Navier–Stokes modeling of a Gaede pump stage in the viscous and transitional flow regimes using slip-flow boundary conditions

Abstract

A three-dimensional model for a Gaede pump, based on the Navier–Stokes equations with no-slip boundary conditions, was introduced by the authors in a previous work. A commercial computational fluid dynamics code was used to obtain the solution in an outlet pressure range corresponding to the viscous laminar regime and incipient transition to molecular flow and the validation against the experimental data showed a good level of accuracy in terms of compression ratio. However, the mechanical power dissipation predicted by the no-slip model shows a trend diverging from the measured data for decreasing pressure, in the transitional flow regime. As most of the mechanical power is dissipated into heat by viscosity, slip-flow boundary conditions are introduced here in order to model the transitional effects on the wall shear stress and improve the accuracy of the Navier–Stokes description at low pressure. The calculation is carried out up to Knudsen numbers Kn≈1, showing a very good agreement of the Navier–Stokes model, even close to molecular flow conditions, and leaving a residual error acceptable for design purposes. The model is used to analyze the flow fields in the Gaede pump and explain its behavior. The slip model needs just one adjusting parameter, i.e., the momentum accommodation coefficient, but exhibits a small sensitivity to its variations. Hence it can predict the compression ratio and power dissipation of Gaede pumps of any size in their whole operating pressure range, from the laminar viscous regime down to the transition to the molecular flow regime.