An efficient correlated-k, scheme referred to as "FAST CK" based on a 5-points Gauss-Legendre quadrature and 43 spectral bands is investigated in terms of accuracy and CPU time for the calculation of radiative intensities, heat fluxes, and source terms. Scenarios investigated for nonisothermal and nonhomogeneous mixtures of gases show that the "FAST CK" approach could reduce the CPU time by a factor of up to 160 with a maximum loss of 15% in accuracy, in comparison with a benchmark 10-points Gauss-Legendre quadrature using 367 spectral narrow bands.

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Recent Developments in the Solution of Radiation Heat Transfer Using the Discrete Ordinates Method

Evaluation of a fast correlated-k approach for radiation calculations in combustion systems

A modified discrete ordinates method (DOM) is used in spherical participating media. The radiative intensity is broken up into two components. One component is traced back to the enclosure's source. It is called direct intensity. The other component is rather traced back to the contribution of the medium itself. It is called diffuse intensity. Thus, the radiative transfer equation (RTE) is transformed into two simultaneous equations: a direct RTE and a diffuse RTE. The direct RTE is solved analytically. The diffuse RTE is solved numerically using the DOM. The streaming angular derivative term appearing in spherical geometry is modeled by making use of the Finite Legendre Transform. We study a pure radiation transfer problem between two concentric spheres. The medium is assumed to be gray and isotropically scattering. The limiting spheres are considered to be opaque, gray, diffusely emitting and diffusely reflecting with uniform emissivity over each surface. The obtained results are compared with available cases reported in the literature. In particular, relative importance of the direct radiation in optically thin media is studied.

A theoretical study of radiation between two concentric spheres using a modified discrete ordinates method associated with Legendre transform

For radiative transfer in complex geometries, Sakami and his co-workers have developed a discrete ordinates method (DOM) exponential scheme for unstructured meshes which was mainly applied to gray media. The present study investigates the application of the unstructured exponential scheme to a wider range of non-gray scenarios found in fire and combustion applications, with the goal to implement it in an in-house Computational Fluid Dynamics (CFD) code for fire simulations. The original unstructured gray exponential scheme is adapted to non-gray applications by employing a statistical narrow-band/correlated-k (SNB-CK) gas model and meshes generated using the authors’ own mesh generator. Different non-gray scenarios involving spectral gas absorption by H2O and CO2 are investigated and a comparative analysis is carried out between heat flux and radiative source terms predicted and literature data based on ray-tracing and Monte Carlo methods. The maximum discrepancies for total radiative heat flux do not typically exceed 5%.

Assessment of an unstructured exponential scheme discrete ordinates radiation model for non-gray media

Thermal radiation is an important physical phenomenon in combustion environments. For the understanding of existing- and the design of new combustion environments computational modelling is a useful tool as it can describe the different transport phenomena. This thesis has focused on studying thermal radiative property models of the participating media, gases and particles. Two specific combustion environments have also been studied, from a thermal radiation perspective. The focus is on radiative property models that are useful specifically for engineering purposes. These property models are often developed from more advanced spectral models by means of correlative or other methods to simplify the treatment of the radiative transfer. One such model is the non-correlated statistical narrow band (SNB) model, which drops spectral relation between intensity and transmissivity, which is used in the correlated SNB model. By doing so a significant decrease in computational demand can be achieved. The accuracy of this model has been questioned in the literature although it has been suggested as an appropriate option for sooty environments. The assessment of the model revealed that it only gives good predictions in large geometries and highly sooty environments. Because of the model’s limited applicability and a still rather high computational demand it is not recommended for use even in sooty environments. A simpler model, and computationally much faster, called the weighted sum of gray gas (WSGG) model accompanied the assessment of the non-correlated SNB model. The WSGG model was shown to be a better choice than the non-correlated SNB model in sooty environments. A gray gas property model was compared with a WSGG model in combustion environments resembling the ones found in grate fired furnaces. In these environments, which also contains particles, the gray model was shown to give predictions of wall heat flux in close agreement with the WSGG model. This shows how the simplest model, which the gray model is, can sometimes be a suitable choice, especially when particles are present. Particle property models were evaluated in various combustion environments. A common approach is to use Planck mean coefficients to represent the particle properties. The use of Planck mean coefficients for fly-ash particles, common in furnaces combusting solid fuels, is shown to give large errors in prediction of both radiative heat flux and the source term in particular.
The two investigated combustion environments are those found in grate fired furnaces and environments with high CO mole fraction. The grate fired furnace was studied in both modelling- and measurement work. Specifically the importance of particle radiation was investigated in the grate fired combustion environment. A preliminary study of the grate fired furnace was a parametric study. The parameters investigated were different particles originating from combustion of biomass and municipal solid waste, different furnace size, and boundary emissivities. The most significant effect on the overall radiative heat transfer is that of particles from municipal solid waste; moderate effects are seen when particles come from biomass. Increased furnace size most affected the heat flux to the hot bed and source term compared with a case without any particles. The choice of emissivity can be as important as considering particles or not. The measurement and modelling work were carried out on a 400 kW grate fired furnace combusting biomass. The boundary temperatures, flue gas temperature, gas mole fraction, particle mass-size distribution, and wall irradiation were measured. A so-called indirect wall irradiation was retrieved when the furnace was modelled with the implemented measured parameters. This indirect wall irradiation was compared with the directly measured wall irradiation. The study revealed that particle radiation is very important in the evaluated furnace, it doubles the wall irradiation in the hot flame zone compared with irradiation only from gases. The CO contribution to the total directional radiation was studied in environments with high mole fractions of CO, often found in gasifiers. CO is normally disregarded in environments where the fuel is fully oxidised, as it is a weak radiating species and small mole fractions of CO exist in these types of environments. The evaluation reveal that disregarding CO is still a good approach even in gasifier environments. These environments still contain small volume fractions of CO2 and H2O, which compared with CO are much stronger radiators. The rotational-vibrational bands of these two species overlaps the important fundamental band of CO reducing the importance of CO to the total directional radiative heat flux.

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Recent Developments in the Solution of Radiation Heat Transfer Using the Discrete Ordinates Method

Citations

Evaluation of a fast correlated-k approach for radiation calculations in combustion systems

A theoretical study of radiation between two concentric spheres using a modified discrete ordinates method associated with Legendre transform

Assessment of an unstructured exponential scheme discrete ordinates radiation model for non-gray media

Modelling and Experimental Investigations on Thermal Radiation in Combustion Environments

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