Radiative transfer model of a pyrotechnic flame

Abstract

A two-line radiative transfer model for predicting the spectral radiant flux of pyrotechnic illuminating flares over a wide range of system variables such as formula, size, and ambient pressure, has been formulated and validated. To solve the transfer equation for observed radiant intensity, the flame is represented by a model whose main characteristics are (a) the flame is a homogeneous gaseous atmosphere with plane-parallel stratification, (b) the gas consists of inert molecules plus sodium atoms which can be excited to the 2 P 1 2 or 2 P 3 2 level, (c) there is local thermodynamic equilibrium governed by the local temperature, (d) the temperature gradient can be represented by a parabola whose vertex is at the center of the flame, (e) the dispersion profile and number density of sodium atoms have average values, inside the flame, that are independent of depth, and (f) the individual line dispersion profile is replaced with a two-line function to simultaneously describe the spectral distribution of both of the sodium D lines. The parameters of the radiative transfer theory were supplied from calculated thermodynamic properties of the flare. Optical thickness as a function of position in the flame was determined using computed sodium atom densities and physical flame size obtained photographically. A flame temperature gradient was constructed numerically as a function of temperature in the flame using the computed temperature at the flame center and the boundary. The two-line dispersion profile was constructed as a function of line broadening. The shape and intensity of the broadened flare spectrum was computed without introducing further assumptions.