• Ka» •

Sp ISSN 00S1 • 3397

The Light-Water-Reactor Versión of

by

K. La/imannA. Moreno

JUNTA DE ENERGÍA NUCLEAR

CLASIFICACIÓN INIS Y DESCRIPTORES

E23U CODESFUEL RODSTHERMAL ANALYSISCREEPPLASTICITYNUMERICAL SOLUTIONSMATHEMATICAL MODELSPWR TYPE REACTORS

Toda correspondencia en relación con este traba-jo debe dirigirse al Servicio de Documentación Bibliotecay Publicaciones, Junta de Energía Nuclear, Ciudad Uni-versitaria, Madrid-3, ESPAÑA.

Las solicitudes de ejemplares deben dirigirse aeste mismo Servicio.

Los descriptores se han seleccionado del Thesaurodel INIS para-describir las materias que contiene este in-forme con vistas a su recuperación. Para más detalles consúltese el informe I3.EA-INIS-12 (INIS: Manual de Indiza- ~ción) y IAEA-INIS-13 (INIS: Thesauro) publicado por el Or-ganismo Internacional de Energía Atómica.

Se autoriza la reproducción de los resúmenes ana-líticos que aparecen en esta publicación.

Este trabajo se ha recibido para su impresión enOctubre de 1977

Depósito legal n° M-41901-1977 I.S.B.N. 84-500-2396-3

2us ammenf as s ung

Es wird die LWR-Version des Rechenprogramms URANüS zur ther-

mischen und mechanischen Analyse von Brennstaben beschrieben.

Die Materialdaten v/erden diskutiert und auf verschiedene Rechen-

beispiele angewandt. Dabei stellen die Ergebnisse keine Nach-

rechnung spezieller Experimente dar sondern sind reine Testbei-

spiele. Die durchgeführten Rechnungen zeigen, daB der URANUS-

Code in seiner LWR-Version schnell und zuverlassig arbeitet

und somit ein wertvolles V?erkzeug für' die thermische und me-

chanische Brennstabanalvse darstellt.Die Entwicklung der

LWR-Version des Rechenprogramms.URANUS wurde von K.LaBmann

durchgeführt, A.Mo/reno stellte die Materialdaten kritisch

zusammen. . ' ' ' • '

The Liglit-water reactor versión of the URAKUS integral

fuel rod code.

1. II-7TEODUCIIOK

2 . HECHAITICAL AKALTSTS

3. MATERIAL PROPERTIES

3.1. Uraniun dioxide

3.1.1. Puel .thermal conductivity and heat transfer

in fuel cladding Gap

3.1.2. Thermal strain

3.1.3. Swelling and hot Pressing

3.1.4. Young's Hodulus, Poisson's ratio, density

3.1.5» Plasticity and Priíaary creep, Cracking

3.1.6. Secondary Creep

3.2. Zircaloy

3.2.1. Thermal conductivity

3.2.2. Thsrraal strain

3.2.3. Young's modulus, Poisson's ratio, density

3.2.4. Plasticity and Primary creep

3.2.5. Secondary creep

3.2.5.1. Cladding Growth

3.2.5.2. Thermal creep

3.2.5.3. Induced and climb strain rates

4. NÜMERICAL • EESULTS

Acknowledgements

References

II

LIST Oí1 PIGDHES

Fig. 1 Fuel rod geometry

2 Progranime structure of the URANUS system

3 Thermal conductivity of UO

4 Young's raodulus of UOg

5 Secondary creep of UOp

6 Creep of Zircaloy

7 Power history for case 2

8 Axial power distribution

9 Axial temperature distribution in coolant and cladding

for Q=50 W/mm :

10 Axial temperatujre distribution in fuel as a i unet ion

of time for Q=50 W/mm

11 Axial variation of radial gap as a function of time

for 0=50 W/mm

12 ' Diametral strain at section 5 as a function of buern up.

13 Comparison between axial strain determined experimental!;?

and via HRA1TUS

14 Axial strain in the fuel rod for two power histories as

a function of time and burn up.

15. Axial strain in the fuel rod as a function of burn-up.

16 Axial strain in the fuel rod as a funotion of fast

fluence

17 Radial stress in the cladding as a function of time.

18 Bunning time for one time step and one slice as a

function of the number of rings

• LIST Oí1 TABLES

Table 1 URAITUS input data for performance test

2 TJRANU5 output

1 . Introduction

The thermal and mechanical analysis of fuel rods is performed

in general by means of large digital coinputer prograrames, in

which the fuel-rod modelling theory is evaluated numerically.

Wordsworth [_1 ] and other authors (e. g. Matthews [2] )

have reviewed such computer programraes, thus it is not neces-

sary to present a. sürvey liere. . One such code is the

URANUS programme system describen recently in two papers by

Lafimann ( [3~] , [4] ) . This code can analyse the fuel rods in

most types of power reactors. In the past, the analysis of

fuel rods in sodium-cooled fast breeder reactors has been of

primary interest; the present study is, however, an analysis

of fuel rods in light water reactors (LWRs)/ the in-pile data

being taken from the literature. Since the data is of varied

origin, consistency cannot be guaranteed;•this must be strived

for in future work. Accordingly, the major part of th^s paper

(Sections 2..<and 4.) documents the capabilities of the URANUS

system in general, as well as the numerical reliability (sta-

bility) and cost of typical URANUS computations. Material pro-

perties are disctissed in ;Section 3. K. Lassman. develo-ped the

LWR versión of the URANUS code used in the present

investigation, material properties' (c.f. section 3) were

reviewed and supplied by A.Moreno.

2• Mechanical Analysis

The mechanical analysis is perfor-med successively for each •

(cross-) section (1) in the fuel rod (c. f. fig. 1). To this

end;analytical solutions,valid within the discretization ine-

vitable in space and time, have been developed. A detailed

description of the theoretical principies in the URANUS system

is envisaged for a future comprehensive review paper, conse-

quently the governing eguations will nct be expounded here.

The section-by-section mechanical analysis generates thus

data also for each slice. On coupling the slices a quasi-two

dimensional analysis of the integral fuel rod results, as

described in detail' in £ 3 ] .

This quasi-two dimensional analysis is the framev.'ork around

which the URANUS computer programme is built. As shown-in -

fig. 2, an axial loop is first processed after the loads have

been defined. V'ithin this loop the thermal and mechanical ana-

lyses are carried out for each section. Coupling follows, ta-

king axial phenomena into account. This procedure is con-

tinued until convergence has been. achieved.

