numerical Simulation Results

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 70

5.1 Conclusions 70

5.2 Recommendations 71

REFERENCES 73

APPENDICES

hppendix A Horizontal Heat Loss Calculations A- 1

Appendix B Q 1 files for various simulation conditions B - l

Appendix C Error Analysis for Determination of Effective C - 1

Thermal Conductivity

vii

No. -

Table 3-1 iMass and hea

LIST OF TABLES

Description - Pace

.t content of char bed in a IOm .u 1Om furnace 15 (Kawaji et al.. 1999)

Table 2-1 Hrat fluxes associated with cooli~g rates (Grace. 1998) 17 Table 3- 1 Summary of the simulation conditions 47 Table 1- 1 Surnmary of density and porosity of char samples 53

LIST OF FIGURES

No. -

Figure 1-1

Figure 2- 1 Figure 2-2

Figure 2-3

Figure 2-4

Figure 2-5

Figure 2-6

Figure 2-7

Figure 2-8

Figure 2-9

Figure 2- 10

Figure 3- 1

Description - Prioe

a) char bed left on the hearth of a recovery boiler following - 3

an emergency shutdown. b) hot pockets in the char brd. Schematic diagram of a recovery boiler (Adams et al.. 1997) 6 Sketch of the lowrr furnace of a decanting-heanh recovery 7 boiler (Adams et al., 1997) Lower furnace arrangement with composite tube wall 8 construction (Adams et al, 1997) Schematic diagrams of char bed near a smelt spout in slanted- 1 1 floor and decanting-hearth recovery boilers (Adams et al.. 1997). A five-junction thennocouple probe (Richardson and Merriam, 1977) Schematic diagram of the bail-heat-flow probe usrd by the ADL (Richardson and Meniam. 1977) Theory of the ball-heat- tlow probe (Richardson and Memam. 1977) Variations of thermal conductivity of poorly connected refractories with tempenture for different sas pressures: (A) chrom-magnesite. p = 1.1 g ~ m ' ~ (N' pressures of ((0) IO-'. (0) 10'. and ( ) 5 x 10' Pa): and (B) yttrium oxide . $ = 45% (He pressures of ( ) 10'. (0) [O-'. and (0) los Pa). (Litovsky et al.. 1996) Variations of thermal conductivity of insulating refractories with temperature for different gas pressures: (A) alumina. p = 1.1 g.cm-3 (N' pressures of (A) IO'. (A) 5 x 10'. (0) 10'. and ( ) IO-' Pa): and (B) tire clay. p = 0.6 g.crn-' (N' pressures of (A) lo5. (A) 2 x 10'. ( ) 10'. and (0) 10.' Pa). (Litovsky et al.. 1996) Cross-sectional view of the conductive-radiative rxperimental apparatus (Nasr et al.. 1994) Experimental apparatus and set up a) Schematic diagram of

the experimental apparatus b) Experimental setup Figure 3-2 Top view of the test chamber Figure 3-3 Coolin_e plate. a) top view of the bottom plate b) side view Figure 3-4 Mill A sarnples Figure 3-5 Laboratory samples a) Lab-1 b) Lab-2 Figure 3-6 Mill B sample Figure 3-7 Tempenture history of Lab-1 sample at set point of 250°C Figure 3-8 Schematic diasram of the simulation mode1 Figure 4- 1 Caiibration results Figure 4-2 Effective thermal conductivity variations with temperature

For Lab- 1 Sarnple

Figure 4-2

Figure 4-4

Figure 4-5

Figure 4-6

Figure 4-7

Figure 4-8

Figure 4-9 Figure 4- 10

Figure 4- 1 I

Figure 4- 12

Figure 4- 13

Figure 4- 14

Figure 4- 15

Effective thermal conductivity variations with temperature for Lab-2 Sample. Effect of structure and porosity on the thermal conductivity behavior for laboratory-made samples Variation of effective thermal conductivity with temperature for Mill A-3 Variation of effective thermal conductivity with temperature for Mill A 4 Effective thermal conductivity variations with temperature for Mill B-80% Effective thermal conductivity of char brd materials measured assurning no heat tnnsfer through the insulation walls Schematics of the sintering process (Adams et al. 1997) SEM photographs of cross-sections of pellets sintered for 1 hour (Adams et al. 1997) Hard c ru t formed when sample was heated beyond 500°C. Mill A 4 Effective thermal conductivity of Mill A 4 before and after sintering Steady temperature profile inside firebrick for heating plate temperature of 600°C Temperature contours indicating the temperiiture distribution inside the experimental apparatus (Mill A-3. 500°C simulation. see Chapter 3 for simulation conditions) Effective thema1 conductivity of char bed materials considering the heat loss through the insulating walls (corrected data) Temperature history at various locations in a char bed following a simulated rmergency shutdown procedure (shutdown was simulated at 2 1 :O)

NOMENCLATURE

cross sectional area. m'

specific heat of material. J/g°C

diameter, rn

rate of temperature change. OC/s

temperature gradient, "Clm

accelention due to gravity. m/s2

Grashof number

average convection heat tram fer coefficient. w / ~ ' K

thermal conductivity, W/m°C

verticai height. m

mas of materid. kg

average Nusselt number

Prandtl number

heat flux. wlm2

heat flow rate. W

Rayleigh nurnber

temperature. O C (K)

temperature difference. OC

difference in Location. m

porosity

exchange factor

Subscript

b

C

cond

eff

f

in

OU t

P

r

S

W

Z-B-S

volumetric thermal expansion coefficient. K"

viscosiry (rn2/s)

Stefan-Boltzman constant. o = 5.67 x 10 " ~ l m ' ~ "

0 = 0.17 11 X 10-' B T U / ~ ~ . A ? ~ R ~

bed

calorimeter

conduction

effective

furnace

inlet

outlet

pore

radiation

surface

water

Zehner-Bauer-Schlunder

surrounding

xii

CHAPTER 1 INTRODUCTION

Recovery boilers are used in the pulp and paper mills to recovcr inorganic materials used during

the pulping procrss and dso to generate svam for the plant. Black liquor. which is the by-

product of chemical pulping. is bumed in recovery boilers. The combustion of black liquor

convens the orgünic constituents of the liquor into gaseous products in a series of processes

involving drying. pyrolyzing. char gasification. and finally combustion in the fumace. Buming of

char, the residue left after pyrolysis occurs largely on the char bed which covers the tloor of the

fumace. As the carbon in the char is bumed. the inorganic compounds in the char are released

and form a molten salt mixture called smelt that flows to the bottom of the fumace and out of the

boiler through smelt spouts (Adams et al.. 1997).

Smelt produced from o kraft recovery boiler consists of approximatel y two-thirds

NalC03. and one-third Na& small amounts of Na2S04. other sodium/sulfur compounds. and

unbumed carbon (Adams et al.. 1997). Different chemical recovery processes and boiler

operating strategies are used by the industry: however. one common feature of dl recovery

boilers is that water rnust never corne into contact with a hot char bed. Molten smelt rems

violently with water generating destructive detonation waves. The mechanical energy generated

in a recovery boiler explosion has been compared to explosions of about 1 to 5 kg of TNT. There

have been over 140 reponed recovery boiler explosions in Nonh America. tn sorne cases injury

and even death of personnel have occurred (Grace. 1999: Green. 1992).

The recovery boiler is imrnediately shutdown if any water is suspectrd to have entered the

combustion chamber. The ernergency shutdown procedure (ESP) involves stopping the firing of

black liquor. draining of water from the boiler tubes, and shutting off the water feed to the boiler.

This leaves a residual bed consisting of hot char. molten smelt. and frozen smelt (Figure 1-1).

which has to be cooled down sufficiently so that water-washing of the fumace tloor c m be safely

performed.

Figure 1-1 Char bed left on the hearth of a recovery boiler a) following an emerzency shutdown. b) hot pockets in the char bed.

There is little known about the cooling mechanisms of the char bed following an ESP. therefore

the boiler shutdown cm last up to a few days. This downtime costs the industry approximately

$ 2 0 . 0 per hour in lost production. It is estimated that about 100 emergency shutdowns occur

per year worldwide. Hence. there is a considerable economic benefit in understanding the heat

transfer mechanisms governing the cooling of char beds following an ESP and avoiding

unnecessary downtime. Heat transfer within char beds also determines the entent that chernical

reactions proceed bencath the bed surface and the magnitude of heat transfrr rates to tloor tubes.

Thus. the processes that occur during cooling of the char bed following an ESP are quite

complex; however. the main heat removal mechanism is by conduction hrat transfer to the tloor

tubes.

While the bed heat transfer depends greatly on the thermal conductivity of smelt and char

matenale. thrre is littlc rcliable data availiible on this important propeny. The only source of

information on the thermal conductivity of char bed materials and smelt is from a report by

Richardson and iMemam of Arthur D. Little Inc. (ADL). (Richardson and Merriam. 1977). They

attempted to measure the themal conductivity of char beds in several operriting boilrrs but rnany

questions have been raised recently about the measurement techniques they used (Kawaji et al..

1999). Nevenheless. Richardson and Meniam (1977) recommended ii model ro predict the

thermal conductivity of char at high tempcratures. This thermal conductivity modrl. however.

has not been vrrifird by more reliable measurements.

1.1 Objectives

The objectives of this study were as follows.

1 . Construct an experirnental apparatus to accurately determine the thermal conductivity of

char bed materials.

2 . Make direct measurements of the thermal conductivity of c h u bed rnaterials from

different recovery boilers.

3. Study the effects of temperature. porosity. and structure on the thermal conductivity of

char bed materials.

4. Using the data obtained. verify Richardson and Merriam's correlation for the char

thermal conductivity. If this correlation can not adequately represent the data. propose a

new correlation to predict the thermal conductivity of char bed materials at different

temperatures.

LITERATURE REVIEW

General recovery boiler design and operation, and char bed characteristics known to date will be

discussed in this chapter. Also, char bed properties measured by Richardson and Merriam (1977)

and their experimental rnethodology, as well as some general procedures for measuring the

effective thermal conductivity of porous materials will be covered.

2.1 Recovery Boiler Design and Operation

As mentioned in Chapter 1, recovery boilers are used in pulp and paper rnills for two

main purposes: firstly to recover the inorganic chemicals used during the pulping process; and

secondly to generate steam for the plant by making use of the chemical energy present in the

organic portion of the black liquor.

B lack liquor contains al1 the inorganic c hemicals and other organic materials that separate

fiom the wood during the pulping process. The initial concentration of dry solid in black liquor

is about 15%. It is concentrated to 65% to 85% dry solids before firing (Adams et al., 1997).

In the furnace of a recovery boiler, combustion convens organic rnaterials into gaseous

produas such as carbon monoxide (CO) and carbon dioxide (C02). As the carbon in the char is

gasified, molten smelt is released which flows to the bottom and out of the through smelt spouts

(Adams et al., 1997).

Under normal operating conditions, black liquor is injected through liquor guns into the

recovery boiler (Figure 2- 1).

Feedwater Steam to miIl

Electrostatic / B m

preapitator

* . =orced r - drah b

fan

- 3 Steam coi1 - - air heater

I

Strong biack Iiquor - Mix l Liquor 1 Secondary air Make-up cherntals - Pnmary air -

b 7 T T *

Stearn Smelt to dissalving iank Smelt spouts

Figure 2-1 Schematic diagram of a recovery boiler (Adams et al.. 1997)

At the same time hot air is blown into the furnace through air ports. As a result. rnost of the water

in the black liquor evaporates off. The presence of air causes the pasified carbon and some of the

pyrolysis gases to burn in the region above the char bed. This combustion releases a large

amount of heat that melts the inorganic compounds. The inorganic materials and the unbumed

carbon; drop to the bottom of the fumace. The char (unbumed-solid-carbon) is a very porous and

flaky material with a very low density. The molten smelt has a higher density and thus flows to

the bottom of the himace. This causes the char to form a bed on top of the smelt (Figure 2-2).

Figure 2-2 Sketch of the lower fumace of a decanting-hearth recovery boiler (Adams et ai.. 1997)

2.1.1 Lower Furnace Construction

The fumace walls are constnicted frorn a series of vertical tubes carrying boilin, = water

(Figure 2-3). These tubes are typically 6.4 to 7.6 cm in diarneter. in modem construction the

tubes are spaced about 1.25 to 2.5 cm apart and are connected by a flat fin. This is called the

membrane construction. Four rows of vertical tubes form the fumace walls and are referred to as

the watewalls. Heat is transferred to the water flowing in the tubes by radiation from the char

bed and flames in the furnace. The fumace watenvalls represent as much as one half of the heat-

m s f e r surface area required to generate high pressure stearn (Adams et al., 1997).

Composite Tubing

Carbon Steel Tubing

Stainiess steel Clad bar fin

Carbon steel t Composite Tubing

Figure 2-7 Lower furnace ;irrangement with composite tube wall construction (Adams et al. 1997)

Waterwall tubes in the lower fumace are exposed to a very hostile eavironment. in the

lower Fumace the smeltlchar bed temperature can reach up to 830°C. In this region. tube wall

corrosion by molten deposits is unlikely since a protective layer of frozen smelt forms on the

outer surface of the water tubes and usuaily tube temperature does not exceed 350°C. Above the

char bed, however, a flue gas containing a corrosive. reduced sulfur species exists at

temperatures of about 1000 to 1250°C. Sulfidation by reduced sulfur gases is the main cause of

tube thinning, since partial pressure of O2 in the lower himace is insufficient ro stabilize Fe304

on the tube surface. Tubes removed from recovery boilers usually show a thick FeS scale on the

surface and no detectable iron oxide. The corrosion rate is typicaily less than 0.2 mrn/year but

can be as high as 0.8 rnm/year. The severity of corrosion increases with tube surface temperature.

and to a lesser extent, with the concentration of sulfur gases. In order to make the waterwalls

more resistant to corrosion, composite tubes are used. These tubes are made with a stainlsss steel

sheath on the outside of a carbon steel tube (Adams et al.. 1997).

3.1.2 Char Bed Characteristics

Black liquor recovery boilers operÿte with char beds at the bottom of their fumaces. As

mentionrd before. char beds consist of carbon. partiaily pyrolyzed black liquor solids. and

rnolten and frozen smelt. Char beds corne in various shapes such ris low. tlat beds. and crater-

shaped beds. Some beds can be as high as 3m (Adams et al. 1997).

Under ideal conditions. al1 the inorganic pulping chernicals in the black liquor would

reach the bed and srparate from the buming char and tlow out of the smrlt spouts without being

oxidized. The carbon in the char would burn to form CO and CO?. or would rext to form

Na2C03. and the sulfur would be convened to Na2S. The rolc of the char beds is to provide an

environment for these chernicd reactions to take place. It provides a surface for lùr/carbon

contact. and a reducing environment to protect sulfide in the molten smelt from being rr-

oxidized to sulfate (Green. 1992).

Despite the central rote of the char bed in the stable. efficient. and safe opention of the

recovery boiler. it is one of the least understood parts of the overall process. There is relative1 y

little field data on char bed properties compared to other parts of black liquor combustion

process. In the past several years the use of bed imaging cameras in addition to laboratory and

cornputer studies of char buming and bed cooling has increased the knowlrdge of bed

characteristics (Grace. 1998).

The size and shape of a char bed are detennined by boiler design. firing technique. air

delivery, and the combustion properties of the black liquor fired. The following description of

char beds was developed by Richardson and Merriam ( 1977) as a result of an Arthur D. Little

Inc. (ADL) study.

In rnost recovery boilers. the char bed is believrd to consist of ü hot. active burning layer

at the bed surface supportrd by a colder. inactive bed at the bottom. The active layrr is typically

15-20 cm thick. The temperature of the active layer decreases with distance into the bed frorn

1000-1200°C at the surface of the bed to 760°C at the bottom of the active char layer where

smelt has solidified. The solid carbon in the active char layer provides structure even though the

char mass is mostly molten smelt. Below the active layer there is the denser and chemically

inactive core of bed that is below the inorganic melting point. This has a thermal conductivity

sirnilar to that of a good insulator. The physical charxtrristics of the active la-r in char beds

are similar in al1 types of recovery boilers. On the othrr hand. the characteristics of the inactive

layer differ with boiler types. These differences affect the tlow of molten srnelt from the char bed

to the spouts and the amount of smelt within the boiler (Richardson and Memam. 1977).

Two different types of recovrry boiler include the slanted floor boiler. and the decanting

hearth boiler (Figure 2-4) . The char beds in slanted-floor boilers are usually a single mount with

a relatively flat top. The height of the bed is limited by air injection at the secondluy air port. The

inactive part of the char bed in these boilers is quite dense and far less permeable than the active

char layer. Smelt collects in troughs around the perirneter of the bed and in channels through the

bottom of the bed to the perimeter. On the other hand various shapes of char beds are observed in

decanting-hearth boilers. The beds are usually low. with moken smelt under most of the bed. The

char characteristics in the inactive bed are quite different frorn those in slanted-tloor boilers. The

char is very porous and mobile. Temperature measurements within these char beds show that the

smelt is molten throughout the bed. Thus the beds sit in a pool of molten smelt that is contained

by the decanting bottom of the boiler, with a layer of solid smelt above the floor tubes (Adams et

al., 1997).

a. Slanted Floor Boiler

Active iayer + pyrolysis, combustion. reductton + 10-25 cm (4-1 0 in.) thick

1 800- 1 200% (1 500-2200'F)

Inactive core +solidified smeit +carbon +c 7603C (1 400'F

-290'C (450-S50ZF\

Srneit spout Liquid srnelt

b. Oecanting Hearth Boiler

l Chemically active layer Secondary pyrolysis. combustion. reduction air +800-120O2C ( 1500-22OO2F)

Smelt swut Heanh 260-340aC (500-650°F)

Physically active layer

Liquid smelt Solid smelt

Figure 2-4 Schematic diagrams of char bed near a srnelt spout in slanted-floor and decanting- hearth recovery boilers (Adams et al., 1997).

2.2 Smelt-Water Explosion

There have been over 140 recovery boiler explosions reported in North Amerka due to

smelt-water contact. The darnages caused by these explosions range from complete destruction

of the boiler to negligible damage (Green. 1992). In some severe cases. injury and rvrn death of

the personnel have occurred. There are an estimated 100 ESP's per yeu worldwide where the

fear of explosion leads to a prolonged shutdown of the boiler (Grace. 1999).

