Modeling Burning Metal Streamers in Pyrotechnic Explosions

We have developed a hydrodynamic model of the flow field created by pyrotechnic explosions. The model is based on a 3-phase version of our AMR code: MAUI. It contains the following elements: (i) a gas-dynamic model: GD of the expansion and mixing in the fireball, (ii) a Discrete Lagrangian Particles model: DLP of the projectiles, and (iii) a heterogeneous continuum model: HC of the burning particle wakes. Adaptive Mesh Refinement (AMR) is used to capture turbulent mixing and combustion on the grid. The grid was initialized with similarity solutions for: (i) the detonation products gases, and (ii) the particles. Results compare well with the photography of pyrotechnic explosions. Proposed here is a Model of the burning metal projectiles and their associated wakes. The projectiles are assumed to be Aluminum droplets, formed by shock-heating Al to the liquid state at 933 K. The droplets loose mass according to an empirical burning law that is proportional to the droplet diameter squared. Mass is conserved, so the droplet mass loss is put into the mass of an ultra-fine droplet mist. The mist is then burned instantaneously in stoichiometric proportions with air. We assume a high-Damköhler limit for the combustion rate which is consistent with the MILES theory of Boris.