臺灣博碩士論文加值系統

本文以兩相模型模擬非牛頓奈米流體於均勻等壁溫三維扭曲橢圓管紊流強制對流之數值計算。應用控制體積法數值求解紊流強制對流奈米流體之橢圓、耦合、穩態之三維統御偏微分方程式。統御方程式則使用標準 紊流模型求解。研究參數包含流動特性指數(n=0.7, 1, 1.3)、奈米粒子體積濃度(1% ≤ ϕ ≤ 4%)，與雷諾數(6000 ≤ Re ≤ 14000)。首先以參考文獻中非牛頓奈米流體於圓管之實驗數據作驗證，其結果吻合，最大誤差在8%以內，接著再進一步延伸應用至扭曲橢圓管。
文中比較不同流變特性流體之奈米流體在扭曲橢圓管中的對流熱傳與流場特性。模擬結果顯示，與直橢圓管相比，流體流經扭曲橢圓管時產生二次流動，造成熱傳性能的增強。分析二次流動與溫度分布，結果顯示扭曲橢圓管因管壁扭曲而產生的二次流造成非牛頓奈米流體的混合進而提高傳熱能力，但扭曲橢圓管引起的擾動也會增加壓降。在本文研究範圍內，扭曲橢圓管的壓降與平均紐賽數，會隨著雷諾數與奈米體積濃度增加而增加。而因為流動特性的不同，剪切增稠流體之壓降會隨著雷諾數增加而提升；相反地，剪切稀化流體的壓降隨著雷諾數增加而減少。
除此之外，本文將以場協同原理判斷熱傳效應，並計算扭曲橢圓管中的耗散率。結果顯示，在扭曲橢圓管中，扭曲的壁面使得速度與溫度梯度有更好的協同性，進而增強熱傳效應。而雷諾數與奈米粒子體積濃度增加時，耗散量會增加，熱阻減少，傳熱效率較佳。

In this study, numerical simulations by two-phase models of non-Newtonian nanofluids forced convection in a three-dimensional twisted elliptical tube with constant wall temperature are investigated. The elliptical, coupled, steady-state and three-dimensional governing partial differential equations for turbulent forced convection of nanofluids are solved numerically using the finite volume approach. The governing equations are solved
with the standard turbulent model. The parameters studied include flow behavior index, nanoparticle volume concentration, and Reynolds number. The numerical results are validated with the experimental data of the non-Newtonian fluid in the circle tube in the literature first, the maximum discrepancy within 8%, and then further extend to a twisted elliptical tube.Different flow behavior index of nanofluids are considered and compared the convective heat transfer in a twisted elliptical tube. Thermal-hydraulic performance is evaluated by average Nusselt number,the field synergy principle and entransy dissipation. The results show that compared with the straight elliptical tube, rotational motions are produced in the twisted elliptical tube, enhancing the heat transfer performance. Both the average Nusselt number and the pressure drop increase with rising Reynolds number and nanoparticle volume concentration. Because of the flow characteristics, the pressure drop of the shear thickening fluid increases as the Reynolds number increases; conversely, the pressure drop of the shear thinning fluid decreases as the Reynolds number increases.

摘要 III
Extended Abstract V
致謝 VIII
目錄 IX
表目錄 XII
圖目錄 XIII
符號說明 XVI
第一章、緒論 1
1-1研究動機與背景 1
1-2 文獻回顧 3
1-3 本文探討主題與研究方法 6
第二章、對流傳熱增強之理論簡介 7
2-1 場協同理論 7
2-2 熵增與對流傳熱過程的耗散 10
第三章、非牛頓奈米流體理論分析 17
3-1 空間流場解析 17
3-2 系統之統御方程式 18
3-2-1 連續方程式(Continuity Equation) 18
3-2-2 動量方程式(Momentum Equation) 18
3-2-3 能量方程式(Energy Equation) 19
3-2-4 體積濃度方程式(Volume Fraction Equation) 19
3-2-4 相對速度 20
3-2 奈米流體 20
3-3 非牛頓流體 21
3-3-1 Ostwald-de-Waele冪律模型 21
3-4 冪次律型非牛頓奈米流體 23
3-4-1 等效密度及比熱、熱傳導係數以及黏滯係數 23
3-4 紊流模式 24
3-5 邊界條件 26
3-6 數據計算 27
第四章、數值方法 32
4-1 概述 32
4-2 統御方程式的座標轉換 33
4-3 格點位置的配置 36
4-4 統御方程式的離散 37
4-5 壓力修正方程式 40
4-6 差分方程式的解法 43
4-7 收斂條件 44
第五章、結果與討論 46
5-1 網格獨立測試與數值驗證 49
5-2 流場特性分析 54
5-3 熱場特性分析 64
第六章、結論與未來展望 79
6-1 結論 79
6-2 建議 80
參考文獻 82

