本研究採用暫態數值模擬探討低溫垂直板面膜式冷凝行為。數值方法採用FLUENT商業軟體之 VOF(void of fluid)數值模型，液膜表面張力採用連續表面力(continuum surface force)，兩相熱質傳部分採用能量跳躍法，透過UDF (user-defined function)進行計算。本研究選用R134a流體，採不同網格尺寸計算溫度梯度與液膜厚度，與不同條件下之Nusselt解析解作比較。特別針對垂直板前沿與中後段冷凝液膜驗證其準確性，結果顯示前沿冷凝液膜受垂直液膜方向網格大小、汽液密度比影響甚大，而中後段液膜厚之準確度較與網格大小、汽液密度比的關係不顯著，顯示介面網格位於壁邊界處時，因薄液膜中溫度梯度之計算誤差，須採用較小網格。隨後進一步提升垂直板長度，使液膜涵蓋層流與波動(wavy film)兩區域，以模擬自然對流下波動液膜冷凝情形。本計算中如未加入外在刺激，在液膜雷諾數遠大於臨界值20~30時液膜仍未產生波動。但當液膜波動因外在因素而形成後，其平均熱對流係數較無波動時增加45%。

In this study, the surface film condensation behavior on the low-temperature vertical plate is investigated by transient numerical simulation. The numerical methods including the VOF (void of fluid) model, continuum surface force for the surface tension, and the energy jump method through UDF (user-defined function) for the two-phase heat and mass transfer are adopted in the commercial software, FLUENT. R134a fluid is selected as the working fluid. The liquid film thickness is compared with the Nusselt analytical solution under different mesh sizes, temperature gradients, and liquid film thicknesses.
The accuracy of the condensate film thickness in the different sections of the vertical plate is examined separately. The results show that the leading-edge of the condensate film was greatly affected by the grid size and the vapor-liquid density ratio in the direction perpendicular to the cooling wall, while the accuracy of the liquid film thickness away from the leading-edge is insensitive to the above factors. The reason is due to the inaccurate calculation of the temperature gradient when the interface grids are located next to the wall boundary, which can be improved using finer grids .
To simulate the fluctuating liquid film under natural convection, the length of the vertical plate is further increased, so that the liquid film covers the laminar flow and wavy film regions. When no external oscillation is imposed, no wave appears for a film Reynolds number much larger than the critical Reynolds number of 20~30. Once surface wave in activated by external flow fluctuations, the average heat convection coefficient is enhanced by 45%.

摘要 2
Abstract 3
致謝辭 4
目錄 6
圖表目錄 7
符號表 9
第一章 緒論 11
1.1 研究背景 11
1.2 液汽介面的VOF解法 12
1.3 沸騰、冷凝過程之動力學分析於相變化之數值分析 13
1.4 能量跳越法應用於相變化之數值分析 16
1.5 垂直板面之冷凝 18
1.6 研究動機與目的 21
第二章 數值模型與理論方法 23
2.1 垂直板面膜式冷凝數值模型統御方程式與條件 23
2.2 VOF-CSF模式與偽流動 25
2.3 二相相變化數值計算方法 26
2.4 相變化模型驗證 27
2.5 數值計算方法與參數設定 28
2.5.1 大係數法(large coefficient method) 28
2.5.2 數值方法(Solution Methods) 29
2.5.2.1 速度壓力求解方程式 29
2.5.2.2 離散化方程式 30
2.5.2.3 模擬參數與收斂判定 31
2.6 介面處理與網格條件 31
第三章 結果與討論 37
3.1 Stefan problem 驗證結果 37
3.2 短垂直板自然對流冷凝(Nusselt condensation) 38
3.3 長垂直板自然對流冷凝 40
3.4 長垂直板自然對流冷凝之波動分析 41
3.5 冷凝過程計算成本與誤差評估 43
第四章 結論與未來工作 54
4.1 結論 54
4.2 未來工作 55
參考文獻 56
 

[1] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, 39(1) (1981) 201-225.
[2] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, 100(2) (1992) 335-354.
[3] Z. Pan, J.A. Weibel, S.V. Garimella, Spurious current suppression in vof-csf simulation of slug flow through small channels, Numerical Heat Transfer, Part A: Applications, 67(1) (2015) 1-12.
[4] R. Gupta, D.F. Fletcher, B.S. Haynes, On the CFD modelling of Taylor flow in microchannels, Chemical Engineering Science, 64(12) (2009) 2941-2950.
