The interaction between particle clustering and iron particle cloud combustion in homogeneous isotropic turbulence

We perform carrier-phase direct numerical simulations (CP-DNS) to investigate the interaction of iron particle cloud combustion and clustering through turbulence.
A pseudo spectral multi-phase solver in combination with a point particle iron reaction model is used, capturing mass, heat and momentum transfer between the phases. We investigate the combustion of 10 µm-sized iron particles with air, in homogeneous isotropic turbulence (HIT) at Stokes number one, varying the equivalence ratios from lean ($\phi=0.1$) to fuel-rich ($\phi=2$). At the start, the particles are homogeneously distributed with a temperature below particle ignition temperature. Particle clusters form through turbulence and ignite. While in the very lean regime ($\phi<0.25$) the $\mathrm{O_2}$ diffusion through the particle boundary layer limits the conversion of $\mathrm{Fe}$ to $\mathrm{FeO}$, for $\phi>0.5$, the oxygen depletion in clusters slows down the overall oxidation progress, and the conversion is limited by the transport of oxygen from regions devoid of particles into clusters. This observation from numerical simulation is supported by a time-scale analysis of the effects involved. We also quantify particle clustering through a Voronoi tessellation and show that through combustion, particle clusters become more prominent. This is caused by two effects. First, if the reacting particles are spaced closely enough to create a local lack of oxygen, a fluid flow is triggered from the regions devoid of particles into clusters. This flow carries particles into the cluster region. Second, finite-size particles cannot follow the fast thermal fluid expansion caused by the exothermic particle reaction as well as the slower compression through heat losses to colder areas.