模拟辐射传热的离散坐标法的改进

针对离散坐标法模拟求解炉内辐射换热的问题,在对辐射传递方程采用控制容积法离散时,按辐射方向上各界面之间的投影关系划分区域,对辐射传递方程在各子控制体上沿辐射传输方向进行积分,求解各子控制体的辐射强度,再取容积平均值作为最终节点的辐射强度的新离散坐标方法,定义为分段积分离散坐标法,并对三维矩型燃气炉内辐射换热进行了数值模拟,与传统离散坐标方法及区域法进行了比较,比较结果表明新离散坐标法较好的解决了假散射问题,提高了离散坐标法的精度.     

辐射传递蒙特卡洛法精度分析及数值试验

本文建立了蒙特卡洛法模拟散射参与性介质内辐射传递计算模型。对蒙特卡洛法的计算精度及运行时间进行了较为详细的分析,提出了几种判断计算精度的方法。同时,借助蒙特卡洛法模拟辐射传递过程,进行数值“辐射实验”。利用该“实验结果”进行了物性反问题研究。在已知光学厚度的前提下,得到散射反照率与后半球辐射热流之间的单值函数关系。     

吸收散射性三维矩形介质内辐射源项的反问题

提出了一种由边界出射辐射强度反演吸收散射性三维矩形介质内辐射源项分布的方法。该方法是在辐射传递方程离散坐标近似的基础上,用求目标函数极小值的共轭梯度法进行反演计算。通过对介质辐射特性、光学厚度等参数对反演精度影响的分析,结果表明,即使存在测量误差,本文所提出的方法可较精确地反演辐射源项。     

强辐照下陶瓷泡沫骨架内的辐射能量传输机理研究

当泡沫材料直接受强光束(如聚集太阳能)照射时,准确描述材料内的热辐射传输过程成为传热模拟的关键。本文数值研究了真实陶瓷泡沫骨架在强辐照下的容积性辐射传输规律。采用离散坐标法求解了半透明氧化铝陶瓷骨架内部的辐射传输,获得了辐射能量的传递、吸收规律。研究表明,辐射在陶瓷骨架内的容积输运本质上表现为散射和吸收两种行为的竞争结果;随着波长的增加,氧化铝半透明骨架吸收的辐射能量逐渐增多。     

三维燃烧介质和壁面温度的非接触联合重建研究

温度分布在线实时测量对于燃烧过程优化和污染物控制具有重要意义, 针对以往非接触三维温度分布重建过程的耗时性问题和忽略壁面辐射的不足, 本文提出了一种新的离散重建模型, 用于三维吸收、 发射和散射性高温燃烧介质以及壁面温度的快速联合非接触测量. 该模型以四个CCD(Charge Coupled Device) 为测量传感器, 通过构建辐射逆问题求解方程, 从CCD输出的辐射投影图像重建温度分布. 介质中不同投影方向内的辐射传递过程通过离散传递法来描述, 介质的散射和壁面反射则通过离散坐标法来近似. 离散后计算局部辐射强度的病态方程通过最小二乘余量法来求解, 论文对其计算速度进行了优化. 通过非对称温度分布测量算例分析了该模型的有效性, 讨论了测量噪音、 介质和壁面辐射特性对重建精度的影响, 并与其他方法对比分析了模型的重建速度. 计算结果表明本文提出的离散模型可以有效地用于大型高温燃烧介质和壁面温度分布的联合非接触测量. 即使在有噪声的情况下, 该模型也能获得准确的测量结果, 与其他计算方法相比, 采用改进的最小二乘余量法, 能有效地提高温度分布的重建计算速度.     

求解辐射传递的非结构混合有限体积／有限元法

本文给了一种适用于任意非结构网格的有限体积/有限元法的混合算法用于求解多维半透明吸收、发射、散射性灰矩形介质内的辐射传递.该方法使用有限元法进行角度离散,有限体积法进行空间离散.与基于辐射传递离散坐标方程的方法不同的是,该方法在迭代求解的过程中,针对每一个空间体元,所有角度方向的辐射强度同时耦合求出.通过两个算例验证了该解法的正确性.     

