READY special report 2: Three-dimensional analytic function expansion nodal model for the TRAB-3D nodal code

Static and dynamic analyses of nuclear reactors are usually carried out with diffusion-theory based nodal methods, in which the fuel assemblies are modelled in the horizontal direction as one or four and in the axial direction as 10-30 homogenized volumes. The homogenized two-group cross sections needed in the nodal analysis are obtained from accurate single-node heterogeneous multigroup transport calculations. The nodal models differ from each other in the way the intra-nodal flux shape is approximated in calculation of the coupling coefficients between adjacent nodes. The simplest methods use polynomials or other simple functions for direct interpolation of the fast and thermal fluxes; a more advanced approach, used e.g. in the HEXBU and TRAB-3D nodal models (Kaloinen & Kyrki-Rajamäki 1997), is to decompose the two-group flux into eigenmodes, which have a better-defined shape than the fast and thermal flux and can thus be interpolated more accurately. Especially in cores with large flux variations between adjacent nodes, it is important to obtain as accurate an estimate of the intra-nodal flux shape as possible. Another need for improving the flux shape comes from pin power reconstruction. Most of the current nodal codes (including TRAB-3D and HEXBU) do not, however, use corner point flux values in the nodal calculations and information about the flux near node corners is therefore limited. A new nodal model, based on the analytic function expansion nodal model (AFEN), initially developed in South Korea (Noh & Cho 1994), has been developed for calculating the three-dimensional neutron flux. In addition to improved accuracy within the core, the analytic function expansion enables also calculation of the flux in reflector areas, thus possibly enabling better evaluation of e.g. the flux seen by ex-core detectors. This paper briefly describes the model and the results of the first test calculations.