Holweck pumps are used as high-pressure drag stages in hybrid turbomolecular vacuum pumps, to extend the maximum compression ratio up to outlet pressures in the 1-10 mbar range. This corresponds, for the typical pump dimensions, to the transitional and the viscous laminar regimes. In this pressure range, thermal problems related to the viscous heating of the rotor become a major issue in the design of the pump.
The fluid dynamic study of Holweck pump stages in the viscous regime was carried out by Boulon et. al., using a three-dimensional no-slip Navier-Stokes model (Vacuum 60, p. 73-83, 2001). They showed a good level of agreement with their experimental data (pressure and throughput) in viscous regime, but the accuracy of their model decreased for pressures corresponding to Knudsen numbers Kn > 0.01, for which they suggested the need of slip-flow boundary conditions.
The benefits of slip-flow boundary conditions at Kn > 0.01 were confirmed by Giors et. al. in part I of the present work (J. Vac. Sci. Technol. A 24(4), p. 1584-1591, 2006), where a three-dimensional fluid dynamic model of a single stage Holweck pump was developed, based on the Navier-Stokes equations, with viscous slip and thermal jump boundary conditions. The results were validated against experimental data in terms of pressure profile in the grooves and mechanical power dissipation. In this companion paper, the emphasis is on the modelling of the heat transfer phenomena occurring between rotor and stator of the Holweck pump, which is very important in view of the potentially critical effect of the rotor temperature on the pump lifetime. Taking advantage of the high Biot number, a lumped-parameter heat conduction model of the rotor and of the static parts of the pump is derived. The heat conduction model is coupled to the three-dimensional fluid dynamic model of part I and the commercial CFD code FLUENT is used to solve the conjugate heat transfer problem in the viscous and transitional regimes, allowing a prediction of the rotor temperature. A dedicated experiment, also presented in this paper, has been then developed and performed at Varian in order to validate the model. It is shown in the paper that the computed results are in good agreement with the measurements. |