Scattering radiative transport

N. E. Wakil and J. F. Sacadura, Some Improvements of the Discrete Ordinates Method for the Solution of the Radiative Transport Equation in Multidimensional Anisotropically Scattering Media, in HTD vol. 203, pp. 119-127, ASME, New York, 1992. 

The discrete ordinates method in a S4-approximation is used to solve the radiation transport equation. Since the intensity of radiation depends on absorption, emission and scattering characteristics of the medium passed through, a detailed representation of the radiative properties of a gas mixture would be very complex and currently beyond the scope of a 3D-code for the simulation of industrial combustion systems. Thus, contributing to the numerical efficiency, some simplifications are introduced, even at the loss of some accuracy. The absorption coefficient of the gas phase is assumed to have a constant value of 0.2/m. The wall emissivity was set to 0.65 for the ceramic walls and to a value of 0.15 for the glass pane inserted in one side wall for optical access. 

The objective of this section is to introduce basic concepts of the transport theory in participating media (ie, absorbing and scattering media) and their physical interpretation. These concepts are well established in the radiative transfer research and are detailed in many reference textbooks, such as Siegel and HoweU (1981), Case and Zweifel (1967), and Goody and Yung (1964). These concepts are not repeated in detail here they are... 

In Section 3.3, Fig. 13, we saw that the equivalent transport problem allows us to separate our radiative study into two simple systems the ballistic photons, for which the exact solution is analytical, and the scattered photons, which correspond to intensity close to isotropy. This relative isotropy of the scattered intensity in the equivalent transport problem suggests that the PI approximation is relevant. Therefore, to formulate the coUimated incidence phenomena, we will address the equivalent transport problem and separate the analysis of ballistic photons from that of scattered photons only scattered photons will be subjected to the PI approximation. In the rest of the chapter, the baUistic population is denoted as (0), whereas the scattered photons wiU be called the diffuse population and denoted as (d). 

A discussion of applications of these concepts to neutron transport theory can be found in the papers [4 5 6 7 8 9]. For the interested reader we also call attention to the applications to radiative transfer theory [1 10 11], to wave propagation, [12 13 14], to random walk and multiple scattering [15 16], and to problems with moving boundaries [9]. 

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