Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation

Abstract

A one-dimensional unsteady mathematical model of solid fuel ignition is presented. The solid fuel is heated by an external radiative heat source. Some radiation is absorbed in depth by the solid fuel and some by the decomposition products in the gas phase. Solid fuel degradation occurs according to a zero-order Arrhenius pyrolysis reaction and gas-phase combustion according to a second-order Arrhenius reaction. Gas-phase heat and mass transfer and solid phase heat transfer are described by differential balance equations that are coupled through the boundary conditions at the interface. The solution is computed numerically by an implicit finite difference method. PMMA radiative ignition is simulated by varying the intensity of the radiative heat flux and predictions show quite good agreement with experiments. The ignition process oceurs in the gas phase in a premixed fashion, rapidly followed by the transition to a diffusion flame. As the radiative heat flux is increased, higher surface temperatures and pyrolysis mass fluxes are reached, ignition occurs closer and closer to the fuel surface, and ignition delay times decrease. Gas-phase absorption of radiation plays a fundamental role in the predicted ignition phenomenon and ignition delay times. In particular, with realistic data and no absorption of radiation in the gas phase, ignition does not occur at all. Finally, a parametric study is performed in order to analyze the dependence of the predicted ignition phenomenon on key parameters used to model degradation and combustion processes, such as preexponential factors and activation energies of the reactions.