Analysis of flame front velocities in planar iron particle cloud flames

We analyze the propagation of planar flames in iron particle cloud combustion through carrier-phase direct numerical simulations (CP-DNS). We use an existing iron combustion point particle model capturing the mass, heat, and momentum transfer between the particle and gas phase. The fluid equations are solved with a pseudo-spectral multi-phase solver. We start with a cold mixture of air at ambient conditions and homogeneously distributed 10 µm-sized particles at an equivalence ratio ϕ = 1. A layer of particles is ignited by external heating, from which a planar flame front propagates through the mixture. Even though particle properties, like temperature and oxidation progress, show a significant standard deviation along the homogeneous planar directions, these local inhomogeneities do not significantly introduce perturbations of the gas phase in directions normal to the propagation. We propose a calculation framework for capturing the flame front velocity vector through a box-counting algorithm, based on the local propagation of the reacting iron particle front. This method can be used for more complex flow setups, e.g. for flame fronts propagating in turbulent flows. For a planar flame propagation, the front velocity can be characterized by just the scalar flame speed, which gives values of around 21 cm/s, comparable to recently determined values of burning velocities for iron dust flames from the literature.