Abstract
Based on the Onsager Equation with Carrier-Maslen end conditions, a linearized sixth-order partial differential equation describing the flow in the interior volume of the rotor of a gas centrifuge is solved using a finite element algorithm employed by the CurvSOL hydrodynamics code. The results are compared to results from the Pancake code, an existing code employing an eigenfunction expansion solution technique to solve the Onsager equation. Comparison of the axial mass flux, streamfunction, upflow ratio, and flow profile efficiency demonstrates excellent agreement between the CurvSOL and Pancake solutions for both the wall temperature gradient and scoop drive mechanisms, as well as the overall mass flux profile for both the Rome and Iguacu centrifuge designs. The radius of the rotor plays a key role in the influence of wall curvature on the flow solution.
The axial mass flux profile derived from the hydrodynamic solution is used in a finite differencing scheme to obtain a numerical solution of the diffusion equation to predict the steady-state transport of uranium hexafluoride molecules in the xPort code. The generally accepted method of approximation describes the axial variation of the radially averaged concentration. The newly developed two dimensional concentration field approximation allows for separative performance calculation at all points along the radial direction. Comparison of the two dimensional solution averaged at each axial plane and the one dimensional radial averaging solution shows that while the results from both methods differed by an atomic fraction of 6% at select axial plane near the middle of the rotor, the averages at the end-caps agree to within 2%.
The separative performance values and separation factors are mapped over ranging process gas feed rates and desired ratios of product to feed, and theses performance maps are subsequently employed in cascade analysis software packages. Using the FixedCascBin code, the stage flow rates and enrichment levels are calculated for cascades utilizing the Rome and Iguacu machines. Comparison of the results from
performance maps derived from the one dimensional radial averaging separation calculations and those from the xPort code show that while the magnitude of the flow in the stripping section is higher in the one dimensional case, both the upflow and downflow in the enriching section is higher in the two dimensional case. Overall, the two dimensional case upflow enrichment is lower at every stage until the top of the cascade, while the downflow enrichment is lower at every stage until the bottom of the cascade.
Two additional potential applications for the centrifuge performance maps are introduced. The CascSCAN code uses a modified version of the FixedCascBin to scan over the possible arrangement of centrifuges in cascades designed to enrich from natural uranium to weapons grade uranium in three or four step batch processes. A breakout study is performed using the Iguacu centrifuge, and a performance map based on the xPort results predicts a lower breakout time as additional inventory of enriched material is added to the feed stream. The results differ by as much as four months in the case of the four step batch process with 1500 kg of additional inventory enriched to 3.5% uranium-235. Finally, a recently proposed method for enrichment plant monitoring and characterization offers a potential application for usage of the newly developed performance maps. The potential utility of the xPort based performance maps is demonstrated by results of several scenarios simulated with TransCasc mapped on a surface that describes all commercial cascades and compared to results from MSTAR, a mixed abundance ratio cascade code. The codes CurveSOL, xPort, and CascSCAN were developed by the author to achieve the research objectives presented in this paper.
