热辐射输运问题的高效蒙特卡罗模拟方法

惯性约束聚变研究中,热辐射光子在介质中的输运以及热辐射光子与介质的相互作用是重要研究课题,蒙特卡罗方法是该类问题的重要研究手段之一.隐式蒙特卡罗方法虽然能正确地模拟热辐射在介质中的输运过程,但当模拟重介质(材料的吸收系数大)问题时,该方法花费的计算时间将变得很长,导致模拟效率很低.本文以离散扩散蒙特卡罗方法为基础,开发了"离散扩散蒙特卡罗方法辐射输运模拟程序",可以较好地解决重介质区的计算效率问题,但是离散扩散蒙卡罗方法在模拟轻介质区时精度不够高.辐射输运问题中通常既有轻介质也有重介质,为了能同时解决蒙特卡罗方法模拟的效率和精度问题,本文研究了离散扩散蒙特卡罗方法与隐式蒙特卡罗方法相结合的模拟方法,并提出了新的扩散区与输运区界面处理方法,研制了混合蒙特卡罗方法的辐射输运模拟程序.典型辐射输运问题模拟显示:在模拟重介质问题时,该程序能大幅缩短模拟时间,且能取得与隐式蒙特卡罗方法一致的结果;在模拟轻重介质均存在的问题时,与隐式蒙特卡罗方法相比,混合蒙特卡罗方法的模拟精度与其相当且计算效率同样能够得到显著提升.     

星载多波段红外光学系统的杂散辐射分析

引入反向蒙特卡罗法与双向蒙特卡罗法对红外光学系统的杂散辐射进行分析,基于光谱辐射传递因子导出了焦平面辐射能流计算式.以某星载多波段红外光学系统为例,在检验计算可靠性的基础上,模拟了各波段辐射能从地球背景和光机内壁面到焦平面的传播过程,分析了壁面吸收率与温度的影响.结果表明,采用双向蒙特卡罗法可有效地模拟辐射能从地球向星载光学系统焦平面的传播过程,采用反向蒙特卡罗法可容易地分析光机内部热辐射的影响;光机内壁面吸收率对视场外杂散辐射的传播有很大影响,温度高于250 K的光机内壁面热辐射成为主要的杂散光源.     

蒙特卡罗方法在解微分方程边值问题中的应用

介绍了蒙特卡罗方法的基本原理以及随机数的产生方法。基于蒙特卡罗方法的思想,结合有限差分方法,建立了求解微分方程边值问题的随机概率模型,并以第一类边界条件的拉普拉斯方程和一个给定初值及边界条件的非稳态热传导方程为数值算例,研究了蒙特卡罗方法在求解微分方程边值问题中的应用。结果表明:利用蒙特卡罗方法,不仅可以有效解决给定边界条件的微分方程,对于给定初值条件的微分方程,也可以从时域有限差分方程出发,采用蒙特卡罗方法进行求解。数值模拟和对误差的理论分析均表明,增加蒙特卡罗试验中的模拟粒子点数,可以提高计算结果的精度。     

源凸域正贡献蒙特卡罗方法

在Duoi和Gerstl的贡献蒙特卡罗方法中,不少次级粒子的贡献是负的[3,10]。负贡献粒子常使蒙特卡罗估计的统计涨落变大,浪费较多的计算时间,因此,解决次级粒子的负贡献问题是很必要的。在本文中,一个新的称为源凸域正贡献方法的贡献蒙特卡罗方法被提出来了。在任何情况下,源凸域正贡献方法一定比Dubi和Gerstl的贡献方法好,因此,前者完全可以替代后者。对于源凸域R解决了次级粒子的负贡献问题,通过例子的实际计算结果表明,本方法的效率可比Dubi和Gerstl的方法提高1.5至3.4倍。     

遗传算法在散射介质光输运逆问题研究中的应用

建立了一个散射介质模型,在用蒙特卡罗方法成功模拟介质中光输运过程的基础上,用遗传算法有效地解决了因蒙特卡罗方法模拟结果的离散性和统计性使其在利用传统化方法进行逆问题研究时存在的困难,从而较好地实现了对散射介质模型的单个光学特性参数的重构和多参数的联合重构,同时还深入地讨论了遗传算法在过程中的作用机理。     

