平板结霜过程数值模拟及热泵机组结霜特性分析
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摘要
结霜的问题是一个复杂的热质传递问题，导热系数、密度、厚度及霜表面温度等都会随着霜层生长而变化。本文在综述国内外相关研究文献的基础上，研究了结霜工况下各特性参数之间的关系及霜层的生长规律。(1)通过建立冷平板结霜的一维饱和模型，利用有关结霜的经验关联式，对霜层比热、水蒸气质量百分比以及霜层厚度这三个因素进行数值模拟计算。同时，引入过饱和度的经验关联式，假定霜层表面水蒸气处于过饱和状态，结合其他研究者的实验数据，得出了有较高精度的霜层厚度计算方法。(2)运用适合模型的弯曲因子经验关系式，对霜层表面和内部的传质过程进行了数值模拟，研究了潜热传热率LHR、霜层导热系数增长率以及霜生长率的变化规律。研究表明，弯曲因子变动14％对总导热率的影响要小于3.3％；霜层导热系数在一小时内的变化仅为2％；传质过程中大于90％的量用于增加霜层厚度。(3)通过采用正则摄动法对翅片管换热器进行换热计算，分析了结霜工况下热泵机组翅片管换热器的传热特性，得出了达到最大肋片传热量的条件方程，并得出了翅片的最优设计尺寸。本文的研究结果，对了解霜层成长规律以及热泵的结霜融霜控制，有一定的参考价值。
Frost formation is a complex heat and mass transfer process. The thermal conductivity, density and frost surface temperature keep changing during this process. In this paper, a one-dimensional saturated model for cold plate frost was set up. The relations among various characteristic parameters under frost operating mode were studied numerically. The variations of the frost specific heat, the weighting factor and frost thickness were analyzed based on the existed correlations. Meanwhile, a method to calculate the frost thickness based on the supersaturation degree concept and the supersaturation model was proposed.
Then, an analysis of the mass transfer on and within frost layer was carried out. The latent heat transfer ratio, the thermal conductivity change ratio and frost growth ratio were analyzed numerically base on a rational tortuosity factor. The result shown that the error for total heat transfer rate with 14% variation of tortuosity factor is less than 3.3%; the frost thermal conductivity changes less than 2% for an hour; and more than 90% of the mass transfer goes to increasing the frost thickness.
Finally, a heat transfer analysis for the fin-tube heat exchanger was carried out base on the Perturbation Methods. An equation for predicting the highest heat transfer rate of ribs in fin-tube heat exchanger of the heat pump unit was derived and optimal sizes of the wing pieces were obtained.
The results of this paper are of use for understanding frost formation processes and for the optimal design of air-source heat pumps.
Frost formation is a complex heat and mass transfer process. The thermal conductivity, density and frost surface temperature keep changing during this process. In this paper, a one-dimensional saturated model for cold plate frost was set up. The relations among various characteristic parameters under frost operating mode were studied numerically. The variations of the frost specific heat, the weighting factor and frost thickness were analyzed based on the existed correlations. Meanwhile, a method to calculate the frost thickness based on the supersaturation degree concept and the supersaturation model was proposed.
Then, an analysis of the mass transfer on and within frost layer was carried out. The latent heat transfer ratio, the thermal conductivity change ratio and frost growth ratio were analyzed numerically base on a rational tortuosity factor. The result shown that the error for total heat transfer rate with 14% variation of tortuosity factor is less than 3.3%; the frost thermal conductivity changes less than 2% for an hour; and more than 90% of the mass transfer goes to increasing the frost thickness.
Finally, a heat transfer analysis for the fin-tube heat exchanger was carried out base on the Perturbation Methods. An equation for predicting the highest heat transfer rate of ribs in fin-tube heat exchanger of the heat pump unit was derived and optimal sizes of the wing pieces were obtained.
The results of this paper are of use for understanding frost formation processes and for the optimal design of air-source heat pumps.