The mechanical analysis can accommodate seven components of .

strain : elastic, time-independent plástic, creep and thermal

strains, as well as st'rains due to swelling, cracking and den-

sification. The temperature distribution, heat generation,

cladding/fuel gap closure, pellet cracking, crack healing.,

fission-gas reléase, corrosión, O/M-distribu—tion and Pu-redi-

stribution are modelled. Geometric non-linearities (large dis-

placements) are included, steady-state or transient loóding

(pressure, temperature) is possible.

The phenomena and parameters pertaining to a fuel rod analy-

sis are given in fig. 2 and table 2.. In the URANUS system, .

temperature calculations include the thermohydraulics of thé;

cooling channel. The geometry of the cooling channel and the .

flow rate are dependent on the axial coordínate Z. Thus

local disturbances or blockages in the cooling channel,such

as rnay occur or. ernergency core cooling, coulá be apprcxima-

ted in a fuel rod analysis.

1 •

o

Fig. 1 : Fuel rod geometry .

Lnitial valúes

loads

7/ a x i a l

disc

loop A.

controlprogramme

axial couDhna

•-<no —S convergence

= t + A t

trie following parametersare evaluated for eachsection (cladding + fuel):

weight

power density

burn-up

O/M-ratio

Pu-redistribution

temperature

hot pressing

creep

swelling

inner/outer corrosio:

sectional mechanics

plastificatión

fracture mechanics

crack healing

fission-gas reléasegeometry

next case

at present a total'ofapprox. 80 subroutine:

Fig. 2 : Programme structure. of the URANUS system.

5. Material Properties

In this section,the thermal and. mechanical properties of

materials used in fuel rods for Light "water Reactors (LWR5)

are discussed.Since the integral system fuel/cladding

behaves in a highly complex ciarme r and several mutually

interacting phenomena take place,it is only feasible to

define a consistent set of material data when recourse can

be made to a large number of diverse experiments.

However,the results of material experiments are rarely

presented in a complete,concise fashion.Material data,

which must therefore be drav/n from various sources in the

open literature,is thus of questionable consistency.Never-

theless,the main goal of the present study is to verify the

capabilities of the URANUS code for integral' fuel rods and

it is sufficient,therefore to use data vhich is consistent

to an arbltr-aT (realistic) degree.

Cholee of material

properties foliows a conservative design approach.In this

way,uncertainties due to inconsistencies in the data are

offset to some extent via conservative results.Conservative

material properties also play heavily on limiting design

criteria,i.e.the code performance test will take place

under the most stringent boundary conditions.

This paper

does not attempt to give an exhaustive covering of all

those phenomena implemented in URANUS and having a vital

7

influence on the irradiation behaviour of fuel rods;it is

limited to a detailed description of those parameters in the

LWR-versión cf URANUS having a direct influence on fuel rod

performance.

The reader is referred to a previous paper [19] for details

on more basic modelling,e.g. hot pressing,svelling,heat

transfer in fuel/cladding gap,etc.

A large amount of data on

the properties of materials used in fuel rcds for LV/Rs has

appeared in the li^erature to date,thus it is expedient to

confine the present investigation to review articles.

3.1 Uranium Dioxide

This fuel has been the subject of many detailed investigations,

accordingly a large amount of material data is available.

Varying experimental conditions,such as temperature,flux/

fluence,etc.,and other phenomena affecting fuel rod performance,

such as fission products,cracking,porosity,grain size,

stoichiometry,etc.,lead to a wide range-with,inevitably,

appropriate scatter-of experimental results as reported in

the literature.The most important UCu properties are discusséd.

below.In general,the following formulae are those used !in •;.' '

the LWR-version of URAMJS;they are represented in the figures'';,

by a solid line.

8

3.1.1 Fuel Thermal Conductivity and Heat Transfer in

Fuel/Claáding Gap

The low thermal conductivity cf UCp is the main disadvantage

associated with the use of this material as a nuclear fuel.

Low thermal conductivity is synonymous with large temperature

gradients in the fuel and thus places bounds on the power

density.For calculating the temperature at the centre of the

fuel (a general design criterion),a thermal conductivity of

optimum accuracy/reliability should be sought.This requisite

is increasingly important when temperature-dependent material

properties are taken into account.

Pig. 3 shows the thermal

conductivity of U0? with a density of 95% ?as taken from

various sources.The Vestinghouse correlation [5.] ,

k = + 8.775* 10J ° 11.3 + 0.O23S x T

w i t h • . .-

k thermal conductivity Pw/cm °cl

T temperature [°c] •;

is represented by a continuous line.For temperatures below •'.•

1500 °C,eq.( 1) is a lower bound on the thermal conductivity.

At higher temperatures,experimental difficulties leadto

increasing uncertainty in the experimental evidence and the •

data is. inevitable strongly case. dependent.A comparison of •'•":

ooEsE

7 o 7

6 -

O5 -

cO 4-1oOE HQ)

JZ

A

0

0AV<£>

RESARTobbe

OldbcrgLyonsTóbbeGESARGehr

( 5 )(9 )(10)( 6 )

(11)(12)( 7 )

Q / Q s !

5 0 0 1,00(

Fig. 3 ' : . Thermal Conductivity of

I.500 2,000

temperature [°C ]

10

data here is meaningless.In the hign-temperature range the

only conclusión possibie is that the thermal conáuctivity

is very lov,r and probably not greater than 0.03 V//cm °C , in

fact near the melting point this valué v/ill be an

upper bound.

Thermal conductivity depends not only on the temperature,

but also on the porosity of the *fuel.Several approximations

v/lth varying degrees of complexity (c.f. Lyons et al. [6 ~] ,

Gehr £7] ,0ndracek et al. \_8~] ) nave be en proposed to take

account of this effect.The Maxwell-Eucken relationship

. 1 - Pk = k • (2)P o -¡ + B p

vith

P porosity [ /] •

B shape factor [ /J

as discussed by Ondracek et al. [8.] ,along with the Meyer et

al. data [18] for determiningthe shape factor' fi, describes •

the influence of the porosity on the thermal conductivity

quite satisfactorily.Valúes for. the shape factor B are

summarized in the table below:

Porosity ( P ) Shape factor (S) . ••'• ";

¿0.1 . 0 . 5 . ' •• . • • ". •••" '•'•

0.10-0.15 1.0 -0.15-0.20 1.40.2Ó-0.25 - 1 . 6

11

It has been shown experimentaliy,that the thermal

conductivity is also dspendent on the stoichiometry o.f the

fuel ( c.f. Lyons et al. [o]. ,Stehle et al. [ 13] ).Thermal

conductivity decreases vith decreasing hyperstoichiometry,in

the hypostoichiometric case a srnall increase in the thermal

conductivity has been observed,but the data is not conclusive.

