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研究生: 吳振瑋
Wu, Jen-Wei
論文名稱: 擬似穩態馬赫反射流場幾何參數量測暨其與參震波理論預測之間的比較
Measurements of geometric parameters of pseudo-steady Mach reflections wave configurations and their comparisons with predictions from the three-shock theory
指導教授: 劉中堅
Liu, Jong-Jian
學位類別: 碩士
Master
系所名稱: 工學院 - 工程科學系
Department of Engineering Science
論文出版年: 2011
畢業學年度: 99
語文別: 中文
論文頁數: 81
中文關鍵詞: 馬赫反射
外文關鍵詞: Mach reflections
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  • 摘要
    本論文主要以理論與實驗兩方面對擬似穩態馬赫(PMR) 流場實驗結果進行分析與比較。理論方面應用整體(global) 與局部(local) 參震波理論求解PMR 流場各震波下游流場性質,實驗方面吾人使用目前文獻中存在著的清晰PMR 流場照片及其實驗數據進行其與上述理論之間的分析與比較。論文中說明如何應用繪圖軟體準確地量測這些PMR 實驗照片上流場的幾何參數。理論方面應用壓力與轉折角之震波極圖說明整體與局部參震波理論分析PMR 流場的結果與實驗量測之間的比較。我們運用整體參震波理論於給予馬赫反射初始條件(Ms、θw) 下得到的三種主要不同型態的解- MR (weak),後向反射弱震波解;MR (strong),後向反射強震波解;vNR,前向反射震波解,依此建構於(Ms, θw) 物理平面上PMR 流場參震波理論的解域,可將此整體理論預測結果有系統、分類地與文獻中現有的實驗數據作比較(Ms 為入射傳播震波馬赫數,θw 是楔形斜平面角)。吾人同時進行系列地這些文獻中實驗與局部參震波理論預測之間的比較,從而說明這些系列實驗數據驗證了Rankine-Hugoniot 關係式的適用或不適用於描述何種條件或何處(Ms、θw) 解域上的PMR 現象。本論文的結論為整體與局部參震波理論可以準確地描述屬於MR (weak) 解域中的PMR 實驗結果;它們的預測與屬於MR (strong) 解域中的實驗量測結果,隨著Ms 與θw 的逐漸變小,兩者之間的差異愈大;它們完全無法描述屬於vNR 解域中的擬似穩態馬赫流場的實驗結果。

    Abstract
    This thesis analyses pseudo-steady Mach reflection (PMR) theoretically and experimentally. Both global and local three-shock theoretical analyses are applied to calculate geometric and thermodynamic parameters of PMR phenomena.
    Experimental data and clear photographic pictures available in current literature are used to compare with their predictions obtained from the global and local theories. Pressure-deflection shock polar diagrams are used whenever possible to assist in analyzing and explaining the comparisons between the theories and experiments. In order to systematically categorizing and analysing large amount of comparisons between these available experiments and both the global and local theories, the analyses are made according to three major global threeshock theoretical solution regimes: MR (weak), backward-facing reflected weak
    oblique shock waves; MR (strong), backward-facing reflected strong oblique shock waves and vNR, forward-facing reflected oblique shock waves. Ms is the incident propagating shock Mach no., θw is the reflecting oblique wedge angle. Local three-shock theoretical calculations are then carried out to verify the applicability or inapplicability of the Rankine-Hugoniot shock relations for
    describing these PMR experiments. It is found that both the global and local three-shock theories can accurately predict PMR phenomena when they are belong to the regime of MR (week). AsMs and/or θw decrease, both the predictions obtained from the global and local theories become to deviate from the experiments from modestly to significantly when they are belong to the regime of MR (strong). Both the theories completely fail to describe the PMR phenomena
    when they are belong to the global three-shock theoretical regime of vNR.

    目錄 摘要................................................. I Abstract .............................................. II 致謝................................................... IV 目錄.................................................... V 表目錄............................................. VII 圖目錄.............................................. VIII 符號說明........................................... XIV 第一章緒論..................................... 1 第二章震波管流場之擬似穩態馬赫反射參震波理論分析................ 4 2.1 擬似穩態馬赫反射之參震波理論............................. 4 2.2 整體擬似穩態馬赫反射流場之參震波理論..................... 9 2.3 局部擬似穩態馬赫反射流場之參震波理論應用.............. 9 2.4 局部與整體參震波理論壓力與轉折角(P-θ) 震波極圖解法..... 10 2.5 單原子與雙原子分子氣體於(Ms − θw) 平面上之解域說明..... 13 第三章擬似穩態馬赫流場幾何參數量測與討論.................... 16 3.1 馬赫反射流場實驗相關之文獻來源........................ 16 3.2 UTIAS 實驗文獻................................ 16 3.3 Smith 實驗文獻................................... 17 3.4 馬赫反射流場幾何參數光學量測方法................. 19 3.5 擬似穩態馬赫反射流場之波角、轉折角與波形的量測方法.... 22 3.6 擬似穩態馬赫反射文獻實驗CAD 量測描繪與其波形物理..... 31 3.7 擬似穩態馬赫反射流場之波角、轉折角與波形的量測誤差的分析.... 32 3.8 CAD 切線量測法與先前" 總表" 量測方法之差異.............. 35 第四章系列實驗量測擬似穩態馬赫反射流場與其參震波理論預測之間的比較..... 38 4.1 整體/局部之參震波理論分析文獻中各不同擬似穩態馬赫反 射流場解域實驗........ 39 4.1.1 屬於vNR 解域之文獻中的實驗數據........................ 41 4.1.2 屬於MR (strong) 解域之文獻中的實驗數據............ 50 4.1.3 屬於MR (weak) 解域之文獻中的實驗數據............. 57 4.2 系列固定θw 然後變化Ms 條件下文獻中擬似穩態馬赫反射實驗與其參震波理論預測之間分析與比較................................ 63 第五章文獻之擬似穩態馬赫實驗與其整體/局部參震波理論預測於(Ms, θw) 解域平面上整體性的比較............................. 68 5.1 參震波理論與CAD 切線量測實驗結果於(Ms, θw) 解域平面上之分析與比較........................................ 68 5.2 參震波理論與" 總表" 實驗數據於(Ms, θw) 解域平面上之分析與比較...... 72 第六章結論.................................. 77 参考文献........................................ 79

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