A model forchoked flowof single-phase uranium hexafluoridethrough thick square-edged restriction orificeplates

Abstract

In the main technologies of uranium enrichment, i.e., the isotopic separation of this element, it appears asgaseous uranium hexafluoride UF6. Simplified treatment on the critical flow of UF6through orificeswas notedin severalworks, either in restrictive flow elements installed in isotopic separation cascades, in the modeling of flow through the internal structure of gas centrifuge feed, or even in cases of analysis studies of risk involving leaks of the gas. The present work proposes a more realistic and careful treatment of this type of flow, by modeling the flow to estimate the discharge coefficient under choked flow conditions Cd*and thereby correcting the ideal mass flow rate. Thus, increasing the accuracy of flow calculations in the various possible types of modeling with UF6. The goal of thisworkwas to study the compressible critical flow at low pressure of single-phase UF6gas through thick orifice plates in order to obtain a correlation for Cd*.Computational fluid dynamics (CFD) was used throughAnsys Fluent softwareto solve the flows numerically. Two subsets of 20 different geometric models each were used. The first subset refers to laminar flows and the second to turbulent flows with low Reynolds number(higher than 8000). Thus, a total of 40 cases were studied through 165 simulations. All of the orifice plate models were set in a 4.45 cm internal diameter pipe and had the orifice diameter equal to the orifice thickness. The parametric variationof Cd*wasguided by the design of computer experiments and wasperformed with two factors: i) the upstream total pressureP0, and ii) theorifice-to-pipediameterratioβ. The CFD method herein proposed could haveits accuracy indirectlyasserted by calibrationusingliterature experimental data from casessimilarto the studied flowsbut with air as the process fluid.In addition, the simulations were tested for the conservation of mass and total enthalpy throughoutthe computational fluid domain to verify whether the physical solution obtained has theoretical support. For the turbulent subset,Cd*presented periodic erratic behavior with respect to the P0factor(parameter). This resulted in observations without direct method to obtain any proper fitting among the tested functions. Cd*showed good polynomial fit for the β factor and it was tested with polynomials ofdegrees1 to 8. Theleast-squares method was used to define the optimal parameters. The best fit was the sixth-degreepolynomialwith minimum squared standard error of the regression s2equals to 7.89 • 10-8. But the second-degreepolynomial with s2=28.6 • 10-8consisted on the actual obtained correlation of Cd*with β.