LWR pellets are almost stoichiometric as-fabricated,the

stoichiometry subsequently increasing slightly with burn-up

at a rate 01 approximately 2 xiO"""5 units per at.-% burn-up

( c.f. Stehle et al. [ 133 )*1these stoichiometry changes

result in a total increment 01 about 1 % ,a valué much

smaller than that given by Lyons et al.£ 6^ . Thus

stoichiometry ... changes much less than those in-'

ferred by the data scattering .in fig. 3 are encountered.

.There is some experimental evldence that the thermal

conductivity decreases with increasing burn-üp at temperaturs

below 500 QC (Lyons et al. [_6] ).However,the available data

would not justify a detailed treatment of this effect in the

analysis oí fuel rods fcr thermal -reactcrs.Lack of con-

clusive experimental evidence,together with the fact that

this phenomena takes place (if at all ) within a limited

temperatura región,means that an alternative (eqüivalent )

approximaticn is usually made in design,i.e.the degree of

conservatism placed on some allied parameters ( e.g.theCial

conductivity of fuel/cladding gap,melting point,etc.) is . •

appropriately increased.

A modified form of the raoáel developed by V/ordsworth (1) is u

for calculating the heat transfer in the radial gap fuel/cláá

12

3.1.2 Therir.ai Strain

Contact pressure between fue! and ciadding is mainly due to

the differential therrnal strain in these two members.An

accurate determinación of this parameter is therefore ess-

ential.Tnus it is not surprising that the thermal strain

has been measured in several laboratories -with a minimum

a-mount of scatter, as evidenced by Lyons [6] , Loch- [14] ,

DuncoinLe '[15] >Ma [16] and Jiménez [17] .A reliable corre-

lation for the thermal strain valia over the whole of the

temperature range occuring in practice has been given by

Lyons [6] ,

£ t n = 1.72 x10" 4 + 6.Sx1O~bx T + 2.9 xío'Sx T2 (3)

v,rith

£ t h thermal strain [ / ] . .

3.1.3 S\'.rellin£ and Hot Pressins;

Swelling and hot pressing are calculated according to

Toebbe [Ti] . Swelling is assumed here- to be a linear

function of burn-up, a valué of 1.0 %/at.-% being typically

representativa of the detailed Toebbe model. :

13

3.1.4 Young's Modulus,Poisson's Ratio,Density

Young's modulus is oí relatively minor importance in com-

parison with other material properties.This parameter

is mainly dependent on temperatura and porosity.Following

standard practice,the temperature-dependence is repre-

sentad by a poiynomial.Numerous experiments have been per-

formed with a view to quantiiying the

effect of porosity en Young's modulus (Stehle ["13J ).The most

common correlation is of the form

= EQ (1 + a P )

where a is an empirical parameter to take'account of the* • »

shape of the pores.

Other parameters infiuencing Young's modulus are,for in-

stance,grain size,stoichiometry,burn-up,etc. ( c.f. Stehle [J13

however,experimental results are not conclusive here and the

effect of these parameters on Young's modulus is usually very

small anyv/ay.Fig. 4 shov/s .Young's modulus asa function of

temperature for a material of 95 % density.The To.ebbe

correlation [9] ,

E = (1 - 2.6 x P) (22.4 x 1O4 - 31 . 19 * T) ' : :" . "í

with ' ,

E Young's modulus £MPaJ •

2 .0 -

1.5-

1.2-

Young's modulus[105MPa]

A

A

ioo

©

nA©

TobbeStehle

> i

DuncombeOldbergLo ch

(11)(13)

a

(15)(10)(14)

O 500 00 2.000

temperature [°C]

H

; Fig. '/+':" Young's Modulus of U0 p

15

is shown in fig.4 as a continuous line. Duncombe's results L

compared with the remaining data,appear to be rather

conservativa, in the sense that a smaller Young's modulus

implies larger strains at the same stress.

Poisson's ratio is a v/eak íuncticn of porosity ( c.f. Toebbe

[9] j Stehle [15], Duncocibe • [15] ),but there is no conclusive

evidence of a temperature dependency.Stehle [13] gives

\ = 0.316 as ajtypical valué for Poisson's ratio.

The theoretical ( 100 % ) density of uranium dioxide is

10.96 g/cvP ( c.f. Loen [14] ).V/her) used asa nuclear fuel,

the densit}r is reduced to about 90-97 % of its theoretical

valué. ' •

3.1.5 Plasticity and Primary Creep,Cracking

Data on primary creep,especially data showing the influence

ofltemperature and irradiation,is rare.Primary creep caused

by rapidly changing loads may lead'to very large strain rates.

Experimental data reported in the literature is not usually

comprehensive,and crucial valúes must be viewed with scepsis.

Thus primary creep is "bestirepresented by introducing a simple

model,independent of time,as an upper bound on the experimental

data. • . . - i , .

The URANUS mpdel for-primary creep is given in [ 1 9 ~J .The.main

parameter in the model is the generalized yield surface 6o> y, Specic

16

attention must be paid to the choice of a flow rule.For this

first versión of URANUS the Prandtl-Reuss equation v/ithout

haraening has been chosen.The valué for (j ,as taken

from Duncombe C^] , are shown below.

Temperature [°c] 0 °/2 [MPa]

O 1 260 713

260 < T<; 1232 . 870. 6-0.606 x T ^ '

1232 < T < 1927 280. -O.127*T

1927 < T . 36

Similarly,a cracking-model has been developed.The basic

assumptions in the model are that .•

(a) cracks can be represented by fictitious (equivalent)

crack strains,

and

(b) crack-planes are normal to the co-ordinate axes.

Two fracture parameters,i.e. fracture strain P _ and

fracture stress 0 F ,•are involved.The latter parameter

is given by Stehle C-^] for a grain size of .15/un:

0 p = (118 + 0.025 x T) (1 - 0.029 xP) (g)V

with

0 fracture stress in tensión [MPal

17

O F is used as a cracking criterion only if the valué

for 0 P as given by eq. (6) is greater than the valué for

0 as given by eq. (5).Partial or total -crack-healing

on sintering is modelled via a residual crack strain £

This parameter is dependent on the history of the cracks,

the crack geometry and the temperature ( c.f. [19] ).

3.1.6 Secondary Creep

Secondary creep of U02 is usually presented as an empirical

function of the salient parameters observed in practice.