辐射传热空间非均匀性对燃油雾化的影响

将整个燃烧室部件(气缸盖-气缸套-活塞组-润滑油膜)作为一个耦合体,在对耦合体进行三维传热数值模拟的基础上,利用分区求解、边界耦合法建立缸内工作过程与燃烧室部件的三维耦合计算模型,并利用离散传递法实现缸内辐射传热与燃烧室部件的耦合三维仿真模拟,以此考察燃烧室部件辐射传热空间非均匀性对缸内燃油雾化的影响.结果表明,辐射换...     

一维瞬态辐射传输的有限元法模拟

随着超短脉冲激光的快速发展,吸收散射性介质内的瞬态辐射传输引起了人们的广泛关注.本文基于离散坐标法和最小二乘有限元法(LSFEM),提出了模拟多维吸收散射性介质内瞬态辐射传输的数值模型.该模型有效地克服了在标准Galerkin有限元法(GFEM)中发生的伪振荡现象,在时间步长较大的情况下仍然可以得到光滑无振荡的解.而且,最小二乘法产生的求解系数矩阵是对称正定的,与GFEM中的系数矩阵相比,仅需要存储一半的非零系数,可以应用许多高效的迭代求解方法进行求解.为了检验模型,本文研究了一维吸收散射性介质内瞬态辐射传输问题,其结果与蒙特卡洛法(MCM)和积分模型法(IE)的结果进行了比较,结果证实:本文的方法可以精确、高效地模拟参与性介质内的瞬态辐射传输.     

空间差分格式对有限体积法数值散射的影响

数值散射是辐射传递方程近似算法中最常见的离散误差。本文主要讨论空间差分格式对有限体积法数值散射的影响。构造激光平行及倾斜入射的物理模型,验证和比较阶梯格式、中心差分格式及指数格式下温度场的计算精度及数值散射特性。计算结果表明,在激光平行入射与倾斜入射两种情况下,阶梯格式引起的的数值散射比菱形格式及指数格式要多,但其计算精度高于菱形及指数格式。不同激光入射条件下,各种差分格式表现出的数值散射分布有明显的差异。     

用DT法求解三维圆柱体半透明介质内辐射与导热的非稳态复合换热

采用控制容积法，离散传递（ＤＴ）法，结合谱带模型，研究了第一类及第三类非线性边界条件下三维圆柱体半透明介质内辐射与导热非稳态复合换热的数值计算方法，经与区域法，改进型蒙特卡洛法的计算结果比较表明，本方法的计算结果的可信的，精度也较高。     

Least-squares collocation meshless approach for radiative heat transfer in absorbing and scattering media

A least-squares collocation meshless method is employed for solving the radiative heat transfer in absorbing, emitting and scattering media. The least-squares collocation meshless method for radiative transfer is based on the discrete ordinates equation. A moving least-squares approximation is applied to construct the trial functions. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted to form the total residuals of the problem. The least-squares technique is used to obtain the solution of the problem by minimizing the summation of residuals of all collocation and auxiliary points. Three numerical examples are studied to illustrate the performance of this new solution method. The numerical results are compared with the other benchmark approximate solutions. By comparison, the results show that the least-squares collocation meshless method is efficient, accurate and stable, and can be used for solving the radiative heat transfer in absorbing, emitting and scattering media.     

Theoretical study of combined radiative conductive and convective heat transfer in semi-transparent porous medium in a spherical enclosure

A new method for the solution of the radiative transfer equation in spherical media based on a modified discrete ordinates method is extended to study radiative, conductive and convective heat transfer in a semi-transparent scattering porous medium. The set of differential equations is solved using the fourth-order Runge-Kutta method. Various results are obtained for the case of combined radiative and conductive heat transfer, as well as for the interaction of those modes with convection. The effects of some radiative properties of the medium on the heat transfer rate are examined.     

Complete matrix solution of radiative transfer equation for PILE of horizontally homogeneous slabs

This article covers the analytical solution of the discretized radiative transfer equation in the matrix form. The equation is discretized according to the discrete ordinates method. The solution is based on the representation of the light field in a scattering medium as a superposition of an anisotropic and a smooth regular parts. The first of them is calculated analytically using the smoothness of the solution angular spectrum. The regular part is obtained from a radiative transfer equation boundary problem with the anisotropic part as a source function by discrete ordinates method with a scaling transformation and a matrix-operator method applied. There is no limitation of the scattering law in a medium.     

Radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems

In graded index medium, the ray goes along a curved path determined by Fermat principle, and the curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectory, the methods not based on ray-tracing technique need to be developed for the solution of radiative transfer in graded index medium. For this purpose, in this paper the streaming operator along a curved ray trajectory in original radiative transfer equation for graded index medium is transformed and expressed in spatial and angular ordinates and the radiative transfer equation for graded index medium in cylindrical and spherical coordinate systems are derived. The conservative and the non-conservative forms of radiative transfer equation for three-dimensional graded index medium are given, which can be used as base equations to develop the numerical simulation methods, such as finite volume method, discrete ordinates method, and finite element method, for radiative transfer in graded index medium in cylindrical and spherical coordinate systems.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Nonaxisymmetric radiative transfer in inhomogeneous cylindrical media with anisotropic scattering

In this paper, the control volume finite element method (CVFEM) is applied for the first time to solve nonaxisymmetric radiative transfer in inhomogeneous, emitting, absorbing and anisotropic scattering cylindrical media. Mathematical formulations as well as numerical implementation are given and the final discretized equations are based on similar meshes used for convective and conductive heat transfer in computational fluid dynamic analysis. In order to test the efficiency of the developed method, four nonaxisymmetric problems have been examined. Also, the grid dependence and the false scattering of the CVFEM are investigated and compared with the finite volume method and the discrete ordinates interpolation method.     

Radiative transfer with internal reflection via the converged discrete ordinates method

In response to the challenge of establishing highly accurate solutions to the plane layer radiative transfer equation with the simplest of methods, the converged discrete ordinates method is presented. With this algorithm of only finite difference, quadrature and acceleration, we show how to obtain highly accurate intensities for radiative transfer in a finite layer with internal surface reflection. The method features angular smoothing and angular interpolation through “faux” quadrature. In addition, a manufactured solution demonstrates the high accuracy of the method for forward peaked scattering. We consider scattering in a heterogeneous medium as a final demonstration.     

Meshless approach for coupled radiative and conductive heat transfer in one-dimensional graded index medium

A meshless local Petrov-Galerkin (MLPG) approach is employed for solving the coupled radiative and conductive heat transfer in a one-dimensional slab with graded index media. The angular distribution term in discrete ordinate equation of radiative transfer within a one-dimensional graded index slab is discretized by a step scheme, and the meshless approach for radiative transfer is based on the discrete ordinate equation. A moving least-squares approximation is used to construct the shape function. Two particular test cases for coupled radiative and conductive heat transfer within a one-dimensional graded index slab are examined to verify this new approximate method. The temperatures and the radiative heat fluxes are obtained. The results are compared with the other benchmark approximate solutions. By comparison, the results show that the MLPG approach has a good accuracy in solving the coupled radiative and conductive heat transfer in one-dimensional graded index media.     

Iterative approach of high-order scattering solution for vector radiative transfer of inhomogeneous random media

By stratifying a random scatter media into multiple thin layers in the vertical z direction, the first-order scattering solution of each thin layer is employed to derive high-order scattering solution of whole random media. Using the Fourier transform and Mueller matrices in discrete ordinates, an iterative approach to solve high-order scattering solution of vector radiative transfer (VRT) equation is newly developed. Numerical results are well compared with the Mueller matrix solutions of the first order for a single layer medium, second order for a half-space, and the results of the discrete ordinate and eigen analysis method. It demonstrates our approach as feasible, effective and especially applicable to high-order solution of VRT for both bistatic scattering and thermal emission of inhomogeneous non-spherical scatter media.     

表面不透明三层漫反射散射性介质耦合换热

本文采用射线踪迹、节点分析法研究了三层吸收、各向同性散射性介质层内的一维辐射和导热瞬态耦合换热,复合层表面不透明漫反射,介质层交界面半透明漫反射,且半透明漫反射交界面的反射率采用Fresnel反射定律确定。采用一层和二层辐射能量传递模型跟踪辐射能量在三层介质内的传递,从而推导出辐射传递系数。运用辐射传递系数求解辐射源项,在辐射对流边界条件下、采用全隐格式求解瞬态能量方程,并从机理上研究了辐射和导热耦合换热过程。