Albedo problem for finite plane-parallel medium

The problem of radiation transfer through a scattering and absorbing finite plane-parallel medium is solved using an efficient and accurate method of analysis which utilizes trial functions based on Case's eigenvalues plus a linear combination of exponential integral functions. The proposed trial functions are used on the integral equation reducing it to a system of algebraic equations to be solved for the expansion coefficients which are used to calculate some interesting physical quantities such as the angular radiation intensity and the reflection and the transmission coefficients. Numerical results are obtained for two different external incidence on the left boundary, x=0. The results are compared with the exact results and with those calculated by the Pomraning-Eddington variational method.     

Radiative transfer in finite participating atmospheric aerosol media

The properties of radiation transfer through a plane-parallel atmospheric aerosol medium has been studied. It has been done by employing Mie theory to calculate the radiation transfer scattering parameters of the medium in the form of extinction, scattering, and absorption efficiencies. Then, the equation of radiative transfer through a plane-parallel atmosphere of aerosol has been solved for partial heat fluxes using two different analytical techniques, namely, the Variational Pomraning -Eddington approximation and Galerkin technique. Average efficiencies over log-normal and modified gamma size distributions are calculated. Therefore, the radiative properties of Carbon, Anthracite, Bituminous, Lignite, and Fly ash have been calculated. The obtained numerical results show very good agreement with each other in addition to the previous published work.     

Radiative transfer in plant leaves

A two-layer model of light scattering and absorption in plant phytoelements is considered, which takes into account absorption of light by pigments and water and light scattering by particles of two types: chloroplasts and air cavities. An elementary light scattering event is described using the Mie theory. Multiple light scattering in a leaf is described within the framework of the theory of radiative transfer. The equation of radiative transfer with a strongly anisotropic phase function is solved using the method of addition of layers and the method of reduction to a medium with effective parameters depending on the propagation direction of light. The spectral dependences of reflection and transmission coefficients are calculated in the visible range as functions of the leaf structure.     

Estimation of the spectral absorption of light by components of human skin

The spectra of the absorption coefficients of external radiation by basic chromophores of human skin, such as melanin, basic tissue, and blood (including oxy- and deoxyhemoglobin), are studied in the wavelength range of 300–1000 nm. For estimates, analytical methods of the theory of light transfer are used, which take into account the multilayer structure of a biological tissue, multiple light scattering in a medium, and multiple rereflections of radiation between layers. The calculated spectra are compared with the wavelength dependences of the absorption indices of these components available from the literature. It is shown that the spectral behaviors of the coefficients and indices of absorption strongly differ, which is related to the selectivity of the optical properties of a biological tissue. The possibilities of predicting the absorption coefficients of the skin components from the absorption coefficient of the entire skin measured under conditions of variation of its biophysical parameters (the volume concentrations of melanin and blood vessels) over a wide range are evaluated.     

Transmission of radiation through an aerosol medium

The properties of radiation through an aerosol medium have been achieved. This has been done by employing Mie scattering theory to calculate the radiation transfer scattering parameters in the form of extinction, absorption and scattering efficiencies. The equation of radiative transfer for the heat flux through a plane parallel atmosphere of aerosol has been solved. The aerosol size distributions are found in practical systems. Average efficiencies over size distribution for spherical particles of complex refractive index are calculated. Therefore, the radiative properties of stratospheric aerosols have been done. The obtained results found to be in a good agreement with the previous work.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

Heat transfer by radiation and conduction in fibrous media without axial symmetry

Coupled radiative and conductive heat transfer in a fibrous medium formed by silica fibres is investigated in this paper by not taking account of the axial symmetry for the distribution of fibres or the boundary conditions. Radiative properties of the medium are calculated by using the Mie theory. The model obtained depends only on optical parameters (indices of silica) and on morphological parameters (diameter and orientation of the fibres, density of the medium). Simulations make it possible to study the strongly anisotropic behaviour of the scattering of the radiation by a fibre and to study the influence of various parameters on the radiative properties of the medium. The results of the Mie theory make possible the simulation of the heat transfer coupled by radiation and conduction. To do this, we introduce a new numerical scheme able to simulate heat transfer in the lack of axial symmetry. With this model, we can show the effects of distribution of fibres and temperature on the thermal behaviour of the medium as well as showing the importance of the phenomenon of scattering in fibrous media.     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning-Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

