多孔介质传热传质及热湿应力分析
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摘要
本论文以建筑材料为工程背景,研究了含湿多孔介质内部传热、传湿的过程,并对由热湿作用引起的介质内部应力进行分析研究。
本文将多孔介质看作宏观意义上的虚拟连续介质,以Luikov方程为耦合模型,采用有限差分法对多孔介质材料的一维和二维瞬态传热、传湿进行模拟研究,得出空心圆柱及平板内部的温度及含湿量的动态分布。在求解过程中考虑了瞬态边界条件,使计算结果更精确,更符合实际。同时探讨了不同无量纲准则数对热湿扩散的影响,从而更好地理解多孔介质传热传质的本质。
在对多孔介质传热传质过程研究的基础上,将热弹性力学理论应用于温湿度耦合的情况,得出热湿作用下的本构方程。从而进行了空心圆柱热湿应力分析及平面板的热湿应力分析,以数值法得到了多孔材料的位移和热湿应力动态分布,同时通过对热应力及湿应力的分别求解,得出了热、湿对热湿应力的作用及影响。热湿应力的研究对多孔材料的裂纹分析具有重要的借鉴作用。
The thesis is mainly on the research of the process of heat and mass transfer in porous media and the analysis of hygrothermal stress induced by temperature and moisture effect by taking building materials as an engineering background.
Based on Luikov’s equations as coupling model , porous media is treated as virtual continuous body in macro-scale. The process of transient coupled heat and moisture transfer in one-dimensional and two-dimensional porous structures are simulated with the finite difference method. The transient distribution of temperature and moisture content of hollow cylinder and plate are obtained. Transient boundary conditions are assumed for heat and moisture transfer at external surface, which is more reasonable. Besides,the influence of dimensionless numbers to the process of heat and mass transfer is discussed, which is useful to understand the process more deeply.
The constitutive equations under hygrothermal effect are discussed by applying the thermal elastic mechanic theory to the condition of coupled temperature and moisture. Hygrothermal stress of hollow cylinder and plate are analyzed and the transient distribution of displacement and hygrothermal stress are simulated. Thermal stress and hydro stress are studied respectively, which finding the impact of temperature and moisture to the hygrothermal stress. The research of hygrothermal stress provides some reference for crack analysis of porous media.
本文将多孔介质看作宏观意义上的虚拟连续介质,以Luikov方程为耦合模型,采用有限差分法对多孔介质材料的一维和二维瞬态传热、传湿进行模拟研究,得出空心圆柱及平板内部的温度及含湿量的动态分布。在求解过程中考虑了瞬态边界条件,使计算结果更精确,更符合实际。同时探讨了不同无量纲准则数对热湿扩散的影响,从而更好地理解多孔介质传热传质的本质。
在对多孔介质传热传质过程研究的基础上,将热弹性力学理论应用于温湿度耦合的情况,得出热湿作用下的本构方程。从而进行了空心圆柱热湿应力分析及平面板的热湿应力分析,以数值法得到了多孔材料的位移和热湿应力动态分布,同时通过对热应力及湿应力的分别求解,得出了热、湿对热湿应力的作用及影响。热湿应力的研究对多孔材料的裂纹分析具有重要的借鉴作用。
The thesis is mainly on the research of the process of heat and mass transfer in porous media and the analysis of hygrothermal stress induced by temperature and moisture effect by taking building materials as an engineering background.
Based on Luikov’s equations as coupling model , porous media is treated as virtual continuous body in macro-scale. The process of transient coupled heat and moisture transfer in one-dimensional and two-dimensional porous structures are simulated with the finite difference method. The transient distribution of temperature and moisture content of hollow cylinder and plate are obtained. Transient boundary conditions are assumed for heat and moisture transfer at external surface, which is more reasonable. Besides,the influence of dimensionless numbers to the process of heat and mass transfer is discussed, which is useful to understand the process more deeply.
The constitutive equations under hygrothermal effect are discussed by applying the thermal elastic mechanic theory to the condition of coupled temperature and moisture. Hygrothermal stress of hollow cylinder and plate are analyzed and the transient distribution of displacement and hygrothermal stress are simulated. Thermal stress and hydro stress are studied respectively, which finding the impact of temperature and moisture to the hygrothermal stress. The research of hygrothermal stress provides some reference for crack analysis of porous media.
