A simplified cell theory applied to the calculation of thermal neutron spectra in light water lattices

Abstract

A simplified polyenergetic cell theory is formulated to determine spatially averaged energy dependent thermal fluxes in the moderator, cladding, and fuel regions within the unit cell of a reactor lattice. The derived spectra are then utilized in the calculations of the thermal integral parameters and average cross sections required for reactor computations. The cell theory, as formulated, postulates an infinite moderator region with the absorption cross section of this region appropriately modified to account for the neutron leakage into and absorption by the fuel element. The modifications to the moderator absorption cross section are formulated both in terms of the net current at the fuel element-moderator interface and in terms of energy dependent moderator and fuel element escape probabilities, the latter approach offering physical transparency and ease of calculation. Analytic expressions for the escape probabilities are presented, integral transport theory being applied to the fuel element region, while diffusion theory is utilized in the moderator region. Using these analytic expressions, the theory is applied to actual lattices in the form of the light water moderated and uranium dioxide fueled cores of the Cornell University Zero Power Reactor. Room temperature parameters and their temperature coefficients are determined using both the monatomic gas model and the Nelkin water kernel to describe the energy transfer process in the moderator. Calculations are made with PROGRAM COUTH, a Fortran-63 program written for use with the Control Data Corporation 1604 digital computer. A typical lattice calculation including the computation of the spatially averaged fuel, cladding, and moderator spectra and the thermal integral properties and average cross sections takes approximately thirty-five seconds of computer time. This figure is exclusive of the compiling time and the time required to calculate the moderator scattering kernel. In an attempt to estimate the accuracy of the calculational results, the method is applied to the Brookhaven National Laboratory uranium dioxide cores and the results are then compared with those predicted by Honeck's THERMOS code. Disadvantage factors agree to within 1.0% while the thermal utilizations agree to within 0.5%. A study of the sensitivity of the calculated integral parameters to variations in the input data leads to the assignment of rather small uncertainties in the results calculated with the simplified cell theory.