IAEA Workshop on Advanced Code Suite for Design, Safety …€¦ · · 2012-10-10IAEA Workshop on Advanced Code Suite for Design, Safety Analysis and Operation of Heavy Water Reactors

INR Coupled Reactor Physics and Thermal Hydraulics Calculation System for CANDU Reactor

IAEA Workshop on Advanced Code Suite for Design, Safety

Analysis and Operation of Heavy Water Reactors

2012 Oct 2 - 5

Institute for Nuclear Research

Pitesti, Romania

I. Patrulescu

INR Coupled Reactor Physics and Thermal Hydraulics Calculation System for CANDU reactor

2

OUTLINE

1. Historic background of physics, thermal hydraulic

and fuel performance codes used in INR

2. Three Dimensional Diffusion Code DIREN

3. Programming features of DIREN

4. Code System Verification and Validation

5. WIMS-DRAGON-DIREN-RELAP Sample Results

6. Fuel performance codes presently used in INR


3

1. Historic background of physics, thermal hydraulic

and fuel performance codes used in INR

AECL reactor physics, thermal hydraulics and fuel performance

codes were available to INR after 1978 and were used on a small size

main frame: CDC CYBER 170/135.

These reactor physics codes were:

-PPV (cell code), MULTICELL (super cell) RFSP, CHEBY,

CERBERUS, FMPD, CEBXEMAX (reactor core).

The AECL thermal hydraulics codes available were FIREBIRD III,

HYDNA-2, HYDNA-3, NUCCP (NUCIRC).

The fuel performance code was ELESIM.

In parallel INR had access to other computer codes from

international libraries (e.g.):

-WIMS (cell), CITATION (reactor core), TWOTRAN (2D transport

calculation) , MCNP (Monte Carlo approximation to transport equation).


When PC’s appeared, some of the above codes were ported from

mainframes to the new personal computers, e.g.:

-PPV, MULTICELL, FIREBIRD III, HYDNA-2, HYDNA-3, NUCCP (NUCIRC).

In the same time work was done to create INR own computer codes.

Reactor physics codes written were: CP2D for the cell , PIJXYZ for the

reactivity devices incremental cross sections and DIREN for reactor core (3D

multi group diffusion). PIJXYZ solve the integral transport equations using first

collision probabilities. CP2D and PIJXYZ were developed by M.Constantin

et.al.

4


Some AECL codes in executable form were available to use in INR, in

the framework of INR – AECL agreement for scientific cooperation and in

certain condition. These were:

-WIMS-AECL-IST for CANDU cell calculations,

-RFSP-IST for reactor core,

-CATHENA-IST for thermal hydraulics,

-ELESTRES-IST for fuel performance evaluation.

-ELOCA-IST

The codes used in fuel performance, including INR created or general

codes adapted for CANDU, are described in section “Fuel performance

codes presently used in INR”.

5


2. Three Dimensional Diffusion Code DIREN

AECL reactor physics design and core performance evaluations

were done for CANDU reactors using the following basic steps:

i)-”Cell calculation”. Homogenized macroscopic cross sections

are generated for the basic cell (fuel bundle and corresponding

moderator).

ii)-”Reactivity device homogenization”. Incremental macroscopic

cross sections due to perturbations induced by reactivity devices

iii)-”Reactor core calculation”. Using the above calculated cross

sections a three dimensional finite difference approximation to diffusion

equation code.(RFSP, Frescura and Wight, 1982) was used to evaluate

Keff and flux distribution

6


For evaluating CANDU- Cernavoda reactor in INR, initially

(1978) and for some time (1990) the AECL reactor physics

calculations were done using POWDERPUFS,-MULTICELL-RFSP

codes system. In the same time alternately WIMS cell code was

used for cell calculations and PIJXYZ for reactivity devices

incremental cross sections.

The same basic steps were used in INR for reactor physics

calculations and in later code development. This successive steps of

homogenization and energy group collapsing is the basis of standard

approximation in reactor physics.

For RFSP, FMDP (for which the author was responsible in INR)

instead of porting to the new FORTRAN compiler on PC’s the

creation of new diffusion code from scratch was preferred.

