coupling the athlet3.0 and the kiko3dmg multigroup 3d ... · and abnormal plant transients, small...
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404.1
Coupling the ATHLET3.0 and the KIKO3DMG multigroup 3D kinetic code developed for the fast spectrum Gen4 reactors
György Hegyi
Centre for Energy Research, Hungarian Academy of Sciences
Konkoly Thege Miklós út 29-33
H-1121, Budapest, Hungary
András Keresztúri, István Pataki, ÁdámTóta
Centre for Energy Research, Hungarian Academy of Sciences
Konkoly Thege Miklós út 29-33
H-1121, Budapest, Hungary
{andras.KERESZTURI; istvan.PATAKI; adam.TOTA}@energia.mta.hu
Kiril Velkov, Ihor Pasichnyk, Yann Perin
Gesellschaft für Anlagen- und Reaktorsicherheit (GRS) mbH
D-85748 Garching, Germany
{kiril.velkov; ihor.pasichnyk; yann.perin}@grs.de
ABSTRACT
Coupled code technique is mandatory for the analysis of transient events when effective
coupling between the core neutronics and the primary circuit thermal-hydraulics exists. The
design and analysis of Generation IV reactors should be conducted by utilizing appropriate
couplings similarly to the present PWRs and BWRs. Several developments of the thermal
hydraulic system and 3D reactor kinetic codes are going on. Presently, their coupling is still
one of the most current tasks to be solved for performing safety analyses for innovative
reactor concepts.
This paper reviews the development of a coupled neutronic/thermal-hydraulic code
system based on the new version of ATHLET (version3.0) thermo-hydraulic system code and
the three-dimensional multi-group KIKO3DMG nodal kinetic code designed for fast spectrum
reactor analyses. The first application of the coupled code system is presented based on the
solution of a special extension of the Sodium Fast Reactor OECD NEA benchmark [1-2]. The
multi-group cross sections were generated by the ECCO module of the ERANOS code system
at the subassembly level. The 3D-Thermohydraulics of the core is described with a parallel
channel approximation.
1 INTRODUCTION
The Generation IV reactors are in the early planning stages throughout the world.
Among others, they have advantages in the utilization of uranium resources and a low
production of radioactive waste. However, these new concepts should show an increased level
of inherent safety over current reactor designs. The work in these areas involves development,
coupling, qualification and application of reactor analysis tools and should focus on
integration of advanced reactor design and safety analysis physics methodologies. Special
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
emphasis must be put on the development of computer codes for coupled space-time
kinetic/thermal–hydraulic system modeling, which are the basis of high fidelity multiphysics
and multi-scale simulations. The application of such method is mandatory for the analysis of
transient events when coupling between the core neutronics and the primary circuit thermal-
hydraulics is strong, and more especially when asymmetrical processes take place in the core
leading to local space-dependent power generation. The study is followed by a typical
application through which the main features and limitations of this technique are discussed.
The coupling scheme follows the traditional approach of loose coupling where the
information exchange is performed via shared memory. The implementation is sufficiently
generic, such that any type of reactor, which can be handled by the involved codes, can be
simulated. In section 2, the brief description of the involved codes and the methodology of the
coupling are explained. The testing of the coupled code system is the object of section 3, also
describing the cross section handling. Finally, some first applications are shown.
2 MAIN FEATURES OF THE STAND ALONE CODES
The former version of the ATHLET thermo-hydraulic system code and KIKO3D kinetic
code were originally developed for the analysis of Light Water Reactor systems. Their
coupled version was validated within the frame of benchmarks and experiments in the last 15
years [3-4]. Recently it was efficiently used for the SCRW reactors, too [5]. Currently both
codes are being extended to the purposes of the new challenges.
2.1 ATHLET
The ATHLET (Analysis of Thermal-hydraulics of Leaks and Transients) [6] is a well
validated thermal-hydraulic computer code developed by the Gesellschaft fur Anlagen- und
Reaktorsicherheit (GRS). It has a wide range of applications for the analysis of anticipated
and abnormal plant transients, small and intermediate leaks as well as large breaks in PWRs
and BWRs. ATHLET offers the possibility of choosing between different models for the
simulation of fluid-dynamics.
