Modeling the radiation of anisotropically scattering media by coupling Mie theory with finite volume method

A new mathematical model and code for radiative heat transfer of particulate media with anisotropic scattering for 2-D rectangular enclosure is developed. The model is based on the coupling of (i) finite volume method for the solution of radiative transfer equation with (ii) Mie equations for the evaluation of scattering phase function. It has not been done before to the authors’ best knowledge. The predictions were compared against the only found results, published 15 years ago. For those results the S-N discrete ordinates method for the solution of radiative transfer equation and the Legendre polynomials expansions for the evaluation of scattering phase function were used. The agreement between the results is very good. The advantages of new model and code are in their straight forward application to any given particles parameters without the need for previously designed analytical expression for scattering phase function. In addition, that analytical expression, with generated expansion coefficients, is restricted and can be used only for that particular case of particle parameters. The new model was applied to the solid particles of several various coals and of an ash and the series of 2-D predictions are performed. The effects of particle size parameter and of scattering albedo on radiative heat flux and on incident radiation were analyzed. It was found that the model developed is reliable and very accurate and thus suitable for extension towards: (i) 3-D geometries, (ii) mixtures of non-gray gases with particles as well as for (iii) incorporation in computational fluid dynamics codes.     

Solution of radiative transfer in a one‐dimensional anisotropic scattering media with different boundary conditions using the DRESOR method

The DRESOR method was applied to analyze the radiative transfer process in anisotropic scattering media with different boundary conditions in this paper. The method was validated by the integral formulation of the radiative transfer equation at first. Some variation regulations about the emissivity were obtained by extensive numerical simulations. When the optical thickness of the media became very large, the emissivity converged to a constant value. The converged emissivity in the forward scattering medium was the largest and that for the backward scattering medium was the smallest. Also the converged emissivity was associated with the scattering albedo of the media. The greater the scattering albedo was, the smaller the converged emissivity was. When the scattering albedo decreased to zero the converged emissivity reached the blackbody emissivity at the same temperature. Furthermore, different boundary conditions were considered. The results showed that if the temperature of the medium and the boundary was equal, the intensity at boundary was the same as that for the blackbody emission at the same temperature, whether the boundary reflectivity was 1.0 or not. When the temperature of the boundary was lower than that of the medium, the boundary emissivity can reach 1.0 only if ρ=1.0. Finally, the radiation flux was studied with different phase functions and different boundary conditions. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(3): 138–152, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20198     

汽轮机叶片的三维几何造型方法综述

通过对汽轮机叶片汽道型面及叶根、叶冠部分几何造型特点的分析,介绍了应用CAD/CAM软件对汽轮机叶片进行三维几何造型的一般方法并指出了在叶片设计及制造过程中的应用。     

A Two—Streamfunction—Coordinate Method for the Numerical Solution of 3—D Aero—Thermoldynamics Direct and Inverse Problems

This paper describes a new method which has been developed for the solution of direct and inverse problemsof 3-D compressible flows in turbomachinery.Two types of streamfunctions are proposed in the paper andthe streamfunction-coordinate system is applied in numerical computations.The algorithm is applied to statorblades and the results are compared with experimental data,It is shown that the comparisons are very satis-factory.     

Conduction and radiation in a rectangular isotropic scattering medium with black surfaces by the RTNAM

The ray tracing-node analyzing method (RTNAM) has been successfully developed to solve 1-D coupled heat transfer in isotropic and anisotropic scattering media in the past, and in this paper it is further extended to solving the 2-D coupled heat transfer in a rectangular isotropic scattering medium. Using the control-volume method, the partial transient energy equation is discretized in implicit scheme. The effect of radiation on heat transfer is considered as a radiative source term (RST) in the discretized energy equation, and in combination with spectral band model, the RST is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Patankar’s linearization method is used to linearize the RST and the opaque boundary condition, and the linearized equations are solved by the ADI method. Before solving the RTCs for isotropic scattering media, the RTCs without considering scattering must be solved at first. And then, the RTCs without considering scattering are normalized according to their integrality relationships. In addition, the correctness of the results obtained by the RTNAM is validated, and effects of scattering albedo and refractive index on transient temperature distribution are investigated.     

DRESOR法对含有边界的一维各向异性散射介质辐射传递方程的求解

通过DRESOR(d istribu tions of ratios of energy scattered or reflected)法求解一维黑体边界发射、介质各向异性散射的辐射传递问题,与理论解、辐射元法、蒙特卡洛方法和有限体积法的计算结果进行比较,验证了该方法计算的准确性;同时,对DRESOR法给出的高方向分辨率的辐射强度进行了分析。计算了带有漫反射边界介质具有吸收、发射、各向异性散射特性的辐射传递问题,对不同工况下的辐射强度和辐射热流进行了比较分析。     

三维地质建模技术在油藏描述中的应用——以大庆油田T区块为例

三维地质建模技术作为精细油藏描述和储层表征的重要组成部分,有效推动了油藏描述技术从定性到定量的转化,为开发后期井型井网的调整和剩余油分布规律的揭示提供了地质基础。以大庆油田T区块为研究对象,综合运用地震、地质、测井、取心资料,采用多步建模思路,建立油藏沉积微相模型和属性参数模型。最后针对储层参数不确定性问题的来源,运用随机建模技术和地质统计学等方法,分析储层不确定性参数的变化范围和规律,特别是针对变差函数中变程求取的不确定性所产生的油藏储量风险评价问题,引入概率储量,采用Monte Carlo方法,对各个参数的概率累计分布函数进行随机抽样,对地质储量分布概率进行统计和不确定性分析。研究表明,此方法基于对储量参数值范围的认识和评估,可以针对不同的独立变量的不确定性进行量化估计,从而计算油藏储量的概率分布,定量分析对模拟结果的影响,预测储层存在的风险和潜力,同时也为油藏数值模拟提供了一组优选的三维地质模型。     

竖直三维内肋管管内变压器油自然对流换热特性

利用田口法对具有不同肋结构参数的竖直三维内肋管管内变压器油自然对流换热特性进行了实验研究,获得了肋高、肋宽、轴向间距和周向间距等肋结构参数对管内自然对流换热性能的影响规律,提出了肋结构参数最佳组合。结果表明,变压器顶层油温从40℃变化至100℃,肋高和肋宽对换热性能的影响占比基本不变,周向间距的影响占比逐渐减小,轴向间距的影响占比逐渐增大;相比光管,三维内肋管的自然对流强化换热性能随顶层油温的增大而增加,变压器油自然对流Nu最大约为光管的1.75倍。拟合了竖直三维内肋管管内变压器油自然对流换热计算关联式,其与实验数据的最大偏差为±16%。     

哈达山工程土坝地震反应三维有限元分析

以哈达山水利枢纽坝址区地震为例,采用三维非线性有限元法建立了土坝和坝基的三维非线性有限元模型,并根据提供的地震动加速度曲线采用动力时程分析法对大坝进行地震反应分析。结果表明,设计地震作用下坝体的加速度、位移和应力反应均小,地震永久变形不明显,约为最大坝高(含坝基覆盖层)的0.10%,整体稳定性满足要求,设计方案合理。     

在温度和机械载荷作用下活塞应力与变形的三维有限元分析

根据有限元法解得的温度场，。利用微机对ω型燃烧室的柴油机活塞进行温度载荷和机械和作用下应力和变形的三维有限元分析。单元网格划分中采用了３１８６个节点、２２１０个８节点六面体等参元，将计算输出的各单元形心的六个应力分量换算为三个主应力分量，再选择合适的插值求得各节点的主应力分布。