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The influence of assembly or cell heterogeneity on neutron leakage has been consistently taken into account in the TIBERE simplified heterogeneous B{sub 1} model. The assumption adopted within the TIBERE model that neutrons are specularly reflected on the boundary introduces two problems. Calculations with this model may become rather time consuming and even unnecessarily long in the case of a Canada deuterium uranium reactor cell, and the peripheral or total coolant voiding of a pressurized water reactor assembly leads to infinite leakage coefficients. These problems have been overcome by the development of another simplified heterogeneous B{sub 1} leakage model, TIBERE-2, which has quasi-isotropic reflecting boundary conditions. The TIBERE-2 model uses similar approximations as the TIBERE model and yields an iterative scheme to simultaneously compute multigroup scalar fluxes and directional currents in a heterogeneous geometry. These values enable the evaluation of directional space-dependent leakage coefficients. This new model requires the classical and directional escape and transmission probabilities in addition to the classical and directional first-flight collision probabilities calculated for an open assembly. The TIBERE-2 model has been introduced for general two-dimensional geometry into the DRAGON multigroup transport code. The numerical results obtained by DRAGON show that the TIBERE-2 model represents leakagesmore » much better than the homogeneous B{sub 1} leakage model. Moreover, the TIBERE-2 model yields results that are extremely close to those obtained by the TIBERE model with considerably shorter computing times.« less

A simple formalism, which can be introduced into routine analyses, is presented for the calculation of the effect of sodium voiding on neutron leakages in a fast reactor lattice. The diffusion coefficients in plane or in two-dimensional lattices are calculated following a method that is very analogous to the method proposed earlier by the author for the treatment of thermal reactors. The two situations, sodium present and sodium voided, are calculated with the same approximations. It is known that it is impossible in the situation where the sodium is voided to calculate buckling-independent diffusion coefficients, for they diverge. These coefficients are hence calculated in both situations at the lowest order of the expansion in terms of the buckling, which introduces a logarithmic term. The calculation is performed in the actual geometry of the lattice without cylindricalizing the cell.

In an earlier work, the author presented a theory of the diffusion coefficient in a reactor lattice, leading to expressions valid in full generality. However, for practical purposes it was necessar...

On the basis of the simple formalism, numerical results for a set of hexagonal fast reactor lattices are presented. This allows the influence of lattice parameters on the diffusion coefficients and the sodium-voiding effect to be pointed out. Comparisons with calculations based on a cylindrical cell model are also given. They lead to the conclusion that the Wigner-Seitz approximation can underestimate the diffusion coefficients in fast lattices with larger gap widths.

A consistent model for the calculation of fast reactor assembly diffusion coefficients is presented. Allowance is made for the treatment of both sodiumfilled and sodium-voided lattices, with the same approximation applied, which is essential for the study of the sodium-voiding effect. The hexagonal steel tube is also taken into account. The formalism is implemented in the ASDIC (Assembly Diffusion Coefficients) program. Numerical results and comparisons with results of other models are given.

In a new method of approximation of the Boltzmann equation, one starts from a particular form of the equation that involves only the angular flux at the boundary of the considered medium and where ...

(1968). The Cn Method of Approximating the Boltzmann Equation in Cylindrical Geometry. Nuclear Science and Engineering: Vol. 32, No. 2, pp. 270-271.