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Research Papers: Radiative Heat Transfer

Modeling of Spectral Properties and the Scattering Phase Function for Lightweight Heat Protection Spacecraft Materials

[+] Author and Article Information
Valery V. Cherepanov

Mem. ASME
Department of Physics,
Moscow Aviation Institute
(National Research University),
Volokolamskoe Highway, 4, A-80, GSP-3,
Moscow 124993, Russia
e-mail: bold2010@live.ru

Oleg M. Alifanov

Department of Space Systems Engineering,
Moscow Aviation Institute
(National Research University),
Volokolamskoe Highway, 4, A-80, GSP-3,
Moscow 124993, Russia
e-mail: o.alifanov@yandex.ru

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received March 28, 2016; final manuscript received September 20, 2016; published online November 16, 2016. Editor: Dr. Portonovo S. Ayyaswamy.

J. Heat Transfer 139(3), 032701 (Nov 16, 2016) (9 pages) Paper No: HT-16-1153; doi: 10.1115/1.4034814 History: Received March 28, 2016; Revised September 20, 2016

This work gives a brief description of the statistical model that takes into account when calculating the physical, in particular, the optical properties of some ultraporous nonmetallic high-temperature materials, the real regularities of the material structure, and the physical properties of substances constituting the material. For the spectral part of the model, some tests are presented, confirming its adequacy. The simulation of the spectra and the scattering of monochromatic radiation pattern by using the representative elements of the model and the material as a whole are carried out. It is found that despite the fact that the scattering pattern based on the use of representative elements of a material can be approximated by the classical distributions, this is not true for the material as a whole. Calculations of the angular scattering probability density of the materials are carried out, and the approximations of obtained distributions that extend the class of modeling scattering phase functions (SPF) are proposed.

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Figures

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Fig. 1

The extinction efficiency of an infinitely long cylinder versus the diffraction parameter x = kR and the incident angle α. The relative refractive index m = 1.6 (ε = 2.56 and μ = 1). (a) Dependencies QexE(x) for different values of the incident angle α. (b) Dependencies QexE(α) and QexH(α) for different values of the diffraction parameter x.

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Fig. 2

Microstructure of the fibrous material TZMK-10 (bar = 10 μm)

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Fig. 3

Unnormalized scattering pattern for one of the representative elementary volumes of fibrous material TZMK-10 in spherical (a) and polar (b) coordinates. Direction of illumination θi = 60 deg and φi = 0 deg. Wavelength λ = 1.15 μm. Sizes of fragments (μm): dx = 3.1422, lx = 301.79, Lx = 29.284; dy = 4.0878 e, ly = 304.13, Ly = 29.284; and dz = 3.2798, lz = 296.37, Lz = 16.269.

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Fig. 4

The spectral weighting function f and the coefficients for the same representative element, as in Fig. 3: (a) the absorption α and scattering β and (b) the transport radiation diffusion coefficient D and the mean free path of photons l. T = 700 K, lighting direction θi = 60 deg, and φi = 15 deg.

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Fig. 5

Influence of the parameter g of the radiation model on the structure of the non-normalized SPF of TZMK-10 in polar coordinates. λ = 0.63 μm and Т = 600 K. (a) g = 0.3, (b) g = 0.4, (c) g = 0.5, (d) g = 0.6, and (e) g = 0.8.

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Fig. 6

The spectral scattering pattern for TZMK-10 in spherical and polar coordinates for different wavelengths. g = 0.3 and T = 600 K. (a) λ = 0.63 μm, (b) λ = 1.15 μm, and (c) λ = 3.9 μm.

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Fig. 7

Unnormalized probability density of the material TZMK-10 distribution in the scattering angle in polar coordinates and its approximation, λ = 0.63 μm: - - - - - - - calculated curve of Fig. 6(a) and - - - - - approximation (2)

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