Analysis of gas flow in a centrifuge

Onsager's sixth order, elliptic, partial differential equation with Ekman boundary layer suction describing linearized flow in a gas centrifuge has been rederived from the linearized compressible Navier-Stokes equations by asymptotic methods. A Galerkin weak formulation is detailed for two-dimensional flow with internal heat and momentum sources and sinks. An exact solution of Onsager's Pancake equation, with a point source or sink of axial momentum, in the long bowl limit has been developed. A high order, smooth, tensor product finite element that has nearest neighbor support is proposed to make practical computations for some symmetric and antisymmetric flow problems. A qualitative description of the singularities due to two-dimensional point sources or sinks is given along with approximations of the resultant flow fields. Effects of Ekman pumping and pure two-dimensional flow are illustrated. Finally, asymptotic solutions are given for the so-called auxiliary equation.