Reactor core design for VVER-440 reactors

Own developed codes like KARATE, KIKO3D and FUROM codes are used widely for the core design and safety investigations of the four VVER-440 units of Paks NPP.

KARATE-440 has been elaborated to calculate VVER reactor cores by a coupled neutron physical-thermal hydraulics model. The main goal of the calculation is core reload design, however, certain safety problems amenable to a static code can be analyzed by KARATE. Accordingly, stationary neutron physics and thermal hydraulics models have been implemented. These models are capable of following burnup and Xenon processes but do not allow for calculating faster transients demanded in a safety analysis. The program serves economic core reload design so that the limitations demanded by the safety analysis should be observed. The reload limitations demanded by the safety analysis are also available from the calculations.

KARATE-440 involves all the libraries and computer programs which are needed to perform fuel cycle calculations and fuel cycle design. The intra assembly power distribution is also determined. The libraries need refreshment if a new fuel type is being used or if the parameter range of an existing fuel is being extended. The calculation is grouped into 3 levels. A level is connected to the higher one through parameterized data libraries. These libraries provide a part of the input data for the higher level. A level is connected to the lower one also, usually boundary condition is provided for a “Lupe”-like calculation. The levels involved in KARATE include:

  • cell level to provide a cell library
  • assembly level to provide homogenized assembly library and to calculate pin powers in selected assemblies
  • global level to determine criticality parameters and power distributions.

Major modules of the three levels are

  • GLOBUS (neutronics), THMOD (thermal hydraulics) on the global level
  • SADR  (neutronics and thermal hydraulics) on the assembly level
  • BETTY (asymptotic neutronics), MULTICELL and COLA (non-asymptotic neutronics) on the cell level.

Input to KARATE are the ENDF/B-VI nuclear data library, engineering data (geometry, core composition etc.).  A typical output comprises the critical boron concentration, power distribution in the core, reaction rate distributions in selected assemblies.

KIKO3D is a coarse-mesh 3D nodal code applied for modelling the fast dynamic behaviour of the reactor core. The nodes are the hexagonal or rectangular fuel assemblies subdivided into axial layers. The neutron kinetics model of KIKO3D solves the two-group diffusion equations in a homogenised fuel assembly geometry using a sophisticated nodal method. A newer version KIKO3DMG was developed for the Gen4 fast spectrum reactors with arbitrary number of the energy groups. Special generalised response matrices of the time-dependent problem are introduced. The unknowns are the scalar flux integrals on the node boundaries. The time-dependent nodal equations are solved using the improved quasi-static (IQS) factorisation method. The code is coupled to the system thermal hydraulic code ATHLET developed by GRS.

To predict the quasi-stationary behaviour and the temperature profile of the nuclear fuel rods during the reactor operation before the transient, the FUROM code is applied. In the code, the majority of the models that simulate the individual physical and mechanical as well as chemical processes in the fuel pellet and the cladding under irradiation are “best estimate” models. To use the proper values of the mechanical parameters, the influence of the irradiation of the cladding is also taken into account. The developments listed below make possible the proper fuel rod behaviour simulation:

  • The radial distribution of the burnup and power as determined by the MUFURC sub-module;
  • The correct handling of the elastic-plastic deformation;
  • Temperature- and burnup-dependent mechanical parameters of the cladding;
  • Creep model for the cladding;
  • Models for the calculation of the temperature- and burnup-dependent heat transfer coefficients;
  • RIM model.



István Panka, MTA EK, Hungary
Head of Reactor Analysis Department