蒙特卡洛法研究随机粗糙表面的光散射特性

本文采用蒙特卡洛(M-C)数值模拟,生成起伏高度满足高斯分布的随机粗糙表面。借助Kirchhoff近似,并在综合考虑辐射传输、光学及电磁学有关理论的基础上,利用M-C方法计算了符合高斯分布的一维随机粗糙表面的单次和多次光散射分布,模型结合射线追踪法考虑了粗糙表面的遮蔽效应。结果表明在考虑多次散射时,存在后向散射增强现象,该结论与实验结果相吻合,证明本文数值模拟方法的正确性。     

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.     

Finite element approach for radiative transfer in multi-layer graded index cylindrical medium with Fresnel surfaces

Because the optical plane defined by the incidence and reflection direction at a cylindrical surface has a complicated relation with the local azimuthal angle and zenith angle in the traditional cylindrical coordinate system, it is difficult to deal with the specular reflective boundary condition in the solution of the traditional radiative transfer equation for cylindrical system. In this paper, a new radiative transfer equation for graded index medium in cylindrical system (RTEGCN) is derived based on a newly defined cylindrical coordinate system. In this new cylindrical coordinate system, the optical plane defined by the incidence and reflection direction is just the isometric plane of the local azimuthal angle, which facilitates the RTEGCN in dealing with cylindrical specular reflective boundaries. A least squares finite element method (LSFEM) is developed for solving radiative transfer in single and multi-layer cylindrical medium based on the discrete ordinates form of the RTEGCN. For multi-layer cylindrical medium, a radial basis function interpolation method is proposed to couple the radiative intensity at the interface between two adjacent layers. Various radiative transfer problems in both single and multi-layer cylindrical medium are tested. The results show that the present finite element approach has good accuracy to predict the radiative heat transfer in multi-layer cylindrical medium with Fresnel surfaces.     

辐射换热的分区计算研究

本文利用蒙特卡洛法模拟圆柱形参与性介质内的辐射换热过程,分区计算了温度仅沿轴向(一维)变化和同时沿轴向和径向(二维)变化的吸收、发射、各向异性散射介质的边界热流分布,将各子区域的边界面假想为等效黑体面,采用由子区间的投射热流计算假想等效黑体面温度的方法,通过分别对介质温度分布一维和二维两种变化情况的研究表明,分区方法可以大大节省计算机内存,同时子区间介质的温度水平,几何尺寸比例以及各区间重合的光学厚度是影响热流分布精度的主要因素。     

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.     

基于能量密度分布的辐射源粒子空间抽样方法研究

利用隐式蒙特卡罗方法模拟热辐射光子在物质中的输运过程时,物质辐射源粒子是需要细致处理的物理量.传统的物质辐射源粒子抽样方法是体平均抽样方法,对于大多数问题,这样处理不会带来大的偏差.但是对于一些辐射吸收截面大、单一网格内温差显著的问题,体平均抽样方法的计算结果偏差较大.分析了产生偏差原因,提出一种基于辐射能量密度分布的辐射源粒子空间位置抽样方法,并推导了相应的抽样公式以解决此类问题.数值实验表明,新方法计算结果明显优于原方法且与解析结果基本一致.     

Curved ray tracing method for one-dimensional radiative transfer in the linear-anisotropic scattering medium with graded index

The curved ray tracing method (CRT) is extended to radiative transfer in the linear-anisotropic scattering medium with graded index from non-scattering medium. In this paper, the CRT is presented to solve one-dimensional radiative transfer in the linear-anisotropic scattering gray medium with a linear refractive index and two black boundaries. The predicted temperature distributions and radiative heat flux at radiative equilibrium are determined by the proposed method, and numerical results are compared with the data in references. The results show that the CRT has a good accuracy for radiative transfer in the linear-anisotropic scattering medium with graded index and the dimensionless emissive power and dimensionless radiative heat flux depend on the dimensionless refractive index gradient. It can also be seen that the dimensionless refractive index gradient has important effects on the temperature discontinuity at the boundaries.     

