Basic Characteristics of Centrifuges, (III)

A method of numerically integrating the Navier-Stokes equations is presented for axisymmetric compressible flows. A modified Newton's method is employed to determine the steady motion of gas in a rotating cylinder without the use of a time-consuming marching process with respect to time. A suitable form of the finite difference equations gives a computationally-stable integration with reasonable representation of the spatial characteristics of the flow. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward substitution. By using an auxiliary constant matrix algorithm, the method gives the solution within reasonably acceptable computation time. As an example of the method, some features of solutions are presented for the steady flow of UF6 gas in the centrifuges which have the openings for feed and withdrawal on the end plates.