以計算流體力學結合排液容器法量測錫液之密度、黏度與表面張力係數

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顏芷珊(Chih-Shan Yen) 查詢紙本館藏

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機械工程學系

論文名稱

以計算流體力學結合排液容器法量測錫液之密度、黏度與表面張力係數
(Using the Draining Vessel Method combined with Computational Fluid Dynamics to Measure the Density, Viscosity and Surface Tension of Tin)

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摘要(中)

現今已有多種方法能夠在冷流場量測流體之密度、黏度與表面張力係數，而對於在熱流場的流體物性量測，其條件變得較困難且儀器較昂貴，且最多只能同時量測兩種物性，本研究發展出可同時量測三種物性的方法，且相較於市售儀器，兼具價格低廉與穩定性高。本研究使用排液容器法 (draining vessel method) 作為基礎，此方法為有一底部開設小孔之容器，將待測液體裝滿容器，液體因受重力影響向下方孔口流出，即可得一組液體高度頭隨時間改變之流動數據。搭配計算流體力學建立排液容器法的流場，在模型中考慮流體黏性與出口處表面張力造成之毛細壓力，得到以質量通量為自變數之高度頭數據，而後進行非線性迴歸，並以敏感度分析之結果發展最佳演算法，利用最小平方誤差準則 (least square solution) 最小化模擬與實驗的高度頭差異求得純水與錫之密度、黏度與表面張力係數。
由以上方法應用於量測冷流場的純水與熱流場的錫液，測量得25 ℃純水的密度相對誤差為-1.71 %，黏度的相對誤差為-4.22 %，表面張力係數的相對誤差為9.81 %；以60 ℃純水作為待測流體進行量測，其密度之相對誤差為-2.33 %，黏度為-3.92 %，表面張力係數為9.51 %。將待測流體改變為量測高溫250 ℃的錫液，密度之相對誤差為-2.25 %，黏度之相對誤差為-0.18 %，表面張力係數之相對誤差為7.86 %。量測誤差之可能原因推斷為實驗與模擬的高度頭誤差、三個物性誤差間相互影響與數值模型的計算誤差。未來要增加物性量測的精準度，可以藉由減小底部孔口尺寸，來增加表面張力的影響。本研究發展一套同時量測三種物性之方法，並已完成在冷流場與熱流場的量測驗證。

摘要(英)

Nowadays, there have been a lot of methods to measure liquid’s density, viscosity and surface tension coefficient at room temperature. However, it become harder and the instrument is more expensive when measuring physical properties at high temperature. In addition, most of the present methods can only measure one or two physical properties at the same time. Recently, a method called Draining Vessel Method has been developed to simultaneously measure density, viscosity and surface tension coefficient. In the draining vessel, the drag force caused by viscosity and surface tension coefficient balances the driving force of gravity. We developed the algorithm by sensitivity analysis. The nonlinear regression was used to calculate the fluid properties of water and tin by minimizing the difference between the elevation heads gained from simulation and experiment.
The obtained results for water at 25 ℃ show the physical properties were measured with the percentage error of -1.71 % in density, -4.22 % in viscosity and 9.81 % in surface tension coefficient compared to the values quoted from literature. The results for 60 ℃ water show the percentage errors of -2.33 %, -3.92 % and 9.51% in density, viscosity and surface tension coefficient, respectively. The measured results for tin at 250 ℃ are -2.25 % in density, -0.18 % in viscosity and 7.86 % in surface tension coefficient. In order to increase the accuracy for measuring, it can decrease the size of the orifice to enhance the influence of surface tension coefficient. This study develops a method of measuring density, viscosity and surface tension coefficient simultaneously, and its feasibility is verified both with the cold and hot fluid fields.

關鍵字(中)

★ 排液容器法
★ 計算流體力學
★ 非線性迴歸
★ 密度
★ 黏度
★ 表面張力係數

關鍵字(英)

★ draining vessel method
★ nonlinear regression
★ density
★ viscosity
★ surface tension coefficient

論文目次

中文摘要 i
Abstract ii
目錄 iii
圖目錄 vi
表目錄 ix
符號表 x
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.2.1 排液容器法 4
1.2.2 物性迴歸方法 5
1.3 研究目的 6
1.4 論文架構 6
第二章研究方法 11
2.1 問題描述 11
2.2 數學模型 11
2.2.1 統御方程式 12
2.2.1.1 連續方程式 12
2.2.1.2 動量方程式 13
2.2.2 初始條件 13
2.2.3 邊界條件 13
2.2.4 COMSOL Multiphysics之簡介與相關設置 14
2.2.4.1 網格設置與收斂性分析 16
2.2.4.2 計算時間步收斂性分析 18
2.2.5 模型驗證 19
2.3 計算流體物性的數值方法 19
2.4 敏感度分析 22
2.4.1 高度頭誤差對於物性之影響 23
2.4.2 物性誤差對於其他物性之影響 25
第三章結果與討論 38
3.1 純水的物性量測 38
3.1.1 模擬正算與實驗數據的高度頭誤差 38
3.1.2 純水之敏感度分析 39
3.1.2.1 密度 40
3.1.2.2 黏度 41
3.1.2.3 表面張力係數 42
3.1.3 兩階段迴歸法—純水 43
3.1.4 量測結果 45
3.1.4.1 25 ℃純水 45
3.1.4.2 60 ℃純水 47
3.2 錫的物性量測 49
3.2.1模擬正算與實驗數據的高度頭誤差 49
3.2.2 錫之敏感度分析 50
3.2.2.1 密度 50
3.2.2.2 黏度 51
3.2.2.3 表面張力係數 52
3.2.3 兩階段迴歸法—錫 53
3.2.4 量測結果 55
第四章結論與未來展望 78
參考文獻 80

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指導教授

鍾志昂(Chih-Ang Chung)

審核日期

2019-8-22

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