基于分形理论的陶瓷隔（蓄）热多孔材料传热特性研究与应用
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摘要
近年来，陶瓷隔热以及蓄热材料是在工业窑炉上应用较为广泛的一种新型节能材料。它具有廉价、耐高温、抗热冲击等优点。为掌握其热性能变化规律，本文提出了一种新的研究方法：根据耐火纤维材料和陶瓷蓄热体这两种隔(蓄)热多孔材料具有复杂微空间结构的物理特性，采用分形理论对它们的传热特性进行研究。
本文根据耐火纤维材料微空间结构特点，利用分形理论，以分形维数和纤维体积分率为表征微空间结构的主要参数，对耐火纤维材料微空间结构进行描述。并用等效热阻法建立了高温条件下耐火纤维材料的导热模型，导出了其有效导热系数的分形计算式。将耐火纤维材料导热计算结果和一维稳态平板法测定的实验值进行比较，两者基本一致，最大相对误差小于15％。这表明了基于分形理论描述的耐火纤维材料有效导热系数的计算式具有较高的表达精度。计算结果表明：在纤维体积分率一定时，其有效导热系数随温度的升高而升高，且是绝对温度的三次方函数；在温度不变时，其有效导热系数会随着纤维体积分率和分形维数的增加而增加，且增加幅度越来越大。
陶瓷蓄热体是蓄热式热交换器中的关键部件。本文选取陶瓷球蓄热体作为研究对象，它具有多孔介质材料的物理特性，传热的内部空间结构类似于耐火纤维材料。本文应用分形理论对陶瓷球蓄热体进行空间结构描述，进而在耐火纤维材料导热分形模型的基础上推导出蓄热体综合传热系数的分形计算式。并且利用该式对不同材质和几何结构参数的陶瓷球蓄热体进行传热系数的计算和比较，得到结论：正排列方式下的陶瓷球蓄热体的传热系数要远大于三角形排列方式的陶瓷球蓄热体；而且，陶瓷球直径越大，蓄热体的传热系数反而越小。另外结合蓄热体的材料特性计算分析得出了陶瓷球直径为10mm，材质取用Si_3N_4，正排列方式的陶瓷球蓄热体，其传热系数最优的结论。在此基础上，将蓄热体综合传热系数的分形计算式引入蓄热式换热器的设计中，建立了一套较为简便和完善的换向型蓄热式换热器的设计方案。
本文提出了将分形理论应用于陶瓷隔(蓄)热多孔材料的传热特性研究的新方法，从而推导出了耐火纤维材料有效导热系数的分形计算式以及蓄热体的综合传热系数的分形计算式，为设计、使用及推广蓄热式换热器提供了理论基础和设计方法。文中得到的关于陶瓷隔(蓄)热多孔材料传热特性的结论和方法，不仅对其实际应用于工业窑炉能量回收具有一定的工程指导意义，还有利于进一步探索陶瓷隔(蓄)热多孔材料的其他特性，开发新型的陶瓷多孔材料，同时也对多孔介质传热传质的研究和分形理论的应用起到了重要的推动作用。
In recent years, heat insulating and retaining ceramic material is a new energy-saving material which is applied comparatively extensively to the industrial furnace. It has advantages of cheap, resisting high temperature, fighting thermal impact. In order to master how the thermal characteristics vary, a new research method is offered in this paper: fractal theory is used to research the heat transfer characteristics of refractory fiber material and ceramic regenerator the two types of heat insulating and retaining ceramic porous material based on their physical characteristics of complex microstructure.
