非均质粒子及其团聚物的辐射特性
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摘要
非均质粒子及其团聚物的辐射特性在燃烧系统、航空航天和大气环境等工程应用中有着广泛深入的研究。在燃烧系统中,煤灰辐射特性的相关实验测量过程繁琐且耗资费时,以及航天器喷射出的相变液滴和多层粒子的辐射特性获得困难。气溶胶中包覆水层和灰尘掺杂的碳黑团聚物辐射特性,以及碳黑团聚物辐射特性的等效计算方法也有待进一步的研究。因而有必要从理论上进一步深入研究非均质粒子及其团聚物的辐射特性。
本文结合有效介质理论与Mie理论研究多组分煤灰粒子、水及氧化铝相变粒子和多层球形粒子的辐射特性,利用有效介质理论结合T矩阵方法,研究大气中碳黑团聚物的辐射特性。主要工作包括以下五个方面:
1.采用有效介质理论和Mie理论研究了多组分人工合成灰渣和天然煤灰粒子的辐射特性,分析了有效介质理论的适用范围。由于煤灰实际组分不同于其相应的工业分析成分,基于工业分析成分有效介质理论结合Mie理论不适用于燃烧生成煤灰的辐射特性计算,但适用于人工合成灰渣。
2.发展了计算多层球粒辐射特性的蒙特卡罗光线踪迹法。对比光线踪迹法和包覆层粒子电磁理论,分析了有效介质理论计算相变粒子辐射特性的适用性,以及有效介质理论计算多层球形粒子辐射特性的适用范围。研究结果表明,有效介质理论结合Mie理论适用于水和氧化铝相变粒子辐射特性的计算。对于多层非均质大粒子,层间折射率和消光系数偏差较小时,有效介质理论结合Mie理论可用来近似估算多层粒子的辐射特性。
3.建立了液滴、液滴层辐射相变模型,分析了液滴温度随时间的变化关系,研究了空间液滴辐射散热器中液滴层流速、粒径分布、液滴相变、液滴层厚、液滴浓度和工质种类对液滴层辐射换热的影响。结果表明在单个液滴相变换热过程中,水滴的蒸发和太阳辐射对液滴温度的影响显著。液滴层内的相变区域和温度分布表明,相变对换热过程的影响不可忽略。
4.采用T矩阵方法研究了炉内不同形态碳黑团聚物的辐射特性,评估了基于体积、投影面积、回转半径及体积和投影面积比等效的球形近似方法计算碳黑团聚物辐射特性的适用性。结果表明:炉内团聚物的辐射特性随形态参数变化较小。四种等效近似法中,对于吸收截面,基于体积和投影面积比等效的近似方法较其它方法偏差小;而对于散射相函数,投影面积近似法的偏差较其它近似法小。
5.利用有效介质理论结和T矩阵法,研究了气溶胶中相对湿度变化时两种形态(枝节状与密实状)团聚物的辐射特性,并分析了包覆水层厚度、灰尘混合结构和掺杂体积分数以及粒径分布对团聚物辐射特性的影响。相对湿度从10%增加到100%时,密实状团聚物的散射截面相对于枝节状散射截面的最大偏差为48.8%,水的包覆导致粒径增加是改变团聚物辐射特性的主要因素。另外,灰尘与碳黑混合结构对团聚辐射特性影响很小。
Research on the radiative properties of inhomogeneous particle and soot aggregate is wide and deep in many engineering applications, especial in the aerospace and atmosphere. However, the radiative properties of coal ash in the furnace are hard to determine from the experimental. The multilayer code of electromagnetism theory always appears overflow when the size parameter becomes larger. The radiative properties of the inhomogeneous coal ash, phase-changing droplets and multilayer particle are also hard to determine in practice. Furthermore, the estimation of the radiative properties of soot aggregate coated with water and adulterated with dust in atmosphere. Approximation methods also need further investigated. Therefore, it is necessary to employ the theoretical model to these inhomogeneous particles for calculating their radiative properties.
