臺灣博碩士論文加值系統

由於傳統石化原料的日趨匱乏，且會衍生相關的環保問題，因此替代能源中之太陽能近年來受到重視。在太陽熱能系統中之主要元件為作為熱能轉換之集熱器，其效率的提昇可縮小設備尺寸、獲得更高溫熱源以作更廣泛的應用。本文以數值模擬方法探討在強制脈衝流下，對裝置有發泡金屬塊之新穎平板式太陽能集熱器的熱傳增強特性。文中統御方程式於純流體區流場遵守非穩態Unsteady Navier-Stoke方程式；於多孔材質區流場則以暫態Transient Forchheimer-Brinkman-Darcy模式來模擬多孔質熱沉內部之流動狀態；而能量方程式則依非局部熱平衡(LTNE)假設，使用固流兩相能量方程式模式，上述統御方程式並導入發泡金屬重要性質之實驗迴歸公式。接著以流線函數-渦度轉換公式及有限體積法(Finite volume method)來求解上述複合層熱流場之聯立方程組。在求解時藉由變化各項參數，來探討熱流場的變化及其對熱傳增強的效益。經由計算結果顯示，脈衝流週期性地改變由發泡金屬塊所引起的迴流結構，會影響到流場及熱場特性。此種結合發泡金屬熱沉與強制脈衝流的方式能有效增加熱傳率，藉此可提高平板式太陽能集熱器的集熱性能。此外，達西數為影響局部熱平衡（LTE）有效性之最主要參數。整體而言，在固相傳導為主導的熱傳輸模式下，隨固液兩相間之界面熱傳效果的增加，會導致局部熱平衡現象變得更加明顯，且太陽能集熱器的傳熱性能亦同時增強。最後，本文使用統計學上的迴歸分析理論，利用數值計算所獲得之數據，推導歸納出有用的迴歸關係方程式來估算平均紐賽數，可作為實際工程設計上之應用。

The solar energy, which is one of alternative renewable energy, becomes more important recently due to the gradual scarcity and derivative environment problems of traditional fossil fuels. The major component of any solar thermal system is the solar thermal collector for thermal energy convert. The efficiency improvement for flat-plate solar collector can reduce its size and obtain higher temperature fluid for wider application. A numerical simulation was carried out to investigate the characteristics of heat transfer enhancement for a novel flat-plate solar thermal collector using metal-foam porous blocks as heat sinks under forced pulsating flow. The analysis is based on the use of unsteady Navier-Stokes equation in the fluid region, the transient Darcy-Brinkman-Forchheimer flow model in the porous region, and the two-phase energy models employing local thermal non-equilibrium (LTNE) assumption on the thermal field. The above governing equations are incorporated with empirical equations of metal-foam. A finite-volume integration method is employed to solve the dimensionless coupled governing equations for this porous/fluid composite system through the use of a stream function-vorticity transformation. This study details the effects of variations in the major control parameters to illustrate important fundamental and practical results. The results show that the periodic alteration in the structure of recirculation flows, caused by metal-foam blocks and flow pulsating, has a direct impact on the flow and thermal characteristics. The synthetic method indeed can be considered as an effective method to augment heat transfer and improve the efficiency of solar thermal collector. Besides, the Darcy number is the most influential parameter in determining the validity of local thermal equilibrium (LTE). In general, when solid conduction is the dominant heat transfer mode, the more efficient the interfacial heat transfer between solid and fluid phases is, the more obvious the local thermal equilibrium becomes. Further, the useful correlated equations to predict Num are proposed by regression analysis here for the application of realistic engineering design.

