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研究生:王佳銘
研究生(外文):Jia-Ming Wang
論文名稱:以離散方向法解具可變折射係數與散漫入射的暫態輻射熱傳
論文名稱(外文):Discrete ordinates methods for transient radiative transfer in a slab with variable refractive index and diffuse irradiation
指導教授:吳志陽
指導教授(外文):C.Y. Wu
學位類別:碩士
校院名稱:國立成功大學
系所名稱:機械工程學系碩博士班
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2008
畢業學年度:96
語文別:中文
論文頁數:95
中文關鍵詞:離散方向法散漫入射可變折射係數暫態輻射熱傳
外文關鍵詞:diffuse irradiationtransient radiative transfervariable refractive indexdiscrete ordinates method
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本研究中,修改離散方向法來解具可變折射係數平板的暫態輻射熱傳。介質考慮吸收及散射輻射,平板的一邊突然曝露於散漫入射,另一邊則為散漫反射。本模擬採用四種方法,包括以donor-cell內差的離散方向法,以van Leer內差的離散方向法,以donor-cell內差的修正的離散方向法,以van Leer內差的修正的離散方向法,其計算結果將與蒙地卡羅法所得到的結果作比較。這些方法的結果比較顯示,在暫態輻射熱傳的起始階段,以van Leer內差的離散方向法的結果比以donor-cell內差的離散方向法的結果較少數值擴散,而兩個修正的離散方向法則是優於普通的離散方向法。接著,求各種光學厚度、散射比和基底反射率的線性可變折射係數平板的時間分解半球反射率( R )與半球穿透率( T )。這些結果顯示:(1) R曲線和T曲線在折射係數的平均值較大時,需要更多的時間到達穩態,而在 時,在穩態的R值隨著折射係數梯度的增加而減少。相對的,在穩態的T值則隨著折射係數梯度的增加而增加。 (2)穩態的R值隨著基底反射率增加而增加,然而穩態的T值則隨著 的減少而增加。 (3) 穩態的R值隨著散射比的增加而增加,R曲線則在散射比較大時,需要更多的時間到達穩態。
In this work, the discrete ordinates method has been adapted to solve transient radiative transfer in a graded index slab suddenly exposed to a diffuse strong irradiation at one of its boundaries. The medium is absorbing, scattering, and the other boundary is diffusely reflecting. The simulation is based on four methods, including the discrete ordinates method ( DOM ) with donor-cell interpolation, the DOM with van Leer interpolation, the modified DOM with donor-cell interpolation and the modified DOM with van Leer interpolation. The computational results are compared with those obtained by the Monte Carlo method. The comparison of the results by these methods shows that the results obtained by the DOM with van Leer interpolation has less numerical diffusion than the DOM with donor-cell interpolation at the early stage of the transient radiative transfer. The two modified DOM’s are superior to the two ordinary DOM’s. The time-resolved hemispherical reflectance ( R ) and transmittance ( T ) of the slabs with linearly varying refractive index are obtained for various optical thicknesses, scattering albedos and substrate reflectances. Effects of these parameters on transient radiative transfer in the planer media are investigated. The results show that (і) Both the R curve and the T curve for the case with a larger average of refractive index take more time to reach the plateau. For the case with the value of R on the plateau decreases with the increase of refractive index gradient. By contrast, the value of T on the plateau increases with the increase of refractive index gradient. (іі) The value of R on the plateau increase with the increases of substrate reflectance, while the value of T on the plateau increases with the decrease of . (ііі) The value of R on the plateau increases with the increase of albedo and the R curve for the case with a larger albedo takes more time to reach the plateau.
中文摘要.............................................................................................................i
英文摘要.............................................................................................................ii
誌謝.....................................................................................................................iv
目錄.....................................................................................................................v
表目錄.................................................................................................................vii
圖目錄.................................................................................................................viii
符號說明.............................................................................................................xii

第一章 緒論........................................................................................................1
1.1 研究動機、背景與文獻回顧....................................................................1
1.2 研究目的與方法簡介................................................................................2
1.3 本文架構....................................................................................................2
第二章 理論分析
2.1 物理模型和基本假設................................................................................4
2.2 數學模式....................................................................................................5
2.2.1 暫態輻射熱傳遞方程式.......................................................................5
2.2.2 將熱輻射強度分成兩部分應用在暫態輻射熱傳遞方程式...............6
2.2.3 熱輻射參數的表示式...........................................................................12
第三章 數值方法................................................................................................15
3.1 離散方向法................................................................................................15
3.2 修正的離散方向法....................................................................................23
第四章 結果與討論............................................................................................33
4.1 數值方法的比較........................................................................................33
4.2 參數之影響討論........................................................................................38
第五章 結論........................................................................................................42
參考文獻.............................................................................................................44
1. S. kumar, K. Mitra, “Microscale aspects of thermal radiation transport and laser applications,” Advances in Heat Transfer, Vol. 33, Academic Press, New York, pp. 187-294, 1999.
2. J. M. Stone, D. Mihalas, “Upwind Monotonic Interpolation Methods for the Solution of the Time Dependent Radiative Transfer Equation,” Journal of Computational physics, Vol. 100, pp. 402-408, 1992.
3. S. Chandrasekhar, Radiative transfer, Dover Publications, New York, 1960.
4. D. B. Olfe, “A modification of the differential approximation for radiative transfer,” AIAA Journal, Vol. 5, pp. 638-643, 1967.
5. R. Siegel, C. M. Spückler, “Effect of index of refraction on radiation characteristics in a heated absorbing, emitting, and scattering layer,” Journal of Heat Transfer (Transactions of the ASME), Vol. 114, pp. 781-784, 1992.
6. R. Siegel, C. M. Spückler, “Variable refractive index effects on radiation in semitransparent scattering multilayered regions,” Journal of Thermophysics and Heat Transfer, Vol. 7, pp. 624-630, 1993.
7. P. Ben Abdallah, V. Le Dez, “Temperature field inside an absorbing-emitting semi-transparent slab at radiative equilibrium with variable spatial refractive index,” Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 65, pp. 595-608, 2000.
8. D. Lemonnier, V. Le Dez, “Discrete ordinates solution of radiative transfer across a slab with variable refractive index,” Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 73, pp. 195-204, 2002
9. G. C. Pomraning, The Equations of Radiation Hydrodynamics , Pergamon Press, New York, 1973.
10. B. van Leer, “Towards the ultimate conservative difference scheme. iv. a new approach to numerical convection,” Journal of Computational physics, Vol. 23, pp. 276-299, 1977.
11. C.-Y. Wu, “Monte Carlo simulation of transient radiative heat transfer in a medium with variable refractive index, ” (paper in preparation for submitting to a journal), 2008.
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