NUREG/IA-0164

RRC KI 2180

IPSN 99/10

International

Agreement Report

Modification of

USNRC's FRAP-T6

Fuel Rod Transient Code

for High Burnup VVER Fuel

Prepared by

A. Shestopalov, K. Lioutov, L. Yegorova, G. Abyshov, NSI-RRC

K. Mikitiouk, INR-RRC

Nuclear Safety Institute of Russian Research Center "Kurchatov Institute"

Institute of Nuclear Reactors of Russian Research Center "Kurchatov Institute"

Kurchatov Square 1

Moscow 12382

Russia

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

May 1999

Prepared for

U.S. Nuclear Regulatory Commission, Institute for Protection and Nuclear Safety

(France), and Ministry of Science and Technologies of Russian Federation

Published by

U.S. Nuclear Regulatory Commission
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NUREG/IA-0164

RRC KI 2180

IPSN 99/10

International

Agreement Report

Modification of

USNRC's FRAP-T6

Fuel Rod Transient Code

for High Burnup VVER Fuel

Prepared by

A. Shestopalov, K. Lioutov, L Yegorova, G. Abyshov, NSI-RRC

K Mikitiouk, INR-RRC

Nuclear Safety Institute of Russian Research Center "Kurchatov Institute"

Institute of Nuclear Reactors of Russian Research Center "Kurchatov Institute"

Kurchatov Square 1

Moscow 12382

Russia

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

May 1999

Prepared for

U.S. Nudear Regulatory Commission, Institute for Protection and Nuclear Safety

(France), and Ministry of Science and Technologies of Russian Federation

Published by

U.S. Nuclear Regulatory Commission

ABSTRACT

The USNRC's transient fuel rod code, FRAP-T6, has been modified to analyze pulse tests with high

burnup VVER fuel rods in the Impulse Graphite Reactor (IGR). New and modified models of separate

phenomena have been developed, including models for heat transfer from the cladding to the stagnant

coolant, the effect of fission gas swelling on the fuel-cladding gap, and the conditions of base irradiation.

Thermal and mechanical properties for the VVER's Zr-i%Nb cladding were added to MATPRO-Vl1,

which is used by the FRAP-T6 code. Changes in the input data file are described, and a sample calculation

is presented with the modified code. A FORTRAN listing for the new and modified models is given in an

Appendix A.

RRC K12180 I
TABLE OF CONTENTS

1. INTRODUCTION ................................................................................................. 4

2.THERM AL, DYNAM[ICS, .......................................................... ........................... 6

2.1. THE MODEL TO ANALYZE POWER RATE IN THE FUEL W ITH CENTRAL H OLE ........................E....... 6

2.2. ALTERNATIVE MODEL OF HEAT TRANSFER UNDER FILM BOILING ........................................... 6

2.3. THE MODEL OF CLAD-To-Am HEAT TRANSFER ....................................................................... 7

2.4. THE MODEL OF THE CLADDING REWETING ........................................................................... 8

3. THERM AL MECHANICS ............................................................... .................. 10

3.1. ACCOUNTING FOR THE FUEL GAS SWELLING WHEN ANALYZING FUEL-CLADDING GAP SIZE ..... 10

3.2. CLADDING BALLOONING MODEL ......................................................................................... 10

4. FISSION GAS BEHAVIOR ............................................................................. . 12

4.1. APPROACH TO ANALYZE FISSION GAS BEHAVIOR UNDER BASE IRRADIATION CONDITIONS ....... 12

4.1.1. Fuel swelling due to accumulation of the fission products ..................................................... 12

4.1.2 Irradiation-induced fuel densification ..................................................................................... 13

4.1.3. Dependence of the power rate radial non-uniformity versus time ............................................ 13

4.2. INITIAL DATA AND THE PROCEDURE TO ANALYZE FISSION GAS BEHAVIOR UNDER THE BASECONDITINONS ..................................................................................................................................... 13

4.2.1. Extension of the power history array ........................................................................................ 13

4.2.2 The method to specify input dasa for the analysis of base irradiation ..................................... 13

4.2.3. Analysis of thejfuel rod behavior under base irradiation conditions ....................................... 13

5. ALTERNATIVE THERMAL - PHYSICAL MATERIAL PROPERTIES

(M ATPRO-V11 LIBRARY EXTENSION) ............................................................ 15

5.1. THERMAL-PHYSICAL PROPERTIES OF FUEL ........................................................................... 16

5.1.1. Fuel specific heat (FCP) and enthalpy (FENTHL) .................................................................. 16

5.1.2. Thermal expansion (FTHEXP) ................................................................................................. 17

5.1.3. Thermal conductivity of the VVER type of UO0 and dependence of thermal conductivity versus fuel

burnup (FTHCON, BURNUP, TCOR) ................................................................................................ 18

5.1.4. Thermal-physical constants (PHYPRP) ................................................................................... 19

5.2. THERMAL-PHYSICAL PROPERTIES OF ZR-I%NB CLADDING ................................................ 20

5.2.1. Thermal-physical constants (PHYPRP) ................................................................................... 20

5.2.2 Specific heat (CCP) and enthalpy (CCINP) .............................................................................. 20

5.2.3. Thermal expansion (CTHEXP) .................................................................................................. 21

5.2.4. Thermal conductivity (CTHCON) ............................................................................................. 23

5.2.5. High temperature oxidation (COBILD) ................................................................................... 24

5.3. MECHANICAL PROPERTIES OF ZR-i%NB CLADDING .......................................................... 25

5.3.1. Young's modulus (CELMOD) and Poisson's ratio (EMCPIR) ................................................ 25

5.3.2. Meyer micro-hardness (CMHARD) .......................................................................................... 26

5.3.3. Plastic deformation of the cladding (CKMN) ........................................................................... 26

5.3.4. Cladding failure criterion (CMULIMT) ...................................................................................... 29

6. CODING ASPECTS ............................................................................................. 31

6.1. DESCRIPTION OF THE NEW GLOBAL VARIABLES .................................................................. 31

6.2. DESCRIPTION OF THE NEW AND MODIFIED SUBROUTINES .................................................... 35

7. USER'S A IANUAL ............................................ ............................................. 38

7.1. DESCRIPTION OF THE NEW INPUT DATA ................................................................................ 38

RRC K122180 2
7.2. DEsCRwroN OF THE OUTPUT INFORMATION ...................................................................... 42

7.2.. Output file FGRAXS.DAT ........................................................................................................... 42

72.2. Outputfile FGRTRAN.DAT and FGR_TOTDAT ................................................................. 43

7.2.3. Output files FGRJ.ADS.DAT and FGRJ.ADT.DAT ............................................................ 43

7.2.4. Output fdes BALOONJ.DAT, BALOON2.DAT ............................................................................. 44

7.2.5. Output file GRAPH.DAT ............................................................................................. 45

7.2.6. File BRIEF.OUT (brief listing) ................................................................................................. 47

7.2.7. Post-processing utilit for the STRIPFfile ............................................................................. 49

7.3. COMMENTS ON THE USERS AND DEVELOPERS OF FRAP-T6/VVER CODE ........................... 50

7.3.1. The limits for applicability of the adapted FRAP-T6/VVER code ................................................. 50

7.3.2. Further development of the adapted version of FRAP-T6 code .................................................... 51

8. CALCULATION EXAM PLES . .................................................. ........................ 52

8.1. THE EXAMPLE OF CALCULATED RE•ULTS OF THE VVER FUEL ROD BEHAVIOR UNDER TESTING

CONDITIONS IN IGR REACTOR ......................................................................................................... 52

1REFERENC.ES... .. 56

APPENDIX A. List of new and modified subroutines of FRAP-T6/VVER codeA-1

APPENDIX B. The revealed mistakes ................... ................... ..................... B-1

RRC K122180 3
1. INTRODUCTION

In the Russian Research Center "Kurchatov Institute", the behavior of high burnup VVER-type fuel rods

was studied under conditions of reactivity-initiated accidents. Testing of these fuel rods in the Impulse

Graphite Reactor (IGR) led to a number of special features. A single fuel rod with an active length of -

150 mm and filled with helium (1.6-2.3 MPa) was put in a capsule that was filled with stagnant coolant

(water or air) at room pressure and temperature. This capsule was put in the IGR reactor central channel,

and the reactor power was pulsed with a pulse width of 0.7-0.9 sec to simulate a reactivity accident. A

large number of tests like this were performed, and they are described in a separate report [1].

A transient fuel rod code was sought to analyze the test data and provide the capability to perform related

safety transient calculations. Two codes were obtained for this purpose. One was the USNRC's FRAP-T6

transient fuel rod code developed at the Idaho National Engineering Laboratory (USA) [2]. The other was

the IPSN's (Institute for Protection and Nuclear Safety (France)) SCANAIR transient fuel rod code

developed at the Cadarache Center for Studies (France) [3]. Both codes required modification for this

application. Modifications to the FRAP-T6 code are described in this report, and modifications to the

SCANAIR code are described in another report [4].

FRAP-T6 code models the following main accident phenomena:

1. change of thermal-mechanical properties of the fuel and cladding materials of the LWR reactor type

versus temperature, burnup, etc.;

2. distribution of temperatures in the fuel rod considering the change of thermal conductivity of the fuelcladding gap, connected with the change of the gap size and gas composition due to the fission product

release out of fuel;

3. stress-strain state of the fuel cladding in the assumption of the <<thin-walledc, cladding, including the

stage of fuel-cladding mechanical interaction. In this case thermal expansion is modeled, elastic

deformation, deformation of the cladding plasticity, as well as thermal expansion of the fuel pellet;

4. cladding failure;

5. high-temperature oxidation of the cladding;

6. fission gas behavior in the fuel rod, gas swelling of the fuel, change of the gas composition and pressure

inside the cladding;

7. water coolant behavior, and heat transfer from the fuel cladding to the water.

FRAP-T6/v.21/90 version of the code was used for the analysis. Two main tasks were to be solved in order

to adapt FRAP-T6 code to the conditions of the VVER fuel rod testing in IGR reactor.

1. to account for specific features of the high burnup VVER fuel rods;

2. to validate FRAP-T6 code for the conditions of the capsule testing.

The following features of the IGR tests were identified to solve the first task:

1. use of the fuel rods of VVER. This required introduction of thermal-physical and mechanical properties of VVER fuel and Zr-l%Nb cladding into MATPRO-V1 1 [5] data base of material properties;

2. testing of high burnup fuel rods. This required introduction into FRAP-T6 code of a number of models

for preliminary analysis of the fuel rod behavior under the base irradiation conditions; such calculations

were necessary to get the data on the fission gas distribution in the fuel at the end of the basis

irradiation mode. The obtained data were used as input data when modeling the IGR tests;

3. use of the air coolant in some tests. This required introduction into FRAP-T6 code of the heat transfer

models with free circulation of the gas coolant and thermal-physical properties of the air.

Verification of the code including the use of the data obtained with the help of instrumented fuel rods was

necessary in order to solve the second task. Verification results were used to modify some of the models of

RRC K12180 4
FRAP-T6 code. Comparison of the obtained calculated and experimental data allowed to reveal a number

of models requiring adaptation to the specific features of the IGR tests. In particular, the alternative models

to calculate gas gap size, and the models for heat transfer from the cladding to the water coolant in the

regimes of film boiling and rewetting of the cladding were developed.

A general description of the computer code modifications for FRAP-T6 and SCANAIR, along with

calculations, material properties, and the data base for validation, are given in another report [1]. The

details of the FRAP-T6 modification are given here.

The second chapter of the report describes modifications of the thermal-physical package of FRAP-T6

code to account for specifics of the design of VVER fuel rods tested in IGR reactor, and for the specifics

of the fuel rod cooling in the capsule experiments. Adaptive models of heat transfer to the water and air

coolants, and thermal-physical properties of the air coolant are presented.

The third chapter of the report presents the changes made to thermal-mechanical block of the code for the

better analysis of both thermal-physical and thermal-mechanical parameters of the burnup fuel rod in the

case of the accident. The model accounting for the influence of the fuel pellet gas swelling onto the gas

gap size is presented.

The fourth chapter reviews modifications of the model describing fission product behavior in the fuel

under the conditions of base irradiation. The above modifications were necessary to obtain the data on

distribution of fission gas accumulated in fuel in the process of burnup. These are the input data when

modeling testing of the burnup fuel rods in IGR reactor.

The fifth chapter presents thermal-physical and thermal-mechanical material properties of the VVER fuel

rods, that were included into MATPRO-V1 1 base of material properties used by FRAP-T6/VVER code.

The sixth chapter reviews the aspects of programming connected with the new version of FRAP-T6IVVER

code. New global variables, new and modified subroutines are described.

The seventh chapter is the user's manual on the practical application of the version. It includes description

of the new input data, alternative program to process the output information, and recommendations to the

users of FRAP-T6IVVER code to model fuel rod behavior under the conditions of pulse testing in IGR

reactor. The chapter also includes proposals and recommendations of the authors to the further broadening

of the capabilities of FRAP-T6/VVER code to model RIA processes.

The example of calculated results of the VVER fuel rod behavior under test conditions in IGR reactor

given in chapter eight demonstrates the limits of applicability of the developed version and can be used for

checking correctness of FRAP-T6/VVER version. Example of the nodalization scheme to model the fuel

rod by FRAP-T6/VVER code is presented.

Appendix A presents a FORTRAN listing of the subroutines described in chapter 6 and containing new

and adaptive models, as well as the example of the input deck file. Bugs found in the texts of FRAP-T6

subroutines are listed in Appendix B.

RRC K 2180 5
2. THERMAL DYNAMICS

FRAP-T6 code performs the analysis of the non-steady-state temperature field in the fuel rod with

consideration of the changes of the geometrical sizes of the fuel pellet and cladding in the radial direction

during the accident.

New models to specify power rate in fuel with central hole during base irradiation and heat transfer from

the fuel cladding to the coolant are added in order to adapt thermal-physical block of FRAP-T6 code to the

specifics of IGR/VVER processes. Model of heat transfer under the conditions of free convection of the

gas coolant, and thermal-physical properties of air are incorporated into code as an additional model of

clad-to-air heat transfer.

2.1. The model to analyze power rate in the fuel with central hole

The method to analyze power rate was changed for correct consideration of the radial power rate in the

fuel pellet with central hole. In the initial version of FRAP-T6 code it is possible to input the radius of the

central hole, the volume of which is considered for the analysis of internal gas pressure of fuel rod. Still,

when calculating power rate radial distribution it is not considered that no heat is generated in the central

hole. This drawback is corrected in the proposed model for the analysis of the power rate radial profile in

the fuel.

RINTIM, FINT, RIMMOD subroutines contain alternative method to specify input data on power rate in

fuel with the central hole. RIMMOD subroutine is developed on the base of PRAD subroutine from

original FRAP-T6 code. FORTRAN text of this subroutines is presented in Appendix A.

2.2. Alternative model of heat transfer under film boiling

In accordance with verification calculations [1] the model to calculate post-critical heat transfer coefficient

based on Bromley-Pomerantz [2] correlation was replaced with the Labuntzov model. Labuntzov model,

developed for the turbulent regimes of film boiling and modified to account for the boiling conditions of

the large volume of subcooling water is [6]:

a,, = 0.25(,tcf(pP ) _)3

SVS

Where aa = heat transfer coefficient (W/m2K);

As = vapor thermal conductivity (Wim K);

cp = vapor specific heat (J/kg K);

pf = fluid density (kg/m3

);

ps = vapor density (kg/m3);

g = gravity acceleration (m/s2);

v = vapor kinematic viscosity (m2

/s).

To take into account the initial subcooling of water, the correction factor is introduced [7]:

aý= a (1+O. ( )075 A)I

pe hfg

RRCKK12180 6
where a;, = corrected heat transfer coefficient (W/m2K);

Ai = enthalpy of fluid at saturation minus enthalpy at fluid bulk temperature (J/kg);

hfi latent heat (J/kg).

Alternative model of the film boiling is included into QDOT subroutine called by HTRC subroutine, text

of which is. presented in Appendix A.

2.3. The model of clad-to-air heat transfer

There exists the capability in HTRC subroutine to model heat transfer coefficient from the fuel rod to

helium coolant in the conditions of forced lengthwise circulation in the bundle of rods. HTRC subroutine

also has the respective base of the helium thermal-physical properties. But in the code there is no heat

transfer model for the conditions of large volume of stagnated air coolant.

Heat transfer model, which is a part of QDOT subroutine, called by HTRC subroutine consists of two

parts: free convection heat transfer and heat transfer due to radiation.

h = h. + h,d,

where h.. = heat transfer coefficient due to convection;

h.0 = heat transfer coefficient due to radiation (the code already has this model).

Heat transfer coefficient due to convection can be determined by the system of the following equations [8]:

Nu =CRa", Ra=GrPr,

Gr = gfl(tW - t1)z3

3

V.a

h. 2Nu

z

where NuM Ra, Gr, Pr = Nusselt number, Rayleigh number, Grashof number, Prandtl number,

respectively;

g = acceleration due to gravity (m/s 2);

,8 = thermal expansion volumetric coefficient (l/K);

z = heating length (m);

1w = wall temperature (K);

tf = fluid temperature (K);

C, n = coefficients;

2= thermal conductivity (W/m K);

h. = heat transfer coefficient due to convection (W/m2 K);

v = kinematic viscosity (m2

/s);

a = temperature conductivity (m2

/s).

RRC IK 2180 7
Nu, Ra, Gr, Pr are calculated at the temperature:

(tw +tf)

2

C, n coefficients are identified according to the data of Table 2.1.

Table 2.1. C, n coefficients vs. Ra, Pr.

Ra Pr C n

0.1 0.32 0.25

1.0 0.54 0.25

10 0.62 0.25

100 0.66 0.25

09- 1013 0.15 0.333

Heat flux due to heat transfer by radiation from the fuel cladding to the capsule wall is analyzed with the

use of FRAP-T6 original model.

The following thermal-physical properties of the air are used in the form of polynomials versus

temperature [8]:

A = 24.407 + 7.978-10-2- t - 3.154-10-5 t

2 + 0.802.10-8. t3 ,

cp = 1004.16- 9.761-10-3. t + 55.229-10-5 _t2 -36.275.10-4- t3,

a = 10-6 (18.788 +13.484. 10-2 . t + 13.959 l0-5- t 2 -4.654- 10'- t 3 ),

a= 10-6- (17.162 + 49.894.10-3 .t - 2.935 -105

- t

2 +1.133-10-4 .t

3,

p = -2.883. l0-3 + 355.06/(t + 273) + 353.527/(t + 273)2,

where X = thermal conductivity (W/n K);

cp = specific heat (J/kg K);

a = temperature conductivity (m2Is);

g-= dynamic viscosity (Pa s);

p = density (kg/m3);

t = average between temperature heated wall and coolant (°C).

2.4. The model of the cladding rewetting

The moment for the beginning of the rewetting is determined by the model developed in RRC -"KI* [9].

The option for analyzing of the rewetting moment is specified in the input data file. Heat transfer

coefficient in the mode of transfer from the film to the nucleate boiling is defined by the linear

interpolation between two points in the boiling curve. The first point corresponds to the heat transfer

coefficient at film boiling at the moment of beginning of the rewetting. The second point corresponds to

the heat transfer coefficient for the complete wetting, i.e. at the nucleate boiling, and it is determined

according to the heat flux of the second type.

RRC KI 2180 8
The main idea of the proposed method is as follows:

" the wetting rate does not depend on the rate of the fluid supplied from the outside; it depends only on

the rate of the steam bubble generation, since under these conditions a free access of the fluid to the

steam film is provided;

" the presence of axial - radial heat leakages through cold end elements of the fuel rod leads to the

generation of wetting waves at the top and bottom boundaries of the heated section of the fuel rod; and

boundaries of wetting waves gradually move to the fuel rod center.

In other words, axial heat leakages into unheated parts of the fuel rod lead to a decrease in the cladding

temperature in axial segments near unheated parts of the fuel rod. Thus, rewetting fronts occur and move

from upper and lower parts of the fuel rod to the center of the heated length.

The solution of the two-dimensional non-stationary equation of the heat conductivity in the solid with

internal heat sources formed the basis of the method:

pc- a =-1 a- r + I Tr )+q,

where p = clad density (kg/m3);

c p clad specific heat (J/kg K);

T = Temperature (K);

X = clad thermal conductivity (W/m K);

q, = volume internal heat source (W/m3

).

In this case, p, cp, k, k are functions of the temperature. Additionally, an axial profile of cladding

temperature is specified in the region of the rewetting front by the corresponding equations. This profile

depends on the velocity of the rewetting front. At the rewetting front the cladding temperature is equal to

the minimum stable film boiling temperature. The solution of this equation is reduced to the solution of a

system of algebraic equations with respect to the dislocation velocity of the rewetting front. The values

obtained for the velocities of the rewetting fronts, moving upward and downward, are used to obtain the

moment of rewetting for each axial slice. Distances, covered by each of the rewetting fronts by the time t,

are found by integration:

I I

where t = current time (s);

Lv (t) = Distance covered by the rewetting front, moving upward (m);

LD (t) = Distance covered by the rewetting front, moving downward (m);

tD = time at which rewetting of the lower heated part of the fuel rod starts (s);

tu = time at which rewetting of the upper heated part of the fuel rod starts (s);

(') = -u Velocity of the rewetting front, moving upward (od/s);

uD (') = Velocity of the rewetting front, moving downward (mis).

Model for the rewetting is realized as the separate REWETT subroutine called by QDOT subroutine in the

block analyzing heat transfer in the HTRC subroutine (Appendix A).

RRC K1 2180 9
3. THERMAL MECHANICS

3.1. Accounting for the fuel gas swelling when analyzing fuel-cladding gap size

Deformation of the fuel pellet is determined with only fuel temperature expansion and potential cracking

of the fuel (if the cracking option is specified in the input deck) in FRAP-T6 Ver.21. Additional possibility

has been introduced to account for the fuel pellet deformation component caused by the fuel gas swelling

when analyzing the fuel-cladding gap size.

GRASF subroutine performs calculation of gas release from fuel matrix, and of the relatively volumetric

swelling of the pellet. Considering isotropic expansion of the fuel pellet, relative radial displacement of

fuel can be presented as:

r 3

where r=- outer fuel radius (m);

V= fuel volume (m3).

The obtained value of the fuel displacement is transferred through the additionally developed COMMON

BLOCK (WWER.H header) to DEFORM subroutine, where the fuel-cladding radial gap is calculated.

3.2. Cladding ballooning model

Local plastic deformation of the cladding is modeled by BALON2 subroutine driven by FRAP-T6 code.

BALON2 belongs to a group of codes that allow to calculate the asymmetric cladding deformation in time.

For this purpose the assumption on the azimuth non-uniformity of the cladding temperature is used during

the initialization of the BALON2 program. In this case, temperature variations significantly affect the

value of the circumferential elongation. The effect of the elongation decrease with the increase in the

temperature non-uniformity was intensively studied in experiments that simulate LOCA [10, 11].

According to experiments, this effect is a key factor that influence the cladding elongation. Parametric

calculations using the FRAP-T6/BALON2 code also demonstrated a significant sensitivity of the

circumferential elongation at burst to the azimuth variation of the cladding temperature (see Fig. 3.1).

Verification of the original version of the code against IGR test data indicates that FRAP-T6 code

significantly underestimates peak clad residual hoop strain for the ballooning area [1]. Joint analysis of the

experimental observations and BALON2 models confirms that azimuth variation of temperature can

sufficiently reduce the cladding circumferential elongation at burst.

Two different approaches were used to describe the fuel rod behavior in the air and water coolant. An

original approach of the BALON2 to simulate the asymmetric temperature field in air-cooled fuel rods

resulted in unrealistic predictions of the cladding deformation at burst. To solve this problem, the

BALON2 program was modified as follows. For the determination of cladding dimensions during the

ballooning, the assumption on the cladding bending in the axial plane is used, that leads to a relative offset

of the fuel pellet and the cladding till the time of the contact. At the time of the contact of the fuel and the

cladding a sharp surge of the cladding temperature is predicted in the contact zone. The use of the bending

model for fuel rods under consideration would be unjustified. Therefore, this model was disabled during

calculations of air-cooled fuel rods.

RRC KI 2180 10
80

HT-waler coolant

110 ~T,..=1223-K 40

0

050 100 150 200 250 300 350

Termperaum variation ( K )

Fig. 3.1. Calculated cladding circumferential elongation at burst vs. azimuth variation of cladding

temperature.

On the other hand, the bending model was used in BALON2 calculations for water-cooled fuel rods. It

should be noted once more that it was difficult to verify the model since there were no data on the azimuth

variation of the temperature. However taking into account the statistic nature of the film boiling and the

presence of the geometric eccentricity in the real fuel rod, the prediction of the fuel and cladding contact

during the ballooning can be considered as a simplified approach to the simulation of the ibot spot) on the

cladding under DNB conditions. In this case modifications were performed for calculations of the gap

thermal conductivity at contact (GCONR2 module), called by the BALON2. To prevent unrealistic results

when the gap tends to zero, the effective gap thickness was limited by 15 p;m.

Correction of the axial length of ballooning region also was made in BALON2 subcode in order to

consider specific features of VVER fuel rods. Original version of BALON2 subroutine suggests to

consider that axial length is equal to 8 cm. But the heated length of VVER fuel rods is equal to 15 cm only.

Use of the axial length of ballooning, which exceeds the half of the fuel rod length, makes it much more

difficult to interpret the calculation results. Axial length in the BALON2 was decreased to 3 cm according

to the post-test examinations of the VVER fuel rods tested in IGR.

RRC K! 2180 I1I
4. FISSION GAS BEHAVIOR

To analyze fission gas release (FGR) in the pulse regime it is necessary to specify initial distribution of the

fission gas. Standard procedure of calculating initial concentration of Xe and Kr in the fuel matrix is done

with the standard FRAPCON-2 [12] code under the base irradiation conditions. FRAPCON-2 code is

interfaced with FRAP-T6 code. The data calculated by FRAPCON-2 code are the input data for FRAP-T6

code i.e. for example, axial and radial distribution of Xe and Kr concentration in the fuel matrix after the

base irradiation.

As the developers of FRAP-T6/VVER version did not have a steady-state code for high burnup VVER

fuel, which provides the whole data set in the form suitable for FRAP-T6 code, the decision was made to

use FRAP-T6 code capabilities to assess fission gas release. Thus, a number of steady-state models of the

fuel and cladding deformation versus burnup and power history were incorporated into FRAP-T6 code. It

is also possible to specify the change of the power rate radial non-uniformity under base irradiation

conditions.

The model of fission gas behavior that realized in the GRASF subroutine calculates the generation of

fission gas atoms and their further distribution in the fuel matrix depending on the temperature and burnup.

In order to get the input data to analyze fission gas release over the IGR test, the following characteristics

are to be calculated by the end of the fuel cycle:

* radial distribution of fission gas concentration in the fuel grains;

" radial distribution of the fission gas concentration on grain surfaces;

" radial distribution of the fission gas concentration at the grain edges.

4.1. Approach to analyze fission gas behavior under base irradiation conditions

It is important to note that FRAP-T6 code was not specially oriented towards analysis of the quasi-steadystate regime of operation of the fuel rods. The existing steady-state models are of auxiliary nature and can

be used to analyze pre-transient condition of only fresh fuel rods or the fuel rods of low burnup. To model

the pre-transient quasi-steady-state regime it is necessary to account for additional physical processes and

effects that determine the state of fuel under deep burnup. Hence, additional models to analyze fuel rod

behavior in the mode of the quasi-steady-state thermal loading were incorporated into the code.

4.1.1. Fuel swelling due to accumulation of the fission products

Despite the fact that it is possible to analyze spatial fuel swelling in the model of fission gas release,

FRAP-T6 code did not account for the radial fuel displacement due to that effect. In the present version the

fuel volumetric swelling converted into the radial displacement is used to identify the fuel-cladding gap

size for both steady-state and accident regime. Accounting for the fuel swelling can be performed

according to three options:

1. Using GRASF subroutine which is a part of FRAP-T6 code original version.

2. Using FSWELL subroutine from MATPRO-V 1.

The model of the steady-state fuel swelling similar to the swelling model in FRAP-S3 code [13] has

been included.

3. The option that does not account for the fuel swelling when analyzing gas gap size.

Option (1) is used for practical calculations of fuel swelling in steady-state and accident conditions. The

option (2) was included as auxiliary. It is based on MATPRO correlation and used only for comparative

RRC IK 2180 12
analysis of fuel swelling calculated with the GRASF and MATPRO routines. The option (3) does not take

into account the fuel displacement due to fuel swelling as postulated in the original FRAP-T6 manual.

4.1.2. Irradiation-induced fuel densification

The model of additional fuel densification due to irradiation from MATPRO-V 11 [5] package (FUDENS

subroutine) has been included into DEFORM subroutine. The incorporated correlation allows to account

for the decrease of the fuel diameter during the initial stage of bumup due to sintering of pores with the

diameter less than 1 prm.

4.1.3. Dependence of the power rate radial non-uniformity versus time

As the input data FRAP-T6 code foresees specification of only power rate radial non-uniformity, constant

with time. For the quasi-steady-state calculations it is necessary to account for the change of the power rate

radial non-uniformity. The possibility to model variable in time radial coefficient of the power rate nonuniformity has been added to the code. This coefficient allows to consider change of the power rate radial

profile (burnup) according to the data of neutronic calculations. To realize this RIMTIM, FINT and

RIMMOD subroutines have been introduced. These subroutines perform interpolation of the earlier

specified 3D data file depending on the fuel radius at every time moment. 3D data file is the dependence of

the specified power rate non-uniformity coefficient along the fuel radius and burnup. Appendix A presents

the texts of RIMTIM, FINT and RIMMOD subroutines.

4.2. Initial data and the procedure to analyze fission gas behavior under the

base-conditions

4.2.1. Extension of the power history array

For more accurate specification of the input data describing power history, that includes both base irradiation conditions and transient heat-up, the array contained time dependence of power rate (PTHA) was

extended from (100,1) to (1200,1)

4.2.2. The method to specify input data for the analysis of base irradiation

The following set of the input data (graphically presented in Fig. 4.1) is proposed to analyze pre-transient

distribution of fission gas in the fuel.

4.2.3. Analysis of the fuel rod behavior under base irradiation conditions

The fuel rod power history is specified according to the data of neutronic calculations. In particular, this

was done to analyze the behavior of VVER fuel rods tested in IGR reactor. To model the behavior of fuel

rods in the quasi-steady-state operation regime the height of the fuel rod active part was divided into the

sections approximately corresponding to the length of re-fabricated samples of fuel rods. Then thermalmechanical analysis of the fuel rod behavior was performed with FRAP-T6 code for the base irradiation

conditions up till the set burnup (-50 MWd/kg U). Input data on the state of fuel in the pre-transient

moment (t--0) are the results of this analysis. At the time moment t--0 the code foresees replacement of the

following fuel rod parameters in accordance with the data base for IGR tests of the VVER fuel rods:

1. Fuel rod geometric dimensions

2. Internal gas pressure in fuel rod

RRC K122180 13
3. Composition of the filling gas

4. Capsule cooling conditions

Then the calculation of fuel rod behavior under transient condition is started up.

The proposed method to analyze fission gas release under the base irradiation conditions with FRAP-T6

code should only be considered as the method allowing to quantitatively evaluate amount of gas in the fuel

matrix, and to download the initial spatial distribution of the fission gas. This method does not claim for

the detailed thermal-mechanical analysis of the fuel rod under base irradiation conditions, which is to be

performed with the codes of FRAPCON-(2,3) [12, 14], TRANSURANUS [15] type.

Fig. 4.1. Interpretation of the power history specification under base irradiation and transient

conditions for FRAP-T6/VVER code.

RRC KI 2180 14
5. ALTERNATIVE THERMAL - PHYSICAL MATERIAL PROPERTIES

(MATPRO-V11 LIBRARY EXTENSION)

We present the choice and justification of the models of the main thermal-physical and mechanical

properties of Zr-l%Nb cladding and U0 2 fuel in order to adapt FRAP-T6 code for modeling fuel rod

behavior under the pulse testing conditions in IGR reactor.

Correlations of physical and mechanical properties of Zr-l%Nb alloy and the Russian type of fuel were

added to the MATPRO-Vl 1 package. Addition to the package of MATPRO-V 11 material properties was

done in the following subroutines:

Fuel

1. FI-CON -Thermal conductivity vs. temperature and burnup

(additional subroutines: TCOR, BURNUP)

2. FTHEXP - Thermal expansion

3. FCP - Specific heat

4. FENTHL - Enthalpy

5. PHYPRP - Thermal-physical constants

Cladding

1. CTHCON - Thermal conductivity

2. CCP - Specific heat

3. CCPINT - Enthalpy

4. CTHEXP - Thermal expansion

5. CMHARD - Micro-hardness

6. CELMOD - Young's modulus

7. EMCPIR - Poisson's ratio

8. CKMN - Strength coefficient, strain hardening exponent, strain rate sensitivity exponent vs.

temperature and strain rate for fresh and irradiated cladding

9. CMLIMT - Ultimate mechanical parameters

10.COBILD - High-temperature oxidation

11 .PHYPRP - Thermal-physical constants

FORTRAN texts of the respective subroutines were prepared in the format of MATPRO-V 11 library

package and are fully presented in Appendix A.

RRC KI12180 15
5.1. Thermal-physical properties of fuel

5.1.1. Fuel specific heat (FCP) and enthalpy (FENTHL)

Table 5.1 and Fig. 5.1 present the dependence of fuel specific heat versus temperature. Fuel enthalpy is

obtained by integrating specific heat dependence for the temperature on condition that enthalpy at 20*C is

equal to zero.

Table 5.1. Dependence of fuel specific heat and enthalpy on temperature [161.

Parameter Temperature (K)

293 500 700 900 1100 1300 1500 1700 1900 2100 2300 2500 2700 2900 3100

Specific heat 280 287 302 310 314 319 320 328 340 364 390 426 470 520 594

(J/kg K)

Enthalpy 0 57.6 116. 177. 240. 303. 367. 432. 498. 569. 644. 726. 815. 914. 1026

(kJ/kg) 5 7 1 4 3 1 9 3 7 3 9 9

600

500 /

S400

300-

200

0 500 1000 1500 2000 2500 3000

Tempereure (K)

Fig. 5.1. VVER fuel specific heat vs. temperature.

