Open AccessTwo-dimensional multi-isotope separation in a gas centrifuge using finite element analysis
Author(s) -
Wisher Paudel,
Houston G. Wood
Publication year - 2022
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2147/1/012001
Subject(s) - centrifuge , isotope , isotope separation , partial differential equation , finite element method , quadrature (astronomy) , isotopes of uranium , gaseous diffusion , mechanics , physics , mathematical analysis , mathematics , thermodynamics , nuclear physics , electrode , quantum mechanics , optics
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.