Formulation of a Generalized Narrow Groove Theory for Spiral Grooved Viscous Pumps

Abstract

The well-established narrow groove theory for spiral groove gas bearings [1] has been generalized to include the effects of rarefied gas and turbulence. The slip flow effect was considered locally depending upon gaseous density and molecular mean free path [2] while the local turbulence effect was introduced by a set of viscosity modification functions [3, 4]. For transition flow, the concept of “mean” local Reynolds number may be adapted [5]. The fundamental governing equation was derived in terms of a generalized coordinate for bodies of rotational symmetry and valid for both incompressible and compressible bearings or seals.