Advanced Heavy Water Reactor

1.2 ADVANCED COMPUTATIONAL TOOLS FOR subspace based solution techniques. The space-time analysis code
PHYSICS DESIGN simulates the transient, due to the disturbed reactor steady state,

. Space-time Analysis code for AHWR

by numerically solving the time dependent diffusion equations.
The code is coupled with a visualization tool to plot fluxes as a
function of transient time, at any planar cross-section of the
The knowledge of the space and time dependent behaviour of reactor core. It is validated against a HWR benchmark problem,
the neutron flux is important for the reactor safety analysis which simulates power rise due to half-core coolant voiding and
under operational and accidental conditions. subsequent control action. Representative snapshot
flux profiles in two central planar cross-sections when power is
Advanced
A time-dependent diffusion theory code called ARK3 (A at a maximum value, are illustrated.
Heavy Water R eactor Kinetics in 3 -D) is being developed for the
AHWR. The code ARK3 has option to use advanced Krylov The code ARK3 is currently being used to analyze AHWR transients
such as LORA, operational transient with xenon and validation
of reactor physics software in AHWR simulator. This code will be
coupled with the thermal-hydraulic analysis code for studying
the combined effects of neutronic and thermal hydraulic
behaviour.

Anurag Gupta <anurag@barc.gov.in>

. ATES3 – Anisotropic Transport Equation

Solver in 3-D

An accurate prediction of the time dependent multi dimensional

& multi energy group neutron flux at successive time instants, is
one of the main aspects of reactor physics design. There are
primarily two main approaches: deterministic (Sn, Collision
probability) and Stochastic (Monte Carlo). Often, the reactor
core calculations are done with diffusion theory, which is an
approximation of the neutron transport theory, a deterministic
approach. But an exact transport theory treatment is necessary
in several cases such as high leakage reactors, for fluxes at the
boundary and beyond, shielding analysis, verification of the
approximate methods etc.

Recently, a neutron-gamma transport theory code, called ATES3,

has been developed in 3-D Cartesian geometry for steady state
criticality and external source problems. Apart from conventional
methods of solutions, the code makes use of a few advanced
ARK3 estimated flux profile for AECL benchmark Krylov subspace based schemes. The code is written in Fortran-
along central XY and XZ planes of the reactor
90 language and has modular structure. These features make it
core at 0.85 sec when power is at maximum
more understandable and comparatively easier to modify. The

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code ATES3 has been validated against a few international

benchmarks and is being subjected for more rigorous testing.
. Monte Carlo Technique: Code Development
and Reactor Physics Simulation
Figure below gives the material layout and the corresponding
thermal flux shape for an LWR benchmark. The flux dip at the Monte Carlo, as a tool in numerical analysis has gained wide
Control Rod (CR) location can be seen clearly. spread applicability over the past few decades. The advent of
high speed computing machines has been mainly responsible for
As is well known, transport problems are highly memory and the continual development of Monte Carlo method. Used
CPU time intensive problems, a single PC or workstation is not properly, Monte Carlo can give quick “first cuts” at difficult
sufficient. Hence, it is very important to adopt the present code problems, that is problems which are intractable by the
to parallel computers. Efforts are being made to parallelize the traditional analytical or numerical techniques.
code on BARC’s ANUPAM parallel systems. Incorporation of
methods of solutions and user-friendly advanced features like The greatest advantage of the Monte Carlo method is the exact
visualization tools etc. are being incorporated. simulation of the geometry. In deterministic methods only some
special geometry can be simulated exactly, for irregular
geometry some approximations must be considered. Monte Carlo
method does not take any approximations in defining geometry.
For this reason Monte Carlo method is essential for reactor
calculations which involves complicated geometry e.g.
Secondary shutdown system of 500 MWe PHWR, hexagonal
geometry of CHTR, Nuclear Power Pack, Pebble bed reactors etc.
as well as for deep penetration problems.

The main objective is to develop a general geometry Monte Carlo

code with burn up, which will be used for criticality calculations,
safety evaluations, accelerator driven sub-critical system’s
calculations, shielding calculations etc. with greater confidence
and wider flexibility.

Development of Random Number Generator

Random number plays an important role in any Monte Carlo

calculation. The accuracy of the results depends on the
randomness of the random numbers, its uniformity and its cycle
length.

To provide uniform random sequences having larger cycle length

required for Monte Carlo calculations a Random Number
Generator (RNG) with large cycle length (2 57 ) has been
developed using bit manipulation technique. Some of its
properties namely uniformity, Expectation Value, Variance,
Material layout and corresponding thermal flux
profile at a planar cross section of an Frequency distribution, Auto-Correlation, Chi-square test etc.
LWR benchmark core have been performed. It was compared with RANDU of PC in
FORTRAN, RAND of PC in Basic, RAND of Honeywell DPS-8
Anurag Gupta <anurag@barc.gov.in> System and RAN of PDP-11/23 and found to be superior among

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Comparison of Auto correlation coefficient

all in respects to its randomness, cycle length, uniform the deliberate flattening of the power distribution. The study of
distribution etc. Correlation Coefficient of this RNG has been the neutronic transient behaviour under accidental conditions in
compared with that of different RNGs in the Table. It is seen such reactors requires accurate methods of solution of system
that current RNG has been much closer to the expected value of coupled multidimensional multi energy group time
(the correlation coefficient between neighboring bits of dependent neutron diffusion equation. Two distinct approaches
a random sequence is expected to be zero). This RNG is ready exist for this purpose namely; the direct (implicit time
to be used in any code, which requires large cycle of uniform differencing) and Improved Quasistatic (IQS) approach. Both
random sequences. the approaches need solution of static space energy dependent
neutron diffusion equations at successive time steps.

