Mathematical Simulation of the Roots Vacuum Pump Operation Process

Abstract

The paper reviews main methods in mathematical simulation of the operation processes of the non-contact vacuum pumps, in particular, the Roots external compression machines. It shows that vast majority of the models, including the CFD models, were developed for the continuum conditions, and they are not applicable in the vacuum conditions. Using a system of differential equations based on the thermodynamic system energy balance of the working fluid variable mass, a mathematical model of the external compression machine was developed. Equations were obtained from the laws of conservation of mass and energy, as well as from the equation of state of the ideal gas, and they did not contain restrictions on the gas flow regime. The system of equations was solved using the LSODE numerical method in the Mathematica package. Initial conditions were accepted as gas pressure and temperature in the pumped volume and the gas parameters at the pump outlet. As a result, dependences of pressure and temperature in the volumes under consideration on the rotors rotation angle were found. The model took into account heat exchange between gas and the pump working chamber walls. Backflows through the rotor mechanism slot channels were determined according to the universal method for calculating conductivities in channels of various geometries in the viscous, transition and molecular flow regimes. Results of mathematical simulation of the double-rotor pump pumping characteristics are presented, and they are compared with the experimental data. Validation was carried out both in terms of action speed and the machine indicator diagrams. The developed mathematical simulation technique could be recommended in analyzing the influence of geometry and operating conditions on pumping characteristics of the Roots non-contact oil-free vacuum double-rotor pumps

Please cite this article in English as:

Isaev A.A., Raykov A.A., Burmistrov A.V., et al. Mathematical simulation of the Roots vacuum pump operation process. Herald of the Bauman Moscow State Technical University, Series Mechanical Engineering, 2024, no. 1 (148), pp. 55--68 (in Russ.). EDN: FBFXCC

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