The influence of flame-pressure waves collisions on the development and evolution of tulip flames

Abstract: 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.