Background: Some isotope separation tasks

for example

the enrichment of recycled uranium and the purge of light impurity

must be completed in a cascade with an additional feed flow.Purpose: It is one of the design aims for this type of cascade to determinate the configuration parameters such as the number of total stages

positions of base and additional feed flows on condition that concentrations of target components in the products and waste flows are given.Methods: In order to design the cascade theoretically

a mathematical optimization model is established for a quasi-ideal cascade.The total substance flow in the cascade is chosen as an objective function.Using penalty function method

the constraint optimization problem is transformed into an unconstraint one which was solved by a simplex method.Results: The optimization method is applied to calculate the cascade in which the recycled uranium is enriched.The results of calculation indicate that the minimum substance flow in the cascade decreases with the increasing of the abundance of 235UF6 in the recycled uranium.Conclusions: It is proved that the mathematical optimization model established for the quasi-ideal cascade with an additional feed flow is reasonable.