Quantification of ignition time uncertainty based on the classical ignition theory and Fourier analysis

This study aims at modeling the effect of incoming heat flux fluctuations, on solid material ignition. In order to propose a general methodology based on the classical ignition theory that can be applied to any kind of solid target, kernels accounting for the target temperature response regarding an incoming heat flux are considered for thermally thick and thin solids with low or high thermal inertia. A Fourier decomposition of the incoming heat flux is then used to calculate the target response to harmonic heat fluxes. Finally, effects of harmonic fluctuations on ignition are discussed based on the previous analytical results, allowing us to discriminate situations where ignition time is expected to be rather predictable from situations where ignition time is expected to be less predictable thanks to an uncertainty quantification of the ignition time.