The code structure is highly modular, and allows an easy implementation of different
physical models. The code is composed of several basic modules for the calculation of the
different phenomena involved in the operation of a reactor:
Thermo-fluid dynamics (TFD)
Heat Transfer and Heat Conduction (HECU)
Neutron Kinetics (NEUKIN)
General Control Simulation Module (GCSM),
Numerical integration method (FEBE)
The latest version (ATHLET 3.0) system code is further developed and adapted to
account for new, various working fluids, such as: Light/Heavy water (H2O/D2O); Helium
(He); Liquid lead (Pb); Liquid lead-bismuth (LBE); Liquid sodium (Na). Both the
thermodynamic and transport properties of these new working fluids were validated [6].
ATHLET provides a modular network approach for the representation of a thermal-
hydraulic system. The GRS methodology is developed for pseudo 3D TH description of the
core with a parallel channel approximation and mapping schemes fitted to the 3D
neutronically simulated active core. A large number of benchmarks have been very
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
successfully solved with the coupled system code and many analyses have been performed for
NPPs with different reactors.
2.2 Coupling of ATHLET with 3D-Core Module
Three types of coupling can be applied to describe the thermal-hydraulic and neutron-
physic processes of the core depending on the codes and the purposes of application:
Internal coupling: coupling of the 3D kinetic model to the system code that models
completely the thermal-hydraulics in the primary circuit including the core region.
External coupling: coupling of the 3D reactor core models describing neutronics and
thermal-hydraulics in the core region to the system code that models only the thermal-
hydraulics in the primary circuit except the core region.
Parallel coupling: the same as above, but the system code models completely the
thermal-hydraulics in the primary circuit including the core region, too. In that case
the 3D reactor model passes only the calculated power to the system code.
The system code ATHLET has an universal interface to 3D nuclear codes with the
following functions:
reading input for neutronics model,
controlling static solutions with iterations between thermal fluid dynamics and
neutronics,
controlling transient calculations with different time-step size in the thermal-fluid
dynamics and neutronics,
interpolation of the transferred data in case of different axial nodalization schemes
of the codes.
It is supposed that the neutronics code is adjusted to these main tasks, corresponding to
the general code structure. The interface is composed of three levels. The first level only
consists of general calls from ATHLET for main program functions to the interface. In this
layer all program control is performed by ATHLET. The second level consists of subroutine
calls for the interface subroutines of the neutronics models. In this level it is be decided which
neutronics model will be used. The third level is specific for each neutronics model.
The assignment of the fuel assemblies of the core loading to the flow channels is
defined by input through a mapping scheme. That allows flexibility by grouping of several
fuel assemblies into one channel or by a 1 to 1 representation. Also the axial mesh width in
neutronics and thermal hydraulics calculations may be different.
2.3 KIKO3DMG
The KIKO3D code was developed about 15 years ago [7-8] and its nodal method
modernization is going on for three years. Meanwhile the multigroup capability was also
developed and the new code is called KIKO3DMG [9]. Both codes are using a special
response matrix method for solving not only the steady state but also the time dependent
diffusion equation. Two specific additional response matrices are used for the kinetics. The
neutron kinetics model solves the diffusion equations in homogenized fuel assembly
geometry by a sophisticated nodal method. The common basic theoretical assumptions of the
old and new version of the code family are given in [8].
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In the advanced version – KIKO3DMG - the basic theoretical assumptions of the older
version were kept, but the following developments have been elaborated, which need for
calculating fast spectrum:
Arbitrary number of energy groups can be used.
Possibility of the up-scattering. (More than one thermal group applied, more
accurate calculations of the thermal reactors in the vicinity of the reflector.)
Optimized iterations for multi-thread processing.
Graphical output for radial distributions (flux, temperature, power distributions, etc).
Hexagonal geometry input can be cut into triangular pieces in an automated way.
The hexagonal output can be synthesized from the triangular results.
Dynamic reactivity a lied in the „ int kinetics” in the Improved Quasi Static
(IQS) method – derived from the factorization in an exact way.
