ABSTRACT
INTRODUCTION Radiative transfer is the most dominant mechanism for the energy transfer in UV source lamps operating at high pressure. The prediction of radiation transfer is one of the most important issues in the overall lamp modeling. Among the various models described in the literature, we have selected the P1 model initially developed to be used for a gray gas solution. We have adapted the model to be used with multiple bands and thus to simulate the radiation in the lamp enclosure. Our lamp consists of a thin glass wall enclosing a plasma. A 2d treatment of this problem is considered since the problem does not depend on the azimuthal angle. The glass is semi-transparent so we deal with semitransparent boundary conditions. Also, we assume that the incident radiation from within the medium is diffuse and the reflected component from wall interface is diffuse as well. Scattering is neglected. Finally, the reflected energy into the plasma is assumed to be small; therefore the calculation of exchange factor is not necessary. In our problem, the plasma medium is considered gray and consists of several bands with temperature dependent absorption properties. Within each band, a mean absorption coefficient has been calculated and it depends on the temperature and pressure and not on the wavelength (or frequency). Therefore we have derived a new formulation of the P1 model that accounts for multiple frequency bands. Note that, the radiation intensity, through emission and temperature-dependant properties, depends on the temperature field and therefore cannot be decoupled form the overall energy equation. Thus the temperature field must be determined through an energy conservation equation that incorporates all three modes of heat transfer; conduction, convection and radiation. In this paper, we will show some results for the radiative heat flux using the P1 model. Our discharge medium is a mercury-argon mixture operating at 1.1atm. The simulation is done for a dc lamp operating at 10A. The mass concentration ratios of Hg and Ar are set to 91% and 9% respectively 141.
MODEL DESCRIPTION In the P1 model, the radiation intensity is decomposed into a series of direction-dependent coefficients and spatial-dependent coefficients PI. The intensity is then rearranged in a way to be function of two terms: a scalar term that is the incident radiation G, and a vector term that is the radiative heat flux -4, . Integrating the radiative intensity over all solid angles and over a predefined frequency band i yields the governing equations for the P1 approximations:
