本研究採用直接模擬蒙地卡羅法(DSMC)模擬低速氣體通過長度很短的二維平板(L/D=6)，選用氮氣、氬氣、氦氣為研究氣體。設定進口氣體的紐森數(Kn)為0.09至0.2。探討改變壁面溫度、進口壓力、模擬流體的不同對於熱傳效果和速度分佈之影響。利用DSMC模擬二維平板的結果計算出其熱傳效果與摩擦係數，並與前人做比較。最後針對模擬結果為過渡流區的流場進行分析，用平均紐賽數 對平均普朗克數( )與平均紐森數( )建立一關係式。

A numerical prediction using the Direct Simulation Monte Carlo method (DSMC)has been performed on low speed gas flows through a short parallel plate microchannel(L/Dh=6). Computations were carried out for nitrogen, argon, and helium gas. Micro pressure driven flows are simulated with the inlet value of the Knudsen numbers ranging from 0.09 to 0.2. The effects of varying pressure, wall temperature, inlet flow and gas transport properties on the wall heat transfer, pressure and velocity distribution were examined. Friction factors and heat transfer from the channel were also calculated and compared with those of previous studies. Finally, the averaged Nusselt number was correlated in a simple form of the averaged Peclet number and Knudsen number in the transition flow regime.

目 錄 頁 次
目錄 i
圖目錄 iii
表目錄 v
符號說明 vi
中文摘要 ix

第一章 緒論 1
1-1 前言 1
1-2 研究背景、動機 2
1-3 文獻回顧 2
1-4 研究重點 4

第二章 理論分析 8
2-1 稀薄氣體的定義 8
2-2 波茲曼方程式 11
2-3 流場性質之定義 13
2-4 N-S方程式配合滑移邊界條件的理論解 15
2-5 流場性質之計算 22

第三章 實驗步驟 25
3-1 直接模擬蒙卡羅法(DSMC) 25
3-2 DSMC之假設與基本流程 26
3-3 DSMC參數設定 28
3-3-1 網格設定 28
3-3-2 時步設定 32
3-3-3 邊界條件 32
3-3-4 碰撞對的選擇 33
3-3-5 VHS分子模型 34
3-3-6 穩態設定 34

第四章 結論與討論 38
4-1 問題描述與模型建立 38
4-2 流體性質 39
4-3 各case的參數與模擬結果 43

第五章 建議 85

參考文獻 86

圖 目 錄 頁次
圖1-1 Kn的範圍及所對應的流體模式 6
圖2-1 Kn與數學式的關係 10
圖2-2 DSMC模擬值與解析解之比較 21
圖3-1 DSMC流程圖 27
圖3-2(a) 矩形網格 29
圖3-2(b) 不規則網格 29
圖3-3 熱場case1、2、3、5、6網格測定 30
圖3-4 熱場case4、7、8網格測定 31
圖3-5 熱場case4速度達穩態之Print cycle 36
圖3-6 熱場case4溫度達穩態之Print cycle 37
圖4-1 流場模型 40
圖4-2 熱場模型 41
圖4-3 不同網格數的壓力模擬結果 46
圖4-4 不同網格數的壓力模擬結果 47
圖4-5 流場模型壓力分佈 49
圖4-6 流場模型Kn分佈 50
圖4-7 流場模型case1速度分佈 51
圖4-8 流場模型case2速度分佈 52
圖4-9 流場模型case3速度分佈 53
圖4-10 流場模型case4速度分佈 54
圖4-11 流場模型立體速度分佈 55
圖4-12 流場模型case1密度分佈 56
圖4-13 流場模型case2密度分佈 57
圖4-14 流場模型case3密度分佈 58
圖4-15 流場模型case4密度分佈 59
圖4-16 流場模型case1、case2馬赫數分佈 60
圖4-17 流場模型case3、case4馬赫數分佈 61
圖4-18 流場模型case1摩擦係數分佈 63
圖4-19 流場模型case2摩擦係數分佈 64
圖4-20 流場模型case3摩擦係數分佈 65
圖4-21 流場模型case4摩擦係數分佈 66
圖4-22(a) 熱場模型case1、2、3、5、6網格分佈 71
圖4-22(b) 熱場模型case4、7、8網格分佈 71
圖4-23(a) case8不同模擬分子之溫度分佈 72
圖4-23(b) case8不同模擬分子之壓力分佈 72
圖4-24 case2中心線溫度分佈與(2.11)式理論解的比較 73
圖4-25 與Farouk熱通量之比較 74
圖4-26 Kn分佈 78
圖4-27 熱通量分佈 79
圖4-28(a) x=0.00048溫度分佈 80
圖4-28(b) x=0.000732溫度分佈 80
圖4-28(c) x=0.000969溫度分佈 81
圖4-28(d) x=0.002397溫度分佈 81
圖4-29 Nu分佈 82
圖4-30 雷諾數分佈 83
圖4-31 與 、 的關係式 84

表 目 錄 頁次
表4-1 氣體性質 42
表4-2 流場模型參數 45
表4-3(a) 熱場模型參數 69
表4-3(b) 熱場模型參數 70

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