RRC KI2180 16
1200 4 1 1 1

900

1600 _ __ __ __ __ _

r~.300

0 500 1000 1500 2000 2500 3000

Temperat=r (K)

Fig. 5.2. VVER fuel enthalpy vs. temperature.

5.1.2. Thermal expansion (FTHEXP)

Table 5.2 and Fig. 5.3 present the temperature dependent correlation of thermal expansion for fresh VVER

fuel.

Table 5.2. Thsermal expansion of VVER fresh fuel (%) vs. temperatur f161.

Temperaure (K) Linear expansion(%

293 0.0000

400 0.077

600 0.240

g00 0.451

1000 0.678

1200 0.922

1400 1.182

1600 1.458

1800 1.751

2000 2.060

2200 2.385

2400 2.727

2600 3.085

2800 3.4600

2300 3.851

3080 4.012

RRCK 2180 17
Fig. 5.3. Fresh fuel thermal expansion vs. temperature for VVER-type fuel [16].

5.1.3. Thermal conductivity of the VVER type of UO) and dependence of thermal

conductivity versus fuel burnup (FTHCON, BURNUP, TCOR)

Fresh fuel thermal conductivity coefficient is determined according to the correlation [17]:

)o = 2.158 Xo.95 p / (32.91 - p),

where AO = fresh fuel thermal conductivity (Wim K);

A0.5 = thermal conductivity of fuel with 95 % of theoretical density (Wim K);

p = fuel density (glcm3

).

Thermal conductivity coefficient of the fuel with the density of 95% of the theoretical density is

determined according to the correlation [ 17]:

Xo" = 100/ (0.0258.T +3.77) + 1.1-10 4 .T + 1.01-10".-T3.exp(7.2 10"4 T),

where T = temperature (K).

Thermal conductivity of the burnup fuel is determined according to the dependencies [18, 19]:

XB =)oK, K2,

where A.B = burnup fuel thermal conductivity (W/m K);

= fresh fuel thermal conductivity (WIm K);

K, and K2= empirical coefficients.

RRC K1 2180 is
Dimensionless Ki and K 2 coefficient are determined as follows [18, 19]:

Ki = (0.053 + 2.2 10-4.T) /(0.053 + 0.00171,b + (2.2- 0.000533,b) 10-4,T),

K2 = 1 - 0.001.c-b,

c = 5.31 - 3.42 1073-T + 0.4 10 °T2 for T < 1773,

c = 0.5 for T > 1773,

where b = bumup (MWd/kg U);

T = temperature (K).

Fig. 5.4 presents dependencies of thermal conductivity coefficient of the VVER fuel type versus temperature for the fresh fuel and fuel with the burnup of 30 and 60 MWd/kg U. Appendix A presents the text

of FCON subroutine that performs selection of the option to calculate fuel thermal conductivity.

Dependencies for thermal conductivity of the VVER fuel are included into TCOR subroutine-function.

BURNUP subroutine contains dependencies of thermal conductivity versus burnup. Texts of these

subroutines are presented in Appendix A.

-*-Fresh fuel6 e Bunp 0Md&

.~3

0 500 1000 1500 2000 2500 3000

Tempemture (K)

Fig. 5.4. VVER fuel thermal conductivity vs. temperature.

5..4. Thermal-physical constants (PHYPRP)

Thermal-physical constants of the VVER fuel are presented in Table 5.3.

Table 5.3. Thermal-physical constants of VVER fuel

Material Stoichiometric U0 2

3111-3.577 * B,

Melting temaperature ) where B - burnup (MWd/kg U)

Heat of fusion (J/g) 269

Theoretical density (kg/m3) 10970

RRC K12180 19
5.2. Thermal-physical properties of Zr-l%Nb cladding

5.2.L Thermal-physical constants (PHYPRP)

Thermal-physical constants of the Zr-l%Nb cladding alloy in accordance with [20] are presented in Table

5.4.

Table 5.4. Thermal-physical constants of Zr-l %Nb alloy.

Material Zr-i%Nb

Melting temperature (K) 2133

Fusion heat (J/g) 210

Beginning of a-0 transition (K) 883

End of a-0 transition (K) 1153

Density kg/rn 3) 6550

5.2.2. Specific heat (CCP) and enthalpy (CCINP)

Table 5.5 and Fig. 5.5 present the dependence of the unirradiated cladding specific heat and enthalpy

versus temperature [21]. Cladding enthalpy is obtained by integrating specific heat dependence for the

temperature on condition that enthalpy at 20*C is equal to zero. The obtained dependence is presented in

Table 5.5 and in Fig. 5.5.

Table 5.5. Dependence of Zr-1%Nb specific heat and enthalpy on temperature.

Parameter Temperatnre (K)

393 473 573 673 773 873 883 973 1025 1073 1153 1173 1200 1300 1400

Specific heat 345 360 370 380 383 385 448 680 816 770 400 392 392 393 393

(J/kg K)

EatWPY 34.1 61.9 97.5 134 171 209 214 262 301 339 385 393 402 445 485

(kl/kg)

RRCK12180 20
IUU 900

800. - F4U C;jJiaUC L~ 600

600 400

78 400- 200~

200 0

0 400 800 1200 1600 2000

Temperature (K)

Fig. 5-5. Zr-1%Nb clad specific heat and enthalpy vs. temperature.

Appendix A presents the text of CCP and CCPINT subroutines where selection of options is performed to

calculate specific heat and enthalpy. Cladding enthalpy is obtained by integrating specific heat for the

temperature.

5.2.3. Thermal expansion (CTHEXP)

Anisotropic model of the Zr-alloy cladding thermal expansion has been approved for the MATPRO-V1 1

package. Table 5.6 presents respective dependencies to determine thermal expansion factor up to the

temperature of 923 K [22].

Table 5.6. Thermal expansion coefficients in hoop and axial directions for Zr-1%Nb cladding.

Temperature (K)

Parameter 293 - 393 393 -573 573-773 773 - 923

Thermal Thermaiexpnts(i/K) expansion57l 5.7 10-6 5.3 5.iO 10-6 5.9 10-6 5.4 10-fi 6.3 10-6 :5.5 10-6 6.8 10-6 561. 5955lO

coefficients (11K) 1

The correlations presented in Table 5.7 were used to determine thermal expansion of Zr-l%Nb alloy at the

temperatures higher than 923 K. Dependencies were obtained on the basis of extrapolation of the data

presented in Table 5.7; it was assumed that general view of the dependence for thermal expansion of Zr1 %Nb alloy was equidistant to the dependence for 7_y alloy.

RRC K1 2180 21
Table 5.7. Temperature dependence of hoop (Oa) and axial (C.) components of thermal expansion of Zr1%Nb alloy for temperature above 923 K.

Temperature (K) Thermal expansion of Zx-1%Nb alloy.(%):

923-1153 ;=-17.95 + 0.0549 T -:5.4 I0 'a + 1.74 10" T3

= -17.28 + 0.0533 T- 5.3 105 T2 + 1.72 10 T3

above 1153 ;=-0.886 + 9.7 104 T

e,_= -1.038 + 9.7 10 T

Fig. 5.6 and Fig. 5.7 present the dependence of thermal expansion versus temperature for the cladding of

Zr-1%Nb alloy in the radial and axial directions. This block of correlations has been incorporated into

CITHCON subroutine (Appendix A).

1.2

0.4

0.0

0 500 1000 1500 2000

Temperatim (K)

Fig. 5.6. Hoop component of Zr-i%Nb clad thermal expansion vs. temperature.

RRCKI2180 22
13 *1 I

~1.0

0.5

0.0

0 500 1000 1500 2000

TemperatM_ (K)

Fig. 5.7. Axial component of Zr-l%Nb dad thermal expansion vs. temperature.

5.2.4. Thermal conductivity (CTHCON)

Thermal conductivity of the cladding material made of Zr-i%Nb alloy was obtained by approximation and

extrapolation of experimental results [20, 22]. Following analytical equation is defined by the formula:

I = 15.0636 exp (0.4618 10.3 T),

where X = thermal conductivity (W/m K);

T = temperature (K).

Table 5.8 and Fig. 5.8 present the dependence of the cladding thermal conductivity versus temperature.

Table 5.& Dependence of Zr-l%Nb thermal conductivity on temperature.

Parameter Temperature (K)

300 500 700 900 1100 1300 1500 1700 1900 2000

Thermal

conductivity 17.31 18.99 20.82 22.84 25.05 27.47 30.13 33.05 36.25 37.96

(W/m K)

Appendix A presents the text of CTHCON subroutine which perform selection of the option to calculate

thermal conductivity of the cladding material.

RRC KI 2180 23
40 [[~1

~35

30

2520

15

0 500 1000 1500 2000

Temperature (K)

Fig. 5.8. Dependence of Zr-l%Nb thermal conductivity on temperature.

5.2.5. High temperature oxidation (COBILD)

MATPRO-Vll package uses the model of parabolic kinetics to describe the process of the cladding

oxidation in the steam and water coolant:

W2 Kp=I}1

where W= a-Zr(0) oxide layer thickness (m);

Kp = proportional factor (determined separately for ZO 2 and ca-Zr(0)) (m2/s);

€= time(s).

Proportion constant is the function of temperature and is described by the Arrenius formula:

Kp(T) = A-exp(- B/ T),

where T = temperature (K);

A, B = factors characterizing zirconium alloy oxidation.

Constants A and B existing in the MATPRO-V1 I package were supplemented with the data on high

temperature oxidation of Zr-1%Nb and Zry alloys, obtained for the atmospheric pressure [23, 5] (see Table

5.9).

Table 5.9. Arrenius formula coeftcients for Kp constant [23, 5].

AllMoy Temperte region (K) 'AB

Zry <1853 2.252.10-6 18063

Zry >1853 2.07.10" 16014

Zr-l%Nb <1773 5.19.10: 15355

Zr-l%Nb >1773 17.72-l0e 14680

RRC K1 2180 24
Specific energy of the metal-water reaction for Zr-l%Nb alloy is assumed to be 6.49 kJ/g [23]. COBILD

subroutine is supplemented with the coefficients for the parabolic kinetics of Zr-i %Nb alloy oxidation.

5.3. Mechanical properties of Zr-1%Nb cladding

.5.3.1L Young's modulus (CELMOD) and Poisson's ratio (EMCPIR)

Correlation for calculating Young's modulus of Zr-l%Nb alloy is presented with the following two

expressions [20]:

273 K < T•5 1073 K E=l.121-10"-6.438-10 7 -T,

1073 K < T < 1273 K E=9.129-10•0-4.500-107 -T,

where T = temperature (K);

E = elastic modulus (Pa).

Fig. 5.9 presents the dependence of the Young's modulus for Zr-l%Nb.

100

s0

60 5

1 40 _ ___ _ _

M 20

0

0 500 1000 1500 2000

. Temperatre (K)

Fig. 5.9. Dependence of Young's modulus of Zr-l%Nb on temperature.

The data on the dependence of the Young's modulus versus temperature are incorporated into CELMOD

subroutine.

Experimental data on the Poisson's ratio for Zr-l%Nb are approximated by the following expression [20]:

g = 0.42628 - 5.556 x 105 T,

where T= temperature (K).

Dependence of the Poisson's ratio is incorporated into EMCPIR subroutine.

Appendix A presents the texts of CELMOD and EMCPIR subroutines which perform selection of options

to calculate the respective properties.

RRC K1 2180 25
5.3.2. Meyer micro-hardness (CMHARD)

Cladding micro-hardness according to Meyer is used to analyze the contact component of the fuelcladding gap thermal conductivity. Micro-hardness of Zr-l%Nb corresponds approximately to three times

value of the yield stress [22]. The values of the cladding micro-hardness are presented in the Table 5.10

versus temperatures from 293 to 773 K according to [22].

Table 5.10. Meyer hardness data for Zr-1%Nb alloy

T (K) 293 373 473 573 673 773

Yield stress (MPa) 230 200 180 161 140 120

Micro-hardness (MPa) 690 600 540 483 420 360

Analytical curve for micro-hardness of Zr-1%Nb alloy based on the data presented in Table 5.10, can be

described by the following formula:

For 298 < T < 773 K

H = 2172.1 - 10.7055.T + 0.02765-*2 - 3.278 10-5-T3 + 1.423 10-T'4 ,

where T = temperature (K).

The following linear extrapolation of the data for the temperature range higher than 773 K has been

accepted due to the lack of data on the micro-hardness of Zr-l%Nb alloy:

H=850.0 - 64.0 T, assuming if H < 0.1 MPa, else H=0.1 MPa.

The option for selection of the Meyer micro-hardness correlation for Zr-l%Nb alloy is realized in

CMHARD subroutine.

5.3.3. Plastic deformation of the cladding (CKMN)

MATPRO-Vll [5] package uses the following basic equation to describe the correlation between the

stress and strain depending on the loading conditions and the state of the cladding material:

a =Ke (.'

where o= true effective stress (MPa);

K = strength coefficient (MPa);

e = true effective strain (per-unit);

n = strain hardening exponent (per-unit);

C = current strain rate (l/s);

to = basic strain rate (1/s);

m = strain rate sensitivity exponent (per-unit).

In framework of the experimental program to measure the mechanical properties of unirradiated and irradiated (-50 MWd/kg U) Zr-1%Nb cladding the analytical correlations for K, n, m were obtained [1].

The values of strength coefficient and strain hardening exponent as function of temperature for two burnup

levels (0 and 50 MWd/kg U) are presented in Fig. 5.10, Fig. 5.11 and in Table 5.11.

RRCKI2180 26
Table 5.11. Correlations to calculate strength coefficient and strain hardening exponent vs. temperature

for Zr-1%Nb cladding.

Parameter Type of cladding

unirradiated irradiated

293<T<•795.18 K 293<T5749.45 K

K=863.33 - 1.90882 T+0.00209374 a2 - K=738.221+0.0395682 T-0.00100875

9.91178 10" "2+ a 0.370178 10-j7Y

749.45<.T-<846.44 K

Strength K=8.34707 W05 exp(-0.01035 1)

coefficient

(MPa) 795'.18&<T.926.62 K 846.44. <T!926.62 K

K =1.08414 1 40xp(-0.00521825 T)

926.62 -dT51123.54 K

K = 396.363 - 0.334806 T

TA 123.54 K.

K = 56.6424 - 0.0324407 T

293 <T•752.37 K

n = 0.0054616 + 3.12237 10.4 T -

0.668358 106 T2 + 0.430236 10-9T

Strain 752.37 <T5854.72K

hardening n =-1.58974 + 0.00500594 T -

exponent 4.99134 10 T2 + 1.62978 10-9 Ta

(per-unit) 293 ~T! 1223 K 854.72<7•1223K

n =0.0462842 + 0.000197952 T - 0.331487 10- T2 +1.39133 10.10 T3

T1=223K K

n = 0.047

RRC KI 2180 27
800

600 it

-correlation

~3400,

~200-

200 400 600 800. 1000 1200 1400

Temperature (K)

Fig. 5.10. Strength coefficient vs. temperature for unirradiated and irradiated Zr-1%Nb cladding.

Fig. 5.11. Strain hardening exponent vs. temperature for unirradiated and irradiated

Zr-l%Nb cladding.

The analysis of the data base on strain rate sensitivity exponent indicated that it was not sufficient. That's

why it was proposed not to develop the correlation for the VVER cladding, but to use the original

MATPRO correlation for strain rates >0.01 us, which well enough describes the obtain data for

unirradiated and irradiated Zr-l%Nb alloy (see Fig. 5.12).

RRC KA2180 28
A irmdiated Zr-1%Nb 93-.

02-0

0.0. ....

200 400 600 800 1000 1200 1400

Temperatum (K)

Fig. 5.12. Comparison of the strain rate sensitivity exponents for Zr-l%Nb alloy and Zircaloy.

The correlations for K, n, m parameters were incorporated into CKMN module. The listing of the module

is presented in Appendix A.

5.3.4. Cladding failure criterion (CMLIMT)

The local tangential stress at burst was used as a failure criterion in the course of FRAP-T6 simulation of

IGR test rods. According to the MATPRO procedure intended to derive the criterion from the Zry

experimental data, the burst test data on Zr-l%Nb in the temperature range 973-1473 K served as a base to

develop analogous failure criterion of VVER cladding [1]. Only the temperature dependence of burst stress

was obtained because it was not revealed noticeable differences between unirradiated and irradiated

cladding (see Fig. 5.13). Table 5.12 contains correlations for local burst stress which were used to predict

Zr-l%Nb cladding failure.

RRC K2180 29
300 -

Presae mincasc t

0.01 MNa(s

200 S

0

800 1000 1200 1400 1600

Tcmperaftw (K)

Fig. 5.13. Measured local burst stresses and new MATPRO correlation for Zr-l%Nb cladding.

Table 5.12. Correlations for local burst stress of Zr-I%Nb cladding.

Range- of temperature (K) Loca bust, stress,(~a vs.ý tempi.erature

973<T51 176.44 qu= 2.99522 10' exp(-0.00952232 T)

1176.44<T:51473 qBff 1.41537 W exp(-0.00301426 T)

The listing of the module

Appendix A.

CMLIMT with incorporated Zr-l%Nb burst stress criterion is presented in

RRC KI 2180 30
6. CODING ASPECTS

. 6.1. Description of the new global variables

The new global variables are introduced for the newly developed and modified models. Table 6.1 contains

the description of the new global variables. All new global variables stored in two headers: WWER.H and

WWER1.H.

The description of following common blocks is not presented here:

COMMON BLOCK IGRF_SI: This common block contains the variables for graphic package of FRAPT6/VVER code, which allows to display thermal-mechanical parameters of fuel rod during calculation (online regime). Graphic package was developed specially for FRAP-T6 code and was used during code

testing and verification. Graphic subroutines were excluded from this version of FRAP-T6 code since it

demands only LAHEY translator.

COMMON BLOCK /Hl_CONDI: This common block contains temporary parameters for printout.

Parameters were applied during code testing and now are not used.

COMMON BLOCK/ /: IMIC, HMAC - variables of QDOT subroutine for post-CHF heat transfer

coefficient calculated with Bromley-Pomerantz model.

Table 6.1. New global variables incorporated into FRAP-T6IVVER code.

Name •Storage TYpe Description

IWWER INTEGER *8 WWER.H Option for selection of VVER/PWR

_ constant COMMON/WWER/ fuel rod design

ITEPLN INTEGER*8 WWER.H Option for coolant type selection

constant COMMON/WWER/

COEALF REAL *8 WWER.H Kutateladze subcooling factor for heat

constant COMMON/WWER/ transfer coefficient in post-C-F regime

ENTH REAL*8 WWER.H Peak fuel enthalpy at each axial slice

_ array (50) COMMON/WWER/

ENTER REAL*8 WWER.H Energy deposition at each axial slice

array (50) COMMON/WWER/

EXT REAL*8 WWER.H Energy leakage at each axial slice

array (50) COMMON/WWER/

LMAX1 INTEGER *8 WWER.H Number of axial slice with peak power

constant COMMON/COORD/ rate

ISTEPPRINT INTEGER *8 WWER.H Number of time steps which are excluconstant COMMON/COORD/ ded from the output proceeding in the

*.DAT files

ISWEL INTEGER *8 WWER.H Option for calculation of gas gap width

constant COMMON/COORD/ with account for fuel swelling:

EPJNFMB REAL *8 WWER.H Uniform hoop clad strain

constant COMMON /LAC BALLON/

EISTABB REAL *8 WWER.H Instability hoop clad strain

I constant COMMON /LACBALLON/

RRC K! 2180 31
N Type Storageon

ERUPB REAL *8 WWER.H Clad hoop strain at clad failure

constant COMMON /LAC-BALLON/

EPB REAL *8 WWER.H Plastic clad hoop strain

constant COMMONILACBALLON/

TIME.M AIL REAL *8 WWER.H Time at clad failure

constant COMMON JLACBALLONI

CBRSTE REAL *8 WWER.H Clad burst stress

constant COMMON LACBALLONI

STRESSBAL REAL *8 WWER.H Not used

constant COMMON /LAC-BALLONI

TEMP_FAIL REAL *8 WWER.H Clad temperature at failure

constant COMMON /LACBALLONN/

PGFAIL REAL *8 WWER.H Internal gas pressure at failure

constant COMMON /LAC BALLON/

EBURST REAL *8 WWER.H Clad hoop strain at failure

constant COMMON /LAC_.BALLONI

Z_BURST REAL *8 WWER.H Axial location at failure

constant COMMON /LACBALLON/

HRADD REAL *8 WWER.H Radiation component of clad-to-air heat

constant COMMON /FOR_HTRCI transfer coefficient

HTCCOOL REAL *8 WWER.H Gas natural convection component of

constant COMMON/FORJITRCI clad-to-air heat transfer coefficient

HTCC REAL *8 WWER.H Total clad-to-air heat transfer

constant COMMON /FORHTRC/ coefficient

KREAL REAL *8 WWER.H Number of current axial slice.

constant COMMON /FORHTRCI

TIMEHTC REAL *8 WWEP.H Time of clad rewetting

constant COMMON /FORHTRC/

FMASSA REAL *8 WWER.H Mass of fuel in fuel rod

constant COMMON /GEOMETRY/

FDLINA REAL *8 WWER.H Heated length of fuel rod

constant COMMON /GEOMETRY/

FRPLOT REAL *8 WWER.H Fraction of fuel theoretical density

constant COMMON /GEOMETRY/

DL REAL*8 WWER.H Length of axial slice

array (50) COMMON /GEOMETRY/

RHOLE REAL *8 WWER.H Radii of central hole

constant COMMON IGEOMETRY/

SWELMAX REAL *8 WWER.H Maximum fuel swelling

constant COMMON/FISGAS/

FGRTOT REAL "8 WWER.H Total fission gas release

constant COMMON/FISGAS/

TDAY REAL *8 WWER.H Current time during base irradiation

I constant COMMON/FISGAS/

RRCK1 2180 32
N ... ..... Type.toe.D

FGR.Z REAL*8 WWER.H Fission gas release at axial slice

array (50) COMMON/FISGAS/

BVSZ REAL*8 WWER.H Fuel swelling at axial slice

array (50) COMMON IFISGAS/

RGL-Z REAL*8 WWER.H Total gas generated in fuel that is

array (50) COMMON/FISGAS/ retained in fuel matrix at axial slice

GJOUTZ REAL*8 WWER.H Fraction of gas released from fuel at

array (50) COMMON/FISGAS/ axial slice

RGGL..Z REAL*8 WWER.H Fraction of gas retained in fuel grains at

array (50) COMMON /FISGAS! axial slice

RGGFZ REAL*8 WWER.H Fraction of gas retained on fuel grain

array (50) COMMON/FISGAS/ faces at axial slice

RGGEZ REAL*8 WWER.H Fraction of gas retained on fuel grain

array (50) COMMON/FISGAS/ edges at axial slice

RGTGR REAL *8 WWER.H Total gas generated in fuel that is

constant COMMON/FISGAS/ retained in fuel matrix

GRFT REAL *8 WWWER.H Total gas released from fuel

constant COMMON/FISGAS!

VOLSV REAL *8 WWERtH Fuel rod free volume

constant COMMON /FISGAS/

POHE REAL *8 WWERM Internal gas pressure at the end of base

constant COMMON/FISGAS/ irradiation

IREWET INTEGER *8 WWER.H Option to calculate clad rewetting time

constant COMMON/REWETI

TEMPCONT REAL *8 WWER.H Average clad temperature at the

constant COMMONICONTA/ beginning of PCMI

TIME._CONT REAL *8 WWER.H Time at the beginning of PCMI

constant COMMON /CONTA/

EHOOPMAX REAL *8 WWER.H Maximum clad hoop strain

constant COMMON /CONTA/

CONBUO REAL *8 WWER.H Fuel thermal conductivity coefficient

constant COMMON/CONTA/ with accounting for bumup effect

CONO REAL *8 WWER.H Fuel thermal conductivity coefficient

constant COMMON/CONTAI without accounting for bumup effect

AX REAL *8 WWER.H Empirical factors for fuel thermal conducCT constant COMMON/CONTA/ tivity coefficient degradation vs. burnup

DTCLADD REAL *8 WWER.H Temperature drop across clad thickness

constant COMMON/CONTA/

DE_DT REAL *8 WWER.H Clad hoop strain rate

constant COMMON/CONTA/

FBU REAL *8 WWERH Maximum fuel burnup

constant COMMON /CONTA/

BURN_Z REAL *8 WWER.H Fuel burnup at each axial slice

array(50) COMMON /CONTAI

RRCK1 2180 33
Nae Type Storgei Description. -

JRUPTURE INTEGER*8 WWER.H Clad failure indicator

constant COMMON/CONTA/

GASWLP REAL *8 WWER.H Gas component of fuel swelling at axial

constant COMMON/SWELLJ slice with peak power

SOLDSWP REAL *8 WWER.H Solid component of fuel swelling at

constant COMMON/SWEUJ axial slice with peak power

SOLD REAL *8 WWER.H Total fuel swelling at axial slice with

constant COMMON/SWELUJ peak power

BUARRAY REAL *8 WWER.H Radial burnup distribution

array(50) COMMON/SWELL/

BURNTOT REAL *8 WWER.H Maximum fuel burnup

constant COMMON /SWELI/

POWRAD REAL *8 WWE.H Distribution of radial power rate

array(50,50) COMMON/SWELUJ

COEFPOW REAL *8 WWER.H Radial power rate coefficient at each

array(50,50) COMMON /SWELIJ axial slice

DENIRR REAL *8 WWER.H Fuel density change due to irradiationconstant COMMON /SWELLI induced densification

RDEN REAL *8 WWER.H Radial fuel displacement due to

array(50) COMMON /SWELIJ. irradiation-induced densification

RSW REAL *8 WWER.H Radial fuel displacement due to

array(5O) COMMON ISWELLJ swelling

BURND REAL *8 WWER.H Axially maximum fuel bumup after

constant COMMON/SWELUJ base irradiation

BUEQ REAL *8 WWER.H Not used

constant COMMON /SWELLJ

VARITER REAL *8 WWER.H Number of iteration at time step

constant COMMON/CHAR/

SUMCR REAL *8 WWER.H Temporary variable for clad failure

array(50) COMMON/CRJTER/ criterion (strain accumulation)

DEFC REAL *8 WWER.H Effective clad strain

array(50) COMMON/CR1TER/

EDOTW REAL *8 WWER.H Effective clad strain rate

constant COMMON /CRTERI/

BURNGRF REAL *8 WWER1H Radial/axial burnup distribution

array(50,50) COMMON/BURN/

RBURN REAL *8 WWER1.H Radial distribution of bumup at axial

array(50) COMMON/BURN/ slice with peak power

BUI REAL *8 WWER1.H Burnup at the beginning of time step at

constant COMMON/BURN/ axial slice with peak power

BU2 REAL *8 WWER1.H Burnup at the end of time step at axial

constant COMMON/BURN/ slice with peak power

All the new variables are stored in two headers: WWER.H and WWER1.H.

RRCKr218O 34
6.2. Description of the new and modified subroutines

Table 6.2 lists the modified and new subroutines incorporated into FRAP-T6/VVER code. Table 6.2

presents description of the new and modified subroutines, including the name, status and initial function of

the subroutine, as well as the main sense of the made change. The ,cmodified,* status means that the

subroutine was a part of the original version of FRAP-T6 code.

Table 6.2. The list of modified and new subroutnes incorporated into FRAP-T6IVVER code.

Module Status- Function Nature of modification

nam

CCP modified Driver for calculation of clad Introduction of option for calculation

specific heat of Zr-i%Nb clad specific heat

CCPINP modified Driver for calculation of clad Introduction of option for calculation

enthalpy of Zr-1%Nb clad enthalpy

CTFIEXP modified Driver for calculation of clad Introduction of option for calculation

thermal expansion of Zr-1%Nb clad thermal expansion

CELMOD modified Driver for calculation of clad Introduction of option for calculation

Young's modulus of Zr-l%Nb clad Young's modulus

CTHCON modified Driver for calculation of clad Introduction of option for calculation

thermal conductivity of Zr-i%Nb clad thermal conductivity

CMHARD modified Driver for calculation of clad Introduction of option for calculation

Mayer micro-hardness of Zr-l%Nb clad Mayer hardness

EMCPIR modified Driver for calculation of clad Introduction of option for calculation

Poisson's ratio of Zr-l%Nb clad Poison coefficient

CKMN modified Driver for calculation of K, m, Introduction of model for calculation

n parameters of clad of Zr-1 %Nb clad K, m, n parameters

with account for clad strain rate

CMLIMT modified Driver for calculation of clad Introduction of model for calculation

short-term strength parameters of Zr-l%Nb clad strength parameters

with account for clad strain rate

PHYPRP modified Driver for calculation of fuel Introduction of option for calculation

and thermal-physical of thermal-physical parameters for Zrparameters l%Nb clad and VVER fuel

QDOT modified Driver for calculation of clad- Introduction of option for calculation

to- water coolant heat transfer of clad-to-water heat transfer

HTRC modified Driver for calculation of clad- Introduction of option for calculation

to- coolant heat transfer of clad-to-air heat transfer

REWETT new Determination of clad Introduce into QDOT subroutine to

rewetting time calculate time of cladding rewetting

RIMTIM new

RIMMOD new Choice of radial peaking factor Time dependence for power radial

FINT new for power vs. time peaking factor

RRC K! 2180 35
Module Status- - Function Nature of modification

BURNUP new Determination of coefficients Introduce into FMHCON subroutine to

for calculation of fuel thermal calculate fuel thermal conductivity

conductivity degradation with degradation with bumup

burnup

TCOR new Data base for determination of Introduce into FIHCON subroutine to

VVER fuel thermal calculate fuel thermal conductivity

conductivity coefficients vs. coefficients vs. temperature for VVER

temperature type of fuel

FCP modified Driver for calculation of fuel Introduction of option for calculation

specific heat of VVER fuel specific heat

FTHEXP modified Driver for calculation of fuel Introduction of option for calculation

thermal expansion of VVER fuel thermal expansion

FENTHL modified Driver for calculation of fuel Introduction of option for calculation

enthalpy of VVER fuel enthalpy

FTHCON modified Driver for calculation of fuel Introduction of option for calculation

thermal conductivity of VVER fuel thermal conductivity

COBILD modified Driver for calculation of high Introduction of option for calculation

temperature oxidation of Zr-oxide layers for Zr-l%Nb clad

GAPTHC modified Calculation of clad-fuel gap Remove the bug

thermal conductivity

STORE6 modified Driver for storing output Remove the bug. Establish additional

information parameters for printout

PCHF modified Driver for calculation of Remove the bug

critical heat fluxes

FRAPT6 modified Input data processing, initiali- Additional input data processing,

zation of calculational initialization of output files

procedures GRAPH.DAT etc.

DEFORM modified Driver for mechanical Introduction of option for calculation

calculation of gas gap width with account for fuel

swelling

GRAFOUT modified Driver for generation of Generation of new graphic

graphic information information. Initialization of brief

listing with general output parameters

GRASF modified Calculation of fission gas Generation of new output files with

release and fuel swelling graphic information

GAPHTC modified Calculation of clad-fuel gap Remove the bug

thermal conductivity

GCONR2 modified Calculation of clad-fuel gap Limitation of minimum gap width by

thermal conductivity for the 15 pm

BALON2 subcode

FSWELL new (from Driver for fuel swelling calcu- Coupling with FRAP-T6 code

MATPRO- lation under base irradiation

V11i) conditions

RRCAU21 0 36
Module Status -Function Nature of modification

name -

FUDENS new (from Driver for fuel densification Coupling with FRAP-T6 code

MATPRO- calculation under base

Vii) irradiation conditions

MELT modified Indication of clad failure due to Remove the bug

melting

BALON2 modified Ballooning calculation Modification of temperature azimuthal

variation

PRNTOT modified Output of information in output Add the list of output parameters

listing

GRAFDATA new Post-processing utility for Generation of output information in _STRIPF file format suitable for PC utilities.

RRC K1 2180 37
7. USER'S MANUAL

7.1. Description of the new input data

Specification of the input data was expanded in order to account for the specific features of fuel rod testing

in IGR reactor. Additional parameters occupy three first strings in the new data specification. Description

of the additional input data parameters is presented in Table 7.1.

Table 7.L List of new parmneters of input data.

Paramneter _Description Type Vahue

TITLE Text string CHARACTER*120 -

NREST Restart INTEGER 0

NCARDS parameters INTEGER 1

IUNCRT (specified by FRAP-T6) INTEGER _0

TI Start calculational time (specified by FRAP-T6) _0_ REAL*8 -7.8 

T2 End calculational time (specified by FRAP-T6) REAL*8 580

ITEPLN Coolant type (additional parameter) ITGER

SWater 0

• Forced Helium 9

* Stagnated Air 10

* Forced Air 11

IWWER VVER/PWR type INTEGER

(additional parameter)

* Cladding - Zircalloy, Fuel - PWR type 0

* Cladding - Zr-i %Nb, Fuel - VVER type 1

IRECVR (specified by FRAP-T6) INTEGER 1

MPTFC2 (specified by FRAP-T6) INTEGER 0

ISTEPPRINT User-specified number of time steps which are INTEGER 20

excluded from the output proceeding in the

•.DAT files (additional parameter)

LMAX Number of axial fuel rod slice with peak power INTEGER 1

(additional parameter)

ISWEL Option for calculation of gas gap width with INTEGER

account for fuel swelling:

* Swelling is not taken into account 0

* Swelling is calculated with FSWELL 1

subcode

* Swelling is calculated with GRASF subcode 2

TITLE Comment CHARACTER*10 REWET

IREWET Option to calculate rewetting time: INTEGER

* rewetting is not taken into account 0

* rewetting is taken into account _ _II 1

RRC KI 2180 38
As an example, specification of the input data to analyze one of the VVER fuel rods tested in IGR reactor

(#H5T) is presented below.