In the present thesis, the radiative properties of inhomogeneous particles, including coal ash, phase-change particles for water, silica, and alumina, as well as multilayer particles, are investigated by effective medium theory in combination with Mie theory. On the other hands, the radiative property of soot aggregate in atmosphere is studied by effective medium theory in combination with T-matrix method. In summary, the scope covered in this dissertation consists of the following five parts:
1. The radiative properties of multi-component synthetic ash and crude ash were investigated by effective medium theory (EMT) in combination with Mie theory, and the applicability of this approach is subsequently analyzed. In principle, the effective medium theory based on industrial analytical species can not be applied to coal ash produced in combustion. While it can be used to analyze synthetic ash slag.
2. Monte-Carlo ray-tracing method (MCRTM) is developed for calculating the radiative properties of multilayer sphere. The applicability of effective medium theory for phase-change particle and multilayer sphere were analyzed in comparison with the BHCOAT code and the MCRTM. And the applicable range of EMT is subsequently analyzed. The results reveal that it is capable of calculating the effective radiative properties of water and alumina by EMT in combination of Mie theory. For the multilayer spherical particle, where each layer has different optical constant, the MCRTM is approximately applicable to calculate the radiative property of multilayer spherical particle by combining EMT with Mie theory, in the case of the deviation between refractive index and extinction coefficient is small.
3. For phase-change particle, phase-change models for droplet and droplet layer are constructed. The corresponding phase process for droplet and droplet layer is then analyzed, respectively. The results reveal that the method of combined effective medium theory and Mie theory is applicable for calculating the radiative properties of phase-change particles. In radiation phase-change process of heat transfer, the evaporation of water droplet in amount and energy irradiated by sun can not be ignored. On the other hand, phase zone and temperature distribution in droplet layer show that the effect of phase-change of droplet on the heat transfer process can not be ignored.
4. Radiative properties of soot aggregate with different morphologies are studied. The applicability of spherical approximation method for computing radiative properties of soot aggregate is estimated and compared with that of T-matrix method, where the spherical approximation method is based on equal volume, equal project area, the radius of gyration, and volume and volume-to-projected area ratio. The computation results show that the radiative properties of soot aggregates vary only slightly with morphologies. For absorption cross section, the values of approximation method based on the volume-to-projected area ratio have the smallest deviation in comparison with that of T-matrix method. Meanwhile, for the scattering phase function, the values from approximation method have the smallest deviation in comparison with that of T-matrix method.
5. By combining effective medium theory with T-matrix method, the effects of two typically morphological structures, water coating, dust mixing and primary particle size distribution on the radiative properties of soot fractal aggregates in atmosphere are investigated using T-matrix method. The results show that the effect of morphological changes on the radiative properties of soot aggregates can not be neglected in wet air, and the largest relative deviation of their scattering cross section is found to be 48.8%. Furthermore, the radiative properties of soot aggregates coated with water increase notably with an increase in the thickness of water shell. On the other hand, the mixing structures of dust are found to have slightly effect on radiative properties of aggregates.
