0RNL/ENG/7M-1

Thermal Design and Analysis of the HTGR Fuel Element Vertical Carbonizing

and Annealing Furnace

G. H. Llewellyn

Printed in the United States of America. Available from National Technical Information Service

U.S. Department of Commerce 5285 Port Royal Road, Springfield, Virginia 22161

Price: Printed Copy $5.00; Microfiche $3 00

j This report was prepared as an account of *ork sponsored by the United States j Government Neither the United States nor thi? Energy Research and Development j

i Administration United States Nuclear Regulatory Commission, nor any ~f their i I employes, nor any o' their contractors, subcontractors, or their employees, mukes !

any warranty, express or implied, orassfin.es any legal liability or responsibility for the I accuracy, completeness or use'..' -n*.r. of any information, apparatus, product 0' ! i process disclosed, or represents that ts i^e would not inf-.ii$,<> privately owned rights

i

ORNL/ENG/TM-1

Contract *o. W-7405-eng-26

ORNL Engineering

THERMAL DESIGN AND ANALYSIS OF THE i; GR FUEL ELEMENT VERTICAL CARBONIZING AND ANNEALING FbRNACL

G. H. Llewel lyn

Date Publ i shed: June 1977

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OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

Nuclear D i v i s i o n for the

ENERGY RESEARCH AND DEVELOPMENT ADMINISTRATION

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iii

CONTENTS

Abstract 1 1. INTRODUCTION 1 2. CRITERIA 3 3 . CARBONIZING AND ANNEALING FURNACE 5

Furnace Operation 5

Thermal Design 9

4 . ENERGY TRANSPORT SIMULATION TN THE MOVING COLUMN 14

Determination of Volumetric Keat Generation Rate 15

Heat Balance in Graphite Column 17

5. HEAT TRANSFER MODELS AND BOUNDARY CONDITIONS 21

6. MATERIAL PROPERTIES USED IN THERMAL ANALYSIS 29

7. RESULTS OF THERMAL ANALYSIS, CONCLUSIONS, AND

RECOMMENDATIONS 36

REFERENCES 42

Appendix A: MASS-FLOW SIMULATION DATA FOR FUEL ELEMENTS FABRICATED FROM H-327 GRAPHITE 45

Appendix B: MASS-FLOW SIMULATION DATA FOR FUEL ELEMENTS FABRICA^cD FROM H-451 GRAPHITE 69

Appendix C: THERMAL CONDUCTIVITY DATA AS A FUNCTION OF TEMPERATURE FOR FUEL ELEMENTS FABRICATED FROM TYPE H-327 AND TYPE H-451 GRAPHITE 79

V

LIST OF FIGURES

Figure Page Number Ti t le Number

1 Typical Fort St . Vrain Active Core Element 4 2 Proposed HTGR Fuel Eleiient Vertical Carbonizing and 6

Annealing Furnace 3 Operational Diagram of Furnace Design 8 4 Desired Temperature of Outer Surface of Fuel Elements 10

as a Function of Axial Location in Furnace 5 Internal Volumetric Heat Generation Rate Required 19

for Simulation of Mass Flow cf Fuel Elements Fabri­cated From H-327 Graphite as a Function of Their Axial Position in the Furnace for the Top-Loaded Configuration

6 Internal Volumetric Heat Generation Rate Required for 20 Simulation of Mass Flow of Fuel Elements Fabricated From H-32? Graphite as a Function of Their Axial Posi­tion in the Fumac: for the Bottom-Loaded Configuration

7 Computer Model of Upper Portion of Furnace for Top- 22 Loaded Configuration

8 Computer Model of Middle Portion of Furnace for Top- 23 ana Bottom-Loaded Configurations

9 Computer Model of Lower Portion of Furnace for Top- 24 Loaded Configuration

10 Computer Model of Upper Portion of Furnace for Bottom- 25 Loaded Configuration

l i Computer Model of Lower Portion of Furnace for Bottom- 26 Loaded Configuration

12 Results of Computer Analysis of Furnace Design Com- 38 pared With Desired Temperature Profile for Top-Loaded Configuration

13 Results of Computer Anal>jis of Furnace Design Com- 39 pared Wich Desired Temperature Profile for Bottom-Loaded Configuration

14 Results of Computer Analyses Obtained By Varying 40 Insulation in Upper Portion of Furnace Compared With Desired Temperature Profile for Top-Loaded Configura­tion

15 Results of Computer Analyses Obtained By Varying I.TSU- 41 lation in Upper Portion of Furnace Compared With Desired Temperature Profile for Botton-Loaded Config­u r a t o r

vi

Figure Page Number Tit le Number

A.l Centigrade Temperature Criteria for the Surface of 54 Fuel Elements Fabricated From H-327 Graphite as a Function of Their Axial Position in the Furnace tor the Top-Loaded Configuration

A.2 Fahrenheit Temperature Criteria for the Surface of 5* Fuel Elements Fabricated From H-327 Graphite us a Function of Their Axial Position in the Furnace for the Top-Loaded Configuration

A.3 Axial Heat Transfer From Mass Flow of Fuel Elements 56 Fabricated From H-327 Graphite as a Function of Their Axial Posit ion in the Furnace for the ??p-Loaded Con­figuration

A-4 Axial Heat Transfer From Axial Conduction in Fuel Ele- 57 ments Fabricated From H-327 Graphite as a Function of Their Axial Posit ion in the Furnace for the Top-Loaded Configuration

A.5 Axial Heat Transfer From Mass Flow of Argon Gas as a 58 Function of Axial Position in the Furnace for the Top-Loaded Configuration

A.6 Total Radial Power Input, Excluding External Losses, 59 Required to Process Fuel Elements Fabricated From H-327 Graphite as a Function of Their Axial Position in the Furnace for the Top-Loaded Configuration

A.7 Composite Axial Power Distribution for Processing Fuel 60 Elements Fabricated From K-327 Graphite a3 a Function of Their Axial Position in the Fr.rnace for the Top-Loaded Configuration

A.8 Centrigrade Temperature Criteria for the Surface of 61 Fuel Elements Fabricated Froti K-327 Graphite as a Function of Their Axia1 Position in the Furnace for the Bottom-Loaded Configuration

A.9 Fahrenheit Tamperature Criteria for the Surface of 62 Fuel Elements Fabricated From H-327 Graphite as a Function of T\eir Axial Position in the Furnace for the Bottom-L aded Configuration

*.10 Axial Heat Transfer From Mass Flow of Fuel Elements 63 Fabricated From H-327 Graphite as a Function of Their Axial Position in the Furnace for the Bottom-Loaded Configuration

A.11 Axial Heat Transfer From Axial Conduction in Fuel Ele­ments Fabricated From H-327 Graphite as a Function of Their Axial Position in the Furnace for the Bottom-Lo.iied Configuration

64

V l l

Figure Page Number T i t l e Number A-12 Axial Heat Transfer From Mass Flow of Argon Gas as a 65

Function of Axial Posi t ion in the Furnace for the Bottom-Loaded Configuration

A-13 Total Padial Power Input . Excluding External Losses, 66 Required to Process Fuel Elements Fabricated From H-327 Graphite as a Function of Their Axial Pos i t ion in the Furnace for the Bottom-Loaded Configuration

A.14 Composite Axial Power Dis t r ibu t ion for Processing Fuel 67 Elements Fabricated From H-327 Graphite as a Function of Their Axial Posi t ion in the Furnace for the Bottom-Loaded Configuration

C.l Axial and Radial Thermal Conduct iv i t ies of Composite gQ Fuel Elements Made With Unirradia ted H-327 Graphite as a Function of Temperature

C.2 Axial and Radial Thermal Conduct iv i t ies of Composite g2 Fuel Elements Made With Unirradiated H-451 Graphite as a Function of Temperature

1

THERMAL DESIGN AND ANALYSIS OF THE HTGR FUEL ELEMENT VERTICAL CARBONIZING AND ANNEALING FURNACE

Abstract

Computer analyses of the thermal design for the proposed HTGR fuel element v e r t i c a l carbonizing and annealing furnace were performed to ver i fy i t s capa­b i l i t y and to determine the required power input and d i s t r i b u t i o n . Although the furnace i s designed for continuous opera t ion , s t e ady - s t a t e temperature d i s ­t r i b u t i o n s were obtained by assuming i n t e r n a l heat generat ion in the fuel elements to simulate t h e i r mass movement. The furnace thermal des ign, the ana l ­y s i s methods, and the r e s u l t s are discussed h e r e i n .

1. INTRODUCTION

One s tep in the process under development a t Oak Ridge National Laboratory (ORNL) for remote fabr ica t ion of fuel elements from recycled 2 3 3 U for use in high-temperature gas-cooled r eac to r s (HTGR) operated on the thorium fuel cycle involves in-p lace carboniza t ion and annealing of pitch-bonded fuel rods in graphite fuel element b locks . Coated fuel par­t i c l e s are bonded in to rods with p i t c h , these rods are loaded in to holes in pr i smat ic graphite b locks , and the e n t i r e fuel element i s heated to carboni7e the p i tch bonding mater ia l and then to anneal the carbon and produce s tab le fuel rods- To accomplish t h i s s t e p , the design for a v e r t i c a l , remotely operable furnace was developed, and the thermal anal­ys i s of tha t furnace design i s described in t h i s r e p o r t .

Thermal analyses were performed as par t of the work involved in the development of the current furnace des ign. The s t e a d y - s t a t e thermal ana lys i s of tha t design reported here in was. performed to ver i fy i t s capa­b i l i t y to achieve the desired axia l temperature d i s t r i b u t i o n in the fuel elements as a function of time and to determine the power input and d i s ­t r i bu t i on to the furnace hea te r s required for maintenance of the de j i red temperature p r o f i l e . As well as the power input to the h e a t e r s ,

2

maintenance of the desired temperature profi le i s dependent upon the mass flow rate of the material going through the furnace, the thermal proper­t i e s of the materials Involved, and the boundary conditions at the cool­ing surfaces.

The cr i ter ia for the carbonizing and annealing furnace are discussed br ie f ly in Section 2, and the furnace operation and thermal design are described in Section 3. The furnace design provided the bas is for devel­opment of two-dimensional mathematical heat transfer models in the form of nodal layouts of the furnace- The HBATING4 computer program, which i s a modification of the generalized heat conduction program HEATING3,1 was used to obtain steady-state temperature distributions in these models. The HEATING programs have been used at ORNL for several years and have been updated during this period with new solution techniques and new boundary condition subroutines to the extent that any of the main varia­bles can be expressed as functions of the other variables . The feature of anisotropic conduction was added to the program capabi l i t i es for anal­ys is of the furnace. This feature vas necessary inasmuch ar the fual elements, furnace l iner , and some of the insulation have different axial and radial thermal conductivities*

The mass movement of fuel elements through the furnace was simulated to obtain heat input data for the HEATING4 program analysis of the fur­nace thermal design. This simulation i s described in Section 4 . The heat transfer models used in the computer analysis are described and the furnace boundary conditions developed for the analysis are discussed in Section 5. The thermal conductivity data for the furnace materials of construction used in the steady-state analysis are given in Section 6, and the resu l t s of the analysis are discussed in Section 7. The conclu­sions drawn from the results of the analysis are also presented in Sec­tion 7, as are recommendations re lat ive to future analyses.

