氣流的非黏性駐波通過不連續管子之探究

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姓名

王裕惇(Yu-Dun Wang) 查詢紙本館藏

畢業系所

數學系

論文名稱

氣流的非黏性駐波通過不連續管子之探究
(Inviscid stationary waves of gas flow through discontinuous nozzles)

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摘要(中)

本論文我們將研究一維有黏性、等熵且可壓縮的流體通過各式各樣的不連續管子的非黏性穩定狀態，透過使用geometric singular perturbation 的技巧來建立駐波(stationary wave)的存在性。我們研究包括supersonic、subsonic、transonic 的駐波都是不連續的，並且將每種情況中的非黏性駐波分類討論。特別是，我們將探討光滑的管子和不連續的管子中的駐波的差別。

摘要(英)

In this work we study inviscid steady-states of one-dimensional viscous isentropic compressible flows through various discontinuous nozzles. We establish the existence of stationary waves by using geometric singular pertur-bation technique. We conclude that all stationary waves including supersonic, subsonic and transonic, are discontinuous. Also, we classify all inviscid stationary waves in every situation.In particular, we discuss the difference of inviscid stationary waves between smooth nozzle and discontinuous nozzle.

關鍵字(中)

★ 水平到擴張之不連續管子
★ 幾何奇異擾動
★ 氣流
★ 穩定狀態.

關鍵字(英)

★ geometric singular perturbation
★ Gas flow
★ transonic steady-state.
★ horizontal- expanding discontinuous nozzle

論文目次

Contents
Abstract (in English) ...i
Contents...ii
1 Introduction...1
2 Standing waves and shocks of inviscid flow in mollified horizontal-expanding duct...3
2.1 Standing waves...4
2.2 Standing shocks...6
3 Inviscid steady-state in mollified horizontal-expanding duct...7
3.1 A dynamical system formulation...8
3.2 Slow manifold, limiting slow and fast dynamics...9
3.2.1 First representation of Z_0 and limiting slow dynamics...10
3.2.2 second representation of Z_0 and limiting fast dynamics...11
3.3 Jump curves of limiting slow orbits and their transversality property...13
3.4 Classification of inviscid steady-states in mollified H-E duct...18
4 Inviscid steady-state in discontinuous horizontal- expanding duct...22
4.1 Properties of inviscid steady-state with discontinuous H-E duct...23
4.2 Classification of inviscid steady-states with discontinuous H-E duct...26
5 Other Case: Contracting-horizontal and Contracting-expanding discontinuous nozzle...30
5.1 Contracting-horizontal uniform nozzle...30
5.2 Contracting-horizontal discontinuous nozzle...39
5.3 Contracting-expanding discontinuous nozzle...45

參考文獻

References
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指導教授

洪盟凱(John M. Hong)

審核日期

2011-6-21

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