Thermal radiation has a considerable contribution to the overall amount of heat transferred in pulverized coal combustions. More specifically, particles occurring in coal combustion strongly interact with thermal radiation. In numerical simulations of coal combustion processes, this particle-radiation-interaction often is described by Mie theory. Important modeling assumptions in Mie theory are sphericity and homogeneity of particles. The aim of this study is to investigate the validity of the homogeneity assumption. Therefore, the Discrete Dipole Approximation method is applied to calculate the scattering and absorption properties of non-homogeneous particles and to compare these with results from Mie theory. Three types of inhomogeneous particles as well as two non-spherical shapes of particles are considered. Scattering and absorption properties are averaged over the incident radiation profile and azimuthal angle. The calculations reveal a deviation in scattering and absorption efficiencies below 10% due to non-homogeneity for all particles, for the scattering phase function, the deviation is on the order of 10%. A strong dependency of the deviation on the particle type can be observed. Nevertheless, Mie theory can predict trends correctly. Taking into account several uncertainties in the input parameters for scattering calculations, Mie theory can be applied in the prediction of scattering and absorption properties in numerical simulations of coal combustion.

In this study, the impact of various treatments of gas and particle radiative properties on modelling radiative heat transfer in a 2D-squared enclosure with conditions representative to the post-burner region of an oxy-coal furnace with wet flue-gas recirculation is systematically investigated. The benchmark solutions for the radiative source terms and the net wall heat fluxes are computed with a narrow-band correlated-k (NBCK) model to account for the non-gray gas radiation in conjuction with the Mie-theory to compute the particle radiative properties. Comparisons with this benchmark solution show that the use of gray Henyey-Greenstein functions obtained with the Planck-mean values for the asymmetry factors of the coal/char and ash particles is sufficient to model accurately the scattering phase functions. In addition, the use of Planck-mean values for all the particle radiative properties provides predictions within 20% of the reference solutions. On the other hand, model results show that the application of a constant refractive index for ash particles induce large discrepancies, whereas such approximation can be made for coal particles without loss of accuracy. Finally, a significant amount of computational cost can be saved with no significant loss of accuracy by considering a wide-band correlated-k model instead of the NBCK model. The full-spectrum correlated-k (FSCK) scheme proposed by Modest and Riazzi (2005) based on gray scattering coefficients and phase functions improves further the computational saving with higher mean relative errors of about 5% for the radiative source terms and net wall heat fluxes. Thus, it is concluded that the FSCK model is appropriate to model the radiative heat transfer including gas and particle radiation for engineering applications. (C) 2019 Elsevier Ltd. All rights reserved.

The radiative behaviour of coal and char particles is an important input parameter for simulations of coal combustion and gasification processes, as those typically feature elevated reactor temperatures. For consideration of radiative heat transfer, accurate knowledge of particle emissivity is a pre-requisite. Combining theoretical considerations and experimental data from literature, a temperature dependent relation for char emissivity is provided.

In this work, the effect of applying different approximations for the scattering phase function on radiative heat transfer in pulverized coal combustion is investigated. Isotropic scattering, purely forward scattering, and a δ-Eddington approximation are compared with anisotropic scattering based on Mie theory calculations. To obtain suitable forward scattering factors for the δ-Eddington approximation, a calculation procedure based on Mie theory is introduced to obtain the forward scattering factors as a function of temperature, particle size, and size of the scattering angle. Also, an analytical expression for forward scattering factors is presented. The influence of the approximations on wall heat flux and radiative source term in a heat transfer calculation is compared for combustion chambers of varying size. Two numerical models are applied: A model based on the discrete transfer method (DTRM) representing the reference solution and a model based on the finite volume method (FVM) to also investigate the validity of the obtained results with a method often applied in commercial CFD programs. The results show that modeling scattering as purely forward or isotropic is not sufficient in coal combustion simulations. The influence of anisotropic scattering on heat transfer can be well described with a δ-Eddington approximation and properly calculated forward scattering factors. Results obtained with both numerical methods show good agreement and give the same tendencies for the applied scattering approximations.