This latter capability is achieved by using the following formulae:
( ) ⟨ ( ( ) ( ) ( )) ( )⟩
⟨ ( ) ( )⟩ (1)
where:
: Weight function: time independent adjoint static flux
( ): Scalar group flux
( ): Net current balance response matrix for the whole reactor
( ): Neutron production rate response matrix, for the whole reactor
The partial derivatives can be deducted from eq. 1 and finally the dynamic reactivity
coefficients taking into account the temperature profile changes are as follows:
(
( ))
∑⟨
( ) ( ( ) ( ) ( )) ( ) ⟩
⟨ ( ) ( ) ⟩ ( )
(2)
( )
∑ ( )
(3)
( ) ∫ (
( ))
( )
(4)
(
( ))
∑⟨
( ) ( ( ) ( ) ( )) ( ) ⟩
⟨ ( ) ( ) ⟩ ( )
( )
(5)
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
( )
∑ ( )
(6)
( ) ∫ ( )
(
( ))
(7)
( ) ( ) ( ) ( ) (8)
The group constants necessary for KIKO3DMG can be generated by using several
codes (ERANOS ECCO used at our institute (MTA EK), HELIOS and SCALE used in GRS).
3 CALCULATION WITH THE COUPLED ATHLET-KIKO3DMG CODE
SYSTEM
The basis of the demonstration of the correct coupling was the calculation of the large
oxide fuelled sodium cooled core defined as a fast reactor benchmark [1, 2] in the OECD
NEA cooperation. Starting from this stationary state, some “transients” were calculated with
the coupled code system. The OECD NEA benchmark which is aiming at the calculations of
four generation-IV advanced sodium cooled fast reactor conceptions, was defined by the
Working Party on Reactor and System, Expert Group on Reactor Physics and Advanced
Nuclear Systems at OECD/NEA. Our preliminary calculations have been presented [10] in
the framework of this cooperation. It includes the determination of the most important
neutronic characteristics (e.g. effective multiplication factor, reactivity feedback coefficients),
control rod worth and breeding ratio of the four core conceptions. The calculations were
erf r ed using the ERANO c de ackage’s ECCO dule and the stand alone
KIKO3DMG nodal multi-group diffusion code.
3.1 Input data set
In this paper, one of the cores of the benchmark specification, namely the large oxide
one was analyzed with the ATHLET – KIKO3DMG coupled code system by extending the
benchmark exercises with the dynamic process of Control Rod Withdrawal.
The thermal power of the reactor is 3600 MW (MWth) and it is loaded with MOX fuel.
The geometry and material data of the core are defined. The radial core layout is presented in
Fig. 1 (right). The oxide core is designed to be self-breeding without a fertile blanket. As the
burnup of the assemblies depends on their locations in the core, two fuel composition sets are
defined: one for the inner- and another for the outer part of the core. The fuel isotope densities
were given for the beginning of the equilibrium cycle. The fuel bundles are placed into
hexagonal wrapper tubes in a triangular arrangement. The outermost fuel pin ring of the fuel
assemblies consist of 13 pins at all sides. All fuel pins are surrounded with helical wire
spacers, the gap between the pellets and the cladding is filled with helium. In the ECCO
model, wire spacers are smeared into the cladding. The oxide fuel pins contain a central hole,
which is filled with helium. The fuel pellets are vertically surrounded with an axial reflector
and a gas plenum. The control rods of the primary and secondary control assemblies are filled
with natural and enriched boron carbide pins. The axial reflectors contain pins filled with steel
pellets.
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Figure 1: ATHLET open core (without primary loop) model (left) and the radial core map
(right)
The ECCO computations were performed by using 1968 energy groups. Two
dimensional axial layers of the fuel subassemblies were calculated with the collision
probability method for the multi-group cross section generation. Homogeneous mixtures of
the materials and one-dimensional geometry were utilized in case of the non-fissile
subassembly calculations. The multi-group cross sections of the radial reflectors were
computed with a model, when the reactor core was represented by concentric cylindrical
layers.
The subassembly cross sections were used as inputs for the KIKO3DMG nodal multi-
group diffusion code, which performed the core and burnup calculations.
The results made by the stand alone KIKO3DMG code at different burnup and control
rod positions by using different set of cross sections are detailed in [10]. At BOC state with
different control rod positions the calculation was repeated with the coupled code system.
