The effect of vacuum core boundary conditions on separation in the gas centrifuge

A vacuum exists in the central region of the cylindrical rotor of a high-speed countercurrent gas centrifuge when operated with UF6 for the enrichment of uranium. Since solutions of the Navier-Stokes equation are used to determine the isotopic distribution in the rotor, the location of the vacuum core boundary has a direct effect on the predicted separative work of the gas centrifuge. Because criteria for terminating the continuum region based on the Knudsen number are somewhat arbitrary, an approximate model developed by Onsager, which yields an analytical solution, has been used to evaluate the location of the boundary of the vacuum core more correctly. The results show that the location of this ''top of the atmosphere,'' in density scale heights, changes with the peripheral speed of the centrifuge. Using this location in the calculation of separation performance parameters of the gas centrifuge reduces, at the higher peripheral speeds, the contribution of axial diffusion to the effective stage length of a theoretical stage in the centrifuge. The correction due to imposing the top of the atmosphere limitation on axial diffusion becomes significant at high speeds and low countercurrent circulation rates