Development of Fast Numerical Method to Solve Nongray Radiative Heat Transfer in Three-dimensional Arbitrary Shaped Systems by Pre-calculating Geometrical Characteristics

本研究的目的是开发一种适用于任意形状系统的三维非灰色辐射对流换热程序。为此，本文提出了一种新的非灰色辐射换热数值分析的快速算法，并以三维非灰色辐射对流换热程序为约束条件，采用蒙特卡罗方法作为辐射换热计算的分析工具。针对非灰色辐射换热数值分析的耗时问题，提出了一种独特的非灰色辐射换热数值分析的快速算法，避免了重复使用该方法的次数(波数分割次数)x(温度收敛的迭代计算次数)。作为价值…吸收系数更多地依赖于温度和波数，光学厚度的值不是系统的唯一值。考虑到光学厚度的这一特性导致在非灰色分析中需要重复计算，提出了将光学厚度分为计算单元间的物理长度和吸收系数两部分的思想。利用单元之间的物理长度是系统的唯一值而不依赖于温度和波数的特点，利用蒙特卡罗方法可以在温度收敛的计算回路外计算这些值。然后，当迭代环中每次需要光学厚度时，可以很容易地将其计算为预先计算的物理长度与依赖于温度的吸收系数的试验值的乘积，由于上述方法的发展，可以多次使用耗时的蒙特卡罗计算，在相同精度的情况下，总计算时间减少到1/6。较少

The objective of this research is to develop a threed-dimensioal nongray radiative-convective heat transfer program for arbitrary shaped systems. For the purpose, new fast algorithm for numerical analysis on nongray radiative heat transfer is developed and confined with a threed-dimensioal nongray radiative-convective heat transfer program for arbitrary shaped systems..In the study, the Monte Carlo method is adopted for the analytical tool for the radiative transfer calculation. As the method is known to be time-consuming, below mentioned unique fast algorithm for numerical analysis on nongray radiative heat transfer is proposed to avoid the repeated use of the method for the times of (number of wave number division)x(number of iterational calculations for temperature convergence).The variables used in the radiative heat transfer analysis are the functions of non-dimensional "optical thichness" which is the product of physical length and absorption coefficient of gas layer. As the valu … More e of the absorption coefficient depends on the temperature and the wave number, the value of the optical depth is not the unique value of the system. Considering that this characteristics of the optical depth is the cause of the necessity of the repeated calculation in nongray analysis, an idea is presented in which optical depth is divided into two parts, physical length between calculational elements and the absorption coefficient. Exploiting that the physical lengths between elements are unique value of the system and do not depend the temperature and wave number the values can be calculated outside the caluculational loop for temperature convergence using the Monte Carlo method. Then, every time when the optical depth is needed in the iteratinal loop, it can easily calculated as the product of the pre-calculated physical lengths and the tentative value of absorption coefficient which depends on the temperature.Owing to the development of the above mentioned method, multiple usage of the time consuming Monte Carlo calculation can be waved, and the total calculating time is reduced to 1/6 for the same accuracy. Less