Solution of the simplified fluid dynamic equation for transient processes in a gas centrifuge

Abstract

The equation describing a transient process in a gas centrifuge is a partial differential equation and has to be solved by using a numerical method. The Crank-Nicolson scheme and a central difference scheme are employed, respectively, for time discretization and space discretization. Under the condition of full circulation flow, the solution of the equation coincides with the result of the linear theory, verifying the correctness of numerical solution. The transient processes of a centrifuge are simulated with two withdrawal models to reveal the variations of the axial velocity with time in the processes. The results shows that for a given rotor peripheral speed, the radial distribution of the axial velocity depends mainly on the wall pressure and the withdrawal strength, but the influence of the withdrawals is much weaker than the wall pressure. The results also demonstrate that the partial differential equations describing the fluid dynamics in a transient process does exhibit the dynamic variations, and can be further applied to the analysis of separation performance.