OECD NEA PBMR Paris, June 2005 1

THE KIKO3D AND THE COUPLED KIKO3D-ATHLET CODE,

GENERAL FEATURES AND VALIDATION

András Keresztúri, Gy. HegyiKFKI Atomic Energy Research InstituteH-1525 Budapest 114, POB 49, Hungary

OECD NEA PBMR-N/TH Benchmark meetingParis

June 16-17, 2005.

OECD NEA PBMR Paris, June 2005 2

Contents

The purpose and applications of the KIKO3D (and the coupled KIKO3D-ATHLET code)

Review of the models keeping in view: which models with which modifications (data and methods) can be applied, which models and data are missing for the PMBR application, how to supplement it.All neutronic and thermohyraulic models (except ATHLET) were developed in in AEKI.

Review of the validation process

OECD NEA PBMR Paris, June 2005 3

The KIKO3D dynamic code, purpose and applications

•A three-dimensional reactor dynamics program for coupled neutron kinetics and thermohydraulicscalculation of VVER type pressurized reactor cores.•Main applications: asymmetric accidents; control rod ejection, start-up of inoperable loop with lower boron concentration or temperature, single control rod withdrawal, steam line break, boron slug entering the core at shut down state•Safety analyses for licensing of fuel modernization at Paks NPP•Application in the CORYS real time simulator for normal operational transients•The pool type research reactor version (plate fuel, uranium-dioxide particles in aluminium matrix, atmospheric pressure) is being developed.

OECD NEA PBMR Paris, June 2005 4

The neutron kinetics model of KIKO3D (1):

• 2 energy groups• The nodes are the fuel assemblies subdivided by axial

layers, hexagonal and rectangular geometries

R-z geometry can not be calculated, hexagonal geometry can beapplied, 1/12 symmetry can be used in the „2D cases”.

According to the validation, large core (7 * 7 * 7 m) with largenode size can also be used, see HWR problem.

• The unknowns are the scalar flux integrals on the reactor node interfaces.

• The scalar flux and net current integrals are continuous on the node interfaces.

OECD NEA PBMR Paris, June 2005 5

The neutron kinetics model of KIKO3D (2):

• Analytical solutions of the diffusion equation inside the nodes.The anysotrpoic diffusion coefficient can be easily built in. The two-group constants are parameterized according to the feed-back parameters. The derivatives are also continuous.

• Generalized response matrices of the time dependent problem; time dependent nodal equations.

• IQS (Improved Quasi Static) factorization; shape function equations point kinetic equations.

The shape function module (set of subroutines) solves the timedependent diffusion equation with given source, it can beapplied for solving the heat conductance equation over thecore.

• The absorbers and reflector are represented by pre-calculated albedo matrices depending on several parameters.

OECD NEA PBMR Paris, June 2005 6

The thermohydraulic model of KIKO3D:

• Separate axial hydraulic channels, each of them relates to one fuel assembly

• Conservation equations of mass, energy and momentum are solved for the mixture of liquid and vapor phases (3 equations)

• Heat transfer calculation in the fuel with several radial meshes for an average representative fuel rod in each node

• The release of prompt and delayed nuclear heat in the fuel is modeled

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The main modules, and connections between them (1)

1. Neutronic model based on IQS (Impose Quasi Static method: factorization)•Shape function calculation in (macro time steps)•Amplitude function calculation (micro time step)•Precursor density distribution calculation•Thermal power generation from the (prompt and decay heat)•Xenon and Samarium evolution (macro), microscopic cross sections are necessary •Cross section generation (micro)•Response matrix calculation (micro)

2. Fuel temperature calculation in 1D cylindrical and slab geometries(micro time steps)

Input: coolant temperature, heat transfer coefficients from the hydraulic module, thermal power, heat conductance, heat capacity dataOutput: heat transferred to the coolant, cladding temperature

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The main modules, and connections between them (2)

2. Hydraulic model: parallel channels with equivalent pressure drop without mixing, three equations for the „mixture”

Input: Inlet flow, outlet pressure, heat transferred to the coolant, flow area, friction coefficient (correlations for the pressure drop), coolant property data, correlation data for the heat transfer coefficient, cladding temperature for the heat transfer coefficientOutput: temperature, pressure distribution, heat transfer coefficient for the for the fuel heat conductivity model

MISSING: Modeling the heat transfer between the touching spheres and structural materials, radiation heat transferThe shape function module, which solves the diffusion equation with given source, could be used for this purpose.

