Direct numerical simulations (DNSs) of nanoparticle formation in reactive flows are challenging, and only greatly simplified DNS test-cases are possible, which help clarify the turbulence–particle–dynamics interaction and guide the necessary modeling efforts. As a basis for such studies, a new DNS database is introduced, which resolves the smallest relevant scales of the nanoparticle concentration field to obtain insights into the statistics of nanoparticle formation in reactive flows. Formation and evolution of iron oxide nanoparticles in premixed and non-premixed flames wrapped-up by a vortex have been investigated using the sectional model and direct chemistry. The DNSs capture the “engulfing” and local dilution of the particle fields. Different zones of high particle number concentration have been found in every flame, and it was shown that the thickness of these zones decreases with increasing Schmidt number, which confirms that in simulations of nanoparticle-forming turbulent reacting flows, the grid resolution has to be very fine to resolve the characteristic scale for high sections. The contributions to the change in particle concentration due to diffusion, coagulation, and nucleation have been analyzed in detail, and dominant contributions across the particle number concentration layers and across the flames have been identified. This analysis has also been carried out in terms of flat, concave, and convex iso-surface geometries, induced by the flame–vortex interaction and characterized by the curvature of the particle number concentration fields and also by the flame curvature. The results demonstrate that the flame curvature effects cannot be ignored in modeling strategies. The probability density functions for the particle number concentrations have been analyzed and quantified in terms of Shannon information entropy, which illustrates the effect of fast diffusion (and entropy production) of the smaller particles and slow diffusion (and entropy production) of the largest particles with high Schmidt numbers. In addition, the unclosed filtered or averaged agglomeration term was evaluated as a basis for future modeling efforts, showing that agglomeration rates will be underestimated by orders of magnitude unless suitable models are developed.
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