* frap-t6, transient fuel rod analysis code *

----------------------------------------------------

* CASE DESCRIPTION: IMPULSE ROD-1 *

* UNIT FILE DESCRIPTION *

*---- ------------------------------------ -- -

* -- Input: *

* 15 Water properties data

* -- Output: *

* 6 STANDARD PRINTER OUTPUT *

* 66 STRIPF FILE FOR GRAFITI *

* - - Scratch: *

* 5 SCRATCH INPUT FILE FROM ECHO1 *

* Input: FRAPT6 INPUT FILE *

* NPA FLAGS

*NPAON

*NPADWG

NPAPAX= ' frapt6'

NPADUH= ' frapt6 .duh'

NPASERV= 'unix: 0.0'

* GOESINS:

FILE05='nullfile', STATUS='scratch', FORM='FORMATTED',

CARRIAGE CONTROL= 'LIST'

FILEIS=" sth2xt', STATUS= 'old', FORM= ' UNFORMIATTED•

* GOESOUTS:

FILE06='PULSE.out', STATUS='UNEROWN', CARRIAGE CONTROL='ILIST'

FILE66='stripf', STATUS=:'UMNONN', FORM= 'FORMATTED',

CARRIAGE CONTROL= 'LIST'

Restart Time-beg Time-end Coolant Clad irecvr mptfc2 => steppint, lmax

0 1 0 -0.75e8 580.0 0 2 1 0

10 1 0

Rev 0

#9ST Q=239 (cal/g) pre-irradiated

/iodata block

input option selecti

si unit

end

output selection opt

si unit option

print interval 5. e7 5. 07

plot output

end

end block

/power specification data block

power history input 2.1478E+00-.7805E+082.1478E+00-.7795E+082.1478E+00-.7700E+08

2.1478E+00-.7600E+082.1541E÷00-. 7500E+082.1732E+00- .7400E÷08

2.1976E+00-. 7300E+082.2002E+00-. 7200E÷082. 1710E+00-. 7100E+08

2.1515E+00-. 7000E+082.1687E+00-. 6900E÷082.1863E+00-. 6800E+08

2.1987E+00-.6700E+082.2106E+00-.6600E+082.2346E+00-.6500E+08

2.2600E+00-.6400E+082.2735E+00-.6300E÷082.2851E÷00-.6200E+08

2.2799E+00-.6100E+082.2657E+00-. 6000E÷082.2911E+00-.5900E+08

2.3244E+00-.5800E+082.3398E+00-.5700E+082.3502E+00-.5600E+08

2.3832E+00-. 5500E+082.4266E+00-. 5400E+082.5909E+00-.5300E+08

2.7492E+00-.5200E+082.8379E+00-.5100E+082.8255E+00-.SOOOE+08

2.8165E÷00-. 4900E+082.8165E+00-.4800E+082.8001E+00-. 4700E+08

2.7118E+00-. 4600E+082.6706E+00- .4SOOE÷082.6635E+00-.4400E+08

2.6365E+00-. 4300E+082.6081E+00-.4200E+082.5942E÷00-. 4100E÷08

2.5733E+00-. 4000E+082.5377E÷00-.3900E+082.5340E+00-. 3800E+08

2.5598E+00-.3700E+082.5845E÷00-.3600E÷082.5729E÷00-.3500E+08

RRC K1 2180 39
2.56133+00-.34003+082.55423+O0-.33003+082.54783+00-.32003+08

2.54633E00-.31003+082.54633+00-.30003+082.53143+00-.29003+08

2.55162÷00-.28003+082.49923+00-..27003+082.44683e+00-.2600Z+08

2.43293+00-.2500E+082.25973+00-.24002+082.19423+00-.23003+08

2.15833+00-.22003+082.1938Z+00-.21001+082.22973+00-.20003+08

2.20202+00-.19003+082.15563+00-.18002+082.1803Z+00-.17003+08

2.21213+00-.1600E+082.21213+00-.15003+082.21213+00-.1400E+08

2.21213+00-.13003+082.21443+00-.12003+082.23053+00-.1100E+08

2.22233•00-.10003+082.19383+00-.90003+072.18633+00-.80003+07

2.1863E+00-.70003+072.19683+00-.60003+072.21103+00-.S0003+07

2.21213+00-.40003+072.20433+00-.30003+072.19163+00-.20003+07

2.18633+00-.10003+072.50903+00-.10003+06 .0000 -. 20003+04

0.00003+000.00003+000.33003-010.50003-010.67003-010.10003+00

0.10003+000.1500E+000.13403+000.20003+000.16703+000.25003+00

0.20003+000.3000E+000.23403+000.35003+000.26703+000.40003+00

0.30003+000.4500E+000.33403+000.50003+000.36703+000.55003+00

0.40103÷000.60003+000.43403+000.65003+000.46803+000.7000E+00

0.50103+000.75003+000.53503+000.80003+000.56803+000.85003+00

0.6320E÷000.90003+000.7010E+000.95003+000.77803+000.10003+01

0.86103+000.10503+010.9S203+000.11003+010.10503+010.11503+01

0.11603+010.12003+010.12703+010.12S03+010.14003+010.13003+01

0.15403+010.13503+010.16803+010.14003+010.18503+010.14503+01

0.20203+010.15003+010.2210E+010.15503+010.24103+010.16003+01

0.26403+010.16503+010.2880Z+010.17003+010.31403+010.1750E+01

0.34203+010.1800E+010.3730E+010.18503+010.40703+010.19003+01

0.44303+010.19503+010.48303+010.20003+010.52602+010.2050E+01

0.57302+010.21003+010.62S03+010.21503+010.68103+010.22003+01

0.7430E+010.22503+010.81003+010.23003+010.88403+010.23503+01

0.96603+010.2400E+010.10603+020.24503+010.11503+020.2500E+01

0.12603+020.25503+010.13903+020.26003+010.15203+020.26503+01

0.16703+020.27003+010.18403+020.27503+010.20203+020.28003+01

0.22303+020.28503+010.24503+020.29003+010.27003+020.2950E+01

0.29803+020.30003+010.32803+020.30503+010.36003+020.31003+01

0.3940E+020.31503+010.42703+020.32003+010.45703+020.32503+01

0.4810E+020.33003+010.49003+020.33503+010.47603+020.34003+01

0.44203+020.34503+010.39803+020.35003+010.35203+020.3550E+01

0.30803+020.36003+010.26703+020.36503+010.2310E+020.3700E÷01

0.20003+020.37503+010.17303+020.38003+010.15103+020.38503+01

0.13103+020.39003+010.11503+020.39501+010.10103+020.40003+01

0.88903+010.40503+010.7860E+010.41003+010.70003+010.41503+01

0.62502+010.42003+010.56103+010.42503+010.50503+010.43003+01

0.45703+010.4350E+010.41503+010.4400E+010.3780E+010.44503+01

0.34503+010.4500E+010.31703+010.45503+010.29203+010.46003+01

0.26903+010.46503+010.25003+010.47003+010.23203+010.47503+01

0.21603+010.48003+010.2010E+010.48503+010.18903+010.49003+01

0.17703+010.49503+010.1660E+010.5000E+010.1570E+010.50503+01

0.14803+010.51003+010.1400Z+010.51503+010.12903+010.52003+01

0.12303+010.52503+010.11803+010.5300E+010.11303+010.53503+01

0.10902+010.54003+010.10503+010.54S03+010.10103+010.55003+01

0.96603+000.5550E+010.9300E+000.56003+010.89503+000.56503+01

0.86203+000.57003+010.83103+000.57503+010.80203+000.58003+01

0.77403+000.5850E+010.7470E+000.59003+010.72203+000.59503+01

0.69903+000.60003+010.67603+000.60503+010.65403+000.61003+01

0.63403+000.61503+010.61503+000.62003+010.5960Z+000.6250E+01

0.57903+000.63003+010.56303+000.63503+010.S4703+000.64003+01

0.53203+000.64503+010.51703+000.65003+010.50403+000.6550E+01

0.49103+000.66003+010.47803+000.66503+010.46603+000.67003+01

0.45503+000.67503+010.44403+000.68003+010.43403+000.68503+01

0.42403+000.69003+010.41503+000.69503+010.40603+000.7000E+01

0.39703+000.70503+010.3890E+000.71003+010.38103+000.7150Z+01

0.37303+000.72003+010.3660E+000.72503+010.35903+000.73003+01

0.35303+000.73503+010.34603+000.7400E+010.34003+000.74503+01

0.33403+000.75003+010.32803+000.75503+010.32303+000.76003+01

0.31703+000.76503+010.31203+000.77003+010.30703+000.77503+01

0.30303+000.78003+010.2980E+000.7850E+010.29403+000.79003+01

0.28903+000.79503+010.28503+000.80003+010.24603+000.9000E+01

0.19803+000.10003+020.15503+000.11003+020.1330E+000.12003+02

0.11503+000.13003+020.1000E+000.14003+020.88003-010.1500E+02

0.78003-010.1600E+020.6900E-010.17003+020.63003-010.1800E+02

0.57003-010.19003+020.5200E-010.20003+020.47003-010.21003+02

0.44003-010.22003+020.41003-010.2300E+020.38003-010.24003+02

0.36003-010.25003+020.34003-010.2600E+020.32003-010.27003+02

0.30003-010.2800E+020.29003-010.29003+020.27003-010.30003+02

0.16003-010.45003+020.1000E-010.60003+020.70003-020.7500E+02

RRC K12180 40
0.5000E-020.9000E+020.3000E-020.1050E+030.3000E-020.1200E+03

0.2000£-020.1350E+030.2000E-020.1500E+030.1000E-020.1650E+03

0.1000E-020.1800E+030.1000E-020.2300E+030.1OOOE-020.2800E+03

0.OOOOE+000.4800E+030.OOOOE+000.5300E+030.0000E+000.5800E+03

axial power profile .1128E+01 .0000E+00 .1128E+01 .4500E-02 .1128E+01 .9500E-02

.1128E+01 .1450E-01 .9926E+00 .1950E-01 .9926E+00 .2450E-01

.9926E+00 .2950E-01 .9813E+00 .3450E-01 .9813E+00 .3950E-01

.9813E+00 .5950E-01 .1004E+01 .6450E-01 .9926E+00 .6950E-01

.9813E+00 .7450E-01 .9700E+00 .7950E-01 .9588E+0Q .8450E-01 .9588E+00 .8950E-01 .9588E+00 .9450E-01 .9700E+00 .9950E-01

.9813E+00 .1045E+00 .9813E+00 .1095E+00 .9588E+00 .1145E+00

.9700E+00 .1195E+00 .9813E+00 .1245E+00 .9926E+00 .1295E+00

.9926E+00 .1560E+00

radial power profilel.0000E-9 0.0 1.0000E-9 0.0010E-02 1.OOOE-9 0.1200E-02

0.9297E+000.1201E-020.9297E+000.1659E-020.9297E÷000.1845E-02

0.9297E÷000.2014E-020.9328E+000.2170E-020.9390E+000.2316E-02

0.9452E+000.2452E-020.9514E+000.2582E-020.9575E+000.2705E-02

0.9637E+000.2824E-020.9699E+000.2937E-020.9761E÷000.3046E-02

0.9911E+000.3151E-020.1015E+010.3253E-020.1039E+010.3352E-02

0.1062E+010.3448E-020.1086E+010.35411E020.1188E+010.3632E-02

0.1369E+010.3721E-020.1868E+010.3790E-02

multiplier 8.20

end block

/design of fuel rod data block

fuel rod data 0.156 9.100e-03 293.4

pellet data .000e-3 0.000e-3 l1.00e-3 0.000e-6 7.58e-3 2.00

.96800 0.e3 0.000 2.0 1883. 6.

cladding data 0.060e-3 0.0 2.0 0.0

upper plenum data 1 .100e-3 5.00e-3 1.00e-3 4.440e-6

lower plenum data 1 .100e-3 5.00e-3 1.00e-3 0.357e-6

gas composition 0.9757 0.0243 0.0 0.0

1.65e+6 293.4

end block

/solution control data block

property initializat'

fuel conductivity 50 273. 5000.

cladding conductivit 50 273. 4000.

end

time control

time step specifica 1.00e5 -10.e+7 1.00e5 -7.7e7

1.00e5 -7.7e+7 1.00eS -l.e5

1.00e4 -5.Oe+4 1.00e4 -1.e4

0.010 0.0 0.010 0.02

0.005 0.02 0.005 5.

0.010 5.0 0.010 12.

0.05 12. 0.05 30.

10.0 30. 10.0 1000.

steady-state 500.

end

convergence control

implicit calculation .001 .001

temperature computat 300 300 1.0

end

nodalization

axial nodalization 10

fuel radial nodaliza 25

cladding radial noda 6

end

end block

/model selection data block

heat conduction

central void 0.0 0.156 1.20e-3

deformation model

internal gas press

plenum

grass

metal-water

cathcart

end block

/boundary condition data block

coolant conditions

geometry l.eO l.eO 0.75

lower pl enthalpy 1360.0e3 -10.e7 1360.e3 -5.e4

85.0e3 0.0 100.e3 620.

RRC K12180 41
pressure

-ass flux

core average enth.

chf correlation

fibm boiling

15.7e6

0. le6

1. e+6

1.e-6

1360.0e3

85. Oe3

w-3

dougall

-10. e7

0.0

-10.e7

0.0

-10. e7

0.0

15.7e6

0. le6

1. e+6

1.OOe-6

1360.e3

100 .e3

-5. e4

620.

-5.e4

620.

-5. e4

620.

end block

/tvmnning

crit

end block

/end

0.93

7.2. Description of the output information

7.2.1. Output file FGR._AX15.DAT

To output the information on the dynamics of fission gas release the following additional output files are

necessary in GRASF subroutine. File FGRAXI5.DAT is formed in GRASF subroutine. The following

data for the maximum power axial slice of the fuel rod under the base irradiation conditions are stored in

that file. Table 7.2 presents the description of parameters.

Table 7.2. Description ofparameters in FGRA.XIS.DAT fe.

Variable Descriptdon units

TDAY Time days

J Number of axial slice

BVSJ(J) Volume swelling of fuel at axial slice %

RGJ Gas retention in fuel matrix at axial slice Mols

GJOUT Total gas released from fuel at axial slice mols

RGGL Fraction of gas retention in fuel grains at axial slice mols

RGGF Fraction gas retention on grain faces at axial slice mols

RGGE Fraction gas retention on grain edges at axial slice tools

FGPJ/AVN Fission gas release at axial slice at axial slice per-unit

SUMRET Fractional sum of retained gas in fuel at axial slice per-unit

TK(1,J)/1.DO Fuel temperature in inner ring at axial slice K

TS(13) Fuel temperature at outer surface of f'rst ring at axial slice K

TS(KF) Fuel temperature at outer fuel surface at axial slice K

POW(J)/0.3048D0 Power rate at axial slice kW/m

BURN(J) Fuel burnup at axial slice MWd/kg

RRC K!2180 42
7.2.2. Output file FGR TRAN.DAT and FGR&TOT.DAT

File FGR_TRAN.DAT is also formed in GRASF subroutine. The overall data for fuel rod during the nonsteady-state process are stored in that file. Table 7.3 presents the description of parameters.

Table 7.3. Description of parameters in FGRJRAN.DATfile.

Variable Description Units

TS0_S Time s

FGRT Total gas released from fuel at axial slice per-unit

RGT*22400.DO Gas retention in fuel matrix at axial slice cm 3

GTOUT*22400.DO Gas release from fuel matrix at time step at axial cm3

slice

GRFT*22400.DO Gas release from fuel matrix step at axial slice cm3

GGT*22400.DO Gas generation cm3

ERR*10D)O Relative error in integration %

RETI*22400DJJ Total iodine retained in fuel rod cm3

RETC*22400.DO Total cesium retained in fuel rod cm3

OUtT*22400D0 Total iodine released in fuel rod cm3

OUTC*22400.D0 Total cesium released in fuel rod cm3

TS(1,LMAX1)IL.ODO Fuel temperature at inner fuel surface at axial K

slice with peak power

TS(KF, LMAXI)1.ODO Fuel temperature at outer fuel surface at axial K

slice with peak power I

FGRTOT.DAT file contains the same output data block for steady-state calculation of fission gas release,

but time variable named as TSOPD/(3600.DO*24.DO) [days] is used instead of TS0_S [s].

7.2.3. Output files FGR..RADS.DAT and FGR..ADT.DAT

Files FGRRADS.DAT and FGRRADT.DAT are necessary to output the calculated data characterizing

fission gas radial distribution. The files are initialized in the GRASF subroutine. The only difference in

calculated data of these files is that FGRRADS.DAT file stores the information by the end of the base

irradiation conditions (pre-transient conditions), and FGR_RADT.DAT file stores the information after the

pulse testing. Below we present the list of parameters for one of the output files. The calculated data are

stored for the maximum power slice which is defined by the LMAX1 variable (see Table 7.4).

RRC K12180 43
Table 7.4. Description ofparameters in FGRRADS.DAT and FGRRADT.DAT files.

Varal Description Uit

K Number of fuel ring

OTNRAD Relative fuel radius per-unit

RGKJ(KJ)*UNLESS Fraction of gas retention per-unit

TS(K,J) Fuel temperature at inner surface of fuel pellet K

BVSKJ(KJ) Volume swelling of fuel %

GOU(KJ)*UNLESS/AVN Fractional gas release per-unit

GFACE (KJ)*UNLESS Fraction of gas retention on grain faces per-unit

G_EDGE (KJ)*UNLESS Fraction of gas retention on grain edges per-unit

GGRAIN(K,J)*UNLESS Fraction of gas retention in fuel grains per-unit

((GSG(KJ)IAVN)IARA(K,J))/GPE Sum of gas retention per-unit

LL

RS(KJ)*10.DO Fuel ring radius cm

(GFACE(KJ)+GEDGE(KJ)+G_ Specific gas retention cm3/g fuel

GRAIN(KJ))*22.4D3/

RMASS

PRFGRF(KJ) Fuel porosity per-unit

7.2.4. Output files BALOONLDAT, BALOON2.DAT

These output files contain time dependent thermal and mechanical parameters specially for ballooning

effect. Thermal and mechanical parameters are given at user specified clad node (KJ), where K-axial

coordinate, J-azimuthal coordinate.

In the case of ballooning absence empty files are formed. Table 7.5 and Table

parameters.

7.6 present the list of

Table 7.5. Description of parameters in BALOONIDAT file.

Variable Description Units

TIMBAL Time s

CTEMP(KJ) Clad temperature K

STRESF(K,J)*I.E-6 Effective clad stress MPa

CTSTRT*I.E-6 Clad ultimate strength MPa

RSTRAN(KJ) Clad strain rate 1/s

FITEMP(K), Fuel surface temperature K

STEMP(KJ) Not used

HTCS(KJ) Not used

TSTM(K,J) Not usedSTRNC(KJ)*I.D2 Tangential component of true plastic strain %

STRNA(KJ)*l.D2 Axial component of true plastic strain %

STRNA(K,J+8)*l.D2 Axial component of true plastic strain %

RRC Kl 2180 44
Table 7.6. Description ofpwnmeters in BALOON2.DATfike.

Variable Description Units

TIMBAL Time s

GPfHLU(K,J)* 1.D3 Gap width m

CTEMP(KJ) Clad temperature K

PSBAL/1.D6 Gas pressure MPa

TCE*100.DO Clad ballooning strain %

BRATE Clad strain rate in ballooning K/s

STRNC(KJ) Tangential component of true plastic strain per-unit

RCLA Not used

RAVE(K) Azimutally averaged midwall clad radius at m,

axial node

RBAR Not used

EIJNFMB Not used

EISTABB Clad instability strain per-unit

RAD(K4) Current midwall clad radius In

DISP(KJ) Not used -

HTCGLU(J,K) Gap conductance in ballooning region kW/m2 K

QLBA Not used

QBAL Not used

7.2.5. Output fie GRAPH.DAT

Additional calculated data and their output format are formed in the GRAFOUT subroutine. Integral

thermal-physical and thermal-mechanical parameters versus time are stored in the GRAPH.DAT file.

Table 7.7 presents the list of parameters.

Table 7.7. Description of parameters in GRAPH.DAT file.

Variable Description Units

TS Time s

ENS-MAX Not used

POW Average power of fuel rod kW

ENTER(LMAX1) Peak energy deposition cal/g fuel

TGAS Gas plenum temperature K

ENTH(LMAX1) Peak fuel enthalpy cal/g fuel

TAVE Average fuel temperature K

RRC1K2180 45
Variable, DescriptionUnt

TS rime s

EXIT(LMAXI) Peak energy leakage cal/g fuel

SUM*100.DO Fraction of molten zone %

PGAS Internal gas pressure MPa

El Ave. energy deposition cal/g fuel

E2 Energy leakage cal/g fuel

E3 Average fuel enthalpy cal/g fuel

CLADAXEX Total clad axial elongation mm

FSAXEX Total Fuel axial elongation mm

HTMODEL Heat transfer indicator per-unit

RT2*2.0D3 Outer diameter of fuel pellet mm

RO12.0D3 Inner diameter of clad mm

R02*2.0D3 Outer diameter of fuel rod mm

TOTMWR Energy of metal-water reaction cal/g fuel

FFR(1) Failure probability per-unit

RTI*2.0D3 Central hole diameter mm

SWELMAX*100.DO*3- Transient volume fuel swelling %

SWEL_0

FGRTOT*100.D0-FGR_0 Transient total FGR %

HGAP Gap thermal conductance W/m2K

HGAS Gas conductance W/m2K

H_SOLID Gap conductance due to PCMI W/m2K

HRAD Gap conductance due to radiation W/m2K

HFUEL Thermal conductance from fuel to spring W/m2

K

HECSP+HECCL Not used

H_IZL Thermal conductance from spring due to W/m2K

radiation

H_COND Spring-clad thermal conductance W/m2K

TSPRING Spring temperature K

TCLADDI Clad temperature in plenum region K

TFBOT End of fuel stack temperature K

HTCC Not used

HTC COOL Not used_

HRADD Not used

RRCKIU2180 446
variable: ecito V nits

TS Time s

FLUX_PL Heat flux from spring to clad W/m2 K

(TPLENB+459.69D0)1l.8D0 Lower plenum temperature K

BIO Not used

FO Not used

TETAl Not used

TETA2 Not used

TAUCON Not used

TAUF Not used

TETAAVER Not used

TCONSTANT Not used

DENIRR Not used

RSW(LMAXI)*Fr*1.D3 Fuel radial displacement due to swelling mm

RDEN(LMAX1)*FTr*1.D3 Fuel radial displacement due to densification umm

SWTOT Total fuel radial displacement mm

HFL_GRF(LMAX1)*FLUX/ Heat flux from fuel rod at axial slice with kW/m2

THOU peak power rate

TCLADD Outer clad Temperature K

7.2.6. File BRIEF.OUT (brief listing)

BRIEF.OUT file stores the limiting thermal-physical and thermal-mechanical fuel rod parameters in the

form of listing, as well as the selected options of the main calculational models. Storing of data into the

BRIEF.OUT file is formed in the GRAFOUT subroutine. Table 7.8 presents the description of parameters.

Table 7.8. Description ofparameters in BRIEF.OJT file.

Variable esrponUnits

ENTER(LMAX1) Maximum energy deposition ca!/g

SEFFMAX Maximum effective stress MPa

El Average energy deposition calg

SIGH-MAX Maximum hoop stress MPa

FKE Maximum to average deposition ratio -

SIGZMAX Maximum axial stress MPa

ENTHMAX Maximum fuel enthalpy cal/g

EHOOPMAX Maximum hoop strain %

ENSMAX Average fuel enthalpy cal/g

RRC K! 2180 47
Variable Descnption- Units

100.DO*TCEBAL Ballooning strain %

FKENTH Enthalpy to energy ratio

TFU COM Maximum fuel temperature K

TIME_FU Time at peak fuel temperature s

TCLCOM Maximum clad temperature K

TIME_CL Time at peak clad temperature s

IFAIL Failure indicator

MODFD Deformation model indicator

TIaM FAIL Failure time s

ENERFAIL Maximum fuel energy at failure cai/g

ENTH_FAIL Maximum fuel enthalpy at failure cailg

FGR_0 Pre-transient FGR %

TEMPFAIL Outer clad temperature at failure K

FGR_END Transient FGR %

TSRFAIL Average clad temperature at failure K

TIN-FAIL Inner clad temperature at failure K

TFAVFAIL Average fuel temperature at failure K

BURND Maximum burnup MWd/kg U

PGFAIL Gas pressure at failure MPa

STRESFAIL Hoop stress at failure MPa

TEMPCONT Average clad temp at PCMI K

TIME CONT Beginning of PCMI time s

DTCLM Peak clad temperature rate K/s

DECLM Peak hoop strain rate %/s

MOLTMAX*100.DO Peak fraction of fuel molten zone %

RTM Peak radius of fuel molten zone mm

TOTMWR Total energy of Zr-water reaction cal/g

ZRO2_MAX ZrO2 layer __n

ZROMAX Oxygen stabilized thickness pim

ZRO2_MAX+ZRO_MAX Sum of oxide layers Ilm

(ZRO2_MAX+ZROMAX)*/0.75 Fraction of oxidized clad thickness %

ZBURST*1000.DO . Axial crack location mm

RRC K12180 48
72.7. Post-processing utility for the STRIPF file

Special GRAFDATA code to process the standard output STRIPF file has been developed.

The following parameters serve as the input data to process the STRIPF file (see Table 7.9).

Table 7.9. Description of input parameters for post-processing utility.

Variable Description . - Units

TEND final transient time s

DZO initial elevation of the fuel rod active part m

LMAX number of maximum power slice

NAXN number of axial slices

ISTEPPRINT number of time steps which are excluded from the -

I output proceeding in the files.

These parameters are specified in the first string of the T file in succession in the free format. The

processed parameters can be specified by the user directly in the T file, or they can be automatically stored

when FRAP-T6/VVER code is in operation.

The following files are generated as the result of processing of the main output STRJPF file (see Table

7.10).

Table 7.10. Description of output parameters for post-processing utility.

File name Variable description. Units

CLADAXSSDAT Clad axial stress MPa

CLADHSN.DAT Cladding hoop strain %

CLADHSS.DAT Cladding hoop stress MPa

CLADTE.DAT Cladding inner temperature K

CLADOTEJDAT Cladding outer temperature K

CLADPASN.DAT Clad permanent axial strain %

CLADPHSN.DAT Clad permanent hoop strain %

CLADPRSN.DAT Clad permanent radial strain %

CLADRSN.DAT Cladding radial strain %

CLADSNLDAT Clad instability strain %

CLADSSLDAT Clad stress at instability MNPa

CLADYSS.DAT Clad yield stress. MPa

COLBLKTE.DAT Coolant bulk temperature K

COLMSFLX.DAT Coolant mass flux kgfm2 S

COLPE.DAT Coolant pressure MPa

COLQL.DAT Coolant quality per-unit

CRTHTFLX.DAT Critical heat flux MW/m2

.CEMRDAT Centerline temperature K

EFCLADSS.DAT Effective clad stress MPa

ELEV.DAT Nodal elevation m

RRC K! 2180 49
FenaeV~ra~ de nunitsFSDSP.DAT Fuel surface displacement Mm.

FSTEMP.)AT Fuel surface temperature K

GAPHTC.DAT Gas gap heat conductance coefficient kW/m2 K

GAPPRLDAT Gap pressure MPa

HEAT1RMD.DAT Heat transfer mode per-unit

IOXTN.DAT Inner oxide thickness pmin

LOCRODPW.DAT Local fuel rod power kWim

MEiTWRE.DAT Metal-water reaction cal/g

OOXTN.DAT Outer oxide thickness Pm

OXSTN.DAT Oxygen stabilized thickness pun

STRUCIP.DAT Structural gap interfacial pressure MPa

STRUCRG.DAT Structural radial gap lpm

SURHTC.DAT Surface heat transfer coefficient kW/m2 K

SURHTFLX.DAT Surface heat flux kWM&2

THMGAPIP.DAT Thermal gap interfacial pressure MPa

THMRG.DAT Thermal radial gap pm

INDATADAT Integral fuel rod data,

7.3. Comments on the users and developers of FRAP-T6/VVER code

Description of the modified FRAP-T6 code presented above should be viewed only as adaptation of the

models for computer analysis of the fuel rod behavior under the pulse testing conditions in IGR reactor.

The code accounts for the major specifics of the IGR tests and the design of experimental fuel rods. Choice

of the nodalization diagram and specification of the input data with consideration of the design specifics of

experimental fuel rods and the capsule were performed to model the fuel rod geometry and the conditions

for heat transfer in the capsule.

7.3.1. The limits for appUcability of the adapted FRAP-T6/VVER code

1. The adapted FRAP-T6/VVER code is intended to model the behavior of experimental fuel rods under

the IGR conditions. Verification of the separate models and the whole FRAP-T6/VVER version was

mainly performed for the specific conditions of IGR reactor. Hence, the authors do not recommend to

use this version of the code to model the fuel rod behavior in the conditions sufficiently different from

those discussed in this report.

2. Analysis of the regimes with the complete or partial melting of the fuel is beyond the capabilities of the

code. Fragmentation of the fuel and cladding are not modeled. Beginning of the fuel melting

corresponds to the fuel peak enthalpy higher than -220 cal/g (radially averaged). Hence, for

interpretation of the calculated results higher than this value, it is necessary to remember that in the

code there are no models analyzing fuel melting.

3. Physical and mechanical properties of the cladding of Zr-l%Nb alloy were mainly obtained for the

temperature range up to 1573 K. Extrapolation of the data is used in case there are no experimental data

RRC KM2180 50
for higher temperatures. From this stand point modeling of the cladding behavior at the temperatures

exceeding this limit can not be considered correct.

4. The models analyzing behavior of fuel, fission gas in the rim-layer, and fuel cracking are desirable to be

improved further correction and improvement. For example, the model of gas release does not account

for recrystallization of the fuel grain in the fuel external layer. This can result in the underestimation of

the fission gas release under the pulse heating up. Recrystallized fuel layer produces a stronger

mechanical interaction with the cladding because of the increased gas pressure in the pores if the temperature loadings are present. Still the verification procedures performed for the main integral parameters

(fission gas release, cladding temperature, internal gas pressure in fuel rod, cladding deformation) allow

to make a conclusion on the applicability of the code till the burnup of 50 MWd/kg U.

7.3.2. Further development of the adapted version of FRAP-T6 code

1. Computer analysis of the fuel rod behavior under high rates of heating (more than 1000 K/s) and

deformations (100 %/s) indicated that the code iteration methods of obtaining solutions to the system of

equations converge only weakly. Hence, instability of solutions (in particular, thermal conductivity in

the gas gap) often takes place in the area of strongly non-linear equations of the material state. In the

future it will be desirable to use more powerful numerical convergence methods for the better accuracy

of calculations when modeling fast accident processes.

2. Improvements can be made in the models analyzing behavior of high burnup fuel. Special attention

should be paid to modeling of the rim-zone with consideration of the fuel properties degradation, and

potential cracking in case of pellet cladding mechanical interaction (PCMl).

3. Development and selection of criteria for the cladding failure under RIA conditions is currently one of

the most important problems in evaluating fuel rod reliability.

4. Assumption of the thin-wall cladding is one of the main approximations in the model of the cladding

mechanical behavior. Still, in case of the fast pulse heating of the cladding, temperature drop across the

wall width can be of several hundreds of degrees. For these conditions, the analysis should account for

the radial and thermal components of the cladding stresses.

5. Lack of the model for the stress-strain condition of the fuel can lead to the inadequate prediction of the

cladding behavior in case of PCMI under the conditions of the fuel cracking (especially in case of

adiabatic power peaks). To obtain spatial distribution of the stresses and deformations in the fuel it is

expedient to review equations of thermal elasticity supplemented with the plastic deformation

components.

6. Analysis has shown that there is a problem in prediction of the ZrO2 thickness for the IGR tests.

Measured results have demonstrated that the ZrO2 thickness are in the range of 0-12 pim (excluding

#H3T fuel rod with fuel and cladding melting). However, original models for the cladding oxidation for

zircalloy and Zr-l%Nb predict the oxide thickness below 2 pm. Thus, this problem should be carefully

studied in future.

RRC K12180 51
8. CALCULATION EXAMPLES

8.1. The example of calculated results of the VVER fuel rod behavior under

testing conditions in IGR reactor

Analysis of the experimental fuel rod (#H5T) behavior in IGR reactor is presented as the Example

Problem. The fuel in #H5T fuel rod has reached the burnup of 49 MWd/kg U. Specification of the input

data is presented in section 7.1 of the User's Manual chapter.

Analysis of the fuel rod main thermal-mechanical parameters consists of two stages:

1. Base irradiation conditions in the power reactor.

2. Pulse heat-up under IGR test conditions.

The recommended nodalization diagram of the fuel rod and main parameters of the input data specification

are presented in Fig. 8.1 and in Table 8.1.

upper gas plenum

N711

cladding

fuel-clad gap

fuel pellet

central hole

4

3'

2'

lower gas plenum

coolant

a axial node - radial node

I

Fig. 8.1. Nodalization scheme.

Table 8.1L Main parameters of input data specification.

* axial nodes: 10

* radial nodes: 31, including:

fuel: 25

cladding: 6

" time step during fast transient: 1-5 1073s

* time step during slow transient: 5 10. - 1.0 s

* parameters of numerical solution accuracy:

fuel temperature ±l K

maximum number of iterations when

calculating gas pressure and radial temperature 200

distribution

relative difference between two iterations 0.1%

(criterion to stop calculations)

RRC IU 2180 52
Change of the power parameters in the process of accident including fuel rod power, energy deposition in

the fuel, fuel enthalpy, and leakage of heat from the cladding surface is presented in Fig. 8.2. Fig. 8.3

presents the change of temperature parameters and the coefficient of heat transfer from the cladding to the

coolant. Fig. 8.4 presents the information on the change of gas pressure inside the fuel rod, and

circumferential component of the loadings in the cladding in the process of the accident. Total hoop strain

of the cladding and fuel, as well as the gas gap size are presented in Fig. 8.5. Change of gas release and

fuel gas swelling versus time is presented in Fig. 8.6.

500

400

300

A -240

~'300

~200

IV

.777vŽ>~r

100

0

//

-- w- Power of fWl rod

..-- Ene -e -.- Peak fiml ei - 0-- Leak ofergy

-. axlatm M mew

180 2,-

120 "

60

0 m A

0 2 4 6 9 10

Time (s)

FIg. 8.2. Time history of fuel rod energy parameters in accident.

RRC K12180 53
3000- 36

.2500--3

2000- 248

-- Fuel centcrlin tempaature .i 9

5000

0 2 46 810

Time (s)

Fig. 8.3. Time history of fuel rod temperature parameters and clad-to-coolant heat transfer

coefficient in accident.