解深穿透问题的小区域蒙特卡罗方法

对于深穿透问题则一般蒙特卡罗方法存在一定的困难。本文提出了一个新的蒙特卡罗计算深穿透问题的小区域方法。在此基础上给出了两个小区域方法,即平几何小区域方法和球几何小区域方法,通过例子的实际计算表明,小区域方法是比较好的和可行的,克服了一般蒙特卡罗方法解深穿透问题的缺点。     

蒙特卡罗方法的两个基本问题

随机数的产生和概率分布的随机抽样方法,是蒙特卡罗方法的两个最基本的问题。对这两个问题的处理目前仍然因循60年前蒙特卡罗方法诞生初期的技术途径,因此长期受一些无法彻底解决的问题所困扰,同时也面临一些新问题的挑战。分析了上述问题,分别对随机数的产生和任意分布的抽样方法给出了新的技术解决途径。The producation of random number and the sampling of random distribution are two foundational problems in Monte Carlo Mothed. In this paper, we carry out some new ways to treat the problems.     

矩形介质内辐射换热的有限元法

利用有限单元法离散求解辐射传递方程和能量控制方程.分别计算了边界为黑体和灰体条件下矩形吸收、发射、各向同性散射介质内的平均入射强度和温度分布,并同蒙特卡罗法(M-C法)计算结果进行了比较.     

量子蒙特卡罗方法及其应用

量子体系的蒙特卡罗研究近十多年来非常活跃，并取得了很多富有意义的成果．量子蒙特卡罗方法愈来愈受到人们的关注．本文结合量子蒙特卡罗方法的建立和发展介绍了它的基本思想．在对几种具体方法作介绍的同时，还分析了它们特点．文中还对超导、主要是高温超导电性研究中的一些有益的量子蒙特卡罗工作作了介绍．最后讨论了量子蒙特卡罗方法存在的主要问题，并展望了量子蒙特卡罗方法的发展前景．     

表面性质对柱状抛物面型辐冷器性能的影响

利用蒙特卡罗光线跟踪法解决曲面间的辐射换热问题 ,模拟计算了抛物柱面式一级反射锥表面和地球屏表面的吸收率和散射率变化时 ,辐射制冷器一级和二级温度的变化。     

Numerical study of heat transfer in an optically thick semi-transparent spherical porous medium

In this paper, heat transfer by simultaneous convection, conduction and radiation in a semi-transparent spherical porous medium is investigated. The ROSSELAND approximation is adopted to take account of radiation in the heat transfer rate. The routine used here to solve the set of differential equations is taken from the IMSL MATH/LIBRARY. Various results are obtained for the dimensionless temperature profiles in the solid and fluid phases, the radiative, conductive, convective and total heat fluxes. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

Développement simultané hydrodynamique et thermique d'un écoulement laminaire dans un tube incliné en régime de convection mixte

In this work, we study numerically the heat transfer and fluid flow inside a circular inclined tube. The thermal boundary condition is that of a constant and uniform (axially and circumferentially) heat flux on the tube wall. A finite volume method is used to solve, in dimensionless form, the parabolic equations of mixed convection. The results, obtained for water with different combinations of the Grashof number and the tube inclination, show that the average heat transfer is improved and the wall shear stress is increased compared to those of pure forced flow.     

Least-squares finite element method for radiation heat transfer in graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a least-squares finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Four cases of radiative heat transfer are examined to verify this least-squares finite element method. Linear and nonlinear graded index are considered. The predicted dimensionless net radiative heat fluxes are determined by the least-squares finite element method and compared with the results obtained by other methods. The results show that the least-squares finite element method is stable and has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium, while the Galerkin finite element method sometimes suffers from nonphysical oscillations.     

Application of multidimensional scheme and the discrete ordinate method to radiative heat transfer in a two-dimensional enclosure with diffusely emitting and reflecting boundary walls

Radiative heat transfer is the dominant mode of heat transfer in many engineering problems, including combustion chambers, space, greenhouses, rocket plume sensing, among others. The aim of this study is to develop an efficient method capable of eliminating ray effects in complex 2D situations and to use the developed code for other problems including combined conduction and convection in connection with CFD codes. A complete genuinely multidimensional discretization in two-dimensional discrete ordinates method is formulated to solve radiative heat transfer in a rectangular enclosure composed of diffusely emitting and reflecting boundaries and containing homogeneous media that absorbs, emits and scatters radiation. A new genuinely multidimensional differencing scheme is used to solve the radiative transfer equation with S₄, S₆, S₈, T₆, T₇, T₈ and T₉ angular quadrature schemes. Different cases are analyzed and the results are compared when possible with those obtained by others researchers.     

