多孔材料传热特性分析与散热结构优化设计
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摘要
防热是航空航天、能源动力、电气电子等工程中普遍关注的问题。空天飞行器热障问题、高温环境下对温度敏感的仪器设备的热保护问题、电子器件散热问题等均需要有效隔热和积极散热措施。多孔材料(包括最新研发的点阵材料)同时具备轻质、多功能和可设计等特点,在满足其他功能的同时具有良好的防热性能。闭孔多孔材料具有低的传热系数可用于隔热;开孔多孔材料由于具有流动通道,可用于主动散热;可设计特点为轻质防热等多功能设计提供了保证。多孔材料隔热、强化传热等性能分析与研究以及以其为基础的散热结构设计优化,具有重要的理论意义和应用价值。
在这一需求的牵动下,本文主要研究了考虑辐射和对流等影响的多孔材料热传输性能的表征方法,建立了考虑辐射影响的闭孔多孔材料热性能分析的多尺度方法、单向开孔金属材料主动散热性能分析的传递矩阵方法和快速数值方法;研究了最优散热结构构型设计理论,建立了基于拓扑优化技术和仿生的最优散热构型设计的数学物理模型和求解方法。主要内容包括:
(1)考虑辐射的多孔材料传热性能表征的多尺度方法。以闭孔类多孔材料(又称空心材料)高温隔热应用为背景,建立了考虑辐射的传热性能表征的多尺度分析方法。该方法首先利用具有严格数学理论的均匀化方法计算具有周期性分布的空心材料的传热性能,得到了纯导热时的等效传热系数和空心材料较为精确的温度场。在此基础上,计算了空心材料等效辐射传热系数。通过与实验结果的比较验证了方法的有效性,并讨论了孔穴形状与尺寸对空心材料换热性能的影响。
(2)金属蜂窝材料主动散热性能表征的新方法:传递矩阵法和快速数值算法。开孔类超轻多孔金属材料除具有良好的力学性能外,本身还是优良的传热介质。以金属蜂窝材料强迫对流换热应用为背景,提出了两种分析方法:传递矩阵方法和快速数值算法。传递矩阵方法以金属蜂窝夹层结构为研究对象,避免了现有理论模型中的一些近似,是一个更精确的理论模型。与现有的理论模型相比,所预测的结果处于皱壁模型和等效介质模型预测的结果之间,且更趋近于数值仿真的结果。快速数值算法是在实际工程应用中会属蜂窝填充的复杂结构的换热性能分析以及多功能优化设计需求的推动下,以及有限元法和传递矩阵方法的双重启发下提出来的。该方法继承了传递矩阵方法的计算精度,同时继承了有限元方法的广泛适用性。与有限体积法相比,计算效率提高3到4个数量级。针对两个具体算例,通过与有限体积方法计算结果比较,验证了方法的有效性。
(3)基于拓扑优化的导热通道的几何构型设计方法。针对电子设备中基本科学问题,体-点导热问题,提出了基于拓扑优化的导热通道的几何构型设计方法。利用该方法所获得的设计结果在性能上远大于仿生优化所获得的结果,且能突破现有构造方法的性能设计极限。另外,设计结果与自然界中自然树的结构相似,比利用构造方法所获得的结果在结构上更趋近于自然树。
(4)最优传热结构设计问题的数学模型。针对许多实际电子元器件不能超过额定最高温度值这一要求,从理论角度探讨了实现最高温度最低的优化模型的建立。利用一个平板导热优化问题,首先评估了以热量传势容耗散(又称散热弱度)为优化目标的现有优化模型来实现设计目的的近似程度,提出了一个基于几何平均温度的散热性能描述指标,并以此为目标函数,建立了一个新的散热结构设计优化模型。通过与现有优化模型和理论最优设计的比较,说明几何平均温度是描述散热性能的良好指标,所建立的优化模型能够有效获得散热结构的最优设计。
(5)基于仿生思想的树状多级通道对流散热结构设计。从实际散热结构设计出发,改进了基于仿生思想获得的树枝状分形通道对流冷却散热结构的设计方法。改进后的设计方法能够满足任意长宽比的生热表面的散热要求,同时提出了一种新的分析方法。研究表明,在各种条件下,最优设计的分形层次均为7,生热表面一定的条件下,最优的长宽比为1.87。这些研究结果能为实际工程设计提供非常有价值的参考。
本文工作得到国家自然科学基金(10332010,90205029,10721062)、国家重点基础研究(973)计划(2006CB601205)和教育部新世纪优秀人才支持计划(NCET-04-0272)的资助。
Thermal management exists widely in engineering fields such as aerospace, energy power and electronics. The heat insulation and active coolings are all needed in the thermal barrier issue of space vehicle, the temperature control of temperature-sensitive equipment, and heat dissipation of electronic devices. The cellular materials (including the truss-material) with light-weight can be easily tailed to a multifunctional application that demands not only heat transfer capacities but also other roles. The close-celled cellular materials with low conductivity are often applied as the heat insulation material and the open-celled cellular material with voids enabling fluid flow in one direction is used to active cooling. The researches on the heat transfer performance of cellular materials and the optimal heat dissipation structure have big significances in theories and application.
