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

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：83

、訪客IP：18.117.189.154

姓名

顏芷珊(Chih-Shan Yen) 查詢紙本館藏

畢業系所

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)

相關論文

★ 溫度調變對二元合金固液介面形態穩定的影響	★ 濃度調變對二元合金固液介面形態穩定的影響
★ 圓錐平板型生物反應器週期性流場研究	★ 圓錐平板型生物反應器二次週期流場研究
★ 圓錐平板型生物反應器脈動式流場研究	★ 濃度調變對單向固化形態穩定的影響
★ 圓錐平板型生物反應器脈動式二次流場研究	★ 模擬注流式生物反應器之流場及細胞生長
★ 週期式圓錐平板裝置之設計與量測	★ 模擬注流式生物反應器之細胞培養研究
★ 軟骨細胞在組織工程支架之培養研究	★ 細胞在組織工程支架之生長與遷移
★ 冷電漿沉積類鑽碳膜之製程模擬分析	★ 格狀自動機探討組織工程細胞體外培養研究
★ 細胞在注流式生物反應器之生長研究	★ 週期式圓錐平板裝置之流場分析

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

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

參考文獻

Baker, P. E. (1957). Density logging with gamma rays. Trans. AIME, 210, 289-294.
Brooks, R. F., Dinsdale, A. T., & Quested, P. N. (2005). The measurement of viscosity of alloys—a review of methods, data and models. Measurement Science and Technology, 16(2), 354-362.
Cheng, J., Gröbner, J., Hort, N., Kainer, K. U., & Schmid-Fetzer, R. (2014). Measurement and calculation of the viscosity of metals—a review of the current status and developing trends. Measurement Science and Technology, 25(6), 062001.
Crawley, A. (1974). Densities of liquid metals and alloys. International Metallurgical Reviews, 19(1), 32-48.
Du Noüy, P. L. (1925). An interfacial tensiometer for universal use. The Journal of general physiology, 7(5), 625-631.
Gancarz, T., Gąsior, W., & Henein, H. (2013). Physicochemical Properties of Sb, Sn, Zn, and Sb–Sn System. International Journal of Thermophysics, 34(2), 250-266.
Gancarz, T., Gąsior, W., & Henein, H. (2014). The Discharge Crucible Method for Making Measurements of the Physical Properties of Melts: An Overview. International Journal of Thermophysics, 35(9-10), 1725-1748.
Gancarz, T., Moser, Z., Gąsior, W., Pstruś, J., & Henein, H. (2011). A Comparison of Surface Tension, Viscosity, and Density of Sn and Sn–Ag Alloys Using Different Measurement Techniques. International Journal of Thermophysics, 32(6), 1210-1233.
Gasior, W., Moser, Z., & Pstruś, J. (2003). Surface tension, density, and molar volume of liquid Sb-Sn alloys: Experiment versus modeling. Journal of Phase equilibria, 24(6), 504-510.
Green, H. (1942). High-Speed Rotational Viscometer of Wide Range. Confirmation of theReiner Equation of Flow. Industrial & Engineering Chemistry Analytical Edition, 14(7), 576-585.
Keene, B. (1993). Review of data for the surface tension of pure metals. International Materials Reviews, 38(4), 157-192.
Kucharski, M., & Fima, P. (2005). The surface tension and density of liquid Ag–Bi, Ag–Sn, and Bi–Sn alloys. Monatshefte für Chemie/Chemical Monthly, 136(11), 1841-1846.
Lagarias, J. C., Reeds, J. A., Wright, M. H., & Wright, P. E. (1998). Convergence properties of the Nelder--Mead simplex method in low dimensions. SIAM Journal on optimization, 9(1), 112-147.
Moser, Z., Gasior, W., & Pstruś, J. (2001). Surface tension of liquid Ag-Sn alloys: experiment versus modeling. Journal of Phase equilibria, 22(3), 254-258.
Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The computer journal, 7(4), 308-313.
Roach, S. J., & Henein, H. (2003). A dynamic approach to determining the surface tension of a fluid. Canadian Metallurgical Quarterly, 42(2), 175-186.
Roach, S. J., & Henein, H. (2005). A new method to dynamically measure the surface tension, viscosity, and density of melts. Metallurgical and Materials Transactions B, 36(5), 667-676.
Roach, S. J., & Henein, H. (2012). Physical Properties of AZ91D Measured Using the Draining Crucible Method: Effect of SF6. International Journal of Thermophysics, 33(3), 484-494.
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., & Tarantola, S. (2008). Global sensitivity analysis: the primer: John Wiley & Sons.
Stauffer, C. E. (1965). The measurement of surface tension by the pendant drop technique. The journal of physical chemistry, 69(6), 1933-1938.
Sugden, S. (1922). XCVII.—The determination of surface tension from the maximum pressure in bubbles. Journal of the Chemical Society, Transactions, 121, 858-866.
Thresh, H., Crawley, A., & White, D. (1968). The densities of liquid tin, lead, and tin-lead alloys. TRANS MET SOC AIME, 242(5), 819-822.
Weast, R. C., Astle, M. J., & Beyer, W. H. (1988). CRC handbook of chemistry and physics (Vol. 69): CRC press Boca Raton, FL.
馮康等編，1978，「數值計算方法」，國防工業出版社，567~593頁
李亞寰，2019，「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」，國立中央大學機械所，碩士論文
江宗軒，2019，「以排水容器法量測液態錫的密度、黏度以及表面張力」，國立中央大學機械所，碩士論文

指導教授

鍾志昂(Chih-Ang Chung)

審核日期

2019-8-22

推文