One general mle that applies to ail recovery boilers is that water must never contact the

char bed, because there can be an explosive reaction betwsen writer and molten smelt. This is a

physical reaction in which water evaporates rapidly when it contacts the hot smelt. This results in

rapid steam expansion genemting highly destructive detonation waves. Smelt-water explosions

are unique to recovery boilers and are the most common type of explosions rncountered. Srnelt-

water explosions can occur any tirne when sufficient amounts of molten smslt and water corne

into contact with cach other. The mechanicd energy generated by evaporation of 0.45 kg ( 1 lb.)

of water in 0.001 second is estirnated to be equivalent to that of 0.22 kg (0.5 lb.) of TNT.

Typically about 7-10 kg (5-25 Ib.) of water is involved in recovery boiler explosions. The major

factor determining the severity of the explosion is the amount of water coming into contact with

the molten smelt. Currently there are no methods of preventing smeli-water explosions by

modifying the chernistry of the process. The only known way of hindering the smelt-water

explosion is to prevent smelt-water contact (Grace. 1992).

2.3 Normal Shutdown vs. Emergency Shutdown Procedure (ESP)

During regular shutdown the liquor guns stop spraying black liquor into the fumace. The

air nozzles continue blowing air into the furnace until the char is complçtely bumt off. The smelt

is allowed to cool down until it solidifies. The operators examine the smelt by prodding i t with

long pipes to make sure that the molten smelt has in fact solidified everywhere bcfore entering

the fumace to wash away the bed with water.

Current operation of rrcovery boilers requires immediate rhutdown if any water is

= are suspected to have leaked from the tubes and rntered the combustion chamber. Followin,

some of the general steps followed in an Emergency Shutdown Procedure (ESP) as

recommended by BLRBAC (Adams et al.. 1997):

Activate a l m s to clear personnel from recovery boiler area.

Stop firing fuel (black liquor).

Shut off the air supply while providing sufficient air above the char bed to purge

gases from the fumace.

Shut off the water feed to the boiler.

Drain watenvalls to a level 8 feet above the low point of the fumacr tloor.

Reduce the s tem pressure as npidly as possible. as soon as the boiler has bcen

drained.

The boiler is drained and the water feed to the boiler is shut off to stop entry of water to the

boiler. In order to prevent overheating of the water tubes. 8 feet of water is left in the waterwalls.

Primary air ports are shut off to prevent combustion in the char bed. Some air tlow is maintained

to purge the fumace and prevent building up of combustible materiais.

2.3.1 Char Bed Coolino,

The cooling characteristics of char beds are of little interest during the normal operation

of the boiler. It is only after an emergency shutdown procedure (ESP) that char bed cooling

becomes very important. An ESP c m last from several houw to a few days with a cost accrued

by the industry of up to 5 10,000 per hour ($117 million per day) in lost production (Grace.

1999).

An ESP c m leave a residual bed consisting of char. molten smelt. and frozen smelt on the

boiler floor. Char has a very low thermal conductivity and thus acts as an insulating Iayer on the

molten smelt pool. iuid around the "hot" pockets within the bed. The size of the char bed

determines the amount of time it trtkes t'or the materials in the furnace to cool down to below the

solidification temperature of srnrlt (about 720-740°C). Water washing can only begin after ihis

temperature is attained everywhere.

The char cnn contain a large amount of heat depending on the size and porosity. Table 2-

1 shows some estimation of the bed m m and heat content in a 1Orn x IO rn fumace brised on the

propmy values reponed by ADL (Richardson and Mrmam. 1977). The heat of oxidation of

carbon is based on the heating value of 32.850 klkg C . The potential heat release frorn oxidation

of sulfide is based on complrte oxidation of sulfate with a srnelt sulfidity of 304 and a reduction

el'ficiency of 90% ( Kawaji et al.. 1999).

Table 2- 1 Mass and k a t content of char bed in a 1Om x IOm furnace (Kawaji et al.. 1999)

Mass, metric tons (US tons) 1 2 12 (234)

Bed Height, rn Porositv

Sensible heat ;it 400°C (750°F). GJ (MM Btu~ 1 105 (100)

Bed 1 2

50%

Sensible heat at 8 15°C ( i50û°Fj, GJ (MM Btu) Sensible heat at 540°C (IOûO°F), GJ (MM Btu)

223 (21 1 ) 145 ( 137)

Bed 2 1

50%

Heat of fusion (5% molten smelt), GJ (MM Btu) Heat of fusion (25% rnolten smelt), GJ (MM Btu) Heat of fusion (6 inch smelt pool). GJ (MM Btu)

Heat of sulfide oxidation, GJ (MM Btu) 1 548 (519)

Bed 3 1

75%

1.5 (1.4) 7.5 (7.1 ) 4.1 (3.9) . . 1 . ,

As seen in Table 2- 1 the heat of fusion of smelt is a small fraction of the sensible herrc that has to

be removed in order to cool the bcd from 8 15°C to 540°C ( Kawaji et al.. 1999).

In order to determine the heat content of a bed it is necessary to determine the bed mass

and the amount of fuel content that burns. Bed mass cm be calculated if the volume and the

porosity are known. Volume of the bed cm be calculated but the porosity can not bti easily

measured. Heat released by combustion is primxily due to oxidation of carbon. which depends

on the amount of carbon and availability of air. Sensibie heat should br removed from a11 the

solid materials so the temperature falls below the melting point of the smelt.

In cooling a char bed. heat is transferred intemally within the bed to the boundaries and

externally from the boundaries to the surroundinp. intemal heat transfer is by conduction

through the solid material. interna1 heat transfer by convection is believed to be very small since

.as flow is minimal within the bed. In some hot regions of the bed heat could be uansferred by uZ

radiation across the pores.

Heat of carbon oxidation (5% C), GJ (MM Btu) Heat of carbon oxidation (2% C), GJ (MM Btu)

347 (329) 139 (132)

Extemal heat transfer is by natural or forced convection to the gases above the bed,

radiation from the bed surface to the surrounding water wails and upper fumace. and conduction

to the floor tubes and side walls. For practical purposes conduction to the side walls is ignored

since the contact area is much smaller compared to that at the top and bottom (Grace. 1998).

Themocouple measurements during char bed cool-down indicate a reiativrly constant

rate of temperature decrease. Since the sensible heat in the bed is miich laser thün the heat of

Fusion of molten smelt. the rate of temperature decline is a direct melisurement of the heat loss

from the bed. Assuming that the bed is cooling from top and bottom. the average heat flux from

the bed c m be calculated using the following equation (Grace. 1998):

Qh = mh Cp.b (dTIdt) 1 (2Ar)

where Q h : average heat tlux from the bed:

mb: mass of the material in bed:

Cp.b: specific heiit of material in bed:

dT/dt: rate of temperature drop:

Af: cross sectional area of furnace.

Table 2-2 summarkes the average heat fluxes from the beds at several different cooling rates for

the three beds discussed in Table 2- 1. It is assumed that the heat of fusion of the molten smeh is

negligible and there is no continued combustion (Grace. 1998).

Table 2-2 Heat tluxes associated with cooling rates (Grace, 1998)

1 Bed 1 Bed 3 Bed 3 Coolino Rate/ Heat Flux 1 ~ / m ' 1 ~tu/hr.ft' 1 ~ / m ' 1 ~tuhr-f t ' 1 w/m2 1 ~tu/hr.ti'

Without any bed disruption. the biggest resistance in cooling from the top surt-acr of the

bed is the internai resistance in heat flow from the bed incerior to the surhce. The thermal

conductivity of the cold char or of a broken slag layer is about 0.087 W/mK (Richardson and

Memam. 1976 and 1977). For these conditions. a temperature gradient of 1870°C/m is required

for a heat flux of only 160 ~ l m ' . This implies that most of the temperature gradient occurs over

ri distance of onIy about 10-15 cm (4 to 6 inches) at the bed surface. where the bed is coldest and

radiation heat transfer within the pores is the lowest. Hence the intemal temperature in cooling

beds is rxpected to rernain unifom rxcept for regions where combustion occurs. For larger beds

heat loss from the top surface tends to be relatively lower than that to the tloor but both

directions are important (Grace. 1998).

The trapped molten smelt pockets in the char bed are considered a potrntial problem

because of the long time required for such isolated pockets to cool and solidify. In a large brd it

could take over 5 days for isolated smelt pockets to solidify (Richardson and Merriam. 1976 and

1977).

Operatoa use several methods to determine if the bed is ready for water washing. Thesr

include waiting for a given period of time. approximately 1 to 7 days. proddins the bed to see if

there are any "hot" spots. and rneasunng the bed temperature. in some mills. the operators

attempt to accelerate the cooling of the bed by spraying a fine mist of water after a certain

mount of time (Richardson and Memarn, 1977). These methods are d l empirical with a lack of

understanding of the heat transfer mechanisms behind thern.

2.4 Accelerated char bed cooling

One way to shonen the bed cool-down time is to inject sodium bicarbonate or liquid

carbon dioxide into the bed to disrupt the bed and ücceleratr the cooling process. It hÿs bern

shown in some cases chat a bed can be cooled in less than eight hours aftrr initiating riccelerated

cooling (Kawaji et al.. 1999). There is a study underway to examine the effectiveness of these

coolants. Some critical unknowns in these investigations rire as follows t Gracr. 1999):

0 Reliable values of the effective thermal conductivity of porous char brds - Knowlrdge of conditions that result in trapped smelt pockrts

Ability to determine porosity and porosity distribution in the bed

2.5 Measurernent of thermal properties of char bed materials

There is little information available about the properties of char and smelt in the recover):

boilers. This is due to the fact that the temperature in the furnace is very high (as high ris 900°C)

and that molten smelt is extremely corrosive. These factors make it difficult to monitor simple

properties such as specific heat. density. temperature distribution. and thermal conductivity of

the char bed rnaterials.

2.6 Arthur De Little Ince (ADL) Report

The ADL report is the only publication that has documented extensive experimental

measuremrnts on the propenies of materials in recovery boilers. ADL's work on recovery boilers

c m be divided into two main parts:

a) an experimental part which includes srveral mil1 visits and collrction of field data.

b ) a thrnal modeling part in which ADL used a heat transfer mode1 and the

experimental data to predict:

i ) thermal properties of the char and the smelt:

i i ) cooling of the char bed.

2.6.1 tnstrumentation Used

2.6.1.1 Ten~prnifiire rçlt.crsrrrrtwi~f Probes

A five-junction thermocouple probe (Figure 2-5) wiis used to measure the temperature

profile inside the char bed. It utilizrd five 0.04-inch diarneter thermocouple wires encloscd in a

51 16-inch OD stainless steel tube with 0.035-inch wdl thickness. The thermocoupk junctions

were spaced ai 8-inch intervals so the temperature could br rneasured iit five locations to a depth

of 40 inches inside the bed. The output from each thermocouple was continuously monitored.

During the mil1 trials. i t was observed that thermocouples with lower thermal mass were

more versatile. This was because the materials with lower thermal m m had a smaller time

constant: hence reached thermal equilibrium much faster. This allowed the thermocouples to

read the tempentures soon after they were inserted into the bed. Thermocouples with long time

constants failed due to corrosion.

47%" - 4

8" 39%" # c- -i

3 1 X" 4 3

8" 23%" 4 C - 16%" - C

I

I I

--J.kc

klismatic Viaw of Proba End I

- Each Fingdr: SJS f uk 5/16" 0.0.. ,035" Wall

- Cctamic Intulalors McOanel #2T-.116-3 16

- Therrnocoii~ile Wiie #I8. Type K. Chtomel-Alumrl

Squi?etc TC Bcad and Weld End

Acturl R o k Loatlon In Adrptmr Pieu

Adapter Piecc SIS

8'. X" Pipe SIS

Figure 2-5 A five-junction thermocouple probe (Richardson and Memam. 1977)

2.6.1.2 Bali Heat-Flow Probe

A heat flow probe with a small spherical mass (Figure 2-6) was used to measure the

thermal conductivity and thermal diffusivity of the char bed.

Tao 6-32 for Sct Scnw ro b u r e TC Junetion at a n t e r of Bal1

Inran 114" OB. 321 SIS f u&

d I L I k - 1

Dauil: 9atl and Adamcr P i m

Figure 2-6 Sçhematic diagram of the ball-heat-flow probe used by the M L (from Richardson and Merriarn, 1977)

This technique used the time rate of temperature rise of a steel sphere to measure the thermal

properties of the surrounding char. As shown in Figure 2-7, the temperature in the region near

the bal1 would initially decrease as the bed loses heat to the initially "cold bail. Meanwhile the

temperature of the bal1 would increase as it gains heat form the surrounding bed. in a short

while, the temperatures of both the ball and the surrounding bed would increase as heat flows

from the farther parts of the bed to the bal1 and the regions near it.

Bed Rqion

Figure 2-7 Theory of the ball-heat-flow probe (Richardson and Memarn. 1977)

ADL calculated the thermal diffusivity from the early part of the temperature nse of the

ball and thermal conductivity frorn the latter portion of the temperature nse. when the

temperatures of the bail and the surroundings approached each other. ADL explained that this

was done because the initial part of the heating curve was suongly dependent on the themai

diffusivity of the medium whereas the latter part of the heating curve was dependent more on the

thermal conductivity.

A small thermocouple probe witï placed at a known distance from the equator of the steel

bal1 to measure the themiil diffusivity and thermal conductivity independently as a check. This

smdl thermocouple. however. failed and hence the thermal diffusivity and the themial

conductivity meuurements could never be cross-checked.

2.6.1.3 Bed Scrntpiing Tubes

Core sampling tubes of l-inch. 1.25-inch. and ?-inch OD and Xoot length werr used to

remove sampIes from the char bed. Samples from different locations in the bed were collecteci.

2.6.2 Mill Visits

ADL researchers visited several mills with decanting-hemh (CE) and slanted-tloor

(B&W) type recovery boilers. The purpose of these visits was to gain a first hand enperience in

the operation of the recovery boilers. and to measure temperature and thermal proputirs in thrsr

beds.

ADL researchers explained that the significant difference in the thermal conductivity of

the char from the Ticonderoga mil1 (CE boilers) and chat from the Androscoggin mi11 (B&W

boilers) was due to the difference in the type of boilers. They described that the CE boilcrs

contained "inactive chai' where no combustion could take place.

The B&W boilers. however. were considered to carry "active zones" where combustion

and smelting would take place ai high tempentures. ADL recommendrd a tempermre

dependent thermal conductivity. as opposed to a constant thermal conductivity. for the "active

zone" of the char accounting for heat uansfer due to radiation in a porous material as given by

Equation 2-2:

w here k: apparent thermal conducti 4): porosity ; Dp: Pore diameter (ft);

vity (BTUh.ft."F);

o: Stefan-Boltzman constant, 0.17 14 X ~O'"BTU/~~.~~'.OR''); T: Temperature (OR).

2.7 Effect of temperature on thermal conductivity of porous materials

There is eirperimental evidence that thermal conductivity of different porous materials in

fact does vary with ternperature (Litovsky et al., 1996). This variation. however. deprnds on the

type and structure of the material under investigation. As Figure 2-8 indicates. the effective

thermal conductivity of chrorn-magnesite does not follow a certain pattern as the ternperature

increases.

Figure 2-8 Variations of thermal conductivity of poorly connected refractories with ternperature for different gas pressures: (A) chrom-magnesite. p = I . I gcm" (N' pressures of ((@) IO-', (0) los, and (O) 5 x 10' Pa): and (B) yttrium oxide . Q = 45% (He pressures of (o) IO', (e) 10'~ , and (O) 10' Pa). (Litovsky et al.. 19%)

Other materials behave differently; for example the thermal conductivity of alurnina

always decreases as temperature increases (Figure 2-9A). On the other hand the thermal

conductivity of fire clay always increases as the temperature increases (Figure 1-98). Therefore

thermal conductivity of char bed materials can lollow either patterns.

Figure 2-9 Variations of thermal conductivity of insulating refractories with temperature for different gas pressures: (A) alumina. p = l . I g.cm-3 (N' pressures of (A) Io3. (A) 5 x lo3. (0) 10'. and (a) 10.' Pa): and (B) fire clay. p = 0.6 gcrn-' (N' pressures of (A) lo5. (A) 2 x Io4. (0) 10'. and (0) IO*' Pa). (Litovsky et al.. 1996)

2.8 Experirnental evaluation of the effective thermal conductivities of packed beds at high temperatures

Nasr et al. (1994) investigated the effect of particle diameter and bed temperature on the

rate of heat transfer due to both conduction and radiation in packed beds of spherical partinicles.

Three different packing materials. alurnina. aluminum, and glas. with various particle diameters

(2.5 to 13 mm) were tested. Interna1 bed temperature profiles and the corresponding effective

thermal conductivities were calculated for a temperature range of 350 K to 1300 K undrr steady

state conditions. It was found that the effective thermal conductivity increases with particle size

and with thermal conductivity of the packing material. Nasr et al. attempted to quantify the

relative contributions of conduction and radiation.

Figure 2- 10 shows the expenmental apparatus used for the investigation. The apparatus

of

1, a

was desipned using guidelines

refractories and insulation materia

from ASTM for measunng the thermal conductivity

1s. The apparatus consisted of an slectnc furnace, a test ce1

cooling system, and a data acquisition unit.

Figure 2-10 Cross-sectional view of the conductive-radiative rxperimental appantus (Nasr et ai., 1994)

Thermocouples were placed at different vertical positions and the particles were

randornly poured into the test cell. The test ce11 was raised into the fumace cavity and water flow

through the flux caiorimeter and the thermal guards were initiated. The heating elements and the

data acquisition system were then activated. Steady state conditions were assumed to have

reached when the temperatures inside the bed changed by no more rhan I°C in a penod of one

hour. It took approximately seven to eight houn to establish steady state conditions.

For each run at a specific fumace temperature the heat flow through the packed bed was

calculated usinz the water flow throuzh the calonmeter and the inlet and outlet temperatures at

steady state. The heat transfer rate was rxpressed as:

Qe = Q Cp ATc ( 2 - 3 )

where

Q,: rate of heat removal by water tlowin_o through the calonmeter:

m: mass llow mtr of watrr through the calorimeter:

C,: heat capacity of water:

AT,: difference between inlet and outlet water temperatures at strlidy state.

