冰球蓄冷器传热过程的数值模拟
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摘要
随着人类文明和工业现代化的高速发展，空气调节技术已经应用到生产和生活的各个领域。空调蓄冷技术能够将日间部分高峰用电负荷转移到夜间时段，因而成为我国当前积极推广和利用的一项利国利民的调荷节电措施。固液相变研究是工程热物理学科研究的重要内容，也是评价蓄冷装置性能的主要基础。因此，对之进行深入研究，不仅有利于蓄冷装置强化传热的实用技术的发展，而且也具有重要的理论价值。
本文基于上述背景，以冰球和冰球蓄冷器传热研究为重点，主要作了下述几项工作：
1．用接触传热的理论对冰球内的融化进行了近似分析求解。在所建立的模型中考虑了固相与液相的密度差和自然对流的影响，得出了各个时刻液膜厚度的分布、融化速率和传熟量等计算结果。计算结果与文献分析结果进行了比较，所得结果更符合实验值。
2．用奇异摄动法对冰球的凝固进行了近似分析求解，得到了第三类边界条件下凝固解的表达式。
3．建立了冰球蓄冷器的数学模型，编制了计算程序，对四个工况的蓄冷和释冷进行了模拟。
4．设计并建立了实验装置，对单个冰球的融化和凝固进行了实验，得到实验数据。与近似分析解比较，分析了误差原因。
With the progress of humanity civilization and the speedy development of industry modernization, the use of air conditioning technology has become increasingly popular. The cold storage technology of air conditioning has become an important measure used to adjust loads and save electricity as the result of transforming a part of high loads in the day to low loads in the night. The solid-liquid phase change is an important research subject of the engineering thermal physics and main foundation of evaluating the cold storage containers, so to have a deep research is benefit to strengthen the heat transfer of that and to have an important theory meaning.
Based of that, the main research contents as follows:
1. The approximate analytical solution of melting process within a spherical enclosure is to presented by contacting heat transfer.A numerical model describing the melting process is presented by considering the difference of the solid-liquid density and natural convection. From which we can get the variation of the melt-film thickness, melting rate and heat transferred. These computing results are more reasonable than those literature from the comparison.
2. Under certain appropriate assumptions, a mathematical model of water undergoing solidification in the spherical enclosure is established .The perturbation technique is employed to solve this problem. The correlation of the entire solidification time under the third boundary condition.
3 . A mathematical model that concerns melting and solidification of the ice storage tank with encapsulated ice is presented .A computer program is developed to solve the model.
4. The experimental apparatus has been designed and constructed. By the
experimental investigation of packed capsules with solidification and melting,
we get experimental data. By incorporating the experimental results and theory
predictions, the good agreements are gotten.
本文基于上述背景，以冰球和冰球蓄冷器传热研究为重点，主要作了下述几项工作：
1．用接触传热的理论对冰球内的融化进行了近似分析求解。在所建立的模型中考虑了固相与液相的密度差和自然对流的影响，得出了各个时刻液膜厚度的分布、融化速率和传熟量等计算结果。计算结果与文献分析结果进行了比较，所得结果更符合实验值。
2．用奇异摄动法对冰球的凝固进行了近似分析求解，得到了第三类边界条件下凝固解的表达式。
3．建立了冰球蓄冷器的数学模型，编制了计算程序，对四个工况的蓄冷和释冷进行了模拟。
4．设计并建立了实验装置，对单个冰球的融化和凝固进行了实验，得到实验数据。与近似分析解比较，分析了误差原因。
With the progress of humanity civilization and the speedy development of industry modernization, the use of air conditioning technology has become increasingly popular. The cold storage technology of air conditioning has become an important measure used to adjust loads and save electricity as the result of transforming a part of high loads in the day to low loads in the night. The solid-liquid phase change is an important research subject of the engineering thermal physics and main foundation of evaluating the cold storage containers, so to have a deep research is benefit to strengthen the heat transfer of that and to have an important theory meaning.
Based of that, the main research contents as follows:
1. The approximate analytical solution of melting process within a spherical enclosure is to presented by contacting heat transfer.A numerical model describing the melting process is presented by considering the difference of the solid-liquid density and natural convection. From which we can get the variation of the melt-film thickness, melting rate and heat transferred. These computing results are more reasonable than those literature from the comparison.
2. Under certain appropriate assumptions, a mathematical model of water undergoing solidification in the spherical enclosure is established .The perturbation technique is employed to solve this problem. The correlation of the entire solidification time under the third boundary condition.