Experiments nave shown that secondary creep is a function of

stress,temperature and the irradiaticn environment (Old-

berg [10] ,Stehle [13] ,Salomón [20] ).0ne of the most

general correlations,including all these parameters and due to

Salomón [20] , is given below ;

£C= A(F) 0 '5'5 exu( ) + A^F)'—r exp( - ) + C 0 F (7!R T d" R T

with

Acr . r. -i i . ' .h. creep rate \_n J

fiss? fi 1fission rate

fiss -1 ^ J

_ . . cm sO stressT temperatura [ O K 1

d grain size [/xm

A(F) =1 .38 x 1O~4 -i- 4.6 x 10 1 7 F

D - 90.5

18

A1 (-F) =9. 7 3 x 1 O6 + 3.2 4 x 10~°F

D - 87.7

ana

Q = 1 32 • "kcal/nol".

Q, = SO 'kcal/mol..

R universal gas ccn.stant

C = 7 x1O~ 2 3

D density in percent of th.eoret.ical density

if D < 92 % - , D = 92 %

A decree.se in activation ertergy v,rith falling hyperstoichio-

metry has "oeen found experimentally ( Stehle [131 ),büt the

data is not consistent;thus a direct influence of changes

in stoichiosetry on secondary creep rate is neglected.Creep

rate/stress ncn-linerarities ,to the exteñt of an exponent

oí about 5 on the stress,are correlated by eq.(7).Ari even

greater sensitivity of creep rate to stress has been ob-

served experinentally,and appropriaxe correlations v/ith

higher exponents on the stress nave been develop.ed ( c.f.

Toebbe [11] ,Stehle [13] ).It is difficult,however,to

put this exceptionally high sensitivity on a firm theoreti-

cal foundation.To a first _approxination,for example,high

exponents on the stress are a consequence of high .stratn

rates.Now,as discussed above,high strain rates are associated

primarily v ith primary -creep,and it is fitting to include . •.'•

the strain associated with the higher powers of stress in "••••••

the strain due to plasticity and primary creep.- • '• ;••• •

19

Data on secondary creep is shown in fig. 5 .The data has

been standardized as follcws ( c.f. fig. 5 ):

tenperature : 1300 [ C"]

fissicn rate : 1.2 *10 1 5 [íiss/car's]

grain size : 15 ["/•£• m ]

density :. 95 %

Squation ( 7 ) ,with F = 0 ,is plotted by the broken line

in fig. 5 ; other data is indicated by various symbols.The

continuous line in fig.5 plots thermal enhanced and

irradiation induced creep rates,superposed according to eq. (7)

Data scattering in fig. 5 is not surprising in view of

experimental difficulties and diversity of investigators. .

Duncombe's data -[21] is independent of the fission rate

at the elevated temperature defined by the standard .case.

Design analyses on the basis of this data are therefore

highly conservative.Perrin1s data [22 3 is,from a design

point of view,even more conservative; it does not compare well

vith other data in the literature (as shown by Olsen £233 )

and will,therefore,not be considered in the following dis-

cuss.Lon.

In eq. ( 7 ),the irradiation-induced creep-strain rate and

the creep - rate independent of irradiation are additive.A •.

lower bound on the creep rate can be found by superposing the';..

lowest creep rates for each of these two types of creep,as ""•.-'.,-•:•.

taken from the literature.Similarly , an upper bóund on the •

stressiMPa]

100-

10-

o

StandardConditions

Thermal creep

- ~—» Solomon (20)O Tóbbe (II)

Duncombe(2l)Robcrís (24)Perrin (22)

T=1,3OO°C (j)=!,2*IO13 fiss/cm3 s

= 95%T.D. G.S. = 15 pm

Fission enhanced + inducod creep

Solomon (20)

(9)BA

TóbbeTobbeElbelPerrin

(M)(25)(22)

Tto- 6

i i ^ i i • i I I I i I T

10—4 JO-3 _*io-z

secondary creep rate [h ]Fig. 5 : Secondary Creep of 20

21

creep-strain rate can be defined.The shaded área in fig. 5

shows the región between lower ana upper bounds on the

creep-strain rate obtained in this manner.Salomen1s data [20"]

( i.e. eq. (7) ) is compatible with other data in the

shaded área and has the advantage of being a consistent set

of data over the whole range of strain rates.Eq. (7)

will,therefore, be taken as being representative of creep straíns.

Nevertheless,the width of the shaded área indicates the degree

of uncertainty reniaining when this correlation is compared

with other data in the literature.

3-2 Zircaloy

Zircaloy-2 and Zircáloy-4 are used as cladding materials in

LWRs.The mechanical behaviour of the two materials is. quite

similar ,and there are no major differences in their material

properties.Zircaloy-4 exhibits a somevmat higher resistance •

to corrosión than Zircaloy.-2.

3*2.1 Thermal Conductivlty . . . . . . .

The thermal conductivity of ¿ircaloy is temperature-dependent

at temperatures upto 600 °C,as shown by Toebbe [9] » •' •

22

Scott [26] and Lustman [27 ] .Valúes quoted by Duncombe

[15] ,Ma [16] and Jimenes [17] are approx. 20 % greater

than those given by Toebbe,Scott and Lustman.Low conductivity

implies stringent operating conditions.In a conservative

design approach it will be assumed,therefore,that Toebbe's

correiation [9 3

k = 0 . 1 3 7 6 + O . 1 2 6 6 > ; 1 0 4 x T - f 0 . 1 2 9 3 x 1 0 8 x T 2 ( 8 )

with

k thermal conductivity [W/cín C~\

T temperature [°C]

adequately represents the thermal conductivity of ¿ircaloy.

3.2.2 Thermal Strain

Máximum fuel/cladding contact pressure (conservative design)

is concomrtant with minimum thermal strain in the cladding.

Toebbe 's valúes for the thermal strain [9] are lov;er than

those given by Duncombe [151 a n¿ Jiménez [17! » n i s ¿ata ..

is represented by the equation

£ t h = 0.65 x 1O~4 + 3.799 x10~6xT + 7 . 10 x 10~9x T 2 -Í.69 x 1O"12»T3

• • ' • . • • " . ( 9 )

with ' .. .

Pth thermal strain [" / ]

23

3.2.3 Young's Modulus,Poisson's Ratio.Density

Data on Young's modulus of elasticity is quite consistent,as

evidenced by Toebbe [9] .Duncombe [15] and Scott [26]

The correlation given by Toebbe [S] is

E = 10.0x10" - 59.0xT (10)

with.

E Young's Modulus [MPa 1

T temperatura [ Cj

There is no evidence that Poisson's Ratio \?" is dependent on

tenrperature. A typical valué for this parameter is \f = 0.325

( c.f.Duncombe [«15] ). The density j> of Zircaloy at 20 °C

is 5> = 6.55 g/ca^ (c.f. Lustman [27] ).