引文
[1]林瑞泰,多孔介质传热传质引论[M],北京:科学出版社,1995。
[2]施明恒,虞维平,王补宣,多孔介质传热传质研究的现状和展望[J],东南大学学报,1994年11月第24卷增刊:1-7。
[3] Z. Sereir ,N. Boualem, Damage of hybrid composites under long term hygrothermal loading and stacking sequence[J],Theoretical and Applied Fracture Mechanics,2007, 47:145–163.
[4] RC. Chang, C. K. Chao,General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media[J],J.Appl. Phys.,1993,74 (12):7085-7093.
[5]王君,杨帆,陈大鹏,计及热效应和湿分扩散的耦合黏弹性本构方程[J],力学学报,2002年9月第34卷第5期:735-742。
[6]张华玲,刘朝,付祥钊,多孔墙体湿分传递与室内热湿环境研究[J],暖通空调, 2006年第36卷第10期:29-34。
[7] Win-Jin Changa,Cheng-I Weng,An analytical solution to coupled heat and moisture diffusion transfer in porous materials.International[J],Journal of Heat and Mass Transfer,2000,43:3621-3632.
[8] Gerson H,dos Santos, Nathan Mendes. Simultaneous heat and moisture transfer in soils combined with building simulation[J],Energy and Buildings, 2006, 38:303–314
[9] B. Wu,W,Yang, C.Jia,A Three-dimensional Numerical Simulation of Transient Heat and Mass Transfer inside a Single Rice Kernel during the Drying Process[J], Biosystems Engineering ,2004,87 (2):191–200.
[10] H. Basirat,Tabrizi1,F. Hamdullahpur. Mathematical modelling of drying based on a surface evaporation source term for coupled energy and mass transfer[J], International journal of energy research:1305.
[11] R. Younsi , D. Kocaefe, S. Poncsak, Y. Kocaefe.,Computational modelling of heat and mass transfer during the high-temperature heat treatment of wood[J],Applied Thermal Engineering ,2007,27:1424–1431.
[12] R. Younsi , D. Kocaefe, Y. Kocaefe,Three-dimensional simulation of heat andmoisture transfer in wood[J],Applied Thermal Engineering ,2006,26:1274–1285.
[13]虞维平,王补宣,施明恒,考虑毛细滞后效应的未饱和含湿多孔介质传热和传质理论[J],工程热物理学报,1994年02期:190-194。
[14]陈启高,多孔维护结构中湿度的计算[J],重庆建筑大学学报,1984年03期:1-18。
[15]王补宣,多孔介质中单相对流换热分析的流体渗流模式[J],上海交通大学学报,1999年08期:966-969。
[16]胡雪蛟,杜建华,王补宣,液相饱和度对多孔介质稳态导热系数的影响[J],工程热物理学报,2001年S1期:125-128。
[17]李俊明,王补宣,多孔介质内受迫对流凝结时两相共存区的非达西模型[J],工程热物理学报,1996年01期:91-95。
[18] Marco Gigliotti , Fre′de′ric Jacquemin , Alain Vautrin,Assessment of approximate models to evaluate transient and cyclical hygrothermoelastic stress in composite plates[J],International Journal of Solids and Structures,2007,44:733–759.
[19] A. Tounsi , E. Adda Bedia , G. Verchery,Influence of anisotropy on the transient hygroscopic stresses in polymer matrix composites with cyclic environmental conditions[J],Composite Structures,2002,55:393–405.
[20] RC.Chang, C.K.Chao,General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media[J],J.Appl. Phys,1993,74 (12):7085-7093.
[21] Pavankiran Vaddadi, Toshio Nakamura, Raman P. Singh,Transient hygrothermal stresses in fiber reinforced composites:a heterogeneous characterization approach.Composites, Part A,2003,34:719–730.
[22] V.V.S. Rao, P.K. Sinha,Dynamic response of multidirectional composites in hygrothermal environments[J],Composite Structures,2004,64:329–338.
