Eulerian-Lagrangian modelling of rotating detonative combustion in partially pre-vaporized n-heptane sprays with hydrogen addition

Rotating detonation combustion (RDC) fuelled with partially pre-vaporized n-heptane sprays and gaseous hydrogen is studied with an Eulerian-Lagrangian method and a simplified two-dimensional model. Our focus is the effects of various pre-vaporized n-heptane equivalence ratios and droplet diameters on detonation wave propagation and droplet dynamics in two-phase RDC. The results show that when the droplets are small, they are fully vaporized by the detonation wave. However, when the droplet diameter is relatively large and/or the detonation wave number is bifurcated, liquid droplets are observable beyond the refill zone. Moreover, the detonation speed is considerably influenced by the droplet pre-vaporization and diameter. The velocity deficits from our simulated two-phase RDC vary between 5% and 30%. Over 70% n-heptane is detonated in the simulated cases, and it is found that there exists a critical droplet diameter (about 20 µm), around which the detonated fuel fraction is minimal. Four droplet trajectories in RDC are identified, which are differentiated by various evaporation times, residence times and interactions between droplets and the basic RDC flow structures. Inside the refill zone, three droplet categories are qualitatively identified. Droplets injected at the right end of the refill zone directly interact with the deflagration surface and meanwhile have relatively long residence time. However, droplets injected closer to the travelling detonation front have insufficient time to be heated and vaporized. Novel technologies and implementations may be needed to enhance the in-situ droplet evaporation during the refill period in practical liquid fuelled RDE's. Our results also demonstrate that when pre-vaporization level is low and initial droplet diameter is large, the liquid fuel droplets may disperse towards the combustor exit. Furthermore, the droplet dispersion height decreases with liquid fuel pre-vaporization, while increases with droplet diameter.