AN EXTENSION OF THE MULTIGROUP ANALYTIC NODAL METHOD (MANM) TO PROBLEMS IN HEXAGONAL-Z GEOMETRY

摘要

There is a significant number of reactor designs where the fuel assemblies are arranged in hexagonal lattices. The mostly widely used methods for global reactor calculations are the transverse-integrated nodal methods. They were primarily developed in Cartesian geometry. In the mid 90's the conformal mapping was used to provide a sound mathematical basis for the extension of these methods to hexagonal geometry. This technique was widely accepted and applied in several production nodal codes employing semi-analytic, analytic and polynomial transverse-integrated nodal methods. In this paper we develop the full multigroup analytic nodal method for hexagonal-z geometry and incorporate it into the MGRAC code. Like the methods cited above, we also employ the conformal mapping of a homogeneous hexagon into an inhomogeneous rectangle in order to establish the auxiliary one dimensional diffusion equations that are used to derive nodal coupling relations. The multigroup one-dimensional equations are solved analytically so that the only approximations that we make are in the transverse leakage representation and in the treatment of the inhomogeneity. We calculate the conformal mapping scale function using a numerically exact calculation based on analytical expressions. The formulation of the spatially discretized diffusion equation is such that a variety of iteration solution strategies can be used in MGRAC. These range from schemes in which the transverse leakage and the geometric source are updated at outer iterations (where eigenvalues are updated) to schemes where theses terms are updated only at feedback iterations (where nodal coupling coefficients are updated). Outer (eigenvalue) iterations are either fission-source driven or (transverse) leakage-source driven. A three color (RGB) Gauss-Seidel scheme is used for the inner (flux) iterations. Numerical results show good accuracy in the prediction of eigenvalues (errors of the order of 50 pcm) and assembly powers (errors of the order of 1 - 2%).