AVS 59th Annual International Symposium and Exhibition
    Vacuum Technology Tuesday Sessions
       Session VT-TuM

Paper VT-TuM9
A Comparison between Numerical and Analytical Models of Turbomolecular Drag Pump’s Stages

Tuesday, October 30, 2012, 10:40 am, Room 14

Session: Pumping, Gas Dynamics and Modeling
Presenter: I.F. Cozza, Agilent Technologies, Italy
Authors: I.F. Cozza, Agilent Technologies, Italy
M. Rose, PI-DSMC, Germany
R. Arpa, Optimad Engineering S.R.L., Italy
H. Telib, Optimad Engineering S.R.L., Italy
Correspondent: Click to Email
The design and optimization of vacuum pumps requires a deep knowledge of the internal gas-dynamics, and a large trial-and-error process to fix the design parameters. A common practice in the TMDP’s industry is to perform an experimental design of new pumps, by testing the global performances of prototypes. This approach has two drawbacks: it doesn’t give indications on the details of the internal fluid dynamics of the problem, and the design and realization of prototypes has significant costs and requires long times, that could affect the time-to-market of new products.

In this framework, an accurate and efficient numerical analysis tool could meet these needs. This tool should model the tridimensional, local flow features, such as pump leakage and development of the rarefied gas flow along the curved channels, and take into account the inertial forces.

In this work, two approaches will be presented: a full 3D Direct Simulation Monte Carlo numerical analysis of the Siegbahn drag stages, and a semi-analytical approach based on the numerical solution of the Linearized Boltzmann Equations.

The DSMC simulations have been performed using a DSMC software package called PI-DSMC. The sampling and collision cells were generated automatically from a triangular mesh describing the shape of the solid body. The reflection of molecules by the walls was investigated to choose the proper particle/surface interaction model. The temperature of the rotor, the stator and the gas at the inlet have a fixed value. The effect of rotor temperature on the performances of the stage has been investigated. The collisions between nitrogen and hydrogen molecules were modeled using the variable hard sphere model with the common parameters.

The semi-analytic model is developed for steady flows in spiral molecular drag stages, and it is based on the solution of the Boltzmann Equation (BE) with a BGK closure. The order of the original problem is reduced in the physical space to 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 to the inlet, in order to recover the integral performances of the pump. The original BGK equation is linearized in the most significant parameters (rotational speed and pressure gradients), and solved in the reference cross-section, by means of a DVM scheme. Maxwell diffuse boundary conditions and impermeability are provided at walls. The local values of pressure and torque are obtained consistently by enforcing the mass flow.