Modeling the diffusion to kinetically controlled burning transition of micron-sized aluminum particles

Aluminum particle burn rates are known to be a strong function of particle size as the mode of burning transitions from diffusion to kinetically controlled. To better understand the rate dependent diffusion and kinetic processes, a fully compressible, one-dimensional, spherically symmetric particle burn model is developed. Several cases are studied to explore the burning of aluminum particles in air, carbon-dioxide and steam environments. Predictions of burn rates versus particle size reveal significant deviations from a diffusion controlled burning limit - highlighting the importance of accounting for finite-rate chemistry in modeling the burning of sub-micron aluminum particles. While overall agreement to data is satisfactory, the detailed model cannot be directly used in system level tools due to computational cost. A reduced modeling strategies are therefore explored to account for finite-rate chemistry effects in simpler models for use in system level CFD analysis. An augmented D² - law where the finite-rate chemistry is treated as a perturbation to flame sheet approximation via augmented burn rate "constants". Predictions using this approach of de agration speeds in dusty aluminum-air gases agree well with experiments and show evidence of a maximum flame speed for a given mass loading.