Numerical study of curved flames under confinement

Dynamics of laminar flames in closed tubes is studied by means of two-dimensional numerical simulations taking into account thermal conduction, fuel diffusion, viscosity and chemical kinetics. Development of the hydrodynamic instability of a flame front is investigated for flames with the chemical reactions of the first and the third order. We found that for a flame with the first order reaction the hydrodynamic instability is strongly reduced or even suppressed in sufficiently short tubes. Unlike this, in the case of a flame of the third order reaction the instability is enhanced due to significant increase of the normal velocity of the planar flame under confinement. The instability development for flames of both the first and the third order reaction is strongly affected by acoustic waves generated by the flame in a closed chamber. Particularly, a weak shock colliding with the flame front may lead to a temporary stabilization of the flame instability. On the contrary, when flame comes to the end of the tube the acoustic waves may cause significant increase of the flame instability. We studied a possibility of the detonation ignition ahead of the flame front as well. We found that the detonation can be ignited at the far end of the tube by the weak shocks and sound waves generated by the flame in a closed tube. Triggering of the detonation ahead of the flame propagating in a closed tube is related to the knock problem in spark-ignition engines