Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media
Extension of the Reduced Integration Scheme to Calculate the Direct Exchange Areas in 3D Rectangular Enclosures with Nonscattering Media
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DOI：
10.1155/2015/703823
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发表时间：
2015-03
影响因子：
--
通讯作者：
Guo-jun Li;Ben-Wen Li;Yasong Sun
中科院分区：
文献类型：
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作者：
Guo-jun Li;Ben-Wen Li;Yasong Sun
由于多重积分计算量大，且存在奇异性，区域法中直接交换面积（DEA）的计算是最重要的工作。Erkku（1959）最初提出了一种减少积分折叠的变量变换技术，用于计算均匀分区圆柱系统的DEA，Tian和Chiu（2003）将该技术扩展到具有大温度梯度的非均匀分区圆柱系统。本文将简化积分格式（RIS）进一步推广到三维矩形方程组中。给出了六重、五重、四重积分到三重积分的详细推导过程，并对灰色介质假设下的矩形系统的差分方程进行了高斯积分（GQI）和RIS的比较计算。结果表明，RIS的精度和效率明显高于GQI。更有趣和实用的是，RIS可以明显地分解和削弱DEA的奇异性。
The evaluation of direct exchange areas (DEA) in zonal method is the most important task due to the heavy computer cost of multi-integrals together with the existing of singularities. A technique of variable transformation to reduce the fold of integrals, which was developed originally by Erkku (1959) to calculate the DEAs of uniformly zonal dividing cylindrical system, was extended by Tian and Chiu (2003) for nonuniformly zonal dividing cylindrical system with large thermal gradients. In this paper, we further extend the reduced integration scheme (RIS) to calculate the DEAs in three-dimensional rectangular system. The detail deductions of six-, five-, and fourfold integrals to threefold ones are presented; the DEAs in a rectangular system with assumption of gray medium are computed by the Gaussian quadrature integration (GQI) and the RIS comparatively. The comparisons reveal that the RIS can provide remarkable higher accuracy and efficiency than GQI. More interestingly and practicably, the singularities of DEAs can be decomposed and weakened obviously by RIS.