This study forms part of a program to develop a micro-electro-mechanical-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 no-slip boundary condition is not accurate. The Knudsen number becomes a dominant non-dimensional parameter in these machines due to their small size and low pressures. As the Knudsen number increases slip flow 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 mean-free-path of the gas molecules. This is validated against an available micro-Poiseuille classical solution at Knudsen numbers between 0.001–0.1 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 two-dimensional simulations are used to evaluate three boundary conditions, classical no-slip, specified-shear and slip-flow. 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 specified shear simulations. As the specified-shear simulations are computationally expensive it is reasonable to use slip-flow boundary conditions. This approach was used to perform three-dimensional simulations of the stage. Again the stage pressure increased when slip-flow was present compared with the classical no-slip boundaries. A characteristic of MEMS scale turbomachinery are the large relative tip gaps requiring three-dimensional simulations. A tip gap sensitivity study was performed and it was found that when no-slip boundaries were present the pressure ratio increased significantly with decreasing tip gap. When slip-flow boundaries were present this relationship was far weaker.

This content is only available via PDF.
You do not currently have access to this content.