以計算流體力學結合排液容器法量測牛頓與非牛頓流體物性

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：97

、訪客IP：18.189.170.65

姓名

翁郡鴻(Chun-Hung Weng) 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牛頓與非牛頓流體物性
(Using CFD combined with Draining Vessel Method to Measure the Physical Properties of Newtonian and Non-Newtonian Fluid)

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)

有鑒現存物性量測方法中，多集中於特定環境條件、單一物性的量測，且儀器成本高昂，本研究旨於發展一具建置成本低廉，並可彈性因應不同操作條件的多物性量測方法。以排液容器法為基礎，本研究摒去習知文獻中對於理論方程式與排放修正係數的使用，並結合計算流體力學與據敏感度分析所設計之多階段回歸流程，最小化實驗與數值模擬間質量流率權重均方誤差，從而獲取欲測定之目標物性值。試以40℃純水為牛頓流體代表，量測其密度、黏度與表面張力係數，可得悉其密度以及表面張力係數與文獻參考值有平均相對誤差約5%以下，並以後者有較佳量測穩定性，而受實驗與模擬間既存偏誤影響，黏度則有平均誤差約15%，最佳可達10%以下。並延伸本量測方法之應用，進行非牛頓流體之黏性參數測定，以30℃下0.1wt%黃原膠水溶液作為代表，探求卡羅黏性模型下的零剪應變率黏度、無限剪應變黏度、時間常數以及冪次指數，並與市售儀器所得剪應變率-視黏度資料群進行擬合，平均可得R2(決定係數)為0.9的匹配程度，最佳來到0.94。然而，相比直接匹配零剪應變率黏度、無限剪應變黏度、時間常數與冪次指數的結果，本研究所得參數與之有著顯著的差異，故針對非牛頓流體的適用性，尚待未來進一步討論與改良。

摘要(英)

Due to the fact that the existing measuring techniques for physical properties nowadays mostly concentrate on single subject and constrain with specified environmental conditions. Furthermore, the cost of the equipment are usually expensive. This study aims to develop an innovative approach which features with relatively low set-up expense and could be adjusted flexibly to respond for different operating circumstances. On the basis of draining vessel method, this study eliminates the use of the theoretical formula and discharge coefficient instead, combining computational fluid dynamic(CFD) approach with multi-state regression procedure established by the results of sensitivity analysis to minimize the weighting mean square error between the mass flow rate of the experiment and those obtained by simulation to acquire the values of targeting properties. Take the pure water at 40℃ as representative of Newtonian fluid, measuring the corresponding density, viscosity and surface tension coefficient. The results show that compared with values quoted from literature, the density and the surface tension coefficient have the averaging error not more than 5%, besides, the latter demonstrate with better measuring stability. On the other hand, affected by the embedded difference between experiment and simulation, there is the averaging error of 15% of the results of the viscosity, and less than 10% for the best. We expand the application of such the approach to measure the viscous parameters of non-Newtonian fluid, and employ it to explore zero shear strain viscosity, infinite shear strain viscosity, time constant and power law index of the apparent viscosity of 0.1wt% xanthan gum aqueous solution at 30℃ under Carerau model. Fit the obtained parameters to the data attained by commercial equipment which obtain with the R2(coefficient of determination) being 0.9 in the mean, and 0.94 for the best. However, obvious differences could be observed between zero shear strain viscosity, infinite shear strain viscosity, time constant and power law index got by the designed approach and by direct regression, for the feasibility of the property-measuring technique proposed by this study to the non-Newtonian fluid, it still take further discussion and improvement in the near future.

關鍵字(中)

★ 排液容器法
★ 計算流體力學
★ 密度
★ 黏度
★ 表面張力係數
★ 黃原膠水溶液黏度

關鍵字(英)

★ draining vessel method
★ CFD
★ density
★ viscosity
★ surface tension coefficient
★ viscosity of xanthan gum aqueous solution

