Discrete ordinates method in the analysis of the radiative transfer in high intensity discharge lamps

Abstract

This paper deals with radiation transfer in cylindrical high pressure discharges for which local thermodynamic equilibrium can be assumed. An S–N approximation (a set of N discrete directions) of the discrete ordinates method is used to solve the radiative transfer equation. A summary of the basic equations and numerical formulations is given in order to calculate the spectral intensities and then to evaluate radiative flux and net emission coefficient. Also, the net emission coefficient is described by a semi-empirical formula which contains terms representing the generation and absorption of radiation. The results are presented for a typical high pressure mercury discharge commonly used as a light source.

Study of the influence of additive on the radiative properties of a HgTℓI high pressure discharge

“…where n (r) is the number density of the absorbing level, A u is the transition probability, g u and g are the statistical weights of the upper and lower levels, respectively, and P λ (r) is the normalized line shape function given by Stormberg and Schafer (1983). The formulation of equation ( 1) in cylindrical coordinates is explained in detail by Bouaoun et al (2005). Here only a summary of the formulation is given.…”

“…Since it is difficult to directly discretize equation ( 4), an energy balance over a directional control volume as well as a spatial control volume is performed. We obtain the equation below (Bouaoun et al 2005):…”

“…Table 1 gives the main atomic characteristics of these lines. The mercury lines have previously been investigated in an earlier paper (Bouaoun et al 2005).…”

“…The DOM method has received considerable attention owing to its efficient integration with other finite difference transport equations (Carlson and Lathrop 1968, Menart 2000, Mezrhab et al 2008. In a recent paper we have applied this method for the case of a pure mercury discharge (Bouaoun et al 2005).…”

Fisher information analysis of list-mode SPECT emission data for joint estimation of activity and attenuation distribution

“…To describe the radiation transfer through a sub-path, we use an approach similar to the discreteordinates method for solving the equation of radiative transport [39]. Each sub-path is defined in terms of a start location and a finite angular range.…”