Solution of the Equation 4A exp 4 H/sub XX/ + H/sub Yy/ + F(X,Y) = 0 to Uncouple Temperature and Angular Velocity in Onsager's Pancake Approximation

摘要

The auxiliary equation to uncouple temperature and angular velocity in the PANCAKESS code is presented in the context of the complete system of linearized continuum equations governing steady state centrifuge gas dynamics. This single, second order, anisotropic diffusion equation is carefully examined, and boundary layer-like character under high-speed conditions (A exp 2 >> 1) is identified through physical reasoning. Both exact and perturbation solutions are constructed for the main drive mechanisms of interest, (e.g., wall temperature, end cap temperature, scoop and feed). Several analytical solutions are greatly simplified in the perturbation approximation of matched asymptotic expansions and simultaneously reduce computational labor. As a result, the physics of this process is described in several cases of interest by very simple expressions. (ERA citation 05:025347)