纤维隔热材料微观结构与热性质演化及热可靠性评估研究
|
摘要
可重复使用运载器要以十几倍音速的速度穿过大气层,与大气摩擦产生的热量高达上千度,开发轻质、低成本、高可靠性、可重复使用的热防护系统(Thermal Protection System TPS)是减少气动热量进入机体内部,保护内部控制系统、电子系统和能源系统的正常运转所必备的关键技术之一。陶瓷纤维隔热材料重量轻、成本低、耐高温、隔热性能优异,已日益成为热防护系统中使用得最具发展潜力的隔热材料。然而纤维隔热材料在服役过程中,除了要经受苛刻而严酷的气动加热外,还要经受着各种环境因素,如碎片撞击、污染、雨水侵蚀、密封泄露、热短路、材料老化等,繁多的影响因素之间往往耦合作用强、变化大、条件极端,环境的变化将对热防护系统的分析与设计产生最直接的影响,材料与热环境的相互作用研究面临着极其严峻的挑战,同时,热响应问题的复杂性以及贯穿在整个服役过程中的高可靠性要求更加剧了这一矛盾,因为服役过程中飞行器内部结构温度的小量过载就可能引发无法预料的灾难性后果。
本文以纤维隔热材料为研究对象,基于材料要在恶劣的高温环境下高可靠性服役的要求,从材料学、工程热物理及可靠性三个学科的角度,对纤维隔热材料的热响应行为及热性质进行了多方位的研究。跟踪了受热状态下材料的微观结构及热性质的演化过程,探讨了纤维隔热材料热辐射性质及热传导性质的确定方法,同时研究了纤维隔热材料的概率热响应过程及热可靠性评估方法。本文的主要研究内容及结论如下:
第一,通过SEM、DSC、XRD、FTIR等手段研究了纤维隔热材料热处理前后的微观结构变化,结果表明:未处理的纤维隔热材料呈非晶态,表面光滑无缺陷。在980°C时析出莫来石晶体。随着热处理温度的升高,析晶过程逐步进行致使晶粒长大、结晶度增加,纤维表面变得粗糙不平,弹性降低。更高温度的热处理使纤维收缩、烧结、变脆。未处理的纤维红外光谱呈现出非晶态结构所特有的较宽的吸收谱带,而经过1000°C的热处理之后出现了莫来石晶体的特征吸收谱带。同时,对材料微结构演化所引发的材料的热性质的演化进行了考察。结果表明有效热导率实验结果在热处理前后变化并不大,而有效热导率的计算结果热处理后的比未处理态的有较为明显的增加。受热过程中材料的辐射性质演变很复杂。当达到某一温度时,晶体的析出会影响光子导热,1000℃热处理后的材料其消光系数相对于未处理材料有所降低,而经过1200℃热处理的材料消光系数又有所增加。热处理前后材料的散射反照率随着热处理温度的增加而逐渐降低。线性各向异性散射相函数的线性系数随热处理工艺的变化并不明显。热处理之后材料的传导热导率有显著的增加,并且随着热处理温度的升高,增加的幅度变大。高温热处理使材料发生析晶,结晶度的增加、晶粒尺寸的增大加大了声子散射的平均自由程,因此增加了固体热导率。此外,热处理后的材料所发生收缩和烧结增大了固体纤维之间的接触面积,因此也增加了材料中的固体传导。
第二,为了研究纤维隔热材料内部辐射传热,采用测量的光谱透过率通过比尔定律计算了材料的光谱消光系数和罗斯兰德消光系数。考虑纤维隔热材料是一种吸收、发射、各向异性散射介质,对测量的热辐射性质进行了修正,定义了消光系数修正因子及等效散射反照率。建立对吸收、发射、各向异性散射弥散介质的热分析模型,并基于实验测得的瞬态热响应数据采用Levenberg-Marquardt非线性优化方法反演了材料的传导及辐射性质。采用反演的结果计算了材料的瞬态热响应及稳态有效热导率,计算与实验结果对比结果表明瞬态响应温度计算结果和实验结果的平均偏差为3.1%,而稳态有效热导率的计算结果与实验结果的平均偏差为9.8%,验证了本文所建立的纤维隔热材料传导及辐射性质的反演分析模型的可靠性。同时也证明,在中等热面温度下反演出来的传导及辐射性质结果不仅可以用来计算更低热面温度下材料的瞬态热响应,还可以向高温进一步拓展应用到980K甚至更高的温度。
第三,借鉴传统的机械设计理念,建立了热防护系统热可靠性的定义及评估方法,并首次将其推广应用到纤维隔热材料的热可靠性评估中。考虑热载荷、材料热性能及几何尺寸等参数的不确定性,基于蒙特卡洛模拟的方法对气动加热条件下的纤维隔热材料进行了概率热分析和热可靠性评估。温度响应的统计特征分析表明材料的响应温度随时间和位置的变化而不断变化;再入的开始1分钟内在发生温度滑移的位置热响应的变异系数、斜度和峰度会发生突变。各输入变量与输出变量的相关系数研究结果表明气动加热温度和初始温度对所考虑的两个位置有显著的影响,而消光系数、母材比热和实密度比对纤维隔热材料的背部温升有不可忽视的影响。此外,还建立了厚度安全因子与热可靠度之间的定量关系。为纤维隔热材料的测试、评价与设计提供了有价值的定性及定量信息。
Reusable launch vehicles entering the earth’s atmosphere at hypersonic speeds encounter aerodynamic heating. The development of reusable thermal protection system (TPS) with low-weight, low-cost, high reliability is one of the key projects in order to limit the maximum temperature of the primary structure of the vehicle during entry. High temperature fibrous insulation is an attractive insulation for the metallic TPS since it provides an excellent combination of low weight, low thermal conductivity and high service temperature. During the service life of fibrous insulation, the fibrous insulation is subject to severe aerodynamic heating. Moreover, many other environmental factors, such as debris impact, contamination, seal leakage, thermal shorts, materials aging, etc., may or may not affect performance. The complexity of various environmental factors and the requirement for high reliability make the materials response problem quite difficult. Little overheating of the primary structure of the vehicle may lead to unexpected disasters.
In present paper, thermal response behavior and thermal properties of fibrous insulation subjected to severe aerodynamic heating are investigated from three standpoints, such as materials, engineering thermophysics and reliability. The evolution of microstructures and thermal properties is observed. The determination of conductive and radiative properties for fibrous insulation is discussed. Additionally, probabilistic thermal analysis and thermal reliability assessment are conducted. The major contents and conclusions are described as follows:
Firstly, the evolution of microstructures and thermal properties for fibrous insulation before and after heat treatment is investigated by SEM, DSC, XRD and FTIR. It is found that the as-received material is amorphous. And mullite is devitrified from the original material at around 980°C. The devitrification will occur progressively with the increase of the heat treatment temperature, causing the mullite grains to grow and crystallinities increase, which reduces the flexibility of the fibers. Eventually the fibers fuse together and the product becomes brittle. The spectra of the untreated fibers show the presence of broad vibration bands which are characteristics of amorphous materials. However, after heating at 1000°C, one can observe the presence of mullite specific bands. The thermal properties correlated with the microstructure evolution are also investigated. The calculated effective thermal conductivity exhibites increase for samples after heat treatment, although no obvious increase is observed with heat treatment in the measured data. The radiative properties evolution is very complex. The devitrifation may affect the photon thermal conductivity at a certain temperature. The extinction coefficient of the sample after heat treatment at 1000℃for 16h is lower than the data of the as-received material, while the result of the sample after heat treatment at 1200℃for 16h is higher than that of the sample after heat treatment at 1000℃. It is observed that the albedo of scattering decreases after heat treatment, and decreases with the increasing of heat treatment temperatures. It should be stated that the thermal conductivity for the samples after heat treatment obviously increases, and the value for the sample after heat treatment at 1200℃for 16h triples the value for the as-received material. This phenomenon can be explained by the fact that after heat treatment, the devitrification and the increased grain size and crystallinities of the sample after heat treatment increase the mean free path of phonon scattering, thus the solid conduction by fibers increase. Furthermore, the sintering and shrinkage occurres after severe heat treatment increase the contact area among the fibers, leading to the increase in the thermal conductivity.