摘 要 i
ABSTRACT ii
誌 謝 iv
目 錄 v
表目錄 viii
圖目錄 ix
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 9
1.2.1 多孔材質及發泡金屬的熱傳研究 9
1.2.2 太陽能集熱器與多孔材質的應用 17
1.2.3 振盪流與多孔材質的應用 23
1.3 研究目的 26
第二章 基礎理論 27
2.1 系統描述 27
2.2 基本假設 30
2.3 統御方程式 31
2.3.1 純流體區統御方程式 31
2.3.2 多孔材質區統御方程式 33
2.3.3 解析區域之起始條件 41
2.3.4 解析區域之邊界條件 41
2.4 無因次化分析 43
2.4.1 無因次化純流體區 44
2.4.2 無因次化多孔材質區 44
2.4.3 無因次化邊界條件 46
2.4.4 紐賽數及壓損的計算 48
第三章 數值分析 51
3.1 流體區差分方程式 52
3.2 多孔材質區差分方程式 59
3.3 流體與多孔材質界面處處理 69
3.4 靠近平板壁面處之渦度邊界問題 71
3.5 鬆弛係數(Relaxation factor) 72
3.6 格點產生(Grid generation) 74
3.7 收斂準則 76
3.8 求解步驟 77
3.9 網格獨立與時間獨立 79
3.10 數值週期性穩定評估 82
3.11 發泡金屬性質的驗證與數值計算驗證 86
3.11.1 發泡金屬材質之實驗迴歸公式的驗證 86
3.11.2 數值計算驗證 89
第四章 結果與討論 97
4.1 穩定流下多孔發泡金屬所引起之熱流場變化 97
4.2 脈衝流下多孔發泡金屬所引起之熱流場變化 107
4.2.1 達西數Da之影響 116
4.2.2 雷諾數Re之影響 124
4.2.3 脈衝流振幅A之影響 131
4.2.4 脈衝流頻率參數St的影響 138
4.2.5 孔隙率ε之影響 145
4.2.6 纖維直徑df之影響 152
4.2.7 孔密度(PPI)之影響 159
4.2.8 有效熱傳導率比λeff之影響 167
4.2.9 不同普郎特數Pr之影響 175
4.2.10 發泡金屬塊高度Hp*之影響 182
4.2.11 發泡金屬塊分佈因子Pb之影響 189
4.2.12 發泡金屬覆蓋率Pc之影響 197
4.3 參數變化對流場壓力降的影響 205
4.4 局部熱平衡假設之有效性的觀察 209
4.4.1 達西數Da之LTE現象觀察 210
4.4.2 雷諾數Re之LTE現象觀察 217
4.4.3 脈衝流振幅A之LTE現象觀察 218
4.4.4 脈衝流頻率參數St之LTE現象觀察 219
4.4.5 孔隙率ε之LTE現象觀察 220
4.4.6 纖維直徑df之LTE現象觀察 221
4.4.7 孔密度(PPI)之LTE現象觀察 222
4.4.8 有效熱傳導率比λeff之LTE現象觀察 223
4.4.9 普郎特數Pr之LTE現象觀察 225
4.5 有用的迴歸關係式 226
4.5.1 迴歸分析簡介 226
4.5.2 數據資料的處理與迴歸關係式 228
第五章 結論 233
參考文獻 237
符號彙編 245

[1]鄭名山，「太陽能發電簡介」，物理雙月刊，第二十九卷，第三期，2007年六月，第707-716頁。
[2]秦朝添，碟王科技開發股份有限公司光電事業處，「我國能源政策暨太陽能光電產業發展契機」，國立臺北科技大學太陽光電論壇，台北，2009年十二月。
[3]S. A. Kalogirou, “Solar thermal collectors and applications,” Progress in Energy and Combustion Science, vol. 30, 2004, pp. 231-295.
[4]莊瑞誠，工業技術研究院能源與環境研究所，「太陽熱能開發技術與應用」，國立臺北科技大學太陽光電論壇，台北，2009年十二月。
[5]S. A. Kalogirou, “The potential of solar industrial process heat applications,” Appl Energy, vol. 76, 2003, pp. 337-361.
[6]張志明，「太陽熱能的應用」，中工高雄會刊，第十七卷，第一期，2009年九月，第34-49頁。
[7]J. A. Duffie and W. A. Beckman, Solar Engineering of Thermal Processes, 3rd ed., John Wiley, 2006.
