Compressible Narrow Groove Analysis—Part 2: Computation of Pressure Field in a Spherical Device Rotating in Either Direction

Compressible Narrow Groove Analysis, as derived in a companion paper (Pan, 1998), is a model implementation of Thin Film High-Resolution Modeling for gas films. This paper describes the numerical procedure to compute the pressure field in a centered spherical device, which has general design features originally intended for a high performance gas bearing gyroscope (Keating and Pan, 1968). The number of groove patterns is varied to bring out the significance of the local compressibility number. Increased local compressibility, associated with reduced number of groove patterns, causes successive degradation of the pressurization capacity until it is entirely suppressed at 32 groove patterns. Further study is made with reversed rotation to create a high vacuum state in the gas film concurrent with a large compressibility number. The evacuation operation (with reversed rotation) is relatively insensitive to the number of groove patterns, but is highly dependent on the accommodation coefficient. Experience in preparing these examples lends evidence to the robustness of Thin Film High-Resolution Modeling. Trouble free iterative computations are routinely performed for the local Knudsen number in excess of 10⁹ and the effective local compressibility number larger than 100.