Direct numerical simulation of auto-ignition of a hydrogen vortex ring reacting with hot air

Direct numerical simulation (DNS) is used to study chemically reacting, laminar vortex rings. A novel, all-Mach number algorithm developed by Doom et al. [J. Doom, Y. Hou, K. Mahesh, J. Comput. Phys. 226 (2007) 1136-1151] is used. The chemical mechanism is a nine species, nineteen reaction mechanism for H₂/air combustion proposed by Mueller et al. [M.A. Mueller, T.J. Kim, R.A. Yetter, F.L. Dryer, Int. J. Chem. Kinet. 31 (1999) 113-125]. Diluted H₂ at ambient temperature (300 K) is injected into hot air. The simulations study the effect of fuel/air ratios, oxidizer temperature, Lewis number and stroke ratio (ratio of piston stroke length to diameter). Results show that auto-ignition occurs in fuel lean, high temperature regions with low scalar dissipation at a 'most reactive' mixture fraction, ζ_{M R} (Mastorakos et al. [E. Mastorakos, T.A. Baritaud, T.J. Poinsot, Combust. Flame 109 (1997) 198-223]). Subsequent evolution of the flame is not predicted by ζ_{M R}; a most reactive temperature T_{M R} is defined and shown to predict both the initial auto-ignition as well as subsequent evolution. For stroke ratios less than the formation number, ignition in general occurs behind the vortex ring and propagates into the core. At higher oxidizer temperatures, ignition is almost instantaneous and occurs along the entire interface between fuel and oxidizer. For stroke ratios greater than the formation number, ignition initially occurs behind the leading vortex ring, then occurs along the length of the trailing column and propagates toward the ring. Lewis number is seen to affect both the initial ignition as well as subsequent flame evolution significantly. Non-uniform Lewis number simulations provide faster ignition and burnout time but a lower maximum temperature. The fuel rich reacting vortex ring provides the highest maximum temperature and the higher oxidizer temperature provides the fastest ignition time. The fuel lean reacting vortex ring has little effect on the flow and behaves similar to a non-reacting vortex ring.