3.2.4 Plasticity and Primary Creep

Analogous to the fuel,plasticity and primary creep in the

cladding are treated as tiine-independent quantities.This

modelling gives an upper bound on the experimental data.

Duncombe's data [15] ,' together with a linear interpolation,

are favoured. ' . • . '•/-.

24

Temperatura [ CJ

26O> T ^ 0

538 > T > 260

T ^ 538

F l u e n c e (E>

0 .

570-1 . 33*T

4 3 1 - 0 . 7 9 - T

4

[MPa]

1 MeV] [n/cm

2.6X1O2 0

689-1.18»T

740-1.37*T

3

2 .0x10 2 1

789-0 .89 * T

1077-2 .0 *T

1(11)

3*2.5 Secondary Creep

A considerable amount of work,both of a theor.etical and

experimental nature,has been performed in an attempt to ana-

lyse the mechanism of secondary creep in Zircaloy ([27 - 35]\.

One of the most comprehensive models is that developed by

Nichols [28] .According to this mcdel,the creep rate £Cris-

É c r'int 'climb

25

with«

P . . intrir.sic strain rate

£, . , climb strain rate C O

¿ . , therrnal creep rate

( A+BO) growth-induced strain rate

0 stress

.(J) fast flux (E>1 MeV)

A,B,C constants,see below.

<The intrinsic strain rate £. , is defined as an upper bound

on the máximum creep rate.This definition is based on the fact

that the strain rate cannot be greater than the fast

straining occuring as a result oí dislocation gliding in a

material with no radiation damage. P. . should be deter-

mined experirnentally at lew plástic strains.When £.."••

dominates,the creep rate is exceptionally sensitive to stress

(stress exponents greater than 10 !).This situation is charac-.

teristic of straining via plasticity and primary creep.

Consequently,high strain rates will be modelled under these

two phenomena.Thus secondary creep ( eq. (12) ) becomes

¿ ^ ( A + BxO)(J) + é t h - é c l i m b . . (13)

The component parts of secondary creep remaining in eq.(i3)

are discussed in detail below. . ' •'•

26

3-2.5.1 Claddins; Growth

This component of secondary creep (c.f.eq.(i3) ) is

dependent solely en the fast flux.The growth oí ¿ircaloy has

been given by Stehle [133 and Duncombe jj52 .Duncombe's

correlatior. is favoured

£? v' e = t b [ 1 - expi, -cD-(.14)

a = 0.3519

b = 7.303

c = 0.27

10io"

- 24

.20

" r a d i a l= 0.574

= 0.337

= 0.089

This correiation holds ior Zircaloy in an annealed state or

witn a small amount oí cold work.

3.2.5.2 Thermal Creer»

Data on thermal creep is taken from Toebbe [9 3 ¡

r 17000 /-T£ = 2.6 x 1OD ex?( ) sinh ( —^— )

. T • 6000

with

• r -n£^, thermal creep rate L h J

T temparature [ °K 1O stress [N/cra2]

(15)

27

3-2.5O Induced and Clisib straluRates

These components of secondary creep have aiso been given

by Duricombe JJ5] :

¿. , , . , = 2.928 x 10" 2 D O O -i- 2.460 x 1O~37 0*'&) (16

O stress C?s\3

(t) fast flux [n/cm"s] (E > 1 MeV)

Fig.6 shows creep data from divers sources.AU the data has

been reduced to standard conditions: ' •

T = 300 °C .and CJ) = 1 . 2 <101 4 n/cm2s

Data on thermal creep, shov.Ti in the upper part of fig. 6,

has been converted to the- standard temperature in accordance

eq.(15)«£q. (15) is plotted in.fig.6 as a broken thick line.

Data on irradiation induced creep,shown in the lower part of '

fig.6 , has been converted to the standard fast flux in ac.cor-.-

dance with eq.(16).Eq.(16) is plotted in fig.6 as a continu-

ous line. The broken thin line in fig.6 was included to assis.t

in distinguishing beteen thermal and irradiation-induced creep

data. .

E

CL

>

AÜJ

o

O

5"

ooooroti

co

-ocoo

T3

O"Oco

oOO

1\\

o.O)

'ñ; « ° w -3- o -- ¡n<-> _ ro rO r e ro rOc\J

c <- f> _ .e « í; ©H - o "o 2 o - -

Q CC " l lO

— O

O

©\

\

oo

-4—»

O

CL0O

O

m-Ó

iO

_ O

asi

00

OHcao

•HNJ

«H

o

•H

29

4. Kumerical Results

This paper does not present a post-irradiation analysis

of in-pile experiments, it illustrates rather typical and

diverse capabilities of the üRANUS LWR-version (c.f. Summary).

Accordingly, two arbitrary power histories were chosen - one

at constant power (the simpleT case) and one at varying power

(c.f. fig. 7). In the foriner case the power was held constant

at 50 W/mm, while in the latter case the power was varied at

the rate of 50 W/mm per 10 hours. The programme can, in general,

analyse an axial power aistribution which is a function of

burn-up and/or other parameters; however, an axial power distri-

bution independent of time was used here (fig. 8). The remaining

input data is summarized in table 1. The ÜRANUS oütput is given

in table Z . As a result of this performance test, the folio- '

wing conclusions can be drawn:

The axial temperature distribution in the cladding and in the

fuel are shown in figs. 9 and 10 for the.constant power case.

A flow rate of 0.936 kg/sec .; along

with channel geometry and the physical properties of water,W

leads to a heat transfer coefficient of c = 0.044 bet-

ween coolant and cladding. The temperature at the

centre of the fuel decreases initially due to gap closure,

subseguently the temperature here increases slightly due to

an increásing amount of fission gas in the gap. The size of

the radial gap is shown in fig. T1. Mechanical contact bet-

ween cladding and fuel occurs for the first time after 1786-h

in the constant power case.The diametral strain %— at section 5 (Z = 1750-mm) of the •'

fuel rod is shown in fig? 12. The diametral strain ^j- isad e r ined as

A d R " R o

R o

1 00 [% ]

v.'here R is the instantaneous radius .

50

25

linear power Q[W/mm]

5000 10000 timelh]

Fig. 7 : Power history for case

30

31

Q / Q

0.5

max

0 1000 2000 3000 [mm]

^section

Fig. 8 : Axial power distribution .

32

temperature T

400-

350-

£=0.044 [W/mm°C]

section 9

Fig. 9 : Axial temperature distribution ¿n coolant

(Tcool} a n d c l a d d i n g { Tc l a d) for Q=SO w/mm.