本文结合有效介质理论与Mie理论研究多组分煤灰粒子、水及氧化铝相变粒子和多层球形粒子的辐射特性,利用有效介质理论结合T矩阵方法,研究大气中碳黑团聚物的辐射特性。主要工作包括以下五个方面:
1.采用有效介质理论和Mie理论研究了多组分人工合成灰渣和天然煤灰粒子的辐射特性,分析了有效介质理论的适用范围。由于煤灰实际组分不同于其相应的工业分析成分,基于工业分析成分有效介质理论结合Mie理论不适用于燃烧生成煤灰的辐射特性计算,但适用于人工合成灰渣。
2.发展了计算多层球粒辐射特性的蒙特卡罗光线踪迹法。对比光线踪迹法和包覆层粒子电磁理论,分析了有效介质理论计算相变粒子辐射特性的适用性,以及有效介质理论计算多层球形粒子辐射特性的适用范围。研究结果表明,有效介质理论结合Mie理论适用于水和氧化铝相变粒子辐射特性的计算。对于多层非均质大粒子,层间折射率和消光系数偏差较小时,有效介质理论结合Mie理论可用来近似估算多层粒子的辐射特性。
3.建立了液滴、液滴层辐射相变模型,分析了液滴温度随时间的变化关系,研究了空间液滴辐射散热器中液滴层流速、粒径分布、液滴相变、液滴层厚、液滴浓度和工质种类对液滴层辐射换热的影响。结果表明在单个液滴相变换热过程中,水滴的蒸发和太阳辐射对液滴温度的影响显著。液滴层内的相变区域和温度分布表明,相变对换热过程的影响不可忽略。
4.采用T矩阵方法研究了炉内不同形态碳黑团聚物的辐射特性,评估了基于体积、投影面积、回转半径及体积和投影面积比等效的球形近似方法计算碳黑团聚物辐射特性的适用性。结果表明:炉内团聚物的辐射特性随形态参数变化较小。四种等效近似法中,对于吸收截面,基于体积和投影面积比等效的近似方法较其它方法偏差小;而对于散射相函数,投影面积近似法的偏差较其它近似法小。
5.利用有效介质理论结和T矩阵法,研究了气溶胶中相对湿度变化时两种形态(枝节状与密实状)团聚物的辐射特性,并分析了包覆水层厚度、灰尘混合结构和掺杂体积分数以及粒径分布对团聚物辐射特性的影响。相对湿度从10%增加到100%时,密实状团聚物的散射截面相对于枝节状散射截面的最大偏差为48.8%,水的包覆导致粒径增加是改变团聚物辐射特性的主要因素。另外,灰尘与碳黑混合结构对团聚辐射特性影响很小。
Research on the radiative properties of inhomogeneous particle and soot aggregate is wide and deep in many engineering applications, especial in the aerospace and atmosphere. However, the radiative properties of coal ash in the furnace are hard to determine from the experimental. The multilayer code of electromagnetism theory always appears overflow when the size parameter becomes larger. The radiative properties of the inhomogeneous coal ash, phase-changing droplets and multilayer particle are also hard to determine in practice. Furthermore, the estimation of the radiative properties of soot aggregate coated with water and adulterated with dust in atmosphere. Approximation methods also need further investigated. Therefore, it is necessary to employ the theoretical model to these inhomogeneous particles for calculating their radiative properties.
In the present thesis, the radiative properties of inhomogeneous particles, including coal ash, phase-change particles for water, silica, and alumina, as well as multilayer particles, are investigated by effective medium theory in combination with Mie theory. On the other hands, the radiative property of soot aggregate in atmosphere is studied by effective medium theory in combination with T-matrix method. In summary, the scope covered in this dissertation consists of the following five parts:
1. The radiative properties of multi-component synthetic ash and crude ash were investigated by effective medium theory (EMT) in combination with Mie theory, and the applicability of this approach is subsequently analyzed. In principle, the effective medium theory based on industrial analytical species can not be applied to coal ash produced in combustion. While it can be used to analyze synthetic ash slag.
2. Monte-Carlo ray-tracing method (MCRTM) is developed for calculating the radiative properties of multilayer sphere. The applicability of effective medium theory for phase-change particle and multilayer sphere were analyzed in comparison with the BHCOAT code and the MCRTM. And the applicable range of EMT is subsequently analyzed. The results reveal that it is capable of calculating the effective radiative properties of water and alumina by EMT in combination of Mie theory. For the multilayer spherical particle, where each layer has different optical constant, the MCRTM is approximately applicable to calculate the radiative property of multilayer spherical particle by combining EMT with Mie theory, in the case of the deviation between refractive index and extinction coefficient is small.