3 . A mathematical model that concerns melting and solidification of the ice storage tank with encapsulated ice is presented .A computer program is developed to solve the model.
4. The experimental apparatus has been designed and constructed. By the
experimental investigation of packed capsules with solidification and melting,
we get experimental data. By incorporating the experimental results and theory
predictions, the good agreements are gotten.
引文
[1] 程俊国，张洪济等．高等传热学．重庆：重庆大学出版社，1991．77～80
[2] 奥齐西克MN．热传导．俞昌铭译．北京：高等教育出版社，1983．427～435
[3] SL Chen, SS Liang. Effects of Natural Convection on Ice Formation Inside a Horizontal Cylinder. Experimental Heat Transfer, 1992,5:131～145
[4] Cheng KC,Inaba H. Effects of Natural Convection on Freezing of Water Around an Isothermally Cooled Horizontal Cylinder. J. Heat Transfer, 1988,110:931～938
[5] Saraf CR, Sharif LK. Inward Freezing of Water in Cylinders. Int. J. of Refrigeration, 1987,10(6):342～348
[6] Saitoh T. Natural Convection Heat Transfer from a Horizontal Ice Cylinder. Appl. Sci. Res., 1976,32:429～451
[7] Moore FE, Bayazitoglu Y. Melting Within a Spherical Enclosures. ASME J. of Heat Transfer, 1982,104:19～23
[8] Roy SK, Sengupta S. Melting of a Free Solid in a Spherical Enclosure: Effects of Subcooling. ASME J. of Solar Energy Eng, 1989,111:32～36
[9] Roy SK, Sengupta S. Gravity-assisted Melting in a Spherical Enclosure: Effects of Nutural Convection. Int. J. Heat Mass Transfer, 1990,33(6):1135～1147
[10] Roy SK, Sengupta SA. Generalized Model for Gravity-Assisted Melting in Enclosures, ASME J. of Heat Transfer, 1990,112:804～808
[11] Jekel,Mitchell TB. Modeling of Ice-storage Tanks. A SHRAE Transactions, 1993,99(1): 1016-1024
[12] S.L.Chen. An Experimental Investigation of Cold Storage In Packed Capsules With Solidification. Experimental Heat Transfer, 1991,4:263～280
[13] Arnold, Dynamic D. Simulation of Encapsulated Ice Stores. ASHRAE Transactions, 1990,96(1):1103～1110
[14] Arnold, Laboratory Performance of an Encapsulated. ASHRAE Transactions, 1991,97(2): 1170～1178
[15] Arnold. Dynamic Simulation of Encapsulated Ice Stores. ASHRAE Transactions, 1994,100(1): 1245～1254
[16] 赵庆珠，蒋久轶．冰球蓄冷过程的传热研究，第一部分：冰球蓄冷过程的数值模拟．全国暖通空调会议集，1994,355～358
[17] 赵庆珠，蒋久轶．冰球蓄冷过程的传热研究，第二部分：融冰过程的传热分析．全国暖通空调会议集，1995,359～363
[18] 陈文振，杨强生．水平圆柱与平板下相变材料接触熔化的基本方程．太阳能学报，1999，20(3)：284～289
[19] 胡耀江，施明恒．固体PCM在热球体外表面上接触融化时液膜厚度变化规律的研究．太阳能学报，1998，1：74～79
[20] 胡耀江等．二维轴对称几何形状下接触迷熔化过程的统一分析．太阳能学报，1999，20(3)：324～328
[21] 陈伟珂等．球体内混合有机材料相变传热特性分析．太阳能学报，2000，1：19～24
[22] 王剑锋，陈光明等．组合相变材料储热系统的储热速率研究．太阳能学报，2000，7：258～263
[23] 刘瑞芝，李汛．蓄冰球内固定融化问题的理论与实验研究．工程热物理学报，2001，7：469～472
[24] 吕昶等．气体水合物蓄冷实验研究．制冷学报．2000,2：14～18
[25] 康艳兵，张寅平等．相变蓄热球体堆积床传热模型及热性能分析．清华大学学报，2000,40(2)：106～
109
[26] 张寅平，胡汉平等．相变贮能——理论和应用．合肥：中国科学技术大学出版社，1996，202～245
[27] 董克用，袁修干．相变材料容器的三维热分析．太阳能学报，1998，3：25～28
[28] 柯秀芳，张仁元．管壳式相变储能换热器的优化设计．能源工程，2001，5：43～45
[29] 侯欣兵，袁修干等．高温相变蓄热容器传热的隐式求解．太阳能学报，2001，24(4)：431～435