激光脉冲在各向异性散射介质内的瞬态热效应

本文考察了激光脉冲在吸收、发射、各向异性散射介质内引起的瞬态热效应。将激光脉冲辐射在介质内的传递过程分为两个子过程：发射－衰减－反射过程和吸收－散射过程。用光线踪迹法结合节点分析导出辐射传递系数和辐射源项,用控制容积法解瞬态能量方程。检验结果表明,本文的计算方法准确。在此基础上,考察了散射特性、初始温度对激光脉冲响应的影响。     

Pure-triplet scattering for radiative transfer in binary discrete random finite media with reflective boundaries and internal source of radiation

The stochastic solution of the monoenergetic radiative transfer equation in a finite slab random medium with pure-triplet anisotropic scattering is considered. The random medium is assumed to consist of two randomly mixed immiscible fluids labelled by 1 and 2. The extinction function, the scattering kernel, and the internal source of radiation are treated as discrete random variables, which obey the same statistics. The theoretical model used here for stochastic media transport assumes Markovian processes and exponential chord length statistics. The boundaries of the medium under consideration are considered to have specular and diffuse reflectivities with an internal source of radiation inside the medium. The ensemble-average partial heat fluxes are obtained in terms of the average albedos of the corresponding source-free problem, whose solution is obtained by using the Pomraning–Eddington approximation. Numerical results are calculated for the average forward and backward partial heat fluxes for different values of the single scattering albedo with variation of the parameters that characterize the random medium. Compared to the results obtained by Adams et al. in the case of isotropic scattering based on the Monte Carlo technique, it can be demonstrated that we have good comparable data.     

Bessel驻波对椭球形液滴的声辐射转矩

在实际的声操控中,由于声辐射力、表面张力和重力的共同作用,液滴往往呈现出椭球的形状,在螺旋声场中会受到力矩的作用而发生转动。从声波的散射理论出发,根据部分波展开法求解得到了椭球形液滴在Bessel驻波场中的声散射系数,并给出了其受到的声辐射转矩的解析式。在此基础上,对椭球形不可压缩液滴和椭球形可压缩液滴分别进行数值计算。仿真结果表明,不可压缩液滴的声辐射转矩与声束半锥角的关系更密切,而可压缩液滴则更依赖于特定的频率;提升Bessel驻波场的阶数有利于增强声辐射转矩的峰值,但在中低频处较难对可压缩液滴产生明显的力矩。该研究结果预期对利用螺旋声场进行液滴的操控具有理论指导作用。      

Albedo problem for pure-triplet scattering in finite planar media

Pure triplet scattering in neutron transport through a finite plane-parallel medium is considered. Galerkin approximation is introduced to calculate some functionals arising in radiative transfer problems such as reflection and transmission coefficients. Some of numerical results are compared with the results calculated by Pomraning-Eddington Variational method.     

A two-step strategy for numerical simulation of radiative transfer with anisotropic scattering and reflection

This article presents a two-step procedure for the computation of radiative heat transfer with anisotropic scattering and reflection. It is based on a concept that the coincident processes of absorption and scattering/reflection can be separated factitiously. All medium elements and wall surfaces are supposed to be pure-absorbing when receiving incident radiation. Afterwards they emit the scattered/reflected radiations. The absorption of both the initial and the secondary radiations can be assessed by the direct exchange area. It is needed to repeat the processes for a few times until the radiations are substantially absorbed. For anisotropic scattering/reflection, a vector summation obtains the directional distribution of emissive power. The method is validated by several benchmark computations in terms of emissive power and heat transfer coefficients. It is shown that the method gives more accurate solution than the isotropic scaling for the heat transfer in anisotropically scattering media.     

Non-Fourier heat conduction with radiation in an absorbing, emitting, and isotropically scattering medium

This article numerically analyses the combined conductive and radiative heat transfer in an absorbing, emitting, and isotropically scattering medium. The non-Fourier heat conduction equation, which includes the time lag between heat flux and the temperature gradient, is used to model the conductive heat transfer in the medium. It predicts that a temperature disturbance will propagate as a wave at finite speed. The radiative heat transfer is solved using the P₃ approximation method. In addition, the MacCormack's explicit predictor-corrector scheme is used to solve the non-Fourier problem. The effects of radiation including single scattering albedo, conduction-to-radiation parameter, and optical thickness of the medium on the transient and steady state temperature distributions are investigated in detail. Analysis results indicate that the internal radiation in the medium significantly influences the wave nature. The thermal wave nature in the combined non-Fourier heat conduction with radiation is more obvious for large values of conduction-to-radiation parameter, small values of optical thickness and higher scattering medium. The results from non-Fourier-effect equation are also compared to those obtained from the Fourier equation. Non-Fourier effect becomes insignificant as either time increases or the effect of radiation increases.     