3

2 - CRITERIA

The re fabr ica ted HTGR fvel elements which the carbonizing and annealing furnace was designed to accommodate are the type to be used in the ac t ive core of the Fort S t . Vrain Reactor (FSVR). As I l l u s t r a t e d in F ig . i , a typica l FSVR fuel element i s a hexagonal prism tha t i s 14-17 i n . across the f l a t s and 31.22 in . long a t room temperature. The prism or fuel block i s to be fabr ica ted from un i r r ad i a t ed needle-coke (type H-327) graphite as manufactured by the Great Lakes Carbon Company. The block may poss ibly be fabr icated from type H-451 graphi te a t a l a t e r da t e . As indicated in F ig . 1, each HTGR fuel element w i l l contain s ix holes for burnable poison, 108 coolant h o l e s , and 210 fuel ho les - The fvel holes w i l l be loaded with "green" fuel rods comprised of a mixture of graphi te-coated uranium-oxide and thorium-oxide p a r t i c l e s bonded with p i t c h . These holes w i l l then be sealed v i t h graphi te plugs cemented in place a t the top . Each assembled fuel element w i l l have a maximum weight of approximately 300 l b .

The thermal c r i t e r i a for the carbonizat ion and annealing of HTGR fuel rods placed in the graphi te blocks specify a beginning minimum car­bonizat ion temperature of 300°C and a thermal r i s e not to exceed 10°C per minute up to a temperature of 800°C, r e s u l t i n g in a carbonizat ion period of 5C minutes. Following carbonizat ion, an annealing s tep i s required to completely drive off any remaining v o l a t i l e ma te r i a l s . During t h i s s t e p , the temperature of the graphi te must be maintained above 1750°C and below 1850 C for a period of at l eas t 15 minutes but not to exceed 90 minutes-Before discharge from the furnace, each fuel element must be cooled so t h a t the temperature of any graphi te exposed to ambient a i r wi l l be below 200°C.

4

0«NL-OW3 70-W233

^-COOLANT HOLE 0500-in. dio (6)

COOLANT HOLE 0.625-in. did (102)

BURNABLE POISON HOLE 0.500-in. dia (6)

FUEL HOLE 0.500-in dia (210)

CEMENTED GRAPHITE PLUG (typ)

UEL HANDLING PICKUP HOLE

DOWEL PIN

HELIUM FLOW (typ)

WEL SOCKET

Typical Fort S t . Vrain Active Core Element.

5

3 . CARBONIZING AND /.NNEALISG FURNACE

A v e r t i c a l furnace was designed for the carbon iza t ion and anneal ing

s tep in the remote HTGR f u e l element r e f a b r i c a t i o n p r o c e s s - The v e r t i c a l

d e s i g n , i l l u s t r a t e d i n F i g . 2, was cons idered the b e s t conf igurat ion with

respect to h o t - c e l l space- From top tc bottom, the furnace p r o c e s s i n g

chamber i s comprised o f a charging gate v a l v e , three temperature-contro l l ed

heat ing zones , two c o o l i n g zones , and a d i scharge gate v a l v e . The pro­

c e s s i n g chamber, wi th an o v e r a l l l ength o f approximately 203 i n . between

valve d i s k s , i s e n c l o s e d wi th s douMe-wal l w a t e r - c c o l e d metal s h e l l which

surrounds the hea t ing e lements and i n s u l a t i o n i n the h e a t i n g zones and

provides containment i n the c o o l i n g zones for the i n e r t atmosphere main­

ta ined w i t h i n the chamber.

The o v e r a l l h e i g h t of the furnace i s increased about 52 i n . >/ the

discharge chamber located below the d i scharge v a l v e . This chamber pro­

v i d e s a d d i t i o n a l c o o l i n g for fue l e lements l e a v i n g the p r o c e s s i n g chamber

anc s e r v e s as a double -per t lock to maintain the i n e r t atmosphere in the

furnace p r o c e s s i n g chamber during d i s c h a r g i n g and unloading of fue l

e lements -

The furnace can accommodate a maximum o f s i x fue l e lements and seven

spacer p a l l e t s at any one t ime. Fuel e lements t r a v e l downward through

the furnace at an e s s e n t i a l l y continuous r a t e , and the furnace i s purged

cont inuous ly with argon gas in a flow path o p p o s i t e the downward movement

of the fuel e l e m e n t . The furnrv..? has a des ign p r o c e s s i n g capac i ty o f

about 14 elements a d -y , and i t s operacion and thermal des ign are d i s ­

cussed i n the f o l l o w i n g s u b s e c t i o n s .

Furnace Operation

A fuel element and i t s attendant spacer p a l l e t are . i t o d u c e u in to

the furnace p r o c e s s i n g chamber froir. a portable charging chamber seated

on the upper face of the charging v a l v e . A p a l l e t i s placed on top of

each element introduced i n t o ;he furnace to r e c e i v e the next element

CRNL 0*G 7 6 - i 8 ! 7 0

fk

SA

*>

•REMOVABLE CHARGING CHAMBER

-CHARGING VALVE

•UPPER HEATING SECTION (low «effipe«tur«)

> >

o TACKED HTGR FUEL ELEMENTS AND SPACERS

•HIGH TEMPERATURE GRAPHITE HEATERS

•COOLING SECTION

CiSCHAPtGE VALVE V(TH .WTERT.EPTOR >-~ORKS

•FUEL ELEMENT UNLOADING MACHINE

2. Proposed HTGR Fuel F.U.ient Vert ical Csrbonl2ing and Furnace >

in t roduced. This spacer p a l l e t i s a 5 - i n . - t h i c k c i r c u U r disk with a hexagonaily shaped socket about 1.5 i n . deep mil led into each face to f i t the tops and bottoms of fuel elements . Thf. - - i n . - t h i c k hexagonal web of each p a l l e t i s d r i l l e d to match the 103 coolant passages of the fuel e l e ­ments. The seated ch rging chamber i s purged with argon, the upper valve gate i s opened, and the charging chamber ho i s t i s driven downward to introduce the element and p a l l e t in to the processing chamber. The bottom of the element i s seated in the p a l l e t r e s t i n g on top of the fuel element below i t in the processing chamber.

The e n t i r e column of elemerts and p a l l e t s is supported on a motor-driven e l eva to r platform in the discharge chamber. This e l e v a t o r cont ro ls the downward movement of the elements through the furnace heat ing and cooling zones to the bottom of the discharge chamber. When the spacer p a l l e t on top of the bottcm element in the column i s a proscribed dis tance above the h o r i z o n t a l l y r e t t a c t a b l e support forks , which are axmnted in the housing of the furnace discharge valve immediately above the valve d i sk , the downward movement of the e leva to r i s continued while the forks are moved inward under the p a l l e t . These forks provide in ter im support for the column of elements and p a l l e t s above while the bottom element i s lowered by the e leva to r to the bottom of the discharge chamber. The d i s ­charge valve i s c losed, the unloading door in the discharge chamber i s opened, and the fuel element and i t s supporting p a l l e t are removed from the furnace. The unloading door i s then closed and the discharge chamber i s purged with argon, the discharge valve i s opened, and the e l eva to r platform i s ra ised to again support the column of elements ard p a l l e t s in the processing chamber. The support f-*rks are r e t r a c t e d , the downward t rave l of the column is resumed, another fuel e lemett is charged in to the top of the furnace processing chamber, and the cycle i s repeated .

A furnace cycle begins with what can be termed a "top-loaded" con­f igura t ion cons i s t ing of s ix ele ' ients and seven p a l l e t s over the dis tance marked "A" in Fig. 3 . About 90 minutes l a t e r , esch element has mov d down to comprise the "hottorn-loaded" configurat ion over the distance marked "B" in Fig. 3 . Production considera t ions led to the use of an average element movement of 3/8 in . per minute. Based on an element length of 31.22 i n . And a p a l l e t web thickness of about 2 i n . , the

a

«v ;•;, "6 ;«;:

w V .'V.Wr rf-W

Fig. 1. Operational Diagram of Furnace Design.

9

travel time for a complete element unit from the top-loaded to the bottom-loaded configuration i s 88-6 minutes. About 10 minutes more are required for unloading and loading procedures, result ing in an average production rate of about 16 fuel elements per day. However, the thermal analysis reported herein was based on the assumption of continuous mass movement of 3/8 i n . per minute.

Thermal Design

The thermal cr i t er ia for carbonization of the HTGR fuel rods in place in the graphite blocks s t ipulate heating of the blocks from 300°C to 800°C at a constant heating rate not to exceed 10°C per minute. A uniform theimal gradient of 26.07*0 per inch (48 °F per inch) was obtained by dividing the heating rate (l0°C/min.) by the mass movement rate (0.375 in . /min) . This information and the annealing cr i t er ia were adequate to es tabl i sh the desired furnace axial temperature profi le i l lus tra ted in Fig. 4 .

Point A on the curve shown in Fig. 4 i s the temperature at the top of the fuel element unit (element plus spacer pa l l e t ) or block introduced into the furnace processing chamber at e levat ion 202 i n . , and Point B i s the temperature at the bottom of that element at furnace elevation 168 in . Point C denotes the beginning of the c r i t i c a l gradient et a temper­ature of 300"C and a furnace elevation of 142 i n - , and Point D denotes th- end of the c r i t i c a l zone at a temperature of 800°C and a furnace e l e ­vation of 123.25 in . The temperature gradient used for carbonization was maintained during annealing to obtain the location of Point E at a tem­perature of 1750°C and a furnace e levat ion of 87.63 in . Point F, the inf lec t ion point of the gradients, i s the maximum temperature of 1800°C reached at furnace e levat ion 81 in . Any zone above th i s point requires net heating, while any zone below i t requires net cooling-

Point G on the curve i s symmetrically adjacent to Point E at a tem­perature of 175Q°C and a furnace e levat ion of 74.37 i n . A heat balance must be achieved and, although i t does not have to be, Point H was con­veniently located at furnace elevation 40 i n . , result ing in a temperature

n rr

3 00

TEMPERATURE OF OUTER SURFACE OF FUEL BLOCKS. °C

x> <D go 5 N £ "* ' f\)Q 8 8

T " 8

-TOP OF FIRST PuOCK-ELEV 302 m.

I 3

01

11

of 770°C. Point I denotes the desired temperature of 200°C at furnace elevation 0 i n . , while Point J demotes the ambient temperature of 25°C at furnace elevation -34 i n .

As previously discussed, the thermal cr i t er ia for carbonization of the fuel rods specify a beginning minimum temperature of 30C°C. However, i f the temperature in the uppermost portion of the furnace processing chamber were permitted to exceed 300°C, the gasket used in the charging valve would f a i l . I f the temperature of the surface of the charging valve internal to the processing chamber were allowed to f a l l below 200°C, hydrocarbons would condense out on this surface. The furnace was there­fore designed to provide an axial temperature profi le ranging from 200°C in the upper section up to a maximum temperature of 1800°C in the center section and back down to a temperature of 200°C in the bottom sect ion , with the temperature range up to about 800°C for carbonisation and that between 800 and 1800°C for annealing.

Attainment of the desired axial temperature prof i le within the fur­nace processing chamber, and thus in the fuel elements, is based on the provision of three controlled heating zones, each designed to increase the temperature of a fuel element by a dif fering amount, and three cool­ing zones. Two of the cooling zones are within the furnace processing chamber (above the discharge va lve) , and the third i s the discharge cham­ber below the processing chamber. Completion of the processing of an element in the furnace i s a function of time and temperature in the various zones.

The f i r s t controlled heating zone in the furnace processing chamber below the charging valve, the low-temperature heating cone, i s approxi­mately <>0 in . long and i s heated with metal l ic s tr ip heating elements interspersed with ceramic fiber insulat ion. When f i r s t introduced into the furnace processing chamber, a fuel element wi l l be at h o t - c e l l ambi­ent temperature, which w i l l be about 25°C. Upon leaving the low-temper­ature heating zone and entering the intermediate-temperature heating zone, the fuel element i s expected to have an outer surface temperature of approximately 300 6C. As indicated in Fig. 4 , the temperature of the outer surface of the bottom of the fuel element i s expected to increase from 25°C to 300°C in approximately 26 in . of travel . At 0.375 in . per minute, this would amount to an increase of about A°C per minute.