[8]A. I. Kudish, E. G. Evseev, G. Walter and T. Leukefeld, “Simulation study of a solar collector with a selectively coated polymeric double walled absorber plate,” Energy Conversion and Management, vol. 43, 2002, pp. 651-671.
[9]K. Vafai and M. Sozen, “Analysis of energy and momentum transport for fluid flow through a porous bed,” ASME J. Heat Transfer, vol. 112, 1990, pp. 690-699.
[10]M. Sozen and K. Vafai, “Analysis of oscillating compressible flow through a porous bed,” Int. J. Heat Mass Transfer, vol. 12, 1991, pp. 130-136.
[11]P. C. Huang, C. F. Yang, J. J. Huang and M. T. Chiu, “Enhancement of forced-convection cooling of multiple heated blocks in a channel using porous covers,” Int. J. Heat Mass Transfer, vol. 48, 2005, pp. 647-664
[12]V. V. Calmidi and R. L. Mahajan, “Forced convection in high porosity metal foams,” ASME J. Heat Transfer, vol. 122, 2000, pp. 557-565.
[13]M. Kaviany, Principles of Heat Transfer in Porous Media, Springer-Verlag, New York, 1991.
[14]S. Amjad, Thermal Conductivity and Noise Attenuation in Aluminum Foams, Master Thesis, University of Cambridge, 2001.
[15]H. P. G. Darcy, “Les Fontaines Publiques de la Ville de Dijon. Victor Dallmont,” Paris, 1856.
[16]P. Forchheimer, “Wasserbewegung durch Boden,” Z. Vereines Deutscher Ingenieure vol. 45, 1901, pp. 1736-1741 and 1781-1788.
[17]H. C. Brinkman, “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,” Applied Science Research, A1, 1947, pp. 27-34.
[18]K. Vafai and C. L. Tien, “Boundary and inertial effects on flow and heat transfer in porous media,” Int. J. Heat Mass Transfer, vol. 24, 1981, pp. 195-203.
[19]K. Vafai and C. L. Tien, “Boundary and inertial effects on convection mass transfer in porous media,” Int. J. Heat Mass Transfer, vol. 25, 1982, pp. 1183-1190.
[20]M. L. Hunt and C. L. Tien, “Effects of thermal dispersion on forced convection in fibrous media,” Int. J. Heat Mass Transfer, vol. 31, 1988, pp. 301-309.
[21]M. Kaviany, “Laminar flow through a porous channel bounded by isothermal parallel plates,” Int. J. Heat Mass Transfer, vol. 28, 1985, pp. 851-858.
[22]A. Hadim, “Forced convection in a porous channel with localized hest sources,” ASME J. Heat Transfer, vol. 116, 1994, pp. 465-472.
[23]T. A. Rizk and C. Kleinstreuer, ”Forced convective cooling of a linear array of blocks in open and porous matrix channels,” Heat Transfer engineering, vol. 12, 1991, pp. 40-47.
[24]R. Rachedi and S. Chikh, “Enhancement of electronic cooling by insertion of foam materials,” Int. J. of Heat and Mass Transfer, vol. 37, 2001, pp. 371-378.
[25]P. C. Huang and K. Vafai, “Analysis of forced convection enhancement in a parallel plate using porous blocks,” AIAA J. Thermophysics and Heat Transfer, vol. 8, 1994, pp. 563-573.
[26]K. A. Yih, “Blowing/suction effect on non-Darcian forced convection flow about a flat plate with variable wall temperature in porous media,” ACTA Mechanica, vol. 131, 1988, pp. 255-265.
[27]H. J. Sung, S. Y. Kim and J. M. Hyun, “Force convection from an isolated heat source in a channel with porous medium,” Int. J. Heat and Fluid, vol. 16, 1995, pp. 527-535.
[28]G. Neale and W. Nader, ”Practical signifcance of brinkman extension of Darcy`s law: coupled parallel flow within a channel and boundary porous medium,” Can. J. Chem. Engng, vol. 52, 1974, pp. 472-478.
