The theory for a cascade of centrifuges described in the preceding report of the same general title is further developed.
First, equations describing the distributions of the flow and the mole concentration are derived from the material balance relations for a square cascade. Corresponding equations are next obtained to cover a squared-off cascade consisting of a series of square cascades. A computer program is outlined which makes it possible to obtain the shape of the most efficient squared-off cascade. The efficiency of the current form of squared-off centrifuge cascade with reflux pipes is found to be lower than obtainable with gaseous diffusion.
The efficiency can be improved by the adoption of a tapered squared-off cascade with centrifuges provided with eccentric cuts to take the place of reflux pipes. The dynamic characteristics are also discussed. Analysis of the start-up behavior reveals that the equilibrium time of the centrifuge cascade is much shorter than for a corresponding gaseous diffusion cascade, and that the mole concentration of the product rapidly rises to attain steady state condition. It is also found that even when the feed flow rate fluctuates, the mole concentration of the product is relatively stable. The effect of a centrifuge failure in the cascade is examined. The optimum mole concentration for the waste effluent discarded from the cascade is calculated from the viewpoint of cost.
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