7


This was done for the following reasons:

-relative difficulty of porting process due to peculiarities of CDC

CYBER, e.g. 60 bits words;

-easier and more flexible use of a own created code,

-simplicity of basic equations to be solved,

-inexpensive verification and validation by comparison to other

classic diffusion codes (in our case CITATION was used),

-possibility of easily implementing new approximations and

methods.

8


The work at DIREN began after the PC were introduced in use

(by 1992). DIREN intended to be an inexpensive solution to reactor

core calculation. Beside the author a large and essential contribution

to the writing of this code was brought by Mr. .

DIREN is a multi group, finite difference approximation of

diffusion equations. The general form of diffusion equation was used.

For solving the time dependent diffusion equation the quasi static

approximation was applied. DIREN has the capability of solving the

diffusion equation in 2 or more (up to 10) energy groups taking into

account the up scattering. The approximations and methods used are

classical in reactor physics computation: finite difference

approximation of diffusion equation and related iterative solutions of

eigenvalue problem.

9

V.Raica


Due to CANDU reactor core complexity (a lot of reactivity

devices perpendicular to horizontal fuel channels) three layers of

arrays are used:

-fuel channel,

-control devices array,

-mesh points positions.

10


A typical diffusion calculation has the following five basic steps:

-1) Cross sections generation for each fuel bundle in the core.

The procedure depends on the type of calculation. For example,

in the case of a simulation, cross sections are calculated by

interpolation as function of irradiation in tables that are given in input.

-2) Obtaining cross section at each mesh point.

This is done firstly by assigning reflector cross sections at all

mesh points. Next fuel cross sections generated at step 1) are

allocated at mesh points that overlap fuel bundles array.

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Volumetric weighing is used when mesh point position differs

from fuel array dimension. Finally incremental cross sections are

added to the volumes affected by each device.

-3) Finite difference discretization.

Diffusion equations are transformed in linear numerical equation

by integrating over mesh point volume and approximation leakage

terms by finite differences. Coefficients of finite difference form of

diffusion equation are calculated at each mesh point using cross

section allocated at each mesh at step 2.

-4) Iterative solution of eigenvalue problem.

The set of linear numerical equations constitutes an eigenvalue

problem.

12


This problem is solved by using a source iteration procedure; in

the case of a multi group with up-scattering inner iterations are used.

After the convergence is attained basic results (Keff and relative group

flux distributions) are calculated.

-5) Obtaining the final primary results.

Group fluxes for each fuel bundle in the core are calculated from

mesh points flux distributions. Fuel bundle fluxes are normalized to

actual core fission power using production cross sections and power

to flux ratios for each bundle. In the process the power distribution for

every fuel bundle is calculated. There are also specific data, e.g.

reactivity core decay rate with burn-up, increase in core reactivity at a

fuel bundle replacement, that may be evaluated using the basic

group flux, power and cross sections distribution on the fuel bundles

array.

13


There are some types of calculations that are usually performed

for CANDU reactors incorporating the above described basic steps:

Direct simulation on discrete time steps.

Beside the direct time step simulation another usual

approximation for CANDU core is the AECL proposed “time-average”

calculation. This approximation is used to evaluate a refueling

equilibrium situation in CANDU.

14


From the point of view of the thermal-hydraulics parameters that

have a significant effect on cross section (fuel temperature, coolant

density, fuel bundle power) the following calculating methods were

developed:

Straight approximation;

Core average values are used for the thermal-hydraulics

parameters mentioned above.

Local parameters approximation;

For each fuel bundle above mentioned parameters are used in

cross sections evaluation. These may be obtained in an interactive

process with a specialized thermal-hydraulic code or reading them

from given files.

15


Local parameters with history for each bundle;

In this case cell code is executed for each bundle with thermal-

hydraulic parameters as specific input data. Besides irradiation other

data are to be kept in memory for each bundle in order the cell code

to run correctly. For the computer memory available now this is no

longer a problem WIMS can be used for this type of calculations.

Local parameters option is the straightforward, “correct” approach.

Coupling with cell and super cell codes was first done with WIMS-

PIJXYZ and later with WIMS-DRAGON.

As the fuel bundle power is a parameter that affects the cross

sections and a product of calculations an iterative procedure with

steps 1 to 4 is used until the axial power distribution is converged. In

case of cell code calculation at each bundle this lead to relative large

calculations time.

