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研究生:周培頌
研究生(外文):Peh-Sung Chou
論文名稱:濃度調變對單向固化形態穩定的影響
論文名稱(外文):The effect of concentration modulation on morphological instability of a binary alloy
指導教授:鍾志昂
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:63
中文關鍵詞:固化調變線性穩定分析形態不穩定同步模態次調和模態
外文關鍵詞:subharmonicsynchronousmorphological instabilitymodulationsolidificationlinear stability analysis
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單向固化製程中合金的缺陷產生原因,與固化過程中在固液介面的過冷現象有關。近幾年來商品朝著輕薄短小發展,造成對固化過程缺陷控制要求的嚴苛,合金固化因此受到許多學者廣泛的研究。
為了改善這種缺陷的情況,本文將模擬鉛-錫單向固化合金流場,研究在固液介面形態的變化情形,並嘗試經由控制某些特定參數,來分析對固液介面形態不穩定(morphological instability)的影響,藉由對單向固化流場作濃度週期性調變,探討基態系統的變化,利用解析解的方法求解基態;接著對基態流場作線性穩定分析,就同步及次調和兩種不穩定模態來探討固液介面的形態不穩定現象。
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 solutal 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 subharmonic modes. The synchronous modes vary with time having the same frequency as that of the oscillatory molten zone, while the sudharmonic modes are of the half frequency.
摘要
目錄
圖目錄
符號說明
第一章 序論 1
1.1前言 1
1.2文獻回顧 1
1.3研究動機 3
第二章 濃度週期性調變下之基態流場 5
2.1問題描述及統御方程式 5
2.2無因次化 7
2.3基態解 8
2.3.1解基態濃度 及固液介面高度 9
2.3.2按照δ的階數整理 9
2.4基態系統分析 15
2.4.1 與基態系統關係 15
2.4.2 與基態系統關係 15
第三章 濃度週期性調變之線性穩定分析 17
3.1線性擾動方程式 17
3.2線性擾動方程式之求解 22
3.3線性穩定分析之應用 26
3.3.1同步模態 27
3.3.2次調和模態 29
3.4數值方法 30
3.5數值計算結果 31
第四章 結論與展望 34
參考文獻 37
附錄一 鉛錫合金物理參數 40
附錄二 Mathematica計算之結果 41
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2. Coriell,S.R.、Cordes,M.R.&Boettinger, W.J. Convective and interfacial during unidirectional solidification of a binary alloy, J. Crystal Growth 49, 13-28 (1979).
3. Coriell,S.R.&McFadden,G.B. Applications of morphological stability theory, J. Crystal Growth 8-13, 237-239 (2002).
4. Delves,R.T. Theory of stability of a solid-liquid interface during growth from stirred melts, J. Crystal Growth 3,4 562-568 (1968).
5. Davis,S.H. Hydrodynamic interactions in directional solidification, J. Fluid Mech.212,241-262 (1990).
6. Mullims,W.W.&Sekerka,R.F. Syability of a planar interface during solidification of a dilute binary alloy,J.Appl. Phys. 35,444-451 (1964).
7. Morris,L.R.&Winegard,W.C. The development of cells during the solidification of a dilute Pb-Sn alloy, J. Crystal Growth 5,361-375 (1969).
8. McCaryney,D.G.&Hunt,J.D. Measurement of cell and primary dendrite arm spacing in directionally solidified aluminium alloys. Acta Mtall.29,1851-1863 (1981).
9. Murray,B.T.、Coriell,S.R.&McFadden,G.B. The effect of gravity modulation on solutal convection during directional solidification, J. Crystal Growth 110,713-723 (1991).
10 Rutter,J.W.&Chalmers,B. A prismatic substructure formed during solidification of metals,Can.J. Phys.31,15-39 (1953).
11. Schulze,T.P.&Davis,S.H. Shear stabilization of morphological instability during directional solidification, J. Crystal Growth 149,253-265 (1995).
12. Tiller,W.A.、Rutter,J.W.、Jackson,K.A.&Chalmer,B. The redistribution of solute atoms during the solidification of metals, Acta Metall. 1,428-437 (1953).
13. Wollkind,D.J.&Segel,L.A. A nonlinear stability analysis of the freezing of a dilute binary alloy, Phil. Trans. R. Soc.Lond. A268, 351-380 (1970).
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