3. For phase-change particle, phase-change models for droplet and droplet layer are constructed. The corresponding phase process for droplet and droplet layer is then analyzed, respectively. The results reveal that the method of combined effective medium theory and Mie theory is applicable for calculating the radiative properties of phase-change particles. In radiation phase-change process of heat transfer, the evaporation of water droplet in amount and energy irradiated by sun can not be ignored. On the other hand, phase zone and temperature distribution in droplet layer show that the effect of phase-change of droplet on the heat transfer process can not be ignored.
4. Radiative properties of soot aggregate with different morphologies are studied. The applicability of spherical approximation method for computing radiative properties of soot aggregate is estimated and compared with that of T-matrix method, where the spherical approximation method is based on equal volume, equal project area, the radius of gyration, and volume and volume-to-projected area ratio. The computation results show that the radiative properties of soot aggregates vary only slightly with morphologies. For absorption cross section, the values of approximation method based on the volume-to-projected area ratio have the smallest deviation in comparison with that of T-matrix method. Meanwhile, for the scattering phase function, the values from approximation method have the smallest deviation in comparison with that of T-matrix method.
5. By combining effective medium theory with T-matrix method, the effects of two typically morphological structures, water coating, dust mixing and primary particle size distribution on the radiative properties of soot fractal aggregates in atmosphere are investigated using T-matrix method. The results show that the effect of morphological changes on the radiative properties of soot aggregates can not be neglected in wet air, and the largest relative deviation of their scattering cross section is found to be 48.8%. Furthermore, the radiative properties of soot aggregates coated with water increase notably with an increase in the thickness of water shell. On the other hand, the mixing structures of dust are found to have slightly effect on radiative properties of aggregates.
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61 S. P. Neshyba, T. C. Grenfell, S. G. Warren. Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 2. Hexagonal columns and plates. Journal of Geophysical Research. 2003, 108(D15): AAC6.1-AAC6.18
62 T. C. Grenfell, S. P. Neshyba, S. G. Warren. Representation of nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 3. Hollow columns and plates. Journal of Geophysical Research. 2005, 110: D17203
63 A. F. Khalizov, H. Xue, L. Wang, J. Zheng, R. Zhang. Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid. Journal of Physical Chemistry A. 2009, 113(6): 1066-1074
64 G. Hanel. The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air. Advances in Geophysics. 1976, 19: 74-83
65 M. Kocifaj, F. Kundracik, G. Videen. Optical properties of single mixed-phase aerosol particles. Journal of Quantitative Spectroscopy & Radiative Transfer. 2008, 109(11): 2108-2123
66 A. D. Clarke, Y. Shinozuka, V. N. Kapustin, S. Howell, B. Huebert, S. Doherty,T. Anderson, D. Convert, J. Anderson, X. Hua, K. G. Moore, C. McNaughton, G. Carmichael, R. Weber. Size distributions and mixtures of dust and black carbon aerosol in Asian outflow: physiochemistry and optical properties. Journal of Geophysical Research. 2004, 109(D15): D15S09.1- D15S09.20
67 M. I. Mishchenko, L. Liu, L. D. Travis, A. A. Lacis. Scattering and radiative properties of semi-external versus external mixtures of different aerosol types. Journal of Quantitative Spectroscopy & Radiative Transfer. 2004, 88(1-3): 139-147
68 L. Liu, M. I. Mishchenko. Scattering and radiative properties of complex soot and soot-containing aggregate particles. Journal of Quantitative Spectroscopy & Radiative Transfer. 2007, 106(1-3): 262-273
69 Y. Hirooka, J. Won, R. Boivin, D. Sze, V. Neumoin, M. Dubois-Violette, T. Masson, T. L. Farias, U. O. Koylu, M. G. Carvalho. Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot. Journal of Quantitative Spectroscopy & Radiative Transfer. 1996, 55(3): 357-371
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71殷之文.电介质物理学.北京:科学出版社, 2003.