11

The intermediate-temperature zone in the processing chsaber i s heated by a graphite resistance heater about 22 i n . long that i s sur­rounded with insulat ion. The evolution of v o l a t i l e s from the pitch bond­ing material in the fuel rods (carbonization) w i l l begin at a temperature of about 300°C and w i l l be completed - t a temperature of about 800°C The coke y i e ld , matrix-particle interact ion, and resul t ing quality of the rods in each element are dependent upon the heating rate in the carbonization range (300 to 800*C). The c r i t i c a l heating rate in the intermediate tem­perature zone must be maintained at near 108C per minute, and carboniza­tion i s expected to be completed when the fuel element leaves th is heat­ing zone with a surface temperature of about 800°C.

A fuel element leaving the intermediate-temperature zone enters the third (high-temperature) heating zone wherein the fuel rods are annealed in place in the element. A graphite resistance heating element about 43.5 i n . long surrounded with insulat ion i s used in the high-temperature zone to attain the maximum element surface temperature of 1300°C required to remove the las t traces of v o l a t i l e s and produce dimensionally stable fuel rods. The heating rate in the annealing zone i s not c r i t i c a l . Once the maximum temperature has been reached, the temperature cf the fuel e l e ­ment w i l l be lowered as rapidly as poss ib le . The surface temperature of an elerent i s expected to already have begun f a l l i n g from the 1800°C max­imum as the element leaves the high-temperature heating zone and enters the hi^h-temperature cooling zone.

Graphite i s used in the high-tempsrature cooling zone, which i s about 26 in . long, to conduct heat to the water-cooled surface of the processing chamber, thereby reducing the temperature of the fuel elcnent as i t pro­gresses through the zone. I t i s estimated that the temperature of an e l e ­ment wi l l be about 1060°C as i t leaves the f i r s t cooling zone and enters the second or low-temperature cooling zone. The water-cooled surface cf the chamber i s in close proximity to a fuel element as i t progresses through the 50-in. long low-temperature cooling zone. I t i s estimated that the surface temperature of the fuel element w i l l be between 200 and A00°C as the element leaves the low-temperature cooling zone and enters the discharge chamber, which serves as the f inal cooling zone. The tem­perature of the element i s expected to be reduced to at least 200°C during the time i t i s retained in the discharge chamber prior to unloading.

13

The radial thermal gradient in the column of fuel elements w i l l a lso vary along the verti-stl length of the furnace- The radial gradieut i s expected to be at a minimum in t i e center of the column of fuel elements at mid-cycle. At the top of the column, the temperature at the center of an element should be l e s s than that at the outer surface, while the temperature at the center i s expected to be higher than that at the sur­face of an element at the bottom of the column. The tenperature of the outer surface of an element in the intermediate-temperature heating zone, wherein carbonization takes place, i s expected to be s l i g h t l y higher than that at the center of the element. This means that the surface cf an element subjected to the "crit ical-zone" temperature increase w i l l reach the desired 800°C temperature sooner than the center of an element. I t i s estimated that the temperature lag w i l l be l ess than 50°C.

14

4 . ENERGY TRANSPORT SIMULATION IN THE MOVING COLUMN

The basic problem in performing a thermal analys is of the furnace design was to determine how the heating and cooling should be distributed in the moving column cf fuel elements to achieve a Gaussian temperature profi le along the axis of the column. In a simple analogy, the colurn of fuel elements and spacer p a l l e t s can be thought of as a rod. If the rod were stationary, i t could be heated at i t s mid-point with a s ingle heat­ing zone and cooled at both ends to achieve the desired axial temperature prof i l e . The heaters would be insulated on the outside to curtai l heat l o s se s . However, when the rod i s moving, more heat must be added in the heating zone to account for the heat absorbed by the moving mass and more cooling must be provided in the downstream cooling zone to account for the heat released by that mass.

The material properties of the graphite spacer pa l l e t s were assumed to be th'i same as those of the fuel elements. On the basis of an average element weight of 295 lb and an assumed pal let weight of 40 l b , the column of elements and p a l l e t s in the furnace wi l l weigh approximately 10.08 lb per linear inch. At an average mass flow rate of 3/8 in . per minute, the furnace w i l l process 3.78 lb of graphite a minute but only about 887. of this weight w i l l be comprised of element material .

If a mean value of 0.33 Btu/lb-°F i s assumed as the spec i f ic heat of the moving column of graphite in the furnace, about 70 kW of power wi l l be required to provide the heat absorbed by th is mass movement. Continu-irg the simplified analogy, heat would be los t at both ends of the moving rod by conduction. This would amount to about 5 kW at the top and about 4.7 kW at the bottom. To t h i s , heat must also be added to account for that lost by the heaters through the furnace insulat ion . This radial heat loss was estimated at about 10 kW- Thus, a rough estimate of the total power required for the furnace i s about 90 kW- These estimated values indicate that the axial heat loss result ing from mass flow w i l l be about seven times the loss from conduction and about 77.87,, of the total heat input. Simulation of the mass movcner.t is therefore quite important in obtaining a r e a l i s t i c solution to a stesdy-state analysis of the furnace.

15

Determination of Volumetric Heat Generation Rate

The amount of heat required to account for that given up or lost by the mass movement of graphite elements and p a l l e t s through the furnace was determined by evaluating an internal heat generation rate duplicating the mass flow l o s s . A negative heat generation rate was applied at the top of the furnace above elevation 81.0 i n . , and a pos i t ive heat genera­t ion rate was used below this elevation for both the top- and bottom-loaded configurations i l lus tra ted in Fig. 3 .

Argon gas i s to be introduced at the bottom of the furnace at an up­ward flow rate of 7.0 scfm and a temperature of 25°C. A flow of 5.0 scfm w i l l be maintained through the fuel element coolant channels via d i s t r i ­bution channels machined in the horizontal surfaces of the spacer p a l l e t s . The remaining 2.0 scfm of argon wi l l flow through the annular space between the column of fuel elements and the furnace processing chamber l iner . A total of about 6 scfm of argon gas w i l l be in contact with the elements, and the total heat capacity of the flowing gas i s about 4.35 kW. The gas w i l l be moving at an average ve loc i ty of about C.333 f t per second w- h a mass flow rate of 0.6204 lb/minute and a mass ve loc i ty of 122 l b / h i u r - f t 2 . The result ing heat transfer coeff ic ient i s l e ss than 2.0 B t u / h r - f t 2 . ° F , and th is l imits the mean difference betwee-i the temperature of the ar&on gas and the fuel elements to about 25"Z. Since the direction of the gas movement in the furnace w i l l be opposite that of the elements, the heat from the argon mass flow was subtracted. Instaad of acting as a heat sink, the gas w i l l act as a distributor of heat. As for the fuel element movement, the volumetric heat generation rate at each increment wi l l pro vide for the heat transport associated with the flow of argon gas.

The equation used to determine the net incremental volumetric heat generation rate i s as follows.

q / ' - (0Wt - QA^//^ , (4.1)

where q,'" = net incremental volumetric heat generation rate, Btu/min- in . 3 ,

QW, = heat input per unit length from mass movement of fuel elements, ^cu/min-in.,

16

QA. • hea t input per un i t length from mass flow of argon gas , Btu /min- in . , and

A = c r o s s - s e c t i o n a l area 01 fuel element • 173.93 i n . 2 / i n . x The heat input r e s u l t i n g from the ma'? movement of fuel elements

QWt = WC (dT/dz), - (4 .2) o o

where V = mass flow rate of fuel elements = 3.78 lb/min,

O

C = spec i f i c hea t of un i r rad ia ted ^uei z~. dent composites = f ( f ) Btu / lb -°F

where T = mean temperature of increment in °F, and (dT/dz) , = incremental ax i a l thermal g rad ien t in fuel elements

- f 2 ( z ) = d ( T / r ) i . The incremental ax i a l thermal gradients were determined from data i l l u s ­t ra ted in F ig s . A. l and A.2 in Appendix A for the top-loaded furnace con­f igura t ion and F igs . A.8 and A.9 for the bottom-loaded conf igura t ion . These f igures show modified p r o f i l e s of the temperature d i s t r i b u t i o n on the surface of the column of graphi te elements and p a l l e t s in the top-and bottom-loaded furnace conf igura t ions . The des i red temperature pro­f i l e i l l u s t r a t e d in F ig . 4 was used as a guide for these curves . Since i n f l e c t i ons cannot be obtained in a r ea l system, smooth functions were used to generate the more r e a l i s t i c temperature c r i t e r i a p r o f i l e s shown in F igs . A . l , A.2, A.8, and A.9. These p r o f i l e s were broken dcwn in to polynomial functions of the s ix th order or l e s s , and i t was a simple mat­t e r to obta in the d e r i v a t i v e s of '.he functions to evalua te the desired incremental q u a n t i t i e s .

The heat input r e s u l t i n g from the mass flow of argon gas QAi - W f l C a (dT/dz) t , (4 .3)

where W - mass flow r a t e of argon gas = 0.607 lb/minute and

a C » spec i f i c heat of argon gas = 0.125 Btu / lb - °F .

17

Heat Balance in Graphite Column

A heat balance was made on incremental sections of the column of fuel elements ard spacer pallets as encountered in the furnace. The heat inputs from the first and last increments wer» obtained from the prevail­ing boundary conditions- The heat entering the second increment by the process of conduction and mass flow of both the graphite and argon was subtracted from the summation for the first increment. The difference is the result of either an external heat input or rejection, depending on the sign. Successive summations were made over the complete range of the fuel elements to obtain the net external heat requirements.

An attempt to perform this heat balance manually by using rather large increments caused anomalies in the plots. The calculations were programmed and processed on the computer with much better results. Dif­ferent heating and cooling rates resulted from not including the heat lost from the heaters through external surfaces of the furnace in the calculations. The difference between the heating and cooling require­ments provides a rough estimate of this loss.

The incremental heat input per unit length from external sources resulting from conduction in the axial direction

QXi = ( Q C i + 1 / 2 - Qq.i/^/dz. , (4.4)

where Q C J + J / 2 - heat flow across increment by conduction

= -k £V<*T/dz) i + 1, 2,

Q C i - i / 2 ^ - k g A x ( d T / d 2 ) i - i / 2 ' a n d

k = axial thermal conduct iv i ty of spec i f ied fuel element 8 composite, Btu/min-f t -°F.

The~efore,

QXi = - k g A x [ ( d T / d z ) i + 1 - ( d T / d z ) i _ x VdZi

= - k g A x ( d 2 T / d z 2 ) . . (4.5)

The equat ions used to perform the heat balance expressed the t o t a l

heat per un i t length (QT) supplied to each increment( i ) from an ex te rna l

source ".$ fol lows.

18

QT± - QWi + QXt ~ QA± . (4 .6)

The pe r t i nen t q u a n t i t i e s were ca l cu la t ed for each increment of the to,*-and bottom-loaded configurat ions ot the furnace. The r e s u l t s for fuel element u n i t s or composites fabr ica ted from H-327 graphi te as ? function of a x i a l pos i t i on in the furnace for the top-loaded configurat ion are given i n Table A-l of Appendix A, and those for the bottom-loaded config­u r a t i o n are given in Table A.2. Comparable data for fuel element compos­i t e s fabr ica ted from H-451 graphi te are given in Tables B. l and B.2 in Appendix B.

A graphics subroutine was w r i t t e n to p lo t the output da ta , and the r e s u l t i n g p l o t s for the fuel element composites fabr ica ted from H-327 graphi te are shown in Appendix A. The ax ia l hea t t r a n s f e r r e s u l t i n g from the mass flow of fuel elements i s shown in F ig . A.3 , t ha t from conduction in fuel elements i s shown in F ig . A.4, and the ax ia l heat t r ans fe r from the mass flow of argo~> gas i s shown in F ig . A.5. The sum of the heat input by a l l mechanisms i s shown in F ig . A.6, which gives a good idea of the power d i s t r i b u t i o n required to produce the desired temperature d i s ­t r i b u t i o n . The composite ax ia l power d i s t r i b u t i o n for the top-loaded furnace configurat ion i s shown i n F ig . A.7- Comparable data for the bottom-loaded configurat ion are shown i n F igs . A.10 through A. 14.