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.     

Finite element method for modeling radiative transfer in semitransparent graded index cylindrical medium

Both Galerkin finite element method (GFEM) and least squares finite element method (LSFEM) are developed and their performances are compared for solving the radiative transfer equation of graded index medium in cylindrical coordinate system (RTEGC). The angular redistribution term of the RTEGC is discretized by finite difference approach and after angular discretization the RTEGC is formulated into a discrete-ordinates form, which is then discretized based on Galerkin or least squares finite element approach. To overcome the RTEGC-led numerical singularity at the origin of cylindrical coordinate system, a pole condition is proposed as a special mathematical boundary condition. Compared with the GFEM, the LSFEM has very good numerical properties and can effectively mitigate the nonphysical oscillation appeared in the GFEM solutions. Various problems of both axisymmetry and nonaxisymmetry, and with medium of uniform refractive index distribution or graded refractive index distribution are tested. The results show that both the finite element approaches have good accuracy to predict the radiative heat transfer in semitransparent graded index cylindrical medium, while the LSFEM has better numerical stability.     

用射线踪迹法解黑表面矩形介质耦合换热

本文用射线踪迹-节点分析法研究了二维黑体表面矩形、各向同性散射半透明介质内辐射与导热瞬态耦合换热。采用全隐格式的有限差分法离散二维瞬态微分能量方程,用辐射传递系数来表示辐射源项,结合谱带模型并采用射线踪迹法求解辐射传递系数。采用Patankar线性化方法将辐射源项及不透明边界条件线性化,并采用附加源项法处理边界条件,运用ADI方法求解名以上的线性化方程组,从而解得二维矩形介质内的瞬态温度分布。     

圆柱坐标系下任意方向辐射强度的源项六流法模拟

基于传统热流法,提出一种圆柱坐标系下的源项六流模型(Source Six Flux,SSF),可快速准确地计算参与性介质内任意方向的出射辐射强度.详细介绍SSF模型的基本原理和求解步骤,以圆柱形吸收、散射、发射性介质为例,模拟其沿任意方向的出射辐射强度,并与反向蒙特卡罗法(Backward Monte Carlo,BMC)和二流法(Two Flux Method,TFM)的计算结果进行比较.结果表明,SSF法与BMC法的计算结果吻合较好,计算精度均高于TFM法,但SSF法的计算效率明显优于BMC法.因此,SSF模型是一种适用于计算任意方向辐射强度问题的高效数值模型.     

配置点谱方法求解一维圆柱梯度折射率介质中的辐射传热

发展一种配置点谱方法，计算包含半透明各向异性散射介质的圆柱系统中的辐射传热.介质具有梯度折射率，并且散射反照率随空间位置变化.通过与精确解或其他方法的结果对比，验证配置点谱方法的准确性.结果表明：配置点谱方法仅采用少量的节点数就可以得到准确的辐射热流量.     

Radiative transfer in finite cylindrical media using transformed integral equations

A modified direct integration method is presented to solve three-dimensional radiative transfer in emitting, absorbing and linear-anisotropic scattering finite cylindrical media. This scheme effectively avoids an integral singularity in the coupled Fredholm type integral equations of radiative transfer. The scheme leads to faster and more accurate results, which are needed in combined mode and non-gray problems. The calculated incident radiation and heat fluxes agree well with published results by discrete ordinates method. Using the transformed integral equations, the effects of boundary emission and reflection can also be easily handled.     

