以排液容器法量測流體的密度 、黏度以及表面張力

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姓名

莊宗翰(Tsung-Han Chuang) 查詢紙本館藏

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機械工程學系

論文名稱

以排液容器法量測流體的密度、黏度以及表面張力
(Measuring the density、 surface tension and viscosity of a fluid by the draining vessel method.)

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摘要(中)

在現今科技中，量測低溫流體之密度、黏度以及表面張力等物性的現有技術已經非常成熟，但若欲測量之液體為高溫的液態金屬，這項任務的操作條件會變成嚴苛、困難且儀器價錢高昂，且至多僅能同時兩測兩種物性，為了克服此窘境，本文使用一種名為排液容器法(Draining vessel method)的方法學並配合本研究發展出之演算法同時量測密度、黏度及表面張力，此方法不僅能應用在冷流場中，在未來也有潛力能安置在高溫爐內進行高溫金屬溶液的物性量測，本研究將專注於將此裝置應用在冷流場中，目前已設計出一套系統，需要一個下方開有小孔之容器，將欲測物性之流體注入容器內並讓流體流出此容器，流體的物性會影響容器內部流體的流動特性，透過架設實驗系統，以及一條描述此容器內部流動特性之修正伯努力方程式來收集在容器內部隨時間變化的高度頭(elevation head)及質量通量數據，再結合數值方法來調整初始給定的物性來尋找最佳化理論與實驗間高度頭最小平方和與流體的密度、黏度與表面張力，同時透過敏感度分析探討容器內部流體的流動特性，發展出適合本研究之演算法，用以提升數值方法最佳化之物性準確度。研究結果顯示，本研究透過敏感度分析結果所發展出之演算法有效的將物性量測準確度提高，將水以及10% wt.甘油水溶液當待測流體量測物性，所迴歸出之物性與真實物性的相對誤差能保持在百分之五左右。

摘要(英)

Most of the well developed and affordable methods used for measuring fluid’s physical properties such as density, viscosity and surface tension are for operation at room temperature. However, if the liquid to be measured is of high temperature like liquid metal, then the operating conditions become severe, and the instruments used are expensive. 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. This method has the potential to be placed in a high temperature furnace for physical property measurement of high temperature molten metal if the measuring accuracy can be improved. In this thesis we study the draining vessel method and propose a new algorithm for processing the measured data to improve the measurement accuracy. The algorithm was tested using a cold flow verification with water and 10% wt. glycerin aqueous solution as the test fluids. An experimental system was built which has a container with a small hole at the bottom plate to inject a fluid of a given physical property out of the container. The physical properties of the fluid affect the flow characteristics inside the container. By collecting the fluid’s elevation head and mass flux data and then performing the regression with a modified Bernoulli equation using the least squares minimization, the fluid’s density, viscosity and surface tension were computed iteratively through minimizing the difference between the theoretical and experimental elevation heads. Based on the sensitivity analysis concerning the errors of the computed physical properties caused by the measured errors of the elevation head, we developed an algorithm to improve the accuracy of the method. The results show that the algorithm developed through the sensitivity analysis effectively improved the accuracy of physical property measurement. The water and 10% wt. glycerin aqueous solution were measured with relative errors of the obtained physical properties less than around 5 percent.

關鍵字(中)

★ 排液容器法
★ 密度
★ 黏度
★ 表面張力
★ 物性量測

關鍵字(英)

★ draining vessel method
★ density
★ viscosity
★ surface tension
★ physical property measurement

論文目次

目錄
中文摘要 i
Abstract ii
符號說明 iii
英文字母 iii
希臘字母 iii
目錄 iv
圖目錄 vii
表目錄 x
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 3
1.3 研究目的 5
第二章實驗設計 5
2.1 實驗裝置 10
2.1.1 排液容器 10
2.1.2 荷重元 11
2.1.3 雷射位移計 11
2.1.4 熱電偶 11
2.1.5 NI 資料擷取系統 12
2.2 實驗程序 12
2.2.1 取得累積質量與時間之關係式 12
2.2.2 雷射位移計驗證累積質量 13
第三章實驗原理 23
3.1 數學公式 23
3.2 修正係數與雷諾數之關係 24
3.3 非線性最小平方配適 26
3.4 敏感度分析 27
3.4.1 高度頭誤差對於物性之影響 27
3.4.2 物性誤差對其他物性之影響 30
3.5 演算法 32
3.5.1 一次迴歸三種物性 33
3.5.2 分段迴歸三種物性 34
第四章結果與討論 47
4.1 10% wt. 甘油水溶液物性量測 47
4.1.1 一次迴歸三種物性的演算法結果 47
4.1.2 敏感度分析之結果 48
4.1.3 分段迴歸演算法之結果 49
4.2 水的物性量測 49
4.2.1 一次迴歸三種物性的演算法結果 50
4.2.2 敏感度分析之結果 50
4.2.3 分段迴歸演算法 52
4.3 修正係數對於物性量測之影響 53
4.3.1 使用水與10% wt.甘油實驗數據做出修正係數與雷諾數之迴歸式，迴歸10% wt.甘油以及水之物性 53
4.3.2使用水、10% wt.、30% wt. 、50% wt.甘油以及乙二醇實驗數據做出修正係數與雷諾數之迴歸式迴歸水之物性 54
4.4 猜測值範圍大小以及測試 55
第五章結論與未來展望 71
5.1 結論 71
5.2 未來展望 73
參考文獻 74

參考文獻

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指導教授

鍾志昂

審核日期

2019-1-29

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