The i n t e r n a l volumetric heat generat ion r a t e required for s imulat ion of the mass movement of fuel elements fabr ica ted from H-327 graphi te i s i l l u s t r a t e d in Fig. 5 for the top-loaded furnace conf igurat ion and in F ig . 6 for the bottom-loaded configurat ion- se data are required as

input to the HEATING4 computer prograir. used to analyze the thermal design of the furnace. Tabular functions were used to put the data in the pro­gram to produce the desired i n t e r n a l heat generat ion for the s t eady- s t a t e a n a l y s i s . I t should be noted that simulation of the mass flow of mater ia l using i n t e r n a l heat generation causes a r ad ia l gradient in the fuel e l e ­ments tha t r e a l l y i s not supposed to be presen t . This gradient amounts to about 100°C a t the point of maximum heat generat ion and p r a c t i c a l l y nothing at the ends of the column of fuel elements and p a l l e t s - There­fore , only the temperatures a t the ou te r surfaces of the fuel elements were used for temperature comparisons-

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21

5. HEAT TRANSFER MODELS AND BOUNDARY CONDITIONS

The mathematical heat transfer models used in the computer analysis of the thermal design for the HTGR fuel element carbonizing and annealing furnace were formulated from the actual furnace design and the operational diagram i l lus tra ted in Fig . 3 . Two furnace heat transfer s«dels were made: one for the top-loaded configuration md the other for the b.>ttoo-loaded configuration. The top-loaded model, shown In Figs. 7, 8, and ?, contains 1005 nodes ganerated from 77 regions. (A node i s generated at the Intersection of b i l a t e r a l grid l i n e s . ) The column of fuel elements and spacer pa l l e t s extends from about furnace e levat ion 202 in . downward to e levation 0.0 i n . in the top-loaded model.

The bottom-leaded model, shown in Figs . 10, 8 , and 11, contains 1036 nodes generated by 76 regions. In th is model, the column of elements and pa l l e t s extends from furnace elevation 168 In. downward to about elevation -34 in . This configuration differs from thv» top-loaded one only in the extent to which the column extends into the discharge chamber, with noie column length being exposed to cooling and l e s s to heating.

Both heat transfer models are axisymmetric and cy l indr ica l , with the cross-sect ional area of the modeled cyl indrical fuel element being equal to that of the actual hexagonal element. In both configurations, the col ­umn of elements and pa l l e t s was assumed co be continuous and uniform. The models were divided into regions, and the data for each region included i t s material properties , dimensions, heat generation and i n i t i a l '^mpera-ture functions, and boundary conditions. Twenty-four regions in the heat transfer models were used to depict furnace heaters .

The low-temperature heating zone in the furnace processing chamber i s heated with 16 e l e c t r i c s tr ip heaters, and the regions In the models representing these heaters ware programmed individually for internal heat generation. To keep the temperature of the bottom 3urface of the charging valve at the top of the chamber from fa l l ing below 200°C, the region depicting the valve gate was programmed with internal heat generation representing a heater.

Both the intermediate- and high-temperature heating zones in the furnace processing chamber are heated e l e c t r i c a l l y with individual, three

22

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25

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27

phase, delta-connected graphite heaters supplied by individual c i r c u i t s . In the heat transfer models, the two graphite heaters are shown in seven regions of internal heat generation. The upper heater, supplying the intermediate-temperature zone, i s represented in the models by two regions; while the lower heater, supplying the high-temperature heating zone, i s represented by f ive regions. These regions were based on variations in the cross-sect ional area of the heater conductor. Theoretical ly, i t prob­ably would have been better to have used seven separate heaters with indi­vidual controls, but bscause of space l imitations and corplexity , the cower supply to th i s area of the furnace was limited to two c i rcu i t s (one for each heater) . This means that power cannot be increased in one region of a heater without increasing i t proportionately in a l l other regions of the heater supplied by the same c i r c u i t . The cross-sect ional area of the conductor can be changed to vary the power distr ibut ion in the dif ferent regions of a heater only within certain l imits based on the strength of the graphite.

Several ordes o f heat transfer at the furnace boundaries were accounted for in the thermal analys is . Internal heat was expected to be radiated to the bottom surface of the charging va l /e at the top of the furnace chamber, and as previously < .ssed, th is surface was assumed to be held at a constant temperature of 200°C. Internal heat i s expected to be transferred by forced convection to cooling surfaces , and i t was assumed that these surfaces could be maintained at a constant temperature by using water-cooled p l a t e s . The column of graphite elements and pa l l e t s w i l l be cooled d irec t ly along a water-cooled surface length of about 86 i n . in the furnace bottom-loaded configuration. The average heat flux in th is con­figuration i s expected to amount to about 7000 B t u / h r - f t 2 , which i s normal for this type of cool ing.

In the furnace top-loaded configuration, the d i rec t ly cooled length i s reduced to about 52 in . In this configuration, the average heat flux i s expected to be about 14,000 Btu/hr-f t 2 at the beginning of the cycle and about 5300 Btu/hr- f t 2 at the end of the cycle -ihen power to the upper (low-temperature) heaters has been reduced. The maximum internal temper­ature of about 1800°C i s expected to be reached at a furnace elevation of about 81 in . Because of the furnace insulat ion, the heat flux on the

28

cooling surface at that location is expected to be about 8000 Btv/hr-ft2. The maximum heat flux on the cooling surface is expected at a furnace ele­vation of about 51.75 in. where the surface is expected to experience tem­peratures of 700 to 1000°C, resulting in radiant heat fluxes as high as 40,000 Btu/hr-ft2.

The difference in these estimated heat fluxes indicates that cooling could be a problem, and it is imperative that the radiation heat exchange to the cooling surfaces be increased as much as possible. To promote radi­ant heat exchange with the graphite, it was assumed that all interior metal cooling surfaces of the furnace were coated with "Japon" black, which is a commercially available blacking paint that will withstand tem­peratures as high as those that can be withstood by the metal it covers. For the thermal analysis, a constant boundary condition teirperature of 25°C was assumed for all water-cooled surfaces. The furnace elevator platform that supports the column of graphite elements and pallets was also assumed to have a constant temperature of 25°C by virtue of cooling.

Heat transfer across the furnace annuli or gaps is expected to be by conduction, convection, and radiation with the shape factors varying from 0.5 to 0.75. All interior argon gas gaps adjacent to the column of fuel elements and spacers have a total spectral emissivity of 0.8, and the shape factor was determined for infinitely long concentric cylinders. Gas radiation is not a factor in the transfer of heat inasmuch as argon is not a rerhdiating gas. However, the argon must be kept free of moisture because of the reradiation properties of water vapor as well as the pos­sibility of a chemical reaction with the graphite. It was assumed that the volatiles produced during carbonization would have no reradiation effects. The net result would be a slight decrease in the efficiency of the furnac>>. Radiation in the coolant holes of the fuel elements and pallet9 was accounted for in the calculated anisotropic conductivity of the graphite.

Heat transfer from the exterior surfaces of the furnace is expected to be by combined natural convection and radiation to the surrounding atmosphere- An emissivity of 0.6 was assumed for pll external surfaces cf the furnace.

6. HATERIAL PROPERTIES USED IN THERMAL ANALYSIS

In a steady-state thermal analysis , the physical property of primary concern i s the thermal conductivity of the materials involved. The ther­mal conductivit ies of the twelve material conditions involved in the fur­nace analysis are given in Tables 1 and 2. The three materials given in Table 1 are anisotropic. At a given temperature, the thermal conductiv­i t y of such a material i n the axial direct ion i s different from that in the radial d irect ion . As indicated in Figs- 7, 9 , and 10, material num­ber one in Table 1 (HLM graphite) was used as a l iner material in the furnace, and the thermal conductivity data given for this material were obtained from prror investigations**- Material 3 , Fiberform insulat ion, was used as a primary insulating material in the furnace, and i t s thermal conductivit ies were obtained from manufacturer's data- 3

The thermal conductivit ies of the fuel element composite, material 2 in Table 1, were developed by using formulations set forth in Ref- 4. The conductivit ies developed and given in Table 1 are based on the use of a fuel block fabricated from unirradiated needle-coke (H-327) graphite as manufactured by the Great Lakes Carbon Comp.my. The total cross-sectional area of the hexagonal graphite prism used for the reference Fort St . Vrain fuel element i s 173.93 i n . 2 To calculate the thermal conductivit ies of the reference fuel elements in the furnace, i t was estimated that 56.95X of the total cross-sect ional area of an element i s comprised of graphite. 24.38% i s comprised of fuel ho le s , and 18.677. i s comprised of voids or coolant holes- These coolant holes wi l l be f i l l e d with argon gas at atmospheric pressure when the fuel element i s being nrocessed in the carbonizing and annealing furnace, and they wi l l be f i l l e d with helium gas under pressure when the element i s in the reactor. However, the intended contents of the coolant holes wi l l have l i t t l e or no ef fect on the thermal conductivit ies of the fuel element composite-

The relationships required to calculate the axial and radial thermal conductivit ies of tne fuel element composite as a function of temperature were programmed for the computer. Essent ia l ly , these relationships are as follows. The axi?l thermal conductivity of tiie fuel element was

30

Teble 1. Thermal Conductivities of Anisotropic Materials Used in Furnace Analysis

Temper­ Conduct iv i ty in Material ature

(°F) Btu/ min-• i n . - ° F Ref.

No. Name ature (°F) Radial Axia l No.

1 Hlh 0 0.08189 0.11940 2 Graphi te 500

1000 1500 2000 2500 3000 3500 4000 4500 5000

0.06250 0.05000 0.04100 0.03430 0 .02920 0.02630 0-02390 0 .02220 0.02110 0.02060

0.09780 0.07080 0.05900 0.04860 0-04160 0.03740 0.03400 0.03190 0.03050 0-02960

2 Fuel 0 0.04429 0.10770 4 Element 200 0.03857 0.09167 &

400 600 800

10C0 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4200 4400 4600 4800

0 .03420 0.03104 0.02893 0.02767 0.02703 0.02678 0.02670 0.02664 0.02653 0.02634 0.02607 0.02573 0.02535 0 .02494 0.02448 0.02400 0.02348 0 02292 0.02233 0 .02170 0.02105 0 .02040 0.01979

0.07859 0.06798 0.05942 0.05255 0.04705 0.04267 0.03919 0.0364? 0.0J423 0.03250 0.03116 0.03013 0.02938 0.02888 0.02861 0.02856 0.02871 0.02905 0.02956 0 . 0 : J 2 0 0.03094 0.03168 0.03236

5

3 Fiberform 0 3 .472 E- 5 1.042 E- 4 3 I n s u l a t i o n 800 6.944 E- 5 1.944 E-•4

1300 8.681 E- 5 2.292 E-•4 1700 i . I S 7 E- 4 2.720 „-•4 2000 1.505 E- 4 3 .472 E-•4 2500 2.315 E- 4 4 .051 E- 4 3000 2.697 E- 4 4 .919 E-•4 3500 3.669 E- 4 6 .076 E-•4 4000 5.208 E- 4 9.838 E- 4

31

Table 2. Thermal Conductivity of Isotropic Mate­rials Used in Furnace Analysis

Temper­Material ature

(°F) Conductivity Ref.

No. Name ature (°F) (Btu/min-in.-"F) No.