[30] 李海梅等．平面相变热传导问题等效热容法的有限元解．大连理工大学学报，2000,40(1)：45～47
[31] 郑青，李京穗．中国国际贸易中心二期冰蓄冷空调工程．暖通空调，2001，31(2)：59～62
[32] 潘毅群．蓄冷球系统的动态模拟及运行分析．[D]．上海：同济大学，1997．10～11
[33] Bareiss M., BeerH. An Analytical Solution of the Heat Transfer Process During Melting of an Unfixed Solid Phase Material inside a Horizontal Tube. Int. J. Heat Mass Transfer, 1984,27(5):739～746
[34] Roy SK.,Sengupta S. The Melting Process Within Spherical Enclosures. ASME J. of Heat Transfer, 1987,109:460～462
[35] Steven H.Emerman and Turcotte.. Stokes's Problem with Melting. Int. J. Heat Mass Transfer, 1983,26(11):1625～1630
[36] Webb BW, Moallemi MK, Viskanta R.. Experimental on Melting of Unfixed Ice in a Horizontal Cylindrical Capsule. ASME J. of Heat Transfer, 1987,109:454～459
[37] Prasad,A. ,Sengupta, S. Numerical Investigation of Melting Inside a Horizontal Cylinder Including the Effects of Natural Convection. ASME J. of Heat Transfer, 1987,109(4):803～806
[38] Saitoh,T.,Kato,H. Numerical Analysis for Combined Natural-Convection and Close-contact Melting in a Horizontal Cylindrical Capsule. Heat Transfer-Japanese Research, 1994,23(2): 198～212
[39] Kim,H.S. ,Kim,C.-J. ,Ro, S.T. Heat Transfer Correlation for Natural Convection in a Meniscus-Shaped Cavity and Its Application to Contact Melting Process. Int. J.Heat Mass Transfer, 1996,39(11):2267～2270
[40] Bahrami ,P.A. ,Wang,T.G. Analysis of Gravity and Conduction-Driver Melting in a Sphere. ASME J. of Heat Transfer, 1987,109:806～809
[41] J.A.Dantzig, Modeling Liquid-Solid Phase Changes with Melt Convection . Int. J. Num. Meth.Eng., 1989,28:1769～1785
[42] Jany,P. ,Bejan ,A. Scaling Theory of Melting within Natural Convection in an Encolsure. Int. J. Heat Mass Transfer, 1988,31(6):1221～1235
[43] 埃克特ERG，德雷克RM．传热与传质分析．航青译．北京：科学出版社，1983．555～559
[44] 郭大钧．大学手册．济南：山东科学技术出版社，1985．37
[45] 刘惠枝，舒宏纪．边界层理论．北京：科学出版社，1991．10～22
[46] Shoichiro, Masahiko. Recent Advances in Research on Water-Freezing and Ice-Melting Problems. Experimental and Fluid Science. 1993,6:90～105
[47] KIM HS. Heat Transfer Correlation for Natural Convection in a Meniscus-shaped Cavity and its Application to Contact Melting Process. Journey of Heat and Mass Transfer. 1996,39(11): 2267～2270
[48] LUHC TAO. Generalized Numerical Solutions of Freezing a Saturated Liquid in Cylinders and Spheres. A.I.Ch.E. Journal. 1967,13(1):165～169
[49] VR Voller, CR Swaminathan. General Source-Based Method for Solidification Phase Change. Num. Heat Transfer B, 1991,19:175～189
[50] Minkowyca, Sparrow. Advances in Numerical Heat Transfer, Volume 1. 1997. 369～375
[51] Lacroix, Voller. Finite Difference Solutions of Solidification Phase Change Problems :Transformed versus Fixed Grids. Num. Heat Transfer B, 1990,17:25～41
[52] Lacroix M. Predictions of Natural-Convection-Dominated Phase-Chang Problems by the Vorticity-Velocity Formulation of the Navier-Stokes Equations. Numerical Heat Transfer, Part B. 1992,22:79～93
