Internal distribution of radiation absorption in a semitransparent spherical particle

The internal distribution of spectral radiation absorption in a semitransparent spherical particle irradiated uniformly and isotropically is determined by the ray tracing method, and the detailed computation formulae for the internal spectral radiation absorption are deduced. The computed results show that the peak of internal volumetric spectral radiation absorption may locate at the interior shell of the particle. The dimensionless volumetric spectral radiation absorption is higher near the center for weakly absorbing or small spheres, but the dimensionless volumetric spectral radiation absorption is higher near the surface for strongly absorbing or large spheres. The corresponding physical interpretations of the internal spectral absorption distribution are given.     

Radiative intensity solution and thermal emission analysis of a semitransparent medium layer with a sinusoidal refractive index

The radiative intensity in a sinusoidal refractive index semitransparent medium layer is solved by the curved ray-tracing method in combination with the pseudo-source adding method. One boundary of the medium layer is an opaque diffuse substrate wall. The other boundary is a semitransparent specular or diffuse surface, from which the medium thermal emission emerges. With considering a linear temperature distribution, the radiative intensity formulae are, respectively, deduced under the two boundary conditions. On the basis of the radiative intensity solutions, the directional and hemispherical emission of the medium layer with a specular surface as well as the hemispherical emission of that with a diffuse surface are calculated. The influences of the optical thickness, sinusoidal refractive index distribution and linear temperature distribution on the thermal emission are investigated. The results show that the effects of refractive index and temperature distribution are significant and are different under the two reflecting modes of the surface.     

Transient coupled radiation-conduction in infinite semitransparent cylinders

A method is developed to analyze the transient coupled radiation-conduction in infinite semitransparent cylinders surrounded by isothermal black walls. The radiative heat source term is calculated by the radiative transfer coefficients and the transient energy equation is solved by an implicit finite difference method. The radiative transfer coefficients are deduced by use of the ray tracing method in combination with the Hottel and Sarofim zonal method. The effects of the related parameters on the transient radiative heat source and temperature distribution are analyzed. It is found that the peak of the dimensionless radial radiative heat source can be located at the interior shell of the cylinder with small optical thickness when heated by the surrounding irradiation. Treating the volume radiation as a surface radiation will result in large errors of transient temperature distribution for the cylinder with small optical thickness.     

Thermal emission and volumetric absorption of a graded index semitransparent medium layer

Both thermal emission and volumetric absorption characteristics of a graded index semitransparent medium layer are investigated numerically. The semitransparent and specular emerging surface of the medium layer is parallel to an opaque and diffuse substrate wall. Monochromatic spectrum or gray medium is considered in the analysis. A pseudo-source adding method is combined with a ray-splitting and -tracing technique to solve the radiative transfer in the medium. As examples, constant and linear refractive index distributions are examined for an isothermal layer and the medium layer with a linear temperature distribution. Directional and hemispherical thermal emissions from the emerging surface as well as the volumetric absorption to the diffuse and parallel incidence of radiation are investigated, respectively. The results show that the refractive index distribution has significant influences on thermal emission and volumetric absorption of a semitransparent medium layer. The optical thickness, temperature distribution and the reflectivity of substrate wall react in combination with the refractive index distribution.     

Radiative transfer in a spherical, emitting, absorbing and anisotropically scattering medium

The atmospheres of planets (including Earth) and the outer layers of stars have often been treated in radiative transfer as plane-parallel media, instead of spherical shells, which can lead to inaccuracy, e.g. limb darkening. We give an exact solution of the radiative transfer specific intensity at all points and directions in a finite spherical medium having arbitrary radial spectral distribution of: source (temperature), absorption, emission and anisotropic scattering. The power and efficiency of the method stems from the spherical numerical gridding used to discretize the transfer equations prior to matrix solution: the wanted ray and the rays which scatter into it both have the same physico-geometric structure. Very good agreement is found with an isotropic astrophysical benchmark [Avrett EH, Loeser R. Methods in radiative transfer. In: Kalkofen W, editor. Cambridge: Cambridge University Press; 1984. pp. 341-79]. We introduce a specimen arbitrary forward- side-back phase scattering function for future comparisons. Our method directly and exactly addresses spherical symmetry with anisotropic scattering, and could be used to study the Earth's climate, nuclear power (neutron diffusion) and the astrophysics of stars and planets.     