For the demands of practical applications above, the methods for predicting the heat transfer performance of cellular materials are investigated: the multi-scale analysis method for thermal conductivity of close-celled cellular with radiation is proposed, and the transfer matrix method and the rapid numerical algorithm for heat transfer efficiency of active cooling by open-celled cellular material with one easy flow direction are presented. The mathematical formulations and the corresponding solving methods for the configuration of the optimal heat dissipation structure based on the topology optimization and bionic idea are studied. The main content and results are given in the following paragraphs:
(1) Multi-scale analysis method for thermal conductivity of cellular material with radiation. The close-celled cellular material is often applied in the high temperature entironment as the heat insulation material. A multi-scale method for the predicting the effective thermal conductivity with radiation of close-celled cellular material is presented, it also considers the effect of geometry and distribution of pores. Using the homogenization method to solve the pure conductive problem of porous materials with periodic structure, the effective thermal conductivity without radiation is predicted, and the temperature field in a local domain of a unit cell is obtained. The temperature field is taken as the good approximation of the real temperature distribution and the radiative thermal conductivity is obtained. Furthermore, the effect of the microstrcutre, the distribution and geometry of pores on heat transfer porous materials is discussed.
(2) The new methods for heat transfer efficiency of active cooling by metal honeycomb structures: Transfer Matrix Method and Rapid Numerical Algorithm. Theopen-celled cellular materials have potential for simultaneous load bearing and active cooling. The transfer matrix method and the rapid numerical algorithm for heat transfer performance of metallic honeycomb structure under the forced convection conditions are presented. The transfer matrix method only used to analyze the heat transfer performance of sandwich metallic honeycombs can overcome the approximations in the corrugated wall model. The heat transfer efficiency predicted by this new method is consistently lower than that predicted by the corrugated wall model, higher than that by the effective medium model, and closer to the numerical simulation results. It indicates that this method is accurate. Motivated in the engineering applications of a variety of structure filled with honeycombs and optimization design of non-uniform honeycomb structure, the rapid numerical algorithm is presented by inspiration from the finite method and the transfer matrix method. It's about 3-4 order of magnitudes improvement in computational velocity of this method compared with the finite volume method. The validity and applicability of the method is proved by two examples.
(3) Design method for the optimal conducting paths based on topology optimization. The new method based on the topology optimization is presented to solve the volume-to-point heat conduction problem which is the fundamental problem in electronics and cooling architecture. The performance of the conducting paths obtained by the present method has great improvement relative to the design of bionic optimization, and can break down the design limit of construct method. Furthermore, the configuration of the optimal conducting paths is more similar to the natural tree than those obtained by other methods.
(4) The optimization model of the heat conduction structure. Generally, the highest temperatures in a package must not exceed a specified value, an optimization model which considers a novel thermal performance index as the objective function is proposed for minimizing the highest temperature. Firstly, the performance of the conventional heat conduction optimization model with the dissipation of heat transport potential capacity as the objective function is evaluated by a one-dimensional heat conduction problem in a planar plate exchanger. Then, a new thermal performance index, named by the geometric average temperature in this paper is introduced. The new heat conduction optimization model with the geometric average temperature as the objective function is developed. The results show that the geometric average temperature is an ideal thermal performance index and the solution of the new model is close to the theoretical optimal solution.
(5) Structural design of forced convection cooled tree-like channels heat sink based on bionic idea. For the demand of industrial cooling, the improved design of fractal channel net based on the bionic idea that can meet the demand for cooling of electronic chip with arbitrary ratio of length to width is presented. A theory model is proposed to estimate the performance of heat transfer and pressure drop approximately. It is found that the best total branching level is 7. If the surface area for cooling is fixed, it is the best choice when the ratio of length to width of heat sink is 1.87. These results are instructive to design the fractal branch net of rectangular shape
The work of this dissertation is supported by National Natural Science Foundation of China through the Grant No.s(10332010, 90205029,10421202), by the national key basic research program of china (Grant No.2006CB601205), and by the program for new century excellent talents in university of china (NCET-04-0272).