5 Fiberfrax-H 0 0.00002315 6 500 0.00004630 1000 0.00009028 1500 0.00014470 2C00 0.00021060 2500 0.00030210 3000 0.00036460 3500 0.00043400

6 Modified 0 0.001260 Stainless 1000 0.001420 Steel 1800 0.001530

7 Argon 0 0.00001250 9 400 0.00002000 800 0.00002640 1200 0.00003330 1600 0.00003820 2000 0.00004170 2400 0.00004510 2800 0.0000486C 3200 0.00005130 3600 O.OOOC5550 4000 0.00005830 4400 0.00006250 4800 0.00006520 5200 0.00006670

9 Strip 0 0.3330 Heaters

11 Electrode 0 0.10560 7 Grade 200 0.09310 Graphite 400 0.08330

600 0.07500 800 0-06810 1000 0-06110 1200 0.05560 1400 0.05000 1600 0.04610 1800 o.owio 2200 0.03860 2800 0.03470 3200 0.031<>0 1632 0.030i0 4532 0.02780 5432 0.02640

1?

Table 2 (continued) Temper­

Material ature (°r,

Conductivity (P tu /min • in. • C F )

Ref. No. Name

ature (°r,

Conductivity (P tu /min • in. • C F ) No.

12 Type 304 0 0.01260 8 Stainless 1000 0.01420 Steel iSOO 0.01530

14 Poious 0 0.001290 7 Carbon 5000 0.007640

17 Argon-3 0 0-00010400 9 500 0.00007180 &

1000 1500 2000 2500 3000 3500

0.00006270 0.00006040 0.00006580 0.00007430 0.00C08330 0.00009030

10

18 Argon-4 0 0.00012300 9 500 0.00008790 & 1000 1500 200C 2500 3000 3500

0.00007160 0.00006900 0-00006780 0.00007430 0-00008330 0.00009030

10

calcula ted by using the following e q u a t i o n . 4

K = Ak + Bk r + Ck , a g f r

where

(6.1)

K = the ax i a l thermal conduct iv i ty of the fuel element corpos i te as a function of temperature, B tu /h r - f t • °F ,

A = r a t i o of c ros s - sec t iona l area of grapr.tte (G) in i n . 2 to t o t a l c ros s - sec t iona l area of fuel element composite (Z) = G/Z

= 99.053/173.93 = 0-5695, k = the ax i a l thermal conduct iv i ty zs a function of temperature of

the p a r t i c u l a r graphi te used in the fuel element, Btu/hr-ft-""F, B = r a t i o of c ros s - sec t iona l area of fuel holes (F) in i n . 2 to t o t a l

c ros s - sec t iona l area of fuel element composite (Z) = F/Z = 42.404/173.93 = 0.2438,

33

k f = thermal conductivity of the fuel rods * a constant 3.0 Btu/hr-ft-°F,

C *• rat io of cross-sect ional area of coolant holes (V) in i n . 2 to to ta l cross-sect ional area of fuel element composite (Z) = V/Z

= 32.473/173.93 = 0.1S67, and k = net equivalent thermal conductivity result ing from radiation

across the coolant ho l e s , Btu/hr-ft-"F .

The axial thermal conduct ivi t ies as a function of temperature (k„) used in Eq. 6-1 for the H-327 graphite were those reported by Fr ice s for the unirradiated material . The net equivalent thermal conductivity result ing from radiation across t\e coolant holes in the reference fuel element i s given by the following equation- 4

k r = (0.444 X 108)CT€dT3 , (6.2)

where cr = Stefan-Boltzmann constant

= 0.171 X 10"" B t u / h r - f t 2 - ° R 4 , e = emissivify of graphite = 0 . 8 , d = diameter of coolant hole = 0.625 i n . , and T = TR/1000

where TR = mean temperature of fuel element, "R.

The algorithm used to calculate the radial thermal conductivity (K r) of the composite fuel element in Btu/hr-ft-°F is as fo l lows . 4

1 + C2T/Kg [ (C 4 + k g / k f ) / ( C 6 + k g / k f ) ] K r » ( C l V l ^ C 3 T / k g [ ( C 5 + k g / k f ) / ( C 6 + k g / k f , ]

where k = radial thermal conductivity as a function of temperature

of the particular graphite used in the fuel element compos­ite, Btu/hr-ft-°F,

T = TR/1000, k f = thermal conductivity of fuel rods = a constant

= 3.0 Btu/hr.ft-'F, and C g = constats whose values are defined4 as C = 0.360,

34

C = 0 . 5 2 2 ,

C = 2-500, 3

C4 = A.1W, C = 1.200, and C = 8.700 .

6

The axial and r ad i a l thermal conduc t iv i t i es and spec i f i c hea t of r e i e r en t s fuel elements fabricated from uni r rad ia ted H-327 graphit*. were computed as a function of temperature, and the r e su l t ing output for tem­peratures frcm zero to 5000 oF are given in Table C.l of Appendix C. The computed conductivi ty data are i l l u s t r a t e d as a function ot temperature in Fig. C.l (Appendix C). The thermal conduct iv i t ies and spec i f i c h»ats wero also computed for reference fuel elements fabr icated from u n i r r a d i ­ated H-451 graphi te . The r e s u l t i n g output i s given in Table C.2 of Appendix C, and the thermal conduct ivi ty data are i l l u s t r a t e d in F ig . C.2.

The remaining nine mater ia ls or mater ia l condit ions involved in the s teady»sta te analysis of the furnace thermal design are not a n i s o t r o p i c , and the thermal conduct iv i t ies for these mater ia ls are given i n Table 2. The area between the s t r i p heaters (material 9) was f i l l e d with Fiberf rax-H Fel t (material 5) , which i s a ceramic f iber insu la t ion whose thermal conductivity data were supplied by the manufacturer. 6 The s t r i p h e a t e r s were given r e l a t i v e l y high conduc t iv i t i es to c u r t a i l i n t e r n a l g r a d i e n t s . Electrode-grade graphite (materia) 11) was used as the mate r ia l of con­s t ruc t ion for the graphite hea ters in the intermediate- and high-temper­ature heat ing tones of the furr.ace, and the thermal conduc t iv i t i e s of t h i s material as a function of temperature were also obtained from manu­fac tu re r ' s d a t a . 7 Ttu, thermal conduct ivi ty data for type 304 s t a i n l e s s s t e e l (material 12) used in the analys is were reported by Kim." Those data were modified in some locat ions (mater ial 6) to permit an increase in nodal sp.-.cing and enhance computer running time. For these reasons , s t r i p heater material (material 9) was subs t i tu ted for the th in s t a i n l e s s s t ee l s t r i p connecting the hot i n t e r i o r of the furnace with the water-cooled wall and usee" as an insu la t ion in t e r f ace , thereby increas ing the material thickr.r-ss by a fac tcr of four and reducing the conduct iv i ty by A factor of four.

15

The thermal conduct iv i t ies of the argon gas in the main channel of the furnace (material 7) used in the analysis vere reported in a National Bureau of Standards Circular . 9 Argon-3 (material 17) and argon-4 (mate­r ia l 18) were defined to account for enhanced chermal conductivity result ing from natural convection in a cyl indrical annulus f i l l e d with stagnant gas* This enhanced conductivity i s a function of the Raleigh number and the length-to-diameter rat ios of the <mnuli . 1 0 and materials 17 and 18 we e used in the analysis tc depict different L/D ratios* No allowance *as made for natural convection in the main channel o f the furnace inas­much as the system was designed to curtai ' this phenomenon. Convection in the interior channels of the fuel elements was accounted for in com­puting the anisotropic conductivit ies of the fuel element composite.

36

7. RESULTS OF THERMAL ANALYSIS, CONCLUSIONS, AND RECOMMENDATIONS

The HEATING4 program was run on the IBM ?60/91 computer at ORNL to perform the thermal analysis of the furn&ce design described herei* Like any other general heat transfer computer program, the HEATING4 pro­gram c a l l s for the heat source distribution to be specif ied by the user. Therefore, the i n i t i a l task of the analysis was performance of a lengthy trial-and-error process by which the power distribution for the heaters was estimated and the result ing temperatures were compared with the desired axial temperature profi le in the furnace. This process was dif­f i c u l t and time consuming because of the complex interaction between the various zones of the furnace. The best distribution of heat sources (heaters) and sinks (cooling water) that could be obtained with a reason­able effort was used for the f inal temperature dis tr ibut ion analys i s .

The power input for the top-loaded furnace configuration totaled 101.44 kW. About 2.28 kW were supplied to the s tr ip heaters in the fur­nace low-temperature heating zone in amounts that varied from 286 watts in the last heater to zero watts in the f i r s t heater at the top of the furnace processing chamber. The charging valve at the top of the chamber was supplied with 325 watts of power. The power i r iu t to the graphite heaters in the intermediate- ant! high-temperature heating zones of the furnace totaled 98.83 kW. The distribution of power to the regions in these portions of the furnace was 23.12 kW to graphite heater region 1, 17.82 kW to region 2, 12.86 kW to region 3, 14.34 kW to region 4 , 7.87 kW to region 5, 12.83 kW to region 6, and 9.99 kW to region 7.

The power input used for the bottom-loaded configuration was 96.6 kW. No power was input to the charging valve or the s tr ip heaters , and that input for the graphite heater regions was the same as for the top-loaded configuration except for region 7. In the bottom*loaded configuration, the power input to graphite heater region 7 was reduced to 8.34 kW. Com­puter runs were made using these power dis tr ibut ions , the furnace boundary conditions discussed in Section 5, the internal he«t generation simulating the energy transport result ing from mass movement discussed in Section 4 , and the materials and their conductivit ies given in Section 6. The

37

computed temperature prof i le i s compared with the desired prof i l e for the top-loaded furnace configuration in Fig . 12 and for the bottom-loaded configuration in Fig. 13.

As a resul t cf the thermal analysis described here It., i t vas con­cluded that the furnace design has the potential capabi l i ty of meeting the desired thermal c r i t e r i a . With respect to the power requirements of the furnace, the resul ts of the computer analysis agree c lose ly with those cf the simple mass transfer ca lculat ions . However, those resul ts are only as re l iab le as the thermal transport data used, and the accuracy tolerance assumed for those data was plus or minus 10 to 15%.

The r e s u l t s of the steady-state analysis indicate that the axial temperature prof i le in the furnace i s quite sens i t ive to both the input and dis tr ibut ion of power to the heaters , pc i l i cu lar ly the s tr ip heaters in the upper portion of the furnace processing chamber. I t was concluded that the desired temperature profi le can be obtained by further refinement of the power supply and distribution to the s tr ip heaters . Further, the data i l l u s t r a t e d in Figs . 14 and 15 indicate that temperature prof i l e s that are both higher and lower than the desired prof i le can be obtained by varying the type and thickness of the ins i la t ion used in connection with the s t r i p heaters in the upper portion of the furnace. This capabil­i t y w i l l afford a means of adjusting the temperature prof i l e i f the thenao physical properties of the furnace were e i ther overestimated or under­estimated.

It should be noted that the analysis reported herein was based on a continuous steady-state simulation. In r e a l i t y , there w i l l be a pause of about 10 minutes at the end of every 90-minute cycle for unloading and loading procedures and a new fuel element and pal le t w i l l be introduced into the furnace, result ing in the disturbance of any equilibrium that may h«ve been achieved. Therefore, i t i s recommended that transient thermal analyses of the furnace design be performed to veri fy the results obtained from the steady-state analysis described herein. Transient anal­yses could also be performed to determine the control l imitations neces­sary for safe operation of the furnace by changing the boundary conditions to simulate mechanical fa i lure , loss -of -coo l ing , and loss-of-power conditions.

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42

REFERENCES

1. W. D. Turner and M. Siman-Tov, "HEATTNG3-- An IBM 36C Heat Conduction Program," USAEC Report ORKL TM-3208, Oak Ridge National Laboratory, Oak Ridge, Tennessee, February 1971.

