Effect of line or band shape on the radiative flux of an isothermal spherical layer

Radiative transfer in a nongray, absorbing-emitting spherical layer is investigated. The absorption coefficient consists of an array of equal-intensity, nonoverlapping, narrow bands or lines. Specific attention is directed toward the evaluation of the effect of band or line shape on the local radiative flux of an isothermal layer. The integral equation for radiative equilibrium is formulated and functions associated with it are studied. Numerical and graphical results are presented for the rectangular, triangular, exponential, Doppler, and Lorentz profiles.     

Expansions for two-dimensional radiative transfer in an isotropically scattering semi-infinite medium

Small spatial frequency expansions for the source function and radiative flux are obtained for a purely scattering, semi-infinite, two-dimensional medium. Both collimated and diffuse boundary conditions are analyzed. With these expansions, other expansions are obtained which are valid at large optical distances away from the incident radiation. Expansions are presented for a finite strip, circular disk and a Gaussian distribution.     

Coaxial radiative and convective heat transfer in gray and nongray gases

Coupled radiative and convective heat transfer is investigated for an absorbing gas flowing in a finite length channel and heated by blackbody radiation directed along the flow axis. The problem is formulated in one dimension and numerical solutions are obtained for the temperature profile of the gas and for the radiation escaping the channel entrance, assuming both gray and nongray absorption spectra. Due to radiation trapping, the flowing gas is found to have substantially smaller radiation losses for a given peak gas temperature than a solid surface that is radiatively heated to this temperature. A greenhouse effect is also evident whereby radiation losses are minimized for a gas having stronger absorption at long wavelengths.     

Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular media

Effect of scattering on radiative heat transfer in two-dimensional rectangular media by the finite-volume method has been studied. Compared with the existing solutions, it shows that the result obtained by the finite-volume method is reliable. Furthermore, relative errors caused by the approximation that linear and nonlinear anisotropic scattering media is simplified to isotropic scattering media have been studied.     

Numerical procedures in two-dimensional radiative transfer

Latko and Pomraning have described an attempt to reduce computer-time requirements substantially for two-dimentional, time-dependent radiation transport by accurately constructing the two dimensional problem from a small number of one-dimensional calculations. Two rapid inversion methods exist for assuring the success of their synthesis technique.     

Benchmark numerical solutions for radiative heat transfer in two-dimensional medium with graded index distribution

In graded index media, the ray goes along a curved path determined by Fermat principle. Generally, the curved ray trajectory in graded index media is a complex implicit function, and the curved ray tracing is very difficult and complex. Only for some special refractive index distributions, the curved ray trajectory can be expressed as a simple explicit function. Two important examples are the layered and the radial graded index distributions. In this paper, the radiative heat transfer problems in two-dimensional square semitransparent with layered and radial graded index distributions are analyzed. After deduction of the ray trajectory, the radiative heat transfer problems are solved by using the Monte Carlo curved ray-tracing method. Some numerical solutions of dimensionless net radiative heat flux and medium temperature are tabulated as the benchmark solutions for the future development of approximation techniques for multi-dimensional radiative heat transfer in graded index media.     

Transient radiative transfer in irregular two-dimensional geometries

This article presents a finite-volume method to calculate transient radiative transfer in two-dimensional irregularly shaped enclosures. The fully implicit scheme is used to discretize the transient term. The step and CLAM spatial differencing schemes are used in this study. The procedure is validated with available published results. The capabilities of the procedure are then examined using two additional test problems. The ability of the present formulation in modeling absorbing, emitting and anisotropically scattering media is examined using wall heat fluxes and incident radiation.     

Nongray radiative transfer in a semi-infinite medium: H-function

Numerical results are presented for the dimensionless emissive power at the boundary of a nongray semi-infinite medium in radiative equilibrium. The adsorption coefficient of an array of equal intensity, nonoverlapping bands or lines. Specifically, the rectangular, triangular, exponential, Doppler and Lorentz profiles are considered.     

Two-dimensional radiative transfer in a finite scattering planar medium

The source function, radiative flux, and intensity at the boundaries are calculated for a two-dimensional, scattering, finite medium subjected to collimated radiation. The scattering phase function is composed of a spike in the forward direction super-imposed on an isotropic background. Exact radiative transfer theory is used to formulate the problem and Ambarzumian's method is used to obtain results. Using the principle of superposition, the results for any step variation in incident radiation are expressed in terms of universal functions for the semi-infinite step case. Two-dimensional effects are most pronounced at large optical thicknesses and albedos.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Radiative decay times for thermal pertubations in a nongray medium

The radiative decay time of harmonic thermal perturbations in a nongray medium of infinite extent is obtained in closed form for two specific band absorption models. These models are the frequently used gray band and the exponential band, the latter being considered more realistic for molecular gases. It is found that the decay time at the boundary of a semi-infinite medium can be obtained in terms of that in an infinite medium. The decay time for combined thermal radiation and conduction is also discussed. The difference in radiative decay rates for a medium with gray bands and one with exponential-tailed bands is marked; in an infinite medium at large Bouguer number, the former falls to zero while the latter rises to a maximum.     

