臺灣博碩士論文加值系統

微通道流的研究主要是反映微機電系統於操作過程中熱控制的需求，在微通道流中由於流動的區域屬於高滑動流區或過渡流區，此時若仍將微通道內氣體的流動視為一種連體的現象，則將導致不正確的結果，故本文乃利用直接模擬蒙地卡羅法（DSMC）作為微通道流動與熱傳模擬分析的工具。
在一維的DSMC模擬中對分子施加固定之加速度以作為稀薄氣體流動之驅動力，當流動條件在連體流、滑動流及低過渡流區並維持在層流及次音速流的狀態下，Kn數對速度、溫度等流動性質的影響，同時藉著與連體流動方程式的比較，來驗證該方程式的適用性。模擬的結果顯示兩者的確存在定量及定性上的差異，另外比較HS分子模式及VHS分子模式在模擬結果上的差異，進而發現VHS模式優於HS模式。並從模擬中建立分子運動的機制而可與巨觀的流動現象相互連結。
在二維的DSMC模擬中改由壓力梯度作為稀薄氣體流動之驅動力，調整入、出口的壓力來改變數量密度之大小以控制Kn數的變化，藉此瞭解稀薄效應對整體流動性質的影響。模擬的結果顯示由於一維及二維在氣流驅動條件上設定的不同，以及分子除了於上、下網格外亦可在左、右網格間移動，造成於橫向上溫度分佈呈現相異的結果，在一維的模擬中流場的溫度較壁溫為高，而在二維的模擬中流場的溫度卻較壁溫為低。此外亦發現稀薄效應會造成壓力分佈的線性化，流向速度橫向分佈曲線的平坦化以及滑移速度的增加，由滑移速度的增加則可推論壁面摩擦效應的減弱，此外溫度降的趨勢會逐漸的減緩。
在二維熱傳的模擬中考慮明顯的熱傳效應如冷流熱壁之問題對微通道內氣體流動性質變化的影響。模擬的結果顯示在相同的入、出口條件下，熱壁效應增加了流場的稀薄度及強化了入口條件的影響度，亦造成流場內前後壓力比的增加。

The study of micro-channel flow is partly in response to the need for thermal control in the operation of MEMS in which the range of gas flow is from slip flow to transition regime. It will lead to incorrect results if we consider gas flow in micro-channel as continuum phenomena. In this paper, molecular approach DSMC has been used to study the flow and heat transfer characteristic of rarefied gas in micro-channel.
In one-dimensional simulation, a constant acceleration body force is applied to the system and the flow is restricted in laminar and subsonic state. The simulation results show that the discrepancies of hydrodynamic prediction are widening as indicated from velocity and temperature profiles when the flow in continuum regime transfers to slip flow regime, then low transition regime by increasing Knudsen number（Kn）. The data predicted by VHS model differ quantitatively from HS model, but it exists qualitative consistency between them. The macroscopic flow phenomena could be related to and described by the microscopic molecular motion based on simulation results.
Pressure-driven flows in micro-channel are simulated by varying inlet/exit pressure for a range of slip to transition regime flows. Both ambient and hot wall temperature cases are investigated. The simulation results of the former case show that the temperature in the flow field is lower than that of the channel wall. It is opposite to one-dimensional flow because of the difference of driving force. It is found that pressure distribution along the channel and streamwise velocity distribution in the transverse direction become more linear and flatter respectively with the increase of the Kn. In addition, the slip velocity increases along the streamwise direction.
In hot surface case, the heat flux through the channel wall is more pronounced than in the cold surface case. The flow properties such as temperature, density and pressure are strongly dependent on Kn and heat transfer. The effect of heat transfer from hot wall increases the rarefaction of the flow field and the inlet influence at the same boundary condition. Additionally, the pressure ratio in the flow field is higher than that without heat transfer.

目 錄
誌謝ii
摘要iii
ABSTRACTv
目錄vii
表錄x
圖錄xi
符號說明xiii
1. 緒論1
1.1 研究動機 1
1.2 研究方法 2
1.3 文獻回顧 8
1.4 論文架構 11
2. DSMC之理論基礎 13
2.1 Boltzmann方程式14
2.2 微觀性質與巨觀性質16
2.3 力矩方程式 17
2.4 H定理 19
2.5 Maxwell速度分佈函數20
2.5.1球座標下之分佈函數21
2.5.2球座標下之分佈函數22
2.6 分子的數量通量 23
2.7 二粒子之彈性碰撞24
2.7.1VHS分子模型27
2.7.2平均碰撞時間31
2.7.3平均自由路徑31
3. DSMC數值方法 32
3.1 數值模擬的程序 32
3.2 蒙地卡羅法之應用35
3.2.1粒子初始狀態35
3.2.2超出邊界的處理36
3.2.3碰撞行為的模擬38
3.3 低速微通道流遭遇之問題40
3.4 邊界條件的設定41
3.4.1 壓力邊界條件42
3.4.2 質流率邊界條件44
4. 各算例之結果與討論 46
4.1 自由分子流算例 46
4.1.1問題之描述與規劃 47
4.1.2分子之運動軌跡 47
4.1.3結果與討論 51
4.2 一維微通道流算例 54
4.2.1問題之描述與規劃 55
4.2.2流體動力方程式之解析解 56
4.2.3DSMC模擬之結果與討論 58
4.3 二維微通道流算例 67
4.3.1 問題之描述與規劃 67
4.3.2 流體動力方程式之解析解 69
4.3.3DSMC模擬之結果與討論 70
4.4 二維微通道流熱傳算例 86
4.4.1問題之描述與規劃 86
4.4.2DSMC模擬之結果與討論 87
5. 結論與建議 101
5.1 結論 101
5.2 未來方向 105
參考文獻 106
附錄A 二維微通道之流體動力方程式 110
附錄B 亂數產生器之應用 114
自傳 117

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