A 3-D radiation model for non-grey gases

A three-dimensional radiation code based on method of lines (MOL) solution of discrete ordinates method (DOM) coupled with spectral line-based weighted sum of grey gases (SLW) model for radiative heat transfer in non-grey absorbing-emitting media for use in conjunction with a computational fluid dynamics (CFD) code based on the same approach was developed. The code was applied to three test problems: two containing isothermal homogenous/non-homogenous water vapor and one non-isothermal water vapor/carbon dioxide mixture. Predictive accuracy of the code was evaluated by benchmarking its steady-state predictions against accurate results, calculated by ray tracing method with statistical narrow band model, available in the literature. Comparative testing with solutions of other methods is also provided. Comparisons reveal that MOL solution of DOM with SLW model provides accurate solutions for radiative heat fluxes and source terms and can be used with confidence in conjunction with CFD codes based on MOL.     

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.     

Evaluation of solution methods for radiative heat transfer in gaseous oxy-fuel combustion environments

The exact solution to radiative heat transfer in combusting flows is not possible analytically due to the complex nature of the integro-differential radiative transfer equation (RTE). Many different approximate solution methods for the solution of the RTE in multi-dimensional problems are available. In this paper, two of the principal methods, the spherical harmonics (P₁) and the discrete ordinates method (DOM) are used to calculate radiation. The radiative properties of the gases are calculated using a non-gray gas full spectrum k-distribution method and a gray method. Analysis of the effects of numerical quadrature in the DOM and its effect on computation time is performed. Results of different radiative property methods are compared with benchmark statistical narrow band (SNB) data for both cases that simulate air combustion and oxy-fuel combustion. For both cases, results of the non-gray full spectrum k-distribution method are in good agreement with the SNB data. In the case of oxy-fuel simulations with high partial pressures of carbon dioxide, use of gray method for the radiative properties may cause errors and should be avoided.     

Radiative transfer in a nongray spherical layer: Simplified rectangular model

The problem of radiative transfer in a nongray, absorbing-emitting spherical layer is investigated. The absorption coefficient is assumed to be only a function of frequency, i.e. k_v = α(v)k, and the function α(v) is allowed only two values, zero or unity (simplified rectangular model). The nongray radiative transfer problem is reduced to a gray solution without the use of any approximation (such asthe Plank or Rosseland means) for an isothermal layer and for radiative equilibr     

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.     

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.     

Theoretical analysis of porous radiant burners under 2-D radiation field using discrete ordinates method

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners (PRBs). In the present work, a 2-D rectangular model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. The gas and the solid phases are considered in non-local thermal equilibrium and combustion in the porous medium is modeled by considering a non-uniform heat generation zone. The homogeneous porous media, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. The radiation effect in the gas flow is neglected but the conductive heat transfer is taken into account. In order to analyze the thermal characteristics of porous burners, the coupled energy equations for the gas and porous medium in steady condition are solved numerically and the discrete ordinates method (DOM) is used to obtain the distribution of radiative heat flux in the porous media. Finally, the effects of various parameters on the performance of porous radiant burners are examined. The present results are compared with some reported theoretical and experimental results by other investigators and good agreement is found.     

Modifications of discrete ordinate method for computations with high scattering anisotropy: Comparative analysis

A numerical accuracy analysis of the radiative transfer equation (RTE) solution based on separation of the diffuse light field into anisotropic and smooth parts is presented. The analysis uses three different algorithms based on the discrete ordinate method (DOM). Two methods, DOMAS and DOM2+, that do not use the truncation of the phase function, are compared against the TMS-method. DOMAS and DOM2+ use the Small-Angle Modification of RTE and the single scattering term, respectively, as anisotropic parts. The TMS method uses the Delta-M method for truncation of the phase function along with the single scattering correction. For reference, a standard discrete ordinate method, DOM, is also included in analysis. The obtained results for cases with high scattering anisotropy show that at low number of streams (16, 32) only DOMAS provides an accurate solution in the aureole area. Outside aureole, the convergence and accuracy of DOMAS, and TMS is found to be approximately similar: DOMAS was found more accurate in cases with coarse aerosol and liquid water cloud models, except low optical depth, while the TMS showed better results in case of ice cloud.     

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.     

Application of variational iteration method and homotopy–perturbation method for nonlinear heat diffusion and heat transfer equations

Perturbation methods depend on a small parameter which is difficult to be found for real-life nonlinear problems. To overcome this shortcoming, two new but powerful analytical methods are introduced to solve nonlinear heat transfer problems in this Letter; one is He's variational iteration method (VIM) and the other is the homotopy–perturbation method (HPM). Nonlinear convective–radiative cooling equations are used as examples to illustrate the simple solution procedures. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. Comparison of the results obtained by both methods with exact solutions reveals that both methods are tremendously effective.     

Transient conductive and radiative transfer in a planar layer with Arrhenius heat generation

Transient conductive and radiative energy transfer in a gray absorbing-emitting planar medium bounded by black walls is studied. The temperature distribution is uniform when the medium starts releasing energy according to the Arrhenius equation. The Crank-Nicolson method is used in the radiative-dominant case with good accuracy. Time-dependent temperature and heat flux distributions are calculated until steady-state is reached. Confirmation of the solution technique is made by comparison with previous investigations. The dimensionless activation energy required for ignition varies from 4.1 for pure conduction to 7.5 for pure radiation.     

气粒混合物非灰辐射特性合并宽窄谱带K分布模型

气粒混合物辐射问题具有全场性、非灰性、耦合性等特点,准确预估高温燃气/粒子非灰辐射特性是非常重要的。本文将合并宽窄谱带K分布模础(CWNBCK)与离散坐标法(DOM)结合,开展了非灰气粒混合物辐射换热问题的模拟工作,分别验证了一维和三维情况下应用该模型的准确性,给出不同工况下的热流源项、壁面热流或辐射热流等。结果表明:该模型能够给出与SNB模型精度基本相同的结果,考虑其计算效率的提高,可以在工程实际中应用该模型计算非灰气粒混合物辐射换热。     

Analysis of radiative transport in a cylindrical enclosure—An application of the modified discrete ordinate method

Application of the modified discrete ordinate method (MDOM) proposed by Mishra et al. [Mishra SC, Roy HK, Misra N. Discrete ordinate method with a new and simple quadrature scheme. J Quant Spectrosc Radiat Transfer 2006;101:249-262.] has been extended for calculation of volumetric radiative information in a cylindrical enclosure. Radiatively, the medium inside a diffuse gray 1-D concentric cylinder is absorbing, emitting and scattering. Three types of problems, viz., an isothermal medium representing non-radiative equilibrium case, a non-isothermal medium representing radiative equilibrium situation and the case of a combined mode conduction and radiation heat transfer have been used to test the robustness of the MDOM. Temperature/emissive power and heat flux/energy flow rate distributions in the medium have been found for the effects of various parameters like the extinction coefficient, the scattering albedo, the boundary emissivity and the conduction-radiation parameter. To check the accuracy of the results of the MDOM, results have been compared with those available in the literature and also by obtaining the radiative information using the finite volume method. MDOM has been found to provide accurate results.     

A semi-analytical numerical method for time-dependent radiative transfer problems in slab geometry with coherent isotropic scattering

We describe a semi-analytical numerical method for coherent isotropic scattering time-dependent radiative transfer problems in slab geometry. This numerical method is based on a combination of two classes of numerical methods: the spectral methods and the Laplace transform (LTS_N) methods applied to the radiative transfer equation in the discrete ordinates (S_N) formulation. The basic idea is to use the essence of the spectral methods and expand the intensity of radiation in a truncated series of Laguerre polynomials in the time variable and then solve recursively the resulting set of “time-independent” S_N problems by using the LTS_N method. We show some numerical experiments for a typical model problem.     

激光诱导荧光水体污染遥测数据定量分析方法

在紫外光的激发下,污染水体中的溶解有机物(DOM)会产生特定的荧光光谱,因此利用激光诱导荧光(LIF)可对水体中的溶解有机物的含量进行定量分析,从而可估计出水体富营养化的程度。提出了一种用于对水质遥测数据进行定量分析的方法,这是一种基于遗传算法(GA)的光谱分离算法。首先确定拉曼散射信号和溶解有机物的荧光在404nm波段的信号强度,然后再利用拉曼散射信号对DOM荧光光谱进行归一化处理。根据浓度校准曲线可得到水体中的溶解有机物的浓度。     

Matrix formulations of radiative transfer including the polarization effect in a coupled atmosphere-ocean system

A vector radiative transfer model has been developed for a coupled atmosphere-ocean system. The radiative transfer scheme is based on the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each atmospheric or oceanic layer through the discrete ordinate solution. The vertically inhomogeneous system is constructed using the matrix operator method, which combines the radiative interaction between the layers. This radiative transfer scheme is flexible for a vertically inhomogeneous system including the oceanic layers as well as the ocean surface. Compared with the benchmark results, the computational error attributable to the radiative transfer scheme has been less than 0.1% in the case of eight discrete ordinate directions. Furthermore, increasing the number of discrete ordinate directions has produced computations with higher accuracy. Based on our radiative transfer scheme, simulations of sun glint radiation have been presented for wavelengths of 670 nm and 1.6 μm. Results of simulations have shown reasonable characteristics of the sun glint radiation such as the strongly peaked, but slightly smoothed radiation by the rough ocean surface and depolarization through multiple scattering by the aerosol-loaded atmosphere. The radiative transfer scheme of this paper has been implemented to the numerical model named Pstar as one of the OpenCLASTR/STAR radiative transfer code systems, which are widely applied to many radiative transfer problems, including the polarization effect.     

水体中溶解有机物激光诱导荧光光谱分析方法

讨论了用激光诱导荧光(LIF)的方法分析水体中溶解有机物(DOM)的含量,利用拉曼散射信号对荧光光谱进行归一化处理,消除激发光强度和水体对荧光的二次吸收和接收条件等因素的影响,并给出了理论依据,由此依据得出了非线性浓度校准的数学模型。利用这个数学模型对实验数据进行非线性拟合,拟合的相关系数高于0.99。该浓度校准的数学模型,考虑到了水体对荧光信号的二次吸收以及溶液浓度的变化对二次吸收的影响,结果表明它可作为不同水体的通用浓度校准的数学模型对水体中的DOM进行定量分析。     

Numerical Simulation of 2-D Radiation-Drive Ignition Implosion Process

A Lagrangian compatible radiation hydrodynamic algorithm and the nuclear dynamics computing module are developed and implemented in the LARED Integration code, which is a radiation hydrodynamic code based on the 2-D cylindrical coordinates for the numerical simulation of the indirect-drive Inertial Confined Fusion. A number of 1-D and 2-D ignition implosion numerical simulations by using the improved LARED Integration code (ILARED) are presented which show that the 1-D numerical results are consistent with those computed by the 1-D radiation hydrodynamic code RDMG, while the simulation results of the 2-D low-mode radiative asymmetry and hydrodynamic instability growth,according to the physical analysis and anticipation, are satisfactory. The capsules driven by the sources from SGII experiments are also simulated by ILARED, and the fuel shapes agree well with the experimental results. The numerical simulations demonstrate that ILARED can be used in the simulation of the 1-D and 2-D ignition capsule implosion using the multi-group diffusion model for radiation.     

Transient coupled heat transfer in a rectangular medium with black surfaces

The main objective of this paper is to extend to two-dimensional (2-D) medium the ray tracing-node analyzing method, which has already been successfully used to solve one-dimensional (1-D) problem of coupled heat transfer in a semitransparent medium. For simplicity, an infinitely long rectangular semitransparent medium with four black opaque surfaces is chosen as our studying object. A control volume method in the implicit scheme is adopted for discretizing the partial transient energy equation. In combination with spectral band model, the radiative heat source term is calculated using the radiative transfer coefficients (RTCs), which are deduced by the ray tracing method. The Partankar's linearization method is used to linearize the radiative source term and the opaque boundary condition, and the linearized equations are solved by the ADI method. Effects of absorption coefficient, refractive index and conductivity on transient cooling process in the 2-D gray rectangular medium are investigated under the condition that the radiation and convection processes cool one side of the rectangular medium while heat the remaining three sides.     

特征荧光光谱法定量检测水质的研究

讨论了一种可同时检测自然水体中有机物和叶绿素a含量的快速分析方法。以武汉东湖水为样品,采用激光诱导荧光(LIF)的方法测量了水体的总荧光光谱(TLS);并用特征光谱荧光标记(SFS)技术对水体中溶解的有机物(DOM)及叶绿素a (Chl-a)的荧光光谱特征进行了分析和指认。并利用水的拉曼散射信号强度进行归一化的方法,分别得到较低浓度腐殖酸和叶绿素a的特征光谱归一化荧光强度以及它们在水体中浓度的标定曲线和线性关系式。另外, 对于较高浓度的腐殖酸溶液,确定了其特征光谱的荧光强度与浓度之间满足的函数关系。结果表明,在一定的浓度范围内,特征光谱的荧光强度与浓度之间仍然有很好的线性关系。该方法在自然水体质量的检测方面有广泛的应用前景,它能快速识别水体中的污染物,定量测量它们在水体中的含量,实现对自然水体的质量状况进行大范围的实时动态监测。