非球形气溶胶粒子散射相函数经验公式

散射相函数是研究电磁波传输特性的重要参数，直接影响电磁波传输方程的简化程度和解的精度。基于电磁散射与辐射传输中的基本理论，对非球形粒子散射相函数的经验公式进行了研究。为了很好的模拟非球形粒子的后向散射峰值，提高辐射传输方程的简化程度和解的精度，提出了一种新的相函数经验公式。分析新的相函数对非球形粒子的适用性，以单个沙尘性气溶胶为例，计算了不同形状粒子的Henyey-Greenstein*相函数和新的相函数随角度的变化，并与T矩阵法的计算结果进行了对比，发现椭球形粒子的长短轴比和有限长圆柱形粒子的径长比大于0.5时，新的相函数在大角度后向散射部分与T矩阵法的吻合程度较高。考虑波长变化，对比了尺寸谱满足对数正态分布的四种气溶胶粒子的Henyey-Greenstein*相函数和新的相函数与T矩阵法的计算结果。研究表明，对于椭球形粒子和有限长圆柱形粒子，在大角度(大于90°)后向散射部分，除了0.694时的椭球形海洋性气溶胶，新的相函数均方根差较小的占100%，证明了新的相函数可以较好的模拟非球形粒子的后向散射特征。新的相函数对准确模拟辐射传输过程具有重要意义。     

改进的单次散射相函数解析表达式

单次散射相函数对电磁辐射传输模拟过程的准确性和计算效率有重要的影响.基于电磁散射与辐射传输中的基本理论,对单次散射相函数的解析表达式进行了研究,提出了一种新的单次散射相函数解析表达式.比较了单个粒子的Henyey-Greenstein相函数、Henyey-Greenstein*相函数与新的相函数随角度的分布,发现新的散射相函数提高了后向散射峰值,可以更合理地描述单个粒子的散射特性.按三种气溶胶粒子谱分布模式计算了Henyey-Greenstein*相函数和新的相函数对应的数值结果,并与多分散系Mie散射相函数进行对比,发现新的相函数提高了与多分散系Mie散射相函数的符合程度.研究表明,对于大角度(大于90°)后向散射,新的相函数与Mie散射相函数均方根差较小的占73.3%,高于Henyey-Greenstein*相函数的26.7%,证明了新的相函数可以显著提高后向散射峰值.新的相函数对准确模拟辐射传输过程具有重要意义.     

辐射传输介质散射相函数的蒙特卡洛算法

复分散系相函数在辐射介质传热中是关键参数,蒙特卡洛法兼具数值算法与试验测量的优点.利用该方法计算复分散系的多重散射相函数克服了以往算法的缺点,可以体现多重散射的影响,并且可以计算任意形状控制体的相函数.大量的数学实验发现当介质系密度增大时,散射能量在4π空间内分布趋于均匀.     

取向比对圆柱状冰晶粒子光散射特性的影响

利用T矩阵方法研究卷云中圆柱状粒子取向比对散射特性的影响,计算了在小尺度范围内圆柱状冰晶粒子的散射特征量如散射相函数、消光效率因子、不对称因子及单次散射反照率,并将计算结果与等表面积、等体积及等效体积与投影面积比三种情况下的球形粒子的相应值进行了对比.结果表明:体积与投影面积比等效最接近真实值;取向比对不同尺度柱状粒子散射特性的影响存在相似性且有必要加以考虑;此外,发现等表面积、不同取向比粒子的散射相函数有一交点.     

紫外波段多分散系气溶胶散射相函数随机抽样方法研究

基于电磁散射与辐射传输中的基本理论,对紫外波段霾尺度范围内满足特定分布的多种气溶胶粒子的散射相函数进行了研究.提出了一种直接随机抽样拟合散射相函数的方法.比较了H-G相函数、改进的H-G相函数及随机抽样拟合的相函数与多分散系Mie相函数的偏离程度.数值计算了不同相函数拟合方法对应气溶胶的传输特性.计算结果表明,相函数的准确模拟计算对于蒙特卡罗方法等辐射传输问题的解决具有十分重要的意义.     

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。     

煤粉颗粒的后向散射特性研究

利用Mie理论研究了单分散煤粉颗粒对光波的散射特性,给出了单次散射相函数、消光效率因子、散射效率因子、不对称因子和单次散射反照率随粒子尺寸的变化关系;当煤粉浓度较大时,需要考虑颗粒系的多次散射特性,根据辐射传输理论,利用蒙特卡洛方法研究了煤粉颗粒的多次散射特性,并给出了其后向散射随观测角度、粒子半径和光学厚度的变化关系,计算结果对煤粉颗粒反演具有一定指导意义。     

多次散射辐射传输计算中的相函数处理

在实际大气中,分子和粒子不仅遭受单次散射,还遭受多次散射。本文首先计算了多次散射在总散射量中的贡献。结果表明当光学厚度大于0.1时,多次散射在总散射量中的贡献将超过10%,因此必须考虑多次散射的作用。在多次散射辐射传输计算时,一般需把散射相函数展开为勒让德(Legendre)函数的多项式。有些介质如云或气溶胶粒子,散射相函数前向非常尖锐。展开的Legendre多项式需数百项甚至上千项才能收敛,而计算时间与展开项数的3次方成正比。本文介绍了在辐射传输计算时对尖锐相函数的δ-M和δ-fit处理方法,比较了两种方法的计算结果。当计算用的流数相同时,δ-fit方法的计算结果比δ-M方法的计算结果要精确得多;当计算结果精确度相同时,δ-fit方法的流数比δ-M方法的流数少得多,运算速度也快很多。δ-fit方法是目前处理散射相函数的理想方法,可以大大提高计算的精度以及缩减运算时间。     

同位素Tl-201的单光子发射CT影像的康普顿散射校正

给出一种基于康普顿散射理论的Tl-201 SPECT影像的散射校正方法,此方法仅考虑一次散射和二次散射的影响.计算中将散射介质分成散射小元,然后积分求出每一小元内所有电子的散射光子数,一个电子的散射几率由Klein-Nishina公式确定,散射光子被分配至散射小元中心对应的探测器接收孔位置.辐射源的奇点问题也通过这种积分方法解决.误差主要来自于计算中有限的散射元体积和受限制的散射介质,但计算的线源响应函数和散射比与Monte Carlo计算结果相符,计算时间缩短40倍.     

