A Continuous Exchange Factor Method for Radiative Exchange in Enclosures With Participating Media

Abstract

A continuous exchange factor method for the analysis of radiative exchange in gray enclosures with absorbing-emitting and isotropically scattering media and diffuse surfaces is developed. In this method two types of exchange function are defined: the direct exchange function and the total exchange function. Certain integral equations relating total exchange functions to direct exchange functions are developed. These integral equations are solved using a Gaussian quadrature integration method. The results obtained based on the present approach are found to be more accurate than those of the zonal method. Unlike the zonal method, in the present approach, there is no need for evaluation of multiple integrations for calculating direct exchange factors.

Analysis of Radiative Heat Transfer in Participating Media Using Arbitrary Nodal Distribution

“…For general geometries, however, numerical evaluation of exchange factors is preferred. Recently, a DEF method has been proposed [15][16][17] that eliminates the need for integration by evaluating direct exchange factors between differential surfaces or volumes, allowing for faster calculation time compared to the zonal and finite-element methods. In addition, since a nonisothennal assumption is used in deriving the governing equations, this method can provide more accurate results than those of the zonal method when employing Gaussian quadrature for discretization [15].…”

“…Following the formulation developed in [15], radiative transfer in an absorbingemitting media with isotropic scattering, confined by diffusely' reflecting walls, can be described in terms of the radiative surface heat flux q;(r.) and volumetric heat source q~(r.) at a location r, via and where E, and E; are the emissive powers at the surface and in the media, respectively. The four total exchange factors, defined as the fraction of energy emitted from a differential surface or volume that reaches another differential surface or volume directly, through multiple reflection off the surfaces, and via scattering within the media, can be expressed as (6) s s .…”

“…(15)-(18), might be found in the simplest of geometries, but solutions to most practical problems require numerical discretization. Explicit matrix formulations have been obtained for the total exchange factors in terms of the direct exchange factors [15]: …”

“…Employing a discrete exchange factor (DEF) method [15][16][17], in which radiative exchange factors are calculated between nodal points (as opposed to zone-zone [9,10,18,19] or point-zone calculations [20]), a program is developed that can use automatic mesh generation techniques developed for finite elements. The element-to-node grid generation scheme not only makes use of the recent advances in element mesh generation (i.e., easy meshing of multidimensional and irregular geometries, local refinement, and adaptive meshes [21]), but also lends itself to grid compatibility with calculations of fluid flow parameters or other heat transfer modes.…”

Modélisation des transferts radiatifs dans un incinérateur des émissions polluantes de la pyrolyse du bois

“…Jusqu'à présent, de nombreuses techniques ont été proposées pour traiter de tels problèmes parmi lesquelles on peut citer la méthode des zones développée initialement par Hottel et Sarofim [7]. Noble [8] et Naraghi et Chung [9] ont utilisé d'autres alternatives introduisant la notion d'aires d'échange. Larsen et Howell [10] ont proposé un schéma alternatif dans lequel les aires d'échange direct (AED) sont déterminées expérimenta-lement vue la complexité, dans certaines configurations, de la voie numérique qui sera appliquée plus tard avec succès par Olsommer et al [4].…”