~1.5.- - - 300~

1.020

0 2 4 6 8 10

Time (s)

Fig. M4. Time history of inner gas pressure and dad hoop stress in accident.

RRC K1 2180 54
10I 030

-- a- Clad boop Warnta_ _

8 . . Fud-clad wid 0-24

.6 6-

0.12

20.06 .

0.06

0 2 4 6 8 10

Time (s)

Fig. 8.5. Time history of total fuel and clad hoop strain and gas gap width in accident.

20

15

10

5

0

Fuel swe lng

-G0- Fission gas releas

_______________________________________ 4

-I, 4

0 681

0 2 4 6 8 10

Time (s)

Fig. 8.6. Time history of fission gas release and fuel swelling.

RRC K92180 55
REFERENCES

1. LYegorova, G.Abyshov, V.Malofeev et. al. (d~ata base to characterize behavior of high burnup fuel

rods with Zr-l%Nb cladding and U0 2 fuel (VVER type) under RIA conditions* NUREG/A-0156,

Vol.2.

2. LJ.Siefken, Ch. Allison, M. Bohn, S. Peck ZFRAP-T6: Computer code for the transient analysis of

oxide fuel rods.)i NUREG/CR-2148, May 1981.

3. F. Lamare, J.C. Latche, "SCANAIR. A Computer Code for Reactivity Initiated Accidents in LWRs",

Rapport Technique SEMAR 95/01.

4. K.Mikitiouk et. al. Modification of IPSN's SCANAIR Fuel Rod Transient Code for High Burmup VVER

Fuel. Report RRC Kl 2181, 1999.

5. D.L.Hagrman, G.A.Reymann, R.E.Mason UMATPRO-Version 11 (revision 1): A Handbook of Material

Properties for Use in the Analysis of Light Water Reactor Fuel Rod Behavior*, NUREG/CR-0497, Rev

1, February 1980.

6. A.Labuntzov. Teploenergetika. 12 (1959). pp. 19-26.

7. S.S.Kutateladze. Fundamentals of Heat Transfer Theory, M., Atomizdat, 1979.

8. P.L.Kirillov, Yu.S. Yuryev, V.P. Bobkov. Thermal-hydraulic Analysis Handbook (Nuclear Reactors,

Heat Exchangers, Steam Generators). -M., Energoatomizdat, 1990.

9. Poletaev G.N. Approximate analytical equations for cladding rewetting under RIA conditions. Report

RRC KI, IAE-6090/5, 1998.

10.H. Chung and T.F. Kassner, Deformation Characteristics of Zircaloy Cladding in Vacuum and Steam

Under Transient-Heating Conditions: Summary Report, NUREG/CR-0344, July 1978.

11.K.Wiehr, FJ. Erbacher and HJ. Neitzel, Influence of Thermohydraulics on Fuel Rod Behavior in a

LOCA, Proceedings of the CSNI Specialist Meeting on Safety Aspects of Fuel Behavior in Off-normal

and Accident Conditions, Helsinki, Finland (1980) 59-73.

12.G.A.Berna et. alIFRAPCON-2: A Computer Code for the Calculation of Steady State ThermalMechanical Behavior of Oxide Fuel Rods. NUREGICR-1845 R3 (January 1981).

13.Dearien J.A. et.al. FRAP-S3: Computer Code TFBR-TR-164, 1978.

14.D.D.Lanning, GA.Berna, C.L.Painter FRAPCON-3: A Computer Code for the Calculation of Steady

State Thermal-Mechanical Behavior of Oxide Fuel Rods. NUREG/CR-6534 PNNL-1 1513 (December

1997).

15.Lassmann K., Blank H. Modeling of fuel behavior and resent advance of TRANSURANUS code.

Nuclear Eng. & Design 1988, v.106 p.291-313.

16.Material properties of VVER-1000 cladding and fuel pellets. State Committee on Atomic Energy,

USSR. M., 1983.

17.Kolyadin V.L e.a. Heat conductance of uranium dioxide. Journal of Atomnaya Energiya, 1974., v.36(3),

p. 59.

18.Lucuta P.G., Matzke H., Verrall R.A., Tasman H.A. Thermal conductivity of SIMFUEL. J. Nucl.

Mater., v. 188, p. 198-204. 1992.

19.Lucuta P.G., Matzke H., Verrall R.A. Modelling of U0 2 based SIMFUEL thermal conductivity. The

effect of the burnup. J.Nucl. Mater. v.217,p.279-286. 1994.

20.B.Yu.Volkov e. a. Material property library for Zr-1%Nb alloy cladding, Report IAE-4941/11, 1989.

RRC KI 2180 56
21 ~justernik VE., Peletski VE., Petrova LL "Experimental research of zirconium reactor materials

thermal properties. Zr-l%Nb alloy." M., J. High Temperature Thermal Physics. v. 31, N4, 1993.

22.A.S.Zaimovsky et. al. Zirconium alloys in nuclear industry, -Moscow, Energoizdat, 1981.

23.Sokolov N.B. et. al. KKinetics of interaction between VVER core materials, (Recommendations for

application in the frame of International Standard Problem on CORA-W2 experiment), Report ASRIIM.

N8068. October 1993 (rus).

RRCK1,8 2180 57

APPENDIX A. List of new and modified subroutines of FRAP-T6/VVER code

FUNCTION CCP (CTEMP)

C

C THIS BLOCK CALCULATES THE SPECIFIC HEAT AT CONSTANT PRESSURE FOR HI-ALLOY CLADDING.

C IF IWWER = 1 THEN DATA IS DERIVED FROM VOLKOV B.YU. ET. AL. MATERIAL PROPERTY

C LIBRARY FOR HI-ALLOY CLADDING*, REPORT IAE-4941/II, 1989. THIS PROPERTY ARE

C INDUCED BY LOW HEATING RATE. IF IWWER = 2 THEN DATA IS DERIVED FROM LJUSTERNIK V.E.

C ET. AL. "EXPERIMENTAL RESEARCH OF ZIRCONIUM REACTOR

C MATERIALS THERMAL PROPERTIES: 110-ALLOY". M.,J. HIGH TEMPERATURE THERMAL PHYSICS.'

C V.31 N.4, 1993. THIS PROPERTY ARE INDUCED BY HIGH-RATE HEATING>=1000 K/S.

C

ELSEIF(IWWER.EQ.1) THEN

C

IF(CTEMP.GE.1173.ODO) GO TO 3

CCP = POLATE(CPWWERCTEMP,NPWWo IU)

C WRITE(O,*) 'LT 1173 ",CCP,CTEMP

RETURN

3 CCP = 392.DO

C WRITE(0,*) 'GE 1173 ',CCP,CTEMP

RETURN

ELSE

C

C IF IWWER=2

C

IF (CTEMP.LE.1100.) THE

CCP = 237.5D0+15.91D-2*CTEKP

ELSEIF(CTEMP.LE.1200.) THEN

CCP = POLATE(CPWWR2,CTEMPNPW2,IU)

ELSE

CCP = 199.7D0÷12.364D-2*CTEMP

ENDIF

C WRITE(0,*) 'FINAL ',CCP,CTEMP

ENDIF

SUBROUTINE CTHEXP (CTEMP, CATHEX, CDTHEX)

IF(IWWER.GT.0) THEN

T=CTEMP

IF(T.GE.2133.DO) THEN

STRS11=1. 0582459D-2

STRS33=1 .3133600D-2

ZNDILA= (2.DO*STRS11+STRS33)/3.DO+0÷.0067D0

C

ELSE IF(T.GT.1153.D0) THEN

STRS11=1.076459D-3+9.7D-6* (T-1153 .DO)

STRS33=3.627600D-3+9.7D-6* (T-1153 .DO)

ZNDILA=(2.DO*STRS11+STRS33)/3.DO

C

ELSE IF(T.GT.883.DO)THEN

TT=T-883 .DO STRSII=3. 0465577D-3÷2.312D-8*TT-7. 358D-8*TT**2+I. 7211D-10*TT**3

STRS33=5.5977000D-3+2. 312D-8*TT-7.358D-8*TT**2+1.7211D-10*TT**3

ZNDILA=(2.DO*STRS11+STRS33)/3 .DO

C

ELSE IF(T.GT. 573.D0) THEN

STRS11=0.13725577D-2+5.4D-6* (T-573.1DO)

STRS33=0.3336985D-8*T**2+5.65390D-6*T-0.199649865D-2

ZNDILA= (2.DO*STRSISTRS33) /3.DO

C

ELSE

STRS11=0.1338985D-8*T**2+3. 85875D-6*T-0.127813365D-2

STRS33=0.3336985D-8*T**2÷5.6539OD-6*T-0.199649865D-2

ZNDILA=(2.D0*STRS11+STRS33)/3.0DO

C PRINT*,'Zi',T,STRS11, STRS33

C PRINT* 'ZR',T,CATHEX, CDTHEX

RRC K1 2080 A-1
ENDIF

C

CDTHEX =STRS33

CATHEX =STRS11

ENDIF

C <VVER<

C

CATHEX = CATHEX*DCEXP

CDTHEX = CDTHEX*DCEXP

RETURN

END

FUNCTION CELMOD (CTEMP, FNCK, CWKF, DELOXY)

C

C

C FOR ZR-1%NB

C

IF(IWAWER.GT.0) THEN

IF(CTEMP.LE. 1073.ODO) THEN

CELMOD = 1.121D11 - 6.438D07 * CTEMP

CELMOD - CELMOD + 3.021D12 * DELOXY

ELSEIF(CTEMP.LE. 2133.ODO) THEN

CELMOD = 9.129DI0 - 4.5D07 * CTEMP

ELSE

CELMOD = 1.OD-10

ENDIF

ENDIF

SUBROUTINE CTHCON (CTEMP, TIME, FLUX, COLDW, CCON, CDKDT)

C

C THIS CODE BLOCK CALCULATES THERMAL CONDUCTIVITY (W/(M*K)) AND DERIVATIVE OF THERMAL

C CONDUCTIVITY WITH RESPECT TO TEMPERATURE (W/(M*K*K)) OF HI-ALLOY. DATA IS DERIVED

C FROM: C VOLKOV B.YU. ET. AL.*MATERIAL PROPERTY LIBRARY FOR HI-ALLOY C CLADDING',

C REPORT IAE-4941/11 1989.

C

100 CONTINUE

IF(CTENP.LE.2133.0D0) THEN

CCON = mEP(O.000461843D0*CTEMP)*15.0636D0

CDKDT = 0.006957018215D0*EXP(O.000461843D0*CTEMP)

ELSE

CCON = 36.DO

CDKDT = 0.D0

ENDIF

FUNCTION CMHARD (CTEMP)

C

C FOR ZR-1%NB:

C

IFP(IWTER.GT.0) THEN

IF(T.LE.773.DO) THEN

CMHARD=2172.1D0 - 10.7055*T÷0.02765*T**2

* -3.278D-5*T**3 + 1.423D-8*T**4

ELSE

CMHARD=850.ODO - 64.DO*T

ENDIF

ENDIF

CMHARD-CMHARD*1.D6

FUNCTION EMCPIR (CTEMP)

IMPLICIT REAL*8(A-H, O-Z)

INCLUDE 'WWER.H'

C

C FUNCTION COMPUTES POISSON'S RATIO

C T = CLADDING TEMPERATURE (KELVIN)

C

C THIS FUNCTION IS A CONVERSION TO KELVIN TEMPERATURES OF AN EXPRESSION RECOMMENDED

C FOR USE IN EVALUATION MODELS BY F.COFFMAN OF ABC-REGULATORY, APRIL 1974.

C CPOIR=.32+5.E-5*T (FAHRENHEIT)

T = CTEMP

C

CPOIR = 0.32D0 + 5.D-5 * (T*1.8D0-459.67D0)

RRC Kf 2080 A-2
C

IF(IWWER.GT.0) CPOIR=0.333 - 0.000126*CTEMP

C

E14CPIR = CPOIR

RETURN

END

FUNCTION CCPINT(T1, T2)

IMPLICIT REAL*8 (A-H,O-Z)

C

C CCPINT INTEGRATES THE FUNCTION CCP BETWEEN THE TEMPERATURE LIMITS

C OF T1 AND T2

C Ti = INPUT LOWER BOUND TEMPERATURE (K)

C T2 = INPUT UPPER BOUND TEMPERATURE (K)

C CCPINT = OUTPUT INTEGRAL OF CCP (J/KG)

C

INCLUDE 'WWER.H'

CANDR

COMMON/INDX/KIII,K1lll1, Klll1, ITRAN

COMMON /ANDREW/ CTHC11,CCPP11,FTHC11,FCPP11,CKM11,CTHE11,FTHEII * Fo F01, FQQII oHTTII

C

DIMENSION CPI(32), CPW1(32), CPW2(32)

C

DATA CPI I 0.0D0, 290.D0, 2800.D0, 300.00, 31950.D0, 400.00,

# 107910.DO, 640.D0, 266760.D0, 1090.D0, 268075.D0, 1093.D0,

# 278995.D0, 1113.D0, 291045.D0, 1133.DO, 304385.D0, 1153.D0,

# 319735.DO, 1173.D0, 335595.D0, 1193.D0, 349485.D0, 1213.D0,

# 360365.D0, 1233.D0, 366553.D0, 1248.D0, 741062.D0, 2300.D0,

# 1.1683D+6 , 3500.DO/

C

DATA CPWI / 0.0D0, 290.D0, 35195.D0, 400.DO, 70731.D0, 500.D0,

# 145246.D0, 700.D0, 214374.D0, 880.D0, 245414.D0, 940.D0,

# 285763.D0, 1000.D0, 325447.D0, 1050.D0, 370510.DO, 1113.D0,

# 390210.D0, 1153.D0, 408714.D0, 1200.D0, 428314.D0, 1250.D0,

# 447914.D0, 1300.D0, 467514.D0, 1350.DO, 839914.D0, 2300.00,

# 1.3103D+6 , 3500.D0/

C

DATA CPW2 / 0.0D0, 290.D0, 33198.D0, 400.00, 110054.D0, 640.D0,

# 181100.D0, 840.DO, 242520.DO, 1000.D0, 262549.DO, 1050.D0,

# 307641.DO, 1113.D0, 321956.D0, 1133.D0, 336271.D0, 1153.DO,

# 350586.D0, 1173.D0, 369911.D0, 1200.D0, 387469.D0, 1250.D0,

# 405336.D0, 1300.D0, 423512.D0, 1350.DO, 827588.D0, 2300.D0,

# 1.4975D+6 , 3500.D0/

C

DATA NCPI /16/ , IV /1/ IY 1/

C

IF(IWWER.EQ.0) THEN

C

CPI1=POLATE( CPI, Ti , NCPI, IV )

CPI2=POLATE( CPI, T2 , NCPI, IY )

CCPINT=CPI2-CPI1

C

RETURN

C

C

C THIS BLOCK CALCULATES THE ENTHALPY AT CONSTANT PRESSURE FOR

C Hi-ALLOY CLADDING. IF IWWER = 1 THEN DATA IS DERIVED FROM

C VOLKOV B.YU. ET. AL. "MATERIAL PROPERTY LIBRARY FOR HI-ALLOY

C CLADDING", REPORT IAE-4941/11, 1989. THIS PROPERTY ARE INDUCED

C BY LOW HEATING RATE. IF IWWER = 2 THEN DATA IS DERIVED FROM

C LJUSTERNIK V.E. ET. AL. "EXPERIMENTAL RESEARCH OF ZIRCONIUM REACTOR

C MATERIALS THERMAL PROPERTIES:1I0-ALLOY*. M.,J. HIGH TEMPERATURE

C THERMAL PHYSICS." V.31 N.4, 1993. THIS PROPERTY ARE INDUCED BY

C HIGH-RATE HEATING>=1000 K/S.

C

C

ELSEIF(IWWER.EQ.1) THEN

C

CPI2=POLATE( CPW1, Ti, NCPI, IV )

CP12=POLATE( CPW1, T2, NCPI, IV

RRC KI 2080 A-3
CCPINT=CPI2 - CPII

C

RETURN

C

ELSE

C

CPI2=POLATE( CPW2, TI, NCPI, IV )

CPI2=POLATE( CPW2, T2, NCPI, IV )

CCPINT--CPI2 - CPII

C

ENDIF

C

C CCPINT=CCPPII*CCPINT

RETURN

END

SUBROUTINE PHYPRP

IF(INWER.GT.0) FTMELT = 3110.15D0- 35.77D0*FBU/10000.

C

C ZR-1%NB ALLOY

C

IF(I-WER.GT.0) THEN

CTMELT = 2133.15D0

CHEFUS = 21.OD+04

C

CC FOR SLOW HEAT RATE:

CTRANB = 883.DO

CTRANE = 1153.DO

CC FOR FAST HEAT RATE:

CTRANB = 1150.DO

CTRANE = 1200.DO

C

CTRANZ = 1135.15DO

ENDIF

C

CALL DIALOT (DELOXY. 29, FDIALA, FDIALM)

CTRANB= (CTRANB+FDIALA) *FDIALM

CTRANE= (CTRANE+FDIALA) *FDIALM

CTRANZ= (CTRANZ+FDIALA) *FDIALH

RETURN

END

SUBROUTINE QDOT (A, B, CPF, CPG, CP, RF, RG, R.

1 G, X, HD, HF, HG, PR, QCRIT, QQ, TBULK. TS, TSAT, TSUR,

# IH. J, L, TEMPCM, ZROXID, DH, AFLOW, DR, BETA,ELAPT)

C

C COMPUTE FIL14 BOILING TERM

646 DTSAT--TSUR-TSAT

DTSAT1=DTSAT

IF (DTSAT1 .LT. 0. 1D0) DTSAT1=0 .ID0

HFB= 0.62D0* ((HD/AL)**0.172D0) *

# ((( (TKG**3) *RG* (RF-RG) * (HG-HF) *GRAVC) / (HD*VSG*DTSATI) ) **0.25D0)

ATB = 2.71828183D0* ((QCRIT-QVAPOR)/DTHSU -(0.96DO-ALPHA)*HTBHSU)

C

C COMPUTE TRANSITION BOILING HTC

C

HTB = ATB*DEXP(-BTB*DTSAT) • ********SHEST

SCOEF=1 ODO

HTOTSHEST=SCOEF* (HTB+HFB)

RRC Ki 2080 A-4
TKGS=THCON(N2, (TSAT+TSUR)/2.D0, RG)

VSG_S=VISC(N2, (TSAT+TSUR)/2.DO, RG)

PROP(I)=(TBULK+459.67D0) /1.8D0

PROP (2) =PR*SIPR

WATER PROPERTIES

CALL STH2X3(THERMO, PROP, IT, ERR)

ALFAS=0.25D0*(TKGS**2.DO * CPG * GRAVC * (RF-RG)

# I (VSGq_S/ )RGC})) **0.33333333D0

HVODA=PROP(5) ! SI

CONVER=0. 00094845D0/2. 2046D0

DH=HF-HVODA*CONVER ! BTU

HVALI=HG-HF ! BTU

ROLIQ=1.DO/PROP(3) ! SI

AT (TSUR+TSAT)/2=TFILM

PROP(l)=((TSUR+TSAT)/2.+459.67D0)/l.8D0

CALL STH2X3(THERMO. PROP. IT. ERR)

ROVAP=1.DO/PROP(3) ! (SI]

COEALF=(1.+0.1*(ROLIQ/ROVAP) **0.75*DH/HVALIj)

ALFA&S=ALFAS*COEALF

FOR ALFAS

QLIQ= (ALFA&S) *DTSAT

T1200=1200*1.8 -460

T630=630*1.8 -460

T800=800*1.8 -460

COR1=LOG10 (1.D0)

COR10=LOG10 (30.DO)

TBEG--TIMEHTC

TEND--TIMEHTC + 0.7

CC(2) =TBEG

CC(1)= COR1

CC(4)=TEND

CC(3)= COR10

TCUR=TSUR

************** FIRST CORRECT

CORREC=l.

IF(ELAPT.GT. TBEG. AND. TBEG.GT.O.DO) THEN

CORREC=POLATE(CC,ELAPT,2,1)

CORREC=0** (CORREC)

ENDIF

SECOND CORRECT

IF(IREWET.EQ. 0) CORREC=l.

QTOT= (QVAPOR + QLIQ) *CORREC

C

C

C

C

IF(KPRINT.EQ.1)

#WRITE(6,986)TSUR,HFB,HTB,DTHSU,HTBHSU,QLIQ

986 FORMAT(39H FOR LOW FLOW, LOW VOID FRACTION, TSUR=.El0.4,5H HFB=,

# EI0.4,5H HTB=,ElO.4,7H DTHSU=,ElO.4,SH HTBHSU=,ElO.4,

# 6H QLIQ=,ElO.4)

DTSAT1=DTSAT

FROM CONDUCTION EQUATION, A*TSUR + B = QTOT

SOLVE ABOVE EQUATION FOR NEW SURFACE TEMPERATURE

IF (DTSATl .LT. 0. iD0) DTSATl=0. ID0

HTOT=QTOT/DTSATl

RETURN

END

SUBROUTINE CKMN (CTEMP ,DELOXY, FNCK, FNCN, CWKF, CWNF, RSTRAN, AKAN, AM)

IMPLICIT REAL*8 (A-H,O-Z)

VVER CLAD PROPERTIES INCLUDED

CKMN CALCULATES PARAMETERS FOR THE CLADDING EQUATION OF STATE

AS A FUNCTION OF TEMPERATURE, AVERAGE OXYGEN CONCENTRATION,

FAST NEUTRON FLUENCE, AND COLD WORK.

C

C

C

C

RRC K1 2080 A-5
200 CONTINUE

C VVER >>>>>>

C CHANGE IRRADIATION FLAG HERE (0 = FRESH, 1= IRRADIATED) !

IRR=I

C

C FIND AM (SAME AS ZRY AT STRAIN RATE > 0.01/S)

IF(T .LE. 730.DO) AN = 0.02D0

C

A = 20.63172161D0

B = - 0.07704552983D0

C = 9.504843067D-05

D = - 3.860960716D-08

IF(T .GT. 730.DO) AM = A + T*(B+ T*(C÷ T*D))

IF(T .GE. 900.DO) AM = -6.47D-02 + T * 2.203D-04

C

C

C FIND STRAIN HARDENING EXPONENT, AN

C FOR IRRADIATED

IF(IRR.EQ.0) GOTO 111

AN= 0.0054616.3.12237D-04*TX-0. 668358D-06*TX**2

1 ÷0.430236D-09*TX**3

IF(T .GT. 752.37D0)

1 AN= -1.58974+0.0050059*TX-4.99134D-06*TX**2

2 +1. 62978D-09*TX**3

C FOR FRESH+IRRAD

IF(T .GT. 854.72D0) GOTO 111

GOTO 112

111 AN= 0.0462842+0.000197952*TX-0.331487D-06*TX**2

1 +1.39133D-09*TX**3

112 IF(T .GT.1223.DO) AN=0.047

C

C

C FIND STRENGTH COEFFICIENT, AK

C FOR FRESH

IF(IRR.EQ.1) GO TO 321

AK= ( 863.33 - T* 1.90882 + 0.00209374*T**2

1 - 9.91178D-07*T**3) * I.D+06

IF(T .GT. 795.18D0)

1 AK = 1.08414D+10*EXP( - 0.00521825D+00 * T)

IF(T .GT. 926.62D0) GOTO 322

C FOR IRRAD

321 AK= ( 738.221+ T* 0.0395682 - 0.00100875*T**2

1 + 0.370178D-06*T**3) * I.D+06

IF(T .GT. 749.45D0)

1 AK = 7.925089D+11*EXP( - 0.01028539D+00 * T)

IF(T .GT. 846.44D0)

1 AK = 1.08414D+10*EXP( - 0.00521825D+00 * T)

IF(T .GT. 926.62D0) GOTO 322

C FOR FRESH÷IRRAD

322 AK = (396.363 - 0.334806*T)*I.D+6

IF(T .GT.1123.54D0) AK = (56.6424 - 0.0324407*T)*I.D÷06

C

C VVER <C<<<

300 CALL DIALOT (CTEMP,20, FDIALA, FDIALM)

AK= (AK+FDIALA) *FDIALM

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 **

END

SUBROUTINE CMLIMT (CTEMP,DELOXYFNCKFNCN,CWKF,CWNFCINWID,

# CINRAD, CDPRES, CAXRAD, CAXSTR, RSTRAN, DELTMP, STRNYT, STRNYE,

# STRNUE, STRNIE, STSRPT, STRRPE, CYLDST, CYLDSE, CULTSE, CBRSTE,

# CBRSST, CTSTRT)

IMPLICIT REAL*8 (A-H,O-Z)

C VVER BURST STRESS INCLUDED

RRC K! 2080 A-6
C VVER >>>>>>>

10 CONTINUE

C LOW TEMPERATURE DATA ARE NOT AVAILABLE, FAILURE EXPECTED ABOVE 973 K

RATIO = 4.5D0

CTSTRT = RATIO *AK

IF(T.GE.973 )

# CTSTRT a EXP(-0.00952232 * T) * 2.99522D+012

IF(T.GE.1176.44)

# CTSTRT = EXP(-0.00301426 * T) * 1.41537D+009

C VVER <<<<<<<

20 CONTINUE

C FIND UNCERTAINTY ESTIMATE FOR CTSTRT

UCTSTT = 0.17D0* CTSTRT

C GO TO 321

C FIND TRUE TANGENTIAL FAILURE STRAIN FOR AZIMUTHALLY SYMMETRIC

C DEFORMATION

IF(CAXRAD .LT. 1.OD-03) CAXRAD = 1.OD-03

IF(CAXRAD .GT. 1.OD+01) CAXSTR = 0.ODO

AXFAC = CAXSTR*CINWID/(2.ODO* CDPRES*CAXRAD)

STSRPT = LOG((CTSTRT*CINWID/(CDPRES*CINRAD) ) **0.5D0+ AXFAC *

# (1.ODO+ 0.5D0* AXFAC) )

C

C FIND TYPICAL CIRCUMFERENTIAL ENGINEERING STRAIN AT RUPTURE

STRRPE = ((CTSTRT*CINWID/(CDPRES*CINRAD))**O.SD0- 1.ODO) *

# EXP(-0.01D0* DELTMPP)

C* DELETE RUPTURE STRAIN LIMIT OF 0.05 IN CMLIMT

C

C FIND EFFECTIVE TRUE TANGENTIAL STRESS AT BURST FOR IDEALIZED

C SYMMETRIC DEFORMATION AND TYPICAL CIRCUMFERENTIAL STRAIN

C FIND TYPICAL CIRCUMEENTI ENGINEERING STRAIN AT INSTABILITY

STRNIE = ((AK * CINWID * (10.DO**(2.DO*AM)) / (CDPRES * CINRAD

# * (0.866D0**(I.DO+ AM + AN))))**0.5D0- 1.0D0)

IF(STRNIE .LT. .05D0) STRNIE = .05D0

IF(STRNIE.GT.0.5D0) STRNIE=.5D0

IF (STRRPE. LT. STRNIE) STRRPE=STRNIE

CBRSST--(CDPRES *CINRAD / CINWID)*((I.OD0+ STRRPE)**2 )

STRNIE = STRNIE * EXP(-0.01D0* DELTMP)

C

C FIND TYPICAL ENGINEERING HOOP STRESS AT BURST

FT = (CTEMP - 273.15DO) * 1.8D0+ 32.DO

CBRSTE =(i0"*(5.00D+00+FT*(3.27D-04-FT* (1.14D-06-FT*2.56D-10))})/

# 1.4505D-04

CALL DIALOT (CTEMP ,21, FDIALA, FDIALM)

STSRPT= (STSRPT+FDIALA) *FDIALM

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 *

END

SUBROUTINE HTRC( ACOND, A, B, DR, HTC, QQ, QCRIT, TSUR,

I IHTREG, LHTC, IDEBUG, NQCHN,

2 KAXN, NSW, ELEV, RL, ICWF, PFACA, SHFRV, FQCRIT, NCHFSW,

3 NCHFMD, TEMPCM, ZROXID, TMELTC, ELAPTM)

C SHEST 10-OCT-95 INSERT AIR COOLANT CONDITIONS *****

C COMPUTE HEAT TRANSFER COEFFICIENT ASSUMING HELIUM OR AIR FLOWING PAST

C CLADDING SURFACE. WARNING ! • HELIUM HTC FOR FORCED CONVECTION

* AIR HTC FOR FREE CONVECTION

C

C TCON = THERMAL CONDUCTIVITY OF HELIUM (BTU/FT-HR-F)

C TVIS = DYNAMIC VISCOSITY OF HELIUM (LBM/HR-FT)

C

C

3000 CONTINUE

RRC. K1 2080 A-7
IF (JCHF.EQ.10) THEN

* SHEST IMPLEMENTATION 10-OCT-95 - AIR FREE CONVECTION MODEL:

* KIRILLOV P.L. YURJEV YU.I., BOBKOV V.P.

* °THERMOHYDRAULIC ANALYSIS HANDBOOK" M., ENERGOATOMIZDAT., 1990

C

**************** CONVERT TEPERATURE FROM F TO K

C IF(ELAPTH.LE.O.ODO) THEN

TTN=(TBULK +459.69D0) / I.8D0

TW =(TBULK+I. +459.69D0) / 1.8D0

IF(ELAPTM.LE.0.ODO) THEN

TAIR_.CL=TTN+1.

TSUR=(TAIRCL * 1.8DO) -459.69D0 TAIRCL IN K, TSUR IN F

ELSE

TAIRCL=(TSUR+459.69D0) / 1.8D0

IF (TSUR.LE.TBULK) TSUR=TBULK+I.

ENDIF

TSH=( (TAIRCL+TT)N *0.5DO)-273. DO

BETAV= 0. 0332D0

GFF=9. 8066D0

ZED=-RL*0. 3048D0

******* ALAN = THERMAL CONDUCTIVITY OF AIR [W/I KI *

ALAX=

* (24.407D0 + 7.978D-2*(TSH)

* - 3.154D-S*(TSH)**2 + .802D-8*(TSH)**3)*I.D-3

CPAIR = SPECIFIC HEAT OF AIR [J/(KG K)] *

CPAIR=1004.16DO-9.761D-3*TSH+55.229D-5*TSH**2 - 36.275D-8*TSH**3

******* ATEMP = TEMPERATURE CONDUCTIVITY OF AIR [M2/S]

ATEMP=

* (18.788D0 + 13.484D-2*(TSH) + 13.959D-5*(TSH)**2

* - 4.654D-8*(TSH)**3)*I.D-6

AMU = DYNAMIC VISCOSITY OF AIR IPA/SI *

AMU=(17.162D0 + 49.894D-3*(TSH) - 2.935D-5*(TSH)**2

* ..+1.133D-8* (TSH) **3) *I.D-6

DENS = AIR DENSITY [K**3***********************************

DENS=

* -2.883D-3 + 355.06D0/(TSH+273.DO) + 353.527D0/(TSH+273.DO)**2

DENS2=

* -2.883D-3 + 355.06DO/(TTN) + 353.527D0/(TTN)**2

VI-(AMU/ 1.0D0)/DENS2 ! KOSTIK ALLOWS TO DELETE "GFF"

T_RA=(TSUR+459.69D0)/1.8D0 ! TSUR [F], THRA [K]

CCC RA= (GFF*BETAV* (TRA-TTN) *ZED**3) / (VI*ATEMP)

RA: (GFF* (DENS2-DENS) *ZED**3) / (AZU*ATEMP)

RA = AMA (RA,I.D-12)

PR=VI/ATEMP

APR=LOG10 (PR)

IF(APR.LE. -0.1D0) APR:-0.1D0

IF(APR.GE. 2.DO) APR= 2.ODO

CSH=POLATE (CC, APR, 4,1)

DEG=0.25D0

C KON

IF(RA.LT.I.D+9) THEN

CSH=0.59

DEG=0.25

ELSE IF(RA.LT.I.D+13) THEN

CSH=0.021

DEG=0.4

ELSE

CSH=0.1

DEG=0.33

ENDIF

ANUSS=CSH*(RA**DEG) ! /I1.10D0

C

C HTC = CALCULATED HEAT TRANSFER COEFFICIENT (W/M2-K)

C

HTCSI=ALAM*ANUSS/ZED * AC_.PL

C

C COMPUTE RADIATION HTC

C

ALPHA=1.0D0 ! VOID FRACTION FOR GAS COOLANT

CALL EMSSF1(TEMPCM, ALPHA, ZROXIDo FE) ! FOR CLAD-TO-VAPOUR RAD

C

C ASSUME CONFIGURATION FACTOR EQUALS ONE

C

FE=0.4D0

RRC K1 2080 A-8
IF (ABS (TRA-TTN).LE.1.-3) T_RA=TTN+O.1

CCCCC FOR HTC=1.20 HRAD=FE*5.67D-B* ( TRA**4 - TTN**4)/(TRA - TTN)

C HRAD=1.30548D-8* ( T_.RA**4 - TTN**4)/(T_RA - TTN) !*1.5

C

C CONVERT HTC FROM (W/M2-K) TO (BTU/HR-F7T2-F)

C T FROM K TO F

C HF FROM (W/142) TO (BTU/HR-FT2)

C

HTC= (HTC.SI+HRAD)/5. 67826334D0

IF(KREAL.EQ.LMAX1) THEN

HTCC=HTC*5. 67826334D0

HTCCOOL=HTCSI

HRADD=HRAD

ENDIF

TW = (BB+HTC*TBULK) / (HTC-AA)

QQ = HTC*(TW-TBULK)

TSUR=TW

ELSE

IF( NHEL.EQ.0) THEN

WRITE(0,*)'

,IRITE(O, *) '

WRITE(O,*) * WARNING ! *

IF (JCHF.EQ.9)

" WRITE(0,*)" * HELIUM IS USED AS A COOLANT *

IF (JCHF. EQ. 11)

" WRITE(0,*)' * AIR IS USED AS A COOLANT *

WRITE(0,*)' * (FORCED CONVECTION MODEL) *

WRITE(0,*)' * ("HTRC* SUBCODE) *

WRITE(O, *)'

WRITE(O,*)'

NHEL=I

ENDIF

IF (JCHF.EQ.11) THEN

**** * CONVERT TEMPERATURE FROM F TO K FOR AIR FORCED CONVECTION

TTN=(TBULK +459.69D0) / 1.8D0

TW =(TBULK +459.69D0) / 1.8D0

TSH--TTN-273. DO

• **** ALAM = THERMAL CONDUCTIVITY OF AIR [W/M K] ********************

ALAM=

*(24.407D0 + 7.978D-2*TSH - 3.154D-5*TSH**2 + .802D-8*TSH**3)*I.D-3

•******* CPAIR = SPECIFIC HEAT OF AIR [J/(KG-K)] *

CPAIR=1004.16DO-9.761D-3*TSH+55.229D-5*TSH**2 - 36.275D-8*TSH**3

•   ATEMP = (A) - TEMPERATURE CONDUCTIVITY OF AIR [M2/S] ** *** *

ATEMP= (18.788D0 + 13.484D-2*TSH + 13.959D-5*TSH**2 • - 4.654D-8*TSH**3)*1.D-6

• **** AMU = DYNAMIC VISCOSITY OF AIR (PA/S] ************************

AMU=(17.162D0 + 49.894D-3*TSH - 2.935D-5*TSH**2 • *+1.133D-8*TSH**3) *i .D-6

•****** DENS = AIR DENSITY  3** *******************************

DENS=

• -2.883D-3 + 355.06D0/(TSH+273.DO) + 353.527D0/(TSH+273.DO)**2

PRSI=6.897D+3 * PR

TEMPK= (TBULK+459.69D0)/1.8D0

GPTHK=O.DO

CPHE=CPAIR/4186.DO

TCON=ALAM* 0.577902D0

TVIS=(AMU/9.8066D0) *2419.09D0

ELSE

C********************** FOR H E L I U M *

C

C**** CPHE = SPECIFIC HEAT OF HELIUM [BTU/(LBM-F)]

C

CPHE = 1.24D0

PRSI=6.897D+3 * PR

RRC KI 2080 A-9
TEMlPK=(TBULK+459.69D0) I1.8D0

GPTHK=0 DO

TCON = 0.577902D0*GTHCON(GMIX, TEKPK, PRSI, GPTHK)

TVIS = 2419.09D0*GVISCO(GMIX. TEMPK)

ENDIF

C

C RE = REYNOLDS NUMBER

C

RE--G*HD/TVIS

C

C PRN = PRANDTL NUMBER

C

PRN = CPH3*TVIS/TCON

C

C FNU = NUSSELT NUMBER

C

ANU = 0.0215D0

BNU = 1.15D0

CNU = 0.8D0

DNU = 0.6D0

FNU=ANU*BNU* (RE**CNU) * (PRN**DNU)

C

C HTC = CALCULATED HEAT TRANSFER COEFFICIENT (BTU/HR-FT2-F)

C

C IF(TSUR.GT.(TSAT+250.DO))GO TO 651

C HRAD=-0.ODO

C GO TO 655

651 CONTINUE

C

C COMPUTE RADIATION HTC

C

CALL EMSSF1(TEMPCM, ALPHA, ZROXID, FE)

C

C ASSUME CONFIGURATION FACTOR EQUALS ONE

C

C WRITE(O,*) ELAPTMTSURTBULK

IF(ELAPTM.EQ.0.0D0) TSUR=TBULK+I.