空间目标可见光散射特性建模方法研究

针对空间目标的可见光散射特性提出一种建模方法.在分析空间目标所处的背景辐射环境基础上建立了空间目标背景辐射物理模型.对目标表面进行面元划分后,基于辐射理论引入双向反射分布函数模型来描述目标表面面元的光散射特性,将目标各个表面所有面元散射分量叠加建立了目标可见光散射特性的数学模型.建立目标本体坐标系,通过坐标变换确定目标、背景辐射源与探测器的相对位置关系,利用矢量坐标法确定目标对观测系统的“可视表面”.根据给定的目标几何结构尺寸和物性参量仿真获得了目标在轨光学特性.计算结果验证了建模的有效性.     

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.     

On the finite volume method and the discrete ordinates method regarding radiative heat transfer in acute forward anisotropic scattering media

The ability of the finite volume method (FVM) and the discrete ordinates method (DOM) to model radiative heat transfer in acute forward anisotropic scattering media has been investigated. The test case involves a purely scattering medium in a cubic enclosure, irradiated by one boundary with diffuse emission. Four phase functions have been considered: three of the Henyey-Greenstein type with respective asymmetry factors of 0.2, 0.8 and 0.93, and a Mie phase function with a strong forward scattering peak (computed for a size parameter of 245 and corresponding to an asymmetry factor of 0.93). Results obtained with the FVM are in good agreement with Monte Carlo reference solutions, whatever the level of acute anisotropic scattering (for asymmetry factors up to 0.93). The DOM combined with the renormalization procedures of the phase function proposed by Kim and Lee (Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures. Int J Heat Mass Transfer 1988;31:1711-21. [1]) and Wiscombe (On initialization error and flux conservation in the doubling method. JQSRT 1976;18:637-58. [2]) provides accurate results only for the smallest asymmetry factor. As the asymmetry factor increases, the renormalization procedures induce strong modifications in the values of the discretized phase function resulting in an underestimation of the effective attenuation by scattering. This error has been found to increase with optical thickness. In fact, when using the DOM, results would be more accurate combining this method with a Delta-Eddington approximation of the phase function, instead of using the actual phase function which is altered too much by renormalization.     

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.     

Numerical investigation of the effect of soot aggregation on the radiative properties in the infrared region and radiative heat transfer

The effect of aggregation on soot radiative properties in the infrared region of the spectrum is numerically investigated using Rayleigh-Debye-Gans theory for fractal aggregates (RDG-FA). In order to use the RDG-FA theory for a wide range of aggregate sizes and wavelengths, the predicted phase functions, scattering and absorption coefficients are compared with a more accurate theory, the integral equation formulation for scattering—IEFS. The importance of scattering when compared with absorption is investigated, as well as the effect of aggregation on the phase function shape and on the scattering cross section. It is concluded that in the case of small aggregates formed with small primary particles the scattering coefficient is negligible compared with the absorption coefficient, and scattering and aggregation of primary particles can be ignored. Thus, the Rayleigh approximation can be used leading to isotropic scattering. In the case of large aggregates constituted by large primary particles, aggregation becomes important and the scattering cross section is of the same order of magnitude of the absorption cross section. Moreover, the phase function becomes highly peaked in the forward direction. Therefore, the Rayleigh and the equivalent volume Mie sphere approximations are not valid, and the RDG-FA method emerges as a good compromise between accuracy and simplicity of application. However, radiative transfer calculations between two infinite, parallel, black walls show that scattering may always be neglected in the calculation of total radiative heat source and heat fluxes to the walls. The minor influence of scattering on the accuracy of the predictions is explained by the shift between the spectral region where scattering is important and the region where the spectral radiative heat source is large.     

Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative-conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative-convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index.     

漫反射各向异性散射介质内的温度热流场

本文采用射线踪迹结合节点分析法和谱带模型,研究了漫反射不透明边界下吸收、发射、各向异性散射介质内的热辐射传递过程。考虑介质辐射能的入射和散射方向,导出漫反射、不透明边界、各向异性散射介质的辐射传递系数。在辐射平衡的情况下,考察了表面发射率和散射反照率对介质内辐射热流和温度场的影响。研究表明,介质不透明边界处存在温度跃迁现象,而且,内界面发射率越大,相应界面温度跃迁越小。     

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.     

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.     

Analysis of collimated radiation in participating media using the discrete transfer method

A general formulation of the discrete transfer method is provided to analyze radiative heat transfer problems in a participating medium subjected to collimated radiation. The formulation is validated by considering 1-D planar absorbing, emitting and anisotropically scattering gray medium in radiative equilibrium. Anisotropy of the medium is approximated by linear anisotropic phase function. For the purpose of comparison, the problem is also solved analytically. Results are obtained for different angles of incidence of the collimated radiation. At a given angle of incidence, results are obtained for forward, isotropic and backward scattering situations. Heat flux results are compared over a wide range of values of the extinction coefficient. Emissive power distributions in the medium are also obtained for some cases. The discrete transfer method results are found to compare very well with the analytic results.     

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.