A flame does not stay in place by itself. The flame front settles where its own propagation speed balances the approach speed of the mixture. If the mixture is fast the flame blows off; if slow it flashes back.
In practice that balance is established by the flow itself.
The recirculation zone
Behind the flame holder (swirl vanes, a cone, a step) a low-velocity recirculation zone forms. Hot combustion products are retained there and continuously ignite the fresh mixture. That is the pilot keeping the flame alive.
The design questions revolve around this zone: its size, the residence time within it, its temperature and its contact area with the fresh mixture.
Swirl number
When axial swirl is imposed, a recirculation region opens on the axis once the swirl number exceeds a threshold — vortex breakdown. This is the most common flame-holding mechanism in industrial burners.
Below the threshold there is no stable recirculation and the flame is open to blow-off. Far above it the flame becomes too short, attaches to the wall and creates local overheating.
Modelling difficulties
Swirling flow is anisotropic. Isotropic two-equation models get vortex breakdown and the size of the recirculation zone wrong; a Reynolds stress model is markedly more realistic [1]. The same limitation applies in cyclones.
The phenomenon may be transient. The vortex breakdown region oscillates; a steady solution struggles to converge, and that is usually a signal from the physics. See the convergence note.
Extinction and ignition are chemical. If the stability limit is the question, a mixing-based combustion model is insufficient. See the combustion modelling note.
The acceptance criterion
What is usually wanted from the analysis is not "is there a flame" but how large the stability margin is: at what excess air and what load does blow-off begin. That is found by scanning a range, not by running a single operating point.
References
- Launder, B. E., Reece, G. J. & Rodi, W. (1975). Progress in the development of a Reynolds-stress turbulence closure. Journal of Fluid Mechanics, 68(3), 537–566.
- Magnussen, B. F. & Hjertager, B. H. (1977). On mathematical modeling of turbulent combustion with special emphasis on soot formation and combustion. Symposium (International) on Combustion, 16(1), 719–729. DOI: 10.1016/S0082-0784(77)80366-4