16


Other capabilities of DIREN are:

-Calculation of higher modes of diffusion equation. Up to 14

modes that are solutions to the same diffusion equation can be

obtained.

-Flux mapping given the flux detector readings and modes

generated previously. These modes are the higher modes that are

solution to the diffusion equation and flux distribution for typical

configurations that can occur in operation.

-Simulation of xenon effects. Usually the xenon effects are

accounted for using equilibrium values. This option can treat xenon

effect by taking into account xenon concentration dependence of

local powers for each bundle.

17


-Global and local simulation of liquid zone control. This

calculation module allows to search for all zone liquid controllers

positions which give a required reactivity in global option or the

individual position of positions which give the closest detector

readings to the specified set of readings.

-3D spatial kinetics solution in quasi static approximation;

-Core burn-up simulation with automatic refueling.

-Coupled physics and thermal hydraulic calculations.

18


Coupling with other codes was first done with WIMSD5-B3 and

PIJXYZ. WIMSD5-B3 cell code was available in source form from

NEA library and super cell code developed in INR.

Later DIREN was coupled with WIMS-DRAGON-RELAP. The

DRAGON 3.05E, developed at Montreal Ecole Politechnique by G

Marleau et.al., available in source form in “open source” license, was

used because it allowed obtaining the incremental cross section

directly in one run.

This code can also be applied to other types of thermal reactors.

Actually the first coupled reactor physics and thermal hydraulic with

RELAP5-MOD3 was done for a PWR reactor namely SPERT-III for

which a lot of transient measurements are available. RELAP is

available only as executable, it is developed at Idaho National

Engineering Laboratory, USA.

19


DIREN can be used in standard command line or with a

graphical user interface. Beside execution and printing options that

can be introduced before the execution is started the user can

examine the results as the execution of the code proceeds. Types of

graphics that can be displayed are:

-volume over which the incremental cross sections are added for

a selected device,

-one dimensional flux distribution over a selected direction and

plane the user select,

-two dimensional flux distribution in section xy, xz, yz for a plane

selected by user,

-colors associated with flux values in a selected cut (color map).

20


Auxiliary programs were developed which can be used to:

-generate kinetics parameters from nuclear library data,

-generate xenon parameters based on nuclear data library,

-generate relevant fuel history irradiation results starting from

primary data provided by DIREN

-couple cell codes WIMS and DRAGON to DIREN,

-couple thermal hydraulic code RELAP to DIREN.

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3.Programming features of DIREN

The programming of DIREN and auxiliary programs were done

generally under versions of FORTRAN that were developed for PC’s.

Graphical interfaces were developed under C++ with mixed

FORTRAN/C++ projects. VISUAL BASIC was only used for

irradiation history auxiliary code.

The programming was done based on the following intents:

-Apply programming principles that make source code easier to

follow and debug;

-Keep the data in the memory for the major calculation

processes, especially in the iteration;

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-Build a simple input interface and easier to use for introducing

data (e.g. each type of data have a preceding comment line

describing the type and format);

-Introduce the graphical interface but only for execution and

printing options. The source code was the same as in command line

and this graphic interface can be used optionally;

-Dimensions of variable in “COMMON” could be easily changed

by dimensions only in one file; that file is introduced by INCLUDE in

any routine that has COMMON blocks;

-Coupling was done in a strait forward (but not necessary the

best) way. The interfacing between DIREN and other codes (cell and

thermal hydraulic) was done using text files and small buffer

programs.

23


A buffer small routine is dedicated to a given code (e.g. for

coupling cell code WIMS is used a different routine that for

DRAGON) .

This simple approach to coupling was imposed partly because

some codes are available only in executable form or the changes in

source code were intended to be kept at a minimum.

Thus in DRAGON no intervention in the source was done and

code was used as recommended by authors in the Cygwin interface

to WINDOWS. An attempt was done to port DRAGON to

FORTRAN PC but this gave slightly different results, probably due to

the way some assembler routines that manage memory allocation

were emulated.

24

In WIMSD-B3 only minor modifications were done to write cross

sections and calculate H factors (power over flux ratios) used in flux

normalization to reactor power.

The coupling to RELAP was done using an dedicate buffer

program (BPR) which is run from within DIREN. The data transferred

to BPR are:

-power distribution for all bundles in the core,

-thermal hydraulic map in the core (fuel channels assignment to

each RIH to ROH pass).