[5] M. Sussman, E.G. Puckett, A coupled level set and volume-of-fluid method for computing 3d and axisymmetric incompressible two-phase flows, Journal of Computational Physics, 162(2) (2000) 301-337.
[6] Z. Pan, J.A. Weibel, S.V. Garimella, A cost-effective modeling approach for simulating phase change and flow boiling in microchannels, in: International Electronic Packaging Technical Conference and Exhibition, ASME, 2015, pp. V003T010A023.
[7] S.C.K. De Schepper, G.J. Heynderickx, G.B. Marin, Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker, Computers & Chemical Engineering, 33(1) (2009) 122-132.
[8] B. Fadhl, L.C. Wrobel, H. Jouhara, CFD modelling of a two-phase closed thermosyphon charged with R134a and R404a, Applied Thermal Engineering, 78 (2015) 482-490.
[9] Y. Kim, J. Choi, S. Kim, Y. Zhang, Effects of mass transfer time relaxation parameters on condensation in a thermosyphon, Journal of Mechanical Science and Technology, 29(12) (2015) 5497-5505.
[10] A. Alizadehdakhel, M. Rahimi, A.A. Alsairafi, CFD modeling of flow and heat transfer in a thermosyphon, International Communications in Heat and Mass Transfer, 37(3) (2010) 312-318.
[11] M. Knudsen, The Kinetic Theory of Gases: Some Modern Aspects (Methuen & Co. Ltd., London), (1934).
[12] W.H. Lee, A Pressure Iteration Scheme for Two-Phase Modeling, Technical Report LA-UR 79-975, (1979).
[13] R.W. Schrage, A Theoretical Study of Interface Mass Transfer, Columbia
University Press, New York, 1953.
[14] I. Tanasawa, Advances in Condensation Heat Transfer, in: J.P. Hartnett, T.F. Irvine, Y.I. Cho (Eds.) Advances in Heat Transfer, Elsevier, 1991, pp. 55-139.
[15] C.R. Kharangate, I. Mudawar, Review of computational studies on boiling and condensation, International Journal of Heat and Mass Transfer, 108 (2017) 1164-1196.
[16] F. Gibou, L. Chen, D. Nguyen, S. Banerjee, A level set based sharp interface method for the multiphase incompressible Navier–Stokes equations with phase change, Journal of Computational Physics, 222(2) (2007) 536-555.
[17] S. Shin, D. Juric, Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity, Journal of Computational Physics, 180(2) (2002) 427-470.
[18] B.A. Nichita, J.R. Thome, A level set method and a heat transfer model implemented into FLUENT for modeling of microscale two phase flows, in: AVT-178 Specialists' Meeting on System Level Thermal Management for Enhanced Platform Efficiency, 2010.
[19] D.-L. Sun, J.-L. Xu, L. Wang, Development of a vapor–liquid phase change model for volume-of-fluid method in FLUENT, International Communications in Heat and Mass Transfer, 39(8) (2012) 1101-1106.
[20] D. Sun, J. Xu, Q. Chen, Modeling of the evaporation and condensation phase-change problems with FLUENT, Numerical Heat Transfer, Part B: Fundamentals, 66(4) (2014) 326-342.
[21] I. Perez-Raya, S.G. Kandlikar, Numerical modeling of interfacial heat and mass transport phenomena during a phase change using ANSYS-Fluent, Numerical Heat Transfer, Part B: Fundamentals, 70(4) (2016) 322-339.
[22] Z. Pan, J.A. Weibel, S.V. Garimella, A saturated-interface-volume phase change model for simulating flow boiling, International Journal of Heat and Mass Transfer, 93 (2016) 945-956.
[23] W. Nusselt, Die oberflachen kondenastion des wasserdamfes, Z. Vereines Dtsch. Ingenieure 60 ((1916) 541–546. 569–575.).
[24] W.M. Rohsenow, Effect of vapor velocity on laminar and turbulent film condensation, Transactions of ASME November, (1956) 1645-1648.
[25] E.M. Sparrow, J.L. Gregg, A boundary-layer treatment of laminar-film condensation, Journal of Heat Transfer, 81(1) (1959) 13-18.
[26] J.C.Y. Koh, E.M. Sparrow, J.P. Hartnett, The two phase boundary layer in laminar film condensation, International Journal of Heat and Mass Transfer, 2(1) (1961) 69-82.