[53] 王华生等．方形腔内二维凝固问题近似求解的新方法．西安交通大学学报，2001,35(5)：485～489
[54] 宋又王．用奇导摄动法解圆柱体的凝固问题．工程热物理学报，1981，2(4)：359～365
[55] 艾詹斯．摄动法在传热学中的应用．余钧译．北京：科学出版社，1992．6～8，77～83
[56] 邓建中等．计算方法．西安：西安交通大学出版社，1984．37～40
[2] 奥齐西克MN．热传导．俞昌铭译．北京：高等教育出版社，1983．427～435
[3] SL Chen, SS Liang. Effects of Natural Convection on Ice Formation Inside a Horizontal Cylinder. Experimental Heat Transfer, 1992,5:131～145
[4] Cheng KC,Inaba H. Effects of Natural Convection on Freezing of Water Around an Isothermally Cooled Horizontal Cylinder. J. Heat Transfer, 1988,110:931～938
[5] Saraf CR, Sharif LK. Inward Freezing of Water in Cylinders. Int. J. of Refrigeration, 1987,10(6):342～348
[6] Saitoh T. Natural Convection Heat Transfer from a Horizontal Ice Cylinder. Appl. Sci. Res., 1976,32:429～451
[7] Moore FE, Bayazitoglu Y. Melting Within a Spherical Enclosures. ASME J. of Heat Transfer, 1982,104:19～23
[8] Roy SK, Sengupta S. Melting of a Free Solid in a Spherical Enclosure: Effects of Subcooling. ASME J. of Solar Energy Eng, 1989,111:32～36
[9] Roy SK, Sengupta S. Gravity-assisted Melting in a Spherical Enclosure: Effects of Nutural Convection. Int. J. Heat Mass Transfer, 1990,33(6):1135～1147
[10] Roy SK, Sengupta SA. Generalized Model for Gravity-Assisted Melting in Enclosures, ASME J. of Heat Transfer, 1990,112:804～808
[11] Jekel,Mitchell TB. Modeling of Ice-storage Tanks. A SHRAE Transactions, 1993,99(1): 1016-1024
[12] S.L.Chen. An Experimental Investigation of Cold Storage In Packed Capsules With Solidification. Experimental Heat Transfer, 1991,4:263～280
[13] Arnold, Dynamic D. Simulation of Encapsulated Ice Stores. ASHRAE Transactions, 1990,96(1):1103～1110
[14] Arnold, Laboratory Performance of an Encapsulated. ASHRAE Transactions, 1991,97(2): 1170～1178
[15] Arnold. Dynamic Simulation of Encapsulated Ice Stores. ASHRAE Transactions, 1994,100(1): 1245～1254
[16] 赵庆珠，蒋久轶．冰球蓄冷过程的传热研究，第一部分：冰球蓄冷过程的数值模拟．全国暖通空调会议集，1994,355～358
[17] 赵庆珠，蒋久轶．冰球蓄冷过程的传热研究，第二部分：融冰过程的传热分析．全国暖通空调会议集，1995,359～363
[18] 陈文振，杨强生．水平圆柱与平板下相变材料接触熔化的基本方程．太阳能学报，1999，20(3)：284～289
[19] 胡耀江，施明恒．固体PCM在热球体外表面上接触融化时液膜厚度变化规律的研究．太阳能学报，1998，1：74～79
[20] 胡耀江等．二维轴对称几何形状下接触迷熔化过程的统一分析．太阳能学报，1999，20(3)：324～328
[21] 陈伟珂等．球体内混合有机材料相变传热特性分析．太阳能学报，2000，1：19～24
[22] 王剑锋，陈光明等．组合相变材料储热系统的储热速率研究．太阳能学报，2000，7：258～263
[23] 刘瑞芝，李汛．蓄冰球内固定融化问题的理论与实验研究．工程热物理学报，2001，7：469～472
[24] 吕昶等．气体水合物蓄冷实验研究．制冷学报．2000,2：14～18
[25] 康艳兵，张寅平等．相变蓄热球体堆积床传热模型及热性能分析．清华大学学报，2000,40(2)：106～
109
[26] 张寅平，胡汉平等．相变贮能——理论和应用．合肥：中国科学技术大学出版社，1996，202～245
[27] 董克用，袁修干．相变材料容器的三维热分析．太阳能学报，1998，3：25～28
[28] 柯秀芳，张仁元．管壳式相变储能换热器的优化设计．能源工程，2001，5：43～45
[29] 侯欣兵，袁修干等．高温相变蓄热容器传热的隐式求解．太阳能学报，2001，24(4)：431～435
[30] 李海梅等．平面相变热传导问题等效热容法的有限元解．大连理工大学学报，2000,40(1)：45～47
[31] 郑青，李京穗．中国国际贸易中心二期冰蓄冷空调工程．暖通空调，2001，31(2)：59～62
[32] 潘毅群．蓄冷球系统的动态模拟及运行分析．[D]．上海：同济大学，1997．10～11
[33] Bareiss M., BeerH. An Analytical Solution of the Heat Transfer Process During Melting of an Unfixed Solid Phase Material inside a Horizontal Tube. Int. J. Heat Mass Transfer, 1984,27(5):739～746
