On the importance and modeling of in-depth spectral radiation absorption in the pyrolysis of black PMMA

In-depth radiation absorption in pyrolysis models is commonly modeled with Beer's law using a constant absorption coefficient. This approximation neglects the effects of spectral variation of absorption coefficient, material emissions, and directional dependency of penetrated thermal radiation. This research aims to address the importance of these factors in flammability analysis of black poly(methyl methacrylate) (PMMA). Accordingly, a pyrolysis model including the separated full spectrum correlated k-distribution (SFSCK) method for spectral modeling, the ordinate weighting method (OWM) with finite volume method (FVM) for directional distribution of the thermal radiation is introduced as the most detailed model. By gradually simplifying this model, five other pyrolysis models are developed with different levels of details in radiation calculations. Simulations are first done using the optimized thermal conductivity and specific heat capacity for the most detailed model, then by optimizing these parameters for each pyrolysis model separately. The results show that the pyrolysis model with a depth and source temperature-dependent absorption coefficient, two-flux method, and diffuse boundary with a scenario-dependent effective reflectivity can predict the measured mass loss rate and ignition time with accuracy similar to the most detailed model, and can be recommended for future pyrolysis simulations.