[23] N.V. Swamy Naidu, P.K. Sinha,Nonlinear transient analysis of laminated composite shells in hygrothermal environments[J],Composite Structures,2006,72:280–288.
[24] A. Benkhedda a,b,A. Tounsi a, E.A. Adda bedia,Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates[J],Composite Structures , 2007:1-7.
[25]李锡夔,李荣涛,张雪珊等,高温下混凝土中热-湿-气-力学耦合过程数值模拟[J],工程力学,2005年8月第22卷第4期:171-178。
[26]苏向辉,多层多孔结构内热湿耦合迁移特性研究,南京:南京航空航天大学博士学位论文,2003年。
[27]戴嘉尊,邱建贤,微分方程数值解法[M],南京:东南大学出版社,2002。
[28]陶文铨,数值传热学[M],西安:西安交通大学出版社,2001。
[29] Yu-Ching Yang , Shao-Shu Chu , Haw-Long Lee , Shu-Lian Lin.Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder[J]. International Communications in Heat and Mass Transfer,2006,33:102–111.
[30] Jeny. Liu, Shun Cheng. Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies[J],Int. J. Heat Mass Transfer,1991, 7(34):1747-1754.
[31] Don Kulasiri,Ian Woodhead. On modelling the drying of porous materials:analytical solutions to coupled partial differential equations governing heat and mass transfer[J],Mathematical Problems in Engineering,2005,3:275–291.
[32] P. K. Parhi,S. K. Bhattacharyya,P. K. Sinha,Hygrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells[J],Journal of Sound and Vibration,2001,248(2):195-214.
[33]竹内洋一郎,热应力[M],北京:科学出版社,1977。
[34]孔祥谦,热应力有限单元法分析[M],上海:上海交通大学出版社,1999。
[35]严宗达,王洪礼,热应力[M],北京:高等教育出版社,1993。
[36]李维特,黄保海,毕仲波,热应力理论分析及应用[M],北京:中国电力出版社,2004。
[2]施明恒,虞维平,王补宣,多孔介质传热传质研究的现状和展望[J],东南大学学报,1994年11月第24卷增刊:1-7。
[3] Z. Sereir ,N. Boualem, Damage of hybrid composites under long term hygrothermal loading and stacking sequence[J],Theoretical and Applied Fracture Mechanics,2007, 47:145–163.
[4] RC. Chang, C. K. Chao,General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media[J],J.Appl. Phys.,1993,74 (12):7085-7093.
[5]王君,杨帆,陈大鹏,计及热效应和湿分扩散的耦合黏弹性本构方程[J],力学学报,2002年9月第34卷第5期:735-742。
[6]张华玲,刘朝,付祥钊,多孔墙体湿分传递与室内热湿环境研究[J],暖通空调, 2006年第36卷第10期:29-34。
[7] Win-Jin Changa,Cheng-I Weng,An analytical solution to coupled heat and moisture diffusion transfer in porous materials.International[J],Journal of Heat and Mass Transfer,2000,43:3621-3632.
[8] Gerson H,dos Santos, Nathan Mendes. Simultaneous heat and moisture transfer in soils combined with building simulation[J],Energy and Buildings, 2006, 38:303–314
[9] B. Wu,W,Yang, C.Jia,A Three-dimensional Numerical Simulation of Transient Heat and Mass Transfer inside a Single Rice Kernel during the Drying Process[J], Biosystems Engineering ,2004,87 (2):191–200.
[10] H. Basirat,Tabrizi1,F. Hamdullahpur. Mathematical modelling of drying based on a surface evaporation source term for coupled energy and mass transfer[J], International journal of energy research:1305.
[11] R. Younsi , D. Kocaefe, S. Poncsak, Y. Kocaefe.,Computational modelling of heat and mass transfer during the high-temperature heat treatment of wood[J],Applied Thermal Engineering ,2007,27:1424–1431.
[12] R. Younsi , D. Kocaefe, Y. Kocaefe,Three-dimensional simulation of heat andmoisture transfer in wood[J],Applied Thermal Engineering ,2006,26:1274–1285.
