Two-dimensional multi-isotope separation in a gas centrifuge using finite element analysis

Abstract

A finite element model of a gas centrifuge is developed to compute the optimal two-dimensional multi-isotope separation. The mass flow field generated using Onsager’s equation without the pancake approximation is used as an input to the diffusion equation for each uranium isotope in the initial form of partial differential equations (PDE). The PDEs are reduced to their weak forms and the resulting integrals evaluated using gauss quadrature. The systems of equations are solved using an optimization routine to satisfy the overall mass and concentration balance inside the machine. The solutions obtained can provide a holistic view of isotopic diffusion inside the centrifuge and the ability to quantify the molecular fraction of various uranium isotopes at a given radial and axial location at any desired initial and operating conditions. While several authors in the past have solved the multi-isotope diffusion problems using 1-D approximations, there are no known 2-D finite element models in literature. The findings of this work, therefore, is not only be significant for the applications of nuclear non-proliferation but also a great analytic tool for nuclear scientific community.