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

Boulet, Pascal; Collin, Anthony; Consalvi, Jean-Louis

doi:10.1016/j.jqsrt.2006.09.010

Cited by 60 publications

(78 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…T t , where T c is the centreline temperature, T t is the top temperature of the furnace, r is the radius from the centreline, and R half the depth of the furnace. Outside the radius R the temperature is set to 800 K. The scattering is introduced by the zeroth order D-Eddington Heat Mass Transfer approximation [29] using the asymmetry factor at the temperature of 1,000 K. The reason for a different treatment of the scattering is that the normalization of the phase function could not be secured, Eq. (10).…”

Section: Case 5-non-isothermal 3dmentioning

confidence: 99%

Evaluation of Planck mean coefficients for particle radiative properties in combustion environments

Hofgren

Sundén

2014

Heat Mass Transfer

View full text Add to dashboard Cite

Thermal radiation is the dominating form of heat transfer in several combustion technologies that combust solid fuels, such as pulverized coal combustion and fixed bed combustion. The thermal radiation originates from the hot combustion gases and particles. For accurate modelling of thermal radiation in these environments the selection of the radiative transport model and radiative property model is important. Radiative property models for gases have received huge attention and several well documented models exist. For particles, soot has received considerable attention whereas other particles have not to a similar extent. The Planck mean coefficients are most commonly used to describe the radiative properties of the particles. For gases the Planck mean absorption coefficient is known to give large deviations from recognised exact models in predicting the radiative heat transfer. In this study the use of Planck mean coefficients for particles are investigated and compared to spectral models. Two particle mass size distributions of fly ash are used, representing biomass and coal combustion. The evaluation is conducted in several combustion-like test cases with both gases and particles. The evaluation shows that using Planck mean coefficients for particles, in combustion-like situations, can give large errors in predicting the radiative heat flux and especially the source term. A new weighted sum of grey gas approach is tested and evaluated. It includes both the particles and gases to better account for the non-greyness of the fly ash absorption coefficient.

show abstract

Section: Case 5-non-isothermal 3dmentioning

confidence: 99%

Evaluation of Planck mean coefficients for particle radiative properties in combustion environments

Hofgren

Sundén

2014

Heat Mass Transfer

View full text Add to dashboard Cite

show abstract

“…It has been shown that numerical calculation of the RTE using the LSE set is accurate especially for isotropic scattering as in the case of neutron transport. However, it has been reported that in highly forwardpeaked scattering media such as biological tissue, the numerical solution of the RTE with the LSE set is inaccurate [15,2]. This is because in highly forwardpeaked scattering, the value of the phase function of the RTE at the small polar scattering angle tends to increase exponentially, resulting in slow convergence of the numerical calculation of the scattering integral.…”

Section: Introductionmentioning

confidence: 99%

“…To overcome the difficulty stated above, several works have proposed approaches to renormalize the phase function for highly forward-peaked scattering in the filed of radiative heat transfer [17,2,14]. At the early stage, Liu and coworkers have renormalized the phase function by an inverse of the quadrature sum of the phase function over the whole directions [17].…”

Section: Introductionmentioning

confidence: 99%

“…In their approach, however, numerical results of the average cosine of the polar scattering angle are deviated from the anisotropic factor, to which the average cosine must be equal. To satisfy the condition for the average cosine stated above, recently, the phase function has been renormalized by weight matrices calculated using the finite volume method [2] or an inverse analysis [14]. It has been actively reported that the renormalization approaches can provide the accurate numerical results.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

et al. 2016

View full text Add to dashboard Cite

Numerical calculation of photon migration in biological tissue using the radiative transfer equation (RTE) has attracted great interests in biomedical optics and imaging. Because biological tissue is a highly forward-peaked scattering medium, renormalization of the phase function in numerical calculation of the RTE is crucial. This paper proposes a simple approach of renormalizing the phase function by the double exponential formula, which was heuristically modified from the original one. Firstly, the validity of the proposed approach was tested by comparing numerical results for an average cosine of the polar scattering angle calculated by the proposed approach with those by the conventional approach in highly forward-peaked scattering. The results show that calculation of the average cosine converged faster using the proposed approach than using the conventional one as a total number of discrete angular directions increases. Next, the accuracy of the numerical solutions of the RTE using the proposed approach was examined by comparing the numerical solutions with the analytical solutions of the RTE in a homogeneous medium with highly forward-peaked scattering. It was found that the proposed approach reduced the errors of the numerical solutions from those using the conventional one especially at a small value of the total number of the directions. This result suggests that the proposed approach has a possibility to

show abstract

“…La connaissance des paramètres optiques est requise, afin de prédire la distribution de la lumière, dans un milieu donné, à partir de modèles stochastiques (Monte Carlo, Monte Carlo hybride) [20,21] ou déterministes (Transferts Radiatifs, ETR) [22,23]. La méthode de Monte Carlo sert de référence en vue de tester d'autres approches moins consommatrices en temps de calcul.…”

Section: Introductionunclassified

Analyse théorique et expérimentale de la diffusion de la lumière générée par une diode électroluminescente dans des répliques tissulaires

Pommellec

L’Huillier

2011

IRBM

View full text Add to dashboard Cite

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. RésuméLa connaissance de la répartition spatiale de la lumière à l'intérieur d'un tissu biologique irradié par un faisceau lumineux (LASER ou LED) est fondamentale pour optimiser le traitement par thérapie photodynamique. Dans cet article, nous développons un modèle analytique relatif à la répartition du flux lumineux à l'intérieur d'une réplique tissulaire irradiée au moyen d'une diode électroluminescente (LED). Le modèle est fondé sur l'utilisation de la transformée de Fourier à deux dimensions et appliqué à un tissu homogène d'épaisseur bien déterminée. Le flux total à l'intérieur du faisceau a été calculé en ajoutant les composantes collimatée et diffuse. La solution analytique a été également utilisée pour étudier l'influence du rayon du faisceau incident et des paramètres optiques du milieu sur l'évolution du flux en fonction de la profondeur. Des résultats de mesures ont été obtenus en utilisant un réservoir rempli par une réplique tissulaire (lait) illuminé au moyen d'un faisceau lumineux issu d'une LED. Le comportement des résultats expérimentaux est cohérent avec les prévisions théoriques. © 2011 Elsevier Masson SAS. Tous droits réservés. AbstractThe knowledge of the spatial distribution of light within a biological tissue exited by a light source (LASER or LED) is fundamental to achieve optimal photodynamic treatment. In this paper, we develop an analytical model relative to the diffuse fluence rate within a tissue-like medium irradiated by a continuous-wave light emitting diode (LED). The model is based on the two dimensional Fourier transform and applied to a homogeneous tissue slab. The total fluence rate along the axis of the medium was computed by adding the collimated and the diffuse components. The analytical solution was also used to study the depth evolution of the photon fluence rate as functions of the finite source beam size and the tissue optical parameters. Measurement results were performed using a tank filled with a liquid-simulating turbid medium (milk) illuminated with a LED beam. The experimental behaviour results agree with the theoretical predictions.

show abstract

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

Cited by 60 publications

References 19 publications

Evaluation of Planck mean coefficients for particle radiative properties in combustion environments

Evaluation of Planck mean coefficients for particle radiative properties in combustion environments

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

Analyse théorique et expérimentale de la diffusion de la lumière générée par une diode électroluminescente dans des répliques tissulaires

Contact Info

Product

Resources

About