基于分形理论的建陶坯体干燥过程热性能研究
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摘要
热性能是研究坯体干燥过程的重要部分,本文的研究是建立在对建陶坯体微观结构的分析了解之上,而像建陶坯体这样的多孔介质,其内部结构及其复杂和不规则,欧氏几何已很难加以定量描述,这样分形几何的优势就可以体现出来。本文首先利用扫面电镜,获得了坯体的显微结构SEM图,在分析了已有的盒维数算法后提出了一种改进的计盒维数算法,并计算了坯体的分维,发现与Sierpinski地毯的分维相接近。
其次,以长度为测度尺度,通过简化假设模型,采用热阻法推导了坯体有效导热系数的数学表达式,发现其导热系数与使用的测度尺度、坯体内固相导热系数及气液混合相导热系数相关。其中测度尺度对计算结果的影响较大,实测坯体不同排水率、不同温度下的导热系数后发现,测度尺度选择20μm较适合。
最后在测度尺度为20μm下计算了不同排水率、不同温度下建陶坯体的有效导热系数、有效比热容及有效导温系数。发现在一定排水率和温度下,坯体的有效导热系数与温度呈线性关系,与排水率呈2次关系,有效比热与温度及排水率均呈线性关系,有效导温系数与温度及排水率均呈2次关系,且温度升高三者增加,排水率升高三者减小。
The investigation of thermal properties is a very important part in researching the drying process. The issue is on the base of analyzing building bodies’microstructure. But as building bodies, the internal structure of porous media is so complicated and irregular that the quantitative analysis is hard to be gained by Euclidean geometry. Then the advantage of fractal geometry is reflected. Firstly, after researching some box-counting algorithms which have been published, this thesis put forward an improved arithmetic and computes the fractal dimension of SEM pictures of building bodies. It’s found that building bodies’dimension is close to the Sierpinski carpet’s.
Secondly, when length is the measure scale, the thermal conductivity’s mathematical expression has been derived by thermal resistance method on the simplified hypothetical model. It’s found that the thermal conductivity is correlative to the measure scale and the thermal conductivities of solid and the gas-liquid mixture in building bodies. The scale is to have a more obvious impact on it. After looking into experimental results relate to different temperature and moisture elimination rate, 20μm is an appropriate measure scale.
The building bodies’effective thermal conductivity, effective specific heat and effective thermal diffusivity have been computed at different temperature and different moisture elimination rate when the measure scale is 20μm. The effective thermal conductivity shows a linear relationship with temperature and a quadratic relationship with moisture elimination rate. A linear relationship between the effective specific heat and temperature and moisture elimination rate, and a quadratic relationship between the effective thermal diffusivity and temperature and moisture elimination rate are found. As the temperature increases, the effective thermal conductivity, the effective specific heat and the effective thermal diffusivity increase. Contrary, as the moisture elimination rate decreases, they reduce.
其次,以长度为测度尺度,通过简化假设模型,采用热阻法推导了坯体有效导热系数的数学表达式,发现其导热系数与使用的测度尺度、坯体内固相导热系数及气液混合相导热系数相关。其中测度尺度对计算结果的影响较大,实测坯体不同排水率、不同温度下的导热系数后发现,测度尺度选择20μm较适合。
最后在测度尺度为20μm下计算了不同排水率、不同温度下建陶坯体的有效导热系数、有效比热容及有效导温系数。发现在一定排水率和温度下,坯体的有效导热系数与温度呈线性关系,与排水率呈2次关系,有效比热与温度及排水率均呈线性关系,有效导温系数与温度及排水率均呈2次关系,且温度升高三者增加,排水率升高三者减小。
The investigation of thermal properties is a very important part in researching the drying process. The issue is on the base of analyzing building bodies’microstructure. But as building bodies, the internal structure of porous media is so complicated and irregular that the quantitative analysis is hard to be gained by Euclidean geometry. Then the advantage of fractal geometry is reflected. Firstly, after researching some box-counting algorithms which have been published, this thesis put forward an improved arithmetic and computes the fractal dimension of SEM pictures of building bodies. It’s found that building bodies’dimension is close to the Sierpinski carpet’s.
Secondly, when length is the measure scale, the thermal conductivity’s mathematical expression has been derived by thermal resistance method on the simplified hypothetical model. It’s found that the thermal conductivity is correlative to the measure scale and the thermal conductivities of solid and the gas-liquid mixture in building bodies. The scale is to have a more obvious impact on it. After looking into experimental results relate to different temperature and moisture elimination rate, 20μm is an appropriate measure scale.