[29]K. Vafai and R. Thuyagaraja, ”Analysis of flow and heat transfer at the Interface region of a porous medium,” Int. J. Heat Mass Transfer, vol.30, 1987, pp. 1391-1405.
[30]T. S. Lundgren, “Slow flow through stationary random beds and suspensions of spheres,” ASME J. Fluid Mech., vol.51, 1972, pp. 273-299.
[31]劉文海，「發泡金屬之應用前景（1）」，鑄造科技，第一百七十四期，2004，第32-35頁。
[32]Ilgaz Akseli, The Application of Aluminum Foam for the Heat and Noise Reduction in Automobiles, Master Thesis, İzmir Institute of Technology, 2005.
[33]K. Boomsma, D. Poulikakos and F. Zwick, “Metal foams as compact high performance heat exchangers,” Mechanics of Materials, vol. 35, 2003, pp. 1161-1176.
[34]S. Y. Kim, J. W. Peak and B. H. Kang, “Thermal performance of aluminum-foam heat sinks by forced air cooling,” IEEE Transactions on Components and Packaging Technologies, vol. 26, 2003, pp. 262-267.
[35]K. C. Leong and L. W. Jin, “Characteristics of oscillating flow through a channel filled with open cell metal foam,” Int. J. Heat Fluid Flow, vol. 27, 2006, pp. 144-153.
[36]J. Banhart, “Aluminum foam for Lighter Vehicles”, Hahn-Meitner-Institut Berlin-Germany, Int. J. of Vehicle Design, 2003, pp. 1-19.
[37]T. M. Jeng, S. C. Tzeng, “Numerical study of confined slot jet impinging on porous metallic foam heat sink”, Int. J. Heat Mass Transfer, vol. 48, 2005, pp. 4685–4694.
[38]S. Y. Kim, J. M. Koo and A. V. Kuznetsov, “Effect of anisotropy in permeability and effective thermal conductivity on thermal performance of an Aluminum foam heat sink,” Numerical Heat Transfer, Part A, vol. 40, 2001, pp. 21-36.
[39]S. Mahjoob and K. Vafai, “A synthesis of fluid and thermal transport models for metal foam heat exchangers,” Int. J. Heat Mass Transfer, vol. 51, 2008, pp. 3701-3711.
[40]P. Naphon, “Effect of porous media on the performance of the double-pass flat plate solar air heater,” Int. Comm. Heat Mass Transfer, vol. 32, 2005, pp. 140-150.
[41]M. A. Qenawy and A. A. Mohamad, “Analysis of high efficiency solar air heater for cold climates,” The 2nd Canadian Solar Buildings Conference, June, 2007, pp. 10-14.
[42]A. Bashria, A. Yousef, N. M. Adam, K. Sopian, A. Zaharim and M. Alghoul, “Analysis of single and double pass V-grooves solar collector with and without porous media,” Int. J. Energy and Environment, vol. 1, 2007, pp. 109-114.
[43]K. Sopian, M. A. Alghoul, E. M. Alfegi, M. Y. Sulaiman and E. A. Musa, “Evaluation of thermal efficiency of double-pass solar collector with porous-nonporous media,” Renewable Energy, vol. 34, 2009, pp. 640-645.
[44]K. S. Reddy and G. V. Satyanarayana, “Numerical study of porous finned receiver for solar parabolic trough concentrator,” Engineering Applications of computational fluid mechanics, vol. 2, 2008, pp. 172-184.
[45]K. R. Kumar and K. S. Reddy, “Thermal analysis of solar parabolic trough with porous disc receiver,” Applied Energy, vol. 86, 2009, pp. 1804-1812.
[46]G. Iordanou, Flat-Plate Solar Collectors for Water Heating with Improved Heat Transfer for Application in Climatic Conditions of the Mediterranean Region, Ph.D. Thesis, University of Durham, 2009.
[47]Z. Chen, M. Gu and D. Peng, “Heat transfer performance analysis of a solar flat-plate collector with an integrated meal foam porous structure filled with paraffin,” Applied Thermal Engineering, vol. 30, 2010, pp. 1967-1973.