論文目次

中文摘要 i
Abstract ii
圖目錄 vi
表目錄 xi
符號表 xiii
英文縮寫 xiii
英文字母 xiii
希臘字母 xiv
上下標 xv
第一章緒論 1
1.1 研究動機 1
1.2 文獻回顧 2
1.2.1 習知物性量測方法 2
1.2.2 排液容器法 5
1.3 研究目的 6
第二章研究方法 8
2.1 問題描述 8
2.2 實驗設計 9
2.2.1 實驗裝置 9
2.2.1.1 排液容器 10
2.2.1.2 環境恆溫裝置 11
2.2.1.3 加熱攪拌器 13
2.2.1.4 荷重元與資料擷取系統 13
2.2.2 實驗程序 16
2.2.2.1 溶液置備 17
2.2.2.2 實驗程序 18
2.2.2.3 數據處理 19
2.3 數學模型 20
2.3.1 統御方程式 21
2.3.2 初始條件 22
2.3.3 邊界條件 23
2.3.4 形變網格 24
2.3.5 COMSOL Multiphysics有限元素法 26
2.4 物性量測之數值方法 28
2.4.1 量測目標 28
2.4.2 誤差準則 29
2.4.3 同步時間 31
2.4.4 敏感度分析 33
2.4.5 最佳化方法 34
2.4.5.1 最佳化演算法 35
2.4.5.2 初始猜測值 36
2.4.5.3 多階段回歸分析 43
第三章結果與討論 45
3.1 數學模型獨立性測試 45
3.1.1 牛頓流體數學模型 45
3.1.1.1 網格規劃與收斂性分析 45
3.1.1.2 計算時間步與收斂性分析 51
3.1.2 非牛頓流體數學模型 56
3.1.2.1 網格規劃與收斂性分析 56
3.1.2.2 計算時間步與收斂性分析 60
3.2 純水的物性量測 66
3.2.1 純水排液實驗結果 66
3.2.2 模擬正算與實驗數據之質量流率誤差 67
3.2.3 純水之敏感度分析結果 69
3.2.3.1 密度 69
3.2.3.2 黏度 70
3.2.3.3 表面張力係數 72
3.2.4 純水物性量測結果 74
3.2.4.1 牛頓流體多階段回歸流程 74
3.2.4.2 純水物性量測結果 75
3.3 黃原膠水溶液的物性量測 80
3.3.1 黃原膠水溶液排液實驗結果 80
3.3.2 黃原膠水溶液參考物性量測 81
3.3.3 模擬正算與實驗數據之質量流率誤差 83
3.3.4 黃原膠水溶液之敏感度分析結果 84
3.3.4.1 零剪應變率黏度 84
3.3.4.2 無限剪應變率黏度 86
3.3.4.3 時間常數 87
3.3.4.4 冪次指數 88
3.3.5 黃原膠水溶液物性量測結果 90
3.3.5.1 非牛頓流體多階段回歸流程 90
3.3.5.2 黃原膠水溶液物性量測結果 92
第四章結論 99
4.1 結論 99
4.2 研究限制與未來展望 101
參考文獻 102

