Numerical determination of iron dust laminar flame speeds with the counter-flow twin-flame technique

Iron dust counter-flow flames have been studied with the low-Mach-number combustion approximation. The model considers full coupling between the two phases, including particle/droplet drag. The dispersed phase flow strain relations are derived in the Stokes regime (Reynolds number much smaller than unity). The importance of solving a particle flow strain model is demonstrated by comparing three different cases: a free unstrained flame, a counter-flow flame where slip effects are neglected and a counter-flow flame where slip effects are included. All three cases show preferential diffusion effects, due to the lack of diffusion of iron in the fuel mixture, e.g. D_Fe,m= 0. The preferential diffusion effect causes a peak in the fuel equivalence ratio in the preheat zone. On the burned side, the combined effect of strain and preferential diffusion shows a decrease in fuel equivalence ratio. Inertia effects, which are only at play in the counter-flow case with slip, counteract this effect and result in an increase of the fuel equivalence ratio on the burned side. A laminar flame speed analysis is performed and a recommendation is given on how to experimentally determine the flame speed in a counter-flow set-up. Novelty & Significance We introduce a novel model to include particle flow strain in a dispersed counter-flow set-up. For the first time, the impact of particle flow strain on the flame structure of iron dust is studied with a one-dimensional (1D) model. Two major effects that modify the flame structure and burning velocity are identified: preferential diffusion and inertia of the particles. Preferential diffusion effects are found to be always present in (iron) dust flames. Inertia effects play a role in the counter-flow case with slip. Due to the inertia of the particles, the particle flow strain is lower than the gas flow strain. As a consequence, higher particle concentrations are reached compared to the other cases. Furthermore, it is shown that each particle size experiences a different particle flow strain rate, which is important when doing experiments as it implies that the PSD at the flame front will be different than at the inlet.