The effective thermal conductivity was computed from Equation 2 4 .

kir = -(Qc/Ac) / (dT/dx ) ( 2 - 4

where kir: cffective thermal conductivity of the panicle bed (includes both conduction and

radiation effects):

A,: cross sectional area of the calorimeter:

dT/dx: temperature gradient at any location in the bed.

Due to the lack of knowledge of the radiative propeny data (extinction coefficient.

absorption coefficient. etc.). Nasr et al. ( 1994) simplified the radiative transfer in the bed using

28

the diffusion approximation. Assuming that natud convection effects are negligible and the

steady state heat tlow is one-dimensional. the heat diffusion equation becomes.

k, have been developec where brr (T) = Lond (T) + kr (T). Many expressions for 1 but in generrtl

they may be representrd by a genrric expression of the Damkohler type for the radiative

conductivity as follows:

The exchang factor E is a model-drpendent parameter and is usually a function of the particle

rmissivity and possibly the particle shape and bed porosity.

The contribution to heat transfer by conduction and radiation was represented by the

followinp equation.

1 kiff = 0.8 kr.und.Z-B-S + JE dp Q TL ( 2-7)

where l&,nd,Z-B-S is the effective thermal conductivity obtained from Zehner-Bauer-Schlunder

mode 1.

C W T E R 3 EXPERIMENTAL APPARATUS AND PROCEDURE

3.1 Apparatus

The measurements of the effective thermal conductivity of char bed samples were performed

using an apparatus constructed with a design similar to that recommended for measuring the

thermal conductivity of carbon refiactories (ASTM, 1999). The apparatus was constructed to

provide a one-dimensional heat transfer through the sample. It allowed for accurate

measurements of the bed temperature profile using thermocouples, and the heat removal rate

fiom which the effective thermal conductivity was calculated. The major components of the

experimental apparatus consisted of a heating unit, a cooling unit, a test chamber, and a data

acquisition unit (Figure 3- 1). Following is the description and function of each unit.

Thermocouple attached to / temperature eontroi unit

Insulati ing walls \

Test Chamb

Water Outlet Water Inlet

Figure 3-1 a) Schematic diagram of the expenmentai apparatus

b) Expcrimentül setup

Figure 3- 1 Experimental apparatus and set up

3.1.1 Cover

The cover was constructed of insulating rirebricks to preveni upward heat loss. Also the

heating plate was mounted under the cover. The cover could be completely lifted off the rest of

the apparatus to dlow for Ioading of the bed sample and cleaning of the test chamber.

3.1.2 Heating: Unit

The heating unit consisted of a ceramic heating plate (15.5 x 15.5 cm). height adjustins

wires. a themocouple. and a tempenture control unit. The heating plate was attached to the

cover by the adjusting wires. The wires allowed for adjusting the heighi of the heating piate

inside the test chamber so that the heating plate could rest just on top of the char sample. A

thermocouple was placed through the top cover in the center of the heating plate to monitor the

surface tempenture of the heating plate. A temperature control unit regulated openting

temperature of the heating plate to a prescribed tempenture set point.

3.1.3 Test Chamber

The test chamber was a cavity in the middle of the apparatus in the shape of a square based

column ( 16 x 16 x 10 cm). It was surrounded by firebrick insulation as shown in Figure 3-2 to

rninimize heat flow in the radial direction.

Figure 3-2 Top view of the test chamber (16 cm x 16 cm x 70 cm)

3.1.4 Coolino Unit

This unit included a cooling plate. two water inlets and two water outlets. thermocouples

to rneasure water temperatures at the inlets and outlets. and a flowmeter. The cooling plate was

made of two square steel plates (15.5 x 15.5 cm). Two water channels were carved in the bottom

steel plate, Figure 3-3. A shret of Teflon with a thickness of approxirnately 5 mm was used in

between the two steel plates to seal water in the channels. The two corresponding water

channels ensured that the temperature in the cooling plate would be uniform. If only one channel

was used then the water inlet side would be colder than the water outlet side. Thennocouples

were used at the water inlet and outlet to monitor the corresponding ternperatures. A flowmeter

was instdilled at the water inlet to measure the tlowrate.

(4

Figure 3-3 Cooling plate. a) top virw

view

(b)

of the bottom plate ( 15.5 cm x 15.5 cm). b) side

3.1 S Insulating Walls

Special attention was paid to the materials used for the walls. It wris important io use

materials with thermal conductivity significantly lower than that of the char samples in order to

induce a one-dimensional heat flow. It was also essential to fabricate the walls from a material

that would withstand the hi& operating ternperatures. Insulating tirebricks were used on the

inner side of the walls because they can endure the high temperatures. and do not react with the

char materials. On the outer side of the walls a layer of porous silica with a thermal conductivity

much lower than that of firebricks was used to funher prevent radial heat loss from the side

walls. The thermal conductivity of this material was reportrd to be 0.028 W/m°C (0.195

~tu.in/hr.ft'."~) at 260 O C .

Despite the low thermal conductivity of the insulüting materiais. there was horizontal

heat loss from the apparatus simply because the insulation was not perfect. However. this heat

loss was srnall and did not signiticantly affect the final results. As shown in Appendix A the

rna~irnurn heat loss from the horîzontal wdls was less than 6% of the total heat tlow through the

char sarnples.

3.1.6 Steel Case

The entire structure of the apparatus was enclosed in a steel square case (44 x W x 28

cm) to protect the individuai components.

3.1.7 Thermocouples

A total of 15 thermocouple holes. each 2 cm a p a . were drilled through two oppositr

sides of the steel case and the insulating walls. The first holr from the bottom was drilled so that

the thermocouple at that location was on top of the cooling plate. The first hole on the opposite

side was 1 cm above the cooling plate. and so on. Only a certain number of thennocouples were

34

used to monitor the temperature profile in each run depending on the amount of char sample.

Thermocouple holes not in use were piugged with a mud sea

As mentioned earlier. thermocouples were installed

lant.

in the water inlets and outlets of the

cooling plaie to monitor the corresponding water temperatures. Also, thermocouples were

mounted on the surface of the steel case to examine the surface temperature of the insulating

walls.

3.1.8 DataAcciuisition

A PC-based data acquisition system with 12 thermocouple channels was usrd to monitor

and record the temperature profile inside the char sarnple. the inlet and outlet watrr temperatures

circulating in the cooling plate. and the surface temperature of the walls. Temperatures were

monitored evcry 4 seconds and recordrd every 5 minutes.

3.2 Calibration

Firebricks with known thermal conductivity were tested in the experimental apparatus to

test the accuracy of the apparatus and the procedure. Firebricks (13 x 1 1 x 6 cm) were cut to f i t

the test charnber. Holes. 7.5 cm long and 0.16 cm (1116") in diameter were drilled horizontdly

through the firebricks ai speci fic locations. ThemocoupIes were insened in to the holes inside the

bricks to monitor temperatures. Thermocouples were pressed against the tirebrick to cnsure good

contact. The following procedure was followed to experimentally detemine the thermal

conductivity. These were compared with the reponed data to verify the accuracy of the

experimental apparatus.

Char Sarnples

Char samples tested were obtained from the following three sources:

3.3.1 Smples From Mill A

Char bed materials were obtained from the smelt spout of an operating recovery boiler.

During the test. the boiler was operating with a low bed and thrrefore it waï difficult to obtain

char bed materials without collecting some molten smelt as it tlowed through the spout. Also. the

draft of air into the spout made it difficult for the operators to collect tlaky char rnatrnals. In a11

the char samples collected. there was frozen smelt present at the bottom once the sample was

allowed to cool. The color of the samples was grayish (Figure 3 4 ) . Four different mns were

conducred using char from this boiler:

3.3.1.1 Mill A I Char sample was directly placed from the recovrry boiler into the

test chamber. Thermal conductivity measurements were performed onsite.

3.3.1.2 Mill A-2 Char smple wcis allowed to cool down once it w u collected from

the boiler. then it was placed in the test charnber. Themiil conductivity measurements were

performed onsite.

3.3.1.3 Mill A-3 Char sample w s taken to the laboratory where thermal

conductivity measurements were done.

3.3.1.4 Mill A-4 Char sarnple labeled iMill A-3 was crushed to a powder with a

&ender to reduce porosity. This sarnple was then used to measure thermal conductivity in the

laboratory .

a) Mill A sample beinp collected b) Mill A sample immediately collected from the smel t spout from the boiler

C) Mill A-?

Figure 3-4 Mill -4 samples

3.3.2 Laboratorv made samples

Char samples were also made in the lab using black liquor from an operating plant. Black

liquor ai room temperature was hrated in a \vater bath for about 1-2 hours at 70-80CC to reduce

viscosity. Heated black liquor was then mixed well and poured into a metal crucible inside a

Iumacr. The cnicible was then placed inside a pyrolysis chamber. The chamber was sealed and

n i t r o p gas at relatively low flow rate. approximately 5 cm3/min. was passed through the

chamber to prevent the combustion of char. The sample was heated for about 10 minutes at

600°C to dry the black liquor and vaporize al1 the waier. The temperature was then increased

from 600 to 700°C. and the sample was kept at this tempenture for 50 minutes to compleie the

pyrolysis of black liquor. After this stage. the furnace was turned off while nitrogen gas was

circulated through the sample until the charred black liquor was cooled to ahout 80-100°C.

About 300-400 g of black liquor produced about 150-170 g of char. Two runs were conducted to

obtained the following samples:

3.3.2.1 Lab- 1 Char made in the lab had a quite different appearance and structure

than that of char obrained from recovery boilers. It was in the shape of a cylinder and had to be

broken up in order to fit into the apparatus. Some fragments of the sample were hollow cylinders

while other fra~ments were cylinders with a flaky struciure inside. This laboratoy-made sarnple

was much hardrr to break and appeared black (Figure 3-5).

3.3.2.2 Lab-2 Char sample iabeled Lab-l was crushed to a powder with a grinder

and tested for thermal conductivity.

a) Lab- 1 sarnple b ) Lab-2 sarnple

Figure 3-5 Laboratory samples

3.3.3 Samples From Mill B

A simulated ESP expenment was conducted at Mill B Industries plant. After the ESP

started, a sarnple of char bed materials was collected by an operator through a primary air port.

Due to the srnail size of the pon. approximately 12 x 15 cm. only a srnall amount of char could

be collected. Unlike the Mill A samples. very littlt molten smrit was scooped out while

collecting the char materials because the sümple was taken from the top of the bed. The char

matenal was covered and allowrd to cool down before it was taken ro the laboratory for testing.

3.3.3.1 M i - 1: The sample wüs very much like the iMill A sarnples in structure.

The sample was black and there waï much less frozen smelt at the bottom than the Miil A

sarnples (Figure 3-6).

Figure 3-6 Mill B sarnple

3.4 Density Measurement

The total weight of each sample was measured before it was placed into the test chamber.

The height of the sample inside the test chamber was also measured. The density of the sample

was calculated from this information as mass per unit volume.

3.5 Porosity Measurement

Porosity is defined as the percentage of total void volume in a total sample volume. This

property was determined as follows:

a) A sample was placed inside a beaker. The volume of this sample. V,. was calculated

by measuring the dimensions of the beaker.

b) the sample was crushed into a fine powder with a grinder.

c) the powder was mixed with a known volume of vegetable oil. V,,. and wüs allowed to

sit for about fifteen minutes to ensure al1 air bubbles were released.

d) the volume of the vegetable oil-powder mixture. VI, was determined,

e) material volume. V,, was determined by subtracting the initiai volume of oil from the

final volume of oil and sample. (VI- V,).

F) total void volume, V,. was found by subtracting the material volume from the total

volume, Va= V, - V,,

g) porosity was calculated by finding the percent void volume in total volume using

equation 3- 1.

Porosity = VJ V, x 100% (3- 1 )

Although it is very difficult to measure the exact volume of voids in a porous material. the above

procedure was developed to determine the porosity of the char bed samples as accurately as

possible. The sample was crushed to break the structure and get rid of as much void volume as

possible. The powder was added to a liquid so that the liquid material would fil1 the spaces

between the solid particles and replace the void. Since char materials are soluble in water. a

vegetable oil was used to prevent dissolution of the sample in the liquid.

3.6 Experirnental Procedure

After positioning thennocouples and measuring their venical locations in the test

chümber. the char particles were randomly poured into the test chamber and the surface was

leveled. The top cover. to which the heating plate was attached. was then lowered so that the

heatins plate would just rit on top of the char sample. The heating plate was tumed on and the

temperature control was set to a specific temperature. The temperature control kept the heating

plate at the specific set point throughout the run. Water tlow through the cooling plate was thrn

initiated. The data acquisition system was activated to monitor and record the temperature profile

inside the sample. inlet and outlet water temperatures. and the surface temperature of the

experimental apparatus.

Typically about five to six hours were required to establish a steady state condition. The

steady stiite condition wüs assurned to have been reached when the ternpentures inside the

sample as well as the water temperaturcs and the vesse1 wall temperatures no longer chansed by

more than 3°C during a one-hour period. After recording the steady state water tlow rate and ail

the temperatures. the heating plate set point tempenture was changed to initiate another run.

After complethg runs at several heating plate temperature set points. the char sample was

allowed to cool down. The panicles were removed from the test chamber. and the test chamber

was cleaned using a vacuum cleaner. The entire procedure was repeated for other char sampies.

3.7 Data Processing

As mentioned earlier. there were a total of seven sarnples investigatrd in this project. For

each of these sarnples. a number of runs at various heating plate temperature-set-points were

conducted. To ensure that steady state had been indeed reached. the temperature history inside

the sarnple was plotted for each run. For example. Figure 3-7 shows such a plot for Lab- 1 sample

at a heating plate set point of 250°C. A constant temperature history üfter 4 hours confirmed that

steady state had been reached.

Thennocouple Lmtions (cm)

Tirne (minutes)

Figure 3-7 Temperature history of Lab- 1 sample at set point of 250°C

Similar tempenture histories were plotted for wall surface temperatures. and inlet and outlet

water temperatures to make sure steady state had been reached.

The steady state temperatures were then used to calculate the effective thermal

conductivity as follows:

a) Heat removed by the circulating water was drtermined using equation 3-2.

where

Q c :

m,:

cp.w:

Tin.w:

Tout.w:

Rate of heat removed by the water at steady stüte ( W )

Mass flow rate of wüier at steady state (gs )

Heat capacity of watcr (J1g.T)

Water inlet temperature at steady state ( O C )

Water outlet temperature at steady state (OC)

b) Assuming a constant temperature gradient between any two thermocouple locations

in the sample. Equation 2-4 was simplifird to equation (3-3)

= -(Q,l&-) 1 (ATIAx ) (3-3

where

bu: effective thermal conductivity of the sarnple (W1m.K)

: cross sectionai area of the dorimeter (m'):

AT: steady state temperature difference between two consecutive thermocouples (OC)

: vertical distance between two consecutive thermocouples (ml

The effective thermal conductivity calculated was assumed to be that of the char bed

materials at the average temperature. Ta",. between the two consecutive thennocouples. Oiher

steady state temperatures were used to determine bfr at other values of T,,,. The above

procedure was repeated in al1 the runs for each sample. A graph of effective thermal conductivity

versus Ta,, was producrd for each sample. The error associated with this calculation was

determined, see Appendix C.

3.8 Numerical Simulation

As explained earlier. in order to calculate the thermal conductivity using the experimental

apparatus. it was assumed that heat transfer through the samplr from the heating plate to the

cooling plate was cornpletely one-dimensional. Therefore it was assumed that no hrat travelcd

through the thick insulation walls surrounding the sample. In order to verify this assumption. a

computational tluid dynarnics (CFD) code. PHOENICS. was used to develop a cornputer model

that could simulate the heating of simples tested in the experimental apparatus.

3.8. L Description of the simulation model

The PHOENICS code was used to mode1 the entire experirnentai apparatus in a 3-

dimensional heat transfer model. Char thermal conductivity determined enperimentally wcis used

in the model and the steady tempenture distribution inside the sarnple was predicted. By

cornparhg the temperature distributions obtained experimentally with those predicted by the

simulation. the vaiidity of the assurnption was determined as discussed in the following section.

Necessary corrections were made to account for the 3-dimensionality of heat tlow.

3.8.2 Geometrv of the computationai domain

Figure 3-8 shows the cornputational domain of the heat transfer rnodel. Al1 the

components of the apparatus and the sarnple were modeled as a different matenal with the

appropriate dimensions and properties.

In the model. the rntire apparatus waï surrounded by air. Also. appropriate sized blocks

of air represented the gap between the cover and the heating plate and the gap between the

cooling plate and the bottom insulation bricks as shown in Figure 3-8. The two wall mûtenals.

the inner insulation bricks and the outer micro-porous silica insulation. were modeled as blocks

with constant thermal conductivity values. Since the simulation was perforrned under steady

state conditions. thermal conductivity was the only value that had to be specified for these

materiais. The thermal conductivity of the matenal was reponed by the brick supplier to be

constant for the temperature range of interest. Thrrefore. constant thermal conductivity values of

0.16 W/m°C and 0.02 W/maC were specified for the blocks representing the insulation brick and

micro-porous insulation blocks. respectively. The heating plate was rnodeled as a slüb with a

constant temperature. The temperature of the hot slab. in O C . was the only variable that had to be

specified. The cooling plate was represented by a heat sink. The constant value of heat removal

rate in W had to be specified for the heat sink. The vertical temperature profile within the sarnple

was recorded by a temperature monitor in the center of sarnple. The PHOENICS q l files. which

include the properties. dimensions. and locations of each constituent component are included in

Appendix B.

Air

Micro-porous lnsulation

Figure 3-8 Schematic diapram of the simulation mode1

3.8.3 Heat transkr equations

PHOENICS provided a solution to the 3-dimensional heat conduction equation in

Cartesian coordinates described by equation 3-1.

q = k [dTldx + dT/dy + dT1dz ] (3-4)

where q is the rate of heat transfer in W. and k is the thermal conductivity in WlmaC. which may

be a function of temperature. The heat transfer rate was specified as the heat removed by the heat

sink. Themal conductivity of each rnatenal was specified sepantrly.