72 E. D. Palik. Handbook of optical constant of solids. New York: Academic Press. 1985: 753-765
73 T. C. Choy. Effective medium theory-principle and applications. Oxford University Press. 1999: 7-15
74 M I. Mishchenko. Light scattering by randomly oriented axially symmetric particles. Journal of the Optical Society of America. A, Optics, Image Science, and Vision. 1991, 8: 871-882
75 E. D. Palik. Handbook of Optical Constant of Solids. 2nd edition. New York: Academic Press. 1991: 765-775
76 S. Onari, T. Arai, K. Kudo. Infrared lattice vibration and dielectric dispersion inα-Fe2O3. Physical Review B. 1977, 16(4): 1717-1721
77 S. A. Self. Optical properties of flyash. Standford University. 1989: 1-29
78 A. G.. Blokh. Heat transfer in stream boiler furnaces. Berlin: Springer Verlag, 1988.
79吴淑岱.工业企业环境保护手册.北京:中国环境科学出版社, 1990.
80郑大伟,翁祖炘,朱瑾,曾锦清,杜志谦.焚化灰渣电浆熔融之熔渣资源化技术与特性研究.第十八届废弃物处理技术研讨会议文集.中国台中, 2003.
81黄明政,郑大伟,曾锦清,邱文通,杨升府.电浆熔融焚化灰渣的著色处理及资源化研究.第二届资源工程研讨会议论文集.中国台南, 2005.
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84 R. Siegel. Transient radiative cooling of a layer filled with solidifying drops. Journal of Heat Transfer. 1987, 109(4): 977-982
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89 M. L. Lang, W. L. Wolfe. Optical constants of fused and sapphire from 0.3 to 25μm. Applied Optics. 1983, 22(9): 1267-1268
90 D. L. Parry, M. Q. Brewster. Optical constant of Al2O3 smoke in propellant flames. Journal of thermophysics and Heat Transfer. 1991, 5(2): 142-149
91 L. H. Liu. Multiple size group analysis for transient radiative heating of particle polydispersions. Journal of Quantitative Spectroscopy & Radiative Transfer. 2003, 76(2): 225-234
92 L. H. Liu. A concept of multi-scale modeling for radiative heat transfer in particle polydispersions. Journal of Quantitative Spectroscopy & Radiative Transfer. 2003, 78(2): 227-233
93 M. Q. Brewster. Thermal radiative transfer and properties. New York: Wiley. 1992.
94 T. A. Witten, L. M. Sander. Diffusion-limited aggregation. Physics Review B. 1983, 27(9): 5686-5697
95 A. V. Filippov, M. Zurita, D. E. Rosner. Fractal-like aggregates: relation between morphology and physical properties. Journal of Colloid and Interface Science. 2000, 229(1): 261-273
96 U. O. Koylu, G. M. Faeth. Structure of overfire soot in buoyant turbulent diffusion flamed at long residence times. Combustion and Flame. 1992, 89(2): 140-156
97 A. M. Brasil, T. L. Farias, M. G. Carvalho. A recipe for image characterization of fractal-like aggregates. Journal Aerosol Science. 1999, 30(10): 1379-1389
98 K. Tian, F. S. Liu, K. A. Thomson, D. R. Snelling, G. J. Smallwood, D. S. Wang. Distribution of the number of primary particles of soot aggregates in a nonpremixed laminar flame. Combustion and Flame. 2004, 138(1-2): 195-198
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59 F. Liu, M. Yang, F. A. Hill, D. R. Snelling, G. J. Smallwood. Influence of polydisperse distributions of both primary particle and aggregate size on soot temperature in low-fluence LII. Applied Physics. B, Laser and Optics. 2006, 83(3): 383-395
60 T. C. Grenfell, S. G. Warren. Representation of nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation. Journal of Geophysical Research. 1999, 104(d24): 31697-31709