33

temperature T [°C]

x

t =t =t =t =

O h

1OOO h

17B6h5000 h

2000

1000

Tfuel'o

í , ,1 L

section

Fig. 10 : Axial temperature distribution in .. •

fuel as a function of time for Q=5O W/mm.

34

100 r

50

radial gap[ [im ]

as - fabricated

section 9

Fig. 11 : Axial variation . of radial gap

as a function of time for Q= 50 W/mm.

35

diametral strain

0,1

o-0.1

-0.5

t burn-up^15000 [MWd/t]

oouter radiuSv

varymg powerinner radius/

outer radius\ , ,)constant power

j Fig. 12 : Diametral strain at section 5 (Z=1750 mm)

; as a functiO-n of burn-up. . ' .;•

36

During the first few operating hours the cladding moves towards

the fue!, but contact does not occur. On contacting, a mutual

contact pressure is built up. and both fuel and cladding

mov.e radially outwards.Ac-

tually, ciadding and fuel contact in practice somewhat earlier

than predicted by the axis y mine trie analyse described here. Two-

dirnensional methods, which can accommodate creep buckling, pre-

dict the onset of contact more realistically. In a future paper,

this aspect will be discussed in detail on the basis of the Nu-

merical Sandwich Method (c.f. [38] ).

Fig. 13 compares the axial strain in the fuel rodeas calculated

with the present URANUS versión on'the basis of equation (14),

with a series of experimental valúes for axial strain as dis-

cussed by Kummerer et al. £39] . The axial strain in the fuel

rod is shown in fig. 14 as a function of time (burn-up) for

the two power histories with no fuel/cladding interaction and

with fuel/cladding interaction at a high-coefficient of

friction. Axial strain •

is clearly dependent on the mechanical interaction between clad-

ding and fuel, as evidenced by the two curves. Atvarying power

the axial strain is somewhat larger than at constant power -

clearly a conseguence of ratchetting. These URANUS results are

compared with experimental valúes (Manzel [_40] ) in figs. 15

and 16. No detailed information is available on the procedures

used by Manzel for averaging burn-up and flux., also the model-

ling and material properties in the LWR versión of URANUS (as

discussed above) are of necessity subject to approximation and

uncertainty respectively. Nevertheless, URANUS calculations and

experimental valúes compare reasonably well. Fig. 17 shows a

typical stress histogram. Mechanical interaction oceurs aftér •

1786 hours of operation, subseguently a centact pressure of'vab.oir

24 MPa is built up. • : . • •':,.:/. '

The sample calculations discussed above were run on a PDP-1O. ;.

Running times using the URANUS code were compared with run'ning-

times using other codes by converting the former to IBM 370-168

times. Calibration tests had shown a conversión factor of 0.06

37

to be appropriate. Converted URANUS times are compared with

COMETHE IIIJ times [41] in fig. 18.

A direct,quantitative comparison between the codes is not

sought; in any case, tñis is not feasible, since the running

times, even after parti--al conversión, are not compatible

(IBM 370-168, CDC 6600). One can conclude, however,that the"

running times of the URANOS and COMETHE IIIJ codes are

similar since the computational speeds of the two machines

in guestion should not differ by a factor of more than 2. In

all fairness, though, it should be stressed that fuel creep,

fuel plasticity and friction due to ÍTiel/cladding interac-

tion, in general highly time-consuming phenomena, are not mo-

delled in the COMETHE IIIJ code.

Total running time with the URANUS code depends mainly on power

history and the numerical accuracy s'tipulated. IBM 370-168 run-

ning time for the test cases discussed above (integral fuel rods]

varied between 22 sec (cladding alone, no fuel, constant power)

and 12 min (completely general case).

The numerical results do not represent post-irradiation analyses

of any particular experiments, they illustrate rather typical

and diverse URANUS usage. Individual experiments can only be

subject to mea-ningful ppst-irradiation analyses when a more

detailed calibration of modelling and material properties in

URANUS has been accomplished. The performance tests show, how-

ever, that the LWR versión of the URANUS code is reliable and

efficient, thus providing a valuable tool for thermal and me-

chanical fuel rod analysis.

38

1.0

C

O

I i m i t ofexperimental coverage [39]

eq.íU)

321 j O 2 2

fast fiuence [n/cm]

Fig. 13 : Comparison between axial strain determined experimentally.

(Kummerer, et al. [39] ). and via URANUS (eg.(14) .) . . ;' >

10

axial strain

^ [ % o ]

o

varyíng power

constant power

no interaction.^S alone)

5000 10000 íimeTTh ]

100001 ;—, Bw»

20000 burn-up [ MWd/t]

Fig. 14 : Axial strain in the fuel rod for two power hisbories as a

.' function of time and burn-up (hot state) .

39;'a

40

Manzel [40]URANUS (strong interaction)URANUS (no interaction)

D

10000 20000burn-up [MWd /t ]

Fig. 15: Axial strain in the fuel rod (constant power) as a

function of burn-up ( cold state ) .

41

0.5

c'o 0.1

Manzel [ 40 ]URANUS (strong ¡nteraction)

URANUS (no interaction )

(J)

OX

o

0.01

i i l i l i J I I l i l i

101 1 Q20

fast f luence [ n /cm 2 ]

Fig. 16 : Axial strain in the fuel rod (constant power) as a

function of fast fluence ( E>1 MeV , cold state ) .

42

-20

-10

. radial stress í MPa ]

R4.735 mm

radius RQ5.355mm

Fig. 17 : Radial stress in the cladding as a function of time.

0.2

0.1

running time (CPU)

' [ s ]

10 20 number of rings-HSW-

Fig;~ > 18 Running time (CPU) for one time step and one slice as a '

function of the number of rings. !

44

Acknowledgements:

URANUS was developed by K.LaSmann at the Technical

University of Darmstadt in the Institute of Reactor

Technology (IRT). The work was decisively supported by

the Fast Breeder Project (PSB) of the Nuclear Research

Centre Karlsruhe (GfK). Special thanks are due to Dr.

Karsten (PSB).

The work described in the present paper was performed

within the framework of a bilateral cpoperation between

the Institute of Reactor Technology'and the Junta de

Energia Nuclear (Spain),the cooperation taking place

under the auspcies of the International bureau (IB) at

the Research Centre Karlsruhe.K.LaSmann developed the

LWR versión of the URANUS code used in the present

investigation,material properties (c.f.section 3) were

reviewed and supplied by A.Moreno.Contributions from

Prof. Dr. Laue (IB) and Prof. Dr. Humbach . (Director,IRT),

which had a marked influence on the success of the work,

are gratefully acknowledged. " . • .

