Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

Wood, Houston G.; Morton, J. B.

doi:10.1017/s0022112080001504

Cited by 91 publications

(66 citation statements)

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“…The separative work ΔU is not a measure of energy, but it is nonetheless a measure of the effort expended by the centrifuge. A function of flows into and out of the centrifuge and the concentrations of the streams, it is calculated by the formula (3) where P, W, and F are product, waste, and feed mass flows, respectively, x F is the concentration of 235 U in the feed, and V(x) is the value function derived by Paul Dirac and is given by (4) The expression for the maximum theoretical performance of a gas centrifuge was also derived by Dirac and given by (5) Dirac's work was published as part of a book by Karl Cohen. 4 In equation 5, L is the length of the centrifuge, ρD is the binary diffusion coefficient, and ΔM is the difference in molecular weights.…”

Section: A New Kind Of Challengementioning

confidence: 99%

The gas centrifuge and nuclear weapons proliferation

2008

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Section: A New Kind Of Challengementioning

confidence: 99%

The gas centrifuge and nuclear weapons proliferation

2008

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“…He showed that only three of the six solutions satisfy Eq (B-4) The remaining solutions, which we denote by fA(t), fB(t) and fc(t), are infinite series containing terms which decay exponentially in t. These solutions (10) are given in the paper by Wood I o.1o…”

Section: (B-4)mentioning

confidence: 99%

The theory of uranium enrichment by the gas centrifuge

Olander

1981

Progress in Nuclear Energy

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Onsager's analysis of the hydrodynamics of fluid circulation in the boundary layer on the rotor wall of a gas centrifuge is reviewed. The description of the flow in the boundary layers on the top and bottom end caps due to Carrier and Maslen is summarized. The method developed by Wood and Morton of coupling the flow models in the rotor wall and end cap boundary layers to complete the hydrodynamic analysis of the centrifuge is presented. Mechanical and thermal methods of driving the internal gas circulation are described. The isotope enrichment which results from the superposition of the elementary separation effect due to the centrifugal field in the gas and its internal circulation is analyzed by the Onsager- This manuscript was printed from originals provided by the author. A. INTRODUCTIONUranium enrichment is an essential component of nuclear fuel cycles based upon light water reactors.For more than thirty years, the uranium enrichment industry has been based solely on gaseous diffusion technology.Because of the substantial electrical power requirements of this process, the gas centrifuge method, which requires only about 5% of the power for comparable enrichment, has been selected for most additional capacity.The early theoretical work on the gas centrifuge is presented in the book by Cohen(l). The recent books by Avery and Davies( 2 ), Villani (J) and Benedict and a1( 4 ) provide more up-to-date discussions, and Soubbaramayer(S) has summarized the current status of non-U.S. theoretical work. Summaries of early hydrodynamic analyses and separation theory are presented in ref.( 6 ) and a semi-technical description of the device is given in ref. (7).There are many reasons for engaging in theoretical analysis of a gas centrifuge. First, such calculations can be used to guide experiments, which for a fully-instrumented test machine, are quite costly. Second, they provide an understanding of ho\v the flow affects isotope separation and may suggest means of altering the flow profiles to improve performance. Third, they permit an assessment of off-optimum performance of the centrifuge. Finally, they can be used in engineering cost optimization studies, the object of which is to design a machine and operate it so that the cost per unit of separative power is a minimum. This last feature of the theory is especially important, because the large number of parameters controlling the internal flow (and hence the separation) makes experimental optimization expensive and tedious. Because of the large scale of the uranium enrichment industry, even a few percent improvement in a separative power of a device (at no expense) means yearly saving of many millions of dollars in the cost of electricity generated by light water reactors. Figure 1 shows an early gas centrifuge. The current models are of the same general type but are larger and are capable of much higher speeds.-1-Machines with diameters as large as 24 inches have been tested. Figure 2 is a schematic of the centrifuge. An electric motor resting on the bo...

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“…The geometry and notation are the same as used in the derivation of the Onsager equation given in [4]. Assuming a baffle similar to that in [3] but having some axial thickness, I use the paths enclosing the baffle shown in Fig.…”

Section: Equation For the Interior Boundary Stream Functionmentioning

confidence: 99%

Numerical treatment of interior boundary conditions of the Onsager equation

Viecelli¹

1982

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Onsager's pancake approximation for the fluid dynamics of a gas centrifuge

Cited by 91 publications

References 5 publications

The gas centrifuge and nuclear weapons proliferation

The gas centrifuge and nuclear weapons proliferation

The theory of uranium enrichment by the gas centrifuge

Numerical treatment of interior boundary conditions of the Onsager equation

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