# Polyisocyanurate Foam Pyrolysis and Flame Spread Modeling
## 3 Results and Discussion
### CAPA II Experimental Results and Modeling  
The average back surface temperature, \(T_{back}\), MLR normalized by the initial front surface area, relative mass (m/m\({}_{0}\)) and thickness change measured for the Tuff-R foam core samples in the CAPA II experiments performed at 70 kW m\({}^{-2}\) of set radiant heat flux are shown in Figure 5. The error bars were calculated from the scatter of the data as two standard deviations of the mean. The data indicate that the majority of the mass loss occurred during the first 200 s after the start of the experiment. The sample first grew in thickness by about 25% and subsequently contracted by about 15% with respect to the original thickness. The sample left about 33% of solid residue at the end of the experiment. Figure 4: Mean experimental results and model predictions for the Microscale Combustion Calorimetry (MCC) tests performed on the PIR foam at 10 K min\({}^{-1}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Component** & \(\Delta H_{c}\) **(l kg\({}^{-1}\))** \\ \hline Gas\_1 & 0 \\ Gas\_2 & \(1.5\times 10^{7}\) \\ Gas\_3 & \(1.5\times 10^{7}\) \\ Gas\_4 & \(0.8\times 10^{7}\) \\ Gas\_5 & \(2.4\times 10^{7}\) \\ Gas\_6 & \(2.0\times 10^{7}\) \\ Gas\_7 & \(3.3\times 10^{7}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Heats of combustion of gaseous products of decomposition of the PIR foam. Positive \(\Delta H_{c}\) represents an exothermic process. To model this experiment, the emissivities, \(\varepsilon\), of all condensed-phase components, with the exception of glass fiber, were set to 0.95. This value of emissivity was derived from an additional CAPA II test performed at 70 kW m\({}^{-2}\) on the sample whose top surface was coated with a 0.95 emissivity paint. This test produced results that were nearly identical to the unpainted sample results shown in Figure 5. The condensed-phase component radiation absorption coefficients, \(\alpha\), were set to 3200 m\({}^{-1}\), which was approximately equal to the reciprocal of the depth of open pores located on the sample surface. The emissivity and absorption coefficient of the glass fiber were obtained from an online property database [41] and were set to 0.81 and 4160 m\({}^{-1}\), respectively. The gas transfer coefficient used in the ThermaKin2 Ds to define the rate of transport of gaseous species through the condense phase in response to a concentration and/or pressure gradient was set to its default value of 2.0 \(\times\) 10\({}^{-5}\) m\({}^{2}\) s\({}^{-1}\), which was used to simulate uninhibited transport. The densities, \(\rho\), and thermal conductivities, \(k\), of all components, with the exception of the glass fiber, were assumed to be independent of temperature and were optimized to fit the experimental \(T_{back}\) and thickness change dependencies on time. The \(\rho\) and \(k\) of the glass fiber were obtained from an online property database [41]. The resulting set of thermal transport property values is summarized in Table 4.  
Figure 5: Mean experimental results and model predictions for the Controlled Atmosphere Pyrolysis Apparatus II (CAPA II) tests performed on the PIR foam at 70 kW m\({}^{-2}\) of set radiant heat flux. As the results shown in Figure 5 indicate, the model fits both the temperature and sample thickness data well and also provides a good prediction of the MLR. Similarly, good predictions were obtained with this model for the 40 kW m\({}^{-2}\) CAPA II experiments. A comparison of these predictions with the experimental data is provided in Figure A2 of Appendix A. At 70 kW m\({}^{-2}\), the total mass loss was somewhat underpredicted by the model. This underprediction was attributed to an inability to account for release of the blowing agent located in the foam pores. This inability was a consequence of the fact that the blowing agent was lost during the preparation of the mg-scale test samples, which were used to parameterize the thermal decomposition mechanism.