Behaviors of a flame ignited by a hot spot in a combustible vortex (vortex-bursting initiation revisited)

Abstract

Ignition characteristics in turbulent flow are different from those in stagnant gas, because strong vortices may significantly modify microscopic flame propagation processes. To gain theoretical insight into misfiring in strong turbulence, we examine behaviors of a flame ignited by a hot spot in a combustible Rankine's vortex. The fate of the flame is classified by the relationship between the vortex strength (magnitude of swirl velocity) and the input heat (including heat of combustion) effects on the azimuthal vorticity wave formation. If the input heat is large enough to realize steady flame propagation along the vortex, the flame front moves at the same constant speed as the propagation speed of azimuthal vorticity wave, which is proportional to the swirl velocity of the vortex. This flame front is stable to any small disturbance because it's convected by the flow induced by the azimuthal vorticity distribution and situated at an equilibrium position in the negative strain rate field. On the other hand, when the vortex is too strong, the flame front is located behind the center of azimuthal vorticity distribution to be elongated in the axial direction and eventually extinguishes cooled from sides by the surrounding cold gas. The propagation speed of azimuthal vorticity wave is an intrinsic property to the vortex and independent on the way of ignition, whereas the intensity of azimuthal vorticity wave, represented by the maximum value of azimuthal vorticity or axial velocity induced at the vortex centerline, increases with the amount of effective input heat. Steady flame propagation is realized only when the latter exceeds the former. Otherwise, the flame extinguishes.