[27] V.P. Carey, Liquid-vapor phase-change phenomena: an introduction to the thermophysics of vaporization and condensation processes in heat transfer equipment, Washington (D.C.): Hemisphere, 1992.
[28] A.S. Dalkilic, S. Yildiz, S. Wongwises, Experimental investigation of convective heat transfer coefficient during downward laminar flow condensation of R134a in a vertical smooth tube, International Journal of Heat and Mass Transfer, 52(1) (2009) 142-150.
[29] R.I. Hirshburg, L.W. Florschuetz, Laminar wavy-film flow: Part I, hydrodynamic analysis, Journal of Heat Transfer, 104(3) (1982) 452-458.
[30] H. Brauer, Stromung and warmeubergang bei rieselfilmen, VDI Forschungself, 457 (1956) B22.
[31] R.P. Salazar, E. Marschall, Three-dimensional surface characteristics of a falling liquid film, International Journal of Multiphase Flow, 4(5) (1978) 487-496.
[32] S.L. Chen, F.M. Gerner, C.L. Tien, General film condensation correlations, Experimental Heat Transfer, 1(2) (1987) 93-107.
[33] P. Kapitza, S. Kapitza, Wave flow of thin layers of a viscous fluid Zh, Teor. Fiz, 19 (1949) 105-120.
[34] T. Nosoko, P.N. Yoshimura, T. Nagata, K. Oyakawa, Characteristics of two-dimensional waves on a falling liquid film, Chemical Engineering Science, 51(5) (1996) 725-732.
[35] J. Liu, J.P. Gollub, Solitary wave dynamics of film flows, Physics of Fluids, 6(5) (1994) 1702-1712.
[36] S. Alekseenko, V.Y. Nakoryakov, B. Pokusaev, Wave formation on a vertical falling liquid film, AIChE Journal, 31(9) (1985) 1446-1460.
[37] D. Gao, N. Morley, V. Dhir, Numerical simulation of wavy falling film flow using VOF method, Journal of computational physics, 192(2) (2003) 624-642.
[38] S. Bo, X. Ma, Z. Lan, H. Chen, J. Chen, Numerical simulation on wave behaviour and flow dynamics of laminar‐wavy falling films: effect of surface tension and viscosity, The Canadian Journal of Chemical Engineering, 90(1) (2012) 61-68.
[39] F.W. Pierson, S. Whitaker, Some theoretical and experimental observations of the wave structure of falling liquid films, Industrial & Engineering Chemistry Fundamentals, 16(4) (1977) 401-408.
[40] R. Hirshburg, L. Florschuetz, Laminar wavy-film flow: Part I, hydrodynamic analysis, (1982).
[41] Z. Liu, B. Sunden, J. Yuan, VOF modeling and analysis of filmwise condensation between vertical parallel plates, 43(1) (2012) 47-68.
[42] Q. Liu, J. Yang, W. Qian, H. Gu, M. Liu, Numerical study of the forced convective condensation on a short vertical plate, Heat Transfer Engineering, 38(1) (2017) 103-121.
[43] J.-B. Dupont, D. Legendre, Numerical simulation of static and sliding drop with contact angle hysteresis, Journal of Computational Physics, 229(7) (2010) 2453-2478.
[44] M.M. Francois, S.J. Cummins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, M.W. Williams, A balanced-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework, Journal of Computational Physics, 213(1) (2006) 141-173.
[45] Y. Renardy, M. Renardy, PROST: A parabolic reconstruction of surface tension for the volume-of-fluid method, Journal of Computational Physics, 183(2) (2002) 400-421.
[46] B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti, Modelling merging and fragmentation in multiphase flows with SURFER, Journal of Computational Physics, 113(1) (1994) 134-147.
[47] T. Abadie, J. Aubin, D. Legendre, C. Xuereb, Hydrodynamics of gas–liquid Taylor flow in rectangular microchannels, Microfluidics and Nanofluidics, 12(1) (2012) 355-369.
[48] S. Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis, 2018.
[49] Y. Zhang, A. Faghri, M.B. Shafii, Capillary blocking in forced convective condensation in horizontal miniature channels, J. Heat Transfer, 123(3) (2001) 501-511.
[50] R. Peyret, Handbook of Computational Fluid Mechanics, Elsevier, 1996.
[51] R.I. Issa, Solution of the implicitly discretised fluid flow equations by operator-splitting, Journal of Computational Physics, 62(1) (1986) 40-65.