臺灣博碩士論文加值系統

本研究以軸對稱、三維、黏性、依時性數學模式，以模擬極超音速反射型震波風洞內複雜之暫態流場問題，並探討在不同馬赫數下穩定流場建立之時間，提供實驗工作者數據資料。本研究採用上風TVD數值法解無黏性Euler方程組或Navier-Stokes方程組；採用人工耗散項最小的Roe’s Solver，配合Kappa高階MUSCL Scheme解決在空間通量計算方面的問題；而在時間離散方面，則採用具二階精度的Hancock法則進行時間積分。程式建立時，即列入非定常流場計算用之可調式網格系統及適型之多區塊網格邊界處理模式，以計算複雜依時性之氣動力變化情形。本研究採用全尺寸之震波風洞模型建立網格系統進行程式運算，研究結果顯示，若是忽略高壓驅動段之存在，是無法模擬真實物理現象。
本研究採用代數法產生計算所需可調式網格系統，同時進行格點精緻化之工作；並分別建立Euler 或是Navier-Stokes方程式組有限體積法模擬主程式；繼而加入Tannehill & Mugge平衡空氣曲線吻合簡化方式之副程式；目標乃探討不同馬赫數下，極超音速反射型震波風洞內穩定流場建立之過程，及其影響穩定流場建立之物理機制；探討不同測試之參數將包括不同之噴嘴外形、不同初始壓力比條件下，極超音速反射型震波風洞內穩定流場建立之機制，以提供實驗工作者所需。研究結果顯示，噴嘴外型與初始壓力比，皆對此非定常流場之發展特性有所影響。

In this thesis, a series of numerical processes combined with Roe’s scheme and van Leer’s kappa scheme are developed to examine the flow mechanisms in a hypersonic reflection shock tunnel.
The mathematical model adopted for computing the flowfields is based on the full Navier-Stokes or Euler algebraic. The thermodynamic properties are modified by Tannehill and Mugge’s polynomial correlations for hypersonic flowfield simulation. A three-dimensional numerical inviscid and viscous model of the time-dependent near field of multi-block hypersonic flow phenomena have been developed in this thesis. The TVD upwind method for solving the governing equations has been developed to simulate these complex problems. For the spatial discretization, the least artificial viscous Roe’s solver with high order Kappa MUSCL interpolation was used and, the second order explicit Hancock method was employed for time integration.
Finally, a computer code was established for the computation of this unsteady hypersonic flowfield. In the construction of grid system, a full-scale test model is adopted to avoid the loss of real physical characteristics. A adaptive grid system is applied by the algebraic method, and the local grid refinement is processed to improve the convergence rates. The aim of present investigation is to test the effects of nozzle geometry and initial pressure ratio on the flow developing within a supersonic reflection shock tube. Both the complex and procedure unsteady flow structure in addition to the time history of Mach number can be evaluated from present numerical results.

目 錄
誌謝…………………………………………………………………II
摘要(中文)…………………………………………………………IV
ABSTRACT………………………………………………………VI
目錄………………………………………………………………VIII
表錄………………………………………………………………XII
圖錄………………………………………………………………XIII
符號與縮寫……………………………………………………XVII
1. 緒論………………………………………………………………1
1.1. 引言…………………………………………………………1
1.2. 研究動機及背景…………………………………………..1
1.3. 文獻回顧……………………………………………………3
1.4. 研究方向…………………………………………………...5
1.5. 研究方法…………………………………………………..6
1.6. 研究內容………………………………………………….10
2. 極超音速震波風洞之特性說明……………………………15
2.1. 工作原理…………………………………………………15
2.2. 流場描述…………………………………………………17
2.3. 極超音速震波風洞流場理論分析……………………18
2.4. 困難與探討………………………………………………20
3 數學模式………………………………………………………23
3.1. 統御方程式………………………………………………24
3.2. 無因次化處理……………………………………………28
3.3. 成份方程式………………………………………………32
3.4. 熱力性質修正……………………………………………34
4. 數值方法………………………………………………………36
4.1. 對流項的離項……………………………………………38
4.2. 有限體積法………………………………………………38
4.3. 空間離散…………………………………………………40
4.4. 時間離散…………………………………………………44
4.5. Roe’s 法則……………………………………………….48
4.6. 熵條件……………………………………………………49
4.7. 殘值的處理………………………………………………50
5. 邊界條件處理…………………………………………………52
5.1. 邊界條件定義……………………………………………53
5.2. 物體壁面邊界條件………………………………………54
5.3. 遠處邊界條件……………………………………………55
5.3.1. 超音速流入………………………………………56
5.3.2. 超音速流出………………………………………57
5.3.3. 次音速流入………………………………………57
5.3.4. 次音速流出………………………………………58
5.4. 網格區塊交接邊界條件……………………………….59
5.4.1. 對稱流場邊界條件………………………………60
5.4.2. 軸對稱流場邊界條件……………………………60
5.4.3. 三維面對稱流場邊界條件………………………61
6. 網格系統………………………………………………………63
6.1. 多區塊網格系統…………………………………………64
6.2. 網格產生…………………………………………………64
6.2.1 突張管………………………………………………64
6.2.2 極超音速反射型震波風洞……………………….65
6.2.3 非均勻結構性網格系統處理…………………….67
6.4. 三維網格系統處理………………………………………68
6.5. Navier-Stokes網格系統處理……………………………70
7. 結果與討論……………………………………………………73
7.1. 程式驗證…………………………………………………73
7.1.1 突張管近場流場…………………………………...74
7.1.2 量測點之超高壓力比較…………………………..75
7.2. 極超音速震波風洞流場現象分析……………………….76
7.3. 非黏性極超音速震波風洞流場現象分析………………79
7.4. 黏性效應下之極超音速震波風洞流場現象分析……..79
7.4.1 黏性效應化學平衡流與化學平衡流比較………86
7.4.2 噴嘴前段管徑不同之黏性化學平衡流比較……88
7.4.3 薄膜破裂強度黏性效應化學平衡流比較………89
7.4.4 背壓不同之黏性效應化學平衡流比較…………90
7.4.5 噴嘴後段管徑不同之黏性化學平衡流比較……92
8. 結論與建議……………………………………………………94
參考文獻…………………………………………………………..97
附錄A……………………………………………………………..180
附錄B………………………………………………………………213
自傳……………………………………………………………….232
簡歷……………………………………………………………….235

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