| OCR Text |
Show (2) Eq. (3) implies that the radiative properties of the combustion products are approximated with a so-called 'Weighted-Grey-Gas Approach' (Ref. 8) with n=4 grey ranges. an is the weighing factor and Kn is the grey absorption co-efficient assigned to the n th range. The radiation model works as follows. The emissive power of all grey ranges (1 st term of Eq. (2» of a volume zone (surface zones are treated in analogy) is distributed among a finite number of beams. The beams are emitted over the whole view angle and traced through the arrangement of volume zones until they impinge on wall. The beam gradually loose energy through absorption. The. amount of energy Qbeam , a absorbed from a beam by a volume zone 1S expressed by : Qbeam, a = Qbeam, in [1-exp (- Kn ds)] (3) Qbeam in is the energy flux of a beam incident on the volume zone and ds is the path length of the beam cut out by this zone. The energy amounts Qbeam ~ absorbed from all beams passing a zone are accumulated. The rad1ative sub-balance according to Eq. (2) is calculated for each iteration cycle necessary to solve the total energy balance (1). since in the current study wall surfaces are treated as grey, diffuse radiators and reflectors, reflected energy amounts from beams incident on a wall are accumulated at the corresponding surface zones, and added to surface emission in the next iteration step. Combined wall emission and reflection is then treated in analogy of volume emission described above, however taking the cosine law into account. The current semistochastic method is distinguished from pure Monte-Carlo methods by the fact that some events in the history of a beam are deterministically influenced rather than based solely on random numbers (see Ref. 6). The zone model considers, besides radiation from wall zones, radiation from gaseous species C02 and H20 and from soot particles. Zonal concentration of these species are calculated from the combustion model descr ibed further below. Weighing factors and specific absorption coefficients of the gaseous species utilized for the 'Weighted-Grey-Gases-Approach' are taken from Ref. 8. The specific absorption coefficients for soot are prescribed according to an approach suggested in Ref. 9. 4 |
