臺灣博碩士論文加值系統

本文以數值方法研究具斜坡之鹽水異重流流動特性。利用有限差分法配合MAC交錯網格求解Navier-Stokes方程組與濃度移流擴散方程式，模擬兩種不同密度流體所造成的異重流現象，並引入大渦模擬(Large Eddy Simulation, LES)計算紊流影響。透過座標轉換，將不規則物理域轉換為方便處理的矩形計算域，使模式能處理具斜坡之邊界問題。求解濃度移流擴散方程式時引入史密特數(Schmidt Number)描述流體動量與質量傳輸之關係，其中對流項使用QUICK法處理，減少數值上的振盪。模式能捕捉異重流之不穩定現象，包括KH不穩定(Kelvin-Helmholtz Instability)與對流不穩定(Advection Instability)。將模擬結果與實驗數據比較，異重流之濃度剖面及頭端到達時間有良好的成果，透過敏感度分析，本文建議鹽水之紊流史密特數範圍為100到1000之間。

A numerical model is set up to simulate the density current on slope channel by solving the Navier-Stokes equations and advection-diffusion equation. This thesis presents a finite difference method with MAC staggered grid system. We apply the turbulent model, Large Eddy Simulation (LES), to calculate the influence of turbulence. By coordinate transformation, unregular physical region can be transformed to rectangular computational region. It is easy to handle the numerical process. The concept of Schmidt number, the ratio of momentum and mass mixings, is used in advection-diffusion equation. QUICK scheme is used for convection terms in advection-diffusion equation. The numerical model can capture the KH instability and convection instability of the density current. The simulation results are in good agreement with the experimental data, such as the concentration profile and the reach time of the head of the density current. Sensitive analysis showed that the range of turbulent Schmidt number of saline water between 100 and 1000 is suggested.

摘要 i
Abstract ii
目錄 iii
表目錄 v
第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 研究動機與方法 9
1-4 論文大綱 11
第二章 理論基礎 13
2-1 控制方程式 13
2-2 動量與質量傳輸關係 15
2-3 紊流模式 16
第三章 數值計算方法 20
3-1 控制方程式無因次化 20
3-2 座標轉換 21
3-2-1 邊界條件 21
3-2-2 控制方程式 22
3-3 網格與流場變數配置 24
3-4 邊界條件 24
3-5 動量方程式之計算 25
3-6 壓力方程式之計算 26
3-7 濃度移流擴散方程式之計算 30
3-8 數值穩定條件 31
3-9 數值計算流程 32
第四章 結果與討論 33
4-1 水平異重流 33
4-2 斜坡異重流 36
4-3 變量入流異重流 38
4-4 異重流參數敏感度分析 38
4-5 大渦數值模擬 39
第五章 結論與建議 41
5-1 結論 41
5-2 建議 41
參考文獻 42

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