One-dimensional simulation of Couette–Poiseuille flow with variable cross section for the full range of gas rarefaction

Abstract

Clearance mass flows are a major loss mechanism in dry running rotatory positive displacement vacuum pumps. Therefore, a detailed knowledge of the clearance mass flow is crucial to calculate the operation of those pumps. The small clearance heights and the large pressure range of such pumps require a wide range of gas rarefaction parameters to be taken into account. The flow in the clearance can be described as a combined Couette–Poiseuille flow with variable cross section. This is typically done by solving the Stokes equation, but especially at high gas rarefaction parameters, the inertia cannot be neglected any more, which can lead to choking of the flow. A one-dimensional approach for the compressible fluid flow was provided by Shapiro. It is shown that this approach can be carried over for the rarefied gas flow. The problem is solved in bounds for the constant total temperature and compared to experimental investigations by varying the pressure ratio and the circumferential speed of the clearance boundary in a wide range of gas rarefaction parameters.