Width effects on downward flame spread over poly(methyl methacrylate) sheets

Abstract

The experiments of downward flame spread over poly(methyl methacrylate) sheets with different dimensions were conducted in this study. In comparison with flame spread over samples under infinite width condition, lateral air entrainment shows significant influence on downward flame spread of finite width. The characteristic angles, defined as those produced on sample residues in a steady-state stage, are constant for different dimensions. Based on the characteristic angles and with reasonable assumptions, a three-dimensional theoretical model is proposed to illustrate the experimental results. Width effects on downward flame spread over thicker samples are more obvious and they fade away with gradual increase in width. Moreover, the heat flux penetrating through the solid surface at the front of the pyrolysis region is higher than that in the twodimensional case. The flame height correlates well with mass loss rate as an exponential function with a mean power value of 0.79.

Prediction of Three-Dimensional Downward Flame Spread Characteristics over Poly(methyl methacrylate) Slabs in Different Pressure Environments

“…Heat flux distributions at the pyrolysis surface and preheated region in Hefei were deduced in our previous study, which are 20.6 and 73.3 kW/m 2 , respectively [14]. According to Equations (6) and (14), distributions of heat flux in other four pressure environments can be derived through Equations (15) and (16) as $q_s^{″}=73.3{(\frac{P}{102})}^{2/3},$ $q_P^{″}=20.6{(\frac{P}{102})}^{1/2},$ where the unit of P is kPa.…”

“…In our previous study [14], a calculating formula was proposed to predict the steady flame spread rate based on heat transfer theory and energy conservation equation, $V_f=4\frac{\left[\frac{{\mathsf{\delta }}^2\cot \frac{\mathsf{\beta }}{2}}{8\sin false(\frac{\mathsf{\alpha }}{2}-\mathrm{sans-serif\gamma }false)}+\frac{W\mathrm{sans-serif\delta }}{4\sin \frac{\mathsf{\alpha }}{2}\sin \frac{\mathsf{\beta }}{2}}-\frac{{\mathsf{\delta }}^2\cot \frac{\mathsf{\beta }}{2}\sin \mathrm{sans-serif\gamma }}{8\sin \frac{\mathsf{\alpha }}{2}\sin false(\frac{\mathsf{\alpha }}{2}-\mathrm{sans-serif\gamma }false)\sin \frac{\mathsf{\beta }}{2}}\right]\times q_P^{″}+false(\frac{\mathsf{\delta }}{2}+\frac{W}{2\sin \frac{\mathsf{\alpha }}{2}}false)\mathrm{sans-serif\epsilon }\times q_s^{″}}{false(h_{\mathrm{deg}}+c_{P}false(T_p-T_{\infty }false)false)\times {\mathsf{\rho }}_{s}W\mathrm{sans-serif\delta }}$ where $h_{\mathrm{deg}}$ is the heat of degradation of solid PMMA. Plugging the measured characteristic angles and the calculated heat fluxes into Equation (17), flame spread rates for different-sized samples in five pressure environments can be estimated.…”

“…A number of experiments and simulations on flame spread over solid combustibles have been performed. The dependence of flame spread characteristics on related physical and ambient conditions has also been proposed [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 ].…”

“…Apart from the theoretical predictions of flame spread rate mentioned above, many investigators have concentrated on experimental and semi-empirical research method [ 2 , 7 , 10 , 11 , 12 , 13 , 14 , 18 , 19 ]. Ayani et al [ 10 ] provided an empirical formula of two-dimensional downward flame spread rate over PMMA through a heat transfer model, which was proved to predict flame spread rate accurately.…”

“…Experimental investigations were only concerned with downward flame spread over solid combustibles in a 2-D situation, where sample was hypothesized to be infinite along the sample width and pyrolysis front was linear and uniform. Very few papers [ 2 , 12 , 14 ] have addressed the flame spread over uninhibited solid materials, where flame spread was unconstrained and should be considered three-dimensional (3-D).…”