在这一需求的牵动下,本文主要研究了考虑辐射和对流等影响的多孔材料热传输性能的表征方法,建立了考虑辐射影响的闭孔多孔材料热性能分析的多尺度方法、单向开孔金属材料主动散热性能分析的传递矩阵方法和快速数值方法;研究了最优散热结构构型设计理论,建立了基于拓扑优化技术和仿生的最优散热构型设计的数学物理模型和求解方法。主要内容包括:
(1)考虑辐射的多孔材料传热性能表征的多尺度方法。以闭孔类多孔材料(又称空心材料)高温隔热应用为背景,建立了考虑辐射的传热性能表征的多尺度分析方法。该方法首先利用具有严格数学理论的均匀化方法计算具有周期性分布的空心材料的传热性能,得到了纯导热时的等效传热系数和空心材料较为精确的温度场。在此基础上,计算了空心材料等效辐射传热系数。通过与实验结果的比较验证了方法的有效性,并讨论了孔穴形状与尺寸对空心材料换热性能的影响。
(2)金属蜂窝材料主动散热性能表征的新方法:传递矩阵法和快速数值算法。开孔类超轻多孔金属材料除具有良好的力学性能外,本身还是优良的传热介质。以金属蜂窝材料强迫对流换热应用为背景,提出了两种分析方法:传递矩阵方法和快速数值算法。传递矩阵方法以金属蜂窝夹层结构为研究对象,避免了现有理论模型中的一些近似,是一个更精确的理论模型。与现有的理论模型相比,所预测的结果处于皱壁模型和等效介质模型预测的结果之间,且更趋近于数值仿真的结果。快速数值算法是在实际工程应用中会属蜂窝填充的复杂结构的换热性能分析以及多功能优化设计需求的推动下,以及有限元法和传递矩阵方法的双重启发下提出来的。该方法继承了传递矩阵方法的计算精度,同时继承了有限元方法的广泛适用性。与有限体积法相比,计算效率提高3到4个数量级。针对两个具体算例,通过与有限体积方法计算结果比较,验证了方法的有效性。
(3)基于拓扑优化的导热通道的几何构型设计方法。针对电子设备中基本科学问题,体-点导热问题,提出了基于拓扑优化的导热通道的几何构型设计方法。利用该方法所获得的设计结果在性能上远大于仿生优化所获得的结果,且能突破现有构造方法的性能设计极限。另外,设计结果与自然界中自然树的结构相似,比利用构造方法所获得的结果在结构上更趋近于自然树。
(4)最优传热结构设计问题的数学模型。针对许多实际电子元器件不能超过额定最高温度值这一要求,从理论角度探讨了实现最高温度最低的优化模型的建立。利用一个平板导热优化问题,首先评估了以热量传势容耗散(又称散热弱度)为优化目标的现有优化模型来实现设计目的的近似程度,提出了一个基于几何平均温度的散热性能描述指标,并以此为目标函数,建立了一个新的散热结构设计优化模型。通过与现有优化模型和理论最优设计的比较,说明几何平均温度是描述散热性能的良好指标,所建立的优化模型能够有效获得散热结构的最优设计。
(5)基于仿生思想的树状多级通道对流散热结构设计。从实际散热结构设计出发,改进了基于仿生思想获得的树枝状分形通道对流冷却散热结构的设计方法。改进后的设计方法能够满足任意长宽比的生热表面的散热要求,同时提出了一种新的分析方法。研究表明,在各种条件下,最优设计的分形层次均为7,生热表面一定的条件下,最优的长宽比为1.87。这些研究结果能为实际工程设计提供非常有价值的参考。
本文工作得到国家自然科学基金(10332010,90205029,10721062)、国家重点基础研究(973)计划(2006CB601205)和教育部新世纪优秀人才支持计划(NCET-04-0272)的资助。
Thermal management exists widely in engineering fields such as aerospace, energy power and electronics. The heat insulation and active coolings are all needed in the thermal barrier issue of space vehicle, the temperature control of temperature-sensitive equipment, and heat dissipation of electronic devices. The cellular materials (including the truss-material) with light-weight can be easily tailed to a multifunctional application that demands not only heat transfer capacities but also other roles. The close-celled cellular materials with low conductivity are often applied as the heat insulation material and the open-celled cellular material with voids enabling fluid flow in one direction is used to active cooling. The researches on the heat transfer performance of cellular materials and the optimal heat dissipation structure have big significances in theories and application.
