On compressible flow in a gas centrifuge and its effect on the maximum separative power

The gas circulation in a gas centrifuge due to temperature differences, differential rotation and injection, and removal of fluid at the ends, as well as due to temperature gradients at the cylinder wall, is treated analytically. The motion consists of a small perturbation on a state of isothermal rigid body rotation. Linear anlysis of conservation of mass, momentum, and energy and the perfect gas law leads to the definition of several vertical layers and regions at various radii: a Stewartson layer near the wall where viscosity and heat conduction are important to allow the thermal and kinematic conditions at the wall; an inviscid region; and an inner layer adjusting the inviscid flow to a diffusion-controlled center region where, due to low density, mass fluxes are negligible. The axial motion in these layers and regions is short-circuited in Ekman layers at the ends. The solutions for the flow field are used to calculate the maximum attainable separative power of a countercurrent gas centrifuge for uranium enrichment. It appears that the separative power is less than Dirac's figure, the difference being primarily determined by the width of the diffusion-controlled region in the center of the rotor. The difference increases with circumferential velocity and cylinder length and decreases with cylinder radius and gas pressure at the wall,