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.
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. These clearance flows are studied experimentally and theoretically in the present work. Therefore, a suitable experimental setup is described together with the requirements of sensors and the necessity of a low leakage. A theoretical approach is presented, and the results are compared to experimental investigations varying the pressure ratio and the circumferential speed of a clearance boundary in a wide range of the gas rarefaction.Published by the AVS. https://doi.
The reduced mass flow rates of a rarefied Couette and Poiseuille flow in a long rectangular channel are calculated in the whole range of the gas rarefaction and a wide range of the width to height ratio. Furthermore the walls may be made of different materials so that different tangential momentum accommodation coefficients (TMACs) may be applied. Analytical solutions are given for the slip regime, where all four surrounding walls may have a different TMAC. Due to a simplified modelling assumption, these solutions can be used to correct the well-known flow rates of a fully diffuse channel for different TMACs in the whole range of the gas rarefaction. If the slip solution and the diffuse solution are known, the procedure can principally be adapted for any channel shape. The results of the analytical model expressions are validated with simulation data of the plane Couette and Poiseuille flow and the Poiseuille flow through a pipe which are found in the literature. In addition the analytical solution is compared to results of the Direct Simulation Monte Carlo (DSMC) method of a Couette and a Poiseuille flow in a rectangular channel, which are provided as tabulated data for a variation of the gas rarefaction parameter at different aspect ratios and different combinations of TMACs. The procedure to calculate the mass flow rate of the certain flow as well as the application limits are discussed.
The mass flow rate of a Couette flow in a long rectangular channel is calculated for constant or linear wall velocities in the whole range of the gas rarefaction and in a wide range of the width-to-height ratio. Analytical solutions for arbitrary width-to-height ratios are given for the hydrodynamic regime, the slip regime, and the free molecular regime. Therefore, both the velocity field and the mass flow rate can be calculated. In the transitional regime, simulations via direct simulation Monte Carlo method are performed. The results are provided as reduced flow rates in tabulated data, which can be used for any constant or linear increasing wall velocity (e.g., bounding walls of working chambers in positive displacement vacuum pumps).
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.
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