2. V. P. Eatherly, Metals and Ceramics Division, Oak Ridge National Laboratory, personal communication to G- H. Llewellyn, Oak Ridge Nationa" laboratory.

3. "Product Data," Fiber Materials , Inc . , Biddeford Industrial Park, Biddeford, Maine 04005.

4 . Public Service Company of Colorado, page 39 in Section 3 of "Prelim­inary Safety Analysis Report for the Fort St . Vrain Reactor (Docket Number 50-267)."

5. R. J. Price, "Thermal Conductivity of Neutron-Irradiated Reactor Graphites," Report GA-Ai3i57, General Atomic Company, San Diego, California 92133, October 8 , W74.

6. "Product Spec i f i cat ions ," The Carborundum Company, Refractories and Electronics Divis ion, Ceramic Fiber Plant, Niagara F a l l s , New York.

7. "Carbon Products Pocke; Handbook," Union Carbiie Corporation, Carbon Products Division, New York, New York.

8. Choong S. Kim, , ,Thermophysical Properties of Sta in less Steels,"' Report ANL-75-55, Argonne National Laboratory, Argonne, I l l i n o i s , September 1975.

9. Joseph Hilsenrath et aL., Tables of Thermal Properties of Gases. National Bureau of Standards Circular 564, U.S. Gove- .ltnent Printing Office, Washington, D. C , November 1, 1955, Table 3-9, p- 129.

10. E. R. G Eckert and R. M. Drake, J r . , Heat and Mass Transfer, McGraw-Hill Book Company, Inc . , New York, New York, 1959, p. 328.

APPENDICES

45

Appendix A

MASS-FLOW SIMULATION DATA FOR FUEL ELEMENTS FABRICATED FROM H-327 GRAPHITE

9*

i f

48

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HEIGHT OF FURNACE ABOVE LIFTING FORKS - INCHES

Fig. A.4. Axial Heat Transfer From Axial Conduction In Fuel Elements Fabricated From H-327 Graphite as a Function of Their Axial Position in the Furnace for the Top-loaded Configuration.

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Fig. A.14. Composite Axial Power Distribution for Processing Fuel Elements Fabricated From H-327 Graphite as b Function of Their Axial Posit ion in the Furnace for the Bottom-Loaded Configuration.

69

Appendix B

MASS-FLOW SIMULATION DATA FOR FUEL ELEMENTS FABRICATED FROM H - 4 5 1 GRA/HITE

72

C =s » • • • c. *- • O O O O O O O O O O O ^ O O O S O O O O C O O O O O O O O C O O O C O O O O O O O O O O O O O O O O D O O C ^

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ft. m. % »- »

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C\» c o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o c o o o c o o o o o o o o o o o o o o »> » • i i • i • i i i i i i i i i i i t i i i i i i ? i i ; i i i i i i i i i i i i i i i i i t i i i t i i i i i

« E © * | I I > I I | I I I I I I I I t t I I t * I ( I 1 t * 1 I t I I t 1 C I I t t » | I 1 | I | 1 I I | I | I | I

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i * ' « B r « o ^ < * « « " O r i c r o < < r « r 9 r r c * t h * , n i r r . ^ ' r - v - « ^ » ^ ^ - * » - « o m r ^ o * » ' " r * - < N ^ « c

i i t t i t t t i i i i i i i i i i i i i i i i • i i i i i i i i i • i i t i i i i i i i i i i t i • i i i

r^ r * c « « o - * » o > o o o o o o o o o o o o o o o < o o t ^ 9 » 9 « « « f t r * r > > « « t f » * , ' v * * < o * < o « # » i o * - « * r * ~ » o v > « a. wi < K o 4

i t i i i i « t i i i i i • i i i i i i t i i i i i i f i t i i i • i i i i i i i i i i i i i i t < i i i

& & c a & a o o o o o o © ^o i o O o o ^ o o o o o o c o o o O o o o o o o o o o o o o o o •> o o o o o <_» o w - 0 < J t J « J O O O O O O O O ' J O O C > 0 » 3 0 0 0 0 v - » 0 0 0 0 0 ' ^ O t - > U O O C ' 0 * - » O t J O O O t ^ O O ' , J W O ^ O O v > « * » - > 0 0 0 - 3 0 0 0 ' : • » I* •?-T*«r*^»^'?'-^^»^*»-« iro-'N^»^^

73

o. t - • o s o o s s o o s o o f t s s c s s c c D o o o a o o s o s a s ^ s o c o s c o s s c i s s c

O • • r « o ^ * » i - ' T * " ' ^ * * f , » ' " " * - * ! » * ^ - * ' 0 ' 4 , ^ « , v » ^ f f c « w o o ^ * s P H , * « « ^ ^ « « ^ * T ^ x « « » k '

B • • O O O O O O O O O O O O O C O O J C O O S O C O O C C o O O O O O O O O C O O O O O O O C M r * xv.» o c o o o o o o c o c o o o o c - o o o c s o o o c s a o o o c c o o o o o o o o o o o o c »• B •

a u * ri^«r*ir^J«3«^cr*^*«*^»*r>«p^««Kc«4jr«oo»oo* p<^-»"6*»r f cOO»ixf f cf ,to* k'r^ ,o** •> B • «t- • I I I I I I I I I I I I I I I I I c «c •

I I I I w "• ~- •• — I I I t I

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c • • " » r ^ « B i » i M » - » - o r ' B r ~ r ' « « - « m ™ i N - - o » - » , x r - f - * « « < ' * ' « » ^ * " » * > « B B « ' T < i » - < u • ^ N « « N « N i < i r m ' » ' » » » » • - • - • - • - ^ . - o e o o o o o o o o o e o o o o o c o o o o o • • o o e o o o o o o e c o o o e o o o o e c o o o o o o o o o o o o c o c o o o o o o o o o

J B * • • C V # o o o c o o o e o o o o o o o o o G o o o o o © o o c o o o © o o e o o o c o o o o o o o •» B * l l l l l l l l l l l l l l l l l l l l l l l l l l l f l l l l l l l t l l l l l t l l l

C B • « a - N « - » - « « > ^ r « - « r ~ e > i s < r c n B o e < ' « - o * > n ) » < M « < v ' - < o i n O B « . a > r < i e « « - i n B f ^

B W * * » . - * » ' < ' » « « « « » « « C > l l " « » l f > B M « I H N N C > l » > - » » ' - » - » » ' » - » > - ^ « - ^ 0 0 0 -C K * o \ * o o o o o o o o e o o o o c o o o o o o c o o o o o o o o o o o o o o e o o o o o o o c c B O « I I I I I I I I I I I T I | I | I I I I I | I I | I I | I I I | | I | I I | I I | I I I I M B *

« M • ^ © ^ • • ' • > J > « r - c * > • © « « ) < j r « " ( r * B ^ ^ o * 9 » c . c ~ r - < e . " ' i o i > i i > , « o r - ~ T « » ' * > a > ^ r - o r i > M » • r ~ B * ) « « B « » ^ » - r « r ' r « m o r * o s i Q o ^ ' B O v ' i « r « * " 0 > s * > « r ' f r i r | « r f « > r ~ « n * 9 a > ^ < 0 * r > * i r

i - i * « r - » « , » r - i » i O B « 5 ^ . B > « » » - f « > " * ) ^ ' * « « < r « r » f x o B O B ^ » r - < ' B ^ M m r f < « r « c r ' r - o r » O B * • O o • "• <jm •

O H I • o t ^ * ^ B « r > B W « « i r > f e * > « > * 9 ' o r « o c > c . ^ « > n m r ^ n « « r < i * > r ^ * " o « » ( > f > - « r - v > ^ r < m a •«« • m « © r " © * > m « > * > o > r « * , * « * « > ~ ^ « f c f , * ' © r * » > * « * * » * > B ' B ^ » r ' . ^ B f > § B r f ' © B ^ » » ' m © » « • . a * r * « » * > * ' K i * * ^ B r < r * ' » i B r . B > i M r » ^ » B M « ^ * c » o * ^ B « ; B ~ ' * " ' . o r > « r « O B . o r 4 r * » v " f N « B I B * « D « I l l l l l l l l l l l l i c i l l l l l l * l l l 1 | - | l t l l t l l | « l l l 1 1 l X B •

» « * . . . . • • . • . . . . . . . . . . . . . . . > . . . . . . . . . . . . . . . . . . . . . O * . • B ^ r > r - « « < c « « < r * > ^ « - * ^ t f ' B a > a > B « f n » m f n t M r M r i r « i N ' N > N ^ ^ « ' - - ' - » " ' ^ ' ' ^ ' ^ o o r > >

• • t i i i t I I i i t i i i i i i i i I i i • i i i i i i i i i i i i i i i i i i i i i i ^ en • K U * to *a • H O *

M ** « e > o > * * ^ ~ - * » « * N B r ' « r f * « i - B > B o * . - r ' O o * « » * e * B B B - ^ r < « » N c r i N © K * B « . > * . f i © > f n - - ^ i n » © r * 3 W * . . . >

»>L>* » » O * I | I » < , » • • " - • * ' r « » « > " ^ B « B P < O B « « > " ' r < ^ » ' « r - » i r , » m f > « ^ o » « r - r ~ ' « » • > • > • ~ — ~ ~ — X t» • t i • ) • t> o •

u a * * B B B ^ o r « i ^ r . r * B * a * o B ^ » r < i ^ « ^ © ^ • » a r » # * \ r f " ^ a ' 0 , , ^ ^ r ^ ' " c « < ™ i B » r f f ^ - r - » ^ * r * B B * i v e > ^ , r - r - o * * * ' o > r * , c r - © * ^ " B « B © B O B O h ' > < r * * ^ i r * i * ^ o r ^ » c ^ r * B O f > < » « o * c > » p - r > i o © 4 O B * * - • » * r- B . w < » f l o o « * « ^ ' , < c ^ r N * ^ f f « n f « n o B < n ^ » f ' i r j M O « « * ' n f « i ^ o e m * B ^ , ^ ' , » " 0 0 » 0 ' B r - r ' * * * - * ^ » » * ^ ' ^ r > t r « r * » ' ^ - ^ ' » - % p o , ' , s © ^ c r o * o » o » c s B * j B O S < ' « B r *

X O • fcj »• • f-t kl •

tn • o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o M • O O O U O W O O w w o O O ( - > O O O O Q < ^ O Q O O O ~ > O C . U t - > 0 0 0 0 0 0 0 0 0 ^ < ^ O O C : > u * n * . • • . • . • • . . • . . • . • . . . . . . • • * . • • • • . • • . • • . • . • . • . . , a M • r ^ x » » ' © ^ - r M ^ * > r f N ^ r * B O * o ^ ' * # ^ * , i r * r * « o * o ^ " ' N ' ^ » r > * r ^ B » ' 0 — ^ * ^ » i r « r » » ^ o » M X * 1 / ^ ^ r f ^ * % c ^ ^ ' « * i « * x ^ o r » ^ > r * ' K ^ r f c f ^ f ^ r ^ r ^ * » a o » B c x a R * 5 » « ? B O > » * 1 » a * o , ' * » » * » y © o t - j * — — "• — - — — - — - — — - — - — . - — . . - — . . ^ . . _ . . _ _ — _ _ — . - — - — — .- — - - - - - , -< w a • a .