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.     

Time-dependent radiative transfer using Chapman-Enskog maximum entropy method

The time-dependent problems of radiative transfer involve a coupling between radiation and material energy fields and are nonlinear because of proposed temperature dependence of the medium characteristics in semi-infinite medium with Rayleigh anisotropic scattering. By means of the limited flux, Chapman-Enskog and maximum entropy technique the time-dependent radiative transfer equation has been solved explicitly. The maximum entropy method is used to solve the resulting differential equation for radiative energy density. The calculations are carried out for temperature (normalized dimensionless) Θ(x,τ), radiative energy density and net flux with Rayleigh and anisotropic scattering for different space at different times.     

Transient heat transfer in a spherical protective material, submitted to flux and mixed boundary conditions: an investigation on zirconia

An analytic solution is presented for describing combined radiation and conduction heat transfer in a spherical fiber thermal protection exposed to combined radiative and convective heating. The solution includes the equation of radiative transfer within the material, coupled to a transient energy equation that contains both radiative and convective terms. At elevated temperatures radiative transfer becomes important, and if several hot surfaces view each other, the radiation exchange process must be considered carefully. Some thermal protections are partially transparent to thermal radiation. Hence, an exchange process is complicated by radiation penetrating into and coming out of material. The radiation leaving an area depends on the temperature distribution inside that area and that is unknown and is affected by the exchange process to other areas. The analysis has allowed for unlimited spectral detail but assumes that the various material properties do not vary significantly with temperature. Transient temperature distributions are obtained for the boundary conditions of external radiation and convection. The present analysis includes the influence of reflectivity, surface radiative properties and spectral properties on the temperature distributions.     

The influence of anisotropic scattering on the radiative intensity in a gray, plane-parallel medium calculated by the DRESOR method

Even though there have been many ways to treat complex anisotropic scattering problems, in most of the cases only the radiation flux or its dimensionless data were provided, and radiative intensity with high directional resolution could merely be seen. In this paper, a comprehensive formulation for the DRESOR method was proposed to deal with the anisotropic scattering, emitting, absorbing, plane-parallel media with different boundary conditions. The method was validated by the data from literature and the integral formulation of RTE. The DRESOR value plays an important role in the DRESOR method, and how it is determined by the anisotropic scattering was demonstrated by some typical results. The intensities with high directional resolution at any point can be given by the present method. It was found that the scattering phase function has little effect on the intensity for thin optical thickness, for example, 0.1. And there is the largest boundary intensity for the medium with the largest forward scattering capability, and the smallest one with the largest backward scattering capability. An attractive phenomenon was observed that the scattering of the medium makes the intensity at boundary can not reach the blackbody emission capability with the same temperature, even if the optical thickness tends to very large. It was also revealed that the scattering of the medium does not mean it cannot alter the magnitude of the energy; actually, stronger scattering causes the energy to have more chance to be absorbed by the medium, and indirectly changes the energy magnitude in the medium. Finally, it is easy to deduce all the associated quantities such as the radiation flux, the incident radiation and the heat source from the intensity, just as done in literature.     