Buffer program uses interface text files to transmit data between

DIREN and RELAP.

25

Starting from a specified file and data taken from DIREN, BPR

creates input data file. Then launches RELAP execution and

retrieves data that is expected by DIREN: average fuel temperature,

average coolant temperature and average coolant density.

The data is retrieved from RELAP restart file using STRIP input

card which writes selected data in a file named stripf. Consistency

tests showed that, besides the data built in restart file, RELAP

requires also the temperature distribution is source. Using the above

procedure that values were extracted and written in input data in

source cards for each restart step.

The use of text files to interface DIREN to RELAP does not

create problems because the amount of data transmitted is not very

large.

26


For the single threaded compilers no special problems occurred

when calling cell code and writing interface text files repeatedly,

especially in cell code call for each bundle. With appearance of multi

threading FORTRAN compilers some problems occurred due to

delayed writing of files. Solution found was to check for files

availability in certain conditions.

The number of mesh points used in DIREN core model is

56x56x52. For the usual PC speed of 2.7 Ghz this leads to a 0.05

sec/iteration in two group calculations and at 0.2 sec/iteration for 7

group. A WIMS cell calculation requires around 0.5 seconds. These

values make local parameters calculation with cell calculation for

each bundle possible.

27


4. Code System Verification and Validation

First step in verification was to compare results for basic solution

to the diffusion three dimensional multi group equations using simple

test cases with classic diffusion code CITATION. A comparison was

also made with results of FMDP.

For complex comparison a CANDU specific test problems

proposed in the framework of IAEA contract ( 1996, 1990) were used.

Configuration is a simplified 600 MW PHWR CANDU reactor with

380 horizontal fuel channels surrounded by moderator. A channel

has 12 axial fuel bundles. A limited number of control devices are

between fuel channel and perpendicular to them. The following

neutron absorption devices, typical for this CANDU reactor, are

represented in model: adjuster rods, liquid zone controllers and shut-

off rods.

28


The cell codes WIMSD5-B3, DRAGON3.05b and libraries used

in INR were compared with benchmark problems gathered in IAEA

WLUP project (WIMP Library Update).

Time dependent solution was verified by comparison with test

problems run with CERBERUS. Also results obtained with DRAGON-

DIREN-RELAP were compared with experiments that were

performed to investigate reactivity accidents on SPERT-III (Special

Power Excursion Test).

Results obtained with WIMS-DRAGON-DIREN for a 130 days

operation history of CERNAVODA unit 1 were compared with similar

results with RFSP that Cernavoda made available to us.

DIREN coupling with RELAP was verified by concistency tests

and by comparison with previous results obtained in INR.

29


5.WIMS-DRAGON-DIREN-RELAP Sample Results

The reactor physics code system WIMS-DRAGON-DIREN-

RELAP was used in INR to obtain result similar to those in Design

Manual Reactor Physics.

It was also applied to retrieve relevant data for irradiation history

which are used by fuel performance analysis:

- burn up and power history for selected bundles in the core,

- power and burn up histograms for all bundles in the core at

selected time steps,

-diagrams which shows the number of bundles that are under or

above defect curves.

30


WDD system was also applied to evaluate the impact on the reactor

core of using other types of advanced fuels in CANDU: SEU (up to

1.1 %), RU, MOX and Thorium fuels.

In order to couple WIMS-DRAGON –DIREN to RELAP following

thermal hydraulic models were developed:

-Simple boundary condition from RIH to ROH for steady state

calculations. The components between RIH and ROH (inlet feeder,

inlet end fitting …) were given for each channel using design data.

-2 loops with two passes with all significant components in the

loop. Also in the model are pressurizer, ECCS, Feed and Bleed. The

secondary loop in steam generators are simulated only with

boundary conditions at inlet and outlet from SG. For some types of

accidents the model for secondary loop in SG should be extended.

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-Two loops with two passes but with two flow channels for

each pass.

-Two loops with two passes with 9 flow channels for each

pass. The limitation to 9 passes is imposed by RELAP limits.

Anyway the calculation time increases significantly (by a factor of

approximately 4).

The RELAP models are used both with point kinetics and

coupled with WIMS-DRAGON-DIREN.