75

M • • f*J*^^^«"*;?~^« ,*X<Xr«'./':M#*,rO*»»'*.r»ah-'' ,">.»'0»<>*t0.r:3» !"•"* — ^ • 3 3 - r ^ » 3 * « » 3 » - * - 3 * . - » -

O X * » • » • • • » • » » » » • » « » * * » » • » » * » * » . » * * • • • * » • - » » » # * » » » » » » » » » » ' * ' ' • * ••"^ U O f • » • # » • . # • • » • • • • % * • » • » » * • • • • • » • • • • * • • • • • • • • • • • » • • • • * * • » • m c •

O * • «-x;*^*i^rt**^«^~^~~^^ m*^r*e^^.P^y~~«B©?H^^f^»©f*->*<nf f cx^'0:***»rf''*x*-^***'»»

B * • 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 C 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C O O O C O O O C 3 D O O O O M E * . . . . . . . . . . . . . . . » . • • • • • , . . . • • • . • • • * • • • • . . . • X X * £_ O O O O O O O O O C O O O O O O O O O O O O O O O O O O O O O O O O o O O O O C O O O O O O = > O o C C O O O *- B •

*. x • ^ r * ^ o ^ * ' X t ^ ^ ^ , « » ^ ^ ^ ^ » ^ t f * x r * r k « x r f c « p f > i ^ » * * r - » i ^ o * 3 » ^ ^ » B * " a * » , * i * , » ' N r * * - x ^ - » c © C B » . . . . « • • • • * - • • • •

« ** • cO*-^r*-*imr*^' i«-r«r-*3»**-^r<imf* *^*f-p |<mm^'»*v*7»***.»BB*«**?*?«*«B****' pt^ >' vt** fr*fri* mr*i»- • i i • i^.»-«~»-*.-.»-^>»-~-,-..-«-^-^..- ,-«-«~,».-^.~.-.- — .- — — —•- — — — « — .- .- .-C * • | | | l | | t ! ! l l t l t : t l l ! | l l | l ! I T | | | | | l | l | f l > * * B *

O M * o » o * » * , ^ o * * - N l ^ o * - » ^ , ' 0 > o ^ » » f f c * 3 » r * ^ o * - ^ * ^ ' 0 0 * B * c » r t « - » r « » » - » * * r , e ' * © ' * - r ' r " O f l C « ^ * - o i K * ^ r « * o o * » ^ * 3 ^ « « ^ ^ r « « * > » w r ^ r i O > « ^ f ^ » r w * ) « ^ f * « » * ^ ^ o o i ^ ^ ( r f » t * « - ^ ^ * r f > * - * f > i « D f f ' r - o i f « i ^ » ^ ^ » ^

-J X • • » • * • • • • « • • • • • • • • • • • • • * • • • • • • - • • • • • • • • • • • • • • • * • • C X * O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O G O O O O O O » • • ! I , 1 I I I I I I I I I I • I I I I I I I • I I I I I • I I I 1 I I I I > I I I •

* > • • € H ^ - « « » r « - ^ » r « < » ^ » e - r - * > o ^ r k r t * * 3 0 « * « * ; * o * « ^ * r « r » * > O B ' t f t o r . r * £ ^ e k * » e r * f - * « « t f > n t w . C O > M K < R »« • v - o r - ^ - * * N ^ B « v o « ^ « ' ' r f M ) n « o n ^ v o « B r ^ ' * - i H » ^ m » « > « t f - > r t « < f t « r t r * r b « 3 « « « c * % 9 > » ( r 9 •> «r *> *> 9 »* o * « • • • • • • • • • • • • O X * »*T*»»-^r^f^^^^ooOOo^^f^Mf>i iM«^wmmmm«#n^^m»^m^i«r^^m^^^^«n* , ^fn^*-»«« ir .#^^>rt^s

• a * i i i i i i i i i • i i i i i i i i i i * i i i i i i i i i i • i i i i i i i i i i •*. B *

t - ff • o > o » - ~ * « C f f i » « c < . t f N r - » * > © r ' i * * © . t f r » © - h « r t * » - * ! r « r r o » N N « r « O f N « » r * ^ « - * ~ - » r * f > i « - © r * , c « > # «

z B • ^ « r * » . * * r * n © ^ r ' « n r « « * i c B r » - ^ o * * ' v o r » r ' * i ' ' * * 3 » i © j B n N o c r ^ i o ^ B o * J * * « » o ^ © ^ > - » o ^ - « r c » < r » o n i ^ * c O K * • • • « • • • • • - • • • • • • • • * . • • . . - . , . . . • . • . . . * • . *x x * c v r f * « o r ^ * ^ « " ^ ^ O i ^ » * n o ' K * o r * - « ^ - « ; * - - r , > f n « « « ^ r i r < i f > i r , « r « r « r « r i » - » - ^ - * - » - ^ — - o o o o o o o o o o O 3 • f » f f n « « « r ) r i » * w m P » N N ^ » ^ i t i i • i i • i t i t i i i * i i i i i i i t i i i i i • U *» • i • i i i i i i • i i i • i i i i • i

O M •

m e t « x * — o * K -0 •

f * B * O m ^ < r ^ * ^ * * ^ * ^ ^ o » ^ ^ * * * 3 * « w © < n * > * t f * t f * t f ' : » » " < © i c © ^ ' ^ ^ * > . » » « . » * " i f ' « % p * w » c ~ « c « < J * r - a f-

r * ^ * < 4 c r * - * 3 0 » © « - r « m » » r f i ^ ) ^ ^ f » r - P f c « « c « i ® « o « ( c r » r - r - * » o < r a » * • t t f i i i i i i i t i i i i i i f i i i i ' i i i • i i

c * . •

m » » « * o * M * > r - . » f ' ' © o < F » * " * ^ : » « 3 » c « c o r * ^ c > r - i N ^ t f r i f l - t e c * - * ^ *• o *" f - o "" « c ~ *~ *- ^ *- K <r 7 o- 9> s r*

t i i i i i i i f • i i i i i i i i i i i t i f i t i i i i i i i i i i i i i i i

Z3 «U * »- o *

^ o ^ j c c r c i i i ^ " 0 9 > r ^ « o t f i a K 0 ^ ' r - ' ' " a ^ s a o n o t a N ^ 1 - r* o ^ o x O ^ M " 0 « « C " O f .» f *

C O * N W •

> « h > 0 * f « f « « ^ « > © •*• Of M o »0 A* O 9 • * * ^ © r * « < T l ^ O t f > » * « t r > « ^ 9 > n ^ f » O 4 iT •*> 9> *^ -» * -ft O • - *" **

K O •

w 9

B w •

'.n B •

O 0 0 0 0 0 © 0 © © 0 0 © 0 © 0 0 0 © 0 0 0 0 0 © © 0 0 0 0 0 0 0 0 0 0 0 © ° © 0 © 0 © 0 0 0 0 © © 0 0 0 0 0 O O O ^ t _ > 0 = ? 0 « ' 1 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C 3 0 C 3 0 0 t - » 0 0 0 ( - > O O O O O C >

77

• J • x ^ - ^ * * ^ r ^ x » » « * » " * , N » - D o r , x ^ - ^ ' * * r ! / , ' ^ « « » * » ^ * » ^ * * ^ ^ * » ' * * ' * ! * » * ' ? » M ? < « ^ i »

fc H • 9 O C 0 = > = > C O 0 3 3 2 S 9 3 0 = > O 0 3 0 O 3 0 0 O O O S 0 0 0 0 0 e o 0 0 O C 0 3 3 O 0 I

K • • O C O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O e O O O O O O k. K • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K X . « O O O O O O C O O O O O O O O O O O O O G O O O O O O O O O O O O O O O O O O O O O O O C

^ » ^ x « * « ^ - <

c « • I - » •

f * O r > * > ^ e « - ^ ' O X « V 9 > « t f ' . ' ^ ' < — v « « ~ r ~ * c « c * r > n w ^ - o " ' « ^ i ^ O O 0 » » » » « ^ - « « l " l * ' » « i » - — — • - • - • - I I I I • I • -1 I I I

I I f* •" » *» m ^- ^- « « ^ r§ m t i i i i • i

*• O : o o •

• • » m n m m n n v > m ^ m ) - i O T r « f < i r < r < N n n ^ ^ o o o o c o c o o o o o o o o o o o o o o J K « . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . c ^ * e o o o o o o o o o o o o o o o o o o o o o o o o c o o o o o o o o o o o o o o o o o »> « • i i i » i t i i i i i i i i i i i i i i i i i i i i i i i i i : ; i t : i i i i f i i

o o C O O O

© N . » m ^ l m m m ^ m m K - f n » » t ^ ^ m m ^ > * . ^ i ^ ^ | M ^ ^ - ^ 0 O O O O O O 0 0 0 0 O O 0 O O O 0 0 O O K B * 1 I I I I I I I I I I I I I I I I J f I I I • t I I I I I I I I I I I I I I I I • I 1 I I

W. X .» O O * C D » (J 0 •

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W « • * • *

I • I • i I I I I I I • I I I i i I i f I I I I I i t l l t l l f l l l i l i . l i i l i

e. *) • • t i i i i > i i i i i t i i i K M *

^ • • »». r i r i ^ i • i i i i

* - ^ i i i i i l i i i i I i l l i i i » » i

3 » t . . ; t* u • r * * o n » » r - < * r w * r - > o * * f c ^ , r f , » » ^ » o t » * » ' ' « ^ « * » ' , * « * o r - « o e r f 1 « o f * - i » ' n « ^ o 't

pa

o

« f ^ ^ « - 9 0 ^ e r » ^ 9 tfr^*r<x^*C'«ooooi

K o • ^ — ^ - - ^ - — ^ — ^ . ^ (^ M •

tn • o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ' mi • 0 0 0 « - * O O C J 0 0 1 - ' O O O c J O O O O ^ O O O ( J « - » O O C > 0 0 0 0 0 * - » * ^ C » O O O O O t J O O « - » 0 :

79

Appendix C

THERMAL CONXTCTiyiTY DATA AS A FUNCTION OF TEMPERATURE FOR FUEL ELEMENTS FABRICATED FROM TYPE H-327 AND TYPE H-451 GRAPHITE

Table C.1- Thermal Conduct iv i ty and S p e c i f i c H Fuel Elements Hade With Unir -ad ia ted H-327 Graphite c Temperature

a1- o f Coaposite 3 a Function o f

TIB ir sire it 11 I I I C O I C S C I I T I T I KABUL C O O O C T i r i l T S ? I C i r i C 1£»T nates r rro /BOOB PT CEC r BTB / BOOB FT lli f B 1 3 / U . D«£ r

0 . 0 7 7 . 5 * 2 * 31 .8901 0 . 1 1 5 2 1C0.0 7 1 . « 8 2 5 29-7C?7 0 . 1 S 2 * 200-0 • 6 . 0 9 0 8 2 7 . 7 6 9 * o->asi 300 .9 6 1 . 0 * 9 6 26.CC21 0 .213 8 • 00 -0 5 6 . 5 8 * 2 2 * . 6 2 5 1 0 . 2 3 9 1 5 0 0 . 0 5 2 - 5 * 2 7 2 3 . 3 * 5 5 0 .2d1 3 6 0 0 . 0 • 8 . 9 * * 0 2 2 . 3 * 9 * 0 . 2 8 0 6 700 .6 • S .6977 21.S022 0 . 2 9 8 1 8 0 0 . 0 • 2 . 7 8 3 8 2 0 . 8 2 7 6 0 . 3 1 3 3 9 0 0 . 0 • 0 . 1729 20.3C73 0 . 3 2 6 9

