Coupling the ATHLET3.0 and the KIKO3DMG multigroup 3D ... · and abnormal plant transients, small and intermediate leaks as well as large breaks in PWRs and BWRs. ATHLET offers the

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

[email protected]

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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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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( )

∑ ( )

(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.

404.6


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,

404.7


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.

404.8


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


Fig. 5. Average fuel temperature during the


Fig. 6. Intercomparison of dynamic and

traditional density reactivity coefficient

history during the symmetrical CR

withdrawal


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

404.9


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


traditional density reactivity coefficient

evolution during the asymmetrical CR

withdrawal


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

404.10


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[3] Gy. Hegyi G. H rdósy A. Keresztúri Cs. Maráczy I. anka M. Tel isz I. Tr sztel,

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Documents

Coupling the ATHLET3.0 and the KIKO3DMG multigroup 3D ... · and abnormal plant transients, small and intermediate leaks as well as large breaks in PWRs and BWRs. ATHLET offers the