有限体积法求解圆柱形散射介质内辐射与导热耦合换热

将谱带模型与有限体积解法相结合;求吸收、发射、散射性非灰介质圆柱体内辐射传递方程。考虑辐射强度场与热扩散温度场的耦合,将控制容积法与有限体积法结合,求解辐射与导热耦合换热。经与光线踪迹法、离散传递法的计算结果比较表明,谱带模型与有限体积解法相结合能处理多场耦合下非灰介质内的辐射换热。     

二维稳态辐射传输方程的有限差分求解法

针对扩散光学层析在小动物成像中的应用问题并基于混浊介质空间光子三维散射的实际物理效应,提出的二维稳态辐射传输方程的有限差分数值求解新方法.在此基础上,研究了不同的空间剖分网格和角度离散密度对求解准确度的影响,并通过将所提方法与蒙特卡洛模拟进行比对,验证方法的正确性.研究表明:在均匀组织体内,当离散角度达到一定数量时,由辐射传输方程的有限差分解获得的透射面和侧面的光子密度对空间网格大小并不敏感,而在反射面上光子密度计算则需要较密的空间网格才能够达到一定准确度.本研究为发展基于辐射传输方程的扩散光学层析理论奠定了基础.     

DRESOR法对平行入射辐射问题的研究

本采用一种基于蒙特卡洛法(Monte Carlo Method,MCM)求解辐射传递方程(Radiative Transfer Equation, RTE)的快捷、有效的方法-DRESOR法(Distributions of Ratios of Energy Scattered Or Reflected)在一维充满吸收、各向同性散射介质平行平板中,外部有平行入射条件下,求解计算空间点的辐射强度沿空间方向角的分布,而不需要辐射平衡和在空间位置坐标和方向角度坐标上同时离散辐射传递方程进行迭代求解。     

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.     

二维稳态辐射传输方程的有限差分求解法

针对扩散光学层析在小动物成像中的应用问题并基于混浊介质空间光子三维散射的实际物理效应,提出的二维稳态辐射传输方程的有限差分数值求解新方法.在此基础上,研究了不同的空间剖分网格和角度离散密度对求解准确度的影响,并通过将所提方法与蒙特卡洛模拟进行比对,验证方法的正确性.研究表明：在均匀组织体内,当离散角度达到一定数量时,由辐射传输方程的有限差分解获得的透射面和侧面的光子密度对空间网格大小并不敏感,而在反射面上光子密度计算则需要较密的空间网格才能够达到一定准确度.本研究为发展基于辐射传输方程的扩散光学层析理论奠定了基础.     

间断有限元法求解一维矢量辐射传输

采用间断有限元法(Discontinuous finite element method,DFEM)求解一维散射性介质内矢量辐射传输问题。推导了散射性介质内矢量辐射传输方程的间断有限元离散格式,空间离散采用间断有限元离散将求解域划分为相互独立的单元,角度离散在传统的均匀分段光滑近似(Piecewise Constant Approximation,PCA)角度离散基础上进行局部加密以得到关键方向上的数值解。采用两个稳态矢量辐射传输算例对间断有限元法求解矢量辐射传输方程的正确性和计算效率进行了验证,在此基础上拓展间断有限元法应用于求解散射性介质内瞬态矢量辐射传输方程,将随着时间推移过程中的瞬态辐射信息和最终的稳态结果相比较验证了本文方法的正确性。     

耦合辐射的三维热化学非平衡流数值模拟

发展耦合辐射的三维热化学非平衡流场计算方法,可用于非结构网格.采用Jameson有限体积法求解耦合辐射源项的三维N-S方程.辐射源项通过求解辐射输运方程(Radiative Transport Equation RTE)获得.在空间方向上离散后,采用有限体积法求解辐射输运方程.化学模型包含11个组元,20个化学反应.采用该数值方法计算MUSES-C模型在速度为11.6 km·s^-1时的绕流流场及前驻点处的辐射热流密度.并通过对比,分析热辐射对流场的影响.     