1000.0 3 7 . 6 3 5 9 • i . 9 2 1 3 0 . 3 3 8 9 1100.0 3 5 . 7 * 6 2 1 9 . 6 * 7 6 0.3*S.7 120Q.0 1 3 . 8 7 9 0 * 9 . « M 6 0 . 3 5 9 * 1300-0 J 2 . 2 1 1 9 . 9 . 3 * 9 9 0 . 3 6 8 1 1*00.0 3 0 . 7 2 * 3 1 9 . 2 8 3 1 0 . 3 7 6 0 1500.0 2 9 . 3 9 7 6 1 9 . 2 * 6 2 3 .383 2 ;*oo.c 2 8 . 2 1 * 9 K . 2 2 4 * 3 . 3 8 9 8 1700.0 2 7 . 1 6 1 2 1».2C59 0 . 3 9 5 8 1800.0 2 6 . 2 2 2 8 1 9 . 1 8 2 * 0 . * 0 1 i 1900.0 2 5 . 3 8 7 7 1 9 . 1 * 8 5 0 . « 0 6 * 2000 .0 2 * . 6 * 5 * 19 . 1 0 1 1 0 . « 1 1 1 2100-0 2 3 . 9 6 6 * 19.C390 0 . « 1 5 « 2200.0 2 3 . * 0 2 7 18 .9621 0 . * 1 9 « 2300.0 2 2 . 8 8 7 3 18 .4713 0 - * 2 3 1 2 * 0 0 . 0 2 2 . * J * 2 18 .7680 0 . * 2 6 i 2500.0 2 2 . 0 3 8 5 1 8 . 6 5 3 * 0 .«29S 2400.0 2 1 . 6 9 5 9 i8.*r .o 0 . * 3 ? 3 2700.0 2 1 . * ' , 2 9 18.396C 0 . « 3 * 8 2800 .0 2 1 . 1 5 6 8 18 .2553 0 - * 3 7 1 2900.0 2 0 . 9 5 5 3 18.1C79 0 . 1 3 9 1 3000.0 2 0 .7965 1 7 . 9 5 * 1 0 . * * 0 9 3100.0 2 0 . 6 7 9 0 1 7 . 7 5 * * 0 . « « 2 * 3200.0 2 0 . 6 0 1 5 17 628* 0 . « « 3 < JiOO.O 2 0 . 5 6 3 0 17.«57«. o.*«so 3*00 .0 2 0 . 5 6 2 * 17 .2796 r . « * 6 0 3500.0 2 0 . 5 9 8 7 17.C957 0 . * « 6 9 3*00 .0 2 0 . 6 7 0 8 16 .9053 0 . « « 7 6 3700.0 2 0 . 7 7 7 2 16.7C8C 0 .««8 3 i « 0 0 . 0 2C.9162 16 .5039 0 . « * 8 9 3900.0 2 1 . 0 * 5 7 16.293C 0 . « * 9 5 • 0 0 0 . 0 2 1 . 2 8 3 0 1 6 . 0 7 5 * O . * 5 0 0 • 1 0 0 . 0 2 1 . 5 0 * 6 1 5 . ( 5 1 6 0 . * 5 0 S • 2 0 0 . 0 2 1 . 7 * 7 1 15.6226 C .«510 • 3 0 0 . 0 2 2 . 0 0 5 2 15.3895 0 .«315 wao.o 2 2 . 2 7 3 * 1 5 . 1 5 * 2 0 . * 5 2 1 • 5 0 0 . l i 2 2 . S**9 H . 9 1 9 1 0 .«52T • 6 0 0 . 0 12.M21 1«.6873 3 . * 5 3 3 • 7 0 0 . 0 2 3 . 0 6 5 8 1 * . * t 2 9 0 .«53 8 •9C0 .0 2 3 . 2 9 5 9 1« .2508 0 - « 5 O WOO. 3 2 3 .«907 54.CS71 0 . « 5 * 7 ^000.0 2 3 . 6 1 7 0 13.8990 0 . « 5 * 9

80

$ V WKC 76-i«:«2

<O0O 2COC . . - i . L_... .3000 40C0 5000 6000

TEMPERATURE, o f r

Fig- C.I . Axial and Radial Thermal Conduct ivi t ies of Composite Fuel Elements Made With Unirradiated H-327 Graphite as a Function of Temperature.

81

Table C 2 . Thermal Conductivity and Specif ic Heat of Composite Fuel Elements Made With Unirradiated H-451 Graphite as a Function of Temperature THU titrate k m i :o iMc; r t t tv t f t » U l C O I B K U t t t t sttciric « » t

t t « t £ S t • T< /now r t etc r BTt / HOBt I t DEC t t T I A I . oti r • » • • • • • * • • • • • • • • • • • •%• • • • • • • • •••*•*•••*••••••••• • • • * . . • • * • • • •

0.3 SO. 4* 39 29 .7272 0 .1152 100 .0 9 * . 4 * 1 0 2 0 . 2 3 2 2 C.1&24 2 0 0 . 0 4 * . 2147 2 * . 9 3 4 0 0 . 1 * 5 1 3 0 0 . 0 4 3 . 8 5 4 4 2 5 . 0 1 * 5 0 . 2 1 3 * »oo. a 4 1 . 4 5 * * 2 9 . ( 7 2 0 0 .2391 5O0.0 3 9 . 1 0 7 2 2 * . 0 0 5 * 0 . 2 * 1 3 6 0 4 . 0 3 * . * S * 4 2 3 . 9 * 5 1 0 . 2 W * 7 0 0 . 0 3 4 . 7 5 5 1 22 .9409 0 . 2 9 * 1 * 0 » . 0 J 2 . * 2 7 5 2 2 . 5 5 4 * 0 .3133 9 0 0 . 0 3 1 . 0 9 * 3 2 2 . 2 * 9 * 0 . 3 2 * 9

1000.0 2 4 . 5 * * 4 2 2 . 1 1 6 * 0 .3389 1100.0 2 * . 23*2 2 2 . 0 2 5 * 0 .349 7 woo.a 2 7 . 7 0 9 * 22 .0C12 0 . 3 5 9 * 1300.0 2 * . 1 * * 5 2 2 . 0 2 7 * 0 . 3 6 * 1 HOC.O 25..>4S1 2 2 . 0 * * 0 . 3 7 * 0 1500. S 26 .7S49 2 2 . 1 7 0 * 0 . 3 * 3 * 1*00.0 2 9 . 2 7 5 7 2 2 . 2 6 0 3 0 . 3 * 9 * 1700.0 2 3 . 8 * 7 * 2 2 . 3 * 7 0 0 . 3 9 5 * iaoo.0 2 3 . 5 * 3 * 22 .9224 0 . * 0 1 3 WOO.O 2 3 . 3 * 1 1 2 2 . 9 * 0 7 0 . 9 0 * * 2000.0 2 3 . 1 3 9 3 2 2 . 1 1 * * 0 .9111 2100.0 2 2 . 9 5 * 6 2 2 . 5 3 4 3 0 . « 1 5 « 2200.0 2 2 . 7 * 2 3 22 .5291 0 .4144 2300.0 2 2 . 0 9 * 7 2 2 . S M S 0 . 4 2 3 1 2«O0.0 2 2 . 3 9 0 1 2 2 . 9 * 3 * 0 . * 2 « 5 2500 .0 2 2 . 1 5 5 3 2 2 . 4 0 9 * 0 . 4 2 9 * 2 *00 .0 2 1 . M 7 5 2 2 . 3 4 * * 0 .432 3 2700 .0 2 1 . 5 * 6 2 22 .2775 0 . 4 3 4 * # 0 0 . 0 21 .2538 22 .2CS* 0 .4371 * 9 0 0 . 0 2 0 . 8 9 5 * 22 .1392 0 . 4 3 9 1 3000.0 2 0 . 5 2 1 7 2 2 . 0 6 * 5 0 .4409 J100.0 2 0 . 1 9 2 3 2 1 . 9 9 * 1 0 . 4 4 2 4 3200.0 19 .7726 2 1 . 9 3 * 2 0 . 4 * 3 * 3300.0 19 .9276 2 1 . 8 7 * 5 0 . 4 4 5 0 1*00.0 19 .1299 2 l .«2SC 0 . *46 0 3SO0.0 l t . W H 2 1 , 7 7 * * 0 . 4 9 * 9 KOO.O 18 .7151 2 1 . 1 2 6 * 6 .4476 5700.0 l t . 6 4 1 * ,21.67*6 0 . 4 4 * 3 3*00.0 1 * . 6 7 5 * 21 .6299 0.1.489 29C0.0 1 * . * 3 0 0 2 1 . 5 7 9 1 0 . 4 4 9 5 •COO.O 19. 1070 21 .5251 0 .4500 1100.0 19 .5097 2 1 . 4 * 7 * 0 . 505 4200.0 20 .0344 21.4C6S 0 .4510 4300. C 2 0 , 6 * 5 3 2 1 . 3 * 3 7 0 . 4 5 1 5 • • 0 0 . 0 2 1 . J * 19 ; i .2«c 0.4S2-1 • 5 0 0 . 0 2 2 . 1 * 0 3 2 1 . 2 2 0 1 0 . 4 5 2 1 4 *00 .0 2 2 . 9 1 0 6 2 1 . 1 6 * 7 C.453 3 47O0.0 2 3 . 6 1 2 5 2 K 1 3 4 2 0 . 4 5 3 * •aoo.o 2 * . 173C 2 1 . 1 2 * 4 0 .454 J 4900.0 2 * . * * 5 6 2 1 . 1 5 * 7 0 . 4 5 4 7 yioo.o 2 4 . 4 * 9 8 21 .2363 0.455 0

82

ORNw DIG 76-18)83

3

o D Q O O

< s Q: UJ X h-UJ

O 0.

O o < X <

80

70,

60

T

RAOIAL DIRECTION

40

30

20

1000 2000 3000 4000 5000 6000

TEMPERATURE, dF

u. o

3

o Z) Q O O

.J

0: Ui X

<t ct:

Fig. C.2. Axial and Racial Thermal ConductiviMes of Composite Fuel Elements Made With Unirradiated H-451 Graphite as a Function of T< mperature.

83

ORNL/EMG/tH-1

Internal Distribution

l . P. Angelini 2. R. J . Beaver 3 . « . Bender 4 . R. J. Braatz 5. R. A. Bradley 6. A. J. Caputo 7. W. G. Cobb 8. H. E. Cochran 9. J. R. Coobs

10. B. F. Crump 11. F. C. Davis 12. R. G. Donnelly 13. B. C. Duggins 14. V. P. Eatherly 15. F. C. Fitzpatrick 16. W. R. Hamel 17. F. E. Harrington 18. L. C. Hensley 19. R. M. Hi l l 20. J. R. Horton 21. L. N. Hove 11 22. D. R. Johnson 23. P. R. Kasten 24. J. J. Kurtz 25. w. J. Lackey 26. G. M. Lawson

27. B. Lieberman 23-29. G. W. U e v i l l y n

30. A. L. Lotts 31. J . E. Mack 32. S. R. McSeany 33. K. J . Notz 34. A. R. Olsen 35. T. W. Pickel 36. A. S. Pruitt 37. D. P. Reid 38. J . E. Rushton 3S. T. F. ScanIan 40. M. Siman-Tov 41 . D. P. Stinton 42. R. R. Suchomel 43. V. J . Tennery 44. S. M. Tieg 45. D. B. Trauger 46. J. E. Van Cleve 47. T. R. Weir 48. R. M. Young

49-50. Central Research Library 51. Document Reference Section

52-64. Laboratory Records Department 65. Laboratory Records, 0RNL R.C. 66. ORNL Patent Office

External Distribution

67. J. G. Grundmann, Penn St^te University, Department of Mechanical Engineering, 208 Mechanical Engineering Building, University Park, Pennsylvania 16802.

68-69. Director, ERDA, Division of Nuclear Fuel Cycle and Production, Washington, D.C. 20545.

70-71. Director, ERDA, Division of Reactor Development and Demonstration, Washington, D.C. 20545.

72. Director, Reactor Division, ERDA, Oak Ridge Operations Office, Post Office Box E, Oak Ridge, Tennessee 37830.

73. Research and Technical Support Division, ERDA, Oak Ridge Opera­tions Office, Post Office Box E, Oak Ridge, Tennessee 37830.

74-100. Technical Information Center, ERDA, Office of Information Services, Post Office Box 62, Oak Ridge, Tennessee 37830.