C WRITE(0,*) ELAPT•,TSUR,TBULK

HRAD=-FE*SIGMA* ( TSUR + FTOR)**4 - (TBULK + FTOR)**4)/

#(TSUR - TBULK) !* AC_PL

655 CONTINUE

IF(Z.GT.ZROUG1.AND.Z.LT.ZROIUG2) FNU=2.DO*FNU

HTCC=FNU*TCON/HD ! * ACPL

HTC=(HTC. C + HRAD)

IF(KREAL.EQ.LMAX1) THEN

HTCC=HTC*5.67826334D0

HTC.COOL=HTC C*5. 67826334D0

HRADD=-HRAD*5. 67826334D0

ENDIF

C

TSUR= (BB+HTC*TBULK) / (HTC-AA)

QQ=HTC* (TSUR-TBULK)

ENDIF

IF(JCHF.EQ. 9) IHTREG= 90

IF(JCHF.EQ.10) IHTREG=100

IF(JCHF.EQ.11) IHTREG=110

QCRIT=O.0D0

RETURN

C CALL THE EVALUATION MODEL HTRC AND COMPANION QDOT

722 CONTINUE

CALL EMHTRC (ACOND ,A ,B ,DR ,HTC ,QQ ,QCRIT

1 TSUR ,IHTREGLHTC ,IDEBUGNQCHN ,KAXN ,NSW

2 ELEV ,EL ,ICWF ,PFACA ,SHFRV

RRC K1 2080 A-10
PRINT*• 'FROM HTRC' ,QCRIT

950 CONTINUE

RETURN

END

SUBROUTINE RIMMOD (PRAD,NPRAD)

BUACT - AVERAGE BURNUP, MWD/KG

IMPLICIT REAL*8 (A-H,O-Z)

INCLUDE 'WWER. H'

PARAMETER( NPOI=23, NBUR=3 )

DIMENSION PRAD(50)

DIMENSION PRADIN (NBUR, NPOI)

DIMENSION WORK1 (NBUR), WORK2 (NPOI)

DIMENSION BUREF (NBUR)

DATA BUREF/ 0.DO, 50.D0, 100.DO/

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

DATA PRADIN/

1.000 ,1.000,

1.000, 1.000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000,

1.0, 1.0000, /

1.000,

1.000,

1.0000,

1.0000,

1.0000,

1.0000•

1.0000,

1.0000,

1.0000,

1.0000

I.E-9,

I.E-9,

0.8820,

0.8820,

0.9573,

0.9573,

1.2000,

1.2000,

1.8380,

1.8380

DATA PRADIN/

1.OOE-9,

1.OOE-9,

1.000,

1.000,

1.000,

1.000,

1.000,

1.000,

1.000,

1.000,

1.E-9,

1.E-9,

0.8820,

0.8820,

0.9573,

0.9573,

1.2000,

1.2000,

1.8380,

1.8380,

/

DATA PRADIN/

* 0.9583,0.9583,0.9583,

* 0.9583,0.9583,0.9583,

* 0.9583,0.9583,0.9583,

* 0.9583,0.9583,0.9583,

* 0.9773,0.9773,0.9773,

* 0.9773,0.9773,0.9773,

* 1.008, 1.008, 1.008,

* 1.008, 1.008, 1.008,

* 1.057, 1.057, 1.057,

* 1.057, 1.057, 1.057

C DATA PRADIN/

C * 1.

C * .

C * 1.

C * 1.

C * 1.

C * 1.

C * 1.,

C * 1.,

C * .

C * 1.

C */

CCCCCCCCCCCCCCCCC FOR

RRC K1 2080

, 0.8820,

0.8820,

0.8820,

0.8820,

,0.9573,

,0.9573,

1.2000,

1.2000,

1.8380,

1.8380,

0.8820,

0.8820,

0.8820,

0.8820,

0.9573,

0.9573,

1.2000,

1.2000,

1.8380,

1.8380

5-NV-NPP (STEADY-STATE) (23 STRINGS)

A-11
*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

DATA PP.ADIN/ 1.03.-9

1.0E-9

1.0E-9

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

1.

*,

1.

1.

1.0E1.0E1. 0E0.882

0.882

0.882

0.882

0.885

0.891

0.897

0.902

0.908

0.914

0.920

0.926

0.940

0.963

0.985

1.008

1.030

1.127

1.298

1 2.

3.868 ccc

* /

C DATA PRADIN/

C * 1.0E-9 , 1.0

C * 1.0E-9 1.0

C * 1.0E-9 , 1.0

C * 1.000 , 0.

C * 1.0000 , 0.

C * 1.0000 , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. , 0.

C * 1. 0.

C * 1. 0.

C * 1. 0.

C * 1. 1

C * 1., 1

C * 1.. 1

C * 1., 1

C * 1., 2.

C *I

SAVE BUOLD, NKAL

C

BUACT = BURNTOT

C WRITE(6,*) " *RIMTI14* BU

C

C-----------------

C CASE 1 : ARRAY SIZE MISMATCH

C

9 1

9 1

-9 1

:35 0

:35 C

'35 C

35 0

29 0

L16 0

03 0

91 0

:78 C

65 C

'53 C

:40 0

62 0

19 0

76 C

:33 1

91 1

75 1

:87 2

86840

:40 1 2

DX2 TOSUREP

E-9

'E-9

)E-9

83554

83554

83554

83878

84526

85173

85821

86469

87117

87764

88412

90385

93683

96981

00279

.03578

.17907

.43267

30544

.0E-9

.OE-9

L.0E-9

3.88235

.88235

.88235

.88235

.88529

.89116

.89703

'.90291

.90878

1.91465

1.92053

1.92640

3.94062

.96319

1.98576

.00833

1.03091

L.12775

.29887

, 1.86840

.86840

1.0E-9

1.0E-9

1.0E-9

0.83554

0.83554

0.83554

0.83878

0.84526

0.85173

0.85821

0.86469

0.87117

0.87764

0.88412

0.90385

0.93683

0.96981

1.00279

1.03578

1.17907

1.43267

2.30544

B

°

tNUP', BUOLD,BUACT

IF(IRIM.EQ.0) THEN

WRITE(*,*) ' *RIMTIM IS USED IF BURNUP > 0

WRITE(*,*) " *RIMTIH POINTS* ',NPOI,NPRAD

IRIM=IRIM+I

ENDIF

IF( NPOI.NE.NPRAD ) THEN

WRITE (6, *) " *RIfTfI* CHECK NUMBER OF POINTS FOR PROFILES

WRITE (*, *) ' *RIHTIM* CHECK NUMBER OF POINTS FOR PROFILES

STOP

ENDIF

C-----------------

C CASE 2 : TEST FOR REPEATED CALL WITH THE SAME BUMWUP - NO ACTION

C

RRC KI 2080 A-12
IF( NKAL.EQ.-1 ) TEEN

IF( BUACT.EQ.BUOLD ) THEN

C WRITE(6,*) ' *RIMTIM* NO UPDATE OF PROFILE'

C WRITE(*,*) , *RfITIM* NO UPDATE OF PROFILE'

RETURN

ENDIF

ELSE

NKAL--

ENDIF

C

C -

C CASE 3 : NEW BURNUP VALUE,

C FIND ACTUAL PROFILE BY LINEAR INTERPOLATION IN PRADIN

C

DO NP = 1,NPRAD

KK = 0

DO NB = 1,NBUR

KK = KK + 1

WORK1(KK) = PRADIN(NB,NP)

ENDDO

AA = FINT (NBUR, BUREF, WORKI, BUACT)

C WRITE(6,*) ' NP,BUACT,AA', NP,BUACT,AA

WORK2 (NP) = AA

ENDDO

C

NP = 0

NPR2 = NPRAD*2

C WRITE(6,*) ' NPRAD,NPR2', NPRAD,NPR2

DO II=1,NPR2,2

NP = NP + 1

C WRITE(6,*) II,PRAD(II),NPWORK2(NP)

PRAD(II) = WORK2(NP)

ENDDO

C

C WRITE(6,*) PRAD'

C DO I=1,NPR2,2

C WRITE(6,*) I, PRAD(I),PRAD(I+I)

C ENDDO

C---------------

BUOLD = BUACT

C

RETURN

END

DOUBLE PRECISION FUNCTION FINT( NT,A,B,X

IMPLICIT REAL*8 (A-H,O-Z)

DfMENSION A(1) ,3(1)

IF( X.LT.A(I) .OR. X.GT.A(NT) THEN

WRITE (6, *) * *RIMTIM* ERROR BURNUP OUT OF RANGE'

STOP

END IF

C

DO 1 I=1,NT

XXX= X-A(I)

IF( XXX.EQ.0.DO) THEN

FINT=B (I)

RETURN

END IF

IF( X.GT.A(I) .AND. X.LT.A(I+I) ) THEN

FINT= B(I) + ( B(1+1)-B(1))/( A(I+1)-A(I) ) *XXX

RETURN

END IF

1 CONTINUE

END

SUBROUTINE RInTIM

IMPLICIT REAL*8 (A-HO-Z)

RRC K12080 A-13
C+PF

C VALUES SAVED IN ' COMINP"

C DIMENSION RADNOD(100)

INCLUDE I SAVEPF. H'

INCLUDE 'WWER. H'

C-PF

C+PF

C SKIP EVERYTHING EXCEPT POWER

GOTO 7777

C-PF

C÷PF -----------------------

C START ONLY HERE

7777 CONTINUE

C

C MODIFY 'PRAD'

C

CALL RInMMD (PRAD, NPRAD)

C

C-Pp -----------------------

C+PF

C SKIP TO RADIAL POWER

GOTO 8888

C-PF

C+PF

C CONTINUE HERE

8888 CONTINUE

C RESTORE INDEXES SAVED IN 'COMINP'

HINDEX= HIN_S

NN = NNS

LMAX = LMAX-S

C-PF

C+PP

C WRITE(6,*) - RIM-ARRAY',L,AI(INDEX1)

DO IZ=1,NAXN

C PRINT*, 'RIMTIM', COEFPOW(IZ,L)

COEFPOW(IZ,L) =AI (INDEX1)

ENDDO

C-PP

C+PF

C ENOUGH I

RETURN

C-PP

SUBROUTINE BURNUP (CON, CONBU, TEMP, BN)

C

C THIS SUBCODE CALCULATES THERMAL CONDUCTIVITY VS. BURNUP

C FOR PWR FUEL

C

IMPLICIT REAL*8 (A-H,O-Z)

INCLUDE 'WWER. H'

DIMENSION ALAM473 (8) ,ALAM2973 (8)

DATA ALAM473 / 1.OODO, O.OODO, * 0.73D0, 30.ODO,

* 0.55D0, 60.ODO,

* 0.35D0, 100.ODO/

RRC K1 2080 A-14
DATA ALAM2973/ 1.OODO, 0.00D0,

* 0.94D0, 30.0D0,

* 0.89D0, 60.0D0,

* 0.84D0, 100.000/

C DATA ALAM473 / 1.00D0, 0.00D0,

C * 1.00D0, 30.ODO,

C * 1.00D0, 60.0D0/

C DATA ALAM29731 1.OODO, 0.00D0,

C * 1.00D0o 30.0D0,

C * 1.00D0, 60.0D0/

TBEG=473 .DO

TEND=1800 .DO

BUZ=BN/86400 .D0

IF (BU_.Z.GE.100.D0) BU_Z=100.Do

IF (TEMP.LE.TBEG) TEMP=TBEG

IF (TEMP. GE.TEND) TEMP=TEND

ACOEF1=POLATE (ALAM473, BUZ, 4,1)

ACOEF2=POLATE (ALAM2973, BUZ, 4,1)

CT=1.DO+ (ACOEF2-ACOEF1) * (TEMP-TBEG) / (ACOEF1* (TEND-TBEG))

AX=ACOEF1*CT

CONO=CON

CONBU=CONO*AX

CONBUO=CONEU

* DEGRADATION FROM PIN

C BB=BUZ/9.375D0

C AB= (0.053+2.2D-4*T)/(0.053+0.016D0*EB+(2.2DO-0.005D0*BB)*T*I.D-4)

C

C ABG=1.-AM/N1(0.05D0,BUZ/600.DO)

C

C IF( (T-273.DO) .GT. 1500.D0) THEN

C B= 0.SD0

C ELSE

C B=4.4D0-1.6D0*(T-273.D0)/500 + 0.1D0*((T-273.D0)/500)**2

C ENDIF

C ABG=1.D0-0.001D0*B*BUZ

C

C CONBU=CON*AB*ABG

CCC PRINT*,AX, TEMP, BUZ

IF(AX .GT. 1.D0 .OR. AX .LT. 0.3 D0) THEN

PAUSE'FROM FTHCON: TOO LARGE/SMALL BURNUP FACTOR FOR CONDUCTIVITY'

ENDIF

RETURN

END

FUNCTION TCOR (D, T, IMOD,BUR, CONDT)

IMPLICIT DOUBLE PRECISION (A-H,O-Z)

TT=T

C SHEST INSERT DOMESTIC FUEL CONDUCTIVTY

IF(IMOD.EQ.1) TCOR=

C PIN (RES MECCHANICA 16(1985) 25-63)

C +(1./(0.0213*TT+8.77))

C F=D/((1.+9.34068*(1-D)-9.5742*(I.-D)**2)*0.6583)

C TCOR--TCOR*F

C IF(TT.GE.1673.) TCOR=0.0253*F

C PIN (RES MECCHANICA 16(1985) 25-63)

C +(38.24/(TT+129.4)+6.1256E-13*TT**3)

C + *((1.025/.95)*(D/(1.+(I.-D)*. 5)))

C PRINT *,TCOR

+(1./(0.0258*TT+3.77)+1.1E-6*TT+1.01E-13*TT**3*EXP(7.2E-4*TT))

RRCKI2080 A-15
+ *((1.025/.95)*(D/(1.+1.-D)*.5)))

C SHEST

IF (IMOD.EQ. 2) THEN

TCOR= (4.82/ (351+TT) +2.434E-17*TT**4) *10.

ENDIF

C SSHEST

IF(IMOD.EQ.3) THEN

TCOR=

+(1./(0.0258*TT+3.77)+1.1E-6*TT+1.01E-13*TT**3*EXP(7.2E-4*TT))

+ *((1.025/.95)*(D/(i.+(I.-D)*.5)))

CC F(D) BtUR=•WT*DAY/KG

BB=BUR/9.375D0

AB=(0.053+2.2D-4*T)/(0.053+0.016D0*BB+(2.2D0-0.005D0*BB)*T*1.D-4)

C ABG=I.-AMINI(0.05D0,BUR/600.DO)

IF( (T-273.D0) .GT. 1500.DO) THEN

B= 0.5D0

ELSE

B=4.4D0-1.6DO*(T-273.D0)/500 + 0.1D0*((T-273.DO)/500)**2

ENDIF

ABG=1.DO-0. 001D0*B*BUR

CONDT=TCOR*100

TCOR=TCOR*AB*ABG

ENDIF

C PRINT *,TCOR,D,T,' TCOR'

C

RETURN

END

FUNCTION FCP (FTEMP,FACMOTFOTMTL,FRDEN)

C

C TABLE OF FUEL SPECIFIC HEAT VS. TEMPERATURE OF FRESH FUEL

C WAS TAKEN FROM A.V.SALATOV ET.AL.// VNIZNH 0575 04.12.89

C

DATA FUTCPW/ 270.ODO, 280.ODO, 287.ODO, 500.ODO,

# 302.ODO, 700.ODO, 310.ODO, 900.ODO, 314.ODO, 1100.DO,

# 319.ODO, 1300.DO, 320.ODO, 1500.D0, 328.ODO, 1700.DO,

# 340.ODO, 1900.D0, 364.ODO, 2100.DO, 390.ODO, 2300.DO,

# 426.ODO, 2500.DO, 470.ODO, 2700.D0, 520.0D0, 2900.DO,

# 594.ODO, 3100.DO /

DATA NWWR, IU / 15, 1 /

C

IF(IWWER.GT.0) THEN

FCP POLATE (FUTCPW,T. N1fTR, IU)

ELSE

FCP = CP(C1U ,C2U ,C3U ,THU ,EDU ,T,FOTMTL)*(I.0D0- FCOMP) +

# CP(CIPU,C2PU,C3PU,THPUEDPUT,FOTHTL) *FCOMP

ENDIF

C

IF (T .LT. (TM-0.1D0)) GO TO 100

IF (IWWER.GT.0) THEN

FCP (1.0D0- R)*FCP + R*485.0D0

ELSE

FCP = (1.0DO- R)*FCP + R*FCPMOL

ENDIF

C

GO TO 100

C

50 CONTINUE

IF (IWWER.GT.0) THEN

FCP - 485.ODO

ELSE

RRC K/ 2080 A-16
FCP = FCPXOL

ENDIF

C

UFCP = 2.ODO

PUFCP = 5.6D0

C

100 CALL DIALOT(FTEMP, 1,FDIALA,FDIALM)

FCP= (FCP+FDIALA) *FDIALf

C FCP=FCPP11*FCP

RETURN

END

FUNCTION FTHEXP (FTEMP,FACHOT)

C

C

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

FOR ZR-1%NB:

DIMENSION EXPDAT (34)

DATA EXPDAT/

0.0, 300.

0.0077, 400.

0.240, 600.

0.451, 800.

0.678, 1000.,

0.922, 1200.,

1.1820, 1400.,

1.4580, 1600.,

1.7510, 1800.,

2.060, 2000.,

2.3850, 2200.,

2.7270, 2400.,

3.0850, 2600.,

3.460, 2800.,

3.851, 3000.,

4.40120, 3080.,

4.40120, 3200. /

C

C

C DATA BASE FOR U02 : BIBI. GKAE 1983.

C

IF(IWWER.GT.0) THEN

C

FTHVV = POLATE(EXPDAT,T,17,1)/100.DO

FTHEXP = FTHVV

ENDIF

C

FTHEXP = FTHEXP*DFEM

RETURN

END

FUNCTION FENTHL (TEMP

1 ,FHEFUS

IMPLICIT REAL*8 (A-H,O-Z)

,FCOMP ,FOTMTL ,FTMELT ,FACMOT

C

C

C

C

C

C

C

C

C

C

f%

THIS FUNCTION IS CALLED BY SUBROUTINE ENERGY AND COMPUTES THE

ENTHALPY OF FUEL AT A POINT RELATIVE TO ZERO DEGREES ABSOLUTE

TEMPERATURE

INPUT ARGUMENTS

C

RRC K1 2080 A-17
C FACMOT - FRACTION OF MOLTEN FUEL

C FCOMP - PU02 FRACTION OF THE FUEL

C FHEFUS - HEAT OF FUSSION OF THE FUEL (J/KG)

C FOTMTL - FUEL OXYGEN TO METAL RATIO

C FTMELT - FUEL MELTING TEMPERATURE (K)

C TEMP - LOCAL TEMPERATURE (K)

C

C **********************************************~***********************

C OUTPUT

C *********************************************************************

C

C FENTHL - LOCAL FUEL ENTHALPY RELATIVE TO ZERO DEGREES-K (J/KG)

C

C **************~*******************************************************

C

C FCPMOL = SPECIFIC HEAT CAPACITY OF MOLTEN FUEL ( J/(KG*K)

C

CANDR

INCLUDE 'WWER. H'

COmmON/ INDX/KIl, KIll11, Kil11, ITRAN

COMMON /ANDREW/ CTHC11,CCPP11,FTHC11,FCPP11,CKMNII,CTHE11,FTHE11

*,FPOII,FQQ11,HTT1

DIMENSION WWRENT (30)

DATA FCPMOL / 503.D0 /

C

C THE FOLLOWING DATA STATEMENTS CONTAIN CONSTANTS FROM MATPRO-11 FCP

C

DATA ClU, C2U, C3U, THU, EDU / 296.7D0, 2.43D-02, 8.7451)07,

1 535.285D0, 1.577D05 I

DATA C1PU,C2PU,C3PU,THPUEDPU / 347.4D0, 3.95D-04, 3.860D07,

1 571.0D0, 1.967D05 I

C

DATA WWRENT/1.9D3, 300.0D0, 57.6D3, 500.0D0, 116.5D3, 700.0D0

# ,177.7D3, 900.ODO, 240.1D3, 1100.D0, 303.4D3, 1300.D0

# ,367.3D3, 1500.D0, 432.1D3, 1700.DO, 498.9D3, 1900.D0

# ,569.3D3, 2100.D0, 644.7D3, 2300.D0, 726.3D3, 2500.D0

# ,815.9D3, 2700.DO, 914.9D3, 2900.D0

# ,1026.3D3, 3100.D0 /

C

C THE FOLLOWING EQUATION IS THE INTEGRAL OF THE FUEL SPECIFIC HEAT

C WITH RESPECT TO TEMPERATURE

C

CPDT(CeTH,C2,OTM,EDT,C3) =

# C1*TH * ( 1.D0/ (EXP(TH/T)-1.DO))

1 + C2 * T *T / 2.DO

2 + C3 * OTH * EXP(-ED /(T * 8.314D0) )/2.D0

C

TX=TEMP

IF (TX. GT. FTMELT) TX=PTNELT

C

FENTHL = CPDT(CIU ,THU ,C2U ,FOTMTL ,EDU

1 ,TX ,C3U ) * C I.D0 - FCOMP

C

IF( FCOMP .GT. 0.D0 )FENTHL = FENTHL + CPDT(CIPU ,THPU

1 ,C2PU ,FOTMTL ,EDPU ,TX ,C3PU )*FCOMP

C

C

IF(IWWER.GT.0) FENTHL=POLATE (WWRENT, TX, 15,1)

C

IF( TEMP .LE. FTMELT - 2.D0 ) GO TO 100

C

C

C

FENTHL = FENTHL + FHEFUS * FACMOT

C

IF(TEMP.LE.(FTMELT+2.DO))GO TO 100

C

C

FENTHL=FENTHL+ (TEMP-FTMELT) *FCPMOL

IF(IWWER.GT.0) FENTHL=FENTHL+

I (TEMP-FTMELT)*485.0D0

100 CONTINUE

IF(ITRAN.NE.1) GOTO 120

C FENTHL=FCPP1*FEN THL

RRC K! 2080 A-18
120 CONTINUE

C

RETURN

END

SUBROUTINE FTHCON (FTEMP,FRADEN,FOTMTL,CON, DKDTBUP)

C

IWWERF=IWWER VVER... CALCULATION

C IWWERF=IWWER-100 ! PWR CALCULATION

IF(IWWERF.GT.0) THEN

IMOD=1 ! PIN-MICRO CORRELATION

IMOD=2 VNIINM CORRELATION

IMOD=3 ! KOLYADIN CORRELATION + BURNUP => PIN-MOD2

BUPP=BUP/86400 .DO

CON=TCOR (FRADEN,FTEMP, IMOD,BUPP,CONDT) *100.DO

CONBUO--CON

CONO=CONDT

*****SHEST 28/10/96 COMMENT FOLLOWING STRINGS FOR ZERO BURNUP

IF(BUP.LE.1.D-10) RETURN

FFTEMP=FTEMP

BN=BUP

C FOR PWR FUEL USE BURNUP

CALL BURNUP (CON, CONBU, FFTEMP, BN)

CCCCCCCCC PRINT*, EN, CON, CONBU

CON=CONBU

ENDIF ! FOR IWWER

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 **

END

SUBROUTINE COBILD ( TI, T2, DT,AM5, DROD, PINT, IP,IP2, Y8, Y9,

# Y9A,Y9B,AAO,ABO,ACO,ADO,AEO,AFO,AGO,AHO,AIO,

# AAI,ABI,ACI,ADI,AEI,AFI,AGI,AHI,AII, Wi, P,

# PERSAT , BWTFR ,AL8)

IF(IWWER.EQ.0) THEN

IF(AZ8.GE.1853.ODO) GOTO 573

570 Y6 = 2.0D0*(1.12569D-02)*EXP(-3.58908D04/(1.987DO*AZ8))

572 Y7 = 2.00D0*0.761490DO*EXP(-4.81418DO4/(1.987D0*AZ8))

ELSEIF(IWWER.EQ.1) THEN

Y6 = 6.4500OD-02*EXP(-20242.ODO/AZ8)

Y7 = 32.26D0*EXP(-1.35800D04/AZ8)

ELSE

IF(AZ8.GE.1773.0D0) GOTO 573

Y6 = 0.51900D-02*EXP(-15355.0DO/AZ8)

Y7 = 3.096D-03*EXP(-1.32850D04/AZ8)

C Y16 = 55. * 0.51900D-02*EXP(-15355.0D0/AZ8)

C Y7 = 50. * 3.096D-03*EXP(-1.32850D04/AZ8)

ENDIF

GOTO 574

573 CONTINUE

IF(IWWER.EQ.0) THEN

Y6 = 2.OD0*(1.035D-02)*EXP(-1.6014D04/AZS)

Y7 = 2.00D0*0.761490D0*EXP(-4.81418D04/(1.987D0*AZ8))

ELSEIF(IWWER.EQ.1) THEN

Y6 = 6.45000D-02*EXP(-20242.0D0/AZ8)

Y7 = 32.26D0*EXP(-1.35800D04/AZ8)

ELSE

Y6 = 1.7720OD-02*EXP(-14680.0DO/AZ8)

RRC K12080 A-19
Y7 = 19.610DO*EXP(-3.05388D04/AZB)

ENDIF

574 CONTINUE

C

C END 1'MER

RETURN

END

SUBROUTINE GAPHTC(GPTHKI, RF, PFC, TG, TF, TC* PG, GASES, FLUX,

# TPLUX,

# RUFC, RUFF, FRDEN, COLDWK, ZRO. FOTMTL, TEMPCM,

* MODFD, HGAPT, JAXIAL)

C SHEST COMMENT NEXT STRING

C IF (GPTHK. LT. TEDEIN) GPTHK=THKMIN

IF (JAXIAL.EQ.LAX1) THEN

HGAP=HGAPT*5.67826334D0

H._GAS=HGAP*SECHR*5.67826334D0

HSOLID=HSOLID*SECHR*5.67826334D0

H_RAD=HGAPR*SECHR*5. 67826334D0

GAP HE=GPTHK *0.3048D6 ! 2.54D0

JUMPjE=DJMPFT *0.3048D6 !I 2.54D0

DROUGHHE=DROUGH *0.3048D6 !I 2.54D0

HGAPJIE=GASCONFRAP/((GPTHK+DJMPFT+DROUGH) *0.3048D0)

C PRINT*, HGAP, HGAS, HSOLID, HRAD

C PRINT*, GPSI,GTHKN

ENDIF

SHEST 10-23-97 05:35PM SET HGAPT LIMIT:

IF(HGAPT*5.67826334D0 .GE. 50000.D0) HGAPT=50000.D0/5.67826334D0

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 **

END

SUBROUTINE STORE6 (LSECH)

COMMON/BAL-SHEST/ ZTMAX,E_BURST

CHARACTER* 3 CHARBAL

CHARACTER*30 STRO

** * FOR CORRECT RECORDING (TPLENUM) TO A STRIP-FILE

TP (1) =TPLNA (1o 2,1)

****** SHEST ADDITIONAL PRINTOUT FOR PRNTOT.F **

IF(T.EQ.0.ODO) THEN

THGAP=1 .E-3

NTRUPT=0

NTCONT=0

J_CON =0

ENDIF

CONTACT ?

TS=T

IF(NSW.EQ.1 ) TS=TCURRS/86400.D0

IF(THGAP.LE. 0.OD0.AND. NTCONT.EQ.0) THEN

IF(J.CON.EQ.0) THEN

TIMEXCONT=TS

RRC K1 2080 A-20
C TEMPCONT=TCLADD

TEMP-CONT=TSREDN

C PRINT*, TIDMECONT, TEMPCONT, JCON, T-S, TCLADD, TICO

J_CON=JCON+1

ENDIF

IF(IGRAF.EQ.0) WRITE(0,1960) TS,TCLADD

1960 FORMAT (/12X, 'BEGINNING OF FUEL-CLADDING INTERACTION',/,

12X,'AT TIME -',F7.2,' SEC; TCLAD =',F7.0,' K',/)

NTCONT=NT_CONT+1

ENDIF

IF( NT-CONT.NE.0.AND. THGAP .GT. I.D-3)THEN

IF(IGRAF.EQ.0) WRITE(0,1962) T_.S,TCLADD

1962 FORMAT (/12X, 'END OF FUEL-CLADDING INTERACTION',/,

* 12X, 'AT TIME =',F7.2,' SEC; TCLAD =',F7.0,' KV,1)

NTCONT=0

ENDIF

********** SHEST BURST TIME ESTIMATION **************

FAILURE ???