多维梯度折射率介质内辐射传递的扩散近似

推导多维梯度折射率介质内稳态辐射传递的扩散近似方程.使用有限元法对扩散近似进行离散和求解,利用两个二维半透明介质的稳态辐射传递问题验证该扩散近似的精度及适用性.算例考虑介质为均匀折射率及梯度折射率两种情况.利用扩散近似分别求解辐射平衡时的边界热流、介质内温度场分布,并与辐射传递方程的求解结果进行对比分析.结果表明:介质折射率变化、散射特性、光学厚度及散射反照率均直接影响扩散近似的精度;在光学厚及强散射条件下,该扩散近似可以作为一种快速算法应用于梯度折射率介质稳态辐射传递的求解.     

散射相函数对一维介质内辐射传递的影响规律

采用有限体积法研究了一维线性各向异性散射介质内散射相函数对辐射传递的影响规律.经与理论解、辐射元法、蒙特卡洛法计算结果比较表明,有限体积法的计算结果更可靠,且不同散射相函数的辐射换热系统中,其无因次热流之比与光学厚度之间存在某种单调变化的函数关系,利用该函数关系可以检验模型的准确度.     

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.     

Hybrid finite volume/ finite element method for radiative heat transfer in graded index media

The rays propagate along curved path determined by the Fermat principle in the graded index medium. The radiative transfer equation in graded index medium (GRTE) contains two specific redistribution terms (with partial derivatives to the angular coordinates) accounting for the effect of the curved ray path. In this paper, the hybrid finite volume with finite element method (hybrid FVM/FEM) (P.J. Coelho, J. Quant. Spectrosc. Radiat. Transf., vol. 93, pp. 89–101, 2005) is extended to solve the radiative heat transfer in two-dimensional absorbing-emitting-scattering graded index media, in which the spatial discretization is carried out using a FVM, while the angular discretization is by a FEM. The FEM angular discretization is demonstrated to be preferable in dealing with the redistribution terms in the GRTE. Two stiff matrix assembly schemes of the angular FEM discretization, namely, the traditional assembly approach and a new spherical assembly approach (assembly on the unit sphere of the solid angular space), are discussed. The spherical assembly scheme is demonstrated to give better results than the traditional assembly approach. The predicted heat flux distributions and temperature distributions in radiative equilibrium are determined by the proposed method and compared with the results available in other references. The proposed hybrid FVM/FEM method can predict the radiative heat transfer in absorbing-emitting-scattering graded index medium with good accuracy.     

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。     

太阳能吸热器玻璃窗辐射与导热计算

在太阳能塔式热发电空气吸热器工作过程中,吸热器玻璃窗受到聚焦太阳光、环境以及吸热面（体）的复合辐射。本文采用改进蒙特卡罗法、有限容积法,研究了太阳能空气吸热器石英玻璃窗半透明介质内部辐射与导热的耦合换热,研究了不同厚度半透明介质石英玻璃窗在工作面处于不同第三类边界条件下的稳态温度分布。研究表明石英玻璃的厚度和内侧空气温...     

Radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and particles using the modified discrete-ordinates method

The radiative heat transfer between two concentric spheres separated by a two-phase mixture of non-gray gas and a cloud of particles is investigated by using the combined finite-volume and discrete-ordinates method, named modified discrete-ordinates method (MDOM), which integrates the radiative transfer equation (RTE) over a control volume and a control angle simultaneously like in the finite-volume method (FVM) and treats the angular derivative terms due to spherical geometry as the conventional discrete-ordinates method (DOM). The radiative properties involving non-gray gas and particle behavior are modeled by using the extended weighted sum of gray gases model (WSGGM) with particles. Mathematical formulation and final discretization equations for the RTE are introduced by considering the behavior of a two-phase mixture of non-gray gas and particles in a spherically symmetric concentric enclosure. The present approach is validated by comparing with the results of previous works including gray and non-gray radiative heat transfer. Finally, a detailed investigation of the radiative heat transfer with non-gray gases and/or a two-phase mixture is conducted to examine the dependence of the radiative heat transfer upon temperature ratio between inner and outer spherical enclosure, particle concentration, and particle temperature.     