OECD NEA PBMR Paris, June 2005 9

The ATHLET system thermohydraulic code:

• Developed and verified by GRS

• Small and intermediate leaks as well as large breaks in PWRs and BWRs

• A two-fluid, 6-equation model, with completely separated equations for mass, energy and momentum for both phases, taking into account also non-condensables is included in the last release version

• In our calculations the 1.2A version is used with the option of 5 equations

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Two possibilities coupling methods of KIKO3D toATHLET

Internal coupling:ATHLET models completely the thermal-hydraulicsin the primary circuit including the core region.ATHLET obtains the heat source from the decayheat model of KIKO3D. The fuel and moderatortemperatures, moderator densities, boronconcentrations necessary for the feedback in KIKO3D originate from the ATHLET program.Parallel coupling: KIKO3D obtains inlet flow rate, enthalpy, boronconcentration distribution and outlet pressure fromATHLET. ATHLET performs calculations in thecore too.

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SG

CORENeutronKinetics

& ThermalHydraulics

Pout

G , T , , cin in B inr in

G , T , , cout out out B outr

External Coupling

SGCORE

ThermalHydraulics

CORENeutronKinetics

& ThermalHydraulics

Pout

G , T , , cin in B inr in

Parallel Coupling

q

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SubSub--channelchannel CoreCore SystemSystemanalysisanalysis Neutron KineticsNeutron Kinetics ThermalThermal--hydraulicshydraulics

Tf (r) , Tm (r)rm (r), cB(r)

Coupled KIKO3D-ATHLET and TRABCO hot channel

calculations taking into account the 3D effects in the reactor protection

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Validation of the KIKO3D code (1):

1. LMW (Langenbuch-Maurer-Werner) rectangular problem: normal operational transient in a pressurized water reactor. The slow variation of the reactivity and the power is induced by the motion of two absorber groups moving in opposite directions.

2. HWR (Heavy Water Reactor) problem: initiated by a hydraulical event, in a CANDU type reactor. The maximum value of the reactivity is near to 1$, and the transient is shutdown by scram. Very large size both of the reactor core (780*780*800) cm and the nodes, asymmetric nature of the perturbations.

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Comparison of Average Power in the HWR Test Problem

Comparison of Thermal Flux Shapes in X Direction Belonging to t=0.0 s and t=0.9 s in the HWR Test Problem

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Validation of the KIKO3D code (2):

3. AER-1 benchmark problem: Asymmetric CRE problem at low power, without feedback. The inserted reactivity is just below 1 $.4. AER-2 benchmark problem: Asymmetric CRE problem starting from low power, with fuel temperature feedback. The inserted reactivity is 2 $.5. AER-3 benchmark problem: Asymmetric CRE problem starting from low power with realistic thermohydraulic feed-back. The inserted reactivity is 2 $.6. AER-4 benchmark problem: Boron dilution transient.7. SCRAM measurements of NPP Paks

OECD NEA PBMR Paris, June 2005 16

Comparison of Nuclear Power in the AER-2 Benchmark

Comparison of Maximum Fuel Temperatures in the AER-2 Benchmark

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Comparison of Maximum Node-Wise Fuel Center-Line Temperatures in Core Calculation and in the Hot Channel Calculation Belonging to Kx=1.25 Excess Power Peaking Factor. AER-3 Benchmark

Comparison of Axial Power Density Distributions in the Hottest Assembly at t=0.4 s and t=1.5 s in the AER-3 Benchmark

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Validation of the coupled ATHLET-KIKO3D code:

7. AER-5 benchmark problem: Symmetric main stem header break

8. Turbine load drop measured at Loviisa NPP (SRR1/95 PHARE project)

9. AER-6 benchmark problem: Asymmetric steam line break

10. MCP trip of NPP Paks

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5. DYNAMIC AER BENCHMARK

0 100 200 300 400 Time [s]

-2000

-1500

-1000

-500

0

500

1000

Reac

tivity

[pcm

]

DYN3D/ATHLETDYN3D/ATHLET (Rez)KIKO3D/ATHLET

Results of the AER-5 (main steam header rupture) benchmark

5. DYNAMIC AER BENCHMARK

0 100 200 300 400 Time [s]

-2000

-1500

-1000

-500

0

500

1000

Reac

tivity

[pcm

]

DYN3D/ATHLETDYN3D/ATHLET (Rez)KIKO3D/ATHLET

Results of the AER-5 (main steam header rupture) benchmark

OECD NEA PBMR Paris, June 2005 20

Conclusions

Using the same thermal hydraulic model by each participant can lead to misleading conclusions.

The modeling of the heat transfer between the touching an radiating spheres can be a sensitive point.

Modification of the KIKO3D code, providing with data is a considerable work (2 man month ?), but it should be done.