引文
[1] Jose Iragorry, Yong-Xin Tao, Shaobo Jia. A Critical Review of Properties and Models for Frost Formation Analysis. HVAC&R Research, 2004, 10(4): 393～420
[2] 吴清前，等．空气源热泵结霜工况数学模型的建立和理论求解[J]．暖通空调HV&AC，2002，32(6)：92～94
[3] 罗鸣，等．风冷热泵机组中的热气除霜方法[J]．节能，2003，(5)：12～14
[4] 任乐，等．关于风冷热泵除霜问题的研究[J]．制冷，2003，22(1)：13～16
[5] 刘井龙．空气源热泵融霜控制过程的改进[J]．制冷与空调，2004，4(2)：34～36
[6] 文星，李先庭，邵双全．房间空调器热气旁通法除霜分析及实验研究[J]．制冷学报，2000，2：29～35
[7] R F Barron, L SHan. Heat and mass transfer to acryosurface in free convection. Heat Transfer, 1965, 87(4): 499～506
[8] P L T Brian, R C Reid, I Brazinsky. Cryogenic frost properties. Technol, 1969, 5: 205～212
[9] P L T Brian, R C Reid, Y T Shah. Frost doposition on cold surfaces. Ind Eng Chem Fundam, 1970, 9(3): 375～380
[10] C T Sanders. The influence of frost formation and defrosting on the performance of air coolers: [PhD. Thesis]. Netherlands: Delft Technical University, 1974
[11] I Tokura, H Saito, K Kishinami. Study on properties and growth rate of frost layers on cold surfaces. Heat Transfer, 1983, 105: 895～901
[12] R Le Gall, J M Grillot. Modeling of frost growth and densification. Heat Mass Transfer, 1997, 40(13): 3177～3187
[13] S M Sami, T Duong. Mass and Heat Transfer during Frost Growth. ASHRAE Transactions, 1989, 95(1): 158～165
[14] B W Jones, J D Parker. Frost formation with varying environmental parameters. Heat Transfer, 1975, 97: 255～259
[15] K S Lee, W S Kim, T H Lee. A one-dimensional model for frost formation on a cold flat surface. Heat Mass Transfer, 1997, 40(18): 4359～4365
[16] Y X Tao, R W Besant, K S Rezkallah. A mathematical model for predicting the densification and growth of frost on a flat plate. Heat Mass Transfer, 1993, 36(2): 353～363
[17] H W Schneider. Equation of the growth rate of frost forming on cooled surface. Heat Mass Transfer, 1978, 21:1019～1024
[18] Y Mao, R W Besant, H Chen. Frost Characteristics and Heat Transfer on a Flat Plate under Freezer Operating Conditions. ASHRAE Transactions, 1999, 4295:231～251
[19] B Na. Analysis of frost formation on an evaporator: [PhD Thesis]. USA: The Pennsylvania State University, 2003
[20] B Na, R L Webb. A fundamental understanding of factors affecting frost nucleation. Heat Mass Transfer, 2003, 46:3797～3808
[21] B Na, R L Webb. Mass transfer on and within a frost layer. Heat Mass Transfer, 2004, 47:899～911
[22] D L O' Neal, D R Tree. A Review of Frost Formation in Simple Geometries. ASHRAE Transactions, 1985, 91:267～281
[23] T Kobayashi, T Kuboda. Snow Crystals. In: I Sungagawa, eds. Morphology of Crystals. Tokyo: Terra Scientific Publishing Company, 1987. 649～743
[24] http://www.its.caltech.edu/～atomic/snowcrystals/primer/primer.htm
[25] D Pitman, B Zuckerman. Effective thermal conductivity of snow at-88,-27, and -27℃. Phys, 1967, 38(4): 2698～2699
[26] R W Besant, K S Rezkallah, Y Mao, J Falk. Measurement of Frost Thickness Using a Laser Beam and Light Meter. ASHRAE Transactions, 1990, 96(1): 519～522
[27] Y A Cengel, M A Boles. Thermodynamics. In: McGraw Hill, eds. fourth ed. New York, 2002. Chapter 16
[28] P W Atkins. Physical Chemistry. sixth ed. Oxford: Oxford University Press, 1998. Chapter 6
[29] N H Fletcher. The Chemical Physics of Ice. Cambridge: Cambridge University Press, 1970.
[30] B Na, R L Webb. New model for frost growth rate. Heat Mass Transfer, 2004, 47:925～936
[31] G H Neale, W K Nader. Prediction of transport processes within porous media: diffusive flow processes within a homogeneous swarm of spherical particles. AIChE J, 1973, 19(1): 112～119
[32] R E Cunningham, R J J Williams. Diffusion in Gases and Porous Media. Plenum Press, 1980.
