本文使用了直接模擬蒙地卡羅法模擬了三種在積體電路中常見的幾何微管，分別是矩形微管、微結構微管與背向式階梯微管，分別利用上述三種幾何微管做了下列幾種探討；首先是利用矩形微管和微結構微管的模擬結果觀察了流場性質與非平衡區之間的關係；接著利用三維五倍的微結構微管與背向式階梯微管觀察位於上下壁面的中心壁面與管角，分析管角效應的影響下與壁面中心的差異度；以及在背向式階梯微管使用了直接模擬蒙地卡羅法以及Gas-BGK法分析了兩個不同稀薄度之流場，觀察兩種模擬方法之間的差異

Microchannel flow has attracted much attention due to the advent of micro-electro-mechanical systems (MEMS), in this paper, the direct simulation Mante Carlo has been applied to compute low-speed Micro-channel Flows, cross-section channel with micro structure, and backward-facing step.
In this work, the direct simulation Monte Carlo (DSMC) method is employed to study the gas flows in a two-dimensional backward-facing step for different degrees of rarefaction, and Gas-Kinetic Bhatnagar-Gross-Krook (Gas-BGK) scheme is also performed for solving Navier-Stokes (NS) equations with velocity slip wall boundary condition.  The results of microchannel flows show that the non-equilibrium distributed is dependence with the velocity field and Knudsen number. The result showed that the fluid flow to the corner of the wall inside the microchannel was different from the fluid flow to the center of the wall. The influence of fluid flow by the corner of the wall inside the microchannel in 3-D simulation was still different from 2-D simulation.