Secondly, in order to investigate the radiative heat transfer in fibrous insulation, spectral extinction coefficients and Rosseland mean extinction coefficients are calculated based on the Beer’s law from the measured transmittance data at various temperatures. Taking into account anisotropic scattering in fibrous insulation, the measured radiative properties are modified, and a modified factor of extinction coefficient and an equivalent albedo of scattering are defined. An inverse conduction–radiation analysis in an absorbing, emitting and scattering medium is conducted for the simultaneous estimation of the conductive and radiative properties using the experimentally measured temperature responses for external temperatures up to 980K. For validation purpose, the estimated thermal properties are used to calculate the transient temperature responses and effective thermal conductivities,which are then compared with the measured data. It is found that the calculated results correspond well with the experimental data within an average of 3.1 percent under transient condition and 9.8 percent under steady-state condition. This confirms the good behavior of the model and the validity of results.
Thirdly, the definitions for thermal protection system thermal reliability are provided borrowing from machine design approaches. And these definitions are firstly applied to thermal reliability assessment for fibrous insulation materials. The probabilistic thermal analysis of the fibrous insulation subjected to aerodynamic heating conditions is performed to account for the uncertainties such as material properties, loading conditions and geometrical variations. The statistical analysis of thermal response shows that the response temperature is significantly dependent on time and location. Large variations in the statistics parameters are observed at the location where temperature slip occurs for the first one minute of entry. To identify the dominant variables which most influence temperature response scatter, the correlation coefficients of various variables are computed. The results show that the aerodynamic heating temperature and initial temperature have significant effects for the considered locations. However, the extinction coefficient, the specific heat of virgin material and the solid fraction ratio have non-negligible effect on the back side temperature scatter of fibrous insulation. Furthermore, the relationship between the probabilistic thermal reliability and thickness factor of safety is developed. Quantitative as well as qualitative information is provided in the present methodology, which is valuable to the thermal analysis, design and testing of fibrous materials.
本文以纤维隔热材料为研究对象,基于材料要在恶劣的高温环境下高可靠性服役的要求,从材料学、工程热物理及可靠性三个学科的角度,对纤维隔热材料的热响应行为及热性质进行了多方位的研究。跟踪了受热状态下材料的微观结构及热性质的演化过程,探讨了纤维隔热材料热辐射性质及热传导性质的确定方法,同时研究了纤维隔热材料的概率热响应过程及热可靠性评估方法。本文的主要研究内容及结论如下:
第一,通过SEM、DSC、XRD、FTIR等手段研究了纤维隔热材料热处理前后的微观结构变化,结果表明:未处理的纤维隔热材料呈非晶态,表面光滑无缺陷。在980°C时析出莫来石晶体。随着热处理温度的升高,析晶过程逐步进行致使晶粒长大、结晶度增加,纤维表面变得粗糙不平,弹性降低。更高温度的热处理使纤维收缩、烧结、变脆。未处理的纤维红外光谱呈现出非晶态结构所特有的较宽的吸收谱带,而经过1000°C的热处理之后出现了莫来石晶体的特征吸收谱带。同时,对材料微结构演化所引发的材料的热性质的演化进行了考察。结果表明有效热导率实验结果在热处理前后变化并不大,而有效热导率的计算结果热处理后的比未处理态的有较为明显的增加。受热过程中材料的辐射性质演变很复杂。当达到某一温度时,晶体的析出会影响光子导热,1000℃热处理后的材料其消光系数相对于未处理材料有所降低,而经过1200℃热处理的材料消光系数又有所增加。热处理前后材料的散射反照率随着热处理温度的增加而逐渐降低。线性各向异性散射相函数的线性系数随热处理工艺的变化并不明显。热处理之后材料的传导热导率有显著的增加,并且随着热处理温度的升高,增加的幅度变大。高温热处理使材料发生析晶,结晶度的增加、晶粒尺寸的增大加大了声子散射的平均自由程,因此增加了固体热导率。此外,热处理后的材料所发生收缩和烧结增大了固体纤维之间的接触面积,因此也增加了材料中的固体传导。
第二,为了研究纤维隔热材料内部辐射传热,采用测量的光谱透过率通过比尔定律计算了材料的光谱消光系数和罗斯兰德消光系数。考虑纤维隔热材料是一种吸收、发射、各向异性散射介质,对测量的热辐射性质进行了修正,定义了消光系数修正因子及等效散射反照率。建立对吸收、发射、各向异性散射弥散介质的热分析模型,并基于实验测得的瞬态热响应数据采用Levenberg-Marquardt非线性优化方法反演了材料的传导及辐射性质。采用反演的结果计算了材料的瞬态热响应及稳态有效热导率,计算与实验结果对比结果表明瞬态响应温度计算结果和实验结果的平均偏差为3.1%,而稳态有效热导率的计算结果与实验结果的平均偏差为9.8%,验证了本文所建立的纤维隔热材料传导及辐射性质的反演分析模型的可靠性。同时也证明,在中等热面温度下反演出来的传导及辐射性质结果不仅可以用来计算更低热面温度下材料的瞬态热响应,还可以向高温进一步拓展应用到980K甚至更高的温度。
第三,借鉴传统的机械设计理念,建立了热防护系统热可靠性的定义及评估方法,并首次将其推广应用到纤维隔热材料的热可靠性评估中。考虑热载荷、材料热性能及几何尺寸等参数的不确定性,基于蒙特卡洛模拟的方法对气动加热条件下的纤维隔热材料进行了概率热分析和热可靠性评估。温度响应的统计特征分析表明材料的响应温度随时间和位置的变化而不断变化;再入的开始1分钟内在发生温度滑移的位置热响应的变异系数、斜度和峰度会发生突变。各输入变量与输出变量的相关系数研究结果表明气动加热温度和初始温度对所考虑的两个位置有显著的影响,而消光系数、母材比热和实密度比对纤维隔热材料的背部温升有不可忽视的影响。此外,还建立了厚度安全因子与热可靠度之间的定量关系。为纤维隔热材料的测试、评价与设计提供了有价值的定性及定量信息。
Reusable launch vehicles entering the earth’s atmosphere at hypersonic speeds encounter aerodynamic heating. The development of reusable thermal protection system (TPS) with low-weight, low-cost, high reliability is one of the key projects in order to limit the maximum temperature of the primary structure of the vehicle during entry. High temperature fibrous insulation is an attractive insulation for the metallic TPS since it provides an excellent combination of low weight, low thermal conductivity and high service temperature. During the service life of fibrous insulation, the fibrous insulation is subject to severe aerodynamic heating. Moreover, many other environmental factors, such as debris impact, contamination, seal leakage, thermal shorts, materials aging, etc., may or may not affect performance. The complexity of various environmental factors and the requirement for high reliability make the materials response problem quite difficult. Little overheating of the primary structure of the vehicle may lead to unexpected disasters.