For the demands of practical applications above, the methods for predicting the heat transfer performance of cellular materials are investigated: the multi-scale analysis method for thermal conductivity of close-celled cellular with radiation is proposed, and the transfer matrix method and the rapid numerical algorithm for heat transfer efficiency of active cooling by open-celled cellular material with one easy flow direction are presented. The mathematical formulations and the corresponding solving methods for the configuration of the optimal heat dissipation structure based on the topology optimization and bionic idea are studied. The main content and results are given in the following paragraphs:
(1) Multi-scale analysis method for thermal conductivity of cellular material with radiation. The close-celled cellular material is often applied in the high temperature entironment as the heat insulation material. A multi-scale method for the predicting the effective thermal conductivity with radiation of close-celled cellular material is presented, it also considers the effect of geometry and distribution of pores. Using the homogenization method to solve the pure conductive problem of porous materials with periodic structure, the effective thermal conductivity without radiation is predicted, and the temperature field in a local domain of a unit cell is obtained. The temperature field is taken as the good approximation of the real temperature distribution and the radiative thermal conductivity is obtained. Furthermore, the effect of the microstrcutre, the distribution and geometry of pores on heat transfer porous materials is discussed.
(2) The new methods for heat transfer efficiency of active cooling by metal honeycomb structures: Transfer Matrix Method and Rapid Numerical Algorithm. Theopen-celled cellular materials have potential for simultaneous load bearing and active cooling. The transfer matrix method and the rapid numerical algorithm for heat transfer performance of metallic honeycomb structure under the forced convection conditions are presented. The transfer matrix method only used to analyze the heat transfer performance of sandwich metallic honeycombs can overcome the approximations in the corrugated wall model. The heat transfer efficiency predicted by this new method is consistently lower than that predicted by the corrugated wall model, higher than that by the effective medium model, and closer to the numerical simulation results. It indicates that this method is accurate. Motivated in the engineering applications of a variety of structure filled with honeycombs and optimization design of non-uniform honeycomb structure, the rapid numerical algorithm is presented by inspiration from the finite method and the transfer matrix method. It's about 3-4 order of magnitudes improvement in computational velocity of this method compared with the finite volume method. The validity and applicability of the method is proved by two examples.
(3) Design method for the optimal conducting paths based on topology optimization. The new method based on the topology optimization is presented to solve the volume-to-point heat conduction problem which is the fundamental problem in electronics and cooling architecture. The performance of the conducting paths obtained by the present method has great improvement relative to the design of bionic optimization, and can break down the design limit of construct method. Furthermore, the configuration of the optimal conducting paths is more similar to the natural tree than those obtained by other methods.
(4) The optimization model of the heat conduction structure. Generally, the highest temperatures in a package must not exceed a specified value, an optimization model which considers a novel thermal performance index as the objective function is proposed for minimizing the highest temperature. Firstly, the performance of the conventional heat conduction optimization model with the dissipation of heat transport potential capacity as the objective function is evaluated by a one-dimensional heat conduction problem in a planar plate exchanger. Then, a new thermal performance index, named by the geometric average temperature in this paper is introduced. The new heat conduction optimization model with the geometric average temperature as the objective function is developed. The results show that the geometric average temperature is an ideal thermal performance index and the solution of the new model is close to the theoretical optimal solution.
(5) Structural design of forced convection cooled tree-like channels heat sink based on bionic idea. For the demand of industrial cooling, the improved design of fractal channel net based on the bionic idea that can meet the demand for cooling of electronic chip with arbitrary ratio of length to width is presented. A theory model is proposed to estimate the performance of heat transfer and pressure drop approximately. It is found that the best total branching level is 7. If the surface area for cooling is fixed, it is the best choice when the ratio of length to width of heat sink is 1.87. These results are instructive to design the fractal branch net of rectangular shape
The work of this dissertation is supported by National Natural Science Foundation of China through the Grant No.s(10332010, 90205029,10421202), by the national key basic research program of china (Grant No.2006CB601205), and by the program for new century excellent talents in university of china (NCET-04-0272).
引文
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