  The effects of pressure waves-flame collisions and tube aspect ratio on flame
evolution and the formation of tulip and distorted tulip flames were
investigated using numerical simulations of the fully compressible
Navier-Stokes equations coupled with a detailed chemical model for a
stoichiometric hydrogen-air mixture. It is shown that: (1) the rarefaction wave
generated by the decelerating flame in the unburned gas is the primary physical
process leading to the flame front inversion and the tulip flame formation, (2)
the flame front instabilities (Darrieus-Landau or Rayleigh-Taylor) do not
participate in the formation of the tulip flame, since the time of the flame
front inversion due to the rarefaction wave is considerably shorter than the
characteristic times of the development of instabilities with wavelengths of
the order of the tube width. The first rarefaction wave in the unburned gas
mixture is generated after the flame skirt touches the tube walls and the flame
is slowed down due to the reduction in flame surface area. The collision of the
flame with the pressure waves reflected from the closed end of the tube leads
to a faster and more pronounced formation of a tulip-shaped flame. In later
stages, flame collisions with pressure waves can lead to the formation of
distorted tulip flames due to short-wavelength Rayleigh-Taylor instability of
the flame front. Because flame acceleration and deceleration occur much faster
in 3D flames than in 2D flames, tulip flame formation also occurs much faster
in 3D flames than in 2D flames.