In present paper, thermal response behavior and thermal properties of fibrous insulation subjected to severe aerodynamic heating are investigated from three standpoints, such as materials, engineering thermophysics and reliability. The evolution of microstructures and thermal properties is observed. The determination of conductive and radiative properties for fibrous insulation is discussed. Additionally, probabilistic thermal analysis and thermal reliability assessment are conducted. The major contents and conclusions are described as follows:
Firstly, the evolution of microstructures and thermal properties for fibrous insulation before and after heat treatment is investigated by SEM, DSC, XRD and FTIR. It is found that the as-received material is amorphous. And mullite is devitrified from the original material at around 980°C. The devitrification will occur progressively with the increase of the heat treatment temperature, causing the mullite grains to grow and crystallinities increase, which reduces the flexibility of the fibers. Eventually the fibers fuse together and the product becomes brittle. The spectra of the untreated fibers show the presence of broad vibration bands which are characteristics of amorphous materials. However, after heating at 1000°C, one can observe the presence of mullite specific bands. The thermal properties correlated with the microstructure evolution are also investigated. The calculated effective thermal conductivity exhibites increase for samples after heat treatment, although no obvious increase is observed with heat treatment in the measured data. The radiative properties evolution is very complex. The devitrifation may affect the photon thermal conductivity at a certain temperature. The extinction coefficient of the sample after heat treatment at 1000℃for 16h is lower than the data of the as-received material, while the result of the sample after heat treatment at 1200℃for 16h is higher than that of the sample after heat treatment at 1000℃. It is observed that the albedo of scattering decreases after heat treatment, and decreases with the increasing of heat treatment temperatures. It should be stated that the thermal conductivity for the samples after heat treatment obviously increases, and the value for the sample after heat treatment at 1200℃for 16h triples the value for the as-received material. This phenomenon can be explained by the fact that after heat treatment, the devitrification and the increased grain size and crystallinities of the sample after heat treatment increase the mean free path of phonon scattering, thus the solid conduction by fibers increase. Furthermore, the sintering and shrinkage occurres after severe heat treatment increase the contact area among the fibers, leading to the increase in the thermal conductivity.
Secondly, in order to investigate the radiative heat transfer in fibrous insulation, spectral extinction coefficients and Rosseland mean extinction coefficients are calculated based on the Beer’s law from the measured transmittance data at various temperatures. Taking into account anisotropic scattering in fibrous insulation, the measured radiative properties are modified, and a modified factor of extinction coefficient and an equivalent albedo of scattering are defined. An inverse conduction–radiation analysis in an absorbing, emitting and scattering medium is conducted for the simultaneous estimation of the conductive and radiative properties using the experimentally measured temperature responses for external temperatures up to 980K. For validation purpose, the estimated thermal properties are used to calculate the transient temperature responses and effective thermal conductivities,which are then compared with the measured data. It is found that the calculated results correspond well with the experimental data within an average of 3.1 percent under transient condition and 9.8 percent under steady-state condition. This confirms the good behavior of the model and the validity of results.
Thirdly, the definitions for thermal protection system thermal reliability are provided borrowing from machine design approaches. And these definitions are firstly applied to thermal reliability assessment for fibrous insulation materials. The probabilistic thermal analysis of the fibrous insulation subjected to aerodynamic heating conditions is performed to account for the uncertainties such as material properties, loading conditions and geometrical variations. The statistical analysis of thermal response shows that the response temperature is significantly dependent on time and location. Large variations in the statistics parameters are observed at the location where temperature slip occurs for the first one minute of entry. To identify the dominant variables which most influence temperature response scatter, the correlation coefficients of various variables are computed. The results show that the aerodynamic heating temperature and initial temperature have significant effects for the considered locations. However, the extinction coefficient, the specific heat of virgin material and the solid fraction ratio have non-negligible effect on the back side temperature scatter of fibrous insulation. Furthermore, the relationship between the probabilistic thermal reliability and thickness factor of safety is developed. Quantitative as well as qualitative information is provided in the present methodology, which is valuable to the thermal analysis, design and testing of fibrous materials.
引文
1夏德顺.重复运载器金属热防护系统的述评.导弹与航天运载技术. 2002, (2): 21~26
2马玉娥,孙秦,蔺国民.可重复使用运载器金属热防护系统的历史与发展动态分析.机械设计与制造. 2005, (2): 108~111
3 S. Cook. X-33 Reusable Launch Vehicle Structural Technologies. AIAA 7th International Space Planes and Hypersonic Systems and Technologies Conference. Norfolk, America, 1996-4563: 1~7
4 C. R. McClinton, V. L. Rausch, L. T. Nguyen, J. R. Sitz. Preliminary X-43 Flight Test Results. Acta Astronautica. 2005, 57: 266~276
5 M. L. Blosser. Advanced Metallic Thermal Protection Systems for Reusable Launch Vehicles. Doctoral Dissertation: University of Virginia. 2000: 32~38
6李贵佳,张伟儒,尹衍升,程之强.无机纤维隔热材料在航空航天热防护工程中的应用.陶瓷. 2004,(2): 28~31
7张克铭.陶瓷纤维衰变及损坏机理.工业炉. 2006, 28(2): 44~52
8 E. J. Rolinski, G. V. Purcell, A. E. Wechsler, P. E. Glaser. Development of High-temperature Insulation Systems. AIAA. 1966-43: 1 ~12
9奚同庚.无机材料热物性学.上海科学技术出版社. 1981: 8~10
10郑明新.工程材料.清华大学出版社. 1983: 3~13
11 F. W. Sear, G. L. Salinger,柳之琦译.热力学.高等教育出版社. 1985: 34~38
12 S. Y. Zhao, B. M. Zhang, X. D. He. Temperature and Pressure Dependent Effective Thermal Conductivity of Fibrous Insulation. International Journal of Thermal Sciences. 2009, 48: 440~448
