Computation of 3D neutron fluxes in one pin hexagonal cell

In this paper we are presenting the method of computation of three dimensional (3D) neutron fluxes in one pin hexagonal cell. Carlvik’s collision probability method of solving neutron transport equation for computing fluxes has been used here. This method can consider exact geometrical details of the given geometry. While using this method, track length computations are required to be done. We have described here the method of computing tracks in one 3D hexagon. A program HX7 has been developed for this purpose. This program has been implemented in the NXT module of the code DRAGON, where tracks in the pins are computed.For computing tracks in 3D, first we use the tracks computed in the two dimensions (2D) and then we project them in the third dimension. We have developed equations for this purpose. In both the regions, fuel pin as well as in the moderator surrounding the pin the fluxes are assumed to be uniform. A uniform source is assumed in the moderator region. Reflecting boundary conditions are applied on all the sides as well as on the top and bottom surfaces. One group 2D and 3D fluxes are compared with the respective results obtained by the EXCELT module of DRAGON. To check the computations, tracks are plotted and errors in the computations are obtained. It is observed by using both the modules EXCELT and NXT that the fluxes in the pins converge faster and in the moderator region fluxes converge very slowly.

► Computations of 3D neutron fluxes in one pin hexagonal cell is performed by Carlvik’s method of collision probability.
► Carlvik’s method requires computation of track lengths in the geometry.
► Equations are developed to compute tracks, in 2D and 3D, in hexagons and are implemented in a program HX7.
► The program HX7 is implemented in NXT module of the code DRAGON, where tracks in pins are computed.
► The tracks are plotted and fluxes are compared with the EXCELT module of the code DRAGON.