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博碩士論文 etd-0731101-101011 詳細資訊
Title page for etd-0731101-101011
論文名稱
Title
液珠在平板上之快速冷卻
Rapid Solidifying of Droplet on a cold substrate
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
34
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2001-06-29
繳交日期
Date of Submission
2001-07-31
關鍵字
Keywords
快速冷卻
Rapid Solidifying
統計
Statistics
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中文摘要
摘 要

本文建立一非穩態軸對稱之物理模型,以數值方法研究附著於低溫之工件表面上的金屬液滴,在其固化過程中之流體流動與熱量傳遞。液滴表面的溫度梯度與表面雜質的濃度梯度所引起的Marangoni forces是造成對流效應的主要驅動力。液滴自由表面的溫度與液滴內部的渦流及能量傳遞有關,而表面的雜質濃度之對流及擴散作用只發生在液滴之自由表面上。座標系統採用曲線正交環影線座標系統。計算結果顯示強大的溫度及濃度的Marangoni forces作用會產生兩個流動方向相反的環流,其對固、液相界面成長的快慢有重要的影響。本文將探討馬諾數(Ma),史蒂芬數(Ste),蒲朗特數(Pr),濃度與溫度的Marangoni forces的比值(E),液滴外形(Contact angle)對液滴之流動情況,溫度分佈以及表面雜質分佈的影響。
Abstract
Abstract
Unsteady, axisymmetric fluid flow and heat transfer in a droplet rapidly solidifying on a cold substrate are investigated. The thermal and solutal Marangoni forces along the droplet surface are the driving forces for fluid motion. Concentration of the insoluble surfactants are determined by surface convection and diffusion. The solidification is governed by an instantaneous nucleation and a subsequent continuous growth induced by a given nucleation temperature. Solute trapping is also accounted for. By using a curvilinear orthogonal toroidal coordinate system, the computed results show that the effects of the supercooling and nucleation temperature, Marangoni, Stefan, Prandtl numbers, ratio of the changes in surface tension due to concentration and temperature gradients, and the contact angle of the droplet on unsteady flow and thermal patterns, distributions of surfactant concentration, cooling effects, recalescence and growth rates. Temperature variations at the axisymmetric axis agrees well with a one-dimensional model. A systematical confirmation and evaluation of surface tension due to solute concentration is also provided.
目次 Table of Contents
摘 要------------------------------------------1
摘 要(英文)------------------------------------2
符號說明------------------------------------------3
第一章 緒論--------------------------------------6
1-1 研究背景及目的----------------------------6
1-2 文獻回顧----------------------------------6
1-3 研究範圍----------------------------------7
第二章 理論分析----------------------------------8
2-1 前言--------------------------------------8
2-2 基本假設及考慮----------------------------9
2-3 統御方程式的建立-------------------------10
2-4 邊界條件及初始條件-----------------------12
第三章 數值分析---------------------------------14
3-1 統御方程式的差分形式--------------------14
3-2 過度鬆弛法與欠鬆弛法--------------------15
3-3 數值分析的收斂條件----------------------16
3-4 數值分析解的步驟------------------------17
第四章 結果與討論-------------------------------18
第五章 結論-------------------------------------19
參考文獻-----------------------------------------32
參考文獻 References
Harlow, F.H., and Welch, J. E., 1965,"Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, Vol.8,pp.2182-2189.
Hirt, C. W., and Nichols, B. D., 1981,"Volume of Fluid(VOF) Method for the Dynamics of Free Boundaries, J. Computational Physics,Vol.39,pp.201-225.
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