| 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 |
| 相關次數: | 點閱:80 下載:1 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
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.
参考文献
AutoCAD (2011), Autodesk, Inc. 111 McInnis Parkway San Rafael, CA
94903, United States, http://usa.autodesk.com/
Ben-Dor, G., (1978), “Regions and Transitions of Nonstationary Oblique
Shock Wave Diffraction in Perfect and Imperfect Gases,”UTIAS Rep. 232.
Ben-Dor, G., (1987), “A Reconsideration of the Three-Shock Theory of a
Pseudo-Steady Mach Reflection,”J. Fluid Mech., Vol. 181, pp. 467-484.
Ben-Dor, G., (1992), “Shock Wave Reflection Phenomena," Springer - Verlag.
Ben-Dor, G. & Takayama, K., (1985), “The Inverse Mach Reflection.”
AIAA Journal, vol. 23, No. 12, pp. 1853-1855.
Colella, P. & Henderson, L. F., (1990), “The von Neumann Paradox for the
Diffraction of Weak Shock Waves.”J. Fluid Mech., Vol. 213, pp. 71-94.
CorelDRAW X3 (2006), Corel Corporation, 1600 Carling Avenue, Ottawa,
ON K1Z 8R7, Canada, http://www.corel.com
Deschambault, R. L., (1984), “Nonstationary Oblique-Shock-Wave Reflections
in Air,”UTIAS Rep. 270.
Henderson, L. F., (1987), “Regions and Boundaries for Diffracting Shock
Wave Systems,”Z. Angew. Math. Mech., Vol. 67, 1-14.
Glass, I. I., (1977), “Shock Waves on Earth and in Space,”Progress in
Aerospace Sciences, Vol. 17, No. 4, pp. 269-286.
Liu, J.J., (1996), “Sound Wave Structures Downstream of Pseudo-Steady
Weak and Strong Mach Reflections,”J. Fluid Mech., Vol. 324, pp. 309-332.
Liu, J.J., (2006 a), “A Clarification of Misconceptions Regarding the von
Neumann Paradox of Weak Mach Reflections,”The 26th International Symposium
on Shock Waves, Abstract, Germany, Gottingen.
Liu, J.J., (2006 b), “A Clarification of Misconceptions of Pseudo-Steady
Mach Reflections,”The 26th International Symposium on Shock Waves, Abstract,
Germany, Gottingen.
Kawamura, R. & Saito, H., (1956), “Reflection of Shock Wave – 1 Pseudo-
Stationary Case,”J. Phys. Soc. Japan, Vol. 11, pp. 584-592.
Kobayashi, S., Adachi, T. & Suzuki, T. (2000), Non-self-similar behavior of
the von Neumann reflection. phys. Fluids, Vol. 12, No. 7, pp. 1869-1877.
Law, C.K. & Glass, I.I., (1971), “Diffraction of Strong Shock Waves by a Sharp Compressive Corner,”CASI. Trans., Vol. 4, pp.2-12.
Mach, E., (1878), “Uber den Verlauf von Funkenwellen in dre Ebene und
im Raume,”Sitzumgsber. Akad. Wiss. Wien, Vol. 78, pp. 819-838.
Olim, M. & Dewey, J.M., (1992), “A revised three-shock solution for the
Mach reflection of weak shocks(1.1<Mi<1.5),”Shock Waves Intl J. 2, pp.
167-176
von Neumann, J., (1945), “Refraction, interaction and reflection of shock
waves,”NAVORD Rep. 203-45. Navy Dept., Bureau of Ordinance, WASHINGTON,
DC.
von Neumann, J., (1943), “Oblique Reflection of Shocks,”Explos. Res.
Rep. 12, Navy Dept., Bureau of Ordinance, Washington, DC.
Sasoh, A., Takayama, K. & Saito, T., (1992), “A Weak Shock Wave Reflection
Over Wedge,”Shock Wave, Vol. 2, No. 4, pp. 277-281.
Yang, J. M., (1995), “An Experimental and Theoretical Investigation on
Weak Shock Wave behavior,”PhD. thesis, Tohuko University.
黃基鴻,「馬赫反射流場初步實驗與理論探討」,國立成功大學工程科
學所碩士論文,台南,(2000)。