In case of space kinetics with DIREN two approximations can

be used: interpolated cross sections and cell calculation at each

bundle.


Tests done on a RIH break both with point kinetics and

3D space kinetics showed good results.

In the near future it is intended to cover, if possible, all the

transients regimes that appear in accident analysis both with

point and space kinetics and compare the results with

previous results obtained previously in INR.

Following slides are samples of graphic DIREN output the

can be obtained during and/or after a run using graphic

interface.


Sample one dimensional flux distribution produced by in line graphic routine in DIREN

34


Sample two dimensional flux distribution produced by in line graphic routine in DIREN at plane 31, xy

35


Sample color map produced by DIREN

36


Evolution of thermal flux shape for a 35 % RIH break

37

T=0. sec, LOCA starts T=0.1sec T=0.2 sec T=0.2914sec, ROP activated

T=0.73 sec T=0.8214 sec , SOR in T=1.1128 sec T=1.5492 sec


38


39


6. Fuel performance codes presently used in INR

A. Normal Reactor Operating Conditions:

The codes simulate thermal and mechanical behavior of a single

fuel element under normal reactor operating conditions.

ROFEM 1B – use a two-dimensional (radial-axial) finite element

approach (starting from original FEMAXI adapted for CANDU);

ELESIM – utilizes a one-dimensional (radial) finite difference

representation;

FEMAXI6 – uses a two-dimensional (radial-axial) finite element

approach (Japanese code adapted to CANDU;

40


ELESTRES-IST 1.0* – contains one-dimensional models of heat

generation rate, temperature distribution, fission-gas release, and

pellet-to-sheath heat transfer. A two-dimensional axi-symmetric

stress-strain analysis is used to compute the stresses and strains

in the pellet and in the sheath.

* Codes that are available in INR-AECL agreement, presently in

renewal process

B. Reactor Accident Conditions:

CAREB – uses to study fuel performance under postulated reactor

accident conditions (LOCA, RIA);

ELOCA* - uses to study fuel performance under postulated reactor

accident conditions (LOCA, RIA);

41


Structural Analyses

ANSYS – Finite element method. Structural analyze of fuel bundle

in normal operating condition.

BUNDLEG – Fuel bundle geometry optimization (developed in

INR)

ROFEM 1B FUEL PERFORMANCE CODE

Main modifications (starting from original basis FEMAXI III):

Microstructure dependent fission gas release;

Temperature dependent grain growth and pellet restructuring;

42


Temperature, porosity and burnup dependence of thermal conductivity;

Burnup dependence of the radial power profile in the fuel pellet;

Pellet to clad heat transfer via solid-solid, gas and radiative components;

Possibility of analyzing CANDU type fuel geometry and operational

conditions.

Verification/Validation

Fuel irradiation experiments performed in TRIGA reactor –Pitesti

PIE performed in INR – Pitesti hot cells;

FUMEX blind code comparison exercise.

43


ROFEM 1B FUEL PERFORMANCE CODE

MAJOR CALCULATIONS

Thermal processes:

Heat transfer between coolant and cladding;

Heat transfer between fuel and cladding;

Heat generation distribution in fuel;

Temperature distribution in cladding;

Fission gas release, inner gas pressure.

44


Fuel mechanics:

Thermal strain;

Elasticity;

Plasticity;

Creep

Cracking and healing;

Initial relocation;

Densification

Swelling

Hot pressing

45

Clad mechanics:

Thermal strain;

Elasticity;

Plasticity;

Creep;

Anisotropy;

Radiation hardening;

Ridging;

Pellet-clad interaction.

Material properties dependent on

temperature, irradiation.


CAREB is a code that calculates the thermal-mechanical behavior of a fuel

elements under transient conditions (LOCA, RIA).

The principal process modeled are:

Transient thermal behavior.

Fuel thermal expansion, cracking and melting.

Stored heat during transient.

Internal gas pressure variation during transient.

Fuel/sheath heat transfer.

Thermal, elastic and plastic sheath deformation (anisotropy).

46


High temperature Zircaloy-4 sheathing creep behavior.

Beryllium assisted crack penetration of the sheath

Clad damage accumulation.

The new version of CAREB code has been compared against

ELOCA code results.