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.     

Monte Carlo simulation for millimeter wave propagation and scattering in rain medium

As the operating frequencies of communications systems more higher into the millimeter wave range, the effects of multiple scattering in precipitation media become more significant. This paper treats the problems of electromagnetic multiple scattering in rain medium by the Monte Carlo method. The em wave is regarded as a Markov chain of photon collisions in a medium in which it is scattered and absorbed. For the sake of simplicity, the polarization is not taken into account, the above mentioned problems are described by the scale integro-diffierential equation of transfer. When the plane wave through a random medium with particle size distribution, the technique of weighted average is used to characterize the radiation intensity, including average scattering, absorption coefficients and phase function. The Monte Carlo simulation algorithms are done for the rain attenuation and reflectance at millimeter wavelength region. Our computational results are in good agreement with experimental data of rain attenuation.     

Radiative transfer in a two-dimensional rectangular medium exposed to diffuse radiation

The integral equation for radiative transfer in a two-dimensional rectangular scattering medium exposed to diffuse radiation is solved numerically by removing the singularity. This method yielded accurate results except at very large optical thicknesses. Graphical and tabular results for the source function, flux, and intensity are presented. The source function is also calculated using the first term of a Taylor series expansion. The Taylor series is fairly accurate for small optical thicknesses and columnar geometries. A method is presented for extending these results to the problem of a strongly anisotropic scattering phase function which is made up of a spike in the forward direction superimposed on an isotropic phase function.     

Radiative and conductive heat transfer in a nongrey semitransparent medium. Application to fire protection curtains

This paper deals with heat transfer in nongrey media which scatter, absorb and emit radiation. Considering a two dimensional geometry, radiative and conductive phenomena through the medium have been taken into account. The radiative part of the problem was solved using the discrete ordinate method with classical S_n quadratures. The absorption and scattering coefficients involved in the radiative transfer equation (RTE) were obtained from the Mie theory. Conduction inside the medium was linked to the RTE through the energy conservation. Validation of the model has been achieved with several simulation of water spray curtains used as fire protection walls.     

Specific features of optical diffusion in nematic liquid crystals

Methods of computer simulation are used to study multiple light scattering in the ordered phase of a nematic liquid crystal. The development of the diffusion regime is studied in detail. It is demonstrated that the transient time depends on the external magnetic field and the direction of the incident radiation. The diffusion coefficients along and across the director are calculated. The validity of the diffusion approximation is controlled using the moments of the distribution function. Analysis of the diffusion coefficients versus the external field shows that the diffusion coefficients remain almost unchanged in the experimental range of the magnetic fields. In the presence of relatively strong fields, the diffusion coefficients increase due to a variation in the shape of the scattering indicatrix and the free-path length of photons. The dependence of the diffusion coefficients on the radiation wavelength is also calculated. Comparison of the simulated results and the experimental data shows that the calculated diffusion rate across the director virtually coincides with the experimental rate. The calculated diffusion coefficient along the director is substantially greater than the corresponding experimental rate.     

DRESOR法对瞬态辐射传递问题的研究

用基于蒙特卡洛法(Monte Carlo Method,MCM)的DRESOR法(Distributions of Ratios of Energy Scattered by the medium Or Reflected by the boundary surface)求解入射辐射经过介质散射、壁面反射传递后辐射强度随时间变化的瞬态辐射传递方程(Transient RadiativeTransfer Equation,TRTE)问题。通过在系统内计算一单位瞬态入射辐射对介质的DRESOR数分布,就能计算任意时间内入射辐射在系统内时间响应特性,这样有效提高数值方法处理瞬态辐射问题的通用性。并且能够获得高方向分辨率的辐射强度随时间变化的结果,这是目前大多数数值处理方法比较难做到的,显示出了DRESOR法处理瞬态入射辐射问题的能力．