C IF(KNONUE.GT.0) THEN

IF(IFAIL.GT.0 .AND. NTRUPT.EQ.0 .AND. IFBALN.GE.1) THEN

JRUPTURE=1

ZBURST=ELEV(KNONUE) *0.3048D0

EBURST--TCEBAL*100 .DO

CHARBAL='YES'

ELSE

CHARBAL= 'NO

IZBURST=LMAX1

EBURST=EHOOPJAX

ENDIF

C PRINT*, "FROM STORE6' ,EHOOPJAX

IF(IFAIL.GT.0 .AND. NT-RUPT.EQ.0) THEN

JRUPTURE=1

TIME_FAIL=T

TEMP_FAIL=TCLADD

PG.FAIL=PGAS_1

IF(IFBALN.GE.1 .AND. IGRAF.EQ.0) *WRITE(0,1961)T,TCLADD,DTCLADD,PGASJ.,CHARBAL,

*ZBURST, E"BURST

1961 FORMAT (/12X,'CLAD FAILURE TIME =',F7.2,' SEC',/,

* 12X,'CLAD FAILURE TEMP =',F7.0,' K ',FB.3,' K/S',/,

* 12X,'CLAD FAILURE PGAS =',F7.2,' MPA',/,

* .12X, 'BALLOONING OCCURRED? ',A3,/,

* 12X,' AT ELEVATION',F7.3,' (M), MAX. STRAIN',F7.2,'(%)',/)

IF(IFBALN.EQ.0.AND.IGRAF.EQ.0 )

*WRITE (0,1963) T, TCLADD, DTCLADD, PGAS1, CHARBAL, *IZBURST, EBURST

1963 FORMAT (/12X,'CLAD FAILURE TIME =',F7.2,' SEC',/,

* 12X,'CLAD FAILURE TEMP =',F7.0," K ',F8.3,' KIS',/,

* 12X,'CLAD FAILURE PGAS =',F7.2,' MPA',/,

* 12X,'BALLOONING OCCURRED? ',A3,/,

* 12X," AT AXIAL NODE',I3,' MAX. STRAIN',F7.2,'(%)',/)

TBURST=T

NTRUPT=NTRUPT+I

ENDIF

GRAFOUT

PGAS_1=PGAS

TCLADD_1I--TCLADD

THGAP_1=THGAP

EHOOPI1=EHOOPMAX

CALL GRAFOUT (UNIT, NROD, TMAX, DZO, FMASS,VOLUME, FUELLEN,

*TCLADD, PGAS, THGAP, T..S, STR0 )

DTCLADD=ABS (TCLADDI-TCLADD)/DT

DE DT--ABS CEHOOPI-EHOOPMAX)/DT

RRC KI 2080 A-21
RETURN

END

SUBROUTINE PCHF( G, HFP, HGP, HIN, P, X, CL, DR, DH, HD, CHF

1 , ICWF, PFACA, SHFRV, ELEV, KAXN, ZZ, J1,

2 TSAT, RF, RG, ALPHA, CPG, TWALL, CPF, TBULK)

C CONVERT SUBCOOLING TEMPERATURE FROM F TO K

C

DTSUBK=TFK (TSAT) -TFK (TBULK)

C SHEST DT IFl

DTSUBF= (TSAT) - (TBULK)

C

C FSUBC=I.DO+0.065D0* ((RF/RG) **0.8DO) * (CPF*DTSUBK/(HGP-HFP))

FSUBC=1.DO÷0.065D0* (CRF/RG)**0.8D0)* (CPF*DTSUBFI (HGP-HFP))

RETURN

END

PROGRAM FRAPT6

READ(55,1941) TITLE

1941 FORMAT(A100)

C READ(55,100.END=I0000) NREST ,NCARDS ,IUNCRT ,Tl,T2,ITEPLNIWWER,

C +IRECVR , MPTFC2

READ(55,*) NREST ,NCARDS ,IUNCRT °Tl,T2,ITEPLN,IWWER,

+IRECVR ,MPTFC2

READ(55,*) ISTEPPRINTLMAX1, IGRAF

READ(55, 1933) TITLE,IREWET

1933 FORMAT(AIO,I40)*************************SHEST

IF(IGRAF.EQ.0) THEN

IF(ITEPLN.EQ.0)WRITE(0,*) ' COOLANT - WATER ',ITEPLN

IF(ITEPLN.EQ.9)WRITE (0,*) COOLANT - FORCED HELIUM',ITEPLN

IF(ITEPLN.EQ.10)WRITE(0,*) ' COOLANT - STAGNATED AIR' , ITEPLN

IF(ITEPLN.EQ.11)WRITE(0, *) " COOLANT - FORCED AIR ',ITEPLN

IF (IWWER. EQ.0) WRITE (0,*) " CLADDING - ZIRCALLOY ',ITENER

IF(IWWER.GB.I) WRITE(0,*) ' CLADDING - ZR÷1%NB ,IWWER

ENDIF

SHEST 13/04/95) *******************************

C

0PEN(UNIT=10, FILE= 'GRAPH. DAT')

OPEN (UNIT=24, FILE='MECHAN. PRO')

NLINES=10

2001 FORMAT(A800)

GRAPHO=' TIME ENTHALPY AVEPOW (KW) ENERMAX1 TPLENU

*M ENT_.AXI AVERTFUEL TERMOCOUPLE MOLTZONE PGAS ENE

*RGYINP ENERGYOUT ENTH (KJ/M) CLADINGEXT FUELEXTEN HT-MODE

* RT2 ROI R02 MWR_.ENERGY FAILPROBAB

• RT1 SWELLING FGR H.GAP HGAS HSOLID

• HRAD HFUEL(SP) H.SPCL(SP) HIZL(SP) HCOND(SP)

*TSPRING TCLADDI TFBOT HTCC HTCCOOL HRADD

• FLUXPL TPLENB BIO FO TETA_1

•TETA2 TAUCONST TAUFUEL TETAJAVE TCONSTANT %DENSIF

• DEL...RSWEL DELDENSIF SWTOT HEATFLUX TCLAD

GRAPH1=' TIME TSREDN ULTIM-STR YIELD-STRS CTSTRT

* STRBURST TGAS GASCONFRAP GASCON-HE GAP_HE JUm

RRC Kf 2080 A-22
*PHEm HE DROUGH-ME HGAP...HE STP.ESS....EL CHSTRS PRBIL PROBABIL'

WRITE(1i0,2001) GRAPHO

WRITE(24,2001) GRAPH1

*********** OUTPUT FOR BALLON2 *

OPEN (UNIT=41, FILE= "BALOONI.DAT')

OPEN (UNIT=42,FILE= ='BALOON2.DAT')

OPEN (UNIT=43,FILE='TABLE.OUT')

OUTPUT FOR PRNTOT

OPEN (UNIT=40,FILE='T')

*********** OUTPUT FOR GRAFOUT *

OPEN(UNIT=80,FILE='T_GRAF.DAT')

OPEN(UNIT=91 ,FILE='TI_RAD.DAT')

OPEN (UNIT=92 FILE= ' T2_.RAD. DAT')

OPENT(UNIT=93,FILE='T3_RAD.DAT')

OPEN (UNIT=94, FILE= 'T4_.RAD.DAT")

OPEN(UNIT=95 FILE='T5_RAD.DAT')

OPEN(UNIT=96 ,FILE='T6_.RAD.DAT')

OPEN (UNIT=81, FILE='MOL1Z.DAT')

OPEN (UNIT=82,FILE= 'MOL2_Z. DAT')

OPEN (UNIT=83,FILE='MOL3_Z. DAT')

OPEN(UNIT=84,FILE='MOL4_Z.DAT')

OPEN(UNIT=85,FILE='MOL5_Z.DAT')

OPEN (UNIT=86, FILE= 'MOL6_Z. DAT')

OPEN(UNIT=71,FILE='DEF1_Z.DAT')

OPEN(UNIT=72,FILE='DEF2_Z.DAT')

OPEN(UNIT=73,FILE='DEF3_Z.DAT')

OPEN(UNIT=74,FILE='DEF4_Z.DAT')

OPEN(UNIT=75 FILE='DEF5_Z.DAT')

OPEN(UNIT=76,FILE='DEF6_Z.DAT')

STOP

END

SUBROUTINE DEFORM (BUO, SW, DBURN).

C SHEST 14/11/96 INTRODUCED FUEL SWELLING + DENSIFICATION

SWELJJ=0. DO

RSWEL=O. DO

IG=0

FRUIDJ= 0.0D0

C PRINT *,'DEFORM (NSW)',NSW

DO55J=LISKP, LFSSKP, LSKP IG=IG+I

IF(NSW .GE. 1 .AND. ISWEL.GT.0) THEN

C FDENS=FRDEN*10970.DO

RSNTR= (10680 .DO-FDENS)

TSINT=1883 .DO

FTEMP=(RWA2(J) + 459.69D0) / 1.8D0

C

C BULAST=BUOO (KREAL) *BUARRAY(IG)

BULAST= (BUI-DBURN (KREAL) ) *BUARRAY (IG)

IF(BULAST.LE.O.DO) BULAST=O.DO

C

BU11=BUI*BUARRAY (IG)

C PRINT*,IG,BU11/86400,BUARRAY(IG)

CALL FUDENS (FTEMP, BUll, FDENS, RSNTR, TSINT, COMPMT, PRVDEN, FRUD)

IF(FRUDO(IG).LE.FRUD) THEN

FRUD=FRUDO (IG)

ELSE

RRC Kf 2080 A-23
FRUD0 (IG) -FRUD

ENDIF

IF(FRUD.LE.-0.4D0) FRUD=-0.4D0

FRUDENT=-FRUD*RNODLS (J)/100 .DO

FRUDJ=FRUDJ+FRUDENT

IF(ISWEL.EQ.1) THEN

CALL FSWELL (FDENS, COMPMT, BUll, BULAST, FTEMP, GASWL, SOLDSW)

* * SWELLING FROM FSWELL

SWELW- (SOLDSW.GASWL)

SWELJJ=SWELJJ+SWELJ*RNODLS (J)

RSWEL=RSWEL+RNODLS (J)

C IF(KREAL.EQ.LMAXI) PRINT*,BUII/86400,BU1/86400,SWELJ

SWEL=SW(KEREAL)

************** SWELLING FROM GRASS

ELSE IF(ISWEL.EQ.2) THEN

SWEL=BVS__Z (KREAL) /I00 .DO

RSWEL=RSWEL+RNODLS (J)

C IF(KREAL.EQ.LMAX1) PRINT*, 'FROM DEFORM" *SWEL,RSWEL

C

**** ** *** ***

ENDIF

DELSW =SWEL*RNODLS (J)/3 !SWELGRF(IG,KREAL) *RNODLS (J)/3

C************* FRUDENT=10.OD-6/0.3048D0

UFS(JROD,K) = DELSW ! + FRUDENT

C PRINT* ,UFS (JROD, K)

RSW (KREAL) =DELSW

RDEN (KREAL) =FRUDENT

C IF(KREAL.EQ.LMAXI) WRITE(6,1961)

C *FTEM,

C *BUI/86400, !RNODLS(J)*FTM,

C *FRUD, !RNODLS(NGAP)*FTM,

C *DELSW*FTM, FRUDENT*FTM, SOLDSW*100

1961 FORMAT (10 (Ell. 4))

ELSE

UFS(JROD,K)= 0.0D0

SWELJJ= 0.ODO

SWEL= 0.0D0

RSWEL= 1.ODO

ENDIF

RWA3(J)=RWA3(J)+ (RNODLS(J)/RNODLS(NGAP)) * UFS(JROD,K)

55 CONTINUE

SWELJJJ=SWELJJ/RSWEL

FRUDJJ=FRUDJ/RSWEL

CC IF (KREAL. EQ. LMAX1) PRINT*, SWELJJJ

CC IF(KREAL.EQ.LMAX1) PAUSE' DEFORM'

IF(ISWEL.EQ.0) SW(KREAL)=0.0D0

IF(ISWEL.EQ.1) SW(KREAL)=SW(KREAL) + SWELJJJ

IF(ISWEL.EQ.2) SW(KREAL)=BVSZ(KREAL)/100.Do

C IF(KREAL.EQ.LMAX1) PRINT*, SW(KREAL),SW(KREAL) *3.78/3, UFS(1,KREAL)

FUD (KREAL) =FRUDJJ

IF(KREAL.EQ.LMAXI) DENIRR=FUD(KREAL) *100.DO

IF(KREAL.EQ.LMAXI) SOLD=SW(KREAL)*I00.D0

IF(KREAL.EQ.LMAX1) GASWLP= GASWL*100.DO

IF(KREAL.EQ.LMAXl) SOLDSWP= SOLDSW*I00.DO

C

* SHEST 11/10/96 INSERT ==> (NSW.EQ.1)

IF(MODFD.EQ.3 .AND. NSW .GE. )

# THKGAP(JRODK)=THKGPI(JROD,K)-THKGPO(1,K)

C IF (MODFD. EQ. 3 )

C I THKGAP (JROD, K) =THKGPI (JROD, K) -THKGPO (1, K)

SHEST 11/10/96 INSERT ==> (NSW.EQ.1 .AND. NSW.EQ.2)

RRC K1 2080 A-24
IF(MODFD.EQ.3 .AND. NSW.GE.1) THKGAP(I,K)=THKGPI(1,)-THKGP0(I,K)

C IF(MODFD.EQ.3) THKGAP(1,K)--THKGPI(1,K)-THKGPO(1,K)

RETURN

END

SUBROUTINE GRAFOUT (UNIT, IROD, TMAXPLOT, DZO, *FMASS, VOLUME, FUELLEN, TCLADD, PGAS, THGAP, TS, STRO)

SHEST* INCLUDE 'WWER.H'

INCLUDE 'WWER.H'

INCLUDE 'WWERI .H'

COMMONIBALSHEST/ ZTMAXS, TCEBAL_S

INTEGER VARITER

DIMENSION PLOTDTA(5000) *,HTMODE(50),FKASSF(1),FLEN(1)

*,TAVERAD(50),TEMPRAD(50),RAD(50),SIGCL(50),SIEFF(50)

*,SIG02(50) ,EMETW S(50),EMWC(50),EHOOP(50),SIGAX(50),TCLIN(50),

*TCLOUT(50 },ZRO2W(50),TSREDN(5O),ZRO(50 ,FENT(50) ,EPOIN(5O)

C-GR

CHARACTER *100 VARTVARTEMPF,VARTEMPC,VARPOWER, VARBURNUP,

*VARENER, VARENTH, VARSTRES, VARSTRAI, VARDT, VARFGR, VARGAP, VARSTRF,

*VARBALL, VARPGAS, VARLEN, VARITER, VARREAL,VARREALO , VARCRIS, VARHELP,

*VARDTFC, VARTAU, VARBIO, VARTETA

C-GR

CHARACTER*30 STR, STRI, STRO, WFAIL, PFAIL, FFAIL

NSHAG=NSHAG+I

IF(NSHAG.EQ.1) THEN

CALL TIME (STRO)

OPEN (UNIT=77, FILE= CLADHSS.DAT')

OPEN (UNIT=50, FILE=' TMPCAV.DAT')

OPEN(UNIT=87,FILE='FENT_RAD.DAT')

OPEN (UNIT=60, FILE= 'BRIEF. OUT')

TEMPCS=68.DO

TKO=TFK (TEMPCS)

BINT=O.DO

TCLADO=O . DO

TFSUR0=0.DO

TAVEO=O.DO

TTECU=0. DO

TTOPL=273.DO

TFU_COM=0.0D0

TSUR_COM=0.OD0

TAVECOM=0.0D0

TCLCOM=O.ODO

SEFFO =O.ODO

SIGHO =O.ODO

SIGZO =O.ODO

EHOOPO =O.ODO

MOLT-MAX= 0. ODO

ZR020=0.0D0

ZROO=0.ODO

DTCLM=O .ODO

DECLM=0.0D0

SED=O.ODO

MCOUNT=ISTEPPRINT

IMCOUNT=0

ITCOOL=0

READ (80,*) ZO

DZO=ZO

READ (80,*) TR1,TM1,TD1

READ (80,*) TR2,TM2,TD2

READ (80,*) TR3,TM3,TD3

RRC K1 2080 A-25
READ (80,*) TR4,TM4,TD4

READ (80,*) TR5,TM5.TD5

READ (80,*) TR6,TM6,TD6

TD6=-TMAXPLOT

L=LMAXl

ENDIF

DO 200 I = KISKP,KMXSKP,KSKP

KZ=KZ+I

C-GRF

HEIGTH(KZ+I) =HEIGTH(KZ)+DZA(I)

C-GRF

FUELLEN=FUELLEN+DZA (I)

TTLMWE = T W + EMETW(IROD, I) * DZA()

SUMV = SUNV + DZA(I) * (RNODLS(LFSSKP) ** 2) * Pi

********SHEST INSERT FOLLOWING CARD INSTEAD OF PREVIOUS**********C

C SMVN = SUMV + DZA(I) *

C #((RNODLS(LFSSKP)**2-RP((M2SKPI,1)**2)*PS)

TA=0.0

NRAD=-NRAD+ 1

C WRITE(0,*) DZA(I)

EMETWIS (KZ) =EMETW(IROD, I) *DT*DZA (I) *FT

EMW(KZ) =EXW (KZ) +E4ETWS (KZ)

DL (KZ) =DZA(I)

FRZED=O.oDO

C-GRF

NRFUEL=IGPNOD

NZED=KZ

C-GRF

DO 100 J - 1,IGPNOD

LDYN = LISKP + (J-1) * LSKP

MDYN = MISKP + (J-1) * MSKP

IF (J .EQ. 1) DV = PI * ((RNODLS(LDYN+LSKP) + RNODLS(LDYN)) I

+ 2.0D0) ** 2 * DZA(I)

IF (J .EQ. IGPNOD) DV = PI * (RNODLS(LDYN) ** 2 -

+ ((RNODLS(LDYN-LSKP) + RNODLS(LDYN)) / 2.ODO) ** 2) * DZA()

IF (J .GT. 1 .AND. J .LT. IGPNOD) DV =

+ PI * (((RNODLS(LDYN) + RNODLS(LDYN + LSKP)) / 2.0D0) ** 2

+ - ((RNODLS(LDYN-LSKP) + RNODLS(LDYN))/2.0D0) ** 2) * DZA(I)

C-GRF

T_.GRF(KZ,J)=TEMPP(MDYN,I.1)/1.8DO +273.D0-17.77777D0

POWRAD (KZ, J) =COEFPOW (KZ, J) ! *PKWA CJRODX, I)/FT

BURN_tRAD (KZ,J) =BURN_GRF (KZ,J)

C PRINT*, 'GRAFOU',KZ,.J,EBURNRAD (KZ,J)

BUPP=BUPNGRF((KZ,J) *86400. DO

C PRINT*, TGRF (KZ,3), FRDEN, FOTMTL, CON, DKDT, BUPP

CALL FTHCON (TGRF(KZ,J) ,FRDEN,FOTMTL,CON, DKDT,BUPP)

ALAMB(KZ,J) --CON

IF(KZ.EQ.LMAX1) THEN

SWTOT=UFS(JRODX,S) *0.3048*1.D3

TEMPG_.AD(J)=(TEMPP(MDYNI,1)+ 459.69D0) I 1.BDO

C pPRINT*, FOTMTL, FTMELT, FRMLTL, FHEFUS

FENT (J) =FENTHL (TEMPDQAD (3J), 0.ODO FOTMTL, FTMELT, 0.ODO, FHEFUS)

-FENTHL(TTK0,0.ODO,FOTnTL,rHELT, O.ODO.FHEFUS)

FENT (3) =FENT (J) / (CALLOR*THOU)

TEHPAX=DMAX1 (T,.R, TEMPtRAD (J))

T_R=TEMPJMAX

c PRINT*, J, TENP_RAD (J), LMAXi

RAD(J)=RP(MDYN,I,1) *FT*THOU

RRC K12080 A-26
RADFUEL(J) =RAD(J)

************* FUEL (CENTER,SURFACE) TEMPERATURE

TFUELK= TEMPRAD (1)

TFUELS= TEMPRAD (IGPNOD)

ENDIF

DVSUM = DVSUM + DV

TSUM = TSUM + DV * TEMPP(MDYN, II)

TA = TA + DV * TEMPP(MDYN,I,1)

IF (J .EQ. 1) GO TO 100

IF (QMAXHM(L1SKP) .LT. 1.OD-10) GO TO 100

R1 = RNODLS (LDYN-LSKP)

R2 = Ri + 0.5D0* (RNODLS(LDYN) - RNODLS(LDYN - LSKP))

DVI = DZA(I) * PI * (R2 ** 2 - R1 ** 2)

R3 = RNODLS (LDYN)

DV2 = DZA(I) * PI * (R3 **2 - R2 *2)

FRZED = FRZED + (QINZ(MDYN,I,IROD) / QMAXHM(LDYN)) * DVI

+ + (QINZ(MDYN+1,I,IROD) / QMAXHM(LDYN+1)) * DV2

SUM = SUM + (QINZ(MDYN, I,IROD) / QMAXHM(LDYN)) * DV1

+ + (QINZ(MDYN+1,I,IROD) / QMAXHM(LDYN+1)) * DV2

100 CONTINUE

FRMOL(KZ)=FRZED/(DZA(I) * (RNODLS(LFSSKP) ** 2) * PI)

C PRINT* ,MOLT.MAX, FRMOL (KZ)

MOLT_.AX=EtAXl (MOLTjAX, FRMOL (KZ))

C*** SHEST ACCONT CENTRAL VOID

C TAK=TA/(DZA(I) * (RNODLS (LFSSKP) **2-RP (M2SKP, I, 1) *2) *PI)

C*** * SHEST WITHOUT ACCONT CENTRAL VOID

TAK=TA/ (DZACI) * (RNODLS (LFSSKP) **2) *PI)

FARENHIET ==> KELVIN

TAVERAD(NRAD)=( TAK + 459.69D0) / 1.8D0

200 CONTINUE

T_S=T

DT_S=DT

IF (DT. GT. 1000.DO) TS=TS/86400.DO

IF (DT. GT. 1000.DO) DTS=DT._S/86400.D0

PLOTDTA(1)=T_S

PLOTDTA(2)=DT_S

WRITE(66, 1000) (PLOTDTA(I),I=1,ICNT)

1000 FORMAT (' PLOTREC ',5X,1P,4E15.6,:/(5EI5.6))

C SHEST 14/04/95 **********************************

C *** OUTER CLADD TEMPERATURE AT AXIAL NODE 'LMAXI *

C *** FUEL-CLADDING STRUCTURAL GAP *******************

THGAP= ROI-RT2

IF(T.GE. 0.DO+DT .AND. IPHE.EQ.0) THEN

VOLSV=VOLSVO

POHE=PGAS

PRINT*, 'WARNING: PGAS=' ,PGAS,' GAP=' ,THGAP*1.D6

PAUSE

IPHE=I

ENDIF

RRC Kf 2080 A-27
IF(NSW.EQ. 1) THEN

TD=T/(24.DO*3600.DO)

ELSE

TD=T

ENDIF

1001 FORMAT (21(E12.4))

N=0

D0174 K=KISKP, KMXSKP, KSKP

NVOIDS=0

IF(NVOID.LT.1)GO TO 173

IF(ELEV(K) .GE.ZVOIDI.AND.ELEV(K).LE.ZVOID2) NVOIDS=l

173 CONTINUE

KDYN=K

N=N+1

C

CALL ENERGY(TEMPP, RNODLS, FOTMTL, TEMPCS, QINZ, QMAXEM,

# ENTH(N), TBAR, KDYN, NVOIDS)

C IF(T.GE.TMAXPLOT-0.0001)

C * WRITE(6,*) 'FROM GRAFOUT- N ',N,' ENTH ',ENTH(N),

C *'TBAR',TBAR,' FOTMTL',FOTMTL,' TEMPCS',TEMPCS,' KDYN',KDYN

174 CONTINUE

IF(NSHAG.EQ. 1) THEN

IF(KREA.LT.LMAX1) THEN

PRINT*, LMAX1,KREA

PAUSE, STOP DUE LMAXl > NZ'

ENDIF

DEN=FRDEN*10960.DO

VDUM= (VOIDT (IROD) *FT**3)

VDI=(FRVOID(2,IROD)+FRVOID(5,IROD) ) *VDUM

VFUEL=PI* (RT2**2-RT1**2) *FUELLEN

CCCCCC VOLUME=VFUEL-VDI

VOLUME=VFUEL

FMASSF (1) =DEN*VOLUME

FLEN (1) =FUELLEN

C PRINT*,FRDEN,RT2,RT1

ENDIF

FMASS=FMASSF (l)

FMASSA=FMASSF (1)

FRPLOT=FRDEN

FUELLEN=FLEN (1)

FDLINA=FUELLEN

CLF=FUELLENIFMASSICALLOR

N=0

11=119

12=129

13=169

El=0 .DO

E2=0 .DO

ENTAL=O. ODO

EHAVE=O .DO

FCAL=FUELLENIFMASSICALLOR

D0188K=KISKP, KMXSKP, KSKP

N=N+1

EPOIN (N) = EPSDOT(K, 1, IROD)

TSREDN(N)=(TMPCAV(IROD,K) + 459.69D0) / 1.8D0

IF(T.EQ.TIME_.FAIL .AND. N.EQ.LMAX1) TSRFAIL=TSREDN(N)

IF(T.EQ.TIMEFAIL .AND. N.EQ.LMAX1) TINFAIL=TCLIN(N)

IF(T.EQ.TIMEFAIL .AND. N.EQ.LMAX1) STRESFAIL=SIGCL(N)

IF (ITCOOL.EQ.0)TCOOLO=((TBULKA(IROD,K)+459.69D0)/1.8D0)-0.1D-3

ITCOOL=ITCOOL+I

DUM=SIGEFF(IRODK) *PSI/1.DO6

RRC K1 2080 A-28
SIEFF (N) =DUM

DUM=SIG(K, 1, IROD) *PSI/1.DO6

SIGCL (N) =DUM

DUM=SIG(K,2,IROD)*PSI/I.D06

SIGAX(N)=DUM

SIG02 (N)=SIGY(IRODK) *PSI/1.D06

EHOOP(N)=EPP(K,1,1) *00.DO

EHAVE=EHAVE+EHOOP (N)

DUM=PRSCLT (JROD, K)

PCOOL=PSI*DUM/1 .DO6

ZRO2W(N)=flMW2 (IROD,K) *FT*THOU*THOU/DOZ

ZRO (N) =flXI2 (IROD, K) *FT*THOU*THOU/DOZ

ZRO2JXAX=EldAX1 (ZR020, ZRO2W(N))

ZROMAX=DMAX1 (ZRO0, ZRO (N))

ZR020=ZRO2_.MAX

ZRO0=ZROMAX

TAUH= (HCOEFA (IROD, K) *HTCO)

DUMP=PKWSUM (K)

DUMH=HFXSUM (K)

IF (U) DUMP=DUMP/FT

IF (U) DU•-l=DUMH/FT

EXIT (N) =DUMH*FCAL

E2=F,2+DUMH*DZA (K) *FT

HT_.ODE(N)=IH(2,1,K,IROD)

ENTER (N) =DUMP*FCAL

EI=EI+DUMP*DZA (K) *FT

ENTAL=ENTH (N) *DZA (K) *FT+lNTAL

ENTH (N) =ENTH (N) / (THOU*CALLOR)

188 CONTINUE

FCAL=FUELLEN/ (FMASS*CALLOR)

********* ENERGY CHARACTERISTICS FOR AXAIL SLICE OF FUEL ROD ***

TOTMEF=TOTMWREN*FCAL

EI=E2*FCAL/FUELLEN

E2=E2*FCAL/FUELLEN E3=EI-E2

ENTALPIA=ENTALr/FUELLEN

DISPLAY OUTPUT ************

T_1=T*10.+ 1.OE-6

IT_1=AINT(TI)

IF(NSHAG.EQ.1 .AND. IGRAF.EQ.0) THEN

WRITE(O,*) " S

WRITE (0, *) " THERMAL PARAMETERS FOR HOTTEST AXIAL NODE:.LMAX1

WRITE(0,*) " '

NSHAG=NSHAG+1

ENDIF

IF(T.GE.O.ODO) THEN

TTOPL=DflAXI (TTECU, TEMPMAX)

C PRINT*,TTOPL, TTECU, TEMPMAX

IF( TTECU.GE.TTOPL)THEN

TTECU=TTOPL-100.DO

T_.R=TEMP_MAX-100.DO

IF (TTOPL.GT. TFUCOM) TINE_FU=T

IF (TTOPL.GT. TFUCOM) TFUCOM=TTOPL

C PRINT*, 'MAX',TFUSCOM, TTOPL, TIME_FU

ELSE

TTECU='TTOPL

ENDIF

TFSUR_MAX=DMAX1 (TFSURO,TFUEL_SS)

TFSUR0--TFSURMAX

IF(TFSURO.GE.TFUELS ) THEN

IF (TFSURMAX. GT. TSURCOM) THEN

TIMESUR=T

TSUR_.COM=TFSURJCAX

ENDIF

TFSURO=TFSURMAX-100 .DO

ENDIF

TAVEJMAX=DMAX1 (TAVE0,TAVE)

TAVE0=TAVEMAX

IF(TAVEO.GE.TAVE ) THEN

IF (TAVEJMAX. CT. TAVE-COM) THEN

RJRCK[J2080 A-29
TIMEAVE--T

TAVE_COM=TAVEJMAX

ENDIF

TAVEO--TAVEJMAX-100 . DO

ENDIF

TCLAD.MAX=DMAX1 (TCLAD0 ,TCLADD)

TCLAD0--TCLAD_lAX

IF(TCLADO.GE.TCLADD ) THEN

IF (TCLAD_IAX. GT. TCLcOM) THEN

TIME_CL=T

TCLCOM=TCLAD(MAX

ENDIF

TCLADO--TCLADJMX-100 .DO

ENDIF

TCLADrJAX=DMlXl (TCLAD0, TCLADD)

TCLAD0--TCLAD_MAX

ENTHJAZ=DAXl (ENTHO, ENTH (LNAX1))

ENTHO=ENTHJAX

IF(IREWET.EQ.0) GOTO 1933

IF(ENTH(LNAX1).LT.ENTHIAX. AND. T.GT.TIMECL .AND. NSW.EQ.2

.AND. ITHTC. EQ. 0 .AND. ENTH(LMAX1) .LE. 160.DO ) THEN

TIMEHTC=T

IF(TINEJHTC.GT. 0.DO ) THEN

ITHTC=ITHTC+I

PRINT*,' TIME OF REWETTING', TIMEJITC

ENDIF

ENDIF

1933 CONTINUE

ENS=ENTALPIA/ (THOU*CALLOR)

ENSJMAX=DMAX1 (ENS0 , ENS

ENSO =ENS_)AX

SEFFJ(AX=DMAX1(SEPF0 ,SIEFF(LMAX1)

SEFFO =SEFFMAX

SIGHaAX=ED1AX1(SIGHO ,SIGCL(LMAX1)

SIGHO =SIGH;MAX

SIGZ.MAX=DMAXI(SIGZ0 ,SIGAX(LMAX1)

SIGZO =SIGZMAX

EHOOP-MAX=DMAX1 (EHOOPO, EHOOP (LMAXl))

EHOOPO =EHOOPdAX

DTtCLM =DMAXl (DTCLM, DTCLADD

DECL =EDAX1 (DECLN, DE._DT )

ENDIF ! FOR T > 0

IF (T. EQ. TIMEJFAIL) ENTHJFAIL=ENTH (LMAXI)

IF (T. EQ.TIME_FAIL) ENERJFAIL=ENTER (LMAXI)

IF (T. EQ. TIMEFAIL) TFAVJFAIL-=TAVERAD (LMAX1)

C

C SED CRITERION:

C

SED=SRD + (SIEFF(LMAX1) * DABS(EDOTW) *DT)

C PRINT*,'SED', SED,SIEFF(LNAX1), EDOTW

C

• WRITE 2001 = DISPLAY THERAL PARAMETERS:

IF(T.GE. 1.OD-4. AND. T.LT.1.E4 .AND. IGRAF.EQ.O)

* WRITE(0,2001)

*TS, ENTER (LMAX,),

* El,

* EXIT(LMAX1),

* ENTH(LMAX1),

* TCLADD,

C * TCLADMAZ,

C * TSREnq(LMAXI), * TFUEL-S,

* TFUELM,

* FFR(1),

* FGRTOT*100.DO

CC TIME CONSTANT

PL=FRDEN* 10960 .DO

CPFUEL= FCP (TAVE, 0.0, FOTMTL, FRDEN)

CALL FTHCON (TAVE, FRDEN, FOTMTL, CONT, DKDT, BU2)

RRC K1 2080 A-30
TAUF= (CPFUEL*PL* (RT2) **3) / (4*CONT* (2*R02))

C TAUF=CPFUEL*PL* (RT2**2)/(4*CONT)

GTEMP= (TFUELS+TEMPRAD ( IGPNOD+I) ) /2

CONG=GTHCON (GASFR, GTEMP, PGAS*I.D+6, GAPSGRF(LHAXI)*I.D-6)

C PRINT*, CONG, GAPS-GRF (LMAXl) *1 .D-6, TAUH

TAUG=(CPFUEL*PL*GAPSGRF(LMAXl}*l.D-6* (RT2**2)) / (CCNG* (2*R02))

DELCL= (R02-ROl)

CALL CTHCON (TSREDN, T, O.DO, O.DO, CCON, CDKDT)

TAUC=CPFUEL*PL*DELCL*RT2**2/ (CCON* (2*R02))

2001 FORMAT *(F8.2,F7.1," °F .o) ' *F7.1,FT.I," 1,3F7.0,' (°,FS.3,')',F6.1,°%')

IF(NSW.EQ.1) THEN

FGR_-O=FGRTOT*100. DO

SWEL_0=SWELHAX*100.D0*3

ENDIF

SW._MAX=DMAXI(SW0, SWELMAX*I00.D0*3-SWEL_0 ) SW0O-SW..CAX

IF(ISTEP. EQ.0) THEN

WRITE(I0,2000)

A TS,

* ENSjAX,

C POW, ! *FUELLEN,

D ENTER(LKAXl),

E TGAS,

F ENTH(LMAX1),

G TAVE,

H EXIT(LKAXI),

I SUM*I00.D0,

J PGAS,

K El,

L E2,

m E3,

N CLADAXEX,

0 FSAXEX,

P HTXODE(L),

Q RT2*2.0D3, RT2 (DIAMETER), MM

R ROI*2.0D3, ! R01 (DIAMETER), MM

S RO2-2.0D3, ! R02 (DIAMETER), MM

T TOTMWR,

u FFR(l),

V RTI*2.0D3, ! RTl (DIAMETER), MM

W SWELMAX*l00.D0*3-SWEL_0, ! VOLUME FUEL SWELLING

X FGRTOT*I00.D0-FGR_0, TOTAL FGR

Y H-GAP,

Z HGAS,

DURING TRANSIENT

A EHSOLID,

B HRAD,

C HFUEL , ! HTC FOR SPRING

D HECSP+H_ECCL, ! HTC FOR SPRING

E HIZL, HTC FOR SPRING

F H-COND, ! HTC FOR SPRING

G TSPRING,

H TCLADDI,

I TFBOT,

G HTCC, ! HTC FOR AIR

K HTCCOOL, ! HTC FOR AIR

L HRADD, ! HTC FOR AIR

M FLUX-PL, ! FLUX FOR SPRING-CLAD

N (TPLENB+ 459.69D0/Il.8D0, ! T FOR BOTTOM PLENUM

0 BIO,

P FO,

Q TETA1,

R TETA2,

S TAUCON,

T TAUF,

U TETAAVER,

V TCONSTANT,

W DENIRR,

X RSW(LMAXI)*FT*I.D3, ! FUEL SWELIING [MM]

Y RDEN(LMAXI)*FT*l.D3, ! FUEL DENSIFIC [MM]

Z SWTOT, ! FUEL SWELIING+DENSISFIC• h TION [MM)

RRC KI 2080 A-31
C A TCLIN(LMAXI)

A HFL.GRF(LMAX1)*FLUX/THOU, ! HEAT FLUX [KW/M2]

B TCLADD . OUTER CLAD TEMPERATURE [XK

C SED

WRITE(77,2000) T-S, (SIGCL(N),N=1,NAXN)

WRITE(50,2000) T-S, (TSREDN(N),N=1,NAXN)

WRITE(87,2000) TS, (FENT(J) ,J=I,IGPNOD)

ISTEP=ISTEPPRINT

ENDIF

ISTEP=ISTEP-1

2000 FORMAT(1PE14.6,60(1PE14.6))

RADIAL TEMPERATURE DISTRIBUTION *

DTD=-DT._S/2.0D0

** 1) MAX RADIAL FUEL TEMPERATURE

C WRITE(50,2000) T, (TEMP-RAD(JK) ,JK=I,IGPNOD)

C PRINT*,'NO*,T_S, TR1+DTD , TRI-DTD

IF(TS.LE. TR1+DTD .AND. T_S.GE. TR1-DTD .OR.