13 M. Bomberg and S. Klarsferd. Semi-empirical Model of Heat Transfer in Dry Mineral Fiber Insulations. Journal of Thermal Insulation. 1983, (6): 156~173
14 P. J. Burns and C. L. Tien. Natural Convection in Porous Media Bounded by Concentric Spheres and Horizontal Cylinders. International Journal of Heat and Mass Transfer. 1979, 22: 929~939
15 G. N. Dulnev, Yu. P. Zarichnyak and A. V. Sharkov. Convective Heat Transfer in Fiber Materials at Elevated Pressure of Gas Medium. Inzhenerno-fizicheskii zhurnal. 1978, 35: 655~662
16 C. Stark and J. Fricke. Improved Heat-transfer Models for Fibrous Insulation. International Journal of Heat and Mass Transfer. 1993, 36: 617~625
17 K. Daryabeigi. Heat Transfer in High-Temperature Fibrous Insulation. AIAA. 2002-3332: 1~15
18 E. M. Sparrow and R. D. Cess. Radiation Heat Transfer, augmented ed.. McGraw-Hill, New York. 1978: 134~145
19 M. W. Futschik, L. C. Witte. Analysis of Effective Thermal Conductivity of Fibrous Materials. NASA-CR. 1993-31636: 56~63
20 M. Knudsen. Kinetic Theory of Gases. Methuen and Company, Ltd., London, England. 1934: 220~224
21 B. G. Dickins. The Effect of Accommodation on Heat Conduction through Gases. Proc. Royal. Soc., London A143. 1934: 517~540
22 P. Welander. Heat Conduction in a Rarefied Gas: the Cylindrically Symmetrical Case. Arkiv Fysik. 1954, 7: 555~564
23 W. D. Dewitt, R. L. Gibbon and R. L. Reid. Multi-foil Type Thermal Insulation. Proceedings of Intersociety Energy Conversion Engineering Conference. 1968: 263~271
24 S. D. Williams, D. M. Curry. Prediction of Rigid Silica Based Insulation Conductivity Using Morphological Data. Proceedings of the 29th National Heat Transfer Conference. Atlanta, Georigia, 1993: 21~28
25 J. D. Verschoor, P. Greebler and N. J. Manville. Heat Transfer by Gas Conduction and Radiation in Fibrous Insulation. Journal of Heat Transfer. 1962, 74(3): 961~968
26 C. Bankvall. Heat Transfer in Fibrous Materials. Journal of Testing and Evaluation. 1968, 1(1): 235~243
27 L. Lee and C. Y. Liu. Kinetic Theory Description of Conduction Heat Transfer from a Fine Wire. The Physics of Fluids. 1962, 5(10): 1137~1148
28 C. Y. Liu and L. Lee. Kinetic Theory Description of Plane Compressible Couette Flow. Advances in Applied Mechanics, Academic Press. New York, 1961: 391~428
29 E.M.斯帕罗, R.D.塞斯著.顾传保,张学学译.辐射传热.高等教育出版社, 1982: 229~234
30 T. Stauffer, M. Joy and P. Ayyaswamy. The Effective Thermal Conductivity of Multi-foil Insulation as a Function of Temperature and Pressure. The 27th AIAA Thermiphysics Conference. Nashville,Tennessee, 1992: 1~18
31 J. D. Verschoor, P. Greebler and N. J. Manville. Heat Transfer by Gas Conduction and Radiation in Fibrous Insulation. Journal of Heat Transfer. 1962, 74(3): 961~968
32 N. E. Hager, R. C. Steere. Radiant Heat Transfer in Fibrous Thermal Insulation. J. Appl. Phys. 1967, 38(12): 4663~4668
33 K. Daryabeigi. Thermal Analysis and Design of Multi-layer Insulation for Re-entry Aerodynamic Heating. AIAA. 2001-2834: 1~15
34 I. H. Tavman. Effective Thermal Conductivity of Isotropic Polymer Composites. Int.Comm. Heat Mass Transfer. 1998, 25: 723~732
35 S. D. Williams and D. M. Curry. Predictions of Rigid Silica Based Insulation Conductivity. NASA TP. 1993-3276: 1~20
36 N. E. Hager, R. C. Steere. Radiation Heat Transfer in Fibrous Thermal Insulation. Journel of Applied Physics. 1967, 38(2): 4663~4668
37 C. Bankvall. Heat transfer in fibrous materials. Journal of testing and evaluation. 1973, 1: 235~243
38 L. A. Dombrovsky. Quartz-Fiber Thermal Insulation: Infrared Radiative Properties and Calculation of Radiative-Conductivity Heat Transfer. Journal of heat transfer Transactions of the ASME. 1996, 118: 408~414
39 R. K. Bhattacharyya. Heat transfer model for fibrous insulations. Thermal insulation performance, ASTM STP 718. ed. by D.L. McElroy and R. P. Tye, American Society for Testing and Materials. Philadelphia, PA, 1980: 272~286
40余其铮.辐射换热原理.哈尔滨工业大学出版社, 2000: 108~110
41 M. F. Modest. Radiative heat transfer, second edition. California: Academic Press, 2003: 235~245
42何诚. DRESOR法求解一维各向异性散射介质中的辐射传递方程.华中科技大学硕士学位论文. 2005: 7~18
43 L. A. Dmobrovsky. Quartz-fiber Thermal Insualiton: Infrared Radiation Properties and Calculation of Radiativ-conductive Heat Transfer. Journal of heat transfer. 1996, 118(3): 408~414
44 J. Marschall, J. Maddren, J. Parks. Internal Radiation Transport and Effective Thermal Conductivity of Fibrous Ceramic Insulations. AIAA. 2001-2822:1~15
45 H. C. Hottel, A. F. Sarofim. Radiative transfer. New York, McGraw-Hill, 1967: 345~354
46 J. M. Hammersley, D. C. Handscomb. Monte Carlo Methods. New York, John Wiley &Sons, 1964: 165~178
47 H. C. Hottel, E. S. Cohen. Radiative Heat Exchange in a Gas-filled Enclosure: Allowance for Nonuniformity of Gas Temperature. AIChE Journal. 1958, 4: 3~14
48 J. R. Howell. The Monte Carlo Method in Radiative Heat Transfer. ASME Proceedings of the 7th AIAA/ASME Joint Thermophisics and Heat Transfer Conference. 1998, 357(1): 1~19
49 M. R. Louthan, R. P. Jr. McNitt and R. D. Sisson. Materials Degradation in Space Environments. AIAA. 1979-1508: 1~6
50 A. N. Gaodu, N. V. Pitak, R. E. Volfson and M. E. Drizheruk. Inorg.Mater.. 1977, 49: 1802
51 G. Vine, J. Young and I. W. Nowell. Ann. Occup. Hyg.. 1984, 28 (3): 356
52 L. E. Olds, W. C. Miller and J. M. Pallo. Am. Ceram. Soc. Bull.. 1980, 59 (7): 739
53 M. P. Belyakova, V. F. Kutukov, V. M. Ust’yantsev and M. G. Tretnikova. Inorg. Mater.. 1981, 17: 948
54 J. Khorami, A. Lemieux, J. Dunnigan, D. Nadeau, Induced Conversion of Aluminium Silicate Fibers into Mullite and Cristobalite by Elevated Temperatures: a Comparative Study on Two Commercial Products. Thermochimica Acta. 1987, 120: 1~7
55 D. J. Dyson, M. A. Butler, R. J. Hughes, R. Fisher and G. W. Hicks. The De-vitrificaiton of Alumino-silicate Ceramic Fiber Materials—the Kinetics of the Formation of Different Crystalline Phase. British Occuoational Hygiene Society. 1997, 41(5): 561~590
56 G. G. Tibbetts, A. K. Sachdev, A. M. Wims, V. Franetovic. Grain Growth in Alumina-silica Fibers. Journal of Materials Science. 1999, 34: 1017~1023
57操光辉,吴申庆,舒光冀.硅酸铝纤维及其预制件的结构转变特性.铸造. 1998, 1: 14~17
58曾令可,黄浪欢,罗民华,孙宇彤,张明,程小苏,王慧.使用环境对硅酸铝纤维性能的影响.华南理工大学学报(自然科学版). 2001, 29(8): 73~76
59 A. K. Bhattacharyya, B. N. Choudhury, P. Chintaiah, P. Das. Studies on a Probable Correlation between Thermal Conductivity, Kinetics of Devitrification and Changes in Fiber Radius of an Aluminosilicate Ceramic Vitreous Fiber on Heat Treatment. Ceramics International. 2002, 28: 711~717
60 A. Michot, D. S. Smith, S. Degot, C. Gault. Thermal Conductivity and Specific Heat of Kaolinite: Evolution with Thermal Treatment. Journal of the European Ceramic Society. 2008, in press