61 S. P. Neshyba, T. C. Grenfell, S. G. Warren. Representation of a nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 2. Hexagonal columns and plates. Journal of Geophysical Research. 2003, 108(D15): AAC6.1-AAC6.18
62 T. C. Grenfell, S. P. Neshyba, S. G. Warren. Representation of nonspherical ice particle by a collection of independent spheres for scattering and absorption of radiation: 3. Hollow columns and plates. Journal of Geophysical Research. 2005, 110: D17203
63 A. F. Khalizov, H. Xue, L. Wang, J. Zheng, R. Zhang. Enhanced light absorption and scattering by carbon soot aerosol internally mixed with sulfuric acid. Journal of Physical Chemistry A. 2009, 113(6): 1066-1074
64 G. Hanel. The properties of atmospheric aerosol particles as functions of the relative humidity at thermodynamic equilibrium with the surrounding moist air. Advances in Geophysics. 1976, 19: 74-83
65 M. Kocifaj, F. Kundracik, G. Videen. Optical properties of single mixed-phase aerosol particles. Journal of Quantitative Spectroscopy & Radiative Transfer. 2008, 109(11): 2108-2123
66 A. D. Clarke, Y. Shinozuka, V. N. Kapustin, S. Howell, B. Huebert, S. Doherty,T. Anderson, D. Convert, J. Anderson, X. Hua, K. G. Moore, C. McNaughton, G. Carmichael, R. Weber. Size distributions and mixtures of dust and black carbon aerosol in Asian outflow: physiochemistry and optical properties. Journal of Geophysical Research. 2004, 109(D15): D15S09.1- D15S09.20
67 M. I. Mishchenko, L. Liu, L. D. Travis, A. A. Lacis. Scattering and radiative properties of semi-external versus external mixtures of different aerosol types. Journal of Quantitative Spectroscopy & Radiative Transfer. 2004, 88(1-3): 139-147
68 L. Liu, M. I. Mishchenko. Scattering and radiative properties of complex soot and soot-containing aggregate particles. Journal of Quantitative Spectroscopy & Radiative Transfer. 2007, 106(1-3): 262-273
69 Y. Hirooka, J. Won, R. Boivin, D. Sze, V. Neumoin, M. Dubois-Violette, T. Masson, T. L. Farias, U. O. Koylu, M. G. Carvalho. Effects of polydispersity of aggregates and primary particles on radiative properties of simulated soot. Journal of Quantitative Spectroscopy & Radiative Transfer. 1996, 55(3): 357-371
70方容川.固体光谱学.合肥:中国科学技术大学出版社, 2001.
71殷之文.电介质物理学.北京:科学出版社, 2003.
72 E. D. Palik. Handbook of optical constant of solids. New York: Academic Press. 1985: 753-765
73 T. C. Choy. Effective medium theory-principle and applications. Oxford University Press. 1999: 7-15
74 M I. Mishchenko. Light scattering by randomly oriented axially symmetric particles. Journal of the Optical Society of America. A, Optics, Image Science, and Vision. 1991, 8: 871-882
75 E. D. Palik. Handbook of Optical Constant of Solids. 2nd edition. New York: Academic Press. 1991: 765-775
76 S. Onari, T. Arai, K. Kudo. Infrared lattice vibration and dielectric dispersion inα-Fe2O3. Physical Review B. 1977, 16(4): 1717-1721
77 S. A. Self. Optical properties of flyash. Standford University. 1989: 1-29
78 A. G.. Blokh. Heat transfer in stream boiler furnaces. Berlin: Springer Verlag, 1988.
79吴淑岱.工业企业环境保护手册.北京:中国环境科学出版社, 1990.
80郑大伟,翁祖炘,朱瑾,曾锦清,杜志谦.焚化灰渣电浆熔融之熔渣资源化技术与特性研究.第十八届废弃物处理技术研讨会议文集.中国台中, 2003.
81黄明政,郑大伟,曾锦清,邱文通,杨升府.电浆熔融焚化灰渣的著色处理及资源化研究.第二届资源工程研讨会议论文集.中国台南, 2005.
