AVS 58th Annual International Symposium and Exhibition | |

Vacuum Technology Division |
Monday Sessions |

Session VT-MoA |

Numerical Modeling of Compact Siegbahn Molecular Drag Stages

Session: |
Optical and Mass Spectroscopy for Gas Analysis and Pump Modeling |

Presenter: |
Ivan Flaminio Cozza, Agilent Technologies s.p.a., Italy |

Authors: |
H. Telib, Politecnico di Torino, ItalyR. Arpa, Optimad Engineering s.r.l., ItalyL. Campagna, Agilent Technologies s.p.a., ItalyI.F. Cozza, Agilent Technologies s.p.a., ItalyE. Emelli, Agilent Technologies s.p.a., Italy |

Correspondent: |
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In the frame of an optimization of single/multi-stage disk-type vacuum pumps, characterized by spiral channels a comprehensive but efficient numerical analysis of performances has to be founded on a careful modeling of the local gas flow features, such as pump leakage and development of the rarefied gas flow along the curved channels. Here, gas flows are in general considered three-dimensional, because of the spiral groove curvature, and driven by pressure gradients and the applied rotation speed as well as inertial forces (centripetal and Coriolis effects), which play the most important role.

Following the assumptions made for a Holweck model by Sharipov et al., we propose a lower-order model for steady flows in spiral molecular drag stages, based on the solution of the Boltzmann Equation (BE) with a BGK closure, in general curvilinear coordinates (properly fitted to the geometrical design of the channel), where the inertial effects explicitly appear in the governing equation. The order of the 3D original problem is reduced in the physical space (2D), by introducing assumption of “locally” known flow development of the distribution function along the spiral channel. Thus, 2D-BE calculations of the flow rates and stresses will be performed in a finite number of sections, suitably positioned along the spiral channel, from the outlet up to the inlet, in order to recover the pressure and torque distribution. In particular, the 2D Boltzmann equation is linearized in the most significant parameters ( local rotation speed and pressure gradients along the pump radial direction), and solved in the reference section. The local valus of pressure and torque are obtained consistently by enforcing the mass flow conservation constraint.

A Discrete Velocity Method (DVM) is used to solve the Boltzmann Equation, with an explicit pseudo-time dependent technique to relax the flow up to its stationary solution. In order to decrease the computational time employed, the solver is designed to work on parallel architectures (MPI).

The performance prediction of the model will be assessed using test cases from the literature and compared to the available experimental data, on both Holweck and Siegbahn geometries. A further verification test will be carried out, to test prediction capabilities in the continuum regime by direct comparison with results obtained by a Navier-Stokes solver, with slip-boundary conditions.