臺灣博碩士論文加值系統

微流管是微機電系統中的重要元件，而微管中的流場會直接影響微機電系統的效能，因此微流管與工作氣體的互動機制便成了一相當重要的課題。
因為微管的特徵長度與氣體分子的平均自由徑，在數量級上已經非常接近。所以本篇論文以分子的觀點，加上機率統計的觀念，直接的模擬氣體分子群在微管中的行為，進而表現出微管流場的形貌，此種模擬方法即為『直接模擬蒙地卡羅法』。
本篇論文成功的模擬出五種不同尺寸大小的超音速管流（入口速度接近五馬赫）的流場形貌，經過交叉比對後，可以得到掌控微管流暢的機制有入口氣體所代表的『慣性效應』、管壁所造成的『黏滯效應』、與出口及管長反應出的『釋放效應』，並且可以觀察到入口附近會出現明顯『震波』，以及管壁附近的流速並非為零與溫度不連續等微觀的物理現象。
最後，透過三維的模擬結果與前人的二維結果比對，可知以二維的結果來解釋『微口徑方管流場』，會造成很大的誤差，許多的物理現象都會往出口方向移動，如震波等等，這是由於二維的模擬忽略其中兩側管壁的影響所造成的結果，因此，以直接模擬蒙地卡羅法分析微系統流場時，實驗模型的建立必須格外的謹慎。

The microchannel is a very important element in Microelectro-
mechanical system, and the gas flow in the channel will affect the performance of microsystem directly. Hence, the regime of interaction between microchannel and working gas becomes a serious topic.
Because of the approach of characteristic length of microchannel to the mean free path of working gas, the thesis takes advantage of the concept of probability and statistics to simulate the behavior of molecules in the system with the theory of molecular gas dynamics, and then show the profiles of flow fields finally. This method is well-known as Direct Simulation of Monte Carlo Method.
The thesis have simulated five different cases of supersonic square microchannel flows with different channel sizes and got the regimes handling the flow field of microchannels. The regimes include the effect of inertia, viscous effect and effect of relaxation. The effects are caused respectively from the gas injected from the inlet, walls of the channel, and the outlet and channel length. The obvious shack waves in the local region of the center of inlet, the non-zero flow velocity and the temperature jump in the region close to walls of channel are also found.
After the comparison of three dimensional simulated results and the two dimensional results done by other researchers, the deviation will be great if two dimensional simulated result is used to explain square microchannel flow field. Many physical phenomena, such as shock waves in the region of the inlet, will be far away from the channel inlet in the direction to channel outlet. This resulted from the ignorance of one side of channel walls. Hence, the simulate model must be built very carefully when DSMC is used to analyse the flow field of microsystem.

第一章 緒論…………………………………………………1
1-1 研究動機及目的…………………………………………1
1-2文獻回顧…………………………………………………3
1-3 論文架構…………………………………………………5
第二章 分子氣體動力學之相關理論……………………6
2-1納森數………………………………………………………6
2-2簡單氣體……………………………………………………8
2-3 速度分佈函數……………………………………………12
2-4三種具代表性的分子熱速率………………………………15
2-5 單位面積之數通量………………………………………17
2-6 二體彈性碰撞……………………………………………18
2-6-1動量與能量守恆……………………………………19
2-6-2 碰撞動力學(collision dynamics) …………………21
2-6-3 VHS分子模型………………………………………23
第三章 數值模擬的過程與實驗案例的參數……………26
3-1 微管流的物理模型…………………………………………26
3-2 直接模擬蒙地卡羅法………………………………………27
3-3 假設與基本流程……………………………………………28
3-4 環境參數的設定原則………………………………………31
3-4-1 網格與時步…………………………………………31
3-4-2 邊界條件……………………………………………32
3-4-3 模擬加權因子與起始流場粒子分佈………………33
3-5 程式的核心…………………………………………………34
3-5-1 粒子的移動…………………………………………35
3-5-2排序與粒子的碰撞…………………………………36
3-5-3 抽樣…………………………………………………38
3-6 巨觀量的表示……………………………………………38
3-7各個實驗案例的參數……………………………………39
第四章 結果與討論………………………………………42
4-1 各個案例的模擬結果……………………………………42
4-1-1 案例一的結果………………………………………43
4-1-2 案例二的結果………………………………………51
4-1-3 案例三的結果………………………………………57
4-1-4 案例四的結果………………………………………65
4-1-5 案例五的結果………………………………………73
4-2 比較與討論………………………………………………81
4-2-1 案例二的討論………………………………………81
4-2-2 流速場的綜合討論…………………………………81
4-2-3 壓力場的綜合討論…………………………………82
4-2-4 溫度場的綜合討論…………………………………83
4-2-5 密度場的綜合討論…………………………………83
第五章 結論與建議………………………………………85
5-1 結論………………………………………………………85
5-2 對未來研究方向之建議…………………………………86
參考文獻…………………………………………………………… 88
附錄 馬克斯威爾速度分佈函數的亂數產生法……………………90

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