CELL CALCULATIONS AND FLUX APPROXIMATIONS FOR SIMPLE SLAB GEOMETRY
Gilles Simon, Alexander Gray · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1957
The results obtained by cell theory are compared with those obtained by two-group diffusion theory and the validity of cell theory calculations is examined. Several simple slab geometries of finite thickness (infinite in their other two dimensions) were used in this study. The first geometry was made up of a series of cells in which the individual cell consisted of a thin control slab symmetrically surrounded by uniformly loaded bare slabs. The second, a seed- blanket core, consisted of a highly enriched seed symmetrically surrounded by a blanket region which contained natural U. The seed-blanket core was controlled by a single control slab at its center, and the cell size was chosen to be equal to the entire seed region. For three variations of seed width the fuel constants of the seed were changed to obtain criticality. In all cases studied, criticality results were obtained with the control slabs fully inserted. To obtain the control material worth, the control slabs were replaced by water. As a further investigation into some of the properties of cell theory, flux approximations for the one-dimensional case are discussed. (auth)