Direct Simulation of Free Molecular Flow in Fully Three-Dimensional Axial Rotor

The pumping performance of turbomolecular pumps (TMPs) in free molecular flow has been investigated experimentally and theoretically by Kruger. His study was based on parallel flat-plate blades with infinite height, and calculations were made on single-row and multirow blades by Monte Carlo methods. Sawada et al. studied flat blades with finite height for a single rotor using an integration method. This method was based on some geometrical calculations for transmission of molecules from elements of the blade and integration of these elements on the blade boundary. However, a closed-form solution for integral equations could not be found due to the complication of multiple reflections between blades, and a solution was obtained using a numerical approach. Katsimichas et al. simulated free molecular flow within a single-rotor machine with a three-dimensional flat-plate blade using the Monte Carlo method. Their calculations were done in the rotational reference frame where the molecular paths were not straight lines; they also neglected effects of clearance between the tip of the blade and the pump casing. The maximum compression ratio was found higher than that calculated via two-dimensional simulation, especially at high rotational speed and when pumping heavy gases. Skovorodko considered the effect of clearance between the blade tip and pump casing. Neglecting the blade thickness, he simulated free molecular flow in a couple of rotor-stator stages using the inertial frame of reference and Monte Carlo method. In an inertial frame the moving path of a molecule is a straight line and following this path is done both in rotor and stator in a similar system of coordinates. This is actually one of the main advantages of using the inertial frame in such simulations. In the present work, the simulation of a single rotor with flat-plate blades is done considering three-dimensional and real topology of the system in an inertial frame of reference. The effects of both blade thickness and blade-casing clearance are also considered.