本文以直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)[1]來模擬改變不同進出口壓力之二維背向式階梯微流場，用以分析不同紐森數對流場現象之影響，接著探討三維背向式階梯微流場的流場現象。本文使用質量流率相等法來修正低速背向式階梯微流場的進出口邊界條件，所模擬的工作流體為氮氣(N2)，分子模型則採用VHS分子模型。
    在本文中，由不同紐森數之二維模擬結果，可以發現當流場kn=0.1時渦流現象將消失，而由流場圖中則是發現當kn值越大，也就是流場越稀薄的時候，階梯的影響將不顯著，由於流場稀薄度變大的關係導致流場內的速度梯度變大，發現流場有發散的跡象。而在三維的模擬中，三維之模擬結果與二維之模擬結果有明顯的差異；就速度分佈來看，三維流場之模擬結果比二維流場之模擬結果低了許多，大約只有二維模擬的70％，這是因為三維模擬流場之管壁效應比二維模擬流場大的結果；也由於這個原因，三維流場模擬結果中，渦流消失的流場之kn值與二維流場是不同的，三維模擬時當流場kn=0.02渦流消失。本文也模擬加大寬高比1，3和5倍，其結果顯現在三維的模擬時，寬高比小於3的時候，兩邊壁的效應對流場的影響就相當顯著，隨著寬高比的增加，此時流場性質愈趨近二維模擬時的結果，所以本文發現當管徑之寬高比大於5時，以二維流場模擬三維實例是合理的。

The Direct Simulation Monte Carlo (DSMC) method has been employed to analyze the rationality of the 2-D simplification for a 3-D backward-facing step flow. An mass flux treatment for low-speed inflow and outflow boundaries for the DSMC of the microchannel flow is employed. The VHS model and Nitrogen was employed in the simulation. The 3-D microchannel flows is simulated with the cross aspect ratio in the range of 1 and 5. The calculated flow properties in the 3-D cases are compared with the results of the 2-D case. It shows that when the aspect ratio < 3, the two extra side walls in the 3-D case have significant effects on the heat transfer and flow properties. When the aspect ratio increases, the flow pattern and heat transfer characteristics tend to approach that of 2-D results. The 2-D simplification is found to be reasonable only when the cross aspect ratio is larger than 5.
In this paper, the effects of rarefaction on flow characteristics are also analyzed and discussed. It is found that flow separation, recirculation, and reattachment will disappear as Knudsen number, Kn, exceeds 0.1 for 2-D case, and will disappear as Kn exceeds 0.02 for 3-D case.

目錄

目錄	I
表目錄	III
圖目錄	IV
符號說明	VI
第一章 緒  論	1
1-1 前言	1
1-2 文獻回顧	4
1-3 研究目的與方法	7
第二章  直接模擬蒙地卡羅法	10
2-1 DSMC 法	10
2-2網格設置與計算時步	11
2-3流場初始條件	12
2-4流場邊界處理	13
2-5低速流之進出口條件設定方法	16
2-6碰撞對(Collision Pair)的選擇	17
第三章  分子模型的選擇	20
3-1  硬球模型(HS)	20
3-2  可變硬球模型(VHS)	20
3-3  可變軟球模型(VSS)	21
3-4 雙原子分子模型	22
第四章 結果與討論	26
4-1 模擬模型	26
4-2 二維模擬結果	26
4-3 不同紐森數區間對二維背向式階梯微流場之影響	27
4-4 三維模擬與二維模擬驗證與比較	28
4-5 不同紐森數區間對三維背向式階梯微流場之影響	29
第五章 結論與未來工作	31
5-1 結論	31
5-2 未來工作	32
參考文獻	33
 
表目錄

表 4-1 VHS 分子模型基本參數	36
表 4-2 二維背向式階梯微流場基本設定	36
表 4-3 二維矩形方管流場基本設定	37
表 4-4 改變三維矩形管口徑之流場設定	37
 
圖目錄
圖1-1  Kn值與統御方程式間的關係圖	38
圖2-1 DSMC流程圖	38
圖2-2分子碰撞面積示意圖	39
圖3-1硬球模型碰撞示意圖	39
圖4-1 Hong Xue與Bin Xu二維背向式階梯微流場模型示意圖	40
圖4-2 三維背向式階梯微流場模型示意圖	40
圖4-3 Hong Xue二維微流場模型示意圖	41
圖4-4 二維背向式階梯微流場驗證圖	42
圖4-5 二維矩形空管流場驗證圖	43
圖4-6 二維不同kn值之流線速度圖	45
圖4-7 二維不同kn值之流場速度圖	47
圖4-8 三維不同管徑寬度與二維模擬之速度比較圖	49
圖4-9 三維不同管徑寬度與二維模擬之壓力分佈比較圖	51
圖4-10 三維kn=0.04之流線速度圖	52
圖4-11 三維kn=0.04之流場速度圖	52
圖4-12 三維kn=0.03之流線速度圖	53
圖4-13 三維kn=0.03之流場速度圖	53
圖4-14 三維kn=0.02之流線速度圖	54
圖4-15 三維kn=0.02之流場速度圖	54
圖4-16 三維kn=0.01之流線速度圖	55
圖4-17 三維kn=0.01之流場速度圖	55

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