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研究生:謝岳樺
研究生(外文):Yue-Hua Sie
論文名稱:溫度調變對單向固化形態穩定的影響
論文名稱(外文):The effect of temperature modulation on morphological instability of a binary alloy
指導教授:鐘志昂
指導教授(外文):Chih-Ang Chung
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
論文頁數:68
中文關鍵詞:固化調變線性穩定分析形態不穩定同步次調和
外文關鍵詞:linear stability analysismorphological instabilitysynchronoussubharmonicsolidificationmodulation
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固化在許多製程中扮演著中重要的角色,而不同的固化過程對生成物的機械性質也有很大的影響。而由固化所得的晶體,晶格排列越規則則其機械性質越佳,例外強度、延展性。單向固化製程由於其鑄造物有較佳的機械性質,所以常用於渦輪葉片的製造,但由於其在固化過程中往往會出現一些缺陷,使的良率降低,這是和生長過程中,固液介面上會產生過冷現象而導致形態的不穩定所造成。本文的目的是探討週期性調變溫度對單向固化形態穩定的影響,並希望藉由改變流場中的一些參數來抑止其形態不穩定的發生。
The main goal of this thesis is to investigate into the influence of temperature modulation on the morphological stability of directional solidification. We study the morphological instability of the melt-solid interface of a dilute binary alloy. The alloy is assumed to undergo directional solidification into a modulated temperature field. Under such a circumstance, the molten zone is oscillated back and forth in a periodic way. The basic state is solved analytically assuming the melt-solid interface is flat and the bulk melt is quiescent by expanding the governing equation in terms of the assumed infinitesimal modulation amplitude. By further neglecting the flow field, we investigate the interfacial stability of the base state by considering two specific instability modes: the synchronous and sub-harmonic modes. The synchronous modes vary with time having the same frequency as that of the oscillatory molten zone, while the sub-harmonic modes are of the half frequency.
摘要
目錄
圖目錄
符號說明
第一章 序論
1.1 問題描述   1
1.2文獻回顧 2
1.3 研究動機 4
第二章 基態流場
2.1系統介紹與數學模式 6
2.1.1系統介紹 6
2.1.2數學模式 7
2.2無因次化尺度 8
2.3無因次化後的統御方程式和邊界條件 8
2.4 基態解 9
2.5 結果與討論 15
第三章 溫度週期性調變之線性穩定分析
3.1 線性擾動方程式 18
3.2 Floquet理論 23
3.3 同步與次調和模態 28
3.3.1 同步模態 28
3.3.2 次調和模態 30
3.4 數值模擬 32
3.5 結果與討論 34
第四章 結論 39
參考文獻
附錄一
附錄二
表一
參考文獻
1. Brattkus, K. & Davis, S. H. 1988 Flow induced morphological
instabilities:Stagnation point flows. J. Crystal Growth
89,423-427.

2. Coriell, S. R., McFadden, G. B., Boisvert, R. F.& Sekerka,
R. F. 1984 Effect of a forced Couette flow on coupled
convective and morphological instabilities during
unidirectional solidification. J. Cryst. Growth 69, 15-22.

3. Coriell,S. R. & McFadden, G. B. 2002 Applications of
morphological stability theory. J. Cryst. Growth 8-13,
237-239.

4. Delves, R. T. 1968 Theory of stability of a solid-liquid
interface during growth from stirred melts. J. Cryst. Growth
3,4, 562-568.

5. Delves, R. T. 1971 Theory of stability of a solid-liquid
Interface during growth from stirred meltsΠ. J. Cryst. Growth
8,13-25.
6. Forth,S.A.& Wheeler,A. A. 1992 Coupled convective and
morphological instability in a simple model of the
solidification of a binary alloy, including a shear flow. J.
Fluid Mech.236, 61-94.

7. Mullims, W. W. & Sekerka, R. F. 1964 Stability of a planar
interface during solidification of a dilute binary alloy.
J.Appl. Phys.35,444-451.

8. Murray, B. T., Coriell, S. R. & McFadden, G. B. 1991 The effect of gravity modulation on solutal convection during directional solidification. J. Cryst. Growth 110,713-723.


9. Rutter,J.W. & Chalmers, B. 1953 A prismatic substructure
formed during solidification of metals. Can.J. Phys.31,15-39.

10. Schulze, T. P.& Davis, S. H. 1995 Shear stabilization of morphological instability during directional solidification. J. Cryst. Growth 149,253-265.

11. Tiller, W. A., Rutter, J. W.,Jackson, K. A. & Chalmer, B.
1953 The redistribution of the solute atoms during the
solidification of metals. Acta Metall.1,428-437.
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