A Finite-Difference Numerical Method for Onsager's Pancake Approximation for Fluid Flow in a Gas Centrifuge

Abstract

Gas centrifuges exhibit very complex flows. Within the centrifuge there is a rarefied region, a transition region, and a region with an extreme density gradient. The flow moves at hypersonic speeds and shock waves are present. However, the flow is subsonic in the axisymmetric plane. The analysis may be simplified by treating the flow as a perturbation of wheel flow. Wheel flow implies that the fluid is moving as a solid body. With the very large pressure gradient, the majority of the fluid is located very close to the rotor wall and moves at an azimuthal velocity proportional to its distance from the rotor wall; there is no slipping in the azimuthal plane. The fluid can be modeled as incompressible and subsonic in the axisymmetric plane. By treating the centrifuge as long, end effects can be appropriately modeled without performing a detailed boundary layer analysis. Onsager's pancake approximation is used to construct a simulation to model fluid flow in a gas centrifuge. The governing 6th order partial differential equation is broken down into an equivalent coupled system of three equations and then solved numerically. In addition to a discussion on the baseline solution, known problems and future work possibilities are presented.