3.8.4 Boundary and initial conditions

For al1 simulations, the natural convection heat transfer coefficient for the surrounding air

was specified to be 3.3 WlmLOC. This value was determined using the method described in

Appendix A. The initial temperature of the surrounding air and al1 the components of the model

was set to be 25°C.

3.8.5 Simulations

The above model was used to mn various simulations. Firebrick and char bed propenies

were used to specify the thermal conductivity of the sample. Al1 the tirebrick çxperiments and

one Mill A-3 rxperiment were simulate using the above model. Table 3-1 sumrnarizes the

propenies used in each simulation.

Table 3- 1 S u m m w of the simulation conditions

Sarnple used in experiment

The first colurnn in Table 3-1 shows the material tested in the experimental apparatus. The

number next to the material indicates the temperature of the heating plate for the specit'c

experimental mn. The second column gives the thermal conductivity value that had to be used in

each simulation in order to duplicate the experimentd steady temperature profile. The hot slab

Firebrick, 600 Firebrick. 700 Firebrick. 800 Firebtick. 900

Themal Conductivity of Sarnple(W/m°C)setin

simulation 0.44 0.45 0.45 0.55

Hot slab Temp.('C)

Herit Sink Rate ( W )

630 62.1 7 10 815 920

68.3 79.4 101

temperature is the temperature prescribed to the heating plate. The heat sink rate is the hsat

removai rate specified for the heat sink. This value was the same as the heat removal rate of the

cooling plate for the corresponding experimental run.

As described earlier. each simulation provided the steady temperature profile in the

vertical direction. Therefore. in order to sirnulate a certain experiment. the above mode1 was used

with the following adjustments:

a) The heat sink nte wils set io be equal to the amount of heat removed by the

cooling plate at steady state for that pmticular experirnental nin. For example. for

the crilibration experiment where thermal conductivity of firebrick was

determined and the heating plate temperature was set to 600°C. the heat removed

by the cooling plate was 62.1 W. Therefore the heut sink rernoval rate in the

simulation wrrs set to 62.1 W.

b) The temperature of the hot slab. representing the heating plate in the simulation.

was set so that the temperature at the location of the highest thermocouple was the

same for both simulation and experiment. For example. for the experimental run.

firebric k-600. the steady temperature recorded b y the hig hest thermocouple.

located at a height of 10.3 cm. was 47 1°C. The hot slab temperature for this

situation was changed until the temperature predicted by the simulation at 10.3

cm was 471°C. This was necessary as the contact resistant at the plate-sample

intedace was unknown.

c) Thermal conductivity ot the sample was thrn vaied to change the dope of the

steady temperature profile. The final thermal conductivity according to simulation

was seiected when the dope of the steady temperature profiles for both

expenmentai and simulation was the same.

d) The thermal conductivity that provided the same steady temperature profile as the

experirnental temperature profile was selected as the thermal conductivity of the

sample when 3-dimensional heat transfer was considered.

CHAPTER 4 RESULTS AND DISCUSSION

4.1 Calibration of the measurement system

As described in the previous chapter, insulation firebricks with known thermal

conductivity values were used to test the accuracy of the experhental method and data analysis

procedure. Figure 4-1 shows a cornparison between the measured thermal conductivity and the

value recommended by the supplier of this particular firebrick.

T e m p e n t u r e ( O C )

, ,, - G O

E o a o -

P w O -6 O -.

b > .I 0.40 - O 3 'P 0.20 - c O 0 0.00

Figure 4- 1 Calibration results

bottom region

'r+ 't

top region

n i @ y 8 ~ @ . - -

middle region Reported

-

Ln this figure. the bottom region refers to the thermal conductivity. k. values measured using the

thermocouples located within 2 cm of the bottom of the sample. Similarly. the top region

represents the k values found using the thermocouples within 2 cm of the top of the sample. The

middle region denotes the k values determined using the thermocouples between the top and the

bottom regions.

The results indicate that there is good agreement between the measurements made in the middle

region and the recommended values. The k values found in the top and bottom rezions. howrver.

overestimated the reported thermal conductivity. The high thermal conductivity measured in the

top region was due to the fact that the temperature gradient between the highest thermocouple

and the one imrnediately below was lower than rxpected. This could be due to three-dimensional

heat transfer in the top region which was close to the hot beating plate. Therefore assuming one-

dimensional heat transfer in the top region of the sample. i.e. within 2 cm to the top surface. may

not yield an accurate measurement of thermal conductivity.

For the bottom region. the higher than recommended thermal conductivity was again dur to the

low temperature gradient between the lowest thermocouple and the one immediately above it. It

was believed that the contact resistance between the cooling plate and the samplr could affect

this temperature gradient. however this behavior was not fully undentood.

Based on the predicted and reported values of thermal conductivity. it was concluded that:

Thermal conductivity determined using the temperature gradients mrasured by

thermocouples located well inside the sample was fairly accurate.

Thermal conductivity values determined from the thermocouples located within 2 cm of the

top and bottom surfaces of the sample were overestimated. Non-linear temperature variations

in these regions are likely due to the 3-dimensional effects and contact resistance.

4.2 Porosity and Density

Porosity of each smple was calculatrd before the sample was tesicd in the thermal conductivity

apparatus usin; the method described in Chapter 3. The density of the sümple was drtetmined

each time the heater temperature was changed by meilsuring the reduction in the sample height.

Table 1-1 sumrnarizes the density and porosity values for rach sample. Density of the matenal

obtained from Mill A without any pores was rstimated to be approximatrly 1.78 @/cm3). The

values of the char samples made in the lab and also the samples obtained from Mill-B boilcr.

were both 2.8 (g/ cm2). indicating that these two sarnples were similar in composition.

Table

Laboratory Samples

43.1 Lab- 1

As described in Chapter 3. the char samples made in the lab had a different structure than those

obtained from recovery boilers. The samples were made in a cylindrical vessel and therefore

took the shape of the vessel. They were in the fom of an alrnost hollow cylinder with a large

void in the center. resembling a pipe.

Richardson and Merriam's

O 1 O0 200 300 400 500 600

Temperature ( O C )

Figure 4-2 Effective thermal conductivity variations with temperature t'or Lab- 1 Simple.

The pipe-shaped simple had to be broken in order to fit the test chamber of the thermal

conductivity apparatus. This resulted in the half-pipe shaped chunks of the char sitting on top of

one another in the thermal conductivity apparatus. The structure and coior of the sample did not

change significantly at the end of the experiment.

The measured effective thermal conductivity of the porous laboratory sample. i ab- 1. was found

to be very low. 0.13 W/m°C at 100°C. then increase sharply with tempenture as s h o w in Figure

4-2. This figure indicates that the temperature-dependent thermal conductivity modrl. cquation

2-2. suggested by Richardson and Memarn ( 1977) and indicated by a solid line can describe the

experimental data relatively accurately. if the porosity and pore diarneter are properly selected.

The porosity of the Lab- 1 sampIe war measured to be 92%. It w u not possible. however. to

measure the pore diameter because the pore sizes varied frorn microscopie ones to those thüt

were about 4 cm in diarneter. A value of 7.5 mm was used in the above equation to fit the

experimental values. The pore diameters for this sample ranged from about 0.2 mm to about U)

mm. Several pore diameters were used in the Richardson and Merriam's mode1 but 7.5 mm fit

the experimental data accurately.

4.3.2 Lab-2

The Iüboratory sample. Lab-2. was obiained by crushing the porous laboratory sample into a fine

powder. The effective thermal conductivity was mensured at various tempentures. as shown in

Figure 4-3. The figure shows rhat thermal conductivity did not vary with temperature as strongly

as it did for the Lab- 1 sample. Thermal conductivity remained relatively constant brlow about

-100-500°C and then increasrd slightly at 650°C.

Modified Richardson 0'

and Meniam's Model ,/ Experimental

Richardson and Merriam's Model

O 100 200 300 400 500 600 700

Temperature (OC)

Figure 4-3 Effective themal conductivity variation with temperature for Lab-2 sample

56

The Richardson and Merriam's temperature-dependent mode1 (4- 1 ) failed to predict these results.

When a porosity of 70% and a pore diameter of 2.5 mm were arbitrariiy used. the model shown

by a solid curve fit the points only at higher temperatures. In the modified Richardson and

Memam's temperature-dependent model shown by a dashed curve. a solid thermal conductivity

of 0.20 Wlm°C was used instead of the recommended 0.087 Wlm°C. while porosity and pore

diameter were unchanged. Now the modified model f i t the data at low temperatures below

300°C. but overestimates the data at higher temperatures. Thus. it c m be concludrd that

Richardson and Memam's model predicts a different temperature dependence from that of thc

experimental data and therefore cm not be used in this case to correlate the thermal conductivity

data.

In cornparhg the thermal conductivity variations between the porous Lab-1 and crushed Lab-2

smples (Figure 44). it was observed that a change took place in the structure of the less porous

sample at higher temperatures. and this completel y changed the thermal conduct ivity variation

with temperature.

O 100 200 300 400 500 600 700 Temperature (OC)

Figure44 Effect of structure and porosity on the thermal conductivity behavior for labontory-made samples

The more dense crushed samplr, Lab-2. had a higher thermal conductivity value of about 0.25

W/m°C at low temperatures below 200°C. while the value for the less dense Lab-1 sample was

about 0.15 W/m°C. This is because the Lab-2 sample was more closely packed and hence the

solid thermal conductivity should be higher in the absence of any radiation effect.

S ince the Richardson and Merriam's tempernture-dependent model could predict the

thermal conductivity of the porous laboratory sarnple. Lab- 1. and the structure of the sample did

not seem to change during the rxperiment. the increase in the thermal conductivity with

temperature is believed to be entirely due to radiation through the pores. As mentionrd brfore.

the Richardson and Memam's model attributes al1 changes in the thermal conductivity at high

temperatures to radiation. Although the porosity of the Lab-2 sarnple after crushing was still

quite high. about 70%. ri change in the structure of the material is believed to have chünged the

mechrinism of heat tramfer.

4.4 Mill Samples

4.4 1 Mill A- 1 and Mill A-2

Thermal conductivity rneasurements for the two mill samples were conducted onsite at a pulp

and paper mill. Due to time constraint. only one run could be performed for each sample. The

results obtained from these tests were in agreement with the results for the Mill A-3 sample.

which was obtained from the same mill.

4.4.2 Mil1 A-3

This sample was obtained from the fumace of an operating recovery boiler. The effective

thermal conductivity for this sample. Mill A-3. was found to remain more or less constant below

about 500°C. Figure 4-5. It then increased sharply with temperature. The trend observed was

different from that predicted by the Richardson and Memam's model. Hence it was concluded

that the increase in the effective thermal conductivity was not soleiy due to radiation. Since the

increase in thermal conductivity began only at tempentures higher than 500°C. which is close to

the first mrlting point of smelt. this increase is thought to be due to the change in the structure of

the char sample. Other factors affecting ihis increase could be the increased solid thermal

conductivity üt high temperütures. and also radiation heat transfer through the pores.

O 100 200 300 400 500 600 700

Temperature ( O C )

Fisure 4-5 Variation of effective thermal conductivity with temperature for Mill A-3

4.4.3 Mill A 4

This sample was obtained by crushing the above sarnple into a powder. Effective thermal

conductivity remained relatively constant for temperatures below 500°C and increased sharply

with temperature beyond 50û0C, Figure 4-6. This behavior is very similar to thiir of porous

version, Mill A-3. Thus. the change in the structure of the sample did not seem to affect the heat

t r ade r rnechanisms through the sarnple significantly.

O 100 200 300 400 500 600 700 800

Temperature ( O C )

Figure 4 6 Variation of effective thermal conductivity with temperature for Mill A l

4.4.4 Mill B

As descnbed before. the Mill B sample was collected from the top of a char bed followin~ an

emergency shutdown procedure. Since the sample had to be obtained through an air port. only a

small arnount of sample would be collected. The thermal conductivity variation is shown in

Figure 4-7. Since the cooling plate temperature was about 10-60°C. when there was only a small

amount of sarnple present, it was not possible to create temperature gradients higher thm about

500°C for this sample. Therefore. i t was not possible to measure thermal conductivity at

temperatures higher than about 550°C.

O 1 O0 200 300 400 500 600 Temperature (OC)

Figure 4-7 Effective thermal conductivity variations with temperature for MillB-80%

The effective thermal conductivity data for al1 the char samples obtained frorn different recovery

boilers and having different porosity and pore size are shown in Figure 4 8 . In dl cases the

thermal conductivity remained constant at temperatures below 500°C and increased sharpl y with

temperature above 5ûû°C. The thermal conductivity of the Mill B-80% sample was lower than

those of the other two sarnples. This is thought to be due to higher densiiy of pores which act as

insulation throughout the sample. Similarly the samplr Mill A-55% had a higher thermal

conductivity than the other two mil1 samples at temperdturss below 500°C. The thermal

conductivity of Mill A-65% was in between that for Mill A-55% and Mill 8-808. As mentioned

earlier. the two sarnples obtained from mil1 A were different in structure, since one waç used

immediütely after removed from the boiler. and the othçr was crushed to a powder. This

di fference in structure. howevrr. did not affect the thermal conductivity behavior as cvidenr in

Figure 4-8.

O 100 200 300 400 500 600 700 800

Temperature (OC)

- a l.oo- a E E 0.80- f- l- m œ OAO- > B 0.40-

O u 3

m 0.20- = c 0 0 0.00

Figure 4-8 Effective thermal conductivity of char bed materials measured assurning no heat transfer through the insulation walls

Memam's mode1 @=65%. Dp=Smm

r 1 1 r 1 1 1

Ruffy, dust-like fume deposits may become hard and resistant to sootblowing through sintering,

a process that can occur at temperatures below the melting point of the material. During sintering

particles become bonded together. First, a gain boundary forms at the location where the

particles touch. Then. as puticles are heated, the difference in free energy between the grain

boundary and the particle surfiiccs causes the material to diffuse as shown in Figure 4-9 (Tran,

1997).

Figure 4-9 Schematic of the sintering process (Tran, 1997)

The rate of sintering is controlled by the rate of material diffusion and is strongly dependent on

the particle size and temperature. Sintering occurs npidly at high temperatures. This raie cm

also be accelerated by a small amount of liquid phase to facilitate the diffusion of materiai at the

bridge area. In recovery boilers, sintenng occurs due to high temperatures. Tran (1997)

suggested that sintenng in most of recovery boilers start at about 300°C. with a more shiinkage

of material occumng at higher temperatures. Figure 4-10 shows the SEM photographs of cross-

sections of pellets sintered in 1 hour.

Figure 4- 10 SEM photographs of cross-sections of pellets sintered for 1 hour ( T m . 1997)

Anderson et al. (1987) and Robinson et al. (2000) both suggest that sintering can cause a

substantial increase in the effective thermal conductivity of the recovery boiler deposits. For the

char materials that reached temperatures above 500°C. the particles fused and fonned a hard

cmst as evident in Figure 4-1 1. Therefore. ir c m be concluded that sintenng in the char bed

materials and melting of the smelt content of char play an important role in increasing the

effective thermal conductivity of char bed materiais as temperature increases. Aiso, the increase

due to sintering in effective thermal conductivity was quantitatively found by measuring hs &ter

the sample was heated up to about 550°C. At this temperature. some sinterhg was expected to

have occurred. Due to lack of enough siunples however. only a few data points were obtained.

Figure 4-12 shows that the thermal conductivity at about 250°C increases from 0.3 W/m0C

before sintering to about 0.6 W/m°C afier sintering was believed to have occurred. It is further

concluded that radiation through pores is not the sole factor in the increased thermal conductivity

of char bed materials as suggested by Richardson and Merriam ( 1977). Radiation may panially

contribute to the increase in effective thermal conductivity.

Figure 4-1 1 Hard cmst formed when sample was heated beyond 500°C. Mill A 4

Series 10 * ~ f t e r Sintering

+ I 4

O 100 200 300 400 500 600 700 800 Temperature (OC)

Figure 4- 12 Effective thermal conductivity of Mill A 4 before and after sintering

The tempenture-dependrnt thermal conductivity model recommended by Richardson and

Merriam (1977) failed to predict the present thermal conductivity data for char bed materials

obtainrd from recovery boilers. Furthemore. it is difficult ro use their temperature-dependent

thermal conductivity model because the porosity and pore diameter of char are difficult to

determine. Moreover it seems thût the r ffective thermal conductivity of char bed materials

increases due not only to radiation at high temperatures. but also sintering which according to

Tran (1997) starts at about J50°C. Another minor factor. which may add to the increase. is the

chanse in the solid thermal conductivity as the temperature varies. This could be an increase or a

decrease in thermal conductivity depending on the properties of the material (Incropera and

DeWitt. 1996).

4.5 Numerical Simulation Results

As described earlier in Chapter 3. in order to calculate the thermal conductivity it was assumed

that heat transfer through the sample. from the heating plate to the cooling plate waî completely

one-dimensional. Therefore it w u assumed that no heat traveled through the thick insulation

walls. in order io verify this assumption. a computationd tluid dynamics (Cm) code.

PHOENICS. was used to develop a computer mode1 that could simulate the heating of siimples

tested in the experirnental apparatus.

Four different simulations were conductrd to predict the heating of firebricks that were

used in the calibration section. Figure 4-13 shows the cornparison between the temperature

profiles obtained from simulation and the experiment.

O 2 4 6 8 10 12 14

Vertical distance from the bottom surface of the sample (cm)

ô 600 O - 500 al L

400 E

300 -

E 0, 200 - )I

100 -

Figure 1-13 Steady temperature profile inside rirebrick for heating plate temperature of 600°C

-

Simulation k=0.12 W/m°C A Experimental -

Simulation k=0.44 W/m°C

O

As Figure 4-13 indicates, when a constant thermal conductivity of 0.44 W/m°C was assigned to

the block representing the firebrick sample in the simulation rnodel, PHOENICS could predict

the experimental temperature profile well within the sample accurately. For the experimental

temperature readings close to the top and the bottom surface. PHOENICS failed to predict the

steady temperature. A much larger k vdue of 1.2 W/m°C had to be used to f i r the top

experimental readings. Similarly the bottom temperature was higher than that predicted by the

simulation. Thus. as in the calibration results shown in Figure 1- 1. the temperature readings irom

areas within 2 cm of the top and bottom surfaces. may not yield an accuratr meuurement of

thermal conductivity. The reason for this behavior was not fully understood.