[13]虞维平,王补宣,施明恒,考虑毛细滞后效应的未饱和含湿多孔介质传热和传质理论[J],工程热物理学报,1994年02期:190-194。
[14]陈启高,多孔维护结构中湿度的计算[J],重庆建筑大学学报,1984年03期:1-18。
[15]王补宣,多孔介质中单相对流换热分析的流体渗流模式[J],上海交通大学学报,1999年08期:966-969。
[16]胡雪蛟,杜建华,王补宣,液相饱和度对多孔介质稳态导热系数的影响[J],工程热物理学报,2001年S1期:125-128。
[17]李俊明,王补宣,多孔介质内受迫对流凝结时两相共存区的非达西模型[J],工程热物理学报,1996年01期:91-95。
[18] Marco Gigliotti , Fre′de′ric Jacquemin , Alain Vautrin,Assessment of approximate models to evaluate transient and cyclical hygrothermoelastic stress in composite plates[J],International Journal of Solids and Structures,2007,44:733–759.
[19] A. Tounsi , E. Adda Bedia , G. Verchery,Influence of anisotropy on the transient hygroscopic stresses in polymer matrix composites with cyclic environmental conditions[J],Composite Structures,2002,55:393–405.
[20] RC.Chang, C.K.Chao,General solution to the hygrothermoelastic interface problem with discontinuity between dissimilar anisotropic media[J],J.Appl. Phys,1993,74 (12):7085-7093.
[21] Pavankiran Vaddadi, Toshio Nakamura, Raman P. Singh,Transient hygrothermal stresses in fiber reinforced composites:a heterogeneous characterization approach.Composites, Part A,2003,34:719–730.
[22] V.V.S. Rao, P.K. Sinha,Dynamic response of multidirectional composites in hygrothermal environments[J],Composite Structures,2004,64:329–338.
[23] N.V. Swamy Naidu, P.K. Sinha,Nonlinear transient analysis of laminated composite shells in hygrothermal environments[J],Composite Structures,2006,72:280–288.
[24] A. Benkhedda a,b,A. Tounsi a, E.A. Adda bedia,Effect of temperature and humidity on transient hygrothermal stresses during moisture desorption in laminated composite plates[J],Composite Structures , 2007:1-7.
[25]李锡夔,李荣涛,张雪珊等,高温下混凝土中热-湿-气-力学耦合过程数值模拟[J],工程力学,2005年8月第22卷第4期:171-178。
[26]苏向辉,多层多孔结构内热湿耦合迁移特性研究,南京:南京航空航天大学博士学位论文,2003年。
[27]戴嘉尊,邱建贤,微分方程数值解法[M],南京:东南大学出版社,2002。
[28]陶文铨,数值传热学[M],西安:西安交通大学出版社,2001。
[29] Yu-Ching Yang , Shao-Shu Chu , Haw-Long Lee , Shu-Lian Lin.Hybrid numerical method applied to transient hygrothermal analysis in an annular cylinder[J]. International Communications in Heat and Mass Transfer,2006,33:102–111.
[30] Jeny. Liu, Shun Cheng. Solutions of Luikov equations of heat and mass transfer in capillary-porous bodies[J],Int. J. Heat Mass Transfer,1991, 7(34):1747-1754.
[31] Don Kulasiri,Ian Woodhead. On modelling the drying of porous materials:analytical solutions to coupled partial differential equations governing heat and mass transfer[J],Mathematical Problems in Engineering,2005,3:275–291.
[32] P. K. Parhi,S. K. Bhattacharyya,P. K. Sinha,Hygrothermal effects on the dynamic behavior of multiple delaminated composite plates and shells[J],Journal of Sound and Vibration,2001,248(2):195-214.
[33]竹内洋一郎,热应力[M],北京:科学出版社,1977。
[34]孔祥谦,热应力有限单元法分析[M],上海:上海交通大学出版社,1999。
[35]严宗达,王洪礼,热应力[M],北京:高等教育出版社,1993。
[36]李维特,黄保海,毕仲波,热应力理论分析及应用[M],北京:中国电力出版社,2004。