61 D. A. Stewart, D. B. Leiser, P. Kolodziej and M. Smith. Thermal Response of Integral, Multicomponent Composite Thermal Protection Systems. Journal of Spacecraft & Rockets. 1986, 23: 420~427
62 D. Baillis, J. F. Sacadura. Thermal Radiation Properties of Dispersed Media: Theoretical Prediction and Experimental Characterization. Journal of Quantitative Spectroscopy & Radiative Transfer. 2000, 67: 327~363
63 S. C. Lee. Effect of Fiber Orientation on Thermal Radiation in Fibrous Media. International Journal of Heat and Mass Transfer. 1989, 32(2): 311~319
64 G. R. Cunnington and S. C. Lee. Radiative Properties of Fibrous Insulations: Theory Versus Experiment. Journal of Thermophysics and Heat Transfer. 1996, 10(3): 460~466
65 S. C. Lee and G. R. Cunnington. Heat Transfer in Fibrous Insulations: Comparison of Theory and Experiment. Journal of Thermophysics and Heat Transfer. 1998,12(3): 297~302
66 P. Boulet, G. Jeandel and G. Morlot. Model of Radiative Transfer in Fibrous Media—Matrix Method. International Journal of Heat and Mass Transfer. 1993, 36: 4287~4297
67 L. A. Dombrovsky. Quartz-fiber Thermal Insulation: Infrared Radiative Properties and Calculation of Radiative-Conductive Heat transfer. Journal of Heat Transfer Transactions of the ASME. 1996, 118: 408~414
68 V. A. Petrov. Combined Radiation and Conduction Heat Transfer in High Temperature Fiber Thermal Insulation. International Journal of Heat and Mass Transfer. 1997, 40(9): 2241~2247
69 N. J. McCormick. Inverse Radiative Transfer Problems: a Review. Nucl. Sci. Eng.. 1992, 112: 185~198
70 L. Dombrovsky, J. Randrianalisoa and D. Baillis. Modified Two-flux Approximation for Identification of Radiative Properties of Absorbing and Scattering Media from Directional-hemispherical Measurements. J. Opt. Soc. Am.. 2006, 23(1): 91~98
71 V. P. Nicolau, M. Raynaud and J. F. Sacadura. Spectral Radiative Properties Identification of Fiber Insulating Materials. International Journal of Heat and Mass Transfer. 1994, 37: 311~324
72 A. Milandri, F. Asllanaj, G. Jeandel. Determination of Radiative Properties of Fibrous Media by an Inverse Method—Comparison with the Mie Theory. Journal of Quantitative Spectroscopy & Radiative Transfer. 2002, 74: 637~653
73 D. Baillis, M. Arduini-Schuster, J. F. Sacadura. Identification of Spectral Radiative Properties of Polyurethane Foam from Hemispherical and Bi-directional Transmittance and Reflectance Measurements. Journal of Quantitative Spectroscopy & Radiative Transfer. 2002, 73: 297~306
74 T. W. Tong, D. L. McEroy, D. W. Yarbrough. Analysis of Transient Heat Transfer Measurements on Porous Thermal Insulations. Journal of Thermal Insulation. 1986, 10: 31~46
75 D. L. McEroy, R. S. Graves, D. W. Yarbrough and T. W. Tong. Non-steady-state Behavior of Thermal Insulations. Journal of Thermal insulation. 1986, 9: 236~249
76 T. W. Tong, D. L. McEroy and D. W. Yarbrough. Transient Conduction and Radiation Heat Transfer in Porous Thermal Insulations. Journal of Thermal Insulation. 1985, 9: 13~29
77 T. W. Tong and C. L. Tien. Analytical Models for Thermal Radiation in Fibrous Insulation. Journal of Thermal Insulation. 1980, 4: 27~44
78 S. Manickavasagam, M. P. Menguc. Inverse Radiation/conduction Problem inPlane-parallel Media, Radiative Heat Transfer: Theory and Applications. ASME-HTD. 1993-244: 67~75
79 C. Zied, A. Fethi, B. N. Sassi. Measurement of Thermal Radiative and Conductive Properties of Semitransparent Materials using a Photothermal Crenel Method. Journal of Quantitative Spectroscopy & Radiative Transfer. 2008, 109: 620~635
80 A. A. Mittenbergs. The Materials Problem in Structural Reliability. AIAA. 1966-2521: 148~158
81 T. W. Clyne, I. O. Golosnoy, J. C. Tan, A. E. Markaki. Porous Materials for Thermal Management under Extreme Conditions. Philosophical Transactions of the Royal Society A. 2006, 364: 125~146
82 J. W. Haney. Orbiter Entry Heating Lessons Learned from Development Flight Test Program. NASA CP. 1983-2283: 719~752
83 D. J. Rasky, P. Kolodziej, M. E. Newfield, B. Laub, Y. K. Chen. Assessing Factors of Safety, Margins of Safety, and Reliability of Thermal Protection Systems. AIAA. 2003-4043: 1~8
84 P. Kolodziej, D. J. Rasky, E. Venkatapathy. Estimates of the Orbiter Thermal Protection System Reliability. AIAA. 2003-3766: 1~20
85 D. Xiu, G. E. Kamiadakis. A New Stochastic Approach to Transient Heat Conduction Modeling with Uncertainty. Int. J. Heat Mass Transfer. 2003, 46: 4681~4693
86 T. Nakamura. Transient Heat Transfer Analysis using Stochastic Finite Element Method. The 20th Symposium on Reliability of Materials and Structures. Kyoto, 2004: 1~10
87 M. Kamiński, T. D. Hien. Stochastic Finite Element Modeling of Transient Heat Transfer in Layered Composites. Int.Comm.Heat Mass Transfer. 1999, 26(6): 801~810
88 T. D. Hien, M. Kleiber. On Solving Nonlinear Transient Heat Transfer Problems with Random Parameters. Comput. Methods Appl. Mech. Engrg. 1998, 151: 287~299
89 T. D. Hien, M. Kleiber. Stochastic Finite Element Modeling in Linear Transient Heat Transfer. Comput. Methods Appl. Mech. Engrg.. 1997, 144: 111~124
90 M. Kamiński. Monte-Carlo Simulation of Effective Conductivity for Fiber Composites. Int. Comm. Heat Mass Transfer. 1999, 26(6): 791~800
91 S. L. Smith, G. B. Spear, M. D.Cornwell. Statistical Monte Carlo Prediction for Thermal Reliability. AIAA. 1994-3183: 1~10
92李金平,陈建军,刘海峰,徐健,黄宵忭.基于Neumann展开Monte-Carlo有限元法的随机温度场分析.西安电子科技大学学报. 2007, 34(3): 453~457
93王小兵,陈建军,梁震涛,李金平.随机温度场Monte-Carlo法的一类近似处理.系统仿真学报. 2007, 19(10): 2156~2164
94邢建申,王树彬,张跃.石英纤维析晶行为.复合材料学报. 2006, 23(6): 75~79
95崔之开.非晶质纤维受热结构变化的探讨.工业加热. 1983, (4): 13~17
96张克铭,李焰.多晶莫来石耐火纤维及其应用技术.冶金工业出版社.北京, 1992: 23
97 J. Leivo, M. Linden , J. M. Rosenholm, M. Ritola, C. V. Teixeira, E. Levanen, T. A. Mantyla. Evolution of Aluminosilicate Structure and Mullite Crystallization from Homogeneous Nanoparticulate Sol–gel Precursor with Organic Additives. Journal of the European Ceramic Society. 2008, 28: 1749~1762
98 J. P. Brazel and B. S. Kennedy. Thermal Conductivity Measurement on Mullite and Silica REI for Space Shuttle: Complementary Guarded Hot Plate and Radial Outflow Measurement. In advances in Thermal conductivity. 1974, 3: 74~82
99 W. T. Engelke. Suitable Steady State Methods for Measurement of Effective Thermal Conductivity in Rigid Insulations. In Heat Transmission Measurement in Thermal Insulations. ASTM STP. 1974-554: 118~134
100 E. Y. Litovsky, S. L. Bondarenko, Y. A. Polonsky and N. I. Gashichev. Infulence of Fiber Diameter on Effective Thermal Conductivity of Thermal Insulation. Teplofizika Vysokikh Temperature. 1979, 17: 997~1000