In this work, the influence of the radiative properties of coal and ash particles on radiative heat transfer in combustion environments is investigated. Emphasis is placed on the impact on the impact of the complex index of refraction and the particle size on particle absorption and scattering efficiencies. Different data of the complex index of refraction available in the literature are compared, and their influence on predictions of the radiative wall flux and radiative source term in conditions relevant for pulverized coal combustion is investigated. The heat transfer calculations are performed with detailed spectral models. Particle radiative properties are obtained from Mie theory, and a narrow band model is applied for the gas radiation. The results show that, for the calculation of particle efficiencies, particle size is a more important parameter than the complex index of refraction. The influence of reported differences in the complex index of refraction of coal particles on radiative heat transfer is small for particle sizes and conditions of interest for pulverized coal combustion. For ash, the influence of variations in the literature data on the complex index of refraction is larger, here, differences between 10% and 40% are seen in the radiative source term and radiative heat fluxes to the walls. It is also shown that approximating a particle size distribution with a surface area weighted mean diameter, D-32, for calculation of the particle efficiencies has a small influence on the radiative heat transfer.

In the present study, absorption and scattering efficiencies as well as the scattering phase function of a cloud of coal particles are described as function of the particle combustion progress. Mie theory for coated particles is applied as mathematical model. The scattering and absorption properties are determined by several parameters: size distribution, spectral distribution of incident radiation and spectral index of refraction of the particles. A study to determine the influence of each parameter is performed, finding that the largest effect is due to the refractive index, followed by the effect of size distribution. The influence of the incident radiation profile is negligible. As a part of this study, the possibility of applying a constant index of refraction is investigated. Finally, scattering and absorption efficiencies as well as the phase function are presented as a function of burnout with the presented model and the results are discussed.

Radiative heat transfer is a very important heat transfer mechanism in pulverized coal combustion. To identify the influence of parameters determining radiatve heat transfer and to give recommendations on the required accuracy of corresponding submodels, a 3D-periodic oxy-fuel pulverized coal combustion test case is investigated. Measurement values determined by the authors or elaborate submodels are applied for each parameter and compared to simplified models or empirical constants. To investigate the interaction between particle radiation and the strong spectral dependence of gas radiation in oxy-fuel scenarios, a comparison between spectrally averaged and spectrally resolved calculations performed. To the best knowledge of the authors, for the first time the contribution of the parameters determining radiative heat transfer are quantified and compared in one comprehensive study.The results indicate a strong influence of coal particle emissivity and scattering phase function as well as the projected particle surface on the radiative source term. For the wall heat flux, the largest influences were found for ash and coal particle emissivity, projected particle surface and the scattering phase function. Additionally, the difference between coal particle and gas temperature was found to have a significant influence on wall heat flux. A comparison of spectrally averaged to spectrally resolved results and the corresponding models for gas radiation (WSGGM and SNBM) yielded similar trends for the influence of each parameter. Thus, based on the models and parameters involved in this study, a spectrally averaged approach seems to be of sufficient accuracy to describe radiative heat transfer in oxy-fuel combustion systems. (C) 2016 Elsevier B.V. All rights reserved.

An analytical approximation for the two-dimensional heat conduction problem with temporally and spatially oscillating thermal boundary conditions is presented. In addition, simplified expressions for the damping and phase shift of the temperature signal between the surface and a measurement position inside the wall are derived and their validity in dependency on the inverse Fourier number is shown. The solution algorithm is implemented in a MATLAB program and made available for other researchers. In two case studies, the analytical solution is applied in order to evaluate the ability of experimental systems to measure instantaneous and local heat transfer coefficients as well as temperatures on a boundary.

In numerical simulations of coal combustion processes, particle-radiation interaction is often described by Mie-theory. An important modeling assumption in Mie-theory is the sphericity of the particles. The aim of this study is to investigate the validity of the sphericity assumption. Therefore, the T-Matrix method is applied to calculate the scattering and absorption properties of non -spherical particles and to compare these with results from Mie-theory. Three types of non-spherical particles are considered: prolate, oblate, and Chebychev-type particles. The scattering and absorption properties are averaged over a particle size distribution, the incident radiation profile, and for non-spherical particles a particle orientation distribution.The calculations reveal a deviation in scattering and absorption efficiencies below 10% due to non sphericity for all particles. For the scattering phase function, the deviation is on the order of 10%. It strongly varies depending on the particle type under investigation. Nevertheless, Mie-theory can correctly predict trends. Taking into account several uncertainties in the input parameters for scattering calculations, Mie-theory can be applied in the prediction of scattering and absorption properties in numerical simulations of coal combustion. (C) 2016 Elsevier Masson SAS. All rights reserved.

In the present investigation, artificial neural networks are applied to model scattering and absorption properties occurring in particle radiation interaction for numerical simulation of pulverized coal combustion. To determine averaged scattering and absorption properties, an averaging procedure over spectral incident radiation profile and particle size distribution is applied. These averaged properties then are approximated by means of an artificial neural network. A study to determine a suitable network architecture is performed.