Coupled analytical approach to predict piloted flaming ignition of non-charring polymers

Abstract

Classical thermal theory of piloted ignition is extended by coupling the heat balance at the exposed sample surface and the finite-rate pyrolysis in the material volume. Approximate analytical solutions for the sample temperature are obtained for an arbitrary sample thickness, with the external radiative heating, surface re-radiation, heat of gasification, and the convective heat flux corrected for blowing taken into account. The volatile mass flux is evaluated by integrating the pyrolysis rate throughout the layer, with the assumption of high activation energy limit. Critical mass flux of combustible volatiles is used as the ignition criterion. This enables the ignition temperature to be evaluated instead of being pre-assumed as is done in the classical thermal theory. Coupled analytical approach proposed in this work is verified by comparisons to the numerical solution obtained by the Pyropolis model for the same problem setup. This approach has also been validated by comparisons to published experimental data (ignition temperatures and times to ignition) for three non-charring thermoplastics: polymethylmethacrylate, polyethylene and polypropylene.