Gy. Hegyi

Development and validation of the three-dimensional dynamic code—KIKO3D

Abstract A three-dimensional reactor dynamics program—KIKO3D—for coupled neutron kinetics and thermohydraulics calculation of VVER type pressurized water reactor cores has been developed and benchmarked. For solution of the time dependent neutronic equations, a nodal method was used. Concerning the geometry, the symmetries of the nodes, and the concrete form of the neutronic equations to be solved inside the nodes (transport or diffusion equation), the method is general enough, only the linear anisotropy of neutron flux on the node boundaries is utilized. Generalized response matrices for the time dependent problem are introduced which can be derived also from the response matrix of the stationary problem. The so obtained time dependent matrix equations show similar structure to the non-discretized equations. Therefore, the Improved Quasi Static factorization of the time dependent matrix equations can be carried out in the usual way, leading to the point kinetic and the shape function equations. In the KIKO3D code, this general nodal method was applied for the special case of rectangular and hexagonal homogenized nodes in which the diffusion equation is to be solved. In this special case, the traditional response matrices of the stationary problem and the generalized matrices necessary for the time dependent problem can be obtained by analytical formulas. The accuracy of the introduced approximations has been validated against rectangular and hexagonal benchmark problems.

General features and validation of the recent KARATE-440 code system

In the last few years several projects aiming at the introduction of new VVER-440 fuel types and resulting in more economic fuel cycles were initiated: increased average enrichment, modification of the lattice pitch and fuel diameter, profiled enrichment, application of burnable absorber, modification of the absorber assembly coupler part. The first version of the KARATE-440 code system was elaborated in the KFKI Atomic Energy Research Institute (KFKI-AEKI) in the mid-1990s for the core design calculations of VVER-440 type reactors. The above fuel modifications and the upgraded regimes requiring more accurate calculations have necessitated the further development and validation of the code system. Owing to the new fuel types (e.g., burnable poison), greater attention has had to be paid also to the spectral calculations of the assemblies, especially to the space-dependent thermalisation in a large heterogeneous system. The fast algorithm applied to solve this problem with satisfactory accuracy is also detailed. The first part of the paper outlines the general features of KARATE, while in the next part the validation results are presented in relation to zero reactor measurements, mathematical benchmark problems and the operational data of the Paks (Hungary) Nuclear Power Plant (NPP).

Qualification of the APOLLO2 lattice physics code of the NURISP platform for VVER hexagonal lattices

Abstract The experiments performed at the ZR-6 zero power critical reactor by the Temporary International Collective (TIC) and a burnup benchmark specified for depletion calculation of a VVER-440 assembly containing Gd burnable poison were used to qualify the APOLLO2.8-3.E (APOLLO2) code as a part of its ongoing validation activity. The work is part of the NURISP project, where KFKI AEKI undertook to develop and qualify some calculation schemes for hexagonal problems. Concerning the ZR-6 measurements, single cell, macro-cell and 2D calculations of selected regular and perturbed experiments are used for the validation. In the 2D cases, the radial leakage is also taken into account by the axial leakage represented by the measured axial buckling. Criticality parameter and reaction rate comparisons are presented. Although various sets of the experiments have been selected for the validation, good agreement of the measured and calculated parameters could be found by using the various options offered by APOLLO2. An additional mathematical benchmark – presented in the paper – also attests for the reliability of APOLLO2. All the test results prove the reliability of APOLLO2 for VVER core calculations.

Hot channel calculation methodologies in case of VVER-1000/1200 reactors

Abstract In VVER-1000/1200 type reactors much higher and geometrically more complex assemblies are applied compared to the VVER-440 design. Additionally, assembly shrouds are not used in the improved reactor types. This implies that the existing sub-channel wise models and hot channel calculation methodologies used in the safety assessment of VVER-440 reactors have to be improved. For this purpose a full core thermal hydraulic model was developed. In the first part of the paper the new model and its connections with the reactor physics of KARATE-1200 code system are demonstrated with results regarding the sub-channel outlet temperature and DNBR. In the second part of the paper the hot channel calculation methodologies to be used in the transient safety analyses of VVER-1200 type reactors are discussed. The appropriate frame parameter concept concerning the limitation of the heating up of the coolant and the single closed sub-channel approach vs. the multi-channel approach are studied, as well.

Some uncertainty results obtained by the statistical version of the KARATE code system related to core design and safety analysis

Abstract The best-estimate KARATE code system has been widely used for core design calculations and simulations of slow transients of VVER reactors. Recently there has been an increasing need for assessing the uncertainties of such calculations by propagating the basic input uncertainties of the models through the full calculation chain. In order to determine the uncertainties of quantities of interest during the burnup, the statistical version of the KARATE code system has been elaborated. In the first part of the paper, the main features of the new code system are discussed. The applied statistical method is based on Monte-Carlo sampling of the considered input data taking into account mainly the covariance matrices of the cross sections and/or the technological uncertainties. In the second part of the paper, only the uncertainties of cross sections are considered and an equilibrium cycle related to a VVER-440 type reactor is investigated. The burnup dependence of the uncertainties of some safety related parameters (e.g. critical boron concentration, rod worth, feedback coefficients, assembly-wise radial power and burnup distribution) are discussed and compared to the recently used limits.

Uncertainties of the KIKO3D-ATHLET calculations using the Kalinin-3 benchmark (Phase II) data

Abstract The best estimate simulation of three-dimensional phenomena in nuclear reactor cores requires the use of coupled neutron physics and thermal-hydraulics calculations. However these analyses should be supplemented by the survey of the corresponding uncertainties. In this paper the uncertainties of the coupled KIKO3D-ATHLET calculations are presented for a VVER-1000 type core using the OECD NEA Kalinin-3 (Phase II) benchmark data, although only the neutronic uncertainties are considered and further simplifications are applied and discussed. Additionally, this study has been performed in the conjunction with the OECD NEA UAM benchmark, as well. In the first part of the paper, the uncertainties of the effective multiplication factor, the assembly-wise radial power distribution, the axial power distribution, the rod worth, etc. are presented at steady-state. After that some uncertainties of the transient calculations are discussed for the considered switch-off of one Main Circulation Pump (MCP) type transient.

HPLWR fine mesh core analysis

Abstract The European version of Supercritical Water Reactors (SCWR), the High Performance Light Water Reactor (HPLWR) operates in the thermodynamically supercritical region of water. Our basic objective was to elaborate a stationary coupled neutronic-thermohydraulic code capable for the calculation of the actual 3-pass core design with fuel assembly clusters. The calculations covered the neutronic transport calculations of HPLWR fuel assemblies, the coupled neutronic-thermohydraulic global calculations and the pin-wise analysis. Applying conservative assumptions, the relation to the linear heat rate and maximum cladding temperature limits was checked for the equilibrium cycle of HPLWR with this new code system.

Development of the Methodology of the Safety Analysis Performed by the Coupled KIKO3D/ATHLET Code System in VVER-440 Type NPP

In the deterministic safety analysis codes are required in order to provide evaluations of potential nuclear plant accidents. In the fields of the core transient behaviour, the computer codes have achieved a high degree of realistic modelling. Nevertheless, some further tools for the investigations of the wide range of physical phenomena in the whole plant transient, such as modeling the ex-core detector signals and the malfunctioning of the emergency control system are unavoidable, too. The programs and methods used in KFKI-AEKI for safety analysis of VVER-440 NPP are presented. The accident analysis methodology for a boron dilution scenario, in which an inactive coolant loop is started, is shown.Copyright