Fractal theory is used in this paper based on the microstructure characteristics of refractory fiber. The microstructure is described with fractal dimension and fiber volume fraction as the major parameters. The model of heat transfer has been established with the equivalent thermal resistance under high temperature. The formula for efficient thermal conductivity is given out in this paper. The efficient thermal conductivity has been compared between theoretical calculation and experimental results. It shows that theoretical calculation is almost in agreement with the experimental results. Its maximal relative error is smaller than 15 %. It has been shown that the theoretical calculative formula, which is based on fractal description, has higher precision. The calculative results show that the efficient thermal conductivity rises as temperature rises under a constant fiber volume fraction, and it is proportional to the third power of absolute temperature; it increases as fiber volume fraction and fractal dimension increase under a constant temperature and the increase rate is faster as the two parameters increase.
The ceramic regenerator is the key unit of regenerative heat exchanger. The ceramic ball-packed regenerator is researched in the paper. It has characteristics of porous media, and its internal structure for heat transfer is similar to refractory fiber. The formula for comprehensive heat transfer coefficient of ceramic regenerator is given out based on the fractal heat transfer model of refractory fiber material in this paper. The formula is used to calculate and compare the heat transfer coefficient of ceramic ball-packed regenerator with different material and different parameters of geometric structure. The results are given out: the heat transfer coefficient of ceramic ball-packed regenerator is far greater when ceramic balls are in the foursquare arrangement than the ones in the triangular arrangement; it decreases as the diameter of ceramic ball increases. And combined with material characteristics of ceramic regenerator, the conclusion can be drawn through calculating and analyzing: the heat transfer coefficient is the maximum value when ceramic ball regenerator is in foursquare arrangement, the diameter of 10mm, and material of Si_3N_4. The formula for comprehensive heat transfer coefficient of ceramic regenerator is introduced to the design of regenerative heat exchanger based on the conclusion. A more convenient and complete design plan is made.
A new method is introduced in the paper about that fractal theory is used to research the heat transfer characteristics of heat insulating and retaining ceramic porous material. The formula for efficient thermal conductivity of refractory fiber and the formula for comprehensive heat transfer coefficient of ceramic regenerator are given out. Theory foundation and design method are provided for design, using and extension of regenerative heat exchanger. Practical application of energy recycling of industrial furnace is guided by conclusions and methods drawn in the paper about the heat transfer characteristics of heat insulating and retaining ceramic porous material. And it is favorable to further explore other characteristics of heat insulating and retaining ceramic porous material, to develop new types ceramic porous material and to give research on heat and mass transfer in porous media and fractal theory application a push forward.
本文根据耐火纤维材料微空间结构特点，利用分形理论，以分形维数和纤维体积分率为表征微空间结构的主要参数，对耐火纤维材料微空间结构进行描述。并用等效热阻法建立了高温条件下耐火纤维材料的导热模型，导出了其有效导热系数的分形计算式。将耐火纤维材料导热计算结果和一维稳态平板法测定的实验值进行比较，两者基本一致，最大相对误差小于15％。这表明了基于分形理论描述的耐火纤维材料有效导热系数的计算式具有较高的表达精度。计算结果表明：在纤维体积分率一定时，其有效导热系数随温度的升高而升高，且是绝对温度的三次方函数；在温度不变时，其有效导热系数会随着纤维体积分率和分形维数的增加而增加，且增加幅度越来越大。
陶瓷蓄热体是蓄热式热交换器中的关键部件。本文选取陶瓷球蓄热体作为研究对象，它具有多孔介质材料的物理特性，传热的内部空间结构类似于耐火纤维材料。本文应用分形理论对陶瓷球蓄热体进行空间结构描述，进而在耐火纤维材料导热分形模型的基础上推导出蓄热体综合传热系数的分形计算式。并且利用该式对不同材质和几何结构参数的陶瓷球蓄热体进行传热系数的计算和比较，得到结论：正排列方式下的陶瓷球蓄热体的传热系数要远大于三角形排列方式的陶瓷球蓄热体；而且，陶瓷球直径越大，蓄热体的传热系数反而越小。另外结合蓄热体的材料特性计算分析得出了陶瓷球直径为10mm，材质取用Si_3N_4，正排列方式的陶瓷球蓄热体，其传热系数最优的结论。在此基础上，将蓄热体综合传热系数的分形计算式引入蓄热式换热器的设计中，建立了一套较为简便和完善的换向型蓄热式换热器的设计方案。
本文提出了将分形理论应用于陶瓷隔(蓄)热多孔材料的传热特性研究的新方法，从而推导出了耐火纤维材料有效导热系数的分形计算式以及蓄热体的综合传热系数的分形计算式，为设计、使用及推广蓄热式换热器提供了理论基础和设计方法。文中得到的关于陶瓷隔(蓄)热多孔材料传热特性的结论和方法，不仅对其实际应用于工业窑炉能量回收具有一定的工程指导意义，还有利于进一步探索陶瓷隔(蓄)热多孔材料的其他特性，开发新型的陶瓷多孔材料，同时也对多孔介质传热传质的研究和分形理论的应用起到了重要的推动作用。