[33] 陈汝东，许东晟．风冷热泵空调器除霜控制的研究．流体机械，1999，28(2)：55～57
[34] 黄虎，虞维平，李志浩．风冷热泵冷热水机组自调整模糊除霜控制研究．暖通空调，2001，31(3)：67～69
[35] 孙玉清，吴桂涛．抑制换热器湿空气侧结霜的研究．工程热物理学报，1997，18(1)：95～98
[36] S N Kondepudi, D L O' Neal. Performance of finned-tube heat exchangers under frosting conditions: I. Simulation model. International Journal of Refrigeration, 1993, 16(3): 175～184
[37] T S Catchilov, V S Ivanova. Characteristics of extended surface air coolers during operation under frosting conditions. International Journal of Refrigeration, 1979, 2(4): 233～236
[38] 邓东泉，徐烈，徐世琼．结霜工况下的冷风机传热性能试验研究．低温与超导，2002，30(2)：7～13
[39] 魏琪．热特性参数可变时等厚度环肋传热的优化研究．江苏大学学报，1989，10(4)：18～23
[40] 侯海炎，魏琪，张战，施爱平．湿空气在等厚度环肋上传热传质的优化研究．建筑热能通风空调，2002，5：12～14
[41] C T Sanders. The influence of frost formation and defrosting on performance of air coolers: [PhD Dissertation Technische Hogeschool]. The Netherlands: Delft University, 1974
[42] H Barrow. A Note on the Frosting of Heat Pump Evaporator Surface [J]. Heat Recovery Systems, 1985, 3: 17～20
[43] A Aziz, T Y Na. Perturbation Methods in Heat Transfer. Berlin: Springer-Verlag, 1984. 21～49
[44] 张祉祐，等．制冷原理与设备(第一版)．北京：机械工业出版社，1987．
[45] 赖建波，臧润清．换热器表面结霜的特性与翅片效率公式的分析．制冷与空调，2003，3(1)：21～24
[46] 陈丽萍．结霜工况下风冷热泵翅片管蒸发器传热特性分析．流体机械，2002，30(7)：59～61
[2] 吴清前，等．空气源热泵结霜工况数学模型的建立和理论求解[J]．暖通空调HV&AC，2002，32(6)：92～94
[3] 罗鸣，等．风冷热泵机组中的热气除霜方法[J]．节能，2003，(5)：12～14
[4] 任乐，等．关于风冷热泵除霜问题的研究[J]．制冷，2003，22(1)：13～16
[5] 刘井龙．空气源热泵融霜控制过程的改进[J]．制冷与空调，2004，4(2)：34～36
[6] 文星，李先庭，邵双全．房间空调器热气旁通法除霜分析及实验研究[J]．制冷学报，2000，2：29～35
[7] R F Barron, L SHan. Heat and mass transfer to acryosurface in free convection. Heat Transfer, 1965, 87(4): 499～506
[8] P L T Brian, R C Reid, I Brazinsky. Cryogenic frost properties. Technol, 1969, 5: 205～212
[9] P L T Brian, R C Reid, Y T Shah. Frost doposition on cold surfaces. Ind Eng Chem Fundam, 1970, 9(3): 375～380
[10] C T Sanders. The influence of frost formation and defrosting on the performance of air coolers: [PhD. Thesis]. Netherlands: Delft Technical University, 1974
[11] I Tokura, H Saito, K Kishinami. Study on properties and growth rate of frost layers on cold surfaces. Heat Transfer, 1983, 105: 895～901
[12] R Le Gall, J M Grillot. Modeling of frost growth and densification. Heat Mass Transfer, 1997, 40(13): 3177～3187
[13] S M Sami, T Duong. Mass and Heat Transfer during Frost Growth. ASHRAE Transactions, 1989, 95(1): 158～165
[14] B W Jones, J D Parker. Frost formation with varying environmental parameters. Heat Transfer, 1975, 97: 255～259
[15] K S Lee, W S Kim, T H Lee. A one-dimensional model for frost formation on a cold flat surface. Heat Mass Transfer, 1997, 40(18): 4359～4365
[16] Y X Tao, R W Besant, K S Rezkallah. A mathematical model for predicting the densification and growth of frost on a flat plate. Heat Mass Transfer, 1993, 36(2): 353～363
[17] H W Schneider. Equation of the growth rate of frost forming on cooled surface. Heat Mass Transfer, 1978, 21:1019～1024