*TS.LE. TR2+DTD .AND. T-S.GE. TR2-DTD .OR.

*TS.LE. TR3+DTD .AND. TS.GE. TR3-DTD .OR.

*TS.LE. TR4+DTD .AND. TS.GE. TR4-DTD .OR.

*T__S.LE. TR5+DTD .AND. T_S.GE. TR5-DTD .OR.

*TS.LE. TR6+DTD .AND. TS.GE. TR6-DTD )THEN

C PRINT*,'YES°,T_S, TR1+DYD , TR1-DTD

KZ=0

DO 3000 K=1,NMESH

K1=K-1

IF(KI.EQ.0) KI=I

RKT=FLOAT (K)

KZ=KZ+1

IF(KZ.EQ.1.AND.TS.LT.TR1+DTD .AND.TS.GT. TR1-DTD )WRITE(91,2110)

IF(KZ.EQ.1.AND.TS.LT.TR2+DTD .AND.TS.GT. TR2-DTD )WRITE(92,2110)

IF(KZ.EQ.1.AND.TS.LT.TR3+DTD .AND.TS.GT. TR3-DTD )WRITE(93,2110)

IF(KZ.EQ.1.AND.TS.LT.TR4+DTD .AND.TS.GT. TR4-DTD )WRITE(94,2110)

IF(KZ.EQ.1.AND.TS.LT.TR5+DTD .AND.TS.GT. TR5-DTD )WRITE(95,2110)

IF(KZ.EQ.1.AND.TS.LT.TR6+DTD .AND.TS.GT. TR6-DTD )WRITE(96,2110)

IF(TS.LE. TR1+DTD .AND. T_S.GE. TR1-DTD)

*WRITE(91,2000)TS,RAD(K) ,TEMPRAD(K) ,COEFPOW(LMAX1,KI) ,RKT,

*COEFPOW (LMAX1, Kl) *BURNZ (LMAXI),

*COEFPOW(LMAX1, Kl) *PKWA(JRODX,Kl) /FT,RAD(K)/RAD(IGPNOD)

IF(T_S.LE. TR2+DTD .AND. TS.GE. TR2-DTD)

*WRITE(92,2000)TS,RAD(K) ,TEMPRAD(K) ,COEFPOW(LMAX1,KI) ,RKT,

*COEFPOW (LMAX1,Kl) *BURN (LMAX1),

*COEFPOW (LIAXl, K1) *PKWA (JRODX, K1)/FT, RAD (K) /RAD (IGPNOD)

IF(TS.LE. TR3+DTD .AND. TS.GE. TR3-DTD)

*,RITE(93°2000)TS,RAD(K),TEMP_.AD(K),COEFPOW(LMAXl,Kl) RKT,

*COEFPOW(LMAX1 Kl) *BURNZ(LMZ 1),

*COEFPOW(LMAXI,Kl) *PKWA(JRODXKl)/FT,RAD(K)/RAD(IGPNOD)

IF(TS.LE. TR4+DTD .AND. TS.GE. TR4-DTD)

*WRITE(94,2000)TS,RAD(K) ,TEMPRAD(K) ,COEFPOW(LMAX1,K1) ,RKT,

*COEFPOW (LMAX1, Kl) *BURNZ (LMAX1),

*COEFPOW(LMAXl,KI) *PKWA(JRODX,KI) /FT.RAD(K) /RAD(IGPNOD)

IF(T_S.LE. TR5+DTD .AND. T_S.GE. TRS-DTD) *WRITE(95,2000)TS,RAD(K) ,TEMPRA(K) ,C0EFFOW(LMAX1,K1) oRKT,

*COEFPOW(LMAXK1) *BURNZ(LMAX1),

*COEFPOW(LMAX1,KI) *PKWA(JRODX,KI) /FT.RAD(K) /RAD(IGPNOD)

IF(TS.LE. TR6+DTD .AND. TS.GE. TR6-DTD)

*WRITE(96,2000)TS,RAD(K) ,TEMP_.AD(K) ,COEFPOW(LMAX1,KI) °RKT,

*COEFPOW(u4AX1, Kl) *BURNZ (LMAX1),

*COEFPOW(LMAX1,KI) *PKWA(JRODX,KI)/FIT,RAD(K)/RAD(IGPNOD)

2110 FORMAT( 'TIME RADIUS TEMPERATURE POWERCOEF

*RADNUMBER BURNUPRAD POWERRAD REL. RADIUS' )

3000 CONTINUE

ENDIF

AXIAL PARAMETERS DISTRIBUTION *

RRC K! 2080 A-32
1** 1) FRACTION OF MOLTEN ZONE, FUEL TEMPERATURE

IF(TS.LT. TM1+DTD .AND. TS.GT. TMI-DTD .OR.

* TS.LT. TM2+DTD .AND. TS.GT. TM2-DTD .OR.

* TS.LT. TM3+DTD .AND. T_S.GT. TM3-DTD .OR.

* TS.LT. TM4+DTD .AND. T_S.GT. TM4-DTD .OR.

* T_S.LT. TM5+DTD .AND. TS.GT. TM5-DTD .OR.

* T_S.LT. TM6+DTD .AND. TS.GT. TX6-DTD) THEN

KZ=O

DO 3006 K=KISKP,EMXSKP,KSKP

MDYN1 = M1SKP + (1-1) * MSKP

MDYN2 = MISKP + (IGPNOD-1) * MSKP

TZEDI=(TEMPP(MDYN1,K,1)+ 459.69D0) / 1.8D0

TZED2=(TEMPP(MDYN2,K,1)+ 459.69D0) / 1.8D0

KZ=KZ+I

IF(KZ.EQ.1.AND.TS.LT.TM1+DTD .AND.T_S.GT. TMI-DTD )WRITE(81,2010)

IF(KZ.EQ.1.AND.TS.LT.TW2+DTD .AND.TS.GT. TM2-DTD )WRITE(82,2010)

IF(KZ.EQ.1.AND.TS.LT.TM3+DTD .AND.T_S.GT. TM3-DTD )WRITE(83,2010)

IF(KZ.EQ.1.AND.T5S.LT.TM4+DTD .AND.TS.GT. TM4-DTD )WRITE(84,2010)

IF(KZ.EQ.1.AND.TS.LT.TM5+DTD .AND.TS.GT. TM5-DTD )WRITE(85,2010)

IF(KZ.EQ.I.AND.TS.LT.TM6+DTD .AND.TS.GT. TM6-DTD )WRITE(86,2010)

2010 FORMAT( 'TIME ELEVATION FRACMOLTEN TFUELMAX TFUEL_SUR * TCLADIN TCLADOUT ENERGYDEP FGR SWELLING GAS

*_GENER GASRELEASE GASGENGR GASGEN_FACE GASGEN-EDGE BURNU

*P RAD SWELL ENTHALPY')

IF(T_.S.LT. TM1+DTD .AND. T_S.GT. T41-DTD ) *WRITE (81, 2000) TS, Z0+ELEV (K) *. 3048D3, FRMOL (KZ) *I00. D0,TZED1, TZED2,

*TCLIN(KZ) ,TCLOUT(KZ), ENTrER(KZ) *FCAL,

* FGRZ(KZ),

* EVSZ(KZ),

* RGJZ(KZ),

* GJOUTZ (KZ),

* RGG_.Z (KZ),

* RGGFZ(KZ),

* RGGEZ(KZ),

* BURNZ(KZ),

* RSW(KZ) *FT*I.D3,

* ETH(KZ),

* ENTER (KZ)

IF(T.S.LT. TM2+DTD .AND. T.S.GT. TM2-DTD

*WRITE(82,2000)T_S,Z0+ELEV(K)*.3048D3,FRMOL(KZ)*I00.DO,TZEDITZED2,

*TCLIN(KZ),TCLOUT(KZ), ENTER (KZ) *FCAL,

* FGRZ(KZ),

* BVSZ(KZ),

* RGJZ(KZ),

* GJOUTZ (KZ),

* RGGLZ(KZ),

* RGGFZ(KZ),

* RGGEZ(KZ),

* BIURNZ(KZ),

* RSW(KZ)*FT*1.D3,

* ENTH(KZ),

* ENTER (KZ)

IF(TS.LT. TM3+DTD .AND. T_S.GT. TM3-DTD ) *WRITE(83,2000)TS,ZO+ELEV(K)*.3048D3,FRMOL(KZ) *I00.DO,TZEDTZED2,

*TCLIN(KZ),TCLOUT(KZ), ENTER(KZ)*FCAL,

* FGRZ(KZ),

* BVS.z (KZ),

* RGJZ (KZ),

* GJOUTZ (KZ),

* RGGLZ(KZ),

* RGGF_.Z(KZ),

* RGGEZ (KZ),

* BURNZ(KZ).

* RSW(KZ)*FT*.D3,

* ENTH (KZ),

* ENTER(KZ)

RRC K! 2080 A-33
IF(TS.LT. TM4+DTD .AND. TS.GT. TM4-DTD ) *WRIT ( 84,2000 )TS, Z0+ELEV (K) *. 3048D3, FRXOL (KZ) * 00. DO, TZEDI, TZED2,

*TCLIN(KZ) ,TCLOUT(KZ), ENTER(KZ) *FCAL,

* FGRZ(KZ),

* BVSZ(KZ),

* RGJ2Z(KZ),

* GJOUTZ (KZ),

* RGGLZ (KZ) ,

* RGGF._Z (KZ) , * RGGEZ(KZ),

* BUFRN.Z(KZ),

* RSW4(KZ) *FT*I1.D3,

* ENTH(KZ),

* ENTER(KZ)

IF(TS.LT. TM5+DTD .AND. TS.GT. TM5-DTD )

*WRITE(85,2000)TS,Z0+ELEV(K) *.3048D3,FROL(KZ) *100.DOTZED1,TZED2,

*TCLfI(fZ) ,TCLOUT(KZ), ENTER((KZ) *FCAL,

* FGRZ(KZ),

* BVSZ(KZ),

* RGJtZ(KZ),

* GJOUTZ (KZ),

* RGGLZ(KZ),

* RGGFZ (KZ) ,

* RGG&Z (KZ),

* BURNZ (KZ),

* RSW(KZ)*FT*1.D3,

* ENTH(KZ),

* ENTER(KZ)

IP(TS.LT. TM6+DTD .AND. T_S.GT. TM6-DTD

*WRITE (86,2000) TS, Z0+ELEV (K} *.•3048D3, FRMOL (KZ) *i00.•D0, TZEDI, TZED2,

*TCLIN(KZ), TCLOUT(KZ), ENTER(KZ) *FCAL,

* FGRZ(KZ),

* BVSZ(KZ),

* RGJZ(KZ),

* GJOUT._Z (KZ),

* RGGLZ(KZ),

* RGGFZ(KZ),

* RGGEZ(KZ),

* BUP±_Z(KZ),

* RSW(KZ) *FT*1 .D3,

* ENTH(KZ),

* ENTER(KZ)

3006 CONTINUE

ENDIF

** 2) CLADDING PERMANENT DEFORMATION

IF(T_S.LT. TDI+DTD .AND. T_S.GT. TD1-DTD OR.

* T_S.LT. TD2+DTD .AND. TS.GT. TD2-DTD OR.

* T_.S.LT. TD3+DTD .AND. TS.GT. TD3-DTD OR.

* T_S.LT. TD4+DTD .AND. TS.GT. TD4-DTD OR.

* T..S.LT. TD5+DTD .AND. T_S.GT. TD5-DTD .OR.

* T_S.LT. TD6+DTD .AND. T_S.GT. TD6-DTD) THEN

KZ=0

DO 3012 K=KISKP,KMXSKP,KSKP

KZ=KZ+÷

IF(KZ.EQ.1.AND.TS.LT.TD1IDTD .AND.T_S.GT. TD1-DTD )WRITE(71, 2011)

IF(KZ.EQ.1.AND.TS.LT.TD2+DTD .AND.T_S.GT. TD2-DTD )WRITE(72,2011)

IF(KZ.EQ.1.AND.TS.LT.TD3+DTD .AND.TS.GT. TD3-DTD )WRITE(73,2011)

IF(KZ.EQ.1.AND.TS.LT.TD4+DTD .AND.TS.GT. TD4-DTD )WRITE(74,2011)

IF(KZ.EQ.1.AND.TS.LT.TD5+DTD .AND.TS.GT. TD5-DTD )WRITE(75, 2011)

IF(KZ.EQ.1.AND.T__S.LT.TD6+DTD .AND.T__S.GT. TD6-DTD )WRITE(76 2011)

2011 FORMAT ('TIME ELEVATION HOOPSTRAIN SIG_EFF SIG-HOOP

* SIG-AXIAL SIG_02 M-WREACTION')

IF(TS.LT. TD1+DTD .AND. T_S.GT. TD1-DTD )

RRC K1 2080 A-34
*WRITE(71,2000)T_S, Z0+ELEV (K) *0. 3048D3, EPP (K, 1,1) "100. DO,

*SIEF R(KZ),SIGCL(KZ),SIGAX(KZ),SIG02 (KZ).,

*EMETW(IROD,K) * DZACK)*FT

IF(TS.LT. TD2+DTD .AND. TS.GT. TD2-DTD

*WRRITE (72,2000)T_S, ZO+ELEV(K) *0. 3048D3, EPP (K, 1, 1) *100.DO, *SIEF7 (KZ),SIGCL(KZ),SIGAX(KZ),SIG02 (KZ),

*D•EEW(IRODK) * DZA(K)*FT

IF(T_S.LT. TD3+DTD .AND. T_S.GT. TD3-DTD

*WRITE (73,2000)TS, Z0+ELEV(K) *0.3049D3, EPP (K, 1, 1) *100. DO,

*SIEFF(KZ), SIGCL(KZ),SIGAX(KZ),SIG02 (KZ),

*EMETW(IROD,K) * DZA(K)*FT

IF(T.S.LT. TD4+DTD .AND. TS.GT. TD4-DTD *WRITE 74,2000)}T_S, Z0+ELEV (K) *0. 3048D3, EPP (K, 1,I) *I00. DO,

*SIEFF(KZ), SIGCL(KZ),SIGAX(KZ) ,SIG02 (KZ),

*EMETW(IROD,K) * DZA(K)*FT

IF(TS.LT. TD5+DTD .AND. TS.GT. TD5-DTD

*WRITE (75,2000) TS, Z0÷ELEV(K) *0.3048D3, EPP (K, 1, 1) *100.DO,

*SIEFFC(KZ),SIGCL(KZ),SIGAX(KZ),SIGAX(KZ),

*EDETW(IROD,K) * DZA(K)*FT

IF(TS.LT. TD6+DTD .AND. TS.GT. TD6-DT

*WRITE(76,2000)T_S,Z0+ELEV(K)*0.3048D3,EPP(K,1,1)*I00.DO,

*SIEFF(KZ), SIGCL(KZ),SIGAX{KZ),SIGAX(KZ),

*EDETW(IRODK) * DZA(K)*FT

3012 CONTINUE

ENDIF

CCCCC BURND= MAX AXIAL BURNUP

IF(NSW.EQ.2) BURND= BU2 / 86400.DO

CCCCC BURND= AVERAGE AXIAL BURNUP :

IF (NSW. EQ.1) BURND= BURNTOT

IF(NSW.EQ.1) THEN

FGRO=FGRTOT*100. DO

ELSE

FGR&END=FGRTOT* 100.DO

ENDIF

C PRINT *, ITRAN

IF(T.GE.TMAXPLOT-0.0001 ) THEN

IF(E1.GT.0.ODO) THEN

FKE= ENTER(LMAXI)/El

FKENTH=ENTHJAX/ENTER (LMAX1) ENDIF

SFUEL=(RT2**2-RT1**2) *I.D6

RTM=SQRT(MOLTMAX*SFUEL+ (RT1*1.D3) **2)

IF(IFAIL.EQ.0) STRES_FAIL=0.DO

IF (IFAIL.EQ.0) TSRFAIL=0. D0

IF(IGRAF.EQ.0) WRITE(0,2021) * ENTER (LMAX1) , SEFFMAX,

* El, SIGH._AX,

* FKE, SIGZMAX,

* ENTHJ(AX, EHOOPJAX,

* ENS-MAX, 100.DO*TCEBAL,

* FKFNTH,

* TFUCOM, TIMEFU,

* TCLCOM, TIMECL,

* JRUPTURE, MODFD, TIMEJAIL,

* ENERJFAIL,

* ENTHFAIL, FGR.0,

* TEMPFAIL, FGREND,

* TSRJFAIL,

* TIN-FAIL,

* TFAVFAIL, BURND,

* PGFAIL, STRESFAIL,

* TEMPCONT, TIMECONT,

* DTCLM

* DECLM,

* MOLTJMAX*100.DO, RTM,

* TOTMWR, ZR02_MAX, ZROJAX, ZR02_WAX+ZROJ4AX,

* (ZRO2_MAX+ZRO.MAX)*100/750,

RRC K1 2080 A-35
* ZEBURST*1000.DO

CALL INPTITLE(60)

WRITE(60, 2021)

* ENTER (LMAX1), SEFFJ(AX,

* El, SIGHCIAX,

* FKE, SIGZNAX,

* ENTHEMAX, EHOOP.MAX,

* ENSMAZ, 100.DO*TCEBAL,

* FKENTN,

* TFUCOM, TIMEFU,

* TCL'COr , TDIMCL,

* IFAIL , MODFD, TIMEFAIL,

* ENERFAIL,

* ENTHEFAIL, FGR.0,

* TEMPFAIL, FGR.END,

* TSRFAIL,

* TINIFAIL,

* TFAVSAIL, BURND,

* PGFAIL, STRES--AIL,

* TEMPCONT, TIME__CONT,

* DTCLM

* DECLM,

* MOLT_MAX*100.DO,RTM,

* TOTMWR, ZRO2_JAX, ZROJIAX, ZRO2._mAX+ZROqAX,

* (ZRO2JMAX+ZROMAX) *100. D0/750 .Do,

* Z3URST*1000.D0

IF(IFAIL.NE.0) WFAIL=" YES

IF(IFAIL.EQ.0) THEN

WFAIL= ' NO

PFAIL= ' NO

FFAIL=' NO

TIME_FAIL=1. D20

ENTHFAIL=1 D20

TEMP-FAIL=1 D20

PGJFAIL=1. D20

ELSE

IF(TCEBAL*100 .DO.GT.0 .ODO) EHOOPMAX=TCEBAL*10O.DO

ENDIF

DPRES= (PGAS-PCOOL) / ((RO2-RO1) / ((R02+ROI)/2 .DO))

IF(IFAIL.NE.0.AAND.STRES-FAIL.GT.DPRES+50.DO) THEN

PFAIL=' YES I

IFC(E.GE.260.D0 ) FFAIL=' YES

ELSE

PFAIL=' NO

FFAIL=' NO

ENDIF

EHAVE=(EHAVE-EHOOP(LMAX1)) / (NAIN)

IF(POHE.LE.O.ODO) PRINT*, WARNING POHE!',POHE

IF(VOLSV.LE.0.ODO) PRINT*,' WARNING VGP!', VOLSV

WRITE(43,2022)

1 BURND,

2 El,

3 ENTH_MAX,

4 TFUCOM,

5 TCLCOm,

c 6 FGR&END-FGR_0,

C 7 SWJEAX,

C 8 SIGH_MAX,

1 WFAIL,

1 WFAIL,

1 PFAIL,

1 FFAIL,

2 TIME-FAIL,

3 ENTFAIL,

4 TEMPFAIL,

5 PG-FAIL,

C 1 TCEBAL*100.DO,

C 7 TIME__CONT,

C 8 TEMPCONT,

C 1 Z_BURST*1000.D0,

1 ZRO2_MAX+ZROJMAX,

9 EHOOPJmAX,

RRC K1 2080 A-36
9 EHAVE,

2 100.DO*GRFT *22400.D0*0.143D0 /(P0HE*9.807*VOLSVr*.D-3),

2 100.DO*GRFT *22400.D0*0.857D0 /(P0HE*9.807*VOLSV*1.D-3),

2 RGT_GR*22400.D0*0.143D0 /(FMASS*THOU)

C 6 STRESFAIL,

C 9 MOLTJ(AX*100.DO,

CALL INPTITLE (43)

2022 FORMAT( 1' BURNUP =',F7.1,' (MWD/KG)',/,

2' ENERGY DEPOSITION =',Fl.Q,' (CALIG)',/,

3' PEAK FUEL ENTHALPY =',F7.0,' (CAL/G)',/,

4' MAX FUEL TEMPERATURE =',F7.0,' ( K )',/,

5' MAX CLAD TEMPERATURE =',F7.0,' C K )',/,

C 6' FGR =',F7.1,' ( % )',/,

C 7' FUEL VOLUME SWELLING =',F7.1,' ( % )',/.

C 8' MAX HOOP STRESS =',F7.0,' (MPA )',/, 1. CLAD FAILURE n',A7 ,' ',

1' * BALLOONING -',A7 ,' *,/,

1' * PCMI =',A7 ,'

1' * FRAGMENT =',A7 , ",/,

2' FAILURE TIME =',F7.1,' C SEC )',I,

3' FUEL ENTH AT FAILURE =',F7.0,' (CAL/G)',/,

4' SUR. CL. TEMP AT FAILs',F7.0,' ( K )',/,

5' PRESSURE AT FAILURE =',F7.1,' (MPA )',I,

C 1' BALLOONING STRAIN =',F7.1," C % )',/,

C 7' TIME AT PCMI BEGIN =,,F7.1,' C SEC )',/.

C 8' AVE. CL. TEMP AT PCMI=',F7.0,' ( K )',

C 1' AXIAL CRACK LOCATION =',F7.0,' ( M1 )',/,

1' OXIDATION LAYER =',F7.1,' ( HEM )',/,

9' RESIDUAL CL. HOOP STRAIN',/, 9" *MAX CL. HOOP STRAIN=',F7.1,' C % )',/,

9s *AVE CL. HOOP STRAIN=',F7.1,' C % )',/,

4' KR COMPOSITION =',F7.2,' C % VOL)',/,

4' XE COMPOSITION =',F7.2,' C % VOL)',/,

4' KR CONCENT. IN GRAINS=',F7.2,' (CM3/G)',///)

C 6' CLAD STRESS AT FAIL =',F7.1,' (MPA )',/,

C 9' MOLTEN ZONE =',F7.0," ( % )',/I/)

CALL DATE (STR)

CALL TIME (STRI)

WRITE(43 ,1997) STR,STR0,STR1

WRITE(60 ,1997) STRSTROSTR1

1997 FORMAT(//,'FRAP-T6 CALCULATION',/,'DATE:

',All) ',AII,/,'TI4E: ',All,/,

2021 FORMATCI,' ENERGY CHARACTERISTICS:

*RACTERICTICS:',*,

*" MAX. ENERGY DEPOSITION =',F6.1,' (CAL/G)

+F6.1,' (MPA)',I,

*' AVE. ENERGY DEPOSITION =',F6.1.' (CAL/G)

+F6.1,' (MPA)',I,

MAX./AVERAGE ......... F6.3,"

+F6.1,' (MPA)',,/

*' MAX. FUEL ENTHALPY =',F6.1,' (CAL/G)

+F6.1," C%)',/,

*' AVE. FUEL ENTHALPY =',F6.1,' (CAL/G)

+F6.1,' C%)',/,

ENTHALPY/ENERGY ...... ',F6.3,//,

MECHANICAL CHA

MAX. EFF. STRESSMAX. HOOP STRESS =',

MAX. AXIAL STRESS=',

MAX. HOOP STRAIN =',

BALLOONING STRAIN=',

*' MAX. FUEL TEMPERATURE =',F6.1,' (K) ..... TIME= ',F6.3,' S',I,

*" MAX. CLAD TEMPERATURE =',F6.1,' (K) ..... TIME= ',F6.3,' S',1I,

*" FAILURE (MODEL) =',I2,' (',12,') ........ TIME= ',F5.2,

,S /,

*' MAX. FUEL ENERGY AT FAILURE=',F6.1,' (CAL/G)',/,

*1 MAX. FUEL ENTH AT FAILURE=',F6.1,' (CAL/G) PRE-TRANSIENT FGR =' *,F6.2,' %,,/, *' SURF. CLAD TEMP. AT FAIL.=',F6.1,' (K) TRANSIENT FGR='

*,F6.2," % ,/,

*' AVER. CLAD TEMP. AT FAIL.=',F6.1,' (K)',/,

*' INNER CLAD TEMP. AT FAIL.=',F6.1,' (K)',/,

* AVERAGE FUEL TEMP AT FAIL=',F6.1,' (K) MAX. BURNUP

*,F6.2,' (MWD/KGU)',/,

*' GAS PRESSURE AT FAILURE =',F6.2,' (MPA) HOOP STRESS AT FAIL='

*,F6.2,' (MPA) ',/.

*' AVE. CLAD TEMP. AT PCMI =',F6.1,' (K) AT TIME= ',F6.3,' S',l,

RRC K! 2080 A-37
CLAD TEMPERATURE RATE =',F6.1,' (K IS)',I,

*' HOOP STRAIN RATE =',F6.1,' (% IS)',I,

*° FRACTION OF MOLTEN ZONE =',F6.1,' (%) RADIUS = ',F6.2,' MM',/,

TOTAL ZR-WATER REACTION =',F6.1,' (CAL/G) ',/,

ZR02=',F5.1,' (MEM) AZRO =',F5.1,' (MKM)',/,

SUM OF OXIDE ',FS.," (MKM)', F9.2,' (%)',/,

*" AXIAL CRACK LOCATION =',FS.1,' (MM)')

GAP=THGAP

CTEMP=TCLADD

PG=PGAS

TLOC=TCEBAL_S

FMASS=FMASS*THOU

VOLUME=VOLUME*I. D6

FUELLEN=FUELLEN*THOU

WRITE(42, 1009) TGAP,CTEMP,PGTCEBALS

CLOSE (10)

1002 FORMAT(,*')

1009 FORMAVT(E12.4,20E12.4)

ENDIF

RETURN

END

SUBROUTINE GRASP (NPRIiT, W, CI ,ACAE, PRF, GSG, GOU, DIS, SV, TKO, HH, POWO,

+TK, POW,VLM, ARA, TFP, RS, TS, PRSO, TGR, RGKJ, BVSKJ, BVSJ, RETG,

+MK, MKI, IQUIT, NSW, TCURR, TMAX, DBURN)

C SHEST INSERT DIMENSIONS FOR RADIAL GAS RETENSION DISTRIBUTION

DIMENSION * GFACE (50,50).

* GEDGE (50,50),

* GGRAIN(50,50),

* BURN(50),

* BURNFR(50)

CHARACTER*400, GRAPHO,GRAPH1, GRAPH3

OPEN (UNIT=38, FILE= 'FGR..TOT.DAT')

OPEN(UNIT=33,FILE='FGR..TRAN.DAT')

OPEN(UNIT=39,FILE== *FGRAXI1.DAT')

OPEN (UNIT=-37, FILE= 'FGRAXI2.DAT')

OPEN (UNIT=-36, FILE= "FGRAXI3.DAT')

OPEN (UNIT=35, FILE="FGR_.AXI4.DAT')

OPEN (UNIT=34, FILE='FGRAXI5 .DAT')

OPEN (UNIT=32, FILE=' FGR._RET1 .DAT')

OPEN (UNIT=31, FILE= ' FGRTEMI.DAT')

OPEN (UNIT=-30, FILE= FGRRADS.DAT')

OPEN (UNITT=29, FILE= 'FGRRADT.DAT )

CCCCCCCCCCCCC FOR GRAIN SIZE:

C OPEN (UNIT=200,FILE='GRAINS.DAT')

C

C

C W(1):TSO

C W(2):GRT

C W(3):TGSIN

C W(4):TGSR

C

BURNTOT=0. DO

DLZTOT=0 .DO

NPRINT = 1

ITRAN = 1

IF(NSW .EQ. 1) ITRAN = 0

TSOPD=W(1) +DELT

DEL9=DELT*. 9999999D0

IF (IBURNO. EQ. 0) THEN

RRC KI 2080 A-38
9000 FORMAT(A400)

GRAPH3=' NUMER RELRLADI GENERATED TEMPERATURE SWELLI

*NG FGRRADI GAS_FACE GASEDGE GASGRAIN GAS_RET

*RADIUS RAD_RETEN POROSITY

GRAPH1=' TIME FGR.TRA RETAINED GASRELEASE GAS-RE

*TAIN GASGENER ERROR I-RETAIN CERETAIN IRELEASE CE_

*RELEASE TCENTER TSURFACE

GRAPHO=' TIME J SWELL (J) GAS_RETAIN GAS-RE

*LESE GASGRAIN GASFACE GASEDGE FGR(J) SUMKRETAIN TRE

*GIONLINE TCENTER TSURFACE POWER BURNUP '

WRITE (39,9000) GRAPHO

WRITE (37,9000) GRAPHO

WRITE(36,9000) GRAPHO

WRITE(35,9000) GRAPHO

WRITE(34,9000) GRAPHO

WRITE(33,9000) GRAPH1

WRITE(38,9000) GRAPH1

WRITE(29,9000) GRAPH3

WRITE(30,9000) GRAPH3

IBURN0=IBURNO+1

ENDIF

**************** SHEST 27/04/96

URAN=238.ODO/(238.0D0+32.ODO)

URAN=0.882

IF(ITRAN.EQ.0 ) TSHEST--TSOPD

IF(ITRAN.NE.0) TSOS=TSOPD-TSHEST

******************************** SHEST 27/04/96 *************************

SUMRET=RGGF+RGGE+RGGL

BVS$=BVS* 100. DO

KEND=AINT (KF1)

TDAY--TSOPD/(3600 .D0*24 .DO)

TMAXO=TMAX- 5.DO*(3600.DO*24.DO)

DLZ=DL (J) *0.3048D0

FMAS=FMASSA*DLZ/FDLINA

POWER=POW(J)/0.3048D0

DTDAY=TDAY-TDAY0

BURN(J) =BURN(J) +POWER*DTDAY*DLZ/(URAN*FMAS*000 .DO)

BURNFR(J)=BURNFR(J)+DBURN(J)/86.4D3

BURNTOT=BURNTOT+BURNFR (J) *DLZ

DLZTOT=DLZTOT+DLZ

BURNZ(J)=BURN(J)

C PRINT *, 'FROM GRASP ',URAN, POWERDTDAY, DLZ,FMAS

C

C PRINT*,"!:!!! GRASF TS',JBURNTOT,TS

C PAUSE 'GRASF !!!'