參考文獻

[1] A. F. Crawley, "Densities of liquid metals and alloys," International Metallurgical Reviews, vol. 19, no. 1, pp. 32-48, 1974.
[2] A. F. Crawley and D. R. Kiff, "Density of liquid bismuth," Metallurgical Transactions B, vol. 2, p. 609–610, 1971.
[3] B. G. Lipták, Process measurement and analysis, Fourth Edition ed., vol. 1, B. Lipták, Ed., CRC Press, 2003, pp. 836-840.
[4] A. Furtado, E. Batista, I. Spohr. and E. Filipe, "Measurement of density using oscillation-type density meters. Calibration,traceability and uncertainties," in 14ème Congrès International de Métrologie, Paris, France, 2009.
[5] F. A. Holland and R. Bragg, "Flow of incompressible non-Newtonian fluids in pipes," in Fluid Flow for Chemical Engineers, Second Edition ed., 1995, pp. 96-98, 102-104.
[6] Y. T. Choi, J. U. Cho, S. B. Choi and N. M. Wereley, "Constitutive models of electrorheological and magnetorheological fluids using viscometers," Smart Materials and Structures, 2005.
[7] B. R. Munson, D. F. Young, T. H. Okiishi and W. W. Huebsch, Fundamentals of fluid mechanics, Sixth Edition ed., John Wiley & Sons, Inc., 2009, pp. 313-315.
[8] P. d. Noüy, "An interfacial tensiometer for universal use," The Journal of General Physiology, vol. 7, no. 5, pp. 625-631, 1925.
[9] M. Korenko and F. Šimko, "Measurement of interfacial tension in liquid-liquid high-temperature systems," Journal of Chemical & Engineering Data, vol. 55, pp. 4561-4573, 2010.
[10] B. Lee, E. Chan, P. Ravindra and T. A. Khan, "Surface tension of viscous biopolymer solutions measured using the du Noüy ring method and the drop weight methods," Polymer Bulletin, vol. 69, no. 4, pp. 1-19, 2012.
[11] F. E. Benedetto, H. Zolotucho and M. O. Prado, "Critical assessment of the surface tension determined by the maximum pressure bubble method," Materials Research, vol. 18, no. 1, pp. 9-14, 2015.
[12] F. Bashforth and J. C. Adams, "An attempt to test the theories of capillary action: By comparing the theoretical and measured forms of drops of fluid," Cambridge: University Press, 1883.
[13] E. Yakhshi Tafti, R. Kumar and H. J. Cho, "Measurement of surface interfacial tension as a function of temperature using pendant drop images," International Journal of Optomechatronics, vol. 5, no. 4, pp. 393-403, 2011.
[14] W. Kwak, J. K. Park, J. Yoon, S. Lee and W. Hwang, "Measurement of surface tension by sessile drop tensiometer with superoleophobic surface," Applied Physics Letters, vol. 112, no. 12, 2018.
[15] S. J. Roach and H. Henein, "A dynamic approach to determining the surface tension of a fluid," The Canadian Journal of Metallurgy and Materials Science, vol. 42, no. 2, pp. 175-186, 2003.
[16] S. J. Roach and H. Henein, "A new method to dynamically measure the surface tension,viscosity, and density of melts," Metallurgical and Materials Transactions B, vol. 36B, pp. 667-676, 2005.
[17] E. K. P. Chong and S. H. Zak, An introduction to optimization, Second Edition ed., WILEY, 2001, pp. 146-148.
[18] S. J. Roach and H. Henein, "Physical properties of AZ91D measured using the draining crucible method: Effect of SF6," International Journal of Thermophysics, vol. 33, pp. 484-494, 2012.
[19] T. Gancarz, J. Jourdan, W. Gąsior and H. Henein, "Physicochemical properties of Al, Al-Mg and Al-Mg-Zn alloys," Journal of Molecular Liquids, vol. 249, pp. 470-476, 2018.
[20] T. Gancarz, J. Pstrus, W. Gąsior and H. Henein, "Physicochemical properties of Sn-Zn and SAC+Bi alloys," Journal of Electronic Materials, vol. 42, no. 2, pp. 288-293, 2013.
[21] S. J. Roach, "Determination of physical properties of melts," University of Alberta Liberary, 2001.
[22] 鍾志昂, 李亞寰, 莊宗翰, 江宗軒, 顏芷珊, 何正榮且鄭憲清, “物性測量裝置及測量物性的方法”. 中華民國專利: I706124, 1 10 109.
[23] "NI 9237 Datasheet".
[24] C. S. H. Chen and E. W. Sheppard, "Conformation and shear stability of xanthan gum in solution," Polymer Engineering and Science, vol. 20, no. 7, pp. 512-516, 1980.
[25] L. Zhong, M. Oostrom, M. J. Truex, V. R. Vermeul and J. E. Szecsody, "Rheological behavior of xanthan gum solution related to shear thinning fluid delivery for subsurface remediation," Journal of Hazardous Materials, Vols. 244-245, pp. 160-170, 2013.