辐射传输介质散射相函数的蒙特卡洛算法

复分散系相函数在辐射介质传热中是关键参数,蒙特卡洛法兼具数值算法与试验测量的优点.利用该方法计算复分散系的多重散射相函数克服了以往算法的缺点,可以体现多重散射的影响,并且可以计算任意形状控制体的相函数.大量的数学实验发现当介质系密度增大时,散射能量在4π空间内分布趋于均匀.     

The radiative transfer in cylindrical medium and partition allocation method by overlap regions

In this paper the radiative transfer in one-dimensional and two-dimensional cylindrical medium is simulated by the Monte-Carlo (M-C) method. Our results agree with the previous ones very well. It indicates that our cylindrical M-C model is creditable. In this paper, the partition allocation method of radiative heat transfer in participating cylindrical media is presented, in which every sub-domain is isolated by imaginary black wall at certain equivalent temperature and overlaps each other. The stitched results of all sub-domains can predict the results of a whole zone accurately. The partitioned treatment by overlap regions can achieve reasonable result, save memory efficiently, and compute parallel.     

非线性二维稳态导热反问题的一种新解法

1引言导热反问题，是指根据实验测得的物体表面或内部某些位置的温度值，通过求解导热微分方程，反推导致这一结果的原因。在数学上是一种不适定问题，求解结果对测量误差十分敏感，即使有较小的测量误差也会带来较大的影响。待定边界条件类型的导热反问题在工程和科学试验中有广泛的应用背景。许多学者对此进行了研究，但多停留在一维和二维线性问题上，对多维非线性问题的研究较少［‘－’］。Beck山对一线问题讨论了五种求解方法：分析法，D’souza法，Weber法，RB方法和HillHensel方法，其中前三种不能求解非线性问题，后两种对非稳…     

基于拓展分离变量法的层合材料瞬态传热分析

层合材料各层热物理参数不同,难以用常规的分离变量法求解.针对此问题对常规分离变量法进行了拓展,将层合材料受热时的温度场在时间域上分成微小时间段,在每个微小时间段内层合材料交界处的温度可认为随时间正比变化,并假设比例系数,此时在微小时间段内对各层分别利用分离变量法单独求得解析解,根据交界处温度相等能量连续的关系可求出比例系数,进而求出该微小时间段内的温度场,通过循环求解可得整个时间段内的温度场.之后,利用拓展的分离变量法对常用层合隔热材料瞬态传热进行了分析,通过与有限元方法计算的结果比较,验证了本文方法的正确性,分析了隔热材料类型、厚度,材料表面对流换热系数,空气温度等参数对隔热效果的影响.拓展分离变量法利用解析的方式求解了层合材料瞬态传热问题,物理意义比常规的数值方法明确,计算效率也较高.     

Simulation of heat transfer processes in an unconventional furnace

Heat transfer simulation is of great significance for the heating equipments control. In this paper, a set of models is proposed to solve heat transfer problems in a furnace, including radiation and convection. The heat transfer models are integrated with a furnace model to simulate the heating process. The heating rate is increased due to enhanced heat transfer at the surfaces by changing furnace chamber geometry. A fixed grid enthalpy formulation is applied to model heat transfer for an oval geometry. The heating temperature was found to increase linearly with curvature of the interior.     

Conductivité thermique de mousses cellulaires de carbone: Mesures par méthode flash et interprétation

This paper deals with the thermal diffusivity measurement of cellular carbon foams by the flash method. The thermal conductivity is obtained from the thermal diffusivity by using specific heat and density of carbon foam. These materials constitute non-homogeneous porous semitransparent media, hence the classic experimental set-up of the flash method must be adapted. A study is carried out in order to show the influence of the sample thickness, of the temperature, of the enclosed gas pressure and of the gas composition on the effective thermal conductivity. Identification functions are established in the monodimensional and bidimensional cases. Results indicate the dependence of the equivalent thermal conductivity upon the sample thickness. This result, attributed to radiative transfer, is confirmed by modelling. Radiative thermal conductivities are obtained with a Monte-Carlo code. Experimental and theoretical results are compared. It is demonstrated that the concept of effective conductivity is not relevant to these materials.