Procedures for the calculation of the separative performance of a countercurrent gas centrifuge

The standard Onsager-Cohen gradient equation predicts reasonably well the separative performance of a gas centrifuge in which half the machine operates as an enriching section and half the machine operates as a stripping section and in which both the enricher and stripper contain several theoretical separation stages. This is due in part to the fact that the approximations used in the development of the standard Onsager-Cohen gradient equation produce results which depart from the more detailed solutions presented in one direction in the enriching section and in the other direction in the stripping section and the errors therefore tend to cancel for the machine as a whole. It follows that for a centrifuge in which most of the bowl is used as an enriching section or as a stripping section this cancellation would not occur and some appreciable error would result from the use of the standard Onsager-Cohen gradient equation. A modified Onsager-Cohen gradient equation is therefore recommended in preference to the standard Onsager-Cohen gradient equation. This equation is developed for the general case in section III.C of this report and for the more specific case under consideration in section IV.C. It is shown in the results of calculations that indeed very little effect is observed by neglecting the term in the gradient equation containing the second derivative of the concentration