Table 1: ÜRANUS inout data for Derformance test

45

Outer radius, fuel

Inner radius, cladding

Outer radius, cladding

Active length

Total length .

Roughness, fuel

Roughness, cladding

Grain size, fuel

Porosity

Flux depression 0 max

0 min

Fast flux (average)

fuel

Linear power (average)

Stoichiometry

Internal pressure (t=0)

External pressure

Number of axial sections

4,645 inm

4,735 mm

5,355 mm

3 500 mm

3700 mm

0.00125 mm

0.004 mm

0.01 mm

0.04

0,919

1.0x10•14 1

cm sec

3 9,1 W/mm

1 .98

50 bar

158 bar

9

46

Table 2 V URANUS output

In this table the following notation is used;

" A r(R,t,z)

a(R,t,Z)

R : Radius

t : time

Z : height above datum

Output:

(R.t,z)

r : radial

t : tangential

a : axial

{s }-

SWG\ .

sine ;•«.sin \

stress

strain

crack strain

thermal strain

swelling strain

hot-pressing strain

creep strain

time independent

plástic strain

crack structure

e

e

crv

R, R

Z, Z

ref

ref

P, C.

: temperature

: porosity

: burn-up

: flux

: fluence

: equivalent

creep strain

: equivalent

.plástic strain

:•equivalent

stress

: heat tfansfer

coef fi.cient

: a c t u a l , •-.'..

reference radius.. ..•

•:. actual, reference'

height above datum

: gas pressure and

composition

47

References

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the design;inpile performance prediction and post-

irradiation anaiysis of arbitrary fue! rods. Part I:

Theory and rnodeiling. NucL. Eng. . Des, , 31 (1974)p. 3oS - 336

/2/ jj. R. Matthews, The quantitative description of de-

formation and stress in cylindrical fast reactor fuel

pins . In : Advances in Nuclear Science

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/3/ K. LaBmann, Zur Behandlung der axialen Reibkrafte in

integralen Brennstabcodes, Atomkernenergie (ATKE) 27,

Lfg. 1, p. 71 (1976)

/.4/ K. Laftmann, Der intégrale Brennstabcode URANUS,

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48

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/I/ H.L. Gehr, Datensammlung zur Kernelementauslegung

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/8/ G. Ondracek and B. Schultz, The porosity dependence of

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J. Nucí. Mater. Vol. 46 (1973) No. 3 .

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Interatom --Technischer Bericht, 73.65 (1973)

/10/ S. Oldberg / Behave-2; Oxide fuel performance code in

two spatial dimensions and time , GEAP-1378.8 (<312.)

/11/ H. Tobbe, Das Brennstabrechenprogramm Iambus zur Auslegung

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/12/ General Electric Corapany, Standard Safety Analysis Reporf/.

(GES/AR) Section 4.2.1.3.4.3. (^9?3;

49

/13/ H. Stehle et al., U0 2 properties for L W R fuel rods,~*

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/14/ L. D. Loch, I. F. Quirk, Ceramics, Reactor Handbook

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/15/ E. Duncombe et al,, CYGRO-3, A computer program to deter-

mine temperatures,stress and deformations in oxide fuel

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/16/ B.M. Ma / Irradiation swelling,creep and thermal stress

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Nucí. Eng. Des. 34 (1975) No. 3y/o.361

/17/ J.L. Jiménez, L W R fuel rod behavicur analysis

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Energia Nuclear No. 102 ( July-August 76

/18/ R. 0. Meyer, B.J. Buescher, A simple method for calcu-

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sche und mechanische Analyse von Brennstaben eines.Kern-,

reaktors (in pre.parat.ion.) . . . ' •'•.•"-'

50

/2O/ A. A. Solomon et al., Fission induced creep of UO-

and its significance to fuel element performance

ANL-7857 (1971)

/21/ E.Duncombe et al., Comparisons with experiment • of"

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of irradiated bulk-oxiáe-fuel test rods using CYGRO-1oomputer programmWAPD- TM- 5*8 3 (1 9 6 7)

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/25/ H. Elbel, D. Gobel, KfK-E.xt 6/73-4 (Sep 1973)

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51

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52

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/39/ K. Kummerer, H. Stehle, H. G. Weidinqer, Verhalten von

Brennstaben bei hoherem Abbrand, atv/ XVI, (1971), p. 549

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rohren,atw XVIJ,(1972), p. 563

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J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid.

"Versión para reactores de agua ligera del código decálculo integral de barras combustibles uranus".LABMANN, K.; MORENO, A. (1977) 52 pp. 18 f i gs . 41 refs.

Se presenta la versión para reactores de agua ligera del código URANUS. Este códigoes un programa para el análisis mecánico y térmico de barras combustibles. Se discutenlas propiedades de los materiales y su influencia sobre el comportamiento de la barrade combustible, según los resultados obtenidos con el código URANUS. Los resultados nu- ¡méricos no representan análisis de post-irradiación ni experimentos dentro del núcleo,i lustran únicamente las diversas posibilidades del código URANUS. Las pruebas realizadasmuestran que el código es f iable y eficiente, por lo que es una herramienta ú t i l en elanálisis de barras combustibles. K. L'assmann ha desarrollado l a versión para reactoresde agua l igera del código URANUS. Las propiedades de los materiales fueron revisadas ysuministradas por A. Moreno.CLASIFICACIÓN INIS Y DESCRIPTORES: E23. U Codes. Fuel rods. Thermal analysis.Creep.P las t ic i ty . Numerical solutions. Mathematical models. PWR type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."Versión para reactores de agualigera del código de

cálculo integral de barras combustibles uranus" •LABHANN, K.; MORENO, A. (1977) 52 pp. 18 f i gs . 41 refs.

Se presenta la versión para reactores de agua l igera del código URANUS. Este códigoes un programa para el análisis mecánico y térmico de barras combustibles. Se discutenlas propiedades de los materiales y su influencia sobre el comportamiento de la barrade combustible, según los resultados obtenidos con el código URANUS. Los resultados nu-méricos no representan análisis de post-irradiación ni experimentos dentro del núcleo,i lustran únicamente las diversas posibilidades del código URANUS. Las pruebas realizadasmuestran que el código es f iab le y eficiente, por lo que es una herramienta ú t i l en elanálisis de barras combustibles. K. Lassmann ha desarrollado la versión para reactoresde agua l igera del código URANUS. Las propiedades de los materiales fueron revisadas ysuministradas por A. MorenoCLASIFICACIÓN INIS Y DESCRIPTORES: E23. U Codes. Füel rods. Thermal analysis. Creep.Plast ie i ty . Numerical solutions. Mathematical models. Pffi type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."Versión para reactores de agua ligera del código de

cálculo integral de barras combustibles uranus".LABMANN, K.; MORENO, A.,(1977) 52 pp. 18 f igs . 41 refs.

