MEMS Scale Turbomachinery Based Vacuum Roughing Pump

Abstract

This study forms part of a program to develop a microelectromechanical systems (MEMS) scale turbomachinery based vacuum pump and investigates the roughing portion of such a system. Such a machine would have many radial stages with the exhaust stages operating near atmospheric conditions while the inlet stages operate at near vacuum conditions. In low vacuum such as those to the inlet of a roughing pump, the flow can still be treated as a continuum; however, the noslip boundary condition is not accurate. The Knudsen number becomes a dominant nondimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases, slipflow becomes present at the walls. The study begins with a basic overview on implementing the slip wall boundary condition in a commercial code by specifying the wall shear stress based on the meanfreepath of the gas molecules. This is validated against an available microPoiseuille classical solution at Knudsen numbers between 0.001 and 0.1 with reasonable agreement found. The method of specifying the wall shear stress is then applied to a generic MEMS scale roughing pump stage that consists of two stators and a rotor operating at a nominal absolute pressure of 500 Pa. The zero flow case was simulated in all cases as the pump down time for these machines is small due to the small volume being evacuated. Initial transient twodimensional (2D) simulations are used to evaluate three boundary conditions, classical noslip, specifiedshear, and slipflow. It is found that the stage pressure rise increased as the flow began to slip at the walls. In addition, it was found that at lower pressures the pure slip boundary condition resulted in very similar predictions to the specifiedshear simulations. As the specifiedshear simulations are computationally expensive it is reasonable to use slipflow boundary conditions. This approach was used to perform threedimensional (3D) simulations of the stage. Again the stage pressure increased when slipflow was present compared with the classical noslip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring 3D simulations. A tip gap sensitivity study was performed and it was found that when noslip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slipflow boundaries were present, this relationship was far weaker.