The thermal conductivity for the firebrick at 30°C was found rxperimentally to be about 0.52

W/maC. Using the simulation. however. this value was found to be 0.44 W/miC resulting in a

difference of about 156 . This was believed to be due to heat loss from the iippüiatus and also

heat transferred through the thick insulating walls.

A simulation was also conducted using propenies of char bed materials for Mill A-3. Similar

behavior as for the firebrick sample was observed. Thermal conductivity according to simulation

was found to be 0.18 W/maC. but experimentally. it was determined to br about 0.2 1 W/m°C. a

difference of 14% from the simulation results. This difference was attributed to heat loss and 3-

dimensionality of heat transfer that was neglected during the caiculations. Figure 4- 14 shows the

temperature contours predicted in the simulation of Mill A-3 sample. This figure shows a

temperature gradient inside the inner insulation Iayer which causes a net heat tlow from the top

to the bottom section of the insulation layer. This heat flow through the inner insulating wall

neglected in the experimental data analysis is considered to be responsible for overîstimation of

the actual thermal conductivity of char sarnples by 14%.

Temperature (C)

Figure4-14 Temperature contours indicating the temperature distribution inside the experimental apparatus (Mill A-3, 500°C simulation. see Chapter 3 for simulation conditions)

If a 14% corrcsiion is accounted for in al1 the thermal conductivity values of c h u bed materials

from the mills. the major data cm be re-plotted as shown in Figure 445.

1.2

Temperature ( O C )

_ n - O E 0.8 -

& x w c 0.6 - a .Z .L .1 5 5 0.4 -

i! s 8 0.2 -

Figure 4-15 Effective thermal conductivity of char bed materials considering the heat loss through the insulating walls (corrected data)

0 Mill A-65%

A Mill A-55% -30%

Mill 8-8096

- Correlation

Based on these results. the corrected thermal conductivity data can be correlated as follows:

For T 5 5 0 ° C

(W/m°C) = 0.21

For T > 500°C

(W/m°C) = 0.0035 T - 1.54

t . ! - -=v- - O -p.-

where T is specified in O C . (4-3)

As indicated in Figure 4- 15. al1 the expenmental data points fdl within t 30 5% of the correlation.

CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS

5.1 ConcIusions

In summary, an experimental apparatus was designed and constructed to measure the effective

thermal conductivity of char bed matenals obtained from differeot mills, and char samples made

in the laboratory. A computational fluid dynamics code was used to simulate the flow of heat in

the char sample in the experimental apparatus. Based on the experiments and numerical analysis

the following conclusions can be drawn:

1. The effective thermal conductivity of ail sarnples examined has a similar temperature

dependence despite the wide difference in sample porosity and structure.

2. A thermal conductivity value of 0.21 W/m°C is suggested for char bed materials below

500°C. At temperatures above 500°C the effective thermal conductivity of char increased

frorn 0.21 W/m°C at 500aC to 0.91 W/m°C at 700aC. Based on the experimental data, a two-

part correlation was developed as follows:

ken (W/m°C) = 0.2 1 for T 5 500°C

kff (W/m°C) = 0.0035 T - 1.54 for T > 500°C.

3. The increase in thermal conductivity beyond 500T is believed to be due to sintering and

melting of smelt, radiation heat transfer through porous char materials.

4. The thermal conductivity model recommended by Richardson and Merriam (1977) did not

predict well the measured thermal conductivity of char bed matenals. even if the porosity and

pore size were adjusted for each sample.

5.2 Recomrnendations

This project is part of an ongoing study focused on understanding the cooling process of char

beds in recovery boilers. The ultimate objective of this project is to minimize the dovntime of

recovery boilers by reducing the time it takes for the char bed to cool following a shutdown. The

thermal conductivity data obtained in this work are mainly usrful for numerically simulating the

cooling of char bed. However. there rire other factors such ris bed mass and bed heat content that

need to be better understood before such modeling can be done. Unlikr the cooling of it uniform

hot object in a known surrounding. the cooling of char bed is cxtremely difficult to model

because chemical reactions and combustion c m take place in the char bed. the shape of the bed is

non-uniform. temperatures at different locations vüry. and there are hot molten smelt pockets

throughout the bed. Figure 5- 1 indicates the temperatures in various locations inside the char bed

following an emergency shutdown procedure. started at approxirnately 11 :30.

Figure 5- 1 Tcmperature history at various locations in a char bcd following ii simulateci emergcncy shutdown procedure (shutdown was started at 2 1 :00)

The different lines in the figure represent the temperature histories in various locations in the

bed. The sudden increase in the temperature is brlieved to be due to combustion taking place at

or near the location of the thennocouple. As indicated by the data. the cooling of a char bed is

much more complicated than just cooling of a hot object. It is hencc necessÿry to understand the

characteristics of the char bed in more detail before m y attempt crui be made in realisticdly

modeling the coolins process.

REFERENCES

Adams, T., I. Frederick, T. Grace, M. Hupa, K. Iisa, A. Jones, and K. Tram 1997. KraP Recovery Builers. Atlanta: Tap pi Press.

Anderson, D. W., R. Viskanta, F.P. Incopera. 1987. Trunsuctiom of the ASME Jmma of Engineering for Gm Turbines and Power. Volume 109: 2 15-22 1.

Annual Book of ASTM Standards. 1999. Standrd Test Mefhod for Thermal Conductiviw of Refratorzes: Carbon and Graphite Producfs: Ac~ivated Carbon: Advanced Ceramics. Vol. 15.01: 54-59.

CHAM.TR100A Guide to the PHOENICS Inpir Lunguage.

Dull ien, F. A. L. 1992. Porozis Media Fluid Tramport and Pore Sfn~ctttre. 2" edition. Toronto: Academic Press.

Grace T. 1999. A F & PA Cornmirtee Meering On Recovery Boiler Char Bed coolirzg Following an ESP. Pulp & Paper Center, University of Toronto.

Grace, T.M. 1998. Cooling Following and ESP. Appleton: T.M. Grace Company, Inc.

Grace, T.M. 1992. Chemical Recovery In ïhe Alkaline Pulping Processes. 3d edition. Atlanta, GA: TAPPI Press.

Green, R. P., G. Hough. 1992. Chemical Recovev In The Alkalirie Pztfping Processes. 3d edition. Atlanta, GA: TAPPI Press.

10. Helte, A. 1993. Radiative and Conductive Heat Transfer in Porous Media, Estimation of the Effective Thermal Conductivity. Arnerican Institute of Physics. Vol. 73, No. 11: 7167-7173.

1 1. Incropera, F., and D. DeWitt. 1996. Infroduction to Heat Transfer. Toronto: John Wiley & Sons.

12. Kaviany M. 1992. Fundameiitals of Heat Transfr in Porous Media. New York: Arnerican Society of Mechanical Engineers.

13. Kaviany, M.. 19%. Principles of Heat Transjer in Purcars Media, 2"' edition. New York: Springer.

14. Kawaji. M. 1999. A F & PA Cmrinzittee Meering On Recovey Boiler Chir Bed cooling Following nn ESP. Pulp & Paper Center. University of Toronto.

15. Kawaji, M.. H. Nikfarman, G. Tan, T.M. Grace. H. Trm. 1999. Recnvery Builer CItm- Bed Cooiing Folloir~iny Ari Errtergenq Sliiitdortw. Task I : Review rind Interpretïition of Avciilabie In/umiririon. Prepared for Amencan Forest and Paper Association's Recovery Boiler R&D Subcommittee. Toronto: University of Toronto.

16. Kmus. R., H. Kaar. T. Tiikma. 1994. Tlienncil Condrictivity of Recoivn Boiler Fireside Deposit. Tallin.

17. Litovsky. E.. and M. Shaprio. 1992. Gas Pressure and Temperature Dependence of Thermal Conductivity of Porous Cenmic matrrials: Part 1. Refractones and Cermics with Porosity Below 308. Joi<rncil of Aniericrin Cerczniic Society 75: 3425- 3439.

18. Litovsky. E.. and M. Shaprio. 1996. Gas Pressure and Temperature Dependence of Thermal Conductivity of Porous Ceramic materials Part 2 . Rrfractories and Ceramics with Porosity Exceeding 30%. Joiinlizl of Arnericmi Cermiic Society 79: 1366- 1376.

19. Nasr. K.. R. Viskanta. rind S. Ramadhani. 1994. An Expenmentai Evaluation of the Effective Thermal Conductivities of Packed Beds at High Ternperatures. Joitnid uj' Heur Trunsfer. 1 16: 879-837.

20. Nasr. K.. R. Viskanta. S. Ramadhyüni. 1994. An Experimentd Evaluation of the Effective Thermal Conductivities of Packcd Beds at High Ternperatures. Jortmril of Heat Trarisfer. Vol. 1 16: 829-837.

Z 1. Nikfarman. H. 1999. Cliuracreri:ation of Properrirs of Char in Kr& Recown Boilers. Bachelor's Thesis. Toronto: University of Toronto.

22. Parrott, J.E.. A. D. Stukes. 1975. Tltemcil Conïlictivify of Soiids. London: Pion Limited.

23. Penner E. 1976. Thermal Condirctivity of Coal. Kingston: Canadian Institute of Guided Ground Transport.

24. Poulikakos. D. 1 994. Condrîction Hrczt Trnnsfer. New Jerse y: Prentice-Hall. Inc.

25. Richardson. D.. and R. Memarn. 1977. Srri& of cooling and Smimelt SoMijk*cirion in Bluck Liqrior Recoveg Boilers. Phase I Report. Cambridge: Arthur D. Little. Inc.

26. Robinson. A.L.. S. G. Buckley. N. Yang, L.L. Baxter. 1000. E.tprimenrd Meosiiremetifs of the Tlilicmnl Coridiïctivity of Ash Deposirs: P m 1. Meos~irenletrr Technique. New Mexico: Sandia National Laboratories.

27. Robinson, AL.. S. G. Buckley. N. Yang, L.L. Baxter. 2000. Experinienrnl Measriremrrrts of rlre Thrrnrcil Coducrivip of Asli Deposits: Pnrt 2. Effects of Sintering and Deposit Microstn~ctiirr. New Mexico: Sandia National Laboratories.

28. Singh, B.P.. M. Kaviany. 199 1. Independent Theory Versus Direct Simulation of Radiation Heat Transkr in Packed Beds. Interncrtional Jurrnlal of Hrrrr Trmsfer. Vol. 34, No. L 1: 2869-2882.

29. Singh. B.P.. M. Kaviany. 1994. Effect of Solid Conductivity on Radiative Heat Transfer in Packed Beds. Iritenrutioiial Jclrinrnl of Hrat Trtrnsfer. Vol. 73. No. 16: 2579-2583.

30. Soylemez M. S. 1998. On the Effective Thermal Conductivity of Building Bricks. Jortrnnl uj' Building and Environmerit. Vol. 34: 1-5.

3 1. Tran H. 1997. Kr& R e c o v q Builers. Chapter 7: Upper Fumacr Drposition and Plugging. Atlanta: Tappi Press.

33. Tan. G. 2000. Coulins Cliaructeristics and Tirennul Properties oj' Kr($ Rt~c*o~vn Boikr 's S~nelt. Master's Thesis. Toronto: University of Toronto.

33. Touloukian. Y.S.. R.W. Powell. C.Y. Ho. P.G. Klemins. 1970. Thennoplryicd Properties of Matter. Volruue 2: Tliennd Condiictivity of Norzrnrtnllic Solids. New York: Pienum.

APPENDIX A HORIZONTAL HEAT LOSS CALCULATIONS

Heat transfer from the horizontal walls of the experimental apparatus due to natural convection

results in a three-dimensional heat tlow and affects the char sarnple thermal conductivity values

measured. tn order to verify that the heat loss was negligible. total heat transkr from the

horizontal walls due to natural convection was calculated using the following correlations

(Incropera et al.. 1996)

Grashof number, which is the ratio of buoyancy force to the viscous force acting on the tluid.

was defined by Equation A- 1.

where

GrL Grashof number

O c acceleration due to gravity ( m d )

P volumetric thermal expansion coefficient (K" )

Ts w d l surface temperature (OC)

T, surrounding ternpenture (OC)

L vertical height of the wall (m)

v viscosity of sunounding fluid ( m h )

Rayleigh number was defined by Equation A-2.

RaL = GrL Pr

where

RaL Rayleigh number

GrL Grashof number

Pr Prandtl number

Nusselt number was defined by Equation A-3.

1 14 9/16 419 NuL = 0.68 + 0.670 RaL 1 [ 1 +(0.492/Pr) ]

(for RaL 5 loO)

(A-?)

Convection heat transfer coefficient was related to Nusselt number by Equation A 4

where

h - convection heat transfer coefficient ( ~ l m ' . ~ )

k thermal conductivity (W1m.K)

L vertical height of the wall (rn)

Heat transfer due to convection was calculated using Equation A-5.

q = h (Ts-T,)

where q is convection heat transfer in w/m2.

Air Propcrties at 300 K:

p 3.33 x (K-')

v 15.89 x 1 (m2/s)

Pr 0.707

Dunng the experiments room temperature was approx ly W C . The surface temperature of

the apparatus wall waï. at most. 10°C higher than the surrounding temperature.

[t was assumed that the surrounding air behaved as an ideal gas. Thrrefore the expansion

coefficient was simply the inverse of the temperature. This is a reasonable assumption since air

was at room temperature and atmospheric pressure. Also. the surface of the walls was assurned

to be isothemai since the temperature variation on the wall was negligible. maximum 2°C.

Using air properties at 300 K. verticai height of wail çqual to 0.28 m. and the above

assumptions. the total heat transfer due to convection from the walls was calculated.

3 3 GrL= 9.8 rn/s2 X 3.33 x 10" K-' (35-25) K (0.38) m 1 ( 15.89 x 16" m2/s)'

=2.84 X 10'

RaL = 1.84 X 10' X 0.707

=IO x 10'

The minimum amount of heat transferred vertically through the char sample was 539 w/m2. This

happened when the temperature set point was 250°C for Liib- 1 sample.

Thrrefore the maximum heat loss from the vertical insulriting walls was round ro be 6% of the

totd heat flow.

APPENDIX B Q1 FILES FOR VARIOUS SIMULATION CONDITIONS

QI created by VDI menu, V e r s i o n 3.3, Date 0 3 / 0 5 / 0 0 CPVNAM=VDI ; S PPNAM=Co r e * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * IRUNN = 1 ;LIBREF = 55 t r f ~ * ~ t r * * + t * * * t ~ * * * * t * * t t * * f t t * * t ~ * ~ f * * w * * * * * * * * * ~ * * * * * * * * *

Group 1. Run T i t l e TEXT (Firebrick, 400 C, constant k) * * * * * * f t * * * * * * * * t * * * * t * * * * * * * * * * * * * * X f * * * * * * * * * * * * * * ~ * * * * * * *

Group 2 . Transience STEADY = T t X * * * * * * * * * t * * * t * * * * * * * * t f * * * * * t * * * t * t . + * * * * * * * * * * * * * ~ * t * * * * *

Groups 3, 4, 5 Grid Information * Overal l , number o f c e l l s , FISET (Mt NX, NY, NZ, colerance)

RSET (M, 40,40f 120) * S e t o v e r a l l domain e x t e n t : f x u l a s t yvlast rwlast

name XSI= 4.380000E-01; YSI= 4.380000E-01; ZSI= 3.590000E-01 3SET ( D, CHAM j * * * * * * * * + * * * + t * * * * * * * * * * * * * * * * * . t * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Group 6. Body-fit ted coordinates * * * * * * * * * * * * * * * * * * * t * * * * * * * t * * * t t * * t * * * * ~ * * * t * * * * * * * * * * * * * * ~

Group 7 . VariaDles: STOREd,ÇOLVEd,NAMEd ONEPHS = T

* Non-default variable names NAME(149) =KOND ; NAME(150) =TEMI

* Solved v a r i a b l e s l i s t SOLVE ( TEM1)

* Stored v a r i a b l e s l i s t STORE (KOND)

* Additional so lver op t ions SOLUTN (TEMI, Y , Y , Y , StNIY)

Group 8. Terms & Devices TERMS (TEMl,Y,Y,Y,Y,Y,Y) C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * . + * * * * * ~ * * *

Group 9 . Proper t ies SETPRPS ( 1, O) RH0 1 = 1.189000E+00 PRESS0 = l.OOOOOOE+O5 TEMPO = 2.730000E+02 CPI = 1.005000E+03 ENUL = 1.544000E-05 ;ENUT = 0.000000E+00 DVOlDT = 3.410000E-03 FRNDTL (TEMI) = -4.400000E-01 ****+******************************************************t

Group 10.Inter-Phase Transfer Processes * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

r-t 4 O 0 0 0 I l -t

W W W 0 0 0 0 0 0 0 0 0 o m o o r - O m m 0 . . . P l r - 4 r - i

O & O 0 + I W W 0 0 O 0 0 0 0 0 oin O r - . . O N

O 4 4 0

O r ( + O 0 W + ! O W W O O 0 O 0 0 O 0 0 O O 0 O o m 0 Pl O . . 0-3' 4

0 4 4 4 O 0

0 4 4- + 0 0 W W + I O 0 W W O 0 0 0 W O 0 O 0 d u O 0 0 0 - O O d P d Z Z O m o , U W orna o t lo rv

r-4 * * = 1 rl m o w u m

- 4 4

4 4 0 0 0 0 I f -f.