Tau method approximation for radiative transfer problems in a slab medium

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.     

Discrete transfer method applied to radiative transfer in a variable refractive index semitransparent medium

Application of the discrete transfer method (DTM) has been extended to the analysis of radiative heat transfer in a variable refractive index participating medium. To validate the DTM formulation, radiative heat transfer in an absorbing, emitting and isotropically scattering planar medium was considered. The participating medium was assumed to be in radiative equilibrium. For both constant and variable refractive indices of the medium, the DTM results were compared with those available in the literature. The DTM was found to provide accurate results.     

Equivalence of MTF of a turbid medium and radiative transfer field

The equivalence of the modulation transfer function (MTF) of a turbid medium and the transmitted radiance from the medium under isotropic diffuse illumination is demonstrated. MTF of a turbid medium can be fully evaluated by numerically solving a radiative transfer problem in a plane parallel medium. MTF for a homogenous single layer turbid medium is investigated as illustration. General features of the MTF in the low and high spatial frequency domains are provided through their dependence on optical thickness, single scattering albedo, asymmetrical factor, and phase function type.     

大气折射对可见光波段辐射传输特性的影响

折射是影响辐射传输的重要因素. 为分析大气折射对辐射传输的影响, 基于Monte Carlo方法, 给出了考虑大气折射的矢量辐射传输模型, 实现了均匀气层和耦合面处光子随机运动过程的模拟, 实现了直射光及漫射光Stokes矢量、偏振度和辐射通量等参数的计算. 在考虑和不考虑大气折射两种条件下, 验证了模型的准确性; 在纯瑞利散射条件下, 讨论了大气折射对不同方向漫射光Stokes矢量的影响; 在不同太阳天顶角、大气廓线、气溶胶及含云大气条件下, 分析了大气折射对辐射传输过程的影响. 结果表明: 大气折射对漫射光Stokes矢量的影响主要体现在天顶角70°–110°区间, 且随着太阳入射角增大, 其影响更为显著; 不同大气廓线情形下, 大气折射对Stokes矢量的影响不一致, 其原因是不同大气廓线对应的折射率廓线存在差异. 含云及含气溶胶大气条件下, 大气折射对辐射传输的影响变弱, 沙尘型及海盐型气溶胶条件下, 折射对辐射传输的影响强于可溶型气溶胶情形; 不同形状气溶胶条件下, 大气折射对辐射传输的影响也存在显著差异; 不同云高条件下, 大气折射对漫射光Stokes矢量的影响无显著差异, 但随着云光学厚度增大, 大气折射的影响减弱.     

Temperature field of radiative equilibrium in a two-dimensional graded index medium with gray boundaries

In this paper, a numerical method is presented for the study of the radiative transfer in a two-dimensional graded index semitransparent medium with diffuse gray boundaries. The numerical method is a combination of the linear refractive index bar model, the discrete curved ray-tracing technique and the pseudo source adding method (LRIB-CRTP). In the traditional ray-tracing technique, it is difficult to deal with the diffuse gray boundary while solving the radiative transfer. Using the pseudo source adding method, the diffuse gray boundary of the medium can be treated as a black boundary. We have also studied the radiative equilibrium temperature field of the medium and analyzed the influence of some parameters involved. The results show that the directional discrete number is important for the medium having a large absorption coefficient. The results also show that the refractive index distribution greatly influences the temperature field, whereas the linear absorption coefficient distribution has little influence on the temperature field.     

An approximate band model for radiative transfer in semitransparent solids

A simplified model for the spectral refractive index and absorption coefficient of semitransparent solids is developed from solid state lattice vibrational theory. This model accurately predicts the total band absorptance and total internal emittance for long pathlengths and selected solids. Total band absorptance is shown to be proportional to the square root of the pathlength when the pathlength is large. Comparison to exact results for α-quartz and lithium fluoride demonstrates that the total radiative transfer properties are accurately predicted by the model when the pathlength exceeds one millimeter.     

Radiative decay time of a nongray medium with arbitrary configurations

Based on the principle of conservation of energy, a simple analytical expression is presented for the radiative decay time of a nongray medium with arbitrary configurations. It is expressed explicity in terms of the mean beam length and the total band absorptance. In the high-pressure limit, where the decay time based on the harmonic thermal perturbation is available for two configurations, comparison is made with the present decay time. Good agreement is found.