Spatial coherence in the transition radiation spectrum

The formal expression of the spectral distribution of the transition radiation intensity will be here derived in the case of a relativistic three-dimensional charged beam. Charged beams with a particle density such as is typically encountered in a particle accelerator will be considered. In particular, a sufficiently high particle density will be supposed so that a continuous spatial distribution function can be reliably attributed to the charged bunch. The formula of the spectral distribution of the transition radiation intensity originated by a relativistic three-dimensional charged beam - already presented in a previous work - will be here submitted to a formal check and interpreted in the physical consequences. The present work contains an additional mathematical derivation of the radiation energy spectrum consisting in a different method to implement the continuous limit in the distribution function of the particle coordinates. In the former derivation of the formula, the average operation with respect to the continuous distribution function of the particle coordinates was applied to the radiation intensity of a N electron bunch. In the present one, it is applied to the radiation electric field of a N electron bunch. The comparison of the two alternative but in any case equivalent formal routes to the spectral distribution of the transition radiation intensity will offer the possibility to directly cross-check the mathematical self-consistency of the presented results within the limits of applicability of the continuous limit approximation. According to such results, both the flux and the angular distribution of the photons emitted at a given wavelength - even shorter than the longitudinal length of the bunch - are expected to undergo a modification as the beam transverse size is varied with respect to the observed wavelength. As a function of the beam transverse size the spatial coherence degree of the transition radiation source is thus expected to change. The physical consistency of such an effect occurring in the transition radiation emission by a charged beam can be argued on the basis of a compatibility criterion with other similar relativistic electromagnetic radiative phenomena and interpreted in the framework of the temporal causality and the Huygens-Fresnel principles. Finally, the aspect of the applicability of the continuous limit approximation to the case of a charged beam in a particle accelerator is treated in terms of a practical quantitative criterion.     

Discontinuous spectral element method for solving radiative heat transfer in multidimensional semitransparent media

A discontinuous spectral element method (DSEM) is presented to solve radiative heat transfer in multidimensional semitransparent media. This method is based on the general discontinuous Galerkin formulation. Chebyshev polynomial is used to build basis function on each element and both structured and unstructured elements are considered. The DSEM has properties such as hp-convergence, local conservation and its solutions are allowed to be discontinuous across interelement boundaries. The influences of different schemes for treatment of the interelement numerical flux on the performance of the DSEM are compared. The p-convergence characteristics of the DSEM are studied. Four various test problems are taken as examples to verify the performance of the DSEM, especially the performance to solve the problems with discontinuity in the angular distribution of radiative intensity. The predicted results by the DSEM agree well with the benchmark solutions. Numerical results show that the p-convergence rate of the DSEM follows exponential law, and the DSEM is stable, accurate and effective to solve multidimensional radiative transfer in semitransparent media.     

Monte Carlo discrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index

A Monte Carlo discrete curved ray-tracing method is developed to analyze the radiative transfer in one-dimensional absorbing-emitting semitransparent slab with variable spatial refractive index, in which the Monte Carlo method is combined with the discrete curved ray-tracing method. A problem of radiative equilibrium with linear variable spatial refractive index is taken as an example to examine the accuracy of the proposed method. The temperature distributions and the dimensionless radiative heat flux are determined by the proposed method and compared with the data in references, which are obtained by other different methods. The results show that the Monte Carlo discrete curved ray-tracing method has a good accuracy in solving the radiative transfer in one-dimensional semitransparent slab with variable spatial refractive index.     

Backward Monte Carlo simulation for apparent directional emissivity of non-isothermal semitransparent slab

A backward Monte Carlo method based on radiation distribution factor is extended to compute the apparent directional emissivity of one-dimensional absorbing-emitting-scattering semitransparent slab with specular semitransparent surface and opaque diffuse substrate. A non-isothermal semitransparent slab is taken as an example to examine the efficiency of backward Monte Carlo method. The apparent directional emissivity of the semitransparent slab is determined by backward Monte Carlo simulation and compared with that determined by forward Monte Carlo simulation. The results show that the backward Monte Carlo method is very efficient in solving the apparent directional emissivity of the semitransparent slab. The backward Monte Carlo method converges more quickly than the forward Monte Carlo method.     

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.     