[1]Hojjat, M., S.G. Etemad, R. Bagheri and J. Thibault, Turbulent forced convection heat transfer of non-Newtonian nanofluids. Experimental Thermal and Fluid Science, 2011. 35(7): p. 1351-1356
[2]Choi, S.U. and J.A. Eastman, Enhancing thermal conductivity of fluids with nanoparticles. 1995, Argonne National Lab., IL (United States).
[3]Eastman, J., U. Choi, S. Li, L. Thompson and S. Lee, Enhanced thermal conductivity through the development of nanofluids. MRS online proceedings library archive, 1996. 457.
[4]Brinkman, H., The viscosity of concentrated suspensions and solutions. The Journal of Chemical Physics, 1952. 20(4): p. 571-571.
[5]Hadad, K., A. Rahimian, and M. Nematollahi, Numerical study of single and two-phase models of water/Al2O3 nanofluid turbulent forced convection flow in VVER-1000 nuclear reactor. annals of nuclear energy, 2013. 60: p. 287-294.
[6]Yang, L., J.-L. Tian, Z. Yang, Y. Li, C.-H. Fu, Y.-H. Zhu and X.-L. Pang, Numerical analysis of non-Newtonian rheology effect on hydrocyclone flow field. Petroleum, 2015. 1(1): p. 68-74.
[7]Gao, S.X. and J.P. Hartnett, Steady flow of non-Newtonian fluids through rectangular ducts. International communications in heat and mass transfer, 1993. 20(2): p. 197-210.
[8]Gao, S.X. and J.P. Hartnett, Heat transfer behavior of Reiner-Rivlin fluids in rectangular ducts. International journal of heat and mass transfer, 1996. 39(6): p. 1317-1324.
[9]Moraveji, M.K., S.M.H. Haddad, and M. Darabi, Modeling of forced convective heat transfer of a non-Newtonian nanofluid in the horizontal tube under constant heat flux with computational fluid dynamics. International Communications in Heat and Mass Transfer, 2012. 39(7): p. 995-999.
[10]Esmaeilnejad, A., H. Aminfar, and M.S. Neistanak, Numerical investigation of forced convection heat transfer through microchannels with non-Newtonian nanofluids. International Journal of Thermal Sciences, 2014. 75: p. 76-86.
[11]Tajik Jamal-Abad, M., M. Dehghan, S. Saedodin, M.S. Valipour and A. Zamzamian, An experimental investigation of rheological characteristics of non-Newtonian nanofluids. Journal of Heat and Mass Transfer Research, 2014. 1(1): p. 17-23.
[12]Asmantas, L., M. Nemira, and V. Trilikauskas, Coefficients of heat transfer and hydraulic drag of a twisted oval tube. Heat transfer. Soviet research, 1985. 17(4): p. 103-109.
[13]Si, Q., Q. Xia, L. Liang and D. Li, Investigation of heat transfer and flow resistance on twisted tube heat exchanger. Journal of Chemical Industry and Engineering (China), 1995. 46(5): p. 601-608.
[14]Zhang, X.-X., G.-H. Wei, and Z.-F. Sang, Experimental research of heat transfer and flow friction properties in twisted tube heat exchanger. Huaxue Gongcheng(Chemical Engineering), 2007. 35(2): p. 17-20.
[15]Bejan, A., A study of entropy generation in fundamental convective heat transfer. Journal of heat transfer, 1979. 101(4): p. 718-725.
[16]Shah, R.K. and T. Skiepko, Entropy generation extrema and their relationship with heat exchanger effectiveness—number of transfer unit behavior for complex flow arrangements. Journal of heat transfer, 2004. 126(6): p. 994-1002.
[17]Guo, Z.-Y., H.-Y. Zhu, and X.-G. Liang, Entransy—a physical quantity describing heat transfer ability. International Journal of Heat and Mass Transfer, 2007. 50(13-14): p. 2545-2556.
[18]Chen, Q., M. Wang, N. Pan and Z.-Y. Guo, Optimization principles for convective heat transfer. Energy, 2009. 34(9): p. 1199-1206.
[19]Chen, Q., X.-G. Liang, and Z.-Y. Guo, Entransy theory for the optimization of heat transfer–a review and update. International Journal of Heat and Mass Transfer, 2013. 63: p. 65-81.
[20]Guo, Z., D. Li, and B. Wang, A novel concept for convective heat transfer enhancement. International Journal of Heat and Mass Transfer, 1998. 41(14): p. 2221-2225.
[21]Manninen, M., V. Taivassalo, and S. Kallio, On the mixture model for multiphase flow. 1996, Technical Research Centre of Finland Finland.
[22]Schiller, L., A drag coefficient correlation. Zeit. Ver. Deutsch. Ing., 1933. 77: p. 318-320.
[23]Miller, A. and D. Gidaspow, Dense, vertical gas‐solid flow in a pipe. AIChE journal, 1992. 38(11): p. 1801-1815.
[24]Ishii, M. and T. Hibiki, Thermo-fluid dynamics of two-phase flow. 2010: Springer Science ＆ Business Media.
[25]Mahian, O., A. Kianifar, C. Kleinstreuer, A.-N. Moh’d A, I. Pop, A.Z. Sahin and S. Wongwises, A review of entropy generation in nanofluid flow. International Journal of Heat and Mass Transfer, 2013. 65: p. 514-532.
[26]Hamilton, R.L. and O. Crosser, Thermal conductivity of heterogeneous two-component systems. Industrial ＆ Engineering chemistry fundamentals, 1962. 1(3): p. 187-191.
[27]Patankar, S.V. and D.B. Spalding, A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows, in Numerical Prediction of Flow, Heat Transfer, Turbulence and Combustion. 1983, Elsevier. p. 54-73.
[28]Hsu, C.-J., Numerical heat transfer and fluid flow. 1981, Taylor ＆ Francis.
[29]Johnson, A.T., Biological process engineering: an analogical approach to fluid flow, heat transfer, and mass transfer applied to biological systems. 1999: John Wiley ＆ Sons.