目錄
中文摘要....................................................................................................I
英文摘要...................................................................................................II
目錄..........................................................................................................III
表目錄 ........................................................................................................ V
圖目錄 ...................................................................................................... VI
符號說明 .................................................................................................... X
第一章 緒論............................................................................................. 1
1-1 研究動機 ........................................................................................ 1
1-2 紐森數的定義 ................................................................................ 1
1-3 波茲曼方程式及其解法 ................................................................ 2
1-4 文獻回顧 ........................................................................................ 5
第二章 直接模擬蒙地卡羅法 .............................................................. 10
2-1 原理及應用 .................................................................................. 10
2-2 網格設置與時步計算 .................................................................. 12
2-3 流場初始條件 .............................................................................. 13
2-4 流場邊界處理 .............................................................................. 14
2-5 碰撞對(Collision Pair)的選擇...................................................... 16
2-6 低速流之進出口條件設定方法 .................................................. 17
2-6-1隱性邊界法 (Implicit Boundary Method Treatment) ............ 17
2-6-2粒子控制邊界法 (Particle Control Treatment) ..................... 19
2-7 流場性質的取樣 .......................................................................... 19
2-8 流場性質的輸出 .......................................................................... 20
2-9 分子模型的選擇 .......................................................................... 20
2-9-1分子模型 ................................................................................. 20
2-9-2硬球模型(HS) ......................................................................... 20
2-9-3可變硬球模型(VHS) .............................................................. 21
2-9-4可變軟球模型(VSS) ............................................................... 22
2-9-5雙原子分子模型 ..................................................................... 22
2-9-6流場性質之計算 ..................................................................... 25
第三章 Gas-BGK方法 ......................................................................... 28
IV
3-1 Gas-BGK方程之基本特性 ........................................................... 28
3-2 Gas-BGK原理 ............................................................................... 28
3-3 邊界設定 ....................................................................................... 30
第四章 結果與討論 .............................................................................. 31
4-1 模擬模型 ...................................................................................... 31
4-2 程式驗證與取樣收斂 .................................................................. 31
4-2-1 矩形微管程式驗證與取樣收斂 .......................................... 31
4-2-2 背向式階梯微管程式驗證與取樣收斂 .............................. 32
4-2-3 微結構微管程式驗證與取樣收斂 ...................................... 32
4-3 二維與三維低速非平衡區 .......................................................... 32
4-3-1 流場的平衡狀態 .................................................................. 32
4-3-2 矩形空管非平衡區探討 ...................................................... 34
4-3-3 微結構微管非平衡區探討 .................................................. 34
4-4 DSMC法與Gas-BGK模擬結果比較 ........................................ 35
4-5 三維管壁中心與管角之比較 ...................................................... 37
4-5-1三維微結構物微管管壁中心與管角分析............................. 37
4-5-2三維背向式階梯微管管壁中心與管角分析 ........................ 39
第五章 結論與建議 .............................................................................. 41
5-1 結論 ............................................................................................... 41
5-2 建議 ............................................................................................... 42
參考文獻 ................................................................................................... 43
表目錄
表4- 1 VHS 分子模型基本參數............................................................. 49
表4- 2二維矩形微管微流場初始設定 .................................................. 49
表4- 3背向式階梯微管流場初始設定 .................................................. 50
表4- 4背向式階梯微管流場初始設定 .................................................. 51
表4- 5微結構微管流場初始設定 .......................................................... 52
圖目錄
圖1- 1 Kn值與統御方程式間的關係圖 ................................................ 53
圖2- 1 稀薄度與密度之關係 ................................................................. 53
圖2- 2 DSMC流程圖 .............................................................................. 54
圖2- 3分子碰撞面積示意圖 .................................................................. 55
圖3- 1硬球模型碰撞示意圖 .................................................................. 55
圖4- 1矩形微流場模型示意圖(a)二維模型 (b)三維模型 ................... 56
圖4- 2背向式階梯微管流場模型示意圖(a)二維模型 (b)三維模型 .. 56
圖4- 3微結構微管流場模型示意圖(a)二維模型 (b)三維模型........... 57
圖4- 4矩形微管滑移速度模擬驗證圖 .................................................. 57
圖4- 5矩形微管流體與壁面溫度差模擬驗證圖 .................................. 58
圖4- 6矩形微管熱通量模擬驗證圖 ...................................................... 58
圖4- 7熱通量模擬驗證圖(a) Xue之模擬結果 (b)本文模擬結果 ...... 58
圖4- 8溫度模擬驗證圖 .......................................................................... 59
圖4- 9流體與壁面溫差模擬驗證圖 ...................................................... 59
圖4- 10熱通量模擬驗證圖 .................................................................... 59
圖4- 11空管微管流場性質穩態圖 ........................................................ 60
圖4- 12 背向式階梯微管流場性質穩態圖 ........................................... 60
圖4- 13微結構微管流場性質穩態圖 .................................................... 60
圖4- 14流場中心線Kn值 ..................................................................... 61
圖4- 15 背向式階梯管之密度分布圖(a)Case2-3(b) Case2-4 .............. 61
圖4- 16背向式階梯管之速度分布圖(a)Case2-3(b) Case2-4 ............... 62
圖4- 17背向式階梯管之溫度分布圖(a)Case2-3(b) Case2-4 ............... 62
VII
圖4- 18壁面密度比較圖(a)Case2-3(b) Case2-4 ................................... 63
圖4- 19中心線速度比較圖(a)Case2-3(b) Case2-4 ............................... 64
圖4- 20滑移速度比較圖(a)Case2-3(b) Case2-4 ................................... 65
圖4- 21中心線溫度比較圖(a)Case2-3(b) Case2-4 ............................... 66
圖4- 22滑移速度比較圖(a)Case2-3(b) Case2-4 ................................... 67
圖4- 23二維矩形方管非平衡區分布 .................................................... 68
圖4- 24三維矩形方管非平衡區分布 .................................................... 68
圖4- 25二維矩形方管Tr/Tt分布 .......................................................... 68
圖4- 26三維矩形方管Tr/Tt分布 .......................................................... 69
圖4- 27二維矩形方管中心線Tr/Tt ....................................................... 69
圖4- 28二維矩形方管Kn值分布 ......................................................... 70
圖4- 29三維矩形方管Kn值分布 ......................................................... 70
圖4- 30二維矩形方管中心線Kn值 ..................................................... 71
圖4- 31二維矩形方管速度分布 ............................................................ 71
圖4- 32三維矩形方管速度分布 ............................................................ 72
圖4- 33二維矩形方管中心線速度 ........................................................ 72
圖4- 34二維微結構物微管非平衡區分布 ............................................ 73
圖4- 35三維微結構物微管非平衡區分布 ............................................ 73
圖4- 36二維微結構物微管Tr/Tt分布 .................................................. 73
圖4- 37二維微結構物微管中心線Tr/Tt ............................................... 74
圖4- 38三維微結構物微管Tr/Tt分布 .................................................. 74
圖4- 39二維微結構物微管溫度分布 .................................................... 75
圖4- 40二維微結構物微管中心線溫度 ................................................ 75
VIII
圖4- 41三維微結構物微管溫度分布 .................................................... 76
圖4- 42二維微結構物微管Kn值分布 ................................................. 76
圖4- 43三維微結構物微管Kn值分布 ................................................. 76
圖4- 44二維微結構物微管中心線Kn值 ............................................. 77
圖4- 45二維微結構物微管速度分布 .................................................... 77
圖4- 46三維微結構物微管速度分布 .................................................... 78
圖4- 47二維微結構物微管中心線速度 ................................................ 78
圖4- 48上壁面牆角與中心壁面滑移速度比較圖 ................................ 79
圖4- 49下壁面牆角與中心壁面滑移速度比較圖 ................................ 79
圖4- 50上壁面牆角與中心壁面溫度比較圖 ........................................ 80
圖4- 51下壁面牆角與中心壁面溫度比較圖 ........................................ 80
圖4- 52上壁面牆角與中心壁面熱通量比較圖 .................................... 81
圖4- 53下壁面牆角與中心壁面熱通量比較圖 .................................... 81
圖4- 54上壁面牆角與中心壁面剪力比較圖 ........................................ 82
圖4- 55下壁面牆角與中心壁面剪力比較圖 ........................................ 82
圖4- 56上壁面牆角與中心壁面壓力係數比較圖 ................................ 83
圖4- 57下壁面牆角與中心壁面壓力係數比較圖 ................................ 83
圖4- 58上壁面牆角與中心壁面滑移速度比較圖 ................................ 84
圖4- 59下壁面牆角與中心壁面滑移速度比較圖 ................................ 84
圖4- 60上壁面牆角與中心壁面熱通量比較圖 .................................... 85
圖4- 61下壁面牆角與中心壁面熱通量比較圖 .................................... 85
圖4- 62上壁面牆角與中心壁面剪力比較圖 ........................................ 86
圖4- 63下壁面牆角與中心壁面剪力比較圖 ........................................ 86
圖4- 64上壁面牆角與中心壁面壓力係數比較圖 ................................ 87
圖4- 65下壁面牆角與中心壁面壓力係數比較圖 ................................ 87

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