碳氢扩散火焰实验研究：燃烧气氛对火焰光谱与温度的影响

辐射是各种燃烧过程中热传递的主要方式。在不同的火焰中,辐射光谱分布十分复杂。在这项工作中,利用光谱仪测量了可见光(200～900 nm),近红外(900～1 700 nm)和中红外(2 500～5 000 nm)波段火焰的光谱强度,分析了空气和富氧气氛下扩散火焰的光谱特征。并基于光谱分析,定量得到了火焰中碳烟以及气体发射的辐射力,计算了火焰的温度分布。结果表明,空气燃烧中的火焰温度低于富氧燃烧中的火焰温度。在空气气氛下,火焰中的碳烟和气体均对中的热辐射起着重要作用。而在富氧气氛下,气体对于火焰热辐射更为重要。在可见光和近红外波段,由于在空气气氛下火焰中碳烟的大量形成,光谱曲线显示出了良好连续性。而富氧气氛下火焰的辐射光谱降低。在中红外波段,空气气氛下火焰的气体辐射明显弱于富氧气氛下火焰的气体辐射。     

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.     

Spectral collocation method with a flexible angular discretization scheme for radiative transfer in multi-layer graded index medium

The spectral collocation method (SCM) is employed to solve the radiative transfer in multi-layer semitransparent medium with graded index. A new flexible angular discretization scheme is employed to discretize the solid angle domain freely to overcome the limit of the number of discrete radiative direction when adopting traditional S_N discrete ordinate scheme. Three radial basis function interpolation approaches, named as multi-quadric (MQ), inverse multi-quadric (IMQ) and inverse quadratic (IQ) interpolation, are employed to couple the radiative intensity at the interface between two adjacent layers and numerical experiments show that MQ interpolation has the highest accuracy and best stability. Variable radiative transfer problems in double-layer semitransparent media with different thermophysical properties are investigated and the influence of these thermophysical properties on the radiative transfer procedure in double-layer semitransparent media is also analyzed. All the simulated results show that the present SCM with the new angular discretization scheme can predict the radiative transfer in multi-layer semitransparent medium with graded index efficiently and accurately.     

Reconstruction of time-averaged temperature of non-axisymmetric turbulent unconfined sooting flame by inverse radiation analysis

A multi-wavelength inversion method is extended to reconstruct the time-averaged temperature distribution in non-axisymmetric turbulent unconfined sooting flame by the multi-wavelength measured data of low time-resolution outgoing emission and transmission radiation intensities. Gaussian, β and uniform distribution probability density functions (PDF) are used to simulate the turbulent fluctuation of temperature, respectively. The reconstruction of time-averaged temperature consists of three steps. First, the time-averaged spectral absorption coefficient is retrieved from the time-averaged transmissivity data by an algebraic reconstruction technique. Then, the time-averaged blackbody spectral radiation intensity is estimated from the outgoing spectral emission radiation intensities. Finally, the time-averaged temperature is approximately reconstructed from the multi-wavelength time-averaged spectral emission radiation data by the least-squares method. Noisy input data have been used to test the performance of the proposed inversion method. The results show that the time-averaged temperature distribution can be estimated with good accuracy, even with noisy input data. The accuracy of the estimation decreases with the increase of turbulent fluctuation intensity of temperature and the effects of assumed PDF on the reconstruction of temperature are small.     

吸收-透射界面下正弦折射率介质内辐射换热

对具有吸收-透射性边界面的梯度折射率半透明介质层,建立了介质内热辐射传递与边界面辐射换热的数理模型,并采用数值弯曲光线跟踪法求解介质内的热辐射传递。通过数值模拟,分析了正弦折射率下,边界面的反射特性、吸收率以及介质层光学厚度对介质内热辐射平衡温度场及热流分布的影响。结果表明,边界面的反射特性与吸收率对介质内辐射换热均有重要影响,吸收率的影响与边界面反射特性、介质层光学厚度及环境条件相关,呈现特征不同的作用。