應用DSMC法於具壓力邊界條件之微氣流場研究

Abstract

發展一個二維、非結構性以及具有壓力邊界處理的直接蒙地卡羅 (Direct Simulation Monte Carlo, DSMC) 程式及其微小尺寸流場之應用描述如下，利用VHS (Variable Hard Sphere) 分子模型、NTC(No Time Counter) 碰撞取樣法以及利用CELL-BY-CELL的粒子追蹤法來完成分子的移動。此程式已藉由比較理論上及計算上之平衡狀態時的碰撞頻率，以及模擬一維非平衡正波得到認證。並且模擬了微小尺寸的應用，如微小T型管、微小噴嘴以及微小滑動氣墊軸承。目的是為了測試我們的程式是否可以處理利用分子流量守恆所推導出來的壓力邊界、複雜的幾何形狀以及具移動邊界的流場。對微小T型管而言，在次音速的流場中我們可以得到入口以二個出口的質量流量是相符的。對微小噴嘴而言，我們固定入口的壓力，發現質量流率會隨著壓力比 (出口比入口) 的減少而增加，但是流率最後保持固定不再隨壓力比改變時，所得到的壓力比相對的比利用連續非流體觀點所分析的值較低。在較高的壓力比情況下，最大的馬赫數會隨著壓力比的減少而向下移動，在較低的壓力比情況下，馬赫數會一路加路到噴嘴的出口，最後當壓力比比0.143還小的時候，在出口的地方會呈現超音速的情況。最後就電腦硬碟機的微小滑動氣墊軸承，在不同的轉動速度下，模擬的氣體壓力結果與先前的研究相符合。但是由於在高速的轉動下，在出口之處會產生非平衡現象，故利用平衡時波茲曼分佈函數所推導出的壓力邊界處理法的可用性是值得討論的。

The development of a two-dimensional DSMC (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, VHS (Variable Hard Sphere) molecular model and NTC (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 1-D normal shock with previous reported work. Applications to micro-scale gas flows includes micro-manifold, micro-nozzle and slider air bearing. This 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.