[34] Roy SK.,Sengupta S. The Melting Process Within Spherical Enclosures. ASME J. of Heat Transfer, 1987,109:460～462
[35] Steven H.Emerman and Turcotte.. Stokes's Problem with Melting. Int. J. Heat Mass Transfer, 1983,26(11):1625～1630
[36] Webb BW, Moallemi MK, Viskanta R.. Experimental on Melting of Unfixed Ice in a Horizontal Cylindrical Capsule. ASME J. of Heat Transfer, 1987,109:454～459
[37] Prasad,A. ,Sengupta, S. Numerical Investigation of Melting Inside a Horizontal Cylinder Including the Effects of Natural Convection. ASME J. of Heat Transfer, 1987,109(4):803～806
[38] Saitoh,T.,Kato,H. Numerical Analysis for Combined Natural-Convection and Close-contact Melting in a Horizontal Cylindrical Capsule. Heat Transfer-Japanese Research, 1994,23(2): 198～212
[39] Kim,H.S. ,Kim,C.-J. ,Ro, S.T. Heat Transfer Correlation for Natural Convection in a Meniscus-Shaped Cavity and Its Application to Contact Melting Process. Int. J.Heat Mass Transfer, 1996,39(11):2267～2270
[40] Bahrami ,P.A. ,Wang,T.G. Analysis of Gravity and Conduction-Driver Melting in a Sphere. ASME J. of Heat Transfer, 1987,109:806～809
[41] J.A.Dantzig, Modeling Liquid-Solid Phase Changes with Melt Convection . Int. J. Num. Meth.Eng., 1989,28:1769～1785
[42] Jany,P. ,Bejan ,A. Scaling Theory of Melting within Natural Convection in an Encolsure. Int. J. Heat Mass Transfer, 1988,31(6):1221～1235
[43] 埃克特ERG，德雷克RM．传热与传质分析．航青译．北京：科学出版社，1983．555～559
[44] 郭大钧．大学手册．济南：山东科学技术出版社，1985．37
[45] 刘惠枝，舒宏纪．边界层理论．北京：科学出版社，1991．10～22
[46] Shoichiro, Masahiko. Recent Advances in Research on Water-Freezing and Ice-Melting Problems. Experimental and Fluid Science. 1993,6:90～105
[47] KIM HS. Heat Transfer Correlation for Natural Convection in a Meniscus-shaped Cavity and its Application to Contact Melting Process. Journey of Heat and Mass Transfer. 1996,39(11): 2267～2270
[48] LUHC TAO. Generalized Numerical Solutions of Freezing a Saturated Liquid in Cylinders and Spheres. A.I.Ch.E. Journal. 1967,13(1):165～169
[49] VR Voller, CR Swaminathan. General Source-Based Method for Solidification Phase Change. Num. Heat Transfer B, 1991,19:175～189
[50] Minkowyca, Sparrow. Advances in Numerical Heat Transfer, Volume 1. 1997. 369～375
[51] Lacroix, Voller. Finite Difference Solutions of Solidification Phase Change Problems :Transformed versus Fixed Grids. Num. Heat Transfer B, 1990,17:25～41
[52] Lacroix M. Predictions of Natural-Convection-Dominated Phase-Chang Problems by the Vorticity-Velocity Formulation of the Navier-Stokes Equations. Numerical Heat Transfer, Part B. 1992,22:79～93
[53] 王华生等．方形腔内二维凝固问题近似求解的新方法．西安交通大学学报，2001,35(5)：485～489
[54] 宋又王．用奇导摄动法解圆柱体的凝固问题．工程热物理学报，1981，2(4)：359～365
[55] 艾詹斯．摄动法在传热学中的应用．余钧译．北京：科学出版社，1992．6～8，77～83
[56] 邓建中等．计算方法．西安：西安交通大学出版社，1984．37～40
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