Numerical simulation and prediction of polymer flammability in non-standard conditions

Fire safety of plastics is commonly characterized in terms of Oxygen Index (OI), or the limit oxygen concentration in oxidizing atmosphere that supports combustion. OI is determined in normal conditions (atmospheric pressure, room temperature, etc.) according to the procedure prescribing the ambient conditions, number of samples, their dimensions. However, polymer materials and products where they are used meet the variety of ambient conditions; low and high temperatures, pressures, flow velocities, accelerations, and etc. The methods of prediction of polymer flammability and OI in the wide range of operating conditions have not been available until now. In this study, a mathematical model is worked out and the theory of limits of polymer combustion is developed to predict OI and other critical values in non-standard conditions; pressure 0.1–100 atm; initial temperature of polymer 250–550 K; gravity force acceleration 0.1–50 g; velocity of oxidizing O2/N2stream 0–50 m/sec; different thickness of polymer layers covering the cold base and their simultaneous action. The model involves two-dimensional numerical simulation of the diffusion combustion of a polymer in the presence of heat losses. The main factor to be taken into account is the decrease of flame temperature due to the cooling effect of different agents. Therefore, the extinction criterion and OI are expressed in terms of the relationship between Damköhler and Peclet numbers. Two critical conditions, observed earlier in the experiments on polymer extinction limits, are explained. The predictions of the model were tested for PMMA and were found to be in good agreement with experimental data available.