In recent years, heat insulating and retaining ceramic material is a new energy-saving material which is applied comparatively extensively to the industrial furnace. It has advantages of cheap, resisting high temperature, fighting thermal impact. In order to master how the thermal characteristics vary, a new research method is offered in this paper: fractal theory is used to research the heat transfer characteristics of refractory fiber material and ceramic regenerator the two types of heat insulating and retaining ceramic porous material based on their physical characteristics of complex microstructure.
Fractal theory is used in this paper based on the microstructure characteristics of refractory fiber. The microstructure is described with fractal dimension and fiber volume fraction as the major parameters. The model of heat transfer has been established with the equivalent thermal resistance under high temperature. The formula for efficient thermal conductivity is given out in this paper. The efficient thermal conductivity has been compared between theoretical calculation and experimental results. It shows that theoretical calculation is almost in agreement with the experimental results. Its maximal relative error is smaller than 15 %. It has been shown that the theoretical calculative formula, which is based on fractal description, has higher precision. The calculative results show that the efficient thermal conductivity rises as temperature rises under a constant fiber volume fraction, and it is proportional to the third power of absolute temperature; it increases as fiber volume fraction and fractal dimension increase under a constant temperature and the increase rate is faster as the two parameters increase.
The ceramic regenerator is the key unit of regenerative heat exchanger. The ceramic ball-packed regenerator is researched in the paper. It has characteristics of porous media, and its internal structure for heat transfer is similar to refractory fiber. The formula for comprehensive heat transfer coefficient of ceramic regenerator is given out based on the fractal heat transfer model of refractory fiber material in this paper. The formula is used to calculate and compare the heat transfer coefficient of ceramic ball-packed regenerator with different material and different parameters of geometric structure. The results are given out: the heat transfer coefficient of ceramic ball-packed regenerator is far greater when ceramic balls are in the foursquare arrangement than the ones in the triangular arrangement; it decreases as the diameter of ceramic ball increases. And combined with material characteristics of ceramic regenerator, the conclusion can be drawn through calculating and analyzing: the heat transfer coefficient is the maximum value when ceramic ball regenerator is in foursquare arrangement, the diameter of 10mm, and material of Si_3N_4. The formula for comprehensive heat transfer coefficient of ceramic regenerator is introduced to the design of regenerative heat exchanger based on the conclusion. A more convenient and complete design plan is made.
A new method is introduced in the paper about that fractal theory is used to research the heat transfer characteristics of heat insulating and retaining ceramic porous material. The formula for efficient thermal conductivity of refractory fiber and the formula for comprehensive heat transfer coefficient of ceramic regenerator are given out. Theory foundation and design method are provided for design, using and extension of regenerative heat exchanger. Practical application of energy recycling of industrial furnace is guided by conclusions and methods drawn in the paper about the heat transfer characteristics of heat insulating and retaining ceramic porous material. And it is favorable to further explore other characteristics of heat insulating and retaining ceramic porous material, to develop new types ceramic porous material and to give research on heat and mass transfer in porous media and fractal theory application a push forward.
引文
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