IF(ITRAN.EQ.0 .AND. J.EQ. LMAX1 .AND. IGRAF.EQ.0) *WRITE(0,2001) TSOPD/(3600.DO*24.DO),TS(KF+1,J),TS(1,J),FGRT*100.DO

*,POWER,BURN(J),BURNFR(J)

C IF(ITRAN.EQ.O .AND. J.EQ. LMAXI .AND. IGRAF.EQ.0)

C *WRITE(0,2011) T,TS(KF+1,J),TS(1,J),FGRT*100.DO

C *,POWER,BURN(J) ,BURNFR(J)

IF(ITRAN.EQ.0 ) THEN

IF(ISTEP. EQ.0) THEN

IF(J.EQ.LMAX1)

*WRITE (39,2009) TDAY,J, BVSJ (J),RGJ, GJOUT, RGGL, RGGFRGGE,

*FGRJ/AVN,

*SUMRET,TK(1,J)/I.DO,TS(1,J) ,TS (KF,J) ,POW(J)/0.3048D0,BURN(J)

RRC K! 2080 A-39
IF(J.EQ.2)WRITE(37,2009)TDAY,J, BVSJ(J) ,RGJ,GJOUT,RGGL,RGGFRGGE,

*FGRJ/AVNo

*SUMRET,TK(1,J)}/.DO,TS(1,J) ,TS(KF,J),POW(J)/0.3048D0,BURN(J)

IF(J.EQ.3)WRITE(36,2009)TDAY°J,BVSJ(J) ,RGJ,GJOUT,RGGL,RGGF,RGGE, *FGRJIAVN,

*SUMRET,TK(1,J)/I.DO,TS(1,J) ,TS(KFJ),POW(J)/0.3048D0,BURN(J)

IF(J.EQ.4)WRITE(35,2009)TDAY,J,BVSJ(J), RGJ,GJOUT,RGGL,RGGF,RGGE,

*FGRJ/A VN,

*SUMRETK1(1,J) /l.DOTS(1,J), TS(KF,J) ,POW(J) /0.3048D0,BBURN(J) IF (J. EQ. 5) WRITE {34,2009) TDAY, J, BVSJ (J),°RGJ, GJOUT, RGGL, RGGF, RGGE,

*FGRJIAVN,

*SUMRET, TK (i,J)/i.DO, TS (,J), TS(KF, J), POW(J) 10.3048D0, BURN(J)

ENDIF

ENDIF

FOR AXIAL DISTRIBUTION

FGRZ(J)=FGRJ*100.DO/AVN

BVS_Z(J)=BVSJ (J)"100.DO

RGJ_Z (J) =RGJ

GJOUTZ (J) --GJOUT

RGGL_Z(J)=RGGL

RGGF_Z (J) =RGGF

RGGEZ (J) =RGGE

IF(J.EQ.LMAX1.AND.TCURR.GE.TMAX_0 .AND. ISTEAD.EQ.0) THEN

IF(IGRAF.EQ.0) WRITE(0,1961)TDAY, TS(1,J),TS(KF,J)

1961 FORMAT(5X,'TIME:'",F7.0, TEMPERATURE:', 2F8.O0)

C PAUSE

ISTEAD=ISTEAD÷I

GPELL=( (GSG (KF,J)/AVN)/ARA(KF,J))

C PRINT*,GPELLGSG(KFJ)/AVNARA(KF,J)

VOLSL=0 DO

RMASS=O.ODO

DO K=2,KF

VOLSL=VOLSL+ VLM(K, J)

ENDDO

C PRINT*, 'MASSA SLICE [KG] ',FMASS

ROFUEL=FMAS*1000/VOLSL ! [G/CM3]

DO K=2,KF

UNLESS=AVN/GSG (K, J)

OTN_RAD=-RS(K,J) /RS (KF,J)

RMASS=VLM(KJ) *ROFUEL .[MASS IN G]

C PRINT', RMASS, ROFUEL,VLM(K,J),VOLSL

WRITE(30,2010)

A K,

B OTN_RAD,

C RGKJ(KJ) SUNLESS,

D TS(KJ),

E BVSKJ(K,J),

F GOU(K,J) *UNLESS/AVN,

J GFACE (K,J) *UNLESS,

H GEDGE (K,J)*UNLESS,

I G-GRAIN(K,J)*UNLESS,

G ((GSG(K,J) /AVN)/ARA(K,J) )/GPELL,

K RSCK,J)*10.DO, [CM]

L (GFACE (K,J)+GEDGE(K,J)+GGRAIN(K,J))*22.4D3/RMASS,! [CM3/G]

* PRFPGRF(KJ) ! POROSITY

ENDDO

ELSE

IF(J.EQ.LMAX1) THEN

IF(ISTEP. EQ.0) THEN

WRITE (32,2009)

A TSOS,

B J,

RRC K! 2080 A-40
C BVSJ (J),

D RGJ,

E GJOUT,

F RGGL,

G RGGF,

H RGGE,

I FGRJ/AVN,

* SUMRET, * TS (1, J)/I1.0OD0, K TS(KF,J)/1.ODO,

* TS(2,J)/1.ODO

SWELMAX=BVSJ (J)/3.ODO

ENDIF

ENDIF

ENDIF

C

IF(J.EQ.LMAX1.AND.TCURR.GE. TMAX-1.OE-6 ) THEN

VOLSL=O .DO

DO K=2,KF

VOLSL=VOLSL+ VLM (K, J)

C PRINT*, ROFUEL, FMAS, VOLSL

ENDDO

ROFUEL=FMAS*1000.DO/VOLSL

DO K=2,KF

OTH-RAD=-RS (K. J)/RS (KF, J)

RMASS=VLM(K,J) *ROFUEL ! [MASS IN G)

UNLESS=AVN/GSG (K, J)

WRITE(29,2010)

A K,

B OTN._RAD,

C RGKJ(K,J)*UNLESS,

D TS(K,J),

E BVSKJ (K, J),

F GOU (K, J) *UNLESS/AVN,

G GFACE (K,J)*UNLESS,

H GEDGE (K,J)*UNLESS,

I G.GRAIN(K,J)*UNLESS,

J ((GSG(K,J)/AVN)/ARA(K,J) )/GPELL,

K RS(K,J)*10.DO, ! [CM]

L (GFACE (K,J)+GQEDGE (K,J)+GGRAIN(K,J))*22400.D0/RMASS, ![C2H3

M PRFGRF(K,J) ! POROSITY

ENDDO

ENDIF

TDAY0=TDAY

C PRINT FUEL ROD TOTAL CHARACTERISTICS

C FOR STEADY-STATE AND TRANSIENT CONDITIONS:

IF(ITRAN.EQ.0) THEN

IF(ISTEP. EQ.0) THEN

WRITE (38,2010)

A TSOPD/(3600.D0*24.D0),

B FGRT,

C RGT*22400.D0,

D GTOUT*22400.DO,

E GRFT*22400.D0,

F GGT*22400.DO,

G ERR*100.DO,

H RETI*22400.DO,

I RETC*22400.DO,

J OUTI*22400.DO,

K OUTC*22400.DO,

L TS(1,LMAX1)/1.DO,

M TS(KF,LMAX1)/1.DO

FGRTOT= FGRT

ISTEP=ISTEPPRINT

ENDIF

ENDIF

RRC K1 2080 A-41
IF(ITRAN.NE.0 .OR. TCURR.EQ.O.ODO) THEN

IF(ISTEP. EQ.0) THEN

WRITE (33,2010) *TSO0S ,FGRT, RGT*22400.D0,

* GTOUT*22400.DO,

* GRFT*22400.DO,

* GGT*22400.DO,

* ERR*100. DO RETI*22400. DO, RETC*22400. DO,

*OUTI*22400.DO,0UTC*22400.DO,TS(1i, AXI)/1.ODO,TS(KF,LMAX1)/I.ODO

FGRTOT=FGRT

ISTEP=ISTEPPRINT

ENDIF

ENDIF

745 CONTINUE

RETURN END

FUNCTION GCONR2(GNIX, GTEMP, GPRES, GPTHK)

C SHEST 5/28/98 5:30AM

IF(GPTHK.LE.4.4D-6) GPTHK=4.4D-6

RETURN

END

SUBROUTINE FSWELL (FDENS, COMP, BU, BUL, FTEMP, GASWL, SOLDSW)

IMPLICIT REAL*8 (A-H,O-Z)

C

C COMP = INPUT PLUTONIA CONTENT (WEIGHT PERCENT)

C FDENS = INPUT INITIAL DENSITY OF THE FUEL (KG/M**3)

C FTE2P = INPUT TEMPERATURE OF THE FUEL RING (K)

C BU = INPUT BURNUP TO END OF TIME STEP (MW-S/KG-U)

C BUL = INPUT BURNUP TO END OF LAST TIME STEP (MW-S/KG-U)

C

C GASWL = OUTPUT FUEL SWELLING DUE TO GAS FISSION PRODUCTS

C (FRACTION)

C SOLDSW = OUTPUT FUEL SWELLING DUE TO SOLID FISSION PRODUCTS

C (FRACTION)

C

C FSWELL WAS DEVELOPED AND PROGRAMMED BY R. E. MASON - JUNE 1978.

C

C THE U02 SWELLING CORRELATION IS BASED ON THE FOLLOWING DATA

C CHUBB,ET AL., NUCLEAR TECHNOLOGY 18 (1973)

C TURNBULL, JOURN. NUCL. MATER., 50 (1974)

C BANKS, JOURN. NUCL. MATER., 54 (1974)

C DANIEL ET AL., WAPD - 263 (1962)

C

C - PROGRAM -

C

BUS = FDENS * 2.974D+10 * (BU - BUL)

SOLDSW = BUS * 2.5D-23

IF (FTEMP .LT. 2800.DO) GO TO 25

GASWL = 0.ODO

GO TO 50

25 CONTINUE

GASWL=(8.80D-50*((2800.D0-FTEMP)**11.73D0)*EXP(-2.4D-10*BU*FDENS)

S*EXP(-0.0162D0* (2800.DO- FTEMP))) * BUS

50 CONTINUE

CALL DIALOT(FEMP, 9,FDIALAFDIALM)

GASWL= (GASWL+FDIALA) *FDIALM

SOLDSW= (SOLDSW+FDIALA) *FDIALM

RRC KI 2080 A-42
RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTNS ** END

SUBROUTINE FUDENS (FTEMP, BU, FDENS, RSNTR, TSINT, COMP, PRVDEN,

* FUDENT)

IMPLICIT REAL*8 (A-H,O-Z) C

C FUDENS CALCULATES IRRADIATION-INDUCED DENSIFICATION.

C

C FUDENS = OUTPUT FUEL DIMENSIONAL CHANGE (%)

C

C FTEMP = INPUT FUEL TEMPERATURE (K)

C BU = INPUT BURNUP (MW-S/KG-U)

C FDENS = INPUT FUEL DENSITY (KG/M**3)

C RSNTR = INPUT MAXIMUM DENSITY CHANGE DETERMINED BY A RESINTERING

C TEST OF 1973 K FOR 24 HOURS (KG/M**3)

C TSINT = INPUT FUEL SINTERING TEMPERATURE (K)

C COMP = INPUT PLUTONIA CONTENT (WEIGHT PERCENT)

C PRVDEN = INPUT TOTAL DENSIFICATION FROM PREVIOUS TIME STEP (%)

C FUDENS WAS DEVELOPED AND PROGPA24ED BY C. S. OLSEN (JANUARY 1975).

C UPDATED AND CORRECTED BY B. W. BURNHAM (OCTOBER 1975).

C FUDENS WAS MODIFIED BY R. E. MASON (NOVEMBER 1978). DIMENSION C(2) ,B(5)

DATA C / 10.97D0, 11.46D0/

DATA B / 3.ODO, 1.00D0, 3.0D0, 2.OODO, 35.OODO/

DLEN2(ALEN, BU,ABU) = -B(1) + ALEN + B(2)* EXP(-B(3)*(BU + ABU))

# + B(4) * EXP(-B(5) * (BU + ABU))

DLEN3(BU) = -B(2)*B(3)* EXP(-B(3)*BU) - B(4)*B(5)* EXP(-B(5)*BU)

FBU = BU * 1.0202D-05

TS = TSINT - 2.7315D02

C IF RSNTR OR TSINT IS NOT DEFINED BY USER, THE DEFAULT VALUE IS

C TSINT - 1873 K.

IF (TSINT .LE. 0.ODO) TS = 1600.ODO

ROTH = C(1)*C(2)/(0.01D0*COMP*C(1) + (1.0DO- 0.01D0*COMP)*C(2))

DE = FDENS/(ROTH*10.ODO)

* <SHEST> IF FUEL DENSITY IS .LT. RSINT

IF((FTEMP .GE. 1000.DO) .AND. (RSNTR .GT. 0.DO))DLEN1 = 0.00285D0*

#RSNTR

IF((FTEMP .LT. 1000.DO) .AND. (RSNTR .GT. 0.D0))DLENI = 0.00150D0*

#RSNTR

** * **~ <SHEST> IF FUEL DENSITY IS .GE. RSINT

IF((FTEMP .GE. 1000.DO) .AND. (RSNTR .LE. 0.DO))

# DLENI = 66.6D0*(100.0D0- DE)I(TS - 1180.ODO)

IF((FTEMP .LT. 1000.DO) .AND. (RSNTR .LE. 0.DO))

# DLEN1 = 22.2D0*(100.0D0- DE)/(TS - 1180.ODO)

X3 = 0.ODO

X4 = 1.0DO

ALl = DLENI

AL3 = 3.0D0- ALl

AL4 = 0.ODO

IF (AL3 .LE. 4.27D-03) GO TO 30

DO 15 I = 1,6

Y2 = DLEN2(AL3,X4,AL4)

Y1 = DLEN2(AL3,X3,AL4)

IF (YI*Y2 .LE. 0.DO) GO TO 20

X3 = X4

X4 = X4 + 1.ODO

IF (I .EQ. 6) GO TO 45

15 CONTINUE

20 CONTINUE

Xl = X3

DO 25 J = 1,50

X = Xl - DLEN2( AL3, Xl, AL4) / DLEN3(Xl)

ERR = ABS((X - Xl) * 100.ODO/X)

IF (ERR .LE. 2.OD-04) GO TO 35

Xl = X

25 CONTINUE

30 AL3 = 2.996D0

AL2 = 5.384D0

GO TO 40

35 AL2 = X

40 CONTINUE

FUDEN = DLEN2( AL3, FBU, AL2)

RRC K! 2080 A-43
IF (BU .LT. 1728) FUDEN = 0.ODO

GO TO 50

C

45 PRINT 100

100 FORMAT (IX,145H NO ROOTS FOUND BETWEEN 0 AND 6000 MMS/MT U02)

FUDEN = O.ODO

50 CONTINUE

FUDENT=-FUDEN

IF (ABS(FUDEN) .LE. ABS(PRVDEN)) FUDENSS = 0.ODO

IF (ABS(FUDEN) .GT. ABS(PRVDEN)) FUDENSS = FUDEN - PRVDEN

C

CALL DIALOT (FTEMP, 11, FDIALA. FDIALM)

FUDENSS= (FUDENSS+FDIALA) *FDIALM

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 **

END

SUBROUTINE MELT (TCLAD, UMELT, CTMELT, PFRI)

C

IMPLICIT REAL*8 (A-H, O-Z)

C

C COMMON BLOCKIMATPRC/STORES MATPRO PARAMETERS USED TO DETERMINE

C CLADDING MATERIAL PROPERTIES

C

C REVISE /MATPRC/ COMMON BLOCK

* SHEST COMMENT FOLLOWING STRING 26/12/96

C INCLUDE 'MATPRC. H'

C DTMPCL a MAXIMUM CIRCUMFERENTIAL VARIATION IN CLADDING TEMPERAC TURE (K)

C CANRIN = CONTRACTILE STRAIN RATIO DURING UNIAXIAL TENSILE TEST.

C CIRCUMFERENTIAL STRAIN/RADIAL STRAIN

C KAXMTP = AXIAL NODE NUMBER

* ** SIHEST COl T FOLLOWING STRING 26/12/96

C INCLUDE 'PHYPRO.H'

C SUBROUTINE MELT DETERMINES IF A ROD HAS FAILED BY MELTING

C -- INPUT ARGUMENTS --

C TCLAD TEMPERATURE OF CLADDING ( DEG K

C UMELT USER-SELECTED MELT TEMPERATURE ( DEG K

C

C -- OUTPUT ARGUMENTS --

C

C PFR1 FAILURE INDICATOR (=1 IF CLADDING MELTED)

C

* SHEST COMMENT FOLLOWING STRING 26/12/96

C DATA DUHI/ 0.DO/

C

* SHEST COMMENT FOLLOWING STRING 26/12/96

C IF ( UMELT .NE. 0.DO) GO TO 5

UMELT = CTMELT

5 IF ( UMELT .GE. TCLAD ) GO TO 10

PFR1 = 1.ODO

GO TO 20

10 PFR1 = 0.ODO

20 CONTINUE

C

C PRINT*, 'FORM MELT = UMELTTCLAD,PRF1', UMELT,TCLAD, CTMELT,PFR1

RETURN

C** THIS PROGRAM VALID ON FTN4 AND FTN5 **

END

SUBROUTINE BALON2 (GMIX ,FTEMP , STRNL , STRNR ,STRNA ,STRNC

# ,RAD ,TWALL ,CTEMP ,DELZ ,FCP ,FRP ,FAP

# ,ACD ,AAD ,ARD ,FNCK ,FNCN ,CWKF ,CINF

# ,STEMP ,HTCS ,TSTM ,RTEMP ,ACS ,AAS ,ARS

# ,ACE ,AAE ,ARE ,DBYTH ,DBYZ ,STRESF ,TSTRES

RRC K1 2080 A-44
# ,DISP ,DEH ,DEA ,RSTRAN ,RAVE ,STRESR ,STRESA

# ,RADC ,RADR ,DZ0 ,CLDBRN

C

C   LU YES/NO BENDING

C DISP(K,J) = 0.D0

C ** **** LU LIMIT

IF(GPTHK.LT.1.5D-05) GPTHK=1.SD-05

C

RETURN

END

SUBROUTINE PRNTOT (T_.BURST, TIMJMAX, DZO, FMASS, VOLUME, FUELLEN, TS, *STRO)

N= 0

D01288K=KAX, KMAX, KSKP

N = N+I

DUM=RSW (N)

IF (.NOT.U) DUM = DUM * DOZ

IF (U) DUM = DUM *FTMM

1288 ADUM(N) = DUM

WRITE (6,1290) DIM(IU,2), (ADUM(K),K=1,N)

1290 FORMAT( 36H DISPLACEMENT DUE TO SWELLING ,A6,1PE13.3,5E14.3)

IF(T.GE.TIM_.MAX-0.00001DO) THEN

C IF (IGRAF.NE.0) PAUSE' PAUSE FOR HISTORY FROM PRNTOT.FOR'

CALL DATE (STR)

CALL TIME (STRI)

WRITE(40,1996) EBURST

WRITE(40,1996) STRAINB*100

WRITE(40,1996) TBURST

FREE GAS VOLUME ***************************

WRITE(40,135)DIM(IU,2) ,V(10)

WRITE(40,501)V(1) *100

WRITE(40,502)V`(2) *100

WRITE (40,503)V(3) *100

WRITE(40,504)V(4) *100

WRITE (40,505)V(5) *100

WRITE(40,506)V(6) *100

WRITE(40,507)V(7) *100

WRITE(40,508)V(8) *100

WRITE(40,509)V(9) *100

WRITE(40, 1002) FNASS,FMASS/VOLUME,FUELLEN

WRITE(40 ,1997) STR,STR0,STRI

WRITE( 6 ,1997) STR,STR0,STRI

1997 FORMAT(//,'FRAP-T6 CALCULATION",/,'DATE: ',All,/,'TIM: ',All,/,

',All)

1002 FORMAT(/,"ASS=',F9.4,/,'DENSITY=",F6.2,/,'FUEL LENGTH=',F9.4)

ENDIF

1995 FORMAT(A20)

RRC KI 2080 A-45
1998 FORMAT(10X,A20)

1996 FORMAT(10E12.4)

RETURN

END

PROGRAM GRAFDATA

CHARACTER*11 STEP

CHARACTER*IS ISTEP, BLANK

REAL IOXTN, LOCRODPW,METWRE,MIDTEMPP

DATA STEP /" PLOTREC' /

ISTEP= '

DIMENSION DATAINT( 13),

*CLADAXSS(50),CLADHSN(50),CLADHSS(50),CLADITE(50),CLADOTE(50),

*•CLADPASN(50),CLADPHSN(50) ,CLADPRSN (50),CLADRSN(50), CLADSNI (50),

*CLADSSI(50),CLADYSS (50),COLBLKTE(50),COLMSFLX(50) ,COLPE(50),

*COLGLC(50),CRTHTFLX(50),CTEMP(50),EFCLADSS(50),ELEV(50),

*FSDSP(50),FSTEMP(50) .GAPHTC(50),GAPPR(50),•EATTRMD(50),

*IOXTN(50),LOCRODPW(50) ,METWRE(50),OOXTN(50) ,OXSTN(50),

*•STRUCIP(50) ,STRUCR (50 },SURHTC(50),SURHTFLX(50),THHGAPIP(50),

*THMRG(50), RPMFS(50),RPMCI(50),ERPMMX (50),1MIDTEMPP(50),FAILFLAG (50,

*DATA (250) ,FDISO(50)

NAMELIST/INP/AKSNUMBER, ISTEPPRINT

OPEN(1,FILE=•STRIPF')

OPEN(51,FILE='T')

READ(51, *) TEND,DZO,LMAX,NAXN,ISTEPPRINT

1961 FORMAT(FO.i,El2.4,315)

IF (ISTEPPRINT.LT. 1)

*PRINT*,' !!! STEP FOR PRINT IS TOO LOW =',ISTEPPRINT

NM=NAXN

NMI=NM*5

OPEN (2, FILE=' INTDATA.DAT',STATUS= 'NEW*)

OPEN (3, FILE= 'CLADAXSS.DAT',STATUS='NEW')

OPEN(4,FILE= 'CLADHSN. DAT',STATUS= 'NEW')

OPEN(5,FILE='CLADHSS.DAT',STATUS='NEW')

OPEN(6 , FILE= 'CLADITE.DAT' ,STATUS='NEW')

OPEN(7,FILE='CLADOTE.DAT',STATUS='NEW')

OPEN (8, FILE="CLADPASN.DAT',STATUS= 'NEW')

OPEN (9, FILE= 'CLADPHSN.DAT' ,STATUS= 'NEW')

OPEN(1i0, FILE= 'CLADPRSN.DAT',STATUS= 'NEW')

OPEN(11,FILE= ' CLADRSN.DAT',STATUS= 'NEW")

OPEN (12, FILE= 'CLADSNI.DAT' ,STATUS= 'NEW')

OPEN(13,FILE='CLADSSI.DAT',STATUS='NEW')

OPEN (14, FILE='CLADSYSS.DAT',STATUS='NEW')

OPEN (15, FILE='COLBLKTE.DAT' ,STATUS= 'NEW')

OPEN(16, FILE= 'COLMSFLX.DAT' .STATUS= 'NEW')

OPEN(17,FILE='COLPE.DAT',STATUS='NEW')

OPEN(18,FILE='COLQL.DAT',STATUS='NEW')

OPEN (19, FILE=' CRTHTFLX.DAT' ,STATUS='NEW')

OPEN(20,FILE='CTEMP.DAT',STATUS='NEW')

OPEN(21,FILE='EFCLADSS.DAT',STATUS='NEW')

OPEN(22,FILE='ELEV.DAT',STATUS='NEW')

OPEN(23,FILE='FSDSP.DAT' ,STATUS='NEW')

OPEN(24,FILE= 'FSTEMP.DAT',STATUS='NEW')

OPEN (25, FILE=' GAPHTC.DAT' ,STATUS= 'NEW')

OPEN(26,FILE='GAPPR.DAT' ,STATUS='NEW')

OPEN (27,FILE='HEA'TRMD.DAT' ,STATUS='NEW')

OPEN(28,FILE='IOXTN.DAT",STATUS='NEW')

OPEN(29,FILE='LOCRODPW.DAT',STATUS='NEW')

OPEN(30,FILE='METWRE.DAT' ,STATUS='NEW')

OPEN(31,FILE='OOXTN.DAT',STATUS='NEW')

OPEN(32,FILE='OXSTN.DAT' ,STATUS='NEW')

OPEN(33,FILE ='STRUCIP.DAT',STATUS='NEW')

OPEN(34,FILE='STRUCRG.DAT',STATUS='NEW')

OPEN(35,FILE='SURHTC. DAT',STATUS='NEW')

OPEN(36, FILE=' SURHTFLX .DAT',STATUS= 'NEW')

OPEN(37,FILE='THMGAPIP.DAT',STATUS='NEW')

OPEN(38,FILE='THMRG.DAT',STATUS='NEW')

RRC KI 2080 A-46
OPEN(39,FILE='RPMFS.DAT' .STATUS='NEW'

OPEN(40,FILE='RPMCI.DAT' *STATUS='NEW')

OPEN(41, FILE='RPMMX.DAT" .STATUS='NEW')

OPEN (42, FILE= 'MIDTEMPP.DAT', STATUS='NEW')

OPEN(43, FILE= 'PAILZLAG.DAT',STATUS= 'NEW')

2 CONTINUE

READ(1,1,ERR=3) ISTEP

IF(ISTEP(1:9).EQ.STEP) THEN

BACKSPACE 1

READ(1,*) BLANK,

*DATAINT,

* (CLADAXSS (L) ,L=1,NM), (CLADHSN(L),L=1,NM), (CLADHSS(L) ,L=1,NM),

* (CLADITE(L),L=1,NM), (CLADOTE(L) ,L=1,NM),

* (CLADPASN(L), L=1,NM), (CLADPHSN(L),L=I,NM), (CLADPRSN(L), L=1,NH),

*(CLADRSNp(L) ,L=1,NM), (CLADSNI (L),L=1,NM),

* (CLADSSI (L), L=, NM), (CLADYSS (L) ,L=I,NH), (COLBLKTE (L) ,L=-1,NM),

*(COLMSFLX (L),L=1,NM), (COLPE (L) ,L=1,NM),

*(COLGL(L),L=I,NM), (CRTHTFLX(L),L=1,NM), (CTEMP (L),L=1,NM},

*(EFCLADSS(L),L=I,NM), (ELEV(L) ,L=1,NM),

* (FSDSP (L) ,L=INM) , (FSTEMP (L), L=1INM), (GAPHTC (L), L=I,NM),

* (GAPPR(L) ,L=1,NM), (HEATTRMD (L) ,L=1,NM),

* (IOXTN (L), L=I,NM), (LOCRODPW(L) ,L=I,INH) , (METWRE (L) ,L=I,NM),

*(OOXTN(L),L=1,NH), (OXSTH(L),L=1,NM),

* (STRUCIP (L) ,L=1,NM), (STRUCRG (L), L=INM), (SURHTC (L), L=I,NM),

* (SURHTFLX (L), L=1,NM), (THMAPIP (L) ,L=I,NM),

* (THMRG (L),L=1,NM),

C RPMFS, RPMCI, RPMMX, MIDTEMPP, FAILFLAG,

* (DATAI (L), L=1,NM1)

DO I=1,NM

RPMFS (I) =DATA1 (1+ (I-1) *5) *1000.

RPMCI (I) =DATA1 (2+ (I-1) *5) *1000.

RPMMX (I) =DATA1 (3+ (I-1) *5) *1000.

MIDTEMPP(I)=DATA1(4+(I-1) *5)

FAILFLAG(I)=DATA1(55+ (I-1) *5)

ENDDO

IF(ISW. EQ. 0) THEN

ISW=ISTEPPRINT

TT=-DATAINT (1)

DTT=DATAINT (2)

IB=IB+I

WRITE(*,*) 'TIME=', TT, 'TIME STEP=',DTT, IB

WRITE(2,4) TT, (DATAINT(K),K=I,13)

WRITE(3,4) TT, (CLADAXSS(K) ,K=1,NM)

WRITE(4,4) TT, (CLADHSN(K)*100,K=I,NM)

WRITE(5,4) TT, (CLADHSS (K) *10.,K=1,NM)

WRITE(6,4) TT, (CLADITE(K) ,K=1,NM)

WRITE(7,4) TT, (CLADOTE(K) ,K=I,NM)

WRITE(8,4) TT, (CLADPASN(K) *100,K=I, N)

WRITE(9,4) TT, (CLADPHSN(K) *100,K=1,NM)

WRITE(10,4) TT, (CLADPRSN(K)*100,K=I,NM)

WRITE(11,4) TT, (CLADRSN(K)*I00,K=1,NM)

WRITE(12,4) TT, (CLADSNI(K)*100,K=1,NM)

WRITE(13,4) TT, (CLADSSI(K),K=I,NM)

WRITE(14,4) TT, (CLADYSS(K),K=1,NM)

WRITE(15,4) TT, (COLBLKTE(K) ,K=1,NM)

WRITE(16,4) TT, (COLMSFLX(K) ,K=1,NM)

WRITE(17,4) TT, (COLPE(K) ,K=1,NM)

WRITE(18,4) TT, (COLGL(K) ,K=,NM)

WRITE(19,4) TT, (CRTHTFLX(K),K=1,NM)

WRITE(20,4) TT, (CTEMP(K),K=1,NM)

WRITE(21,4) TT, (EFCLADSS(K),K=1,NM)

WRITE(22,4) TT, (ELEV(K) ,K=1,NM)

IF(IB.EQ.1) RPMFS0=RPMFSS(I)

IF(TT.GE.0. AND . ITT.EQ.0) THEN

DO L=1,NM

FDISO (L) =FSDSP (L) *100./RPMFSO

IF(FDISO (L) .LE.0.000001) FDISO(L)=0.

ENDDO

ITT=ITT+1

ENDIF

WRITE(23,4) TT, (FSDSP(K)*100./RPMFS0-FDIS0(K),K=1,NM)

WRITE(24,4) TT, (FSTEMP(K),K=1,NM)

RRC V12080 A-47
WRITE(25.4) TT, (GAPHTC(K) ,K=.,N14)

WRITE(26,4) TT, (GAPPR(K) ,K=I,NM)

WRITE(27,4) TT, (HEATTRND(K) ,K=1,NM)

kRITE(28,4) TT, (IOXTN(K),K=1,NM)

WRITE(29,4) TT, (LOCRODPW(K) ,K=I,NK)

WRITE(30,4) TT, (mETME(K) ,K=1,Nm) WRITE(31,4) TT, (00XTN(IC "1000.-3. °K=I,NM}

WRITE(32,4) TT, ((OXSTN(K)+OOXTN(K))*1000.-3.,K=I,NM)

WRITE(33°4) TT, (STRUCIP(K) ,K=1,NH)

WRITEC34o4) TT, (STRUCRG(K),K=1,NM)

WRITEC35,4) TT, (SURHTCCK)/1000,K=I,NM)

MITE(36,4) TT, (SURHTFLx(K)/1000.,K=1,NM)

WRITE(37,4) TT, (TH•mAPIP(K),K=1I,NM) WRIETE(38.4} TTo (THMRG(K),rK=I,NM)

WRITE(39,4) TT, (RPMFS(K),K=1,NM)

WRITE(40,4) TT, (RPXCI(K),K=1,NM)

WRITE(41,4) TT, (RPMX (K) ,K=I,NN)

MRITE(42,4) TT, (MIDTEMPP (K) ,K=INM)

WRITE(43,4) TT, (FAILFLAG(K) ,K=1,NM)

ENDIF

Isw=Isw-I

ENDIF

GOTO 2

1 FORMAT (A18)

4 FORMAT (IP50E14.6)

3 CONTINUE

STOP

END

RRC Kf 2080 A-48
APPENDIX B. The revealed mistakes

1. Zero values of the pressure in the gas accumulator saved in the output STRIPF file.

In STORE6 subroutine the procedure of saving gas pressure into the STRIPF output file has been

changed. Prior to calling for GRAFOUT subroutine, the following string was inserted:

TP(1)=TPLNA(1,2,1).

2. TUNING subroutine controls the input data block option, which specifies the multiplication

factors for some physical parameters. It was revealed that the suboptions were not suitable for

numerical tuning apart from the following suboptions:

" Fuel thermal conductivity;

* Pool boiling heat transfer coefficient;

" Free convection heat transfer coefficient;

" Critical heat flux.

Other suboptions are apparently in disagreement with the FORTRAN format specifications.

3. Critical heat flux (PCHF subroutine)

To calculate critical heat flux subcooling factor is used in the following form:

Fs = 1 + 0.065 (pf ipg)O8 AI/hfg,

where pf and pi= water and steam densities;

hfg= latent heat;

g= gravity acceleration;

AI= difference between enthalpy of the liquid saturation and fluid bulk temperature.

In the text of the code the subcooling factor is expressed as follows:

FSUBC = 1.DO+0.065D0*((RF/RG)**0.8D0)*(CPF*DTSUBF/(HGP-HFP)),

where AI = CPF*DTSUBF, CPF - specific heat of fluid and DTSUBF - subcooling temperature).

Calculations in the PCHF subroutine are performed in the British Thermal Units (BTU). Still,

subcooling temperature is presented in the SI system. The mistake was eliminated by converting

DTSUBF parameter from Kelvin to Fahrenheit.

4. Ross and Stout model to calculate gas gap thermal conductivity (GAPHTC subroutine):

The following formula is used to calculate thermal conductivity of the non-zero fuel-cladding gap:

ag = x.gas

A+C(Rf 9g + R,)+(gf +gg)

where )L,.= thermal conductivity of the gas mixture in the gap (W/m K);

Ag= fuel-cladding gap in the hot state (m);

Rf= mean arithmetic of the fuel roughness value (m);

RRC K1 2080 B-1
R=- mean arithmetic of the cladding roughness value (m);

C= empirical constant;

gf + g&= temperature jump distance at the external fuel surface and at the internal cladding

surface, respectively.

In the text of the subroutine this is expressed as:

hgap = gpcon/(gpthk + gjmpft + drough),

where gpcon = thermal conductivity of the gas mixture in the gap;

gpthk = fuel-cladding gap in the hot state;

gimpft = gr + g.;

drough = C(Rf + R&) mean arithmetic of the fuel roughness value (m).

In the subroutine the complex is calculated as:

DROUGH = FROUGH* (RUFF+RUFC)/12 .DO

RUFF = RI; RUFC = Re; FROUGH = C

Still, the condition under which the fuel-cladding gap can not be less than C(Rf + RJ) value was

already specified as:

THKMIN = 3.6D0*(RUFF+RUFC)/12.DO

IF (GPTHK.LT.THKMIN)GPTHK = THKMIN

This leads to the mistake in calculating thermal conductivity of the fuel-cladding gap according to

the Ross and Stoute model. That is why the condition 4,iF (GPTHK.LT.THKMIN)GPTHK--THKMIN>

was taken out of the text of GAMTIC subroutine.

RRC K1 2080 B-2
NRC FORM 238 U.S. NUCLEAR REGULATORY COMMISSION 1. REPORT NUL13ER

(24-9) (Assined by NRC. Add Val. Supp.. Rev. NRCM NMI, 1102. ad Addendum Numbers. Ir'wn.) 3=Z BIBLUOGRAPHIC DATA SHEET

(Sao k=sh=t= an t nwww NUREGAA-0164

... RRC K1 2180 -TILE AND SUBTITLE IPSN 99/10

Modification of USNRC's FRAP-T6 Fuel Rod Transient

Code for High Bumup WER Fuel 3. DATE REPORT PUSISHED

MONTH YEAR

May 1999

4. FIN OR GRANT NLUMBER

W6500

5. AUTHOR(S) 6. TYPE OF REPORT

A Shestopalov, K Uoutov, L Yegorova, G. Abyshov, K Miktiouk Technical

7. PERIOD COVERED &=kuA Das)

1995-1998

8. PERFORMING ORGANIZATION - NAME AND ADDRESS Vrmr( pr.ova Dwam. i offr cn e * u.S M b-ni end w

Russian Research Center -Kurchatov Institute

Kurchatov Square I

Moscow 12382

Russia

9. SPONSORING ORGIANZATIO61- NAME AND ADDRESS ONR bW tye Sarmabomift. s clatr, Wov• NRC Ov•m. Offiec• om U.S-. c18wPer da~y *•~x

&7d meMo& ad-.

Division of Systems Analysis and Regulatory Effectiveness

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington. DC 20555-0001

10. SUPPLE10-ENTARY NOTES

11. ABSTRACT j= wid crA-)

The USNRCs transient fuel rod code, FRAP-T6, has been modified to analyze pulse tests with high bumIup WER fuel rods in the

Impulse Graphite Reactor (IGR). New and modified models of separate phenomena have been developed, including models for

heat transfer from the cladding to the stagnant coolant; the effect of fission gas swelling on the fuel cladding gap, and the

conditions of base irradiation. Thermal and mechanical properties for the WER's Zr-1 %Nb cladding were added to

MATPRO-VI 1, which is used by the FRAP-T6 code. Changes in the input data file are described and a sample calculation is

presented with the modified code. A FORTRAN isting for the new and modified models is given in an Appendix A.

12. KEY WORDSIDESCRIPTORS Aitt Ids oraphmw UNvel wX ast mhsewacws in Ace•n, Mee ,.•) 13. AVALAB"I STATEMENT

reactivity initiated accident unlimited

impulse graphite reactor 14. SECU.RIrY CLASSIFICATION

cladding-to-coolant heat transfer model (Th Page)

FRAP-T6 computer code unclassified

material properties (_

cladding strain and ballooning unclassified

15. NUIBER OF PAGES

16. PRICE

NR FR 23(29 IllIm uI ioua Iic~ eellFmb IySt 

NRC FORM 335 (24W) This form was elemaracally produced by Eft Federal Fawks, Irc.
Federal Recycling Program

NlJKE(i/tA-Ulb4 

* FOR HIGH BURNUP VVER FUEL

UNITED STATES

NUCLEAR REGULATORY COMMISSION

WASHINGTON, DC 20555-0001

SPECIAL STANDARD MAIL

POSTAGE AND FEES PAID

USNRC

PERMIT NO. G-67

1

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PENALTY FOR PRIVATE USE, $300