On modeling the diffusion to kinetically controlled burning limits of micron-sized aluminum particles

Abstract

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. Two reduced modeling strategies are therefore explored to account for finite-rate chemistry effects in simpler models for use in system level CFD analysis. The first is 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 deflagration speeds in dusty aluminum-air gases agree well with experiments and show evidence of a maximum flame speed for a given mass loading. The second modeling approach uses a reduced numerical model and kinetics mechanism resulting in computationally efficient solutions. Results using this approach show up to two orders of magnitude reduction in computational effort while maintaining reasonable accuracy for predictions of flame structure, burn rates and burn times.