[48]S. Uchida, “The pulsating viscous flow superposed on the steady laminar motion of Incompressible fluid in a circular pipe,” ZAMP, VII, 1956, pp. 403-422.
[49]R. Siegel and M. Perlmutter, “Heat transfer for pulsating laminar duct flow,” ASME J. Heat Transfer, vol. 84, 1962, pp. 111-123.
[50]S. Y. Kim, B. H. Kang and J. M. Hyun, ”Heat transfer in thermally developing region of a pulsating channel flow,” Int. J. Heat Mass Transfer, vol. 36, 1993, pp. 4257-4266.
[51]T. Moschandreou and M. Zamir, “Heat transfer in a tube with pulsating flow and constant heat flux,” Int. J. Heat Mass Transfer, vol. 40, no. 10, 1997, pp. 2461-2466.
[52]J. M. Khodadadi, “Oscillatory fluid flow through a porous medium channel bounded by two impermeable parallel plates,” ASME J. Fluid Engineering, vol. 113, 1991, pp. 509-511.
[53]S. Y. Kim, B. H. Kang and J. M. Hyun, ”Heat transfer from pulsating flow in channel filled with porous media,” Int. J. Heat Mass Transfer, vol. 37, 1994, pp. 2025-2033.
[54]Z. Guo, S. Y. Kim and H. J. Sung, “Pulsating flow and heat transfer in a pipe partially filled with a porous medium,” Int. J. Heat Mass Transfer, vol. 40, no. 17, 1997, pp. 4209-4218.
[55]S. Y. Kim, B. H. Kang and J. M. Hyun, ”Convection from a rectangular heated block in pulsating channel flow,” Proceedings of the 10th International Heat Transfer Conference, Brighton, UK, vol. 4, 1994, pp. 267-272.
[56]S. Y. Kim, B. H. Kang and J. M. Hyun, ”Forced convection heat transfer from two heated blocks in pulsating channel flow,” Int. J. Heat Mass Transfer, vol. 41. no. 3, 1998, pp. 625-634.
[57]J. W. Moon, S. Y. Kim and H. H. Cho, “Frequency-dependent heat transfer enhancement from rectangular heated block array in a pulsating channel flow,” Int. J. Heat Mass Transfer, vol. 48, 2005, pp. 4904-4913.
[58]P. C. Huang and C. F. Yang, “Analysis of pulsating convection from two heat sources mounted with porous blocks,” Int. J. Heat Mass Transfer, vol. 51, 2008, pp. 6294-6311.
[59]Cooper, W. L., Nee, V. W., and Yang, K. T., “An experimental investigation of convective heat transfer from the heated floor of a rectangular duct to a low frequency large tidal displacement oscillatory flow,” Int. J. Heat Mass Transfer, vol. 37, 1994, pp. 581-592.
[60]T. Zhao and P. Cheng, “The friction coefficient of a fully developed laminar reciprocating flow in a circular pipe,” Int. J Heat Fluid Flow, vol. 17, 1996, pp. 167-172.
[61]C. Sert and A. Beskok, “Numerical simulation of reciprocating flow forced convection in two-dimensional channels,” ASME J. Heat Transfer, vol. 125, 2003, pp. 403-412.
[62]P. Li and K.T. Yang, “Mechanisms for the heat transfer enhancement in zero-mean oscillatory flows in short channels,” Int. J. Heat Mass Transfer, vol. 43, 2000, pp. 3551-3566.
[63]K. C. Leong and L. W. Jin, “An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam,” Int. J. Heat Mass Transfer, vol. 48, 2005, pp. 243-253.
[64]K. C. Leong and L. W. Jin, “Heat transfer of oscillating flow and steady flows in a channel filled with porous media,” Int. Comm. Heat Mass Transfer, vol. 31, no. 1, 2004, pp. 63-72.
[65]H. L. Fu, K. C. Leong, X. Y. Huang and C. Y. Liu, “An experimental study of heat transfer of a porous channel subjected to oscillating flow,” Transactions of the ASME, vol. 123, 2001, pp. 162-170.
