Numerical simulation of fuel mixing with air in laminar buoyant vortex rings

The formation and evolution of vortex rings consisting of methane-air mixtures have been numerically simulated for different stroke to diameter (L/D) ratios (1.5, 3.5 and 6), Reynolds numbers (1000 and 2000) and initial mixture compositions (fuel with 0%, 15% and 30% of stoichiometric air). The numerical simulations are first validated by comparing with the results of earlier computational studies and also with in-house data from smoke visualization studies. In pure methane case, buoyancy significantly aids the upward rise of the vortex ring. The increase of vortex core height with time is faster for larger L/D ratio, contributed mainly by the larger initial puff volume. The radial size of the vortex also increases rapidly with time during the formation stage; this is followed by a slight shrinkage when piston comes to a stop. Later, a slow radial growth of the ring occurs due to the entrainment of ambient air, except during vortex pinch-off. The boundary layer thickness δe at orifice exit decreases as Re−0.5 at a fixed L/D ratio; this in turn, results in a vortex of smaller size and circulation level, at a relatively higher Reynolds number. For L/D values greater than the critical value, a trailing stem is formed behind the ring vortex which feeds circulation and fuel into the vortex ring in the later stages of vortex evolution. Mass fraction contours indicate that fuel-air mixing is more effective within the vortex than in the stem. Ambient air entrainment is larger at higher L/D ratio and lower Re, for the range of conditions studied. The effect of initial premixing with air reduces the buoyancy effect. Therefore, the increase of core height and core radius with time is relatively less for the air-premixed cases.