# 臺灣博碩士論文加值系統

(18.204.48.69) 您好！臺灣時間：2021/07/29 14:55

:::

### 詳目顯示

:

• 被引用:0
• 點閱:167
• 評分:
• 下載:38
• 書目收藏:0
 本文應用Sharma提出的光線覓跡法於蒙地卡羅模擬，藉此可一空間可變折射係數介質的輻射熱傳，Sharma提出的光線覓跡法包含一個變數變換以及用Runge-Kutta法求解光線方程式。本文的方法可應用在模擬折射係數函數為解析函數的二維矩形介質以及一維平板或是只知道離散位置上折射係數的一維平板的輻射熱傳，結果顯示當正確地選用光線覓跡法中的變數改變量可以用本文提出的方法計算出精確的解，且計算結果的誤差隨著光包數的增加而減少。在固定介質的光學以幾何尺寸下，散射比與散射相函數對於光線覓跡法中的變數改變量及光包數的大小沒有明顯的影響。再要求計算輻射平衡介質之溫度場有一定精度時，光包數需要隨著空間網格數的增加而增加。光線在變折射係數介質中行進軌跡會偏轉，因此邊界無因次化熱通量與溫度場分佈會呈現不對稱的分佈。高長寬比之矩形介質中心附近計算出的輻射熱通量或入射輻射會接近一維平板的計算結果。
 To solve radiative transfer in a medium with a spatially varying refractive index, we develop the Monte Carlo simulation incorporating the ray tracing method presented by Sharma. The Sharma’s method includes a variable transformation and the solution of the ray equation by the Runge-Kutta method. The method is applied to simulate radiative transfer in planar and rectangular media with analytical refractive index and radiative transfer in a planar medium with known refractive indices at discrete points. The results show that the present method can generate accurate results when choosing the variable increment of the ray equation properly. By increasing the number of bundles, the error of simulation results can be decrease. For a medium with constant optical and geometry size, the dependence of the scattering albedos and the phase function on the variable increment in the ray tracing method or the number of bundles is very small. To solve the temperature fields of radiative equilibrium medium accurately, the number of bundles shall increase with the number of spatial grids. Because of the deflection of the ray trajectory in varying refractive medium, the radiative heat flux of the wall and the temperature field of the medium display a unsymmetrical distribute. The radiative heat flux or incident radiation around the center of a rectangular medium with a large aspect ratio is close to the radiative heat flux in a planar medium.
 摘要------------------------------------------------------iAbstract-------------------------------------------------ii致謝-----------------------------------------------------iii目錄------------------------------------------------------iv表目錄-----------------------------------------------------vi圖目錄-----------------------------------------------------x符號說明--------------------------------------------------xvi第一章 緒論-------------------------------------------------11.1 研究動機與文獻回顧----------------------------------------11.2 研究目的與方法-------------------------------------------31.3 本文架構------------------------------------------------4第二章 理論分析與計算-----------------------------------------62.0章節概述-------------------------------------------------62.1物理模型與基本假設-----------------------------------------62.1.1 二維介質與已知折射係數分佈-------------------------------62.1.2 一維介質與節點折射係數資料-------------------------------82.2應用蒙地卡羅法於空間變折射係數介質的輻射熱傳遞------------------82.2.1 放射位置----------------------------------------------92.2.2 放射方向---------------------------------------------102.2.3 在介質中被吸收或散射-----------------------------------102.2.4 被散射後的新行進方向-----------------------------------102.3 蒙地卡羅法解輻射熱傳之運算步驟-----------------------------122.3.1 二維可變折射係數介質的模擬步驟---------------------------122.3.2一維可變折射係數介質的模擬步驟----------------------------24第三章 結果與討論-------------------------------------------263.1光包數和變數t改變量對計算一維平板輻射熱傳的影響----------------273.2 改變節點折射係數資料數目計算一維平板無因次熱通量--------------293.3 以有誤差值的節點折射係數資料計算一維平板無因次熱通量-----------323.4光包數和變數t改變量對計算二維矩形介質輻射傳遞的影響-------------333.5 以路徑解析式為未知之折射係數計算二維矩形介質的溫度場分佈--------383.6 改變長寬比計算二維矩形介質的輻射熱傳------------------------413.7 以空間折射係數與平均折射係數計算二維矩形介質輻射熱傳-----------43第四章 結論與展望-------------------------------------------454.1 結論--------------------------------------------------454.2 展望--------------------------------------------------46參考文獻---------------------------------------------------47附錄 50附錄A：三次雲線內插 ( cubic spline interpolation ) 50附錄B：Newton-Raphson 法： 53