[66]M. S. Phanikumar and R. L. Mahajan, “Non-Darcy natural convection in high Porosity metal foams,” Int. J. Heat Mass Transfer, vol. 45, 2002, pp. 3781-3793.
[67]A. Amiri and K. Vafai, “Analysis of dispersion effects and non-thermal equilibrium, non-Darcian, variable porosity incompressible flow through porous media,” Int. J. Heat Mass Transfer, vol. 37, 1994, pp. 939-954.
[68]B. Alazmi and K. Vafai, “Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions,” Int. J. Heat Mass Transfer, vol. 45, 2002, pp. 3071-3087.
[69]V. V. Calmidi and R. L. Mahajan, “The effective thermal conductivity of high porosity metal foams,” ASME J. Heat Transfer, vol. 121, 1999, pp. 466-471.
[70]D. L. Koch and J. F. Brady, “The effective diffusivity of fibrous media,” AIChE Journal, vol. 32, 1986, pp. 575-591.
[71]A. Zhukauskas, “Heat transfer from tubes in cross flow,” in J.P. Hartnett and T.F. Irvine, Jr., Eds., Advances in Heat Transfer, vol. 8, Academic Press, New York, 1972.
[72]F. P. Incropera and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2002, 5th edition, Chap. 7.
[73]V. V. Calmidi, Transport Phenomena in High Porosity Metal Foams, Ph.D. Thesis, University of Colorado, Boulder, CO, 1998.
[74]A. Bhattacharya, V. V. Calmidi and R. L. Mahajan, “Thermophysical properties of high porosity metal foams,” Int. J. Heat Mass Transfer, vol. 45, 2002, pp. 1017-1031.
[75]S. C. Tzeng, “Convective heat transfer in a rectangular channel filled with sintered bronze beads and periodically spaced heated blocks,” ASME J. Heat Transfer, vol. 128, 2006, pp. 453-464.
[76]A. Amiri and K. Vafai, “Transient analysis of incompressible flow through a packed bed,” Int. J. Heat Mass Transfer, vol. 41, 1998, pp. 4259-4279.
[77]S. V. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980, Chap. 5-6.
[78]P. J. Roache, Computational Fluid Dynamics, Hermosa. Albuquerque, NM, 1998, Chapter 3.
[79]D. A. Anderson, J. C. Tannehill and R. H. Pletcher, Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1984, Chapter 5.
[80]G. O. Roberts, “Computational Meshes for Boundary Layer Problems,” Proc. Second Int. Conf. Num. Methods Fluid Dyn., Lecture Notes in Physics, vol. 8, Springer-Verlag, New York, 1971, pp. 171-177.
[81]A. D. Gosman, W. M. Pun and A. K. Runchal, Heat and Mass Transfer in Recirculating Flows, Academic Press Inc.(London) LTD, 1969.
[82]T. J. Young and K. Vafai, “Convective flow and heat transfer in a channel containing multiple heated obstacles,” Int. J. Heat Mass Transfer, vol. 41, 1998, pp. 3279-3298.
[83]D. A. Nield and A. Bejan, Convection in Porous Media, Springer-verlag, 2nd-edition, 1998.
[84]I. Ghosh, “Heat-transfer analysis of high porosity open-cell metal foam,” ASME J. Heat Transfer, vol. 130, 2008, pp. 034501-1–034501-6.
[85]S. J. Kim and S. P. Jang, “Effects of the Darcy number, the Prandtl number and the Reynolds number on local thermal non-equilibrium,” Int. J. Heat Mass Transfer, vol. 45, 2002, pp. 3885-3896.
[86]H. Schlichting, Boundary-layer Theory, McGraw-Hill, New York, 1979.
[87]Neter, John 等著，劉應興譯，應用線性迴歸模型 (Applied Linear Regression Models)，台北：華泰書局，1996，第3版。
[88]George Seber, C. J. Wild, Nonlinear Regression, New Edition, John Wiley & Sons, 2006.