Asymptotic and approximate solutions for piloted ignition of thermally thick solids under power-law heat flux

Abstract

New asymptotic solutions are established in this work to describe the piloted ignition behaviors of thermally thick solids exposed to power-law thermal radiation accounting for convective, radiative and their combined heat loss effects. In all scenarios, the derived surface temperature and ignition time correlations share a similar form. The ignition time to the power of −0.5 linearly depends on the transient radiation. The asymptotic solutions are validated by comparison with numerical solutions and compared for accuracy with previous approximate correlations. Moreover, according to the surface temperature history, an asymptotic mass flux solution is attained. Accuracy of all solutions are verified by numerical and experimental results where vertical PMMA was heated by five power-law heat fluxes. The predicted surface temperatures fit the numerical and experimental curves well if the ignitor is located at the top sample holder. However, for center ignitor the developed model overestimates experimental surface temperatures at ignition time due to the neglected pyrolysis caused by increased thermal penetration effects. Effects of ignitor location are important for low heat fluxes. The asymptotic mass loss rates agree well with numerical and experiential results. Both critical temperature and critical mass loss rate are used to estimate ignition times, and good agreement is found except for the experimental cases of top ignitor.