MATHEMATICAL MODEL OF NON-STATIONARY HYDRAULIC PROCESSES IN GAS CENTRIFUGE CASCADE FOR SEPARATION OF MULTICOMPONENT ISOTOPE MIXTURES

It is known that the optimal modes of gas centrifuge (GC) cascades are violated occurring the non-stationary hydraulic processes for a separation of multicomponent isotope mixtures. The perturbation arise and lead to violations of operating specifications and intolerable overloads equipment. The non-stationary hydraulic processes affect the cascade efficiency and the quality of the product. The GC cascades for the separation of multicomponent isotope mixtures have insignificant gas content, and, as a consequence, low inertia. It leads to increased influence of non-stationary processes on the cascade efficiency. In this regard, an important urgent task is the comprehensive investigation and modeling of these processes. We solved this problem by creating mathematical model and software for it. The separation stage of the GC cascade is presented in the form of four dedicated object (a feed manifold, GC, a heavy fraction manifold and a light fraction manifold). The calculation of non-stationary hydraulic amounts to replacing the first order differential equations by difference equations of the implicit Euler scheme [1] and the decision obtained by non-linear algebraic equations. The calculation is iteratively performed; the pressures and  flow are determined in all objects at each time step, satisfying  the equation of material balance in the cascade. These values must satisfy the balance of substances in the GC cascade. The developed mathematical model was tested for isotope separation of Si, Xe, Ni, W. The deviation of the calculated and actual values was 7.5%. As a result, this mathematical model is universal for calculation of hydraulic parameters of GC cascades for separation of multicomponent isotope mixtures by using different working substances. 

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