超音速燃燒衝壓引擎(Supersonic Combustion Ramjet, Scramjet)為一種高效率推進系統，本身僅需攜帶燃料不用額外的助燃劑，重量大幅減輕，是未來航空科技之重要研究課題。Scramjet周圍流場為高稀薄度之流場，在此區域連續體的假設將不成立，須以分子觀點來討論，其中直接模擬蒙地卡羅(Direct simulation Monte Carlo, DSMC)法為目前被認為是較精確且使用最廣泛的方法。
本文利用DSMC法模擬Scramjet之極音速稀薄氣體流場。飛行器飛行於低密度高空流場時，進氣道入口分子會受到外緣震波作用造成性質改變，進而影響引擎內流場之結構。而當流場稀薄度增加時，變化亦可能由下游延伸至上游。探討不同稀薄度之自由流在極音速流場下所呈現的物理現象。針對氣流流經不同突張結構之內流場所產生之特性(流場內震波與邊界層互相作用、階梯結構後方產生的膨脹波等)加以討論與分析。最後模擬三維引擎流場，並比較二維與三維結果差異。

Supersonic combustion ramjet (Scramjet) is a high-efficiency propulsion system. Scramjet only needs to carry fuel not to bring booster, the weight of vehicle reduces greatly. It is an important topic of aerospace sciences in the future. Because the flow around the scramjet is high-rarefaction, the assumption of continence isn’t valid. Hence, we have to discuss flow fluid by molecular model.  In molecular gas dynamics, the direct simulation Monte Carlo (DSMC) method is a popular and accuracy simulation technique for low density flows.
Hypersonic rarefied gas flows around a Scramjet inlet model have been analyzed using DSMC method. In the flows around vehicles operating at high altitudes, the molecules at the entrance and the flows properties inside the engine are affected by the shock wave. As the rarefaction of the flows field becomes increasingly, the effect may extend from downstream to upstream. This article discusses the physical phenomenon of different rarefied hypersonic flow field. We analyze the properties, including the shock-boundary interaction and expansion effect, of the gas flow in different sudden expansion structure. Finally, the results of three-dimensional scramjet flow are compared with those of two-dimensional scramjet flow.

誌謝.....................................I
中文摘要.................................II
英文摘要.................................III
目錄.....................................IV
表目錄...................................VII
圖目錄...................................VIII
符號說明.................................XII
第一章 緒  論............................1
  1-1前言................................1
  1-2文獻回顧............................2
  1-3研究目的與方法......................5
  1-4紐森數的定義........................6
  1-5波茲曼方程式及其解法................8
第二章  直接模擬蒙地卡羅法...............13
  2-1直接模擬蒙地卡羅法..................13
  2-2網格設置與計算時步..................14
  2-3流場初始條件........................15
  2-4流場邊界處理........................16
  2-5碰撞模型............................19
    2-5-1硬球模型........................19
    2-5-2可變硬球模型....................19
    2-5-3可變軟球模型....................20
    2-5-4雙原子分子模型..................21
  2-6碰撞	................................24
  2-7巨觀性質............................25
第三章 超音速燃燒衝壓引擎................28
  3-1超音速燃燒衝壓引擎介紹..............28
  3-2超音速燃燒衝壓引擎構造..............29
  3-3超音速燃燒衝壓引擎遭遇的困難........30
第四章 結果與討論........................31
  4-1程式驗證與網格測試..................31
  4-1-1程式驗證..........................31
  4-1-2網格測試..........................32
  4-2模擬構型............................33
  4-3不同ICR (相同擴張率)比較............34
    4-3-1 12馬赫算例.....................34
    4-3-2 15、18馬赫算例.................37
  4-4不同擴張率(相同ICR)比較.............40
  4-5二維結果與三維結果比較..............41
第五章 結論與建議........................43
  5-1結論................................43
  5-2未來工作............................44
參考文獻.................................45

表目錄

表 4-1 網格測試之對照表	49
表 4-2 突張構型條件設置	49
表 4-3 自由流條件設置	50
表 4-4 可變硬球分子模型基本參數(273K，1atm)	50