[18] Y Mao, R W Besant, H Chen. Frost Characteristics and Heat Transfer on a Flat Plate under Freezer Operating Conditions. ASHRAE Transactions, 1999, 4295:231～251
[19] B Na. Analysis of frost formation on an evaporator: [PhD Thesis]. USA: The Pennsylvania State University, 2003
[20] B Na, R L Webb. A fundamental understanding of factors affecting frost nucleation. Heat Mass Transfer, 2003, 46:3797～3808
[21] B Na, R L Webb. Mass transfer on and within a frost layer. Heat Mass Transfer, 2004, 47:899～911
[22] D L O' Neal, D R Tree. A Review of Frost Formation in Simple Geometries. ASHRAE Transactions, 1985, 91:267～281
[23] T Kobayashi, T Kuboda. Snow Crystals. In: I Sungagawa, eds. Morphology of Crystals. Tokyo: Terra Scientific Publishing Company, 1987. 649～743
[24] http://www.its.caltech.edu/～atomic/snowcrystals/primer/primer.htm
[25] D Pitman, B Zuckerman. Effective thermal conductivity of snow at-88,-27, and -27℃. Phys, 1967, 38(4): 2698～2699
[26] R W Besant, K S Rezkallah, Y Mao, J Falk. Measurement of Frost Thickness Using a Laser Beam and Light Meter. ASHRAE Transactions, 1990, 96(1): 519～522
[27] Y A Cengel, M A Boles. Thermodynamics. In: McGraw Hill, eds. fourth ed. New York, 2002. Chapter 16
[28] P W Atkins. Physical Chemistry. sixth ed. Oxford: Oxford University Press, 1998. Chapter 6
[29] N H Fletcher. The Chemical Physics of Ice. Cambridge: Cambridge University Press, 1970.
[30] B Na, R L Webb. New model for frost growth rate. Heat Mass Transfer, 2004, 47:925～936
[31] G H Neale, W K Nader. Prediction of transport processes within porous media: diffusive flow processes within a homogeneous swarm of spherical particles. AIChE J, 1973, 19(1): 112～119
[32] R E Cunningham, R J J Williams. Diffusion in Gases and Porous Media. Plenum Press, 1980.
[33] 陈汝东，许东晟．风冷热泵空调器除霜控制的研究．流体机械，1999，28(2)：55～57
[34] 黄虎，虞维平，李志浩．风冷热泵冷热水机组自调整模糊除霜控制研究．暖通空调，2001，31(3)：67～69
[35] 孙玉清，吴桂涛．抑制换热器湿空气侧结霜的研究．工程热物理学报，1997，18(1)：95～98
[36] S N Kondepudi, D L O' Neal. Performance of finned-tube heat exchangers under frosting conditions: I. Simulation model. International Journal of Refrigeration, 1993, 16(3): 175～184
[37] T S Catchilov, V S Ivanova. Characteristics of extended surface air coolers during operation under frosting conditions. International Journal of Refrigeration, 1979, 2(4): 233～236
[38] 邓东泉，徐烈，徐世琼．结霜工况下的冷风机传热性能试验研究．低温与超导，2002，30(2)：7～13
[39] 魏琪．热特性参数可变时等厚度环肋传热的优化研究．江苏大学学报，1989，10(4)：18～23
[40] 侯海炎，魏琪，张战，施爱平．湿空气在等厚度环肋上传热传质的优化研究．建筑热能通风空调，2002，5：12～14
[41] C T Sanders. The influence of frost formation and defrosting on performance of air coolers: [PhD Dissertation Technische Hogeschool]. The Netherlands: Delft University, 1974
[42] H Barrow. A Note on the Frosting of Heat Pump Evaporator Surface [J]. Heat Recovery Systems, 1985, 3: 17～20
[43] A Aziz, T Y Na. Perturbation Methods in Heat Transfer. Berlin: Springer-Verlag, 1984. 21～49
[44] 张祉祐，等．制冷原理与设备(第一版)．北京：机械工业出版社，1987．
[45] 赖建波，臧润清．换热器表面结霜的特性与翅片效率公式的分析．制冷与空调，2003，3(1)：21～24
[46] 陈丽萍．结霜工况下风冷热泵翅片管蒸发器传热特性分析．流体机械，2002，30(7)：59～61