82 M. Harald. Database of optical constants for cosmic dust: optical constants of silicates. Laboratory Astrophysics Group of the AIU Jena. 2004.
83 L. H. Liu, H. P. Tan, T. W. Tong. Internal distribution of radiation absorption in a semitransparent spherical particle. Journal of Quantitative Spectroscopy & Radiative Transfer. 2002, 72(6): 747-756
84 R. Siegel. Transient radiative cooling of a layer filled with solidifying drops. Journal of Heat Transfer. 1987, 109(4): 977-982
85周力行.湍流气粒两相流动和燃烧的理论与数值模拟.北京:科学出版社. 1994: 76-80
86王补宣.工程传热传质学.北京:科学出版社. 2002: 401-405
87 G. M. Hale, M. R. Querry. Optical constants of water in the 200-nm to 200-μm wavelength region. Applied Optics. 1973, 12(3): 555-563
88 S. G. Warren. Optical constants of ice from the ultraviolet to the microwave. Applied Optics. 1984, 23(5): 1206-1225
89 M. L. Lang, W. L. Wolfe. Optical constants of fused and sapphire from 0.3 to 25μm. Applied Optics. 1983, 22(9): 1267-1268
90 D. L. Parry, M. Q. Brewster. Optical constant of Al2O3 smoke in propellant flames. Journal of thermophysics and Heat Transfer. 1991, 5(2): 142-149
91 L. H. Liu. Multiple size group analysis for transient radiative heating of particle polydispersions. Journal of Quantitative Spectroscopy & Radiative Transfer. 2003, 76(2): 225-234
92 L. H. Liu. A concept of multi-scale modeling for radiative heat transfer in particle polydispersions. Journal of Quantitative Spectroscopy & Radiative Transfer. 2003, 78(2): 227-233
93 M. Q. Brewster. Thermal radiative transfer and properties. New York: Wiley. 1992.
94 T. A. Witten, L. M. Sander. Diffusion-limited aggregation. Physics Review B. 1983, 27(9): 5686-5697
95 A. V. Filippov, M. Zurita, D. E. Rosner. Fractal-like aggregates: relation between morphology and physical properties. Journal of Colloid and Interface Science. 2000, 229(1): 261-273
96 U. O. Koylu, G. M. Faeth. Structure of overfire soot in buoyant turbulent diffusion flamed at long residence times. Combustion and Flame. 1992, 89(2): 140-156
97 A. M. Brasil, T. L. Farias, M. G. Carvalho. A recipe for image characterization of fractal-like aggregates. Journal Aerosol Science. 1999, 30(10): 1379-1389
98 K. Tian, F. S. Liu, K. A. Thomson, D. R. Snelling, G. J. Smallwood, D. S. Wang. Distribution of the number of primary particles of soot aggregates in a nonpremixed laminar flame. Combustion and Flame. 2004, 138(1-2): 195-198
99 E. F. Mikhailov, S. S. Vlasenko, I. A. Podgorny, V. Ramanathan, C. E. Corrigan. Optical properties of soot-water drop agglomerates: an experimental study. Journal of Geophysical Research. 2006, 111: D07209
100 M. I. Mishchenko. Light scattering by randomly oriented axially symmetric particles. Journal of the Optical Society of America A: Optics, Image Science, and Vision. 1991, 8(6): 871-882
101 D. W. Mackowski, M. I. Mishchenko. Calculation of the T matrix and the scattering matrix for ensembles of spheres. Journal of the Optical Society of America A: Optics, Image Science, and Vision. 1996, 13: 2266-2278
102 F. S. Liu, G. J. Smallwood. Radiative properties of numerically generated fractal soot aggregates: the importance of configuration averaging. Journal of Heat Transfer. 2010, 132(2): 023308
103 G. A. d'Almeida, P. Koepke, E.P. Shettle. Atmospheric aerosols: global climatology and radiative characteristics. Hanpton: VA Deepak, 1991.
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