圖目錄
圖1-1 Kn值與統御方程式間的關係圖	51
圖2-1稀薄度與密度之關係圖	51
圖2-2直接模擬蒙地卡羅法流程圖	52
圖2-3硬球模型碰撞示意圖	53
圖2-4分子碰撞面積示意圖	53
圖3-1 X-43A	54
圖3-2 超音速燃燒衝壓引擎內外流場整合示意圖	54
圖3-3 超音速燃燒衝壓引擎與渦輪引擎之差異	55
圖4-1 12馬赫算例之壁面壓力與實驗比較圖	56
圖4-2 15馬赫算例之壁面壓力與實驗比較圖	56
圖4-3 12馬赫算例之馬赫數分布比較圖	57
圖4-4 15馬赫算例之馬赫數分布比較圖	57
圖4-5 網格測試之12馬赫算例切面圖	58
圖4-6 網格測試之15馬赫算例切面圖	59
圖4-7 網格測試之18馬赫算例切面圖	60
圖4-8 模擬二維超音速燃燒衝壓引擎外型示意圖	61
圖4-9 模擬三維超音速燃燒衝壓引擎外型示意圖	61
圖4-10 算例一之外流場等馬赫線分布	62
圖4-11 算例一之外流場等壓線分布	62
圖4-12 算例二之外流場等馬赫線分布	63
圖4-13 算例二之外流場等壓線分布	63
圖4-14 算例三之外流場等馬赫線分布	64
圖4-15 算例三之外流場等壓線分布	64
圖4-16 算例一之馬赫分布	65
圖4-17 算例一之壓力分布	65
圖4-18 算例一之溫度分布	66
圖4-19 算例一之密度分布	66
圖4-20 算例二之馬赫分布	67
圖4-21 算例二之壓力分布	67
圖4-22 算例二之溫度分布	68
圖4-23 算例二之密度分布	68
圖4-24 算例三之馬赫分布	69
圖4-25 算例三之壓力分布	69
圖4-26 算例三之溫度分布	70
圖4-27 算例三之密度分布	70
圖4-28 算例一之中心壓力切面圖	71
圖4-29 算例一之中心溫度切面圖	71
圖4-30算例二之中心壓力切面圖	72
圖4-31算例二之中心溫度切面圖	72
圖4-32算例三之中心壓力切面圖	73
圖4-33算例三之中心溫度切面圖	73
圖4-34算例一之平均全壓分布	74
圖4-35算例二之平均全壓分布	74
圖4-36算例三之平均全壓分布	74
圖4-37算例一之燃燒室頂部、底部X軸速度分布	75
圖4-38算例二之燃燒室頂部、底部X軸速度分布	75
圖4-39算例三之燃燒室頂部、底部X軸速度分布	75
圖4-40算例一之壁面C 值分布	76
圖4-41算例一之壁面C 值分布	77
圖4-42算例二之壁面C 值分布	78
圖4-43算例二之壁面C 值分布	79
圖4-44算例三之壁面C 值分布	80
圖4-45算例三之壁面C 值分布	81
圖4-46算例一之內流場壓力分布	82
圖4-47算例二之內流場壓力分布	83
圖4-48算例三之內流場壓力分布	84
圖4-49 算例一之不同擴張率之流場中心性質切面圖	85
圖4-50 算例二之不同擴張率之流場中心性質切面圖	86
圖4-51 算例三之不同擴張率之流場中心性質切面圖	87
圖4-52 算例一之不同擴張率之平均全壓切面圖	88
圖4-53 算例二之不同擴張率之平均全壓切面圖	88
圖4-54 算例三之不同擴張率之平均全壓切面圖	88
圖4-55 算例一之三維馬赫數分布	89
圖4-56 算例一之三維壓力分布	89
圖4-57 算例二之三維馬赫數分布	90
圖4-58 算例二之三維壓力分布	90
圖4-59 算例三之三維馬赫數分布	91
圖4-60 算例三之三維壓力分布	91
圖4-61 算例一之流場中心壓力分布比較圖	92
圖4-62 算例二之流場中心壓力分布比較圖	92
圖4-63 算例三之流場中心壓力分布比較圖	92

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