Validation of inhomogeneous chamber states in rotary positive displacement vacuum pumps

Abstract

Chamber model simulation is a common approach to simulate rotary positive displacement vacuum pumps. Therefore the pump is abstracted into working chambers and connecting clearances, whereby the clearance leakages can be identified as the major loss mechanism in such machines. The clearance mass flow rates are calculated with respect to the thermodynamic states in the adjacent chambers, which are inhomogeneous for rarefied gases due to the movement of the rotors which causes a pressure gradient within the chamber. This effect increases with higher Knudsen numbers, because of the increasingly dominant friction. These inhomogeneous chamber states are assumed to be quasi-static in case that the chamber volume is constant with time. Therefore the chamber must not have a connection to the suction or discharge port. This can be modelled with a one-dimensional approach for geometrically abstracted chambers. In order to validate the one-dimensional characteristics in circumferential direction three-dimensional steady state simulations of a working chamber are performed using a Computational Fluid Dynamics (CFD) solver. To improve the accuracy for rarefied gases Maxwell velocity slip boundary conditions are applied. It is shown, that the inhomogeneous chamber states can be approximated by a regression analysis of a dimensionless number. Furthermore the housing clearance and the radial clearance mass flow rates for given boundary conditions are geometrically abstracted and calculated using a one-dimensional model. The new clearance models and the inhomogeneous chamber states are implemented in a chamber model simulation software and results of a test machine are compared to measurements and to previous simulations.