Numerical study of the stability of premixed flames propagating in half-open tubes

This paper studies premixed flame dynamics in half-open tubes by solving the two-dimensional, fully compressible, reactive Navier-Stokes equations on a dynamically adapting mesh using a high-order algorithm. A simplified chemical-diffusive model was used to describe the chemical reaction and diffusive transports in a stoichiometric hydrogen-air mixture. The influence of the length scale was examined by considering four tube heights at a fixed aspect ratio alpha = 7. The numerical simulations show that the flame evolves into a tulip flame (TF) in all the tubes shortly after being ignited at the open end. Variation in tube size leads to differences in the evolution of TF and generation of expansion waves. In a sufficiently large tube (d > 0.5 cm), the TF further develops into a series of more unstable distorted tulip flames (DTFs). By contrast, in a small tube (d < 0.5 cm), the TF shape remains until the end of the combustion. In addition, both the flame and pressure oscillate significantly almost in the entire process of flame propagation in the large tubes, while the oscillating behaviour in flame or pressure is negligible in the small tube after TF forms. It was found that the TF formation mechanism is length-scale dependent even for the same type of geometry and condition. A detailed examination of the interactions between flame, boundary layer, and pressure waves showed two mechanisms of TF formation: (1) boundary layer effect for the larger tubes (d >= 0.5 cm), and (2) Rayleigh-Taylor instability driven by compression waves for the smallest tube (d = 0.25 cm). The DTF formation in the half-open tubes is closely related to the expansion waves generated by the collapse of the TF cusp. The expansion waves cause a reverse flow in the boundary layer ahead of the flame front and consequently initiate the DTF.