Katsutada Aoki

Application of the Response Matrix Method to Criticality Calculations of Two-Dimensional Reactors

Response matrix method was applied lo criticality calculations of two-dimensional reactors. The response matrices of component blocks in a reactor were first calculated analytically with group-diff...

Modified One-Group Diffusion Scheme for Calculating Gross Power Distribution in a BWR Core

A new modified one-group diffusion scheme for one- and two-dimensional calculations of the gross power distribution in the BWR core is presented. The particularity of the present method is that the fine distribution of the ratio between thermal and fast neutron fluxes within each fuel assembly is estimated analytically. Since this estimation can be performed locally and without requiring knowledge of the fast neutron distribution, the method is quite effective in reducing computing time. Procedures for special treatment at the two-dimensional core-reflector boundaries are also derived from analytical considerations. The results obtained from a series of test calculations indicate that the present method assures an accuracy almost equal to the conventional two-group calculation, and without requiring much more computing time than the conventional one-group calculation. The applicability of the method to three-dimensional calculations is also discussed.

New difference equation for diffusion calculation

A new difference equation for the numerical solution of the one-dimensional diffusion equation was obtained by using a semi-analytic method, in which the only approximation employed is that the source distribution within a mesh-region is represented by a linear function. A test program, EXX-1, was prepared and run for BWR calculations, and comparisons were made with the conventional method. The results show that by using the new difference equation, a very coarse mesh model (1 mesh point per material region) can be applied without seriously impairing the computational accuracy. It is also shown that the conventional difference equation becomes identical to the new expression if group-constants are multiplied by correction factors and the treatment of the source term appropriately modified. New difference equations for spherical and cylindrical geometries are also given, in an appendix.

Convergence and acceleration of void iterations in boiling water reactor core calculations

A theoretical background for the convergence of void iterations in boiling water reactor (BWR) core calculations is considered. First, the process of each void-iteration step is interpreted as a transformation in a set of vectors representing the characteristics of the core, and the condition for convergence is derived in terms of the spectral radius of the transformation operator. Second, to visualize the convergence condition, the concept of a trajectory of channel power is introduced. Third, it is explained that the spectral radius of the transformation operator can be changed by changing the number of source iterations within each void iteration step. Based on this analysis, an optimum number of source iterations, when the Chebyshev polynomial acceleration technique is employed, is estimated for a typical BWR core. Numerical examples, presenting both divergent and convergent cases, show the validity of the present theoretical analysis.