圆筒形半透明介质内非稳态复合导热与辐射的研究

本文研究细长电加热体在圆筒形半透明介质中的温度响应，通过对控制非稳态导热与辐射复合传热过程的积分-微分方程直接进行数值求解，分析了热辐射对内部径向热流及温度变化的影响．模拟计算结果对热线法测量半透明介质导热系数的研究具有理论指导意义。     

Numerical solution of radiative and conductive heat transfer in concentric spherical and cylindrical media

A new technique is presented to improve the performance of the discrete ordinates method when solving the coupled conduction-radiation problems in spherical and cylindrical media. In this approach the angular derivative term of the discretized one-dimensional radiative transfer equation is derived from an expansion of the radiative intensity on the basis of Chebyshev polynomials. The set of resulting differential equations, obtained by the application of the S_N method, is numerically solved using the boundary value problem with the finite difference algorithm. Results are presented for the different independent parameters. Numerical results obtained using the Chebyshev transform method compare well with the benchmark approximate solutions. Moreover, the new technique can easily be applied to higher-order S_N calculations.     

求解介质内热辐射传递的双向统计蒙特卡罗法

基于热辐射传输的光路可逆性原理,提出了求解介质内热辐射传递的双向统计蒙特卡罗法(BSMC法)。该方法采用等温等权抽样,利用能束传输路径的可逆关系进行辐射传递的双向统计计算,充分利用了能束跟踪的计算信息。以二维矩形区域内吸收性介质的热辐射传递为例,介绍了BSMC的求解过程,分析了其计算误差。通过数值模拟,从辐射传递因子计算结果的倒易性满足程度与辐射平衡温度场两方面,将BSMC法与传统的蒙特卡罗法(TMC法)进行了比较。结果表明,在相同的计算量下,BSMC法比TMC有更高的模拟精度。     

The method of lines solution of discrete ordinates method for non-grey media

A radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) for radiative heat transfer in non-grey absorbing-emitting media was developed by incorporation of a gas spectral radiative property model, namely wide band correlated-k (WBCK) model, which is compatible with MOL solution of DOM. Predictive accuracy of the code was evaluated by applying it to 1-D parallel plate and 2-D axisymmetric cylindrical enclosure problems containing absorbing-emitting medium and benchmarking its predictions against line-by-line solutions available in the literature. Comparisons reveal that MOL solution of DOM with WBCK model produces accurate results for radiative heat fluxes and source terms and can be used with confidence in conjunction with computational fluid dynamics codes based on the same approach.     

椭圆柱形光学黑洞红外辐射特性分析

本文主要采用时域有限差分(FDTD)方法计算了二维椭圆柱形光学黑洞的红外辐射特性。并且采用几何光学近似(GOA)对椭圆柱形的光学黑洞的光线入射轨迹进行分析和比较。研究结果表明,FDTD计算的光学黑洞内的能流分布结果与GOA计算的光学黑洞内的光线入射轨迹结果相吻合,椭圆柱形光学黑洞的红外辐射特性主要受折射率梯度和入射波长的影响。     

The method of lines solution of discrete ordinates method for radiative heat transfer in cylindrical enclosures

A radiation code based on method of lines solution of discrete ordinates method for radiative heat transfer in axisymmetric cylindrical enclosures containing absorbing-emitting medium was developed and tested for predictive accuracy by applying it to (i) test problems with black and grey walls (ii) a gas turbine combustor simulator enclosing a non-homogeneous absorbing-emitting medium and benchmarking its steady-state predictions against exact solutions and measurements. Comparisons show that it provides accurate solutions for radiative heat fluxes and can be used with confidence in conjunction with CFD codes based on the same approach.     

Application of the lattice Boltzmann method to transient conduction and radiation heat transfer in cylindrical media

In this paper, the lattice Boltzmann method (LBM) is applied to solve the energy equation of a transient conduction-radiation heat transfer problem in a two-dimensional cylindrical enclosure filled with an emitting, absorbing and scattering media. The control volume finite element method (CVFEM) is used to obtain the radiative information. To demonstrate the workability of the LBM in conjunction with the CVFEM to conduction-radiation problems in cylindrical media, the energy equation of the same problem is also solved using the finite difference method (FDM). The effects of different parameters, such as the grid size, the scattering albedo, the extinction coefficient and the conduction-radiation parameter on temperature distribution within the medium are studied. Results of the present work are compared with those available in the literature. LBM-CVFEM results are also compared with those given by the FDM-CVFEM. In all cases, good agreement has been obtained.