From Table 1 one can see that rather similar results are obtained by the different codes.
Table 1: Comparison of the eigenvalue of different calculations
primary, secondary & mov.
CR positions (see fig. 1.)
Calculated eigenvalue keff[-]
Stand-alone KIKO3DMG ATHLET-KIKO3DMG
140 cm, 140 cm, 140 cm 0.943327 0.942702
140 cm, 140 cm, 220 cm 0.944070
220 cm, 160 cm 0.988060 0.987623
220 cm, 170 cm 0.991172
3.2 Control rod withdrawal
Two types of calculation have been performed with the coupled code ATHLET-
KIKO3DMG using the same initial core loading and nodalisation but the control rod (CR)
position and the time steps were different, the speed of CR was v=2.0 mm/s in both cases,
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
which is the recommended value. Results of this coupled code calculations are used for
testing.
In the first case the control rods from the second ring were withdrawn starting from the
initial position of 160 cm to 170 cm (see fig. 1.). The reactivity insertion equals 317.8 pcm
during the 50 s long transient. The maximum time step was 0.05 s. As a consequence of the
transient a rather large reactor power increase is observed at the beginning and after about 53
sec a decrease of power takes place (Fig. 2.). This power history is a result of fuel
temperature (Fig. 5.) and coolant density (Fig. 4.) change. The excess reactivity is detailed on
Fig. 2. Dynamic and the traditional reactivity of fuel temperature and coolant density as a
function of time can be seen in Fig. 6 and 7.
In the second case one rod from the inner ring was withdrawn from 140 cm to 220 cm.
The reactivity insertion is 83.4 pcm during the 400 s long transient. The maximum time step
was 0.1 s. The consequence of the transient is a milder (max. rel. kq=1.8) but very asymmetric
reactor power increase. The nominal power practically does not change after stopping the
withdrawal (Fig. 8.). The change of fuel temperature and the density during the transient can
be seen on Fig. 10. and 11. The excess reactivity is detailed on Fig. 9. Dynamic and the
traditional reactivity of fuel temperature and density as a function of time can be seen on Fig.
12 and 13.
The assessment of the results calculated with the coupled code system has confirmed
that the applied procedures for exchange of data between neutron kinetics, thermofluid-
dynamics and heat conduction and also the time synchronization procedure provide a stable
convergence of the stationary calculations and gives plausible results by simulating different
transients in a 3-D multi-channel core representation cases.
4 SUMMARY AND OUTLOOK
A new coupled code, based on the ATHLET Mod 3.0 Cycle A thermo-hydraulic system
code and the new 3 dimensional multi-group KIKO3DMG reactor kinetic code was developed
with the goal to enable modeling of fast spectrum Gen4 reactors. It has been successfully used
in the calculation of the large oxide fuelled sodium cooled fast reactor benchmark defined in
the OECD NEA WPRS SFR cooperation. The obtained steady state k-eff value of the initial
state was reasonably close to the benchmark value defined without feedbacks by supposing a
constant average temperature of the fuel and the coolant. Starting from this core stationary
state tw “transients” were modeled and calculated with the goal to verify the coupling. The
time dependent behavior of the obtained power, reactivity and temperatures showed that the
thermal and the neutronic processes are influencing each other in the expected, reasonable
way.
The group constants necessary for the KIKO3DMG can be generated by using several
codes (ERANOS was used at the MTA EK, HELIOS and SCALE were used at the GRS) and
by applying different methods. The influence of the different methodologies can be studied in
one code by avoiding the influence of other effects. For the steady state, calculated values of
the main safety related neutronic parameters like Doppler, void coefficients and control rod
worth can be compared. The influence of the different reactor physic methods can be
investigated not only for the steady state but also for the transient behavior. Different
transport methods of the assembly homogenization, heterogeneous or homogeneous
modeling, delayed neutron data, cross section data, number of energy groups in the core
analysis can be mentioned as examples in this respect. Reflector modeling can also play an
important role. Additionally, in the future, the comparative analysis of the three most
important reactor concepts (sodium, lead, gas) could be investigated.
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
Fig. 2. Relative/total power during the
symmetrical CR withdrawal
Fig. 3. Dynamic reactivity as a function of
time during the symmetrical CR withdrawal
Fig. 4. Average density during the
symmetrical CR withdrawal
Fig. 5. Average fuel temperature during the
symmetrical CR withdrawal
Fig. 6. Intercomparison of dynamic and
traditional density reactivity coefficient
history during the symmetrical CR
withdrawal
Fig. 7. Intercomparison of dynamic and
traditional temp. reactivity coefficient history
during the symmetrical CR withdrawal
3600
4100
4600
5100
5600
6100
6600
7100
7600
1.0
1.2
1.4
1.6
1.8
2.0
2.2
0 20 40 60
tota
l po
we
r (M
W)
rel.
po
we
r
Time (s)
-0.004
-0.003
-0.002
-0.001
-1E-17
0.001
0.002
0.003
0.004
0 20 40 60
r (
reac
tivi
ty)
Time (s)
Inserted reactivity from the static CR worth
Inserted reactivity from the balance
Coolant density contribution
Dynamic reactivity
Fuel temperature contribution
0.834
0.835
0.836
0.837
0.838
0.839
0.840
0.841
0 20 40 60
de
nsi
ty (
g/cm
3 )
Time (s)
Average coolant density
1400
1500
1600
1700
1800
1900
2000
2100
2200
2300
0 20 40 60
Tem
pe
ratu
re (K
)
Time (s)
Average fuel temperature
-0.095
-0.093
-0.091
-0.089
-0.087
-0.085
-0.083
-0.081
-0.079
-0.077
-0.075
0 20 40 60
ar
c (c
m3 /
g)
Time (s)
Traditional coolant density coefficient
Dynamic coolant density reactivity coefficient
-5.8E-06
-5.6E-06
-5.4E-06
-5.2E-06
-5.0E-06
-4.8E-06
-4.6E-06
-4.4E-06
-4.2E-06
-4.0E-06
0 20 40 60
aTf
(1
/°C
)
Time (s)
Traditional fuel temperature reactivity coeffitient
Dynamic fuel temperature reactivity coefficient
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Fig. 8. Relative/total power during the
asymmetrical CR withdrawal
Fig. 9. Dynamic reactivity evolution and its
components during the asymmetrical CR
withdrawal
Fig. 10. Average density history during the
asymmetrical CR withdrawal
Fig. 11. Average Doppler temperature history
during the asymmetrical CR withdrawal
Fig. 12. Intercomparison of dynamic and
traditional density reactivity coefficient
evolution during the asymmetrical CR
withdrawal
Fig. 13. Intercomparison of dynamic and
traditional temp. reactivity coefficient history
during the asymmetrical CR withdrawal
3600
3700
3800
3900
4000
4100
4200
4300
4400
4500
1.00
1.05
1.10
1.15
1.20
1.25
0 100 200 300 400
tota
l po
we
r (M
W)
rel.
po
we
r
Time (s)
-1.3E-03
-8.0E-04
-3.0E-04
2.0E-04
7.0E-04
1.2E-03
0 100 200 300 400
r (
reac
tivi
ty)
Time (s)
Inserted reactivity from the static CR worthInserterd reactivity from the balanceCoolant density contriburionDynamic reactivityFuel temperature contribution
0.8388
0.8390
0.8392
0.8394
0.8396
0.8398
0.8400
0.8402
0.8404
0 100 200 300 400
de
nsi
ty (
g/cm
3 )
Time (s)
Average coolant density
1400
1460
1520
1580
1640
1700
1760
0 100 200 300 400
Tem
pe
ratu
re (K
)
Time (s)
Average fuel temperature
-0.080
-0.075
-0.070
-0.065
-0.060
0 100 200 300 400
ar
c (c
m3 /
g)
Time (s)
Traditional coolant density reactivity coefficient
Dynamic coolant density reactivity coefficient
-5.5E-06
-5.3E-06
-5.1E-06
-4.9E-06
-4.7E-06
-4.5E-06
-4.3E-06
-4.1E-06
0 100 200 300 400
aTf
(1
/°C
)
Time (s)
Traditional fuel temperature reactivity coefficient
Dynamic fuel temperature reactivity coefficient
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Proceedings of the International Conference Nuclear Energy for New Europe rt r l enia e te er 11, 2014
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