結合計算流體力學與排液容器法 量測流體之密度、黏度與表面張力係數

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姓名

李亞寰(Ya-Huan Lee) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

結合計算流體力學與排液容器法量測流體之密度、黏度與表面張力係數
(Measuring the Surface Tension and Viscosity Using the draining Vessel Method combined with Computational Fluid Dynamics)

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摘要(中)

掌握得流體的密度、黏度與表面張力係數，能有助於幫助瞭解流體的流動特性，增益於工業技術、學術研究。因此，本研究欲發展出一套相較於市售儀器，兼具價格低廉與穩定性高之量測方式。本研究使用排液容器法（draining vessel method）作為基礎。此方法主體為一個底部開了孔道的容器，將待測液體倒入容器後，液體受重力驅動下自底部的開孔流出，即可得到一組液體高度頭高度隨時間變化之流動數據。研究方法是首先以計算流體力學建置一個排液容器法的流場，並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，經模擬計算可整理數據，得一組以質量通量為變數之高度頭數據。而後進行非線性迴歸，以最小平方誤差準則（least square solution）最小化模擬與實驗的高度頭差異求得流體之密度、黏度與表面張力係數。
將以上方法應用於量測純水與乙二醇，量得純水密度的相對誤差為-1.77%、黏度為-5.00%，表面張力係數的誤差較大為-30.42%；乙二醇的最佳結果為，密度誤差4.95%、黏度為11.98%，與表面張力係數為34.02%。量測誤差的原因可能為實驗系統的幾何尺寸之不確定性與數值模型的計算誤差，若能降低以上兩者的誤差應可有效地改善本研究方法之準確度，則此方法可推廣至更廣泛的流體量測，藉此發展一套具系統性地量測流體之密度、黏度與表面張力係數的方法。

摘要(英)

The draining vessel method is used to simultaneously measure density, viscosity and surface tension coefficient of fluid. This study propose using CFD instead of the modified formulation to improve the accuracy of results. In the draining vessel, the drag force caused by viscosity and surface tension balancing the draining force by gravity. The fluid elevation head and the mass flux of the flow through the orifice at the vessel bottom reveal the influence quantitatively by the physical properties of viscosity, surface tension and fluid density. A nonlinear and multi-variable regression is used to calculate the values of fluid properties by minimizing the difference between the elevation head gained from simulation and experiment.
The obtained results for water at 299K show the physical properties were measured with the percentage error of -1.77 % in density, -5 % in viscosity and -30.42 % in surface tension coefficient compared to the values quoted from literature. In addition, results for ethylene glycol also yield percentage errors of 4.95 %, 11.98 %, and 34.02 % in density, viscosity and surface tension coefficient, respectively. According to the error analysis, the uncertainty of the size of device and computational error may be responsible for the calculation error of the fluid properties. While the accuracy exhibited by the results is high, it can be further enhanced by decreasing the uncertainties as mentioned above, this method could be extended for use in various applications and become a relatively affordable option.

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)

論文目次

目錄
圖目錄 i
表目錄 iii
符號表 iv
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 3
1.2.2 物性迴歸方法 4
1.3 研究目的 5
1.4 論文架構 6
第二章研究方法 8
2.1 問題描述 8
2.2 數學模型 8
2.2.1 統御方程式 9
2.2.1.1 連續方程式 9
2.2.1.2 動量方程式 10
2.2.2 初始條件 10
2.2.3 邊界條件 11
2.2.4 COMSOL Multiphysics之簡介與相關設置 12
2.2.4.1 網格設置與收斂性分析 12
2.2.4.2 計算時間步收斂性分析 14
2.3 計算流體物性的數值方法 15
2.3.1 三階段迴歸法 18
2.3.2 物性對高度頭誤差的敏感度分析 21
2.3.2.1 密度 23
2.3.2.2 黏度 24
2.3.2.3 表面張力係數 24
第三章結果與討論 39
3.1 純水的物性量測結果 39
3.1.1 模擬正算與實驗數據的高度頭誤差 40
3.1.2 改良第三階段迴歸所得的量測結果 42
3.2 純水物性的量測誤差分析 42
3.2.1 密度 43
3.2.2 黏度 44
3.2.3 表面張力係數 45
3.3 乙二醇的物性量測結果 46
3.4 乙二醇物性的量測誤差分析 47
3.4.1 模擬正算與實驗數據的高度頭誤差 47
3.4.2 密度 49
3.4.3 黏度 49
3.4.4 表面張力係數 51
3.4.5 改變目標高度頭的黏度結果分析 51
3.5 物性量測的誤差分析 53
3.5.1 高度頭誤差的來源 53
3.5.2 物性與敏感度係數之關係 54
第四章結論與未來展望 69
參考文獻 71

參考文獻

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指導教授

鍾志昂

審核日期

2019-1-30

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