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This paper presents results of experimental and numerical investigations of flame spread along a thin solid in an opposed oxygen flow in a narrow channel. Experiments are conducted at various oxygen flow speeds and gas-phase heights. For a low gas-phase height or a low oxygen flow speed, a large portion of solid is left unburned, and the burned region forms a finger-like pattern. It is noted that both the flame spread velocity and the fraction burned increase with an increase in the gas-phase height or oxygen flow speed. A simple, two-equation model is then developed to simulate the phenomenon. The original 3-D equations are reduced to 2-D forms, which are solved numerically. To simplify the model, it is assumed that the rate of solid pyrolysis is linearly proportional to that of gas-phase oxidation. A comparison between the numerical predictions and the experimental data, however, indicates that because of this assumption, prediction error tends to increase with increase in the gas-phase height or oxygen flow speed. Nevertheless, model predictions agree reasonably well with the experimental data, thus validating the assumptions of the model, at least qualitatively. A weakly nonlinear stability analysis is finally conducted to derive a relationship between the scaled flame spread velocity and a dimensionless parameter that combines the effects of material properties and experimental parameters such as the gas-phase height and oxygen flow speed. The presented numerical and experimental results support the stability analysis. |
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