Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method

Abstract

The development of a two-dimensional direct simulation Monte Carlo program for pressure boundaries using unstructured cells and its applications to typical micro-scale gas flows are described. For the molecular collision kinetics, variable hard sphere molecular model and no time counter collision sampling scheme are used, while the cell-by-cell particle tracing technique is implemented for particle movement. The program has been verified by comparison of simulated equilibrium collision frequency with theoretical value and by comparison of simulated non-equilibrium profiles of one-dimensional normal shock with previous reported work. Applications to micro-scale gas flows includes micro-manifold, micro-nozzle and slider air bearing. The aim is to further test the treatment of pressure boundaries, developed previously by the first author, by particle flux conservation for gas flows involving many exits, complicated geometries and moving boundaries. For micro-manifold gas flows, excellent mass flow conservation between the inlet and two exits is obtained at low subsonic flows. For micro-nozzle gas flows, with fixed inlet pressure, the mass flow rate increases with decreasing pressure ratio (exit to inlet), but remains essentially the same at pressure ratios much lower than that obtained by continuum inviscid analysis. For higher specified pressure ratios, the locations of maximum Mach number moves further downstream as the pressure ratio decreases; while, for lower specified pressure ratios, the Mach number increases all the way through the nozzle to the exit. Eventually, supersonic speed is observed at the exit for pressure ratios equal to or less than 0.143. Finally, for slider air bearing gas flows of the computer hard drive, the simulated gas pressures, at different rotating speeds, agree very well with previous studies. However, there exists strong translational non-equilibrium in the gas flows at the high rotating speeds. The applicability of the treatment of pressure boundaries using the equilibrium Maxwell–Boltzmann distribution function is discussed in terms of the magnitude of the local Knudsen number at the pressure boundary for micro-nozzles and slider air bearing applications.