47


48

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100

TIME (s)

PR

ES

SU

RE

(M

Pa

)

37-element:outer element

43-element: inner element

43 element: outer element

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80 90 100

TIME(s)

PR

ES

SU

RE

(M

Pa)

37-element: outer element

43-element: inner element

43-element: outer element

20% RIH INTERNAL GAS PRESSURE. (ELOCA

results)

The comparison of

CAREB predictions to

ELOCA predictions

show a good

agreement between

the codes results.

20% RIH INTERNAL GAS PRESSURE. (CAREB

results)


49

Axial (Z-direction) displacements distribution in RU-43

short fuel bundle end plate (ANSYS results). Single

side-stop case.

ANSYS - Structural analyze of fuel

bundle.

BUNDLEG - CANDU FUEL BUNDLES DESIGN

BUNDLEG code is used to determine a

lots of geometrical fuel bundle variants.

At the end of calculation the designer

could be select the optimal variant.


RELEVANT REFERENCES

J. R. Askew, (1968), “A General Description of the Lattice Code WIMS” J.B.N.E.S., 564

H.C. Chow and M.H.M. Roshd (1980), “SHETAN- A Three Dimensional Integral Transport Code for Reactor Analysis”, AECL-6878, September 1980

M.Constantin et al. ,(1996) “Some Approaches for Improving the Performances of 3D Integral Transport Codes”, in Proceedings of Annual Meeting on

Nucl. Technology, Manheim, Mai 23-25, 1996, p.7

M.Constantin et al, (1995), ” Performances Evaluation of 3D integral transport code:PIJXYZ”, (In Romanian) INR,Pitesti

A. R. Dastur,D.B.Buss (1983) “ MULTICELL A 3-D Program for the Simulation of Reactivity Devices in CANDU Reactors”, AECL-7544

G.M.Frescura and A.L. Wight, (1982), “CANDU-PHW Fuel Management “in “Operational Physics of Power Reactors”, Proceedings of the Training Course

held at Trieste, IAEA-SMR-68/II

E.Lewis, W.F.Miller Jr, (1984) “Computational Methods of Neutron Transport”, Chap.1 John Wiley&Sons,

A. A. Pasanen, (1982), “ Fundamentals of CANDU Nuclear Design” in “Operational Physics of Power Reactors”, Proceedings of the Training Course held

at Trieste, IAEA-SMR-68/II

I.Patrulescu et al.,(1993), ”User’s Manual for 3D diffusion code DIREN”, (In Romanian) Internal Report, INR Pitesti, 1993

Rouben B et al., (1988),“Calculation of 3D Flux Distributions in CANDU Reactors Using Lattice Properties Dependent on Several Local Parameters”,

Nucl. Sci. Eng.,98, 139

51


Simionovici et al (1984), “Developing of a code based on collision probabilities and interface currents” (in Romanian), Institute for Nuclear Research,

Pitesti

X.Warin, (1993), “Methodes deterministes de resolusion de l’equation integrale du transport neutronique” , EDF 94NJ0057

***, (1996), “In-Core Fuel Management Benchmarks for PHWRs”, IAEA-TECDOC-887,June 1996

***, (1990), “Summary Report of First Research Coordination Meeting on In-Core Fuel Management Programs Related to Core of PHWRs”, Buenos Aires,

Argentina, 14-21 December 1990.

"Design Manual-Reactor Physics “ AECL -79-01100-DM-000

K.O. Ott and D.A. Menley, “ Accuracy of the Quasistatic Treatment of Spatial Reactor Kinetics”, Nuclear Science and Engineering 36,402-411,1969

W.H. Reed and K. F. Hansen , “ Alternating Direction Methods for the Reactor Kinetics Equations” ,Nuclear Science and Engineering 41,431-422,1970

J. Devooght and E. Mund, " Generalized Quasi-Static Method for Nuclear Space-Time Kinetics” , Nuclear Science and Engineering 76,10-17,1980

A.R. Dastur and D.B. Buss, " Space-Time Kinetics of CANDU Systems” , AECL Report AECL-5181,1975

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Documents

IAEA Workshop on Advanced Code Suite for Design, Safety …€¦ · · 2012-10-10IAEA Workshop on Advanced Code Suite for Design, Safety Analysis and Operation of Heavy Water Reactors