101 D. A. Stewart, D. B. Leiser, P. Kolodziej and M. Smith. Thermal Response of Integral, Multicomponent Composite Thermal Protection Systems. Journal of Spacecraft & Rockets. 1986, 23: 420~427
102 K. Daryabeigi. Effective Thermal Conductivity of High Temperature Insulation for Reusable Launch Vehicle. NASA/TM. 1999- 208972:1~30
103耐火材料导热系数试验方法(平行热线法).中国国家标准. GB/T17106-1997
104耐火材料导热系数试验方法(水流量平板法).中华人民共和国黑色冶金行业标准. YB/T 4130-2005
105耐火陶瓷纤维制品导热系数试验方法.中华人民共和国国家标准. GB/T17911.8-2002
106 V. Giaretto, E. Miraldi, G. Ruscica. Simultaneous Estimations of Radiative and Conductive Properties in Lightweight Insulating Materials. High Temp.-High Press. 1995/1996, 27/28: 191~204
107 R. Siegel, J. R. Howell. Thermal Radiation Heat Transfer. Taylor & Francis. London, 1992: 335
108 E. M. Sparrow, and R. D. Cess. Radiation Heat Transfer augmented ed.. McGraw-Hill, New York, 1978: 255~271
109 J. Bernard. On the Mean Value Theorem for Integrals. Amer. Math. Monthly. 1982, 89(5): 300~301
110 A. S. Jamaluddin, P. J. Smith. Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method. Combustion Science and Technology. 1988, 59: 321~340
111刘林华、谈和平、余其铮.半透明平板边界入射辐射热流密度的反问题.计算物理. 1999, 16(3): 235~242
112刘玉英,Thomas Kabayabaya,张欣欣.闪光法测量半透明材料热扩散率的理论研究.北京科技大学学报. 2006, 28 (7): 681~686
113 J. V. Beck, K. J. Arnold. Parameter Estimation in Engineering and Science. Wiley, New York, 1977: 179~192
114 M. N. Ozisik. Heat Conduction, 2nd Edition. Wiley, New York, 1993: 241
115 D. W. Marquardt. An Algorithm for Least-squares Estimation of Non-linear Parameters. Journal of the Society for Industrial and Applied Mathematics. 1963, 11: 431~441
116 A. Fguiri, N. Daouas, N. Borjini, M. S. Radhouani. Experimental Inverse Analysis for the Determination of Boundary Conditions in the Parallel Hot Wire Technique. Experimental Thermal and Fluid Science. 2007, 31: 209~220
117 N. J. McCormick. Inverse Radiative Transfer Problems: a review. Nucl. Sci. Eng.. 1992, 112: 185~198
118袁荫棠.概率论与数理统计.中国人民大学出版社.北京, 1985: 131~136
119 M. E. Pate-Cornell and P. S. Fischbeck. Risk Management for the Tiles of the Space Shuttle. Interfaces. 1994, 24(1): 64~86
120 J. R. Fragola. Probabilistic Risk Asssessment of the Space Shuttle: A Study of the Potential of Losing the Vehicle During Nominal Operations. Volume I Final Report. SAIC/NY. 1995- 02-05: 3~10
121李湘洲.“哥伦比亚”号坠毁与表面防热材料.金属世界. 2003, 4: 4~8
122 A. A. Mittenbergs. The Matertials Problem in Structural Reliability. AIAA. 1966-2521: 1~10
123 W. W. Yuen, E. Takara, G. Cunnington. Combined Conductive/radiative Heat Transfer in High Porosity Fibrous Insulation Mmaterials: Theory and Experiment. TED-AJ. 2003-126:1~10
124 B. M. Ayyub and R. H. McCuen. Probability, Statistics and Reliability for Engineers. CRC Press, 1997: 171
2马玉娥,孙秦,蔺国民.可重复使用运载器金属热防护系统的历史与发展动态分析.机械设计与制造. 2005, (2): 108~111
3 S. Cook. X-33 Reusable Launch Vehicle Structural Technologies. AIAA 7th International Space Planes and Hypersonic Systems and Technologies Conference. Norfolk, America, 1996-4563: 1~7
4 C. R. McClinton, V. L. Rausch, L. T. Nguyen, J. R. Sitz. Preliminary X-43 Flight Test Results. Acta Astronautica. 2005, 57: 266~276
5 M. L. Blosser. Advanced Metallic Thermal Protection Systems for Reusable Launch Vehicles. Doctoral Dissertation: University of Virginia. 2000: 32~38
6李贵佳,张伟儒,尹衍升,程之强.无机纤维隔热材料在航空航天热防护工程中的应用.陶瓷. 2004,(2): 28~31
7张克铭.陶瓷纤维衰变及损坏机理.工业炉. 2006, 28(2): 44~52
8 E. J. Rolinski, G. V. Purcell, A. E. Wechsler, P. E. Glaser. Development of High-temperature Insulation Systems. AIAA. 1966-43: 1 ~12
9奚同庚.无机材料热物性学.上海科学技术出版社. 1981: 8~10
10郑明新.工程材料.清华大学出版社. 1983: 3~13
11 F. W. Sear, G. L. Salinger,柳之琦译.热力学.高等教育出版社. 1985: 34~38
12 S. Y. Zhao, B. M. Zhang, X. D. He. Temperature and Pressure Dependent Effective Thermal Conductivity of Fibrous Insulation. International Journal of Thermal Sciences. 2009, 48: 440~448
13 M. Bomberg and S. Klarsferd. Semi-empirical Model of Heat Transfer in Dry Mineral Fiber Insulations. Journal of Thermal Insulation. 1983, (6): 156~173
14 P. J. Burns and C. L. Tien. Natural Convection in Porous Media Bounded by Concentric Spheres and Horizontal Cylinders. International Journal of Heat and Mass Transfer. 1979, 22: 929~939
15 G. N. Dulnev, Yu. P. Zarichnyak and A. V. Sharkov. Convective Heat Transfer in Fiber Materials at Elevated Pressure of Gas Medium. Inzhenerno-fizicheskii zhurnal. 1978, 35: 655~662
16 C. Stark and J. Fricke. Improved Heat-transfer Models for Fibrous Insulation. International Journal of Heat and Mass Transfer. 1993, 36: 617~625
17 K. Daryabeigi. Heat Transfer in High-Temperature Fibrous Insulation. AIAA. 2002-3332: 1~15
18 E. M. Sparrow and R. D. Cess. Radiation Heat Transfer, augmented ed.. McGraw-Hill, New York. 1978: 134~145
19 M. W. Futschik, L. C. Witte. Analysis of Effective Thermal Conductivity of Fibrous Materials. NASA-CR. 1993-31636: 56~63
20 M. Knudsen. Kinetic Theory of Gases. Methuen and Company, Ltd., London, England. 1934: 220~224
21 B. G. Dickins. The Effect of Accommodation on Heat Conduction through Gases. Proc. Royal. Soc., London A143. 1934: 517~540
22 P. Welander. Heat Conduction in a Rarefied Gas: the Cylindrically Symmetrical Case. Arkiv Fysik. 1954, 7: 555~564
23 W. D. Dewitt, R. L. Gibbon and R. L. Reid. Multi-foil Type Thermal Insulation. Proceedings of Intersociety Energy Conversion Engineering Conference. 1968: 263~271
24 S. D. Williams, D. M. Curry. Prediction of Rigid Silica Based Insulation Conductivity Using Morphological Data. Proceedings of the 29th National Heat Transfer Conference. Atlanta, Georigia, 1993: 21~28
25 J. D. Verschoor, P. Greebler and N. J. Manville. Heat Transfer by Gas Conduction and Radiation in Fibrous Insulation. Journal of Heat Transfer. 1962, 74(3): 961~968
26 C. Bankvall. Heat Transfer in Fibrous Materials. Journal of Testing and Evaluation. 1968, 1(1): 235~243
27 L. Lee and C. Y. Liu. Kinetic Theory Description of Conduction Heat Transfer from a Fine Wire. The Physics of Fluids. 1962, 5(10): 1137~1148
28 C. Y. Liu and L. Lee. Kinetic Theory Description of Plane Compressible Couette Flow. Advances in Applied Mechanics, Academic Press. New York, 1961: 391~428
29 E.M.斯帕罗, R.D.塞斯著.顾传保,张学学译.辐射传热.高等教育出版社, 1982: 229~234
30 T. Stauffer, M. Joy and P. Ayyaswamy. The Effective Thermal Conductivity of Multi-foil Insulation as a Function of Temperature and Pressure. The 27th AIAA Thermiphysics Conference. Nashville,Tennessee, 1992: 1~18
31 J. D. Verschoor, P. Greebler and N. J. Manville. Heat Transfer by Gas Conduction and Radiation in Fibrous Insulation. Journal of Heat Transfer. 1962, 74(3): 961~968