W W W 0 0 0 0 0 0 0 0 0 O m o W W O OcVO O . 0 W N r - 4 +

W 4 - 4 O

r l r l O c ; O r ( 0 0 0 0 0 0 I I + I O I

W W W W O W 0 0 0 0 0 0 0 0 0 0 * O 0 0 0 0 r t O o lnoo O U 3 W O Q 4 0

m w 0 0 0 0 . . . . l n . -J'Ndr( cn

~ 4 4 . 4 4 . 4 . 4 5 . 4

m ~ z , ~ ) m m r n r , m m m m m m 9btY'3'3'3'3'3btYb'3'3 m m m m m m m m m m m m m 0 0 0 0 0 0 0 0 0 0 0 0 0

A A A A A A A A A

Group 11.Initialise Var/Porosi=y Fie lds FIINIT(K0ND) = 6.000000E-01 ;FIINITiTEMl) = 2.500000E+01

No P A T C X e s used f o r this Group

3roup 12. Convecticn and d i f f u s i o n adfustmenrs No ?LTCHes used f o r this Group

+ r r r t l * w r r * r t f i t t * f t t t f f t t * t t * * t * t t t t t * t t * t Y * * t * * * * t W * t * * * * w

Group 1 3 . Boundary & Special Sources No ?ATCYes used for t h i s Grouo

Sroup : S . T e r m i n a t e Sweeps LSNEE? = 60 ?.ES?AC = 1. CIÛOOOOE-03 r t * t * * * * t * * * t t * * C t * t * C * t * * * t t * * t t t t w W . c t t t * * * * * * ~ * * * * * t t r w * t *

Croup 13. ZARTH Calls To GROUXD S t a t i o n c- 4 7 ';scG?,C = S ;üSEGRX = w

.?.SAP - - T r t t r r f f ~ r ~ t * ~ ~ ~ t ~ C t t t t ~ ~ V + * + t t t ~ t t t t t t t t ~ ~ ~ ~ r t ~ t t ~ ~ ~ ~ ~ ~ t ~ ~ ~ ~

,- srsu? 2:. ? i n ~ - o u t cf Variables r ~ t f r t ~ w t ~ ~ t t ~ t f + + ~ f t t t f w t f t t r * t t t t r C f * t t t t t ~ * ~ t r r * v t r t ~ ~ w ~ ~ t

Group 23.Fieid Print-Out & P l o t C o n t r o l YPRINT = 100000 TSWPRF = I ;ISWPRL = 100000 IPROF = 3

PATCH (TI , PROFIL,7, 0,0,0,0,0, 1, 1) PLOT (Tl , K O N D , 0.000000E+00, 0.000000E+00) PLOT (Tl , T E M I , 0.000000E+00, 0.000000E+QO) t*******t+***t*******~***t********************************tt

Group 2 4 . Dumps For Restarts .'3WIPE = T

> OBJS, > OBJ5, > OBJ5, > OBJS, > OBJS, > OBJS, > OBJ5, > oaJs,

> OBJiO, > OBJ10, > OBJlO,

* -- > OBJIO, > OBJIO, > OBJIO,

HEAT FLUX, I N I - TEMP,

N M , POSITION, SIZE, CLIPART, ROTATION24, TYPE, MATERIAL, FIXED TMP, - NAME, POSITION, SIZE, CLIPART, ZOTATION24, TYPE, MATER IAL, AD IABAT IC, IN1 TFMP, SCAE - FIXE.

NAME, POSITION, SI ZE, CLIPART, ROTATION24, TYPE,

NAME, POSITION, SIZE, CL I PART, ROTATION24, TYPE , LINR - HEAT,

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE , LINR HEAT, -

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE,

HEATER 1.400000E-01, 1.400000E-01, 2.050000E-01 1.580000E-01, l. 580000E-01, 1.500000E-02 cube4

I BLOCKAGE

111 0.000000E+00, 6.200000E+02

AIR 1.4000001-01, 1.400000E-01, S. 2000002-'31 1.580000E-01, 1.580000E-01, 3.500000E-02 cubet

1 BLOCKAGE

2 0.000000F+~O, ?.000000E+00 2.500000E+OI 0.000000E+00

1 USER DEFINED - TOP 0.000000E+00, 3.000000E+00, 2.590000E-01 4.380000E-01, 4.380000E-01, 0.000000E+00 cube 13

1 PLATE 3.300000E+00, 2.500000E+01

BOTTOM 0.000000E+0Of 0.000000E+00, 0.000000E+OC 4.380000E-01, 4.380000E-01, 0.0000COE+00 cube 1 3

1 PLATE 3.300000E+00, 2.500000E+01

SIDEXl 0.000000E+00, 0.000000E+00, 0.000000E+00 0.000000E+00, 4.380000E-01, 3.590000E-01 cube 13

1 PLATE

LINR - HEAT,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, LINR - HEAT,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, LINR - HEAT,

NME , POSITION, S 1 ZE, CL1 PART, ROTATION24, TYPE, LINR - HEAT,

NAME, POSITION, S 1 ZE, CLIPART, ROTATIONS4, TYPE , MATERIAL, ADIABATIC, IN1 TEMP, SCAL - FIXF,

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE, MATERIAL, ADIABATIC, IN1 TEMP, SCG - FIXF,

NAME, FOSITION, SIZE, CL 1 PART,

4.380000E-01, 0.000000E+00, 0.000000E+00 0.000000E+00, 4.380000E-01, 3.590000E-01 cube 13

1 PLATE 3.300000F+00, 2.500000E+01

cube 13 1

?LATE 3.300000Et00, 2.500000E+OI

SIDEY2 0.000000E+00, 4.390000E-01, 3.03000OE+OO 4.380000E-01, 0.000000E+00, 3.590000E-01 cube 13

1 PLATE 3.300000Ei00, S.SOOOOCE+OL

cubet 1

BLOCKAGE 2

0.000000E+00, a.000000E+00 2.500000C+01 0.000000E+00

cubet 1

BLOCKAGE 2

0.000000E+00, 0.000000E+00 2.500000~+01 0.000000E+00

TOP3AIR 0.000000E+00, 7.600000E-02, 2.750000E-01 7.600000E-02, 2.860000E-01, 8.399999E-02 cubet

ROTATION24, TYPE, -rnTERIAL, ADIABATIC, I N 1 TEMP, SCAE - FIXF,

XAME f ?OSITION, SIZE, CL1 PART, ROTATION24, TYPE, MATERIAL, ADIABATIC, I N 1 TEMP, SCAL - FIXF,

NAME, ?OSITION, SIZE, CL1 PART, 2OTATION24, TYPE, MATERIAL, ADIABATIC, INI-TEMP, SCAL - FIXF,

L BLOCKAGE

2 0.000000E+00, 0.000000E+00 2.500000E+01 0.000000E+00

TOP4AIR 3.620000E-121, 7.600000E-02, 2.750000L-51 7.600000E-02, 2.960000E-01, 8 .399999Z-52 cubet

I - BLOCKAGE

? L

0.000000E+00, 0.000000E+00 2.5000002+01 0.000000E+00

AIRBOT l.4OOOOOE-OL, 1.300000E-51, 5.10000OE--2 1. MOOOOL-01, 1. ~ ~ O O O O E - ~ X , 7 . C>OOOOOL-1;: c u b e t

I - aLocmm

2 0.000000C-00, 0.000000E'~O 2.500000E~01 0.000000E+00

Q1 created by VDI menu, Version 3.3, Date 03/05/00 CPVNAM=VDI;SPPNAM=Core t * * * * * * * * * * * * * * * * * * * * * * ~ * * * * * * * * * * * + f * * * * * * * * * * * * * * * * * * * * * * *

Group 1. Run T i t l e TEXT (Firebrick, TOOC, constant k) [7lO, k=0.45] + * * r * f + * + * f * * * + f + t t i * u i f * * * * ~ + t t * * * * f w t * * = * * * * w * * * w * * * w * * * * *

Group 2. T r a n s i e n c e STEADY = T t**********ttt********t**f*********+ft***~**********7*******

Groupç 3, 4, 5 Grid Information Overall n b e r of cells, RSET (M, NX, NY, NZ, tolerance)

FISET (M, 40,40,120) * Set overall domain e x t e n t : t xulast yvlast z w l a s t

name XSI= 4.380000E-01; YSI= 4.380000E-01; ZSI= 3.590000E-01 3SET ( D, CHAM 1 r r + + t t t * + + t f * + * r t t * f * t t * * u ~ t * t t * * t i i . * * * * * * * * * * * * * * * * * * * * T * * *

Group 6 . Body-FFttea c o o r d i n a t e s * * * * t t * * * * t * * * t * * t * ~ * * * * * * * * * * * * * * * t * t * * * * t * * * * * * * t * * * * * * * ~ ~

Group 7 . Variables: STOREd,SOLVEd,NAMEd ONEPHS = T

* Non-default variable names NAME(149) =KOND ; NAME(150) =TEMI

* Solved variables list SOLVE ( TEMI )

* Stored variables list STORE (KOND)

Additional solver options SOLUTN(TEM1, Y , Y , Y , N , N , Y)

Group 8. Terms & Devices TERMS (TEMl,Y,Y,Y,Y,Y,Y) *****+*************~*******t**********t*********************

Group 9. Properties SETPRPS ( 1, O) RH01 = 1.18 9000E+00 PRESS0 = 1.OOOOOOE+05 TEMPO = 2.730000E+02 ce1 = I . O O ~ O O O E + O ~ ENUL = 1.544000E-05 ;ENUT = 0.000000E+00 DVOlDT = 3.410000E-03 PRNDTL(TEM1) = -4.500000E-01 *********************************t**************************

Group l 0 . I n t e r - P h a s e T r a n s f e r P rocesses ************************************************************

Group L1.Initialise V a r / P o r o s i t y F i e l d s FIINIT (KOND) = 6.000000E-01 ; FIINIT ( T E M I ) = 2.5OOOOOE+OI

No PATCHes used f o r this Group

INIADD = F r * * * * * * ~ t * * * f * + * * * * * * * * * * * * * * * * * t * * * 7 * * * * * * * * * * w * 7 * ~ w 7 * * * * * 7

Group 12. Convect ion and d i f f u s i o n a d j u s t m e n r s No PATCHes used f o r this Group

* * * * X l t * W X * * * ~ * * * * * * * * * t * f * * * * f * * * * 7 * 7 * f * * * * * * * * * * * 7 * * * * 7 t * *

Group 1 3 . Boundary & S p e c i a l Sources No PATCHes used f o r t h i s Grcup

Group 1 4 . Downstream Pressure For PARAB

Group 1 5 . Terminate Sweeps LSWEEP = 60 RESFAC = I.OOOOOOE-G3

Group I5. Terminate Iterations r v * ~ + * * 7 * * * * * * * * * * * * 7 * * * * * * * 7 * * * * 7 + * * * * t * * w * + * * * 7 * * * * * * * * * ~ 7

Group :S. Lirnits + r t f t t t + r t * * * f * ~ f t t * * t * * * * * * f f t * * * t t t t t t * * * * * * * * * * * r * * * * * * v *

Group 2 0 . Preliminary P r i n t o u t zcfio - - T

Group 2 1 . P r i n t - o u t o f Variables **77**7*******************7*************7*****7*7***7*****77

Group 2 2 . X o n i t o r Print-Out IXMON = 22 ;IYMON = 22 ;IZMON = 5 4 NPRMON = 100000 NPRMNT = 1 TSTSWP = -1 f * * * * * * * * * * * * * * * * + * * * * * * * * * * * * 7 * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

Group 23.Field Print-Out 5 Plot C o n t r o l NPRINT = 100000 ISWPRF = 1 ;ISWPRL = 100000 IPROF = 3

PATCH (Tl ,PROFIL,7,0,0,0,0,0r1,1~ PLOT (Tl , K O N D , 0.000000E+00, 0.000000E+00) PLOT (Tl ,TEMI, 0.000000E+00, 0.000000E+00) ************************+t*~******************

Group 2 4 . 3umps For Restarts NOWIPE = T

> DOM, > DOM, ; DOM, > DOM, > GRID, > DOM,

S I Z E , MONIT, S CALE, SNAPSIZE, RSET 7 4 , - - RELAX,

NAME, POSITION, S I Z E , CL1 PART, ROTATfON24, TYPE, .IATE3I%.L, AD IAEF.TIC, INI-TEMF,

NAYE , ?OS I T I O N , S I Z E , CLIPART, ROTATLON24, TYPE, MATERIAL, ADIABATIC, IN1 - TFM?,

NAME, POSITION, S 1 2 2 , CLIP4RTt 3OTATION24, TYPE, MATERIAL, ADIABATIC, I N 1 TEMP, S C A ~ FIXE',

cube 14 1

E 1OCKAGE L 6 1 ~ . 0 O 0 0 0 0 E + 0 O r 2 . 5 0 0 0 0 0 E + 0 1

82 7 . 6 0 0 0 0 0 E - 0 2 , 2 . 8 6 0 0 0 0 E - 0 1 , cube 14

CHAR 1 . 4 0 0 0 0 0 E - 0 1 , 1 . 4 0 0 0 0 0 E - 0 1 , 7 . 5 0 0 0 0 0 E - 9 2 1 . 5 8 0 0 0 0 E - 0 1 , 1 . 5 8 0 0 G O E - 6 1 , L. 300000E-021 cube t

I BLOCKAGE

-1 0 . 0 0 0 0 0 0 E + 0 0 , 0 . 0 0 0 0 0 0 E + 0 0 2 . 5 0 0 0 ~ 0 E + 0 1 0 . 0 0 0 0 0 0 E + 0 0

NAME, COOLER POSITION, 1 . 4 0 0 0 0 0 E - 0 1 , S 1 ZE, 1 . 5 8 0 0 0 0 E - 0 1 , CLIPART, cube 4 ROTATION24, 1 TY PEI BLOCKAGE MATERIAL, 111

> 0854, XEAT FLUX, > 0854, I N 1 - TEMP,

> OBJ5, > OBJ5, > OBJ5, > CBJ5, > OBJS, > OBJ5, > O B J 5 , > GBJS,

NAME, ?OSITION, SIZE, CL1 PART, ROTATION24, TYPE, XATERIAL, XIXED - TNP,

NAME, POSITION, SIZE, ZLI PART, ?.OTATION24, TYPE , YWTERIAL , ADIABATIC, IN1 TEMP, SCAE - FIXF.

> Q B Z Ï , NAME, > GBJ?, ?OSITION, > oan, SIZE, > OBJ7, CLIPART, > OB27, 3OTATION24, > O B J 7 , TYPE,

>138J6, NAME, > O B J 8 , ?OSITION, >OBJ8, SIZE, > 33BJ8, CLIPART, > O B J 8 , 3OTATION24,

OBZ8 TYPE, > OBJ8, LINR-HEAT ,

> O B J 9 , NAME, > 0829, POSITION, > OBJ9, SIZE, > OBJ9, CLIPART, > O B J 9 , ROTATION24, > O B J 9 , TYPE, > OBJ9, LINR HEAT, - >OBJlO, NAME, > OBJ10, 2OSITION, > OBJ10, SIZE, > OB310, CLIPART, > OBJ10, ROTATION24, > OBJ10, TYPE,

HEATER 1.400000E-01, ;.400000E-01, 2.050000t-CI 1.580000E-01, 1.580000E-01, 1.500000F-'2 cube4

1 BLOCKqGE

111 0.COOOOOE-93, 7.i00000E+02

AIR 1.400000E-~~1, 1.100000E-01, 2.200000E-,l1 1.580000E-GI, L.580000E-01, 7.5000ûOE-22 cube t

1 BL ICKAGC

3 L

3.000ûOOE-~~0, 2 . û0000GE+00 2.5OCOOOC-~~, 0.00000oc-~Q

Tl 2.190000E-51, 2. ~90000E-~2I1 " . 5000002-:: 2.000000E-'33, 2.000000E-a3, 1.300000E-51 de t a u 1 t

I USER DEFINEC -

TOP 0~000000E~GC1 3~000000E+001 3.590000E-3' 4.380000E-01, 4.390000E-01, 0.000000E+1382 cube 13

1 3LATE 3.300000E-00, 2.500000E~01

BOTTCM 0.000000C+OC, 9.000000E+00, 0.000000E-GC 4.380000E-01, 4.390000E-01, 0.000000E~00 cube i 3

I ?LATE 3.3G0000E-GO, 2.500000E+01

SIDEXl 0.000000E+00, 0.000000E+00, 0.000000E-9C 0.000000E+00, 4.3800COE-01, 3.590000E-31 cube 13

I PLATE

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE, LINR - HEAT,

NAME, POSITION, SIZE, CL1 PART, 3OTATION24, TYPE, LINR - HEAT,

NAME, POSITION, S 1 ZE, CL 1 PART, 3OTATION24, TYPE, LINR - HEAS,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, YATERIAL, ADIABATIC, IN1 TYMP, SCAE - FIXE',

NAME, POSITION, SIZC, CL1 PART, ROTATIONZ4, TYPE, MATERIAL, ADIABATIC, I N 1 TEMP, SCAL - FIXF,

NAME, POSITION, SIZE, CL1 PART,

T O P 2 A I 2 3. 00000OE+00, 3.620000E-01, 2.75L1000L-t31 4.390000E-01, '. 800000E-02, 3. I S C C C O E - 5 . 2 cube t

1 SLOCXAGE

2 0*000000E+00, 0.000000E+00 2.500000E+OI 0.000000E+00

9BJl8, > OBJ18, i OB319, > OBJiS, > OBJl8, > 08318, > OBJ18, > OBJ18, > OBJ18, > 08318, STOP

ROTATICN24, TY PEI MATERIAL, ADfABATIC, I N 1 TEMP, SCAL - TIXF,

NAME, P O S I T I S N , SIZE, CL1 PART, ROTATICN24, TYPE, rnTEF. I A L , ADIABATIC, IN1 TSLTP, SCAL - PIXF,

EIAME, ?OSiLICN, SIZE, CL1 PART, 3OTAT I5N2 4 , TYPE, MATER EXL , ADIABATIC, I N 1 TCLIP, SCAL - FIXE,

TOP4AIR 3.820000E-01, '.600000E-52, 2.750000E-451 7.600000E-02, 2.360000E-01, 9.399909E-02 rubet

AIRBOT L . .IOOOCOZ-C)L, 1. ~OOOOOE-I~I, 5.1SOOGOF-22 1.58000CE-*31, 1.580000E-01, - . 3COOOOE-123 cube t

1 3LOCKAC-Z

2 0.000000Z+00, 3.000000E~00 2.5G0000E+OI 0.000000E+00

Qi c r e a ï e d by V D I menu, Version 3.3, Date 0 3 / 0 5 / 6 0 ZPVNX4=VDI ; SPPNAM=Core w r * % t r t t ~ ~ t * + + f t t + + ~ * t t f t t t t t t * * f w * * t w w t w w w * w * w w * w t w w ~ ~ w w ~ ~ w

