Limits of one dimensional modeling of rarefied Couette Poiseuille clearance flow in vacuum pumps

Abstract

Clearance flows are the main loss mechanism in dry running positive displacement vacuum pumps. In order to calculate the operation of those pumps a detailed knowledge of the clearance mass flow rates is crucial. The dimensions of such pumps and the large pressure range of the operating points require a wide range of gas rarefaction to be taken into account. The clearance flow can be described by a combined Couette Poiseuille flow due to the pressure gradient between two chambers and the rotation of the rotary pistons. A clearance of variable cross section is investigated and in order to determine the mass flow rate, the DSMC (direct simulation Monte Carlo) method is used. Results in the slip and transition flow regime are compared to experimental findings and a good agreement can be found. In addition, a one dimensional theory is presented based on a linear superposition of Poiseuille and Couette flow rates. The aim of the present work is to determine the limits of the one dimensional theory concerning the geometry of such clearances. For this, the boundary conditions circumferential speed, inlet and outlet pressure are varied.