Numerical investigation of high Knudsen number flow in rectangular enclosures

Abstract

Nowadays, enlightening unknown aspects of rarefied gas flow is one of the critical issues of fluid dynamic research to ensure correct and proper operations of manyMicro- Electro-Mechanical-Systems (MEMS). Thermally driven motion of rarefied gases is gaining in importance to develop Knudsen compressors having better performance or to improve single crystal growth processes. Therefore, accurate prediction of the physics lying behind the thermal creep in the transition regime as well as slip flow regime is one of the main motivations of this study. The other emphasis is possible flow instability of the rarefied gases in enclosures. For this purpose, an asymptotic approximation has been performed in the first part of the study to find analytical solutions. In the second one, linear disturbance theory of hydrodynamic stability has been applied to the problem to determine bounds of instabilities. Analytical solutions of two-dimensional stability analysis have been introduced. Critical states have been identified for different models and for varying Knudsen numbers. More generally, eigen-spectrum of the perturbation equations has been identified in three-dimensions. At the last part, by applications of an artificial viscosity scheme, a computer program has been constructed to solve Burnett and also Navier-Stokes equations. Mechanisms of the thermal creep flow have also been verified by inspecting stress tensors of Burnett equations. Most importantly, the insufficiency and the failure of Navier-Stokes equations for the creeping flows have been proved. Moreover, it has been shown that Burnett equations can correctly model such creeping flows.