T 3 U N N = I ;LIBREF = 5 5 t t t r r r t r t t w + t 7 * t t 7 r 7 * * * 7 7 t t t f * . t f ~ w t t ~ t t t * * * * * * * ~ * * * * t ~ ~ ~ ~ w * r

Grcc9 I. Xun T i t l e m I - - ,,AL . : ~ r e D r i c k 800 C, constani k ) 1 8 1 5 , K = O . 451

r r * * * t t r + + + t t t i t + t t t 7 t t + f t t t t * t t t C * 1 ' w ~ w t * * * w * * f * 7 * r * * * t w w w ~ t

Group 9 . 2roperties SET?F?PS ( 1, 9 ) ?.HO I = 1.189000E+00 2RESSO = i.O00000E+05 TEMPO = 2.730000E+02 C O 1 = 1.005000E+03 =NUL = 1.544000E-05 ;ENUT = 0.000COOE+00 DVOlDT = 3.410000E-03 PRNDTL (TEMI) = -4.500000E-01 **t*+t***********t****'**t******************************~****

Group :O.Inter-Phase Transfer Processes * * + X t * t t f * * * t t * * f * * * * t t t * * * * * t * * * * * * * * * t * * * * * * * t * ' * * ~ * * * * * * * *

Group II. I n i t i a l i s e V a r / P o r o s i t y ~ "elds F ' I I N I T (KOND) = 6.000000E-01 ; F I ~ N I T ( T E M I ) = ?.500000E+Ol

No PATCHes u sed f o r this Grcup

Group 15. T e r m i n a t e Çweeps LSWEE? = 60 ?.ESI ... C = L.OOOOOOE-03 I * l t * * ~ T l ~ * * r l * t * * * * t * * * * * t * t w T w * * ~ t ~ * t * t ~ * * * * * l ~ * * * * * * * * ~ * *

Group Y . Relaxation w t * + r r r r + + t + + t + t + t t t t f * t ~ t - v t ~ t t i * t r t * 1 ~ * r * w * * t * * w * * * * * * * * * w r

Group 3. 3ARTH Calls T o G2OUND S t a t i o n JSEGRD = T ;USEGRX = T ASAP - - T * * * ~ t * t * C * * ~ t t * t * * * * * * C t * * * * t t t t * * t t ~ t t t + * * * * * * t * * * ~ t * * * * ~ * *

Group 2 2 . Monitor Crint-3ut IXMON = 22 ;IYMON = 22 ;IZMON = 54 NPRMON = 190000 ?JPRMPIT = I TSTSNP = -1 t * * * * r + * t * * * * * * * * t * * * * * f t * * f * * * * ~ * * * t t t * * * * * * * c * * * * * * * * * * + ~ *

Group 23.Fieid Print-Out a ?lot Control NPRINT = 100000 ISWPRF = 1 ;ISWPRL = 100000 IPROF = 3

PATCH iT1 ,PROFIL,7,0,0,0,0,0,1,11 ?LOT (Tl ,KOND, 0.000000E+00, 0.000000E+00) ?LOT (Tl , TEMl, 0.000000E+00, 0.000030E+00) t*****t*t***ff**t*t***t******t**C*t*Y********t*******t******

Group 2 4 . 3umps For Restarts NOWIFE = T

SIZE, MONIT, SCALE, SNAPS 1 ZE, RSET Z 4, - - ilELFX,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, MATERIAL, ADIABATIC, I N 1 - TEMP,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, MATERIAL, ADIABATIC, IN1 - TEMP,

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE, MATERIAL, ADIABATIC, IN1 TEMP, SCAL FIXF, INI TEL - j< - 1, INI-VEL Y-1, INI-VEL-z - - - 1,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, MATERIAL,

cube14 1

BLOCKAGE 16 1 L000000E+00, 2.5OOOOOC+O 1

a2 7.6000C3E-02, 2.860000E-01, cube 14

I aLOCKAGE

162

CHAR 1.400000E-01, I.4OOOOOE-01, 7.500COaE-52 1. 580000E-Oit i. 5800002-31, 1.3000KE-:1 cuDe t

I BLOCKAGE

-1 0.000000E+00, 0.000000E+00

COOLER L.400000E-Olt L. 400000E-01, 1.580000E-01, L580000E-01, cube4

1 BLOCKAGE

111

> OBJ4, SEAT - FLUX, > 0 8 5 4 , INI-TEMP,

XALXZ, ?OSITION, SIZE, ZLI?ART, 3.CTAT 1 ON 2 4 , TYPE, MATFXIAL, TIXFD - TMP,

> OBJ9, !iAKE, > OBJ9, ?CSITION, > CBJ9, 'TZE,

,-t ' > OBJ9, L,L?ART, > OBJ9, 3OTATION24, > O B J 9 , TYPE, > OBJ9, LINR - HEAT,

> OSJIO, !JAiiS, > OBJIO, X?SITION, > OBJTC, S I Z E , > OBJ10, CLIPART, > OBJ10, 3OTATION24, > O B J X , TYPE,

XEATEEI 1 . 4 0 0 0 0 0 E - 0 1 , 1 .400000E-01 , 2 .050000E-9: 1. 5 8 0 0 0 0 E - 0 1 , L . 580000E-01, 1 . 5 0 0 0 0 0 F - 0 2 cube?

1 3LGCKAGt

IL1 0 . 0 0 0 0 0 0 E + 0 0 , 3 .150000E+O2

T 1 2 . l d 0 0 0 0 E - ; 3 i t Z . 13û000E-131, '. 5 0 0 0 0 0 2 - < 2 2 . 0 0 0 0 0 0 E - 0 3 , 2 .000000E-03 , 1 . 3 0 0 0 0 0 E - 3 1 d e f a u l t

1 USER - 9EFfNED

TOP 0 . 0 0 0 0 G 9 F + 0 0 , I.QGOOOOY~GCI, 3 .590000E- '11 4 . 38OOOOE-13If 4 .380000E-01 , 0 .000000E-~ ;2 rube l3

- ?LATE

3 .3000ûOE+00 , Z.SOOOOOE+CI

3OTTOP.I 0 . 0 0 0 0 0 0 E ~ 0 0 , 3.COOOOOE-OG, 3.30030CS-*2'2 4 .3800CûE-01 , 4 .380030E-01 , L 0 0 0 0 0 0 E + O C cube l 3

a

PLATE 3 . 3 0 0 0 0 0 E + 0 0 , 2 . 5 0 0 0 0 0 E + 0 1

SIDEXl 0 .00000@E*00 , Q.O00000E+00, 3 . 0 0 0 0 0 0 E 4 0 0 . 0 3 0 0 0 0 E + 0 0 , 4 .380000E-01 , 3.530000E-121 cube 1 3

1 &

PLATE

CL1 PART, ?.OTATION2 4, TYPE, LINR - FiEAT,

NAME, ?OSITION, SIZE, CLIPART, 2OTATION24, TYE'Z, LINR - HEAT,

YAME, 3 s ITION, SIZE, ZLI PART, 3OTATION24, TYPE, 31NR SEAT,

S I Z E , CLIPART, 3OTATION24, TYPE, YATERIAL, AD IAaAT 1 C , IL11 - :LM?, 3CAL - X X f ,

YAME , POSITION, SIZE, CL1 PART, 3OTATION24, TYPE , MATERIAL, ADIABATIC, IN1 TEMP, SCAE - EIXF,

S 1 DEX2 4. 3S!IOOOE-Olf S. OOOOOGE+OO, O. 000000E+00 0.000000E+00, L.380000E-01, 3.59000GZ-9L tube13

?

PLATE 3.300000E+Xt :.500000E+01

SIDEY2 3.0000OOE-GO, t.33CGOCE-ClI, 1. S00000S-32 4.3800COE-QI, 1. :SCOOCE-rjC, 3.5.300O%E-,21 cune 13

1 PLATE 3.3000GOE~G<, Z.5COOOCS-31

cube t 1

BLOCKAGE 2

0.000000E+00, 3.000000E+00 2.500000E-OI O*OOOOOOEL~O

9.OTATIONS4, TY PEI -MATERIAL, ADIABATIC, I N 1 TEMP, SCAL-FIXF,

NAME, POSITION, SIZE, CL 1 PART, 2OTATICN2 4, TYPE, 'IATEF. I..L, ADIABATIC, I N 1 TEMP, s c E d FIXF,

YAME , ? O S I T I 3 N , SIZZ, CLIPART, 3OTATION24, TYPE, !!ATEF.IAL, ADIABATIC, I N 1 TEMP, scnE - z x ~ ,

I BLOCKAGE

2 0.000000E+00, 3.OCOOOOE+00 2.500000C~01 3.0000COE+00

AIRBOT 1 . 4 G O O O O C - ' 3 1 , 1. -1OCS3SE-51, 5.1~30000Z-132 1.580000t-31, I. SJClC3SP-01, '. ~ O O O O O E - L ~ 3 r u D e t

4 - BLOCKAGE

-l i -

O.OOOOOOE+OOI 3.Q00OOOE+QO 2.500000E41 ~.000000ErOG

Group 7 . Variab les : STOREd,SOLVEd,NAMEd QNEPKS = T

Ncn-defauit ï a r i a b l e names NAME(149) =KOND ; NAME(150) =TEMI

Solved ï a r i a b l e s l i s t SOLVE (TSMl)

* Sto red var iables List STORE (KOND)

* Addit ional s o l v e r c p t i o n s SOLUTN (TEMI,'!, Y, Y , N t N , ' i !

Group 3. Properties SETPRPS(1, 0 ) RH0 l = 1.189000Et00 PRESS0 = I.OOOOOOE+05 TEMPO = 2.730000E+02 CPT = 1.005000E+03 ENUL = 1.544000E-05 ;ENUT = 0.000000E+00 DVOIDT = 3.410000E-03 PRNDTL (TEMI} = -5.500000E-01 **********************~**********f*t***t***+**t*t**tt*~*tt**

Group I0.Inter-Phase Transfer Processes **+************************************t**t*****t**********t

Group I l . I n i t i 3 l i s e ?!ar /PorosFty F ie lds F I I N I T (KOND) = 6.000000E-01 ; F I I N I T (TEM1) = 2 .500000E+01

No PATCHes u s e d f o r this Group

I N I A D D = P - ~ r t * + * t t f * t + * t t t t t r * * t t * * * + ~ f t * t f t t ~ t t t t * * w t * t * * t t t t w t t t t w w t

Group 1 3 . Boundar:~ & S p e c i a l Sources No PATCHes used f o r t h i s Group

Group 1 4 . Downstrecrn P ressu re For ?.\RAB r * * * * t * * t * * * * t * t t * t t * * t t * * * * * * * t t * * * * * * t * t * * * * * * * * * * * ~ v * t * ~ *

Sroup 10. T e r m i n a ï e X e r a c i o n s . * t * t t t * t t * t * t t t t t ~ t w * t t t ~ * * * * t t ~ * t t * t * w w w t w * * * * * * * * * * * * * t * *

Sroup 13. Linits * * * * * * * * t t * t T * ~ * * * ~ ~ * * t t t * * t t t t t * * t t t * t t * * t * * ~ * * t * * * * t * t * * * *

Ûroup 20. Prelirnir.âr:~ F r i n t o u t ECHO - - T r t t * t t * * w * t f t t + t w t * t * * t * t t * t * * t t ~ . * * ~ * t t t * * * t + * * ~ * * ~ w ~ * t w t w * v

Sroup 22. Monitcr P r in t -Ou t ZXMON = 22 ;I?MON = 22 ; I Z M O N = 5 4 NPRMON = 100000 NPRMNT = 1 TSTSWP = -1 ~ * * * t * * * t * * t * * * * * t ~ f t t t * t t t t t t t t * t * t * * t * t * * * * * t ~ * t * * * * * * * * * *

Group 2 3 . Field Prix-Out & ?lot Control N P R I N T = 100000 ISWPRF = 1 ;ISWPRL = 100000 IPROF = 3

PATCH (Tl , P R O F I L , 7 , 0 , 0 , 0 , 0 , 0 , hl) PLOT ( T l , KOND, 0 .000000E+00 , 0 . 0 0 0 0 0 0 E + ~ O ) PLOT ( T l ,TEMI , 3 .000000E+00, û . O 0 0 0 0 0 t + 0 0 ) t t * * * * * * t * * * * * * * * + * * f t * + * * t * t t t t * * t t + t f t + * * * * * * * t * * * * * * * * * * *

Group 24. Dumps For Restarts NOWIPF = T

> DOM, SIZE, 4.380000E-01, 4.380000E-01, 3.590000E-01 > DOM, MONIT, 2.265000E-01, 2.265000E-01, i.543000E-01 > DOM, S CALE, 1.000000E+0Ot I.OOOCOOE+C)O, l.C)00000E+00 > DOM, SNAPS 1 ZE, 1.000000E-02 > GRID, RSET Z 4, - - 50, i.000000E-00 > DOM, RELAX, 5.000000E-01

> OBJI, > OBJI, > OBJ1, > OBJ1, > OBJ1, > OBJ1, > OB51, > OBJ1, > 0831,

MAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, MATERIAL, ADIABATIC, I N 1 - TEMP,

B1 0.000000E+00, 0.000000E+00, 0*000000E+00 4.380000E-01, 4.38000CE-01, 2.750000E-01 cube 14

1 BLOCKAGE

16 1 0.000000E+00, 0.00COOOE+00 2.500000E+91

NAME, 52 POSITION, 7.600000E-02, -.600000E-02, 0.000000F~OC SIZE, 2.860000E-01, 2.860000E-01, 3.590000E-01 CLIPART, cube 14 ROTATION24, 1 ?Y PE , BLOCKAGE MATERIAL, 162 ADIABATIC, O.OOOOOOE+OOt O.OOOCOOE+GC IN1 - TFMP, 2.500000E+01

NAitlE , POSITION, S 1 ZE, CLIPART, ROTATION24, TYPE, MATERIAL, ADIABATIC, IN1 TEMP, SCAL FIXF.

CHAR 1.400000E-01, 1.400000E-01, 7.5000002-02 1.580000E-01, L.580000E-Oit 1.300000s-31 cubet

1 BLOCKAGE

-1 O.OOOOOOE+OCt 3.000000E~00 2. 5OOOOOE+0 1 0.000000C+00 0.000000E+00 0*000000E+00 0.000000E+00

> 08J4, NAME, COGLER > O B J 4 , POSITION, 1.400000E-01, 1.400000E-01, 5.9OOQOOE-02 > OBJ4, SIZE, 1.580000E-01, I.5800OOE-01, 1.700000E-02 > 0834, CLIPART, cube4 > OBJ4, ROTATION24, 1 >0BJ4, TYPE, BLOCKAGE > 0854, MATERIAL, 11 l

> O B J S , > OBJ5, > OBJS, > OBJ5, > OBJS, > OBJ5, > O B J S , > OBJ5,

HEAT FLÜX, INI - E M P ,

NAME, POSITI3N, SIZE, CL1 PART, ROTATION24, TYPE, MATERIAL, FIXED - TXP,

NAME, ?OSITIC)N, SIZE, CL1 PART, ROTATIGN24, TYPE, .IATF?.IAL, ADIA3P.TiC, IN1-XW, SCAL - 'IXF,

NAME, ?OSIYIC)N, SIZE, CLIPART, ROTATIGN24, TYPE ,

NAME, ?OSITION, SIZE, CLIPART, 3OTATION24, TYPE , LINR - XAT,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, LINR - HEAT,

NAME, POSITIQN, SIZE, CLIPART, ROTATION24, TYPE ,

HEATER 1.400000E-01, 1.400000E-01, 2.050000E-01 1.580000E-01, 1.580000E-01, L.500000E-02 cilbe4

1 SLOCKAGE

111 0.000000E+00, 3.230000E+02

AIR 1.400000E-01, -,400000E-01, 2.2000002-51 1.580GOOE-01, L.580000E-01, 3.500000E-02 cubet

1 BLOCKa=

9 i

0.000000E+00, S.OOOOOOE+00 S. 5OOOOOE+O I 0.000000E+00

Tl 2.190000E-01, 2.190000E-01, 7.500000E-92 2.000000E-03, 2.000000E-03, L.300000E-01 def ault

1 USER - DEFINED

TOP 0.000000E+00, 3.000000E700, 3.59OOOOE-01 4.380000E-01, 4.380000E-01, 0.000000E+00 cube 1 3

I ?LATE 3.300000E+00, 2.500000E+OI

BOTTGM 0.000000E+00, 0.000000E+00, 0.000000E+00 4.380000E-01, 4.380000E-01, 0.000000E+00 cube i 3

1 4,

PLATE 3.300000E+OO, 2.500000E+OI

SIDEXl 0.000000E+00, 0.000000E+00, 0.000000E+00 O1000000E+00, 4.380000E-01, 3.590000E-Gi cube 1 3

I PLATE

> OBJI1, > OBJII, > OBJll, > OBJll, > OBJ11, > OBJll, > OBJ11,

LINR - HEAT,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, LINR - HEAT,

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE , LINR - HEAT,

NAME, POSITION, SIZE, CLIPART, ROTATION2 4, TYPE, LINR - HEAT,

NAME, POSITION, SIZE, CL 1 PART, ROTATION24, TYPE, WTERIAL, ADIABATIC, IN1 TEMP, SCAE - FIXF,

NAME, POSITION, SIZE, CLIPART, ROTAT ION2 4, TYPE, MATERIAL, ADIABATIC , IN1 TEMP, SCAL - FIXF,

NAME, POSITION, SIZE, CLIPART,

S 1 DEX2 4.380000E-01, 0.000000E+00, 0.000000E+00 0.000000E+00, 4.380000E-01, 3.590000E-01 cube 13

1 PLATE 3.300000E+00, 2.500000E+OI

SIDEYl 0.000000E+00, 2,000000E+00, 0.300000E+Cd 4.380000E-01, 0.000000E+00, 3.5900COE-01 cube 13

1 PLATE 3.300000E+00, 2.500000Ei01

SIDEY2 3.G00000E+00, t.380000E-01, 3.300000E+CG 4.380000E-01, 0.000000E+00, 3.550000E-1:: cube 13

I ?LATE 3.300000Et00, 2.500000E+OI

TOPlAIR 0.000000E+00, 0.000000E+00, 2.750000E-01 4.380000E-01, 7.600000E-02, 8.399999E-52 cube t

i BLOCKAGE

2 0.000000E+00, Q.O00000E+OG 2. SOOOOOE+O 1 0.000000E+00

TOP2AIR 0.000000E+00, 3.620000E-01, 2.750000E-a1 4.3800002-01, '.600000E-02, 3.400000L-132 cube t

1

TOP3AIEI 0.000000E+00, 7.0000OOE-02, 2.75000OE-01 7.600000E-02, 2-860000E-01, 9.399999E-02 cube t

ROTATION24, TYPE, MATERIAL, ADIABATIC, IN1 TEMP, SCAL - FIXF,

NAME, POSITION, SIZE, CL1 PART, ROTATION24, TYPE, V!ATERIP.L, ADIABATIC, I N 1 TEMP, SCAL - FIXF.