32 N. E. Hager, R. C. Steere. Radiant Heat Transfer in Fibrous Thermal Insulation. J. Appl. Phys. 1967, 38(12): 4663~4668
33 K. Daryabeigi. Thermal Analysis and Design of Multi-layer Insulation for Re-entry Aerodynamic Heating. AIAA. 2001-2834: 1~15
34 I. H. Tavman. Effective Thermal Conductivity of Isotropic Polymer Composites. Int.Comm. Heat Mass Transfer. 1998, 25: 723~732
35 S. D. Williams and D. M. Curry. Predictions of Rigid Silica Based Insulation Conductivity. NASA TP. 1993-3276: 1~20
36 N. E. Hager, R. C. Steere. Radiation Heat Transfer in Fibrous Thermal Insulation. Journel of Applied Physics. 1967, 38(2): 4663~4668
37 C. Bankvall. Heat transfer in fibrous materials. Journal of testing and evaluation. 1973, 1: 235~243
38 L. A. Dombrovsky. Quartz-Fiber Thermal Insulation: Infrared Radiative Properties and Calculation of Radiative-Conductivity Heat Transfer. Journal of heat transfer Transactions of the ASME. 1996, 118: 408~414
39 R. K. Bhattacharyya. Heat transfer model for fibrous insulations. Thermal insulation performance, ASTM STP 718. ed. by D.L. McElroy and R. P. Tye, American Society for Testing and Materials. Philadelphia, PA, 1980: 272~286
40余其铮.辐射换热原理.哈尔滨工业大学出版社, 2000: 108~110
41 M. F. Modest. Radiative heat transfer, second edition. California: Academic Press, 2003: 235~245
42何诚. DRESOR法求解一维各向异性散射介质中的辐射传递方程.华中科技大学硕士学位论文. 2005: 7~18
43 L. A. Dmobrovsky. Quartz-fiber Thermal Insualiton: Infrared Radiation Properties and Calculation of Radiativ-conductive Heat Transfer. Journal of heat transfer. 1996, 118(3): 408~414
44 J. Marschall, J. Maddren, J. Parks. Internal Radiation Transport and Effective Thermal Conductivity of Fibrous Ceramic Insulations. AIAA. 2001-2822:1~15
45 H. C. Hottel, A. F. Sarofim. Radiative transfer. New York, McGraw-Hill, 1967: 345~354
46 J. M. Hammersley, D. C. Handscomb. Monte Carlo Methods. New York, John Wiley &Sons, 1964: 165~178
47 H. C. Hottel, E. S. Cohen. Radiative Heat Exchange in a Gas-filled Enclosure: Allowance for Nonuniformity of Gas Temperature. AIChE Journal. 1958, 4: 3~14
48 J. R. Howell. The Monte Carlo Method in Radiative Heat Transfer. ASME Proceedings of the 7th AIAA/ASME Joint Thermophisics and Heat Transfer Conference. 1998, 357(1): 1~19
49 M. R. Louthan, R. P. Jr. McNitt and R. D. Sisson. Materials Degradation in Space Environments. AIAA. 1979-1508: 1~6
50 A. N. Gaodu, N. V. Pitak, R. E. Volfson and M. E. Drizheruk. Inorg.Mater.. 1977, 49: 1802
51 G. Vine, J. Young and I. W. Nowell. Ann. Occup. Hyg.. 1984, 28 (3): 356
52 L. E. Olds, W. C. Miller and J. M. Pallo. Am. Ceram. Soc. Bull.. 1980, 59 (7): 739
53 M. P. Belyakova, V. F. Kutukov, V. M. Ust’yantsev and M. G. Tretnikova. Inorg. Mater.. 1981, 17: 948
54 J. Khorami, A. Lemieux, J. Dunnigan, D. Nadeau, Induced Conversion of Aluminium Silicate Fibers into Mullite and Cristobalite by Elevated Temperatures: a Comparative Study on Two Commercial Products. Thermochimica Acta. 1987, 120: 1~7
55 D. J. Dyson, M. A. Butler, R. J. Hughes, R. Fisher and G. W. Hicks. The De-vitrificaiton of Alumino-silicate Ceramic Fiber Materials—the Kinetics of the Formation of Different Crystalline Phase. British Occuoational Hygiene Society. 1997, 41(5): 561~590
56 G. G. Tibbetts, A. K. Sachdev, A. M. Wims, V. Franetovic. Grain Growth in Alumina-silica Fibers. Journal of Materials Science. 1999, 34: 1017~1023
57操光辉,吴申庆,舒光冀.硅酸铝纤维及其预制件的结构转变特性.铸造. 1998, 1: 14~17
58曾令可,黄浪欢,罗民华,孙宇彤,张明,程小苏,王慧.使用环境对硅酸铝纤维性能的影响.华南理工大学学报(自然科学版). 2001, 29(8): 73~76
59 A. K. Bhattacharyya, B. N. Choudhury, P. Chintaiah, P. Das. Studies on a Probable Correlation between Thermal Conductivity, Kinetics of Devitrification and Changes in Fiber Radius of an Aluminosilicate Ceramic Vitreous Fiber on Heat Treatment. Ceramics International. 2002, 28: 711~717
60 A. Michot, D. S. Smith, S. Degot, C. Gault. Thermal Conductivity and Specific Heat of Kaolinite: Evolution with Thermal Treatment. Journal of the European Ceramic Society. 2008, in press
61 D. A. Stewart, D. B. Leiser, P. Kolodziej and M. Smith. Thermal Response of Integral, Multicomponent Composite Thermal Protection Systems. Journal of Spacecraft & Rockets. 1986, 23: 420~427
62 D. Baillis, J. F. Sacadura. Thermal Radiation Properties of Dispersed Media: Theoretical Prediction and Experimental Characterization. Journal of Quantitative Spectroscopy & Radiative Transfer. 2000, 67: 327~363
63 S. C. Lee. Effect of Fiber Orientation on Thermal Radiation in Fibrous Media. International Journal of Heat and Mass Transfer. 1989, 32(2): 311~319
64 G. R. Cunnington and S. C. Lee. Radiative Properties of Fibrous Insulations: Theory Versus Experiment. Journal of Thermophysics and Heat Transfer. 1996, 10(3): 460~466
65 S. C. Lee and G. R. Cunnington. Heat Transfer in Fibrous Insulations: Comparison of Theory and Experiment. Journal of Thermophysics and Heat Transfer. 1998,12(3): 297~302
66 P. Boulet, G. Jeandel and G. Morlot. Model of Radiative Transfer in Fibrous Media—Matrix Method. International Journal of Heat and Mass Transfer. 1993, 36: 4287~4297
67 L. A. Dombrovsky. Quartz-fiber Thermal Insulation: Infrared Radiative Properties and Calculation of Radiative-Conductive Heat transfer. Journal of Heat Transfer Transactions of the ASME. 1996, 118: 408~414
68 V. A. Petrov. Combined Radiation and Conduction Heat Transfer in High Temperature Fiber Thermal Insulation. International Journal of Heat and Mass Transfer. 1997, 40(9): 2241~2247
69 N. J. McCormick. Inverse Radiative Transfer Problems: a Review. Nucl. Sci. Eng.. 1992, 112: 185~198
70 L. Dombrovsky, J. Randrianalisoa and D. Baillis. Modified Two-flux Approximation for Identification of Radiative Properties of Absorbing and Scattering Media from Directional-hemispherical Measurements. J. Opt. Soc. Am.. 2006, 23(1): 91~98
71 V. P. Nicolau, M. Raynaud and J. F. Sacadura. Spectral Radiative Properties Identification of Fiber Insulating Materials. International Journal of Heat and Mass Transfer. 1994, 37: 311~324
72 A. Milandri, F. Asllanaj, G. Jeandel. Determination of Radiative Properties of Fibrous Media by an Inverse Method—Comparison with the Mie Theory. Journal of Quantitative Spectroscopy & Radiative Transfer. 2002, 74: 637~653
73 D. Baillis, M. Arduini-Schuster, J. F. Sacadura. Identification of Spectral Radiative Properties of Polyurethane Foam from Hemispherical and Bi-directional Transmittance and Reflectance Measurements. Journal of Quantitative Spectroscopy & Radiative Transfer. 2002, 73: 297~306
74 T. W. Tong, D. L. McEroy, D. W. Yarbrough. Analysis of Transient Heat Transfer Measurements on Porous Thermal Insulations. Journal of Thermal Insulation. 1986, 10: 31~46
