Linearized thin-wing theory of gas-centrifuge scoops

A steady hypersonic rotating flow of a perfect gas past a system of thin stationary scoops in a gas centrifuge of annulus type is studied. The gas is assumed inviscid; its ratio of specific heats is assumed to be approximately 1. The scoops are set at zero angle of attack and are periodic with respect to the azimuthal variable. The flow is assumed to be a three-dimensional small perturbation on a basic state of rigid-body rotation. New scaling laws are proposed as appropriate to realistic operating conditions of gas centrifuges. Basic equations, boundary conditions and shock conditions are linearized for a weakly hypersonic flow by an analytical procedure similar to that used in the thin-wing approximation in high speed aerodynamics. The solution of the basic equations is obtained by the eigenfunction expansion method. The solution provides a simple addition theorem for the scoop drag which makes the resultant drag of a system of several scoops equal to the product of the number of scoops and the drag of a standard system with a single scoop. The solution makes it clear that despite the above addition theorem, the scoops interact in their effects on the flow. (author)