Finite element analysis of rotating flow in a skewed shrouded rotor geometry

The present investigation is concerned with the effects which are produced by the slight geometrical distortion of an axisymmetrical shrouded rotor. A distortion of this nature can occur in connection with the manufacture of high precision machinery, such as gyroscopic equipment in inertial guidance systems. In such cases, the effect of the geometrical error on the performance of the rotor has to be reduced to an acceptable amount by means of an appropriate adjustment procedure. The problem of fully viscous flow between a stationary and a tilted rotating disk has been studied by Bar-Yoseph et al. (1981). The current investigation considers the more general problem of the fully viscous flow within a complex domain. Solutions are obtained by the finite element method. Two numerical schemes are developed, including one which is based on mixed finite elements and another which utilizes the penalty formulation.