75 D. L. McEroy, R. S. Graves, D. W. Yarbrough and T. W. Tong. Non-steady-state Behavior of Thermal Insulations. Journal of Thermal insulation. 1986, 9: 236~249
76 T. W. Tong, D. L. McEroy and D. W. Yarbrough. Transient Conduction and Radiation Heat Transfer in Porous Thermal Insulations. Journal of Thermal Insulation. 1985, 9: 13~29
77 T. W. Tong and C. L. Tien. Analytical Models for Thermal Radiation in Fibrous Insulation. Journal of Thermal Insulation. 1980, 4: 27~44
78 S. Manickavasagam, M. P. Menguc. Inverse Radiation/conduction Problem inPlane-parallel Media, Radiative Heat Transfer: Theory and Applications. ASME-HTD. 1993-244: 67~75
79 C. Zied, A. Fethi, B. N. Sassi. Measurement of Thermal Radiative and Conductive Properties of Semitransparent Materials using a Photothermal Crenel Method. Journal of Quantitative Spectroscopy & Radiative Transfer. 2008, 109: 620~635
80 A. A. Mittenbergs. The Materials Problem in Structural Reliability. AIAA. 1966-2521: 148~158
81 T. W. Clyne, I. O. Golosnoy, J. C. Tan, A. E. Markaki. Porous Materials for Thermal Management under Extreme Conditions. Philosophical Transactions of the Royal Society A. 2006, 364: 125~146
82 J. W. Haney. Orbiter Entry Heating Lessons Learned from Development Flight Test Program. NASA CP. 1983-2283: 719~752
83 D. J. Rasky, P. Kolodziej, M. E. Newfield, B. Laub, Y. K. Chen. Assessing Factors of Safety, Margins of Safety, and Reliability of Thermal Protection Systems. AIAA. 2003-4043: 1~8
84 P. Kolodziej, D. J. Rasky, E. Venkatapathy. Estimates of the Orbiter Thermal Protection System Reliability. AIAA. 2003-3766: 1~20
85 D. Xiu, G. E. Kamiadakis. A New Stochastic Approach to Transient Heat Conduction Modeling with Uncertainty. Int. J. Heat Mass Transfer. 2003, 46: 4681~4693
86 T. Nakamura. Transient Heat Transfer Analysis using Stochastic Finite Element Method. The 20th Symposium on Reliability of Materials and Structures. Kyoto, 2004: 1~10
87 M. Kamiński, T. D. Hien. Stochastic Finite Element Modeling of Transient Heat Transfer in Layered Composites. Int.Comm.Heat Mass Transfer. 1999, 26(6): 801~810
88 T. D. Hien, M. Kleiber. On Solving Nonlinear Transient Heat Transfer Problems with Random Parameters. Comput. Methods Appl. Mech. Engrg. 1998, 151: 287~299
89 T. D. Hien, M. Kleiber. Stochastic Finite Element Modeling in Linear Transient Heat Transfer. Comput. Methods Appl. Mech. Engrg.. 1997, 144: 111~124
90 M. Kamiński. Monte-Carlo Simulation of Effective Conductivity for Fiber Composites. Int. Comm. Heat Mass Transfer. 1999, 26(6): 791~800
91 S. L. Smith, G. B. Spear, M. D.Cornwell. Statistical Monte Carlo Prediction for Thermal Reliability. AIAA. 1994-3183: 1~10
92李金平,陈建军,刘海峰,徐健,黄宵忭.基于Neumann展开Monte-Carlo有限元法的随机温度场分析.西安电子科技大学学报. 2007, 34(3): 453~457
93王小兵,陈建军,梁震涛,李金平.随机温度场Monte-Carlo法的一类近似处理.系统仿真学报. 2007, 19(10): 2156~2164
94邢建申,王树彬,张跃.石英纤维析晶行为.复合材料学报. 2006, 23(6): 75~79
95崔之开.非晶质纤维受热结构变化的探讨.工业加热. 1983, (4): 13~17
96张克铭,李焰.多晶莫来石耐火纤维及其应用技术.冶金工业出版社.北京, 1992: 23
97 J. Leivo, M. Linden , J. M. Rosenholm, M. Ritola, C. V. Teixeira, E. Levanen, T. A. Mantyla. Evolution of Aluminosilicate Structure and Mullite Crystallization from Homogeneous Nanoparticulate Sol–gel Precursor with Organic Additives. Journal of the European Ceramic Society. 2008, 28: 1749~1762
98 J. P. Brazel and B. S. Kennedy. Thermal Conductivity Measurement on Mullite and Silica REI for Space Shuttle: Complementary Guarded Hot Plate and Radial Outflow Measurement. In advances in Thermal conductivity. 1974, 3: 74~82
99 W. T. Engelke. Suitable Steady State Methods for Measurement of Effective Thermal Conductivity in Rigid Insulations. In Heat Transmission Measurement in Thermal Insulations. ASTM STP. 1974-554: 118~134
100 E. Y. Litovsky, S. L. Bondarenko, Y. A. Polonsky and N. I. Gashichev. Infulence of Fiber Diameter on Effective Thermal Conductivity of Thermal Insulation. Teplofizika Vysokikh Temperature. 1979, 17: 997~1000
101 D. A. Stewart, D. B. Leiser, P. Kolodziej and M. Smith. Thermal Response of Integral, Multicomponent Composite Thermal Protection Systems. Journal of Spacecraft & Rockets. 1986, 23: 420~427
102 K. Daryabeigi. Effective Thermal Conductivity of High Temperature Insulation for Reusable Launch Vehicle. NASA/TM. 1999- 208972:1~30
103耐火材料导热系数试验方法(平行热线法).中国国家标准. GB/T17106-1997
104耐火材料导热系数试验方法(水流量平板法).中华人民共和国黑色冶金行业标准. YB/T 4130-2005
105耐火陶瓷纤维制品导热系数试验方法.中华人民共和国国家标准. GB/T17911.8-2002
106 V. Giaretto, E. Miraldi, G. Ruscica. Simultaneous Estimations of Radiative and Conductive Properties in Lightweight Insulating Materials. High Temp.-High Press. 1995/1996, 27/28: 191~204
107 R. Siegel, J. R. Howell. Thermal Radiation Heat Transfer. Taylor & Francis. London, 1992: 335
108 E. M. Sparrow, and R. D. Cess. Radiation Heat Transfer augmented ed.. McGraw-Hill, New York, 1978: 255~271
109 J. Bernard. On the Mean Value Theorem for Integrals. Amer. Math. Monthly. 1982, 89(5): 300~301
110 A. S. Jamaluddin, P. J. Smith. Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method. Combustion Science and Technology. 1988, 59: 321~340
111刘林华、谈和平、余其铮.半透明平板边界入射辐射热流密度的反问题.计算物理. 1999, 16(3): 235~242
112刘玉英,Thomas Kabayabaya,张欣欣.闪光法测量半透明材料热扩散率的理论研究.北京科技大学学报. 2006, 28 (7): 681~686
113 J. V. Beck, K. J. Arnold. Parameter Estimation in Engineering and Science. Wiley, New York, 1977: 179~192
114 M. N. Ozisik. Heat Conduction, 2nd Edition. Wiley, New York, 1993: 241
115 D. W. Marquardt. An Algorithm for Least-squares Estimation of Non-linear Parameters. Journal of the Society for Industrial and Applied Mathematics. 1963, 11: 431~441
116 A. Fguiri, N. Daouas, N. Borjini, M. S. Radhouani. Experimental Inverse Analysis for the Determination of Boundary Conditions in the Parallel Hot Wire Technique. Experimental Thermal and Fluid Science. 2007, 31: 209~220
117 N. J. McCormick. Inverse Radiative Transfer Problems: a review. Nucl. Sci. Eng.. 1992, 112: 185~198
118袁荫棠.概率论与数理统计.中国人民大学出版社.北京, 1985: 131~136
119 M. E. Pate-Cornell and P. S. Fischbeck. Risk Management for the Tiles of the Space Shuttle. Interfaces. 1994, 24(1): 64~86
120 J. R. Fragola. Probabilistic Risk Asssessment of the Space Shuttle: A Study of the Potential of Losing the Vehicle During Nominal Operations. Volume I Final Report. SAIC/NY. 1995- 02-05: 3~10
121李湘洲.“哥伦比亚”号坠毁与表面防热材料.金属世界. 2003, 4: 4~8
122 A. A. Mittenbergs. The Matertials Problem in Structural Reliability. AIAA. 1966-2521: 1~10
123 W. W. Yuen, E. Takara, G. Cunnington. Combined Conductive/radiative Heat Transfer in High Porosity Fibrous Insulation Mmaterials: Theory and Experiment. TED-AJ. 2003-126:1~10
124 B. M. Ayyub and R. H. McCuen. Probability, Statistics and Reliability for Engineers. CRC Press, 1997: 171