Modelling 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 normally considered to be homogeneous. In this work it is shown, that the chamber state is inhomogeneous for rarefied gases due to the movement of the pistons which causes a pressure gradient within the chamber. This effect increases with higher Knudsen numbers, because of the increasingly dominant friction. An efficient way to model these inhomogeneous states with a one-dimensional approach for geometrically abstracted chambers is shown. The approach is applied to chamber model simulations of a screw spindle vacuum pump (SSVP) and the results are compared to simulations with homogeneous chamber states and to measurements.

Validation of inhomogeneous chamber states in rotary positive displacement vacuum pumps

“…Regarding the inhomogeneous model from reference [10] (blue line) the curve is not affected in the high pressure regime, but collapses at low suction pressures in qualitatively good agreement with the measurements. But the new model in the current implementation slightly seems to overrate the effect, as the results indicate a worse suction speed than the measurements.…”

“…In a previous paper it was shown that the chamber states are not homogeneous for rarefied gases but that a pressure gradient occurs in tangential direction of the rotor lobe [10]. This is again highlighted in Figure 2 which shows the chamber model abstraction for a screw spindle vacuum pump (SSVP) with the sketched network of chambers and connecting clearances.…”

“…In the previous sections the impact of the homogeneous chamber states on the boundary conditions of the clearances have been discussed in detail. In reference [10] the clearance mass flow rates for given boundary conditions have been determined by interpolation of measurement [5] for static walls with simulation data for moving walls in the free molecular regime by Stratmann [3]. This procedure was questioned in recent works as large deviations can occur for clearances in the transitional and slip regime (0.1 < δ < 100) that are dominated by Couette flow.…”

“…Therefore the geometric properties of the chambers and clearances as a function of the rotation angle are needed. The geometric model used in this paper is the same as in reference [10]. Therefore the clearances are not simply connected with two chambers, but with a certain chamber position.…”

Transient chamber filling in rotary positive displacement vacuum pumps

“…The calculation of clearance flows for rarefied gases including moving boundaries has previously been investigated in references [3], [4] and [5] where a data base for different clearance shapes was created and by [6], [7] and [8] where a 1D model was derived and validated in order to calculate the clearance mass flow rates. The impact of the clearance flow models is shown in reference [9].…”