Thermally, mechanically or externally driven flows in a gas centrifuge with insulated horizontal end plates

Publisher Summary This chapter provides an overview of the technical basis of the gas centrifuge. The performance of the gas centrifuge is based primarily upon the equations of diffusion and hydrodynamics that govern the phenomena occurring in the device. The two parameters obtained from the separative analysis are the separation factor α and the separative power δU of a single centrifuge. These two properties are related to the design features of the centrifuge, the physicochemical properties of the process gas such as uranium hexafloride, the flow pattern, and controllable variables such as the throughput and the cut. However, at higher peripheral speeds, the separation factor becomes significantly larger than unity. The separative properties of the centrifuge depend upon two fluid mechanical characteristics of the device: (1) the flow pattern efficiency E and (2) the internal circulation parameter m . Both of these parameters depend upon double integrals of the axial velocity profile. A major theoretical obstacle is encountered in the hydrodynamic analysis of centrifuges operating at high peripheral speeds.

Technical basis of the gas centrifuge

A thermally driven steady axisymmetric flow of gas of small diffusivity in a vertical circular cylinder rotating rapidly about its axis of symmetry is studied. The side wall is a thermal insulator and the horizontal end plates are perfect conductors. The temperature of the top end plate is kept slightly higher than that of the bottom one. The boundary-layer method is applied to solve the linearized basic equations and the following results are obtained. The axial velocity in the inner core is fully controlled by the Ekman suction on the horizontal plates and is the same as that in the case of a perfectly conducting side wall. The closed circulation in the side-wall Stewartson E ½ layer is strongly suppressed compared with the case of a perfectly conducting side wall. This situation is reflected in the inner temperature field, which deviates from that in the case of a perfectly conducting side wall. The critical parameter governing the solution is found to be (γ − 1) PrG 0 E −1/3 /4γ, where Pr is the Prandtl number, γ the ratio of specific heats, E the Ekman number and G 0 the square of the Mach number based on the peripheral speed of the cylinder.

Thermally driven flow in a gas centrifuge with an insulated side wall

There are two sets of principles involved in the development of the gas centrifuge, the internal separation physics and the external means of spinning a rotor at very high speeds. Only the first aspect is discussed in this part of the review. First, the industrial requirement for the separation of the uranium isotopes is defined so that the separation history can be put in a modern perspective. The history of separation physics itself is then traced back to the theory of centrifugal force by Huygens and the equivalence of this force to that of gravity. The barometric equation giving the variation of atmospheric pressure with height and the law of partial pressures can then be adapted to the centrifuge to give the steady-state theory of separation. This work was completed in the last century but was not confirmed in its application to isotope separation until 1936. The detailed separation physics for non-steady-state conditions required for a production centrifuge was developed during the American wartime Manhattan Project. During this work the theory giving the maximum output of a centrifuge was developed by Dirac, and soon afterwards Cohen and Kaplan showed that the best method of operation for a production centrifuge is in a countercurrent mode of operation. This method gives a large separation factor at relatively small flow rates through the rotor. The theory of how to set up an internal countercurrent was given by Martin during an equivalent wartime German project, and refinements to the theory, showing how the countercurrent persists along a centrifuge rotor, was given by Dirac and Steenbeck, the latter during a postwar Russian project. This theory was extended by Parker, Ging, and Mayo of the University of Virginia, whose work was completed by 1962, the limit of this review.

Review of the gas centrifuge until 1962. Part I: Principles of separation physics

Diffusion separation methods refer collectively to processes such as gaseous diffusion and gas centrifugation, developed specifically for difficult separations such as those involving the isotopes of uranium. These processes, used worldwide primarily for uranium enrichment, are based on the differences that exist in the rates of gaseous diffusion of the particular isotopes. These difficult separations almost always involve an aggregation of separation units known as a casade.



Casade design, unit separative capacity, ideal and real casades, and various separation factors are presented. Equipment and plant design for the enrichment of uranium-235 by gaseous diffusion, by various pressure diffusion processes, and by jet diffusion, also known as the separation nozzle process, is discussed.


Keywords:

Diffusion separations;
Design selections;
General processes;
Cascade;
Gaseous diffusion;
Pressure diffusion;
Separation nozzle

Diffusion Separation Methods

The influence of a gas flow pattern in a rotor of a countercurrent gas centrifuge upon the separation factor and the separative power is studied. The optimum gas concentration gradient, at which the centrifuge has maximum separative power, us obtained from the equation of the diffusion velocity. The equations with respect to the separation properties are derived in two regions of the rotor separately, one of which is an upper part above the feed point as a stripping section, the other a lower part as an enriching section. The effects of the radial concentration gradient on the performance of the centrifuge are considered by means of the flow pattern coefficient K, which depends only upon the flow pattern and approaches the maximum value, unity, as the neutral layer between the counter currents approaches the rotor wall.

https://www.jstage.jst.go.jp/article/jaesj1959/3/11/3_11_868/_pdf

On the Isotope Separation by Counter-current Gas Centrifuge, (I)

An empirical relationship for the windage losses of a rotating inner cylinder in a concentric stationary outer cylinder was obtained as a function of the rotaing speed of the inner cylinder and the gap width between both cylinders, through analysis of theories by Taylor, Davey and Batchelor, and experiments by Wendt, Taylor and Donnelly. lnformation was also gained on the critical speed at which instability sets in, which depends on the gap width. The formula relating the friction factor f to rotating Reynolds number Red*, and to the ratio between gap width and radius d* can be applied to a range of Red* values from the critical value to about 200 times thereof and to a range of d* from 0 to 1, within an error of 30%.Measurements of the windage loss of a Zippe-type gas centrifuge 34.9cm long with a radius of 5.20cm have been made for three mantle inner radii of 6.30, 7.04 and 8.20cm.Experimental results plotted in f vs. Red* with d* as parameter agree well with the curves calculated by the present formula.

https://www.jstage.jst.go.jp/article/jaesj1959/10/3/10_3_118/_pdf

Akira Kanagawa

Papers

On the Isotope Separation by Counter-current Gas Centrifuge, (I)

Windage Losses of Rotating Cylinder