Se presenta la versión para reactores de agua l igera del código URANUS. Este códigoes1 un programa para el análisis mecánico y térmico de barras combustibles. Se discutenlas propiedades de |os materiales y su influencia sobre el comportamiento de l a barrade combustible, según los resultados obtenidos con el código URANUS. Los resultados nu-méricos no representan análisis de post-irradiación ni experimentos dentro del núcleo,i lustran únicamente las diversas posibilidades del código URANUS. Las pruebas realizadasmuestran que el código es f iable y eficiente, por lo que es una herramienta ú t i l en elanálisis da barras combustibles. K. Lassmann ha desarrollado la versión para reactoresde agua l igera del código URANUS. Las propiedades de los materiales fueron revisadas ysuministradas por A. Moreno.CLASIFICACIÓN INIS Y DESCRIPTORES: E23. U Codes. Fuel rods. Thermal analysis. Creep.Plnst ic i tv . Nuroirical solutions. Mathematical models. PWR type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."Versión para reactores de agua ligera del código de

cálculo integral de barras combustibles uranus".LABMANN, K.; MORENO, A. (1977) 52 pp. 18 f igs . 41 refs.

Se presenta la versión para reactores de agua l igera del código URANUS. Este códigoes un programa para el análisis mecánico y térmico de barras combustibles. Se discutenlas propiedades de los materiales y su influencia sobreseí comportamiento de la barrade combustible, según los resultados obtenidos con el código URANUS. Los resultados nu-méricos no representan análisis de post-irradiación ni experimentos dentro del núcleo,i lustran únicamente las diversas posibilidades del código URANUS. Las pruebas realizadasmuestran que el código es f iab le y eficiente, por lo que es una herramienta ú t i l en elanálisis de barras combustibles. iK. Lassmann ha desarrollado la versión para reactoresde agua l igera del código URANUS. Las propiedades de los materiales fueron revisadas ysuministradas por A. Moreno.CLASIFICACIÓN INIS Y DESCRIPTORES: E23. U Codes. Fuel rods. Thermal analysis. Creep.Plast ic i ty . Numerical solutions. Mathematical models. Pffi type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."The I igh t -Water -Reac tor Vers ión of the URANUS Inte

g r a l Fue l -Rod Code" .LABMANN, K.; MORENO, A. (1977) 52 pp. 18 f igs. 41 refs.

The LWR versión of the URANUS codo, a digital computer programme for the thermal andmechanical analysis of fuel rods, is presented. Material properties are discussed and ' 'their effect on integral fuel rod behaviour elaborated via URANUS results for some care-ful ly selected reference experiments. The numorical results do not represent post-irra-diation analyses of in-pile experiments, they illustrate rather typical and diverseURANUS capabilities. The performance test shows that URANUS is reliable and efficient,thus the code is a most valuable tool in fueV rod analysis work. K. LaBmann developsdthe LWR versión of the URANUS code, material properties were reviewed and supplied byA. Moreno.INIS CLASSIFICATION AND DESCRIPTORS: E23. U Code. Fuel rods. Thermal analysis. Creep.Plasticity. Numerical solutions, Mathematical models. PWR type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid.

"The Light-Water-Reactor Versión of the URANUS Integral Fuel-Rod Code".LABMANN, K.; MORENO, A. (1977) 52 pp. 18 figs. 41 refs.

The LWR versión of the URANUS code, a digital computer programme for the thermal andmechanical analysis of fuel rods, is presented. Material properties are discussed andtheir effect on integral fuel rod behaviour elaborated vía URANUS results for some care-ful ly selected reference experiments. The numerical results fo not represent post-irra-diation analyses of in-pile experiments, they illustrate rather typical and diverseURANUS capabilities. The performance test shows that URANUS is reliable and efficient,thus the code is a most valuable tool in fuel rod analysis work. K. LaBmann developedthe LUIR versión of the URANUS code, material properties were reviewod and supplied by

A. Moreno.INIS CLASSIFICATION AND DESCRIPTORS: E23. U Code. Fuel rods. Thermal analysis. Creep.Plasticity. Numerical solutions. Mathematical models. PVJR type reactors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."The Light-Water-Reactor Versión of the URANUS Inte

gral Fuel-Rod-Code".LABMANN, K.; MORENO, A. (1977) 52 pp. 18 figs. VI refs.

The LWR versión of the URANUS code, a digital computer programme for the thermal andmechanical analysis of fuel rods, is presented. Material properties are discussed andtheir effect on integral fuel rod behaviour elaborated via URANUS results for some cara-ful 1 y selected reference experiments. The numerical results do not represent post-irra-diation analyses of in-pile experiments, they illustrate rather typical and di verseURANUS capabilities. The performance test shows that URANUS is reliable and efficient,.thus the code is a most valuable tool In fuel rod analysis work. K. LaBmann rievelopedthe LWR versión of the URANUS code, material properties were roviewed and supplied byA. Moreno.INIS CLASSIFICATION AND UESCRIPTORS: E23.'U Code. Fuel rods. Thermal analysis. Creep.

- - • « • > - - ! U t , rp.ar.tors.

J.E.N. 397

Junta de Energía Nuclear. División de Metalurgia. Madrid."The Light-Water-Reactor Versión of the URANUS Inte

gral Fuel-Rod-Code".LABMANN, K.; MORENO, 'A. (1977) 52 pp. 18 figs. 41 refs.

The LWR versión of the URANUS code, a digital computer programme for the thermal andmechanical analysis of íuel rods, is presented. Material properties are discussed andtheir effect on integral fuel rod behaviour elaborated via URANUS results for some care-ful ly selected reference experiments. The numerical results do not represent post-irra-diation analyses of in-pile experiments, they illustrate rather typical and diverseURANUS capabilities. The performance test shows that URANUS is reliable and efficient,thus the code is a most valuable tool in fuel rod analysis work. K. LaBmann developedthe LWR versión of the URANUS code, material properties were reviewed and supplied byA. Moreno.INIS CLASSIFICATION AND DESCRIPTORS: E23. U Coda. Fuel rods. Thermal analysis. Creep.Plasticity. Numérica! solutions.Mathematical models. PWR typo reactors.