NAME, ?OS I T I O N , S I Z E , CLIPART, liOTATION2 4 , TYPE, %TERIAL, ADIABATIC , IN1 TEMP, SCAL - FIXF,

1 SLOCKAGE

2 0 . 0 0 0 0 0 0 E + 0 0 , 0.000000E+OC 2 .500000E+O? 0 . 0 0 0 0 0 0 E + 0 0

c u b e t 1

SLOCKAGE 2

0 . 0 0 0 0 0 0 E ~ O 0 , 3.000000E+YO 2 . 5 0 0 0 0 0 E + 0 1 0 . 0 0 0 0 0 0 E + 0 0

C C t C C t * C t t C C t C C t e b C C t C t ç C C C b C t r t C C b C b C C C ). C C C C C C C + b b t C C C C Ç F t t dJ i 4 C + C C C C C C t t u ( - 1 t b t C C k b t ci t t r: I r * + c c c C O c c + t Kl h l C C t c t C C O t c t C L I O C * + C t # a ' . C C t r a, O t C C t * C c m c C C t 4 O C C C C * t C O * c c O O C 4 C C + \ t c + t A> al r t t t + + # r n * C - t C k ln C C C C C (r

* O c c h!t . C C + C O + + c C t C 2 ir) C C + C O 4 * C Q , + t u t C 4 c C t C + c + C U * c C C c > II + r + + W c * c r u e c a ç r z c c t 4 O c * r n r c L J W c . rn c k a t t O c W C * c r w c t X C t O + a , * t t c r w 4 . c t C C * z C Z : t C O * w + r m t c O C c C m. r C < c c O c 0 4 r r c ' b r 5: 4 * a = t c O * a + + F I b u ? + t C .' C 3 t C r t t O * C + In* C C + E' u I c t a C )i O C O + C C * r y c + d W VI hl t V ) C I ~ r( t t * & C C O + c c * O tn a O + Q I + > C t c II * a s C - 4 * C O C + r i Da a - 4 O + U C 4 V ) W + C + C C u l * t O C @ bJ 3 O * m e 0 al€-' v) C c c & * c k c c i r i c c a - c r i O C C UI E I I C c t 4 a + c a , r + c a! CO r . 4 ~ . a O t c p d + w t ; E.; u + > + I l * 4 + ci e 7 Y c - U C - . f c c 5 O * t o c + r I. a ) + t 0 . 4 x c , C L ~ C W o u AJ u t c Z I C : * c . + k t - 4 ~ c w w a i t n --r t o r e c u w w tn a. C U I + W W * a * C 9 * W b + C U a C O C O 4 - -4 O - * C u - t O * & * r e r a t E : C l-4 4 II t u c e . - 4 - 4 $4 t u >4 * O * F * c a i @ + C O + r d + t lu 4 c * t r i t d W 1 4 4 c - ~ & + o m ~ r n m m o ~ + r E h + H C W C 4 . d 0 r 6 h 1 + a * tn ai5 C 3 > 4 t O O O O O O O C a , + C O C t l t * a , t . 4 4 r (U, ' 2 * I . r a, h * w + + + + I I O * V I * * H u i 0 . 1 8 1 1 ) b O 4 4 k C O ( . vi r d 2 4 4 f t C l > + a! W W W W W W a 3 * a + + I C ] I I + t 4 3 t c ac, O. C J J C W > a .a 0 4 t .* .d o o o o w o * + . c c * 4 c ci.,+ Q, - w 4 + . A C +

r - . i u r - d C *-rd a ? * a > # ci 0 0 0 0 0 0 ~ *

O 1-4 a O -- c ILI r .Q LJ 4 4 - c * k 0 0 0 0 0 0 1 4 1 + + h Z i I + b O c vi C~~IIQJI c 1 t (O 413k L4 4 t 4 O i O O I n V O + h * C . a a C r m e C p w C - I r ( l 3 E W t t 4 5 a a - : E , - a , o m o v t + i , r a , * (I a,# t c t ( d t . - k 5 < : ( D O b ' t ) C L4 r l f Q > ? d?4 9 > C O O 4 - 4 O P O U I W + 4 J * C + 9 - + k + W r - f O O ) C O C O * ftJ ' U X 0 - + Q) - C k 9 - 4 4 a,*.+ + d r d * w c 4 ~ 4 ~ o x r m c :, 4 O H C e I r c - i d C O 0 4 t r C E r - c 4 m a * II r . - i t - 1 1 t m ~ ~ o ~ X C a b II I L I c - W C * & I I II II II II II m e O C r a,> c r * f , - i c (Y t a,- JJ r T i y r c c > * r - C c n c ( b j 0 O d t 4 t m p t m - E - c * ri+

t -4 t t W > - a . C c 0 0 r - t VI U t * : U $ : * Q,Z r o.> * 0.0 F: cn -r n c a,+ o . t n z r c ~ ~ . - ~ ~ - < r l : / . r a + a& O a* c z c 3 - c 3 a t 3 -- - - c 3 , 3 J: --- [ I I [ I I t 3 v ) c r i a ; w o Q E + C z l * : r i B r z t o d r O r F d r e I I t < + o r o n < * > r a * I; o c b o f i d v i a . c i d o * O *

c O > * 3 c ~ c X t k w t k bl & + W C L t t Lcw c-1 O b - l (. h a ; * U F O W W C D O O * Q * I. a * l x @ C ~ L ~ I C U P C (3 w y ; : I * I + u z o ~4 ~3 + u w + u W m o : w a . z > a + a + c r I # i I fn r n; . . b ( 3 , t ( 1 ) f o + F 4 c tn rr, nl c.4 I LLJ n r i 4 r t

Grcup 1 1 . I n i t i a l i s e Vax/Porosity Fie lds C L I X I T (KOND) = 6.000000E-OL ; FIINIT (TEMI) = 2.500000E+OI

No FATCHes used f o r c h i s Group

INIRDD = F r t r r r + + * + t t t t t C * * * t t t t t i r t t * t + t u * * * r T r s I * * * * t * t t t Y t * * * t t t * * * r v

P uroup 13. B o u n d a r y & Special Sources

Xo ?ATCHes used f o r this Group

P =rocp 1 4 . Downstream P r e s s u r e For ?ARAB r r w t + t + + + + Ç * f C t t + + + * t t t C ~ t * t t t ' 5 f f t * * t t t ~ * * * * + * * t * ~ t t v t t * * * r *

S r z x c 22. Xonitor ? r i n ~ - + ~ u t IXMCtl = 22 ;TYMON = 22 ;IZNON = 0 5 NPRMON = 1 0 0 0 0 0 XPRL.INT = I TSTSX? = -1 t t t r r t t f * f f + f f t t C f * * * * * t t t f t + t * ~ t X * t t ~ t * + * + * * * * t * * * * * * T * t * * *

Group 23.Field Print-Out 5 ?lot C o n t r o l XPRINT = 1 0 0 0 0 0 ISWPRF = 1 ;ISWPRL = 100000 XPROF = 3

?ATCE (Tl ,PROFILf7,0,0,0,0,0,i,1) PLOT (Tl ,KOND, 0 . 0 0 0 0 0 0 E + 0 0 , 0 . 0 0 0 0 0 0 E + 0 0 ) PLCT :Ti ,TEMI , 0 .000000E+00 , 0 .0G0000E+00) +f*~t+********************t***f****t*************t*******~tt

Group 2 4 . Dumps For Restarts NOWIPE = T

> DOM, > DOM, > DOM, > DOM, > GRID, > 9OM,

SIZE, !<ON1 T, SCALE, SNAPS 1 ZE,

30SITION, SIZE, ZLIPART, ?.OTATIONS 4 , TYPE,

!%ME, ?GSITION, 3ïZCt JLIPART, SOTATION24, TYPE , WTERIAL, .?.DIABATIL, IN1 - TEMP,

NAME, TOSITION, SIZE, CLIPART, 3OTATION24, TYPE, XITERIAL,

82 7 . 6 0 0 0 0 0 E - 3 2 , ' . 600000E-02 , 3 . 0 0 0 0 0 0 E ~ G C 2 .860000E-01 , 2 .860000E-01 , 3.590000E-13: cube l - l

1

CHAR 1 . 4 0 0 0 0 0 E - 0 1 , 1 .400000E-01 , 7 .500000E-G2 1 . 5 8 0 0 0 0 E - O i , L .S80000E-01, 9 .000000E-92 cuber

1 *

i3LOCKAGE

COOLER 1 . 4 0 0 0 0 0 E - 0 1 , 1 .400000E-01 , 5 .800000E-02 1 . 5 8 0 0 0 0 E - 0 1 , 1 .580000E-01 , 1 .700000E-G2 cube4

1 BLOCKAGE

111

> OBJ4, HEAT-FLUX, > 0 8 3 4 , I N 1 TEMP, - > OBJS, > OBJ5, > OBJ5, > OBJS, > OBJS, > OBJS, > OBJ5, > OBJ5,

NAME, POSITION, S IZE , CLIPART, ROTATIOM24, TY PE , MATERIAL, FIXED - T N P ,

NAME, POSITICN, SIZE, CL1 PART, 3OTATTON24, TYPE, ?IATERIRL, ADIABATI:, I N 1 TEMP, SCG-FIE.

> 0 8 5 7 , NAME, > OBJ7, ?OSITISN, > OBJ7, SIZE, > OBJ7, CLIPART, > OBJ7, ROTATION24, > OBJ7, TYPE,

> O B J 8 , NAME, > O a J 8 , POSITICN, > OBJ8, SfZE, > OBJ8, CLIZART, > OBJ8, ROTATICN24, > O B J 8 , TYPE, > OBJ8, L I N R - XEAT,

> OBJ9, NAME, > 0 B J 9 , POSITION, > OBJ9, S I Z E , > OBJ9, CLIPART, > OBJ9, ROTATION24, > O B J 9 , TYPE, > OBJ9, L I N R - HEAT,

> OBJTO, NAME, > 0B310 , P O S I T I O N , > OBJ10, S IZE , > OBJ10, CLIPART, > OBJlO, ROTATION24, > OBJlO, TYPE,

HEATER 1 . 4 0 0 0 0 0 E - 0 1 , 1 . 4 0 0 0 0 0 E - 0 1 , 1 . 6 5 0 0 0 0 E - 0 1 1 . 5 8 0 0 0 0 E - 0 1 , 1 . 5 8 0 0 0 0 E - 0 1 , 1 .500000E-02 cube 4

1 8LOCKAGE

111 0 . 0 0 0 0 0 0 E + 0 0 , 5 . 5 0 0 0 0 0 E t 0 2

A I R 1.400300F-431, 1 .40000CE-01 , 1. 900000E-i21 1 , 5 8 0 0 0 0 E - 0 1 , 1 . 5 8 0 0 0 0 E - 0 1 , 7 . 5 0 0 0 0 0 E - 3 2 cube t

1 BLOCKAGE

7 I

0 . 0 0 0 0 0 0 E - 0 0 , 3 . 0 0 0 0 0 0 E ~ 0 0 S.5OOOOOE+O 1 0 .C00000E+00

Tl 2 . 1 9 0 0 0 0 E - 0 1 , 2 . 1 9 0 0 0 0 5 - 9 1 , 7 .500000E-G2 2 . 0 0 0 0 0 0 E - 0 3 , 2 . 0 0 0 0 0 0 E - 0 3 , 9 . 0 0 0 0 0 0 E - a 2 default

1 USER DEFINED -

TOP 0 . 0 0 0 0 0 0 E + 0 0 , ~ . 0 0 0 0 0 0 E + 0 0 , 3.590000E-13: 4.380000E-01, 4 .380000E-01 , 0 ~ 0 0 0 0 0 0 E + O C cube13

1 PLATE

3 . 3 û 0 0 0 0 E + 0 0 f 2 .500000E+O1

BOTTOM 0 . 0 0 0 0 0 0 E + 0 0 , 0 . 0 0 0 0 0 0 c + 0 0 , 0 . 0 0 0 0 0 0 ~ + 0 0 4 . 3 8 0 0 0 0 E - 0 1 , 4 .380000E-01 , 0 . 0 0 0 0 0 0 E + 0 0 cube i 7

1 PLATE

3 . 3 0 0 0 0 0 E + 0 0 , 2 . 5 0 0 0 0 0 E + 0 1

SIDEXI 0 . 0 0 0 0 0 0 E + 0 0 , 0 . 0 0 0 0 0 0 E + 0 0 , 0*000000E+Oû 0 . 0 0 0 0 0 0 E + 0 0 , 4 .380000E-01 , 3 .590000E-Cl cube i 3

1 PLATE

LINR - HEAT,

NAME, POSITION, SIZE, CL 1 PART, ROTATION24, TYPE , LINR HEAT,

NAME, POSITION, SIZE, CLIPART, ROTATION24, TYPE, LINR - K A T ,

NAME, POSITION, SIZE, CL1 PART, ROTATION21, TYPE, LINR FiEAT, -

NAME, POSITION, SIZE, CL I PART, 3OTATIGN24, TYPE, NATERIAL, ADIABATIC, IN1 'TFMP, S C A ~ - FIXE,

NAME, POSITION, SIZE, CL1 PART, F!OTATION24, TYPE, MATERIAL, ADIABATIC, IN1 TEMP, SCAE - FIXF,

NANE, POSITION, SIZE, CL1 PART,

&

PLATE 3.300000E+00, 2.500000E+OI

SIDEY1 0.000000E+00, 3.000000E+00, 0.000000E~00 4.380000E-01, 0.000000E+00, 3.590000E-01 cube 13

1

?LATE 3.30COOOE+00t 2,500000E+01

SIDEY2 0.000000E-00, 4. 3@0000E-01, J . COOOOCE+~3C 4.380000E-01, 3.00QCOOE+00, 3.590003C-q31 cube 13

I PLATE 3.300000F+00, 2.500000E+OI

TOPlAIR 0.000000E+00, 0.000000E+00, 2.750000L-0i 4.380000E-01, 7.600000E-02, 8.399099E-02 cubet

I BLOC7KAGE

-l L

0.000000E+Oû, ~~.cJ00000E+00 2.500000E+01 0.000000E+00

TOP2AIR 0.000000E+00, 3.620000E-01, 2.750000E-01 4.380000E-01, 7.600000E-02, 3.400000Z-d22 cube t

1 BLOCKAGE

2 0.000000E+00, 0.000000E+00 2.500000E+OI 0.000000E+00

> 3BJ18, > OBJlS, > OB318, > 08518, > OBJ18, > OBJ19, > OBJ18, > OBJ18, > OBJ18, > OBJ18, STOP

ROTATION24 TYPE, MATERIAL, ADIABATIC, I N 1 TEMP, SCAE - FIXFr

NAME, E'OSITION, S I Z E , CLIPART, ROTATION24 TYPE, x4TERIAL, ADIABATIC, I N 1 TEMP, SCAL - FIXF,

XAME , ?OSITION, SIZE, CL1 PART, 3OTATION24, TYPE , YATERIAL, ADIABATIC, I N 1 TEMP, SCAE - FIXF,

cube t I

BLOCEWGE 3 L

0.000000E+00, G.000000E+00 2.500000E~01 0.000000E+00

AIRBCT 1.4000ûOE-01, 1,300000E-01, 5.1000005-52 1.5800COE-01, 1.580000E-01, " .000000€-~2S cube t

1 3LOCKAGZ

3 L

0.000000E+00, 0.000000E+00 2.500000E+Ol 0.000000E+00

APPENDIX C ERROR ANALYSIS FOR DETERMINATION OF EFFECTIVE

THERMAL CONDUCTIVITY

The error associated with the measurement of the effective thermal conductivity using the

procedure outlined in Chapter 3 is explained in this Appendix.

The following uncertainties existcd in the measuremrrnts:

Thermocouples: k 0.5 "C

Daia Acquisition: f 0.5 O C

Dis tance: + 0.05 cm

lZllass Flow Rate: k0.1 $s

The absolute uncenainty was found for addition and subtraction by simply adding the

individual uncertainties. For multiplication and division the surn of relative uncertainties

for each quantity was calculated and then it was convened back tu absolute uncertainty as

shown in the following sections.

For example. for the following situation:

x 1 = 4.2 + 0.05 cm

x 2 = 6.2 $r 0.05 cm

T 1 = 363 2 I OC

T 2 = 484+ 1 OC

T i , = 17k1OC

T out = 48 I 1 OC

m = l.Sk0.1 g/s

where x 1 and x 2 refer to location of two consecutive rhermocouples. TI and T: refer to

the temperature rit the correspondhg locations, Ti" and T,,, refer to water inlet and out let

temperatures. respectively. and m represents the mass fiow rate of water in the coolin_o

plate, the accumulated uncenainty is calculated as follows.

Q = m C p A T

but.

cc- 1 )

Therefore the total heat removed by the circulating water c m be calculated.

the accumulated error in determination of Q is then found as follows:

error in Q / Q = error in rn / rn + error in AT / AT

error in Q = Q (error in m / m + error in AT / AT)

=60.20(0.1 / L.8+2/31)

= 7.2 W

therefore the heat removed by the circulating water was 60.2 t 7.2 W.

The heat tlux q was calculated by dividing the heat removai rate by the coolin? plate ÿrea

as described in Chapter 3. The relative error was found using the above procedure.

Therefore

Finaily the error in determination of thermal conductivity was found.

there fore

kff = 0.45 k 0.08 W/m°C.