Experiment and modeling of stochastic ignition and combustion of fuel droplets impacting a hot surface

The ignition dynamic of liquid fuel droplets impacting hot surfaces is critical for fire-safety analysis in engineering systems, as well as for controlling wall-filming effects in IC engines. The scenario of slow fuel-leakage rates poses challenges associated with the stochastic processes of droplet splashing, break-up, turbulent mixing, and combustion. To address this, we conduct controlled experiments of liquid n-heptane droplets impacting a heated surface in the Leidenfrost regime, targeting the individual-droplet-deposition conditions. The experiment encompasses a range of surface temperatures and droplet-deposition rates. The experiments are complemented by theoretical analysis, where we developed a stochastic low-order numerical model, demonstrating good accuracy for predicting ignition probability and overall combustion dynamics. Notably, we observe a broad region of intermittent combustion behavior, with ignition probability varying based on surface temperature and droplet deposition rate. Additionally, we find that the transition to consistent ignition relies heavily on both surface temperature and deposition rate. Experimental and numerical model results shed light on the roles of the complex interplay between droplet breakup, chemical kinetics, and evaporation and mixing time scales, as well as the interaction among subsequent droplet combustion events, in governing the ignition and combustion of impacting droplet trains. The revealed dynamic of droplet/hot-surface ignition and the proposed stochastic model hold promise for advancing predictive capabilities of hot-surface-induced ignition and combustion arising from accidental leaks in flammable-liquid piping and wall-filming, particularly in the stochasticity-dominated individual-droplet-deposition regime.