[26] B. Katzbauer, "Properties and applications of xanthan gum," Polymer Degradarion and Stability, vol. 59, pp. 81-84, 1998.
[27] S. Kalia and A. R. Choudhury, "Synthesis and rheological studies of a novel composite hydrogel of xanthan, gellan and pullulan," International Journal of Biological Macromolecules, vol. 137, pp. 475-482, 2019.
[28] D. M. Price and M. Jarratt, "Thermal conductivity of PTFE and PTFE composites," Thermochimica Acta, Vols. 392-393, pp. 231-236, 2002.
[29] F. M. White, Fluid mechanics, Seventh Edition ed., McGraw-Hill, 2011, pp. 8-9.
[30] W. B. J. Zimmerman, COMSOL Multiphysics有限元法多物理場建模與分析, 人民交通出版社, 2007.
[31] S. Dokos, Modelling organs, tissues, cells and devices: Using MATLAB and COMSOL Multiphysics, Springer Nature, 2017, pp. 63-65, 93-96.
[32] P. K. Kennedy and R. Zheng, Flow analysis of injection molds, Second Edition ed., Hanser, 2013, pp. 23-24.
[33] A. E. Beaton and J. W. Tukey, "The fitting of power series, meaning polynomials, illustrated on Band-Spectroscopic data," Technometrics, vol. 16, no. 2, pp. 147-185, 1974.
[34] P. W. Holland and R. E. Welsch, "Robust regression using iteratively reweighted least-squares," Communications in Statistics - Theory and Methods, vol. 6, no. 9, pp. 813-827, 1977.
[35] R. W. Hill and P. W. Holland, "Two robust alternatives to least-squares regression," Journal of the American Statistical Association, vol. 72, no. 360, pp. 828-833, 1977.
[36] J. O. Street, R. J. Carroll and D. Ruppert, "A note on computing robust regression estimates via iteratively reweighted least squares," The American Statistician, vol. 42, no. 2, pp. 152-154, 1988.
[37] L.M.Kocić and G.V.Milovanović, "Shape preserving approximations by polynomials and splines," Computers & Mathematics with Applications, vol. 33, no. 11, pp. 59-97, 1997.
[38] F. N. Fritsch and R. E. Carlson, "Monotone piecewise cubic interpolation," SIAM Journal on Numerical Analysis, vol. 17, no. 2, pp. 238-246, 1980.
[39] J. D. Faires and R. Burden, Numerical methods, Fourth Edition ed., Brooks/Cole, Cengage Learning, 2013, pp. 83-86.
[40] C. B. Moler, "Interpolation," in Numerical computing with MATLAB, Society for Industrial and Applied Mathematics, 2004, pp. 9-10.
[41] J. Norton, "An introduction to sensitivity assessment of simulation models," Environmental Modelling & Software, vol. 69, pp. 166-174, 2015.
[42] J. A. Nelder and R. Mead, "A simplex method for function minimization," Computer Journal, vol. 7, no. 4, pp. 308-313, 1965.
[43] D. Constales, G. Yablonsky, D. D′hooge, J. W. Thybaut and G. B. Marin, Advanced data analysis and modelling in chemical engineering, First Edition ed., Elsevier, 2017, pp. 285-290.
[44] J. C. Largarias, J. A. Reeds, M. H. Wright and P. E. Wright, "Convergence properties of the Nelder-Mead simplex method in low dimensions," SIAM Journal on Optimization, vol. 9, no. 1, pp. 112-147, 1998.
[45] W. M. Haynes, D. R. Lide and T. J. Bruno, CRC handbook of chemistry and physics, Ninety-seventh ed., CRC Press, Taylor & Francis Group, 2016-2017.
[46] Q. H. Zhao, D. Urosević, N. Mladenović and PierreHansen, "A restarted and modified simplex search for unconstrained optimization," Computers & Operations Research, vol. 36, no. 12, pp. 3263-3271, 2009.
[47] M. Tanaka, G. Girard, R. Davis, A. Peuto and N. Bignell, "Recommended table for the density of water between 0 C and 40 C based on recent experimental reports," Metrologia, vol. 38, pp. 30--309, 2001.
[48] “IAPWS R12-08,” Berlin, Germany, 2008.
[49] A. Mulero, I. Cachadiña and M. I. Parra, "Recommended correlations for the surface tension of common fluids," Journal of Physical and Chemical Reference Data, vol. 41, no. 4, p. 043105, 2012.
[50] M. Yusuf, S. Y. Khan and N. Sardar, "Studies on rheological behavior of xanthan gum solutions in presence of additives," Petroleum & Petrochemical Engineering Journal, vol. 2, no. 5, 2018.
[51] S. M. A. Razavi and A. Alghooneh, "Understanding the physics of hydrocolloids interaction using rheological, thermodynamic and functional properties: A case study on xanthan gum-cress seed gum blend," International Journal of Biological Macromolecules, vol. 151, no. 15, pp. 1139-1153, 2020.

指導教授

鍾志昂(Chih-Ang Chung)

審核日期

2021-5-7

推文