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.     

Modeling of radiative heat transfer in 3D complex boiler with non-gray sooting media

The radiative heat transfer problem is solved for 3D complex industrial boiler with five baffles containing a mixture of carbon dioxide and water vapor for non-uniform temperature fields. A numerical formulation using the FTn finite volume method coupled with the bounded high-order resolution CLAM scheme, the blocked-off-region procedure and the narrow-band based weighted-sum-of-gray-gases (WSGG) [Kim OJ, Song T-H. Data base of WSGGM-based spectral model for radiation properties of combustion products, JQSRT 2000; 64: 379-94] model is adapted. The effect of soot volumetric fraction, particle temperature and uniform particle concentration on the radiative heat flux and radiative heat source is investigated and discussed. Also the advantages, in non-gray media, of the FTnFVM compared to the classical FVM are highlighted.     

Prediction of radiative heat transfer in 3D complex geometries using the unstructured control volume finite element method

In this paper, a 3D algorithm for the treatment of radiative heat transfer in emitting, absorbing, and scattering media is developed. The numerical approach is based on the utilization of the unstructured control volume finite element method (CVFEM) which, to the knowledge of the authors, is applied for the first time to simulate radiative heat transfer in participated media confined in 3D complex geometries. This simulation makes simultaneously the use of the merits of both the finite element method and the control volume method. Unstructured 3D triangular element grids are employed in the spatial discretization and azimuthal discretization strategy is employed in the angular discretization. The general discretization equation is presented and solved by the conditioned conjugate gradient squared method (CCGS). In order to test the efficiency of the developed method, several 3D complex geometries including a hexahedral enclosure, a 3D equilateral triangular enclosure, a 3D L-shaped enclosure and 3D elliptical enclosure are examined. The results are compared with the exact solutions or published references and the accuracy obtained in each case is shown to be highly satisfactory. Moreover, this approach required a less CPU time and iterations compared with those of even parity formulation of the discrete ordinates method.     

非规则形状介质内辐射-导热耦合传热的间断有限元求解

采用间断有限元法(discontinuous finite element method,DFEM)求解非规则形状介质内的辐射导热耦合传热问题,得到了典型非规则形状介质内辐射导热耦合传热问题的高精度数值结果.和传统连续型有限元方法不同,DFEM将计算区域划分成相互独立的离散单元,形函数的构造、未知量的加权近似以及控制方程的求解均在每一个离散单元上进行.通过在单元之间施加迎风格式的数值通量,DFEM保证了整个计算区域的连续性,因此这种方法兼具良好的几何灵活性和局部守恒性.推导了辐射传输方程和能量扩散方程的射导热耦合传热问题,得到了典型非规则形状介质内辐射导热耦合传热的高精度数值结果.     

Discontinuous finite element method for radiative heat transfer in semitransparent graded index medium

To avoid the complicated and time-consuming computation of curved ray trajectories, a discontinuous finite element method based on discrete ordinate equation is extended to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two cases of radiative heat transfer in two-dimensional rectangular gray semitransparent graded index medium enclosed by opaque boundary are examined to verify this discontinuous finite element method. Special layered and radial graded index distributions are considered. The predicted dimensionless net radiative heat fluxes and dimensionless temperature distributions are determined by the discontinuous finite element method and compared with the results obtained by the curved Monte Carlo method in references. The results show that the discontinuous finite element method has a good accuracy in solving the multi-dimensional radiative transfer problem in a semitransparent graded index medium.     

Finite element method for radiation heat transfer in multi-dimensional graded index medium

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium.