A full spectrum k-distribution based non-gray radiative property model for unburnt char

By using the concept of weighted sum of four gray particles and spectrum k-distribution (WSGP-SK), a non-gray radiative property model for unburnt char particles is developed. Based on the carbon burnout kinetic model for structure during oxidation, and the linear mixed approximation theory for complex index of refraction, spectral radiative properties of unburnt char particles are first calculated as function of the burnout ratio by Mie theory. Referring to the full spectrum k-distribution model, k-distribution is applied to reorder absorption and scattering efficiencies of particles. Then, weighting factors and efficiency factors of the non-gray radiative property model are directly obtained from Gaussian integral points of k-distribution. The model is validated against the benchmark solutions of line-by-line (LBL) model. Maximum relative errors of this model are 3% and 15% for radiative heat fluxes and source terms in non-isothermal inhomogeneous particulate media, respectively. The assumption of linearly varying radiative properties with burnout ratio (Lockwood et al. 1986) will result in a predicted deviation of 53% for radiative source terms. Results also show that this non-gray model is remarkably better than the Planck mean method. Moreover, a satisfactory comparison with LBL solutions is achieved in the gas and particle mixture by combining the non-gray WSGG-SK model (Guo et al. 2015). As a radiation sub-model, this non-gray radiative property model can significantly improve prediction accuracy of radiative heat transfer in oxy-fuel combustion.     

Simultaneous solution of Kompaneets equation and radiative transfer equation in the photon energy range 1-125 keV

Radiative transfer equation in plane parallel geometry and Kompaneets equation is solved simultaneously to obtain theoretical spectrum of 1-125 keV photon energy range. Diffuse radiation field are calculated using time-independent radiative transfer equation in plane parallel geometry, which is developed using discrete space theory (DST) of radiative transfer in a homogeneous medium for different optical depths. We assumed free-free emission and absorption and emission due to electron gas to be operating in the medium. The three terms n, n² and (∂n/∂x_k) where n is photon phase density and x_k=(hν/kT_e), in Kompaneets equation and those due to free-free emission are utilized to calculate the change in the photon phase density in a hot electron gas. Two types of incident radiation are considered: (1) isotropic radiation with the modified black body radiation I^MB[1] and (2) anisotropic radiation which is angle dependent. The emergent radiation at τ=0 and reflected radiation τ=τ_max are calculated by using the diffuse radiation from the medium. The emergent and reflected radiation contain the free-free emission and emission from the hot electron gas. Kompaneets equation gives the changes in photon phase densities in different types of media. Although the initial spectrum is angle dependent, the Kompaneets equation gives a spectrum which is angle independent after several Compton scattering times.     

Grey and multigroup radiation transport models for two-dimensional stochastic media with material temperature coupling

Current theories for approximating the effects of stochastic media on radiation transport assume very limited physics such as one dimension, constant grey opacities, and no material energy balance equation. When applied to more complex physical problems, the standard theory fails to match the results from direct numerical simulations. This work presents the first direct numerical simulations of multigroup radiation transport coupled to a material temperature equation in a 2D stochastic medium that are compared to closures proposed by various authors. After extending it from grey to multigroup physics, one closure that is not commonly used successfully models the results in dilute systems where one material comprises less than 5% of the total. This closure is more accurate for related grey transport problems than it is for the multigroup problem. When the specific heats are material- and temperature-dependent, it is much more difficult to fit the direct numerical solutions with an approximate closure.     

UV Radiation of Low Pressure XeCl* and KrCl* Glow Discharges

The positive column of low pressure DC glow discharges in Xe/Cl₂ and Kr/Cl₂ gas mixtures has been investigated with respect to its UV radiation power and radiative efficiency for a wide range of parameters (total gas pressure: 1–30 mbar, current 10–30 mA, partial pressure of Cl₂: 1–33%). Also the radial distribution of the particle number densities of XeCl* (B) and KrCl* (B) has been determined by absolutely calibrated emission spectroscopy. Optimum UV (190–350 nm) output and efficiency has been found in gas mixtures with a relative Cl₂ partial pressure of 2–3% and total gas pressure of 12–18 mbar. At these parameters, the UV radiation power per column length is greater than 40 Watt/m with a radiative efficiency of 15–18%. These discharges could be used for UV induced photochemical processes.     

Multi-scale k-distribution model for gas mixtures in hypersonic nonequilibrium flows

A k-distribution model is presented for gas mixtures in thermodynamic nonequilibrium, containing strongly radiating atomic species N and O together with molecular species of N₂, N₂⁺, NO and O₂. In the VUV range of the spectrum there is strong absorption of atomic radiation by bands of N₂. For this spectral range, a multi-scale model is presented, where RTEs are solved separately for each emitting species and overlap with other species is treated in an approximate way. Methodology for splitting the gas mixture into scales and evaluation of the overlap parameter between different scales is presented. The accuracy of the new model is demonstrated by solving the radiative transfer equation along the stagnation line flow field of the Crew Exploration Vehicle (CEV).     

Ne、Ar、Kr、Xe等离子体Planck和Rosseland平均不透明度的近似计算

根据平均原子模型和类氢光吸收系数，近似地计算了Ne、Ar、Kr、Xe等惰性元素高温、高密度等离子体的Planck和Rosseland不透明度。在计算线谱吸收过程中，采用了唯象方法处理线谱演化成谱带时的加宽效应及谱带重叠效应。将不透明度数据拟合成温度和密度的幂函数形式，它能够用于辐射体的数值拟合。     

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.     

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P₁ forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.     

辐射与物质强耦合问题的二维输运数值模拟

分析确定性输运数值方法模拟辐射与物质强耦合问题的难点,给出在任意四边形网格上求解该类问题的简单隅角平衡算法,并应用灰体输运综合加速算法提高输运方程的源迭代收敛速度,最后给出数值例子.     

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 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.     

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.     

Modelling nongrey gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modelling with respect to the treatment of nongrey radiation from both gas-phase species and soot particles, while radiation modelling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (M.F. Modest, 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured computational fluid dynamics (CFD) code for nongrey radiation modelling. The mixture full-spectrum k-distributions including nongrey absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongrey soot modelling is shown to be of greater importance than nongrey gas modelling in sooty flame simulations, with grey soot models producing large errors. The nongrey treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongrey treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongrey soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model

The gas absorption process scheme in the broadband radiative transfer code “mstrn8”, which is used to calculate atmospheric radiative transfer efficiently in a general circulation model, is improved. Three major improvements are made. The first is an update of the database of line absorption parameters and the continuum absorption model. The second is a change to the definition of the selection rule for gas absorption used to choose which absorption bands to include. The last is an upgrade of the optimization method used to decrease the number of quadrature points used for numerical integration in the correlated k-distribution approach, thereby realizing higher computational efficiency without losing accuracy. The new radiation package termed “mstrnX” computes radiation fluxes and heating rates with errors less than 0.6 W/m² and 0.3 K/day, respectively, through the troposphere and the lower stratosphere for any standard AFGL atmospheres. A serious cold bias problem of an atmospheric general circulation model using the ancestor code “mstrn8” is almost solved by the upgrade to “mstrnX”.     

A diffusion-based approximate model for radiation heat transfer in a solar thermochemical reactor

An approximate numerical method for fast calculations of the radiation heat transfer in a solar thermochemical reactor cavity is formulated based on the separate treatment of the solar and thermal radiative exchange by the diffusion approach. The usual P₁ approximation is generalized by applying an equivalent radiation diffusion coefficient for the optically thin central part of the cavity. The resulting boundary-value problems are solved using the finite element algorithm. The accuracy of the model is assessed by comparing the results to those obtained by a pathlength-based Monte Carlo simulation. The applicability of the proposed model is demonstrated by performing calculations for an example problem, which incorporates a range of parameters typical for a solar chemical reactor and the spectral radiative properties of polydisperse zinc oxide particles.     

Deviations from LTE in a stellar atmosphere

Deviations from LTE are investigated in an atmosphere of hydrogen atoms with one bound level, satisfying the equations of radiative, hydrostatic, and statistical equilibrium. The departure coefficient and the kinetic temperature as functions of the frequency dependence of the radiative cross section are studied analytically and numerically. Near the outer boundary of the atmosphere, the departure coefficient b is smaller than unity when the radiative cross section α_ν grows with frequency ν faster than ν²; b exceeds unity otherwise. Far from the boundary the departure coefficient tends to exceed unity for any frequency dependence of α_ν. Overpopulation (b > 1) always implies that the kinetic temperature in the statistical equilibrium atmosphere is higher than the temperature in the corresponding LTE atmosphere. Upper and lower bounds on the kinetic temperature are given for an atmosphere with deviations from LTE only in the optically shallow layers when the emergent intensity can be described by a radiation temperature.     

Gain studies on a uranine-damc dye mixture laser under nitrogen laser pumping

The radiative and Forster type of energy transfer processes in a dye mixture laser of 7-diethylamino-4-methyl coumarin (donor) and fluorescein disodium salt (acceptor) under nitrogen laser pumping were investigated. The Forster transfer rate calculated from the absorption and emission spectra of acceptor and donor is 1.3 × 10¹¹ liter mole^?1sec^?1. The gain of acceptor at 550 nm was measured for acceptor concentrations N_A from 10^?3M to 3 × 10^?3M for a fixed ratio F = 1 of donor to acceptor concentrations at different pump powers. The results agreed with the rate equation model proposed for the dye mixture laser. The radiative rate constant calculated from these results is 3.1 × 10¹⁰ liter mole^?1sec^?1. Numerical simulation of the rate equations showed that the acceptor reaches peak emission with a time lag of 3 ns with respect to the donor peak emission for F = 0.998, N_A = 10^?5M. This time lag decreases with increasing N_A and becomes zero for N_A = 10^?1M, F = 0.048.     

Comparison of different radiation treatments for a one-dimensional diffusion flame

A comparison of several radiative heat transfer models is made for a stagnation-point diffusion flame at low stretch rate, with CO2 and H2O as the participating media. Computed results of the radiative source distribution for wideband, narrowband and SLWSGG show reasonable agreement with each other. Results from the optically thin and grey gas models with Planck mean absorption coefficient are shown to underestimate the self-absorption and overestimate the emission substantially for the low stretch flame. The relative computation times of using the various radiation models are also given.