本研究利用尺寸因次分析預測在低功率電子束或雷射焊接過程中受馬里哥尼(熱毛細)流影響的熔區形狀。低功率密度雷射意味著熔池是淺而窄的，也有可能在熔池中產生孔洞。熔化區的強度、微結構和機械性質和熔池的形狀是密切相關的。在此研究裡，隨著相變化在固液介面發生，未知形狀的固液交界面和在自由表面、角落區及邊界層的交會處，都會影響熔區裡複雜的流場。當Pr Number小於1時，熔融金屬的Ma Number和Re Number 則會有 大，適當的質量、動量及能量傳輸的尺寸因次分析可藉由自由表面上黏滯力和表面張力的平
衡。此外，在各個區域裡，不同的熱邊界層、黏滯邊界層有著不同的長度、速度、溫度尺寸因次分析。最後結果發現熔池的形狀、表面速度、溫度分佈與Pe Number、Bi Number、Ma Number、Pr Number、入射能量及固液熱傳導係數比有密切關係。此預測經由我們數據模擬所得証。

In this study, shapes of the molten region and transport processes affected by thermocapillary convection in melting or welding pool irradiated by a low-power-density beam are determined from a scale analysis for the first time. A low-power-density-beam heating implies no deep and narrow cavity or keyhole taking place in the pool. A quantitative determination of the fusion zone shape is crucial due to its close relationship with the strength, microstructure, and mechanical properties of the fusion zone. In this work, the complicated flow pattern in the pool is influenced by an unknown shape of solid-liquid interface, and interactions between the free surface layer, corner regions, and boundary layer with phase transition on the solid-liquid interface. Since Prandtl number is much less than unity while Marangoni and Reynolds number can be more than in melting metals, an appropriate scaling mass, momentum, and energy transport subject to a force balance between viscous stress and surface tension gradient on the free surface account for distinct thermal and viscous boundary layers in these regions of different length, velocity, and temperature scales. The results find that shapes of the fusion zone, free surface velocity and temperature profiles are determined by Marangoni, Prandtl, beam power, Peclet, and Biot numbers, and solid-to-liquid thermal conductivity ratio. The predications agree with numerical computations.

目錄 i
表目錄 iii
圖目錄 iv
符號說明 v
中文摘要 viii
英文摘要 ix
第一章 緒論 1
1-1 相關文獻回顧 1
1-2 研究動機及目的 4
第二章 系統模型 5
2-1 模擬方式 5
2-2 理論分析 7
2-3 尺寸因次分析 11
第三章 結果與討論 16
3-1 模擬結果 16
3-2 尺寸因次分析結果 25
第四章 結論 30
附錄一 31
附錄二 38
參考文獻 43

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