The building bodies’effective thermal conductivity, effective specific heat and effective thermal diffusivity have been computed at different temperature and different moisture elimination rate when the measure scale is 20μm. The effective thermal conductivity shows a linear relationship with temperature and a quadratic relationship with moisture elimination rate. A linear relationship between the effective specific heat and temperature and moisture elimination rate, and a quadratic relationship between the effective thermal diffusivity and temperature and moisture elimination rate are found. As the temperature increases, the effective thermal conductivity, the effective specific heat and the effective thermal diffusivity increase. Contrary, as the moisture elimination rate decreases, they reduce.
引文
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[7]孙喜山,廉乐明,李力能.粘土砖湿坯对流干燥过程的传热传质研究[J].哈尔滨建筑大学学报,1998,31(2):67-72.
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[9]王唯威.分形多孔介质内导热与流动数值模拟研究[D].北京:中国科学院研究生院,2006.
[10] J贝尔著.李竞生,陈崇喜译.孙讷正校.多孔介质流体动力学[M] .北京:中国建筑工业出版社,1983.
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[12]忤彦卿.多孔介质污染物迁移动力学[M].上海:上海交通大学出版社,2007.
[13]刘相东,杨彬彬.多孔介质干燥理论的回顾与展望[J].中国农业大学学报,2005,10(4):81-92.
[14]郁伯明.多孔介质输送性质的分形分析研究进展[J].力学进展,2003,33(3):333-346.
[15] Peng Xu, Arun S Mujundar, Boming Yu. Fractal theory on drying: a review[J]. Drying Technology, 2008, 26: 640-650.
[16] J F thovert, F Wary, P M Adler. Thermal conductivity of random media and regular fractals[J]. Journal of applied physics, 1990, 68(8): 3872-3883.
[17] I S Jang, J M Kang, J Choe, et al. Numerical investigations on the transport properties of fractally fractured media[J]. Energy sources, 2002,24: 145-157.
[18] Yongting Ma, Boming Yu, Duanming Zhang, et al. Fractal geometry model for effective thermal conductivity of three-phase porous media[J]. Journal of applied physics, 2004, 95(11): 6426-6434.
[19] Boming Yu, Jianhua Li. Some fractal characters of porous media[J]. Fractals, 2001, 9(3): 365-372.
[20] Boming Yu. Fractal dimensions for multiphase fractal media[J]. Fractals, 2006, 14(2): 111-118.
[21]江东,王建华,郑世书.多孔介质孔隙结构的分形维数:测试、解算与意义[J].科技通报,1999,15(6):453-456.
[22]陈永平,施明恒.基于分形理论的多孔介质导热系数研究[J].工程热物理学报,1999,20(5):608-612.
[23]陈永平,施明恒.应用分形理论的实际多孔介质有效导热系数研究[J].应用科学学报,2000,18(3):263-266.
[24]施明恒,陈永平.多孔介质传热传质分形理论初探[J].南京师大学报(工程技术版),2001,1(1):6-13.
[25]张东辉,金峰,施明恒,等.分形多孔介质中的热传导[J].应用科学学报,2003,21(3):253-257.
[26]王唯威,淮秀兰.分形多孔介质导热数值模拟分析[J].工程热物理学报,2007,28(5):865-867.
[27]李小川,施明恒.多孔介质热导率的数值计算[J].工程热物理学报,2008,29(2):291-293.
[28] Moongyu Park, Natalie Kleinfelter, John Cushman. Scaling laws and fokker-planck equations for 3-dimensional porous media with fractal mesoscale[J]. Multiscale Modeling & Simulation, 2005, 4(4): 1233-1244.
[29] Pitchumani R, Yao S C. Correlation of thermal conductivities of unidirectional fibrous composites using local fractal techniques[J]. ASME J Heat transfer, 1991, 113: 788-796.
[30] Shashwati R, Tarafdar S. Archie's law from a fractal model for porous rocks[J]. Physical review B, 1997, 55(13): 8038-8041.
[31]施明恒,樊荟.多孔介质导热的分形模型[J].热科学与技术,2002,1(1):28-31.
[32]李小川,施明恒,张东辉.非均匀多孔介质有效导热率分析[J].工程热物理学报,2006,27(4):644-646.
[33]张东辉,施明恒.分形多孔介质中的热传导[J].工程热物理学报,2004,25(1):112-114.
[34]许志,王依民,王勇.运用分形方法预测石墨化碳泡沫方向导热系数[J].材料导报,2009,23(8):74-77.
[35]张新铭,彭鹏,王金灿.基于分形理论的石墨泡沫新材料导热系数[J].重庆大学学报,2004,27(9):109-111.
[36]李守巨,刘迎曦,于贺.多孔介质等效导热系数与分形维数关系的数值模拟研究[J].岩土力学,2009,30(5):1465-1470.
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