Development of 69-group spherical geometry

A three-dimensional computer code 3D-FAST was developed
Criticality Code
based on Incomplete LU (ILU) preconditioned Biconjugate
Stabilized method. The code was parallelized on ANUPAM
Monte Carlo code for criticality calculation has been developed
distributed memory parallel system. The domain decomposition
for spherical geometry with WIMS 69 group energy
technique was used to create parallelism. The parallel
treatment. This code is being extended for AHWR/ PHWR lattice
cell with WIMS 69 group cross-section data.

Brahmananda Chakraborty <rahma@barc.gov.in>

. Simulations of Reactivity Induced Transients

for Thermal and Fast Reactors and Stability
Studies

An accurate prediction of the consequences of an accident in a

nuclear reactor is vital from the reactor safety point of view. This
in turn requires the solution of coupled time-dependent neutron
diffusion equations, time-dependent heat conduction equations
and single and two phase coolant dynamics equations. All of
these require large computer memory and computational time.
Present day large-sized power reactors are neutronically loosely Neutron Flux Profile
coupled. The looseness of the coupling is further enhanced by

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computational scheme was tested by analyzing a well-known disassembly of the core, which introduces sufficient negative
Canadian PHWR benchmark problem, which simulates a loss of reactivity. The calculation of disassembly reactivity requires the
coolant accident. solution of coupled neutronics and hydrodynamics equations.
A computer code for pre-disassembly calculations, which
The transient was simulated using two energy groups and calculates coolant voiding, fuel melting, fuel and clad
52×52×40 meshes. Twenty-nine space and energy dependent deformation and molten fuel slumping, is being developed.
calculations were done with time step of the order of 0.1 sec. For the disassembly phase a computer code DISA is developed.
Table presents the CPU gain due to parallelization. The code was This solves point kinetics equations coupled with two

CPU times for Parallelised BiCGSTAB[ILU] for IQS Approach (e = 10 –6 )

used to analyze the inadvertent withdrawal of two control rods

along with drainage of light water from the zone controller
units (ZCUs) for 540 MWe PHWR. Figures show the variation of
reactivity and power as a function of time for this transient.

The accident analysis of fast reactors is generally carried

out in two phases. The first phase is generally called as
pre-disassembly phase and the second one as disassembly phase.
In pre-disassembly phase, the transient is analyzed up to coolant
voiding and fuel melting. The disassembly phase calculations are
carried out with reactivity rates estimated from coolant voiding
and fuel slumping. These transients are terminated by the

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code by replacing the point kinetics

calculations by multidimensional,
multi energy group neutron diffusion
code 3D-FAST. It is also planned to
couple both phase calculations.

New concepts have emerged in the

dynamics of nonlinear systems in last
t w o d e c a d e s . A s p a r t of our
nonlinear studies in reactor physics
we have studied some of these issues
for a typical PWR. Here the dynamics
refer to a single-phase coolant using
point kinetics and a feedback
through fuel & coolant temperature
coefficient of reactivity. Typical
scenario of limit cycle reactor
operation were observed as a
function of coolant temperature
coefficient. The temporal behaviors
can be identified for certain values
of this parameter.

dimensional hydrodynamics equations. Figures show the For a specific value of coolant temperature coefficient the critical
equation of state for fuel used in DISA. The variation of net state becomes an oscillatory state [limit cycle]. This latter state
reactivity and power as function of time for a hypothetical constitutes a new operational regime for reactor dynamics. These
transient in a typical fast reactor are shown in figures. It is studies contribute towards understanding safety and
planned to improve the neutronics model of pre-disassembly performance of reactors.

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using Microsoft Visual C++. It is also possible for the WIMS-D

library users to compare the energy dependence of cross section
data of various nuclides, different WIMS-D libraries and different
temperatures.

The first version of this software ‘XnWlup1.0’ helps to obtain

the histogram plots of the values of cross section data of an
element/isotope as a function of energy. The second version of
this software ‘XnWlup2.0’ is serving as an exhaustive equivalent
handbook of WIMS-D cross section libraries for thermal reactor
applications and used for comparing different WIMS-D
compatible nuclear data libraries originating from various
countries. The next version of this software ‘XnWlup3.0’ was
developed to plot the cross sections of a resonant nuclide using
resonance integral tabulated data of WIMS-D library for the
given background dilution cross section and temperature. Also
the revised software ‘XnWlup3.0’ is now capable of plotting
either the resonance integral data as a function of dilution cross
section for a selected temperature grid point or as a function of
temperature for a selected dilution cross section grid point for
a given resonance energy group.

H.P. Gupta <hpgupta@barc.gov.in>

<hpgupta@barc.gov.in>

. ‘XnWlup’ Software for Reactor Physics

Applications

As a result of the IAEA coordinated research program entitled

“Final Stage of the WIMS library Update Project” new and updated
WIMS-D libraries are generated by processing evaluated nuclear
data files such as ENDF/VI.6, JENDL-3.2 and JEF-2.2. These
WIMS-D libraries provide knowledge about the various relevant
neutron-nuclear cross sections data in the form of 69/172 neutron
energy groups. In order to help the WIMS-D library users to
quickly view the plots of the energy dependence of the multi-
group cross sections of any nuclide of interest, a computer
program ‘XnWlup’ is developed for MS-Win operating system

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Illustration of plots of absorption resonance integral data of 232 Th at 600 K and for various
background dilution cross sections

T. K. Thiyagarajan <thiyag@barc.gov.in>
<thiyag@barc.gov.in>

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