On the Flame Spreading over a Polymer Surface

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Abstract
Steady propagation of a diffusion flame spreading over a surface of a solid polymer placed in a quiescent gaseous oxidizer environment is investigated under assumptions of negligible radiation effects. A model proposed for the flame configuration is a complex of smoldering preheat zone followed by a diffusion flame sheet. According to this model governing equations (viz., energy equations of gaseous and condensed phase and a single equation for chemical species) reduce to Oseen's equation in which no reaction kinetics intervene. The whole system comprises an eigenvalue problem to determine the flame propagation velocity. It turns out that to the first order in (density of gas/density of solid)1/2 which is considered small for environmental pressure less than 30 atm, analytical expression for the burning velocity is obtained. The burning velocity as a function of the pressure is calculated for Nitrogen-diluted Oxygen/plexiglass system, and is compared with experimental data of McAlevy et al. This leads to an indirect derivation of a regression rate formula for the polymer. It is also shown that there exists a scaling law describing the effect of inert diluent gas on the propagation velocity, according to which the cited experimental data fit on a single curve. Effect of the initial temperature on the propagation velocity is also compared with experiments. Also, the surface temperature profiles in the vicinity of the flame foot are calculated for various values of the pressure.

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