Flame acceleration and deflagration-to-detonation transition in hydrogen-air mixture in a channel with an array of obstacles of different shapes

Numerical simulations were conducted to study the flame acceleration and deflagration-to-detonation transition (DDT) in a channel with a bank of aligned obstacles. The multidimensional, fully compressible reactive Navier–Stokes equations coupled to a calibrated chemical-diffusion model for stoichiometric hydrogen-air mixture were solved using a high-order numerical algorithm. The results in the case with circular obstacles show that occurrence of DDT arises from shock focusing at flame front. Higher blockage ratio leads to faster flame acceleration and facilitates the formation of choked flame. Heat losses can significantly attenuate flame acceleration and delay detonation initiation in case of DDT, and even hinder occurrence of DDT for high blockage ratio. To understand the effect of shape of obstacle on the flame acceleration and DDT, circular, square, left triangular, and right triangular shapes, always maintaining the same formal blockage ratio, were simulated. The simulations indicate that there are significant differences in flame acceleration and DDT among these differently shaped obstacles, although the basic mechanism for detonation initiation is similar in all of the cases studied and involves interactions of shock wave with flame front and reactivity gradient. Square obstacles produce the largest growth rate of flame surface area in the flame-acceleration stage and thus result in the fastest flame acceleration and shortest detonation onset time compared to circular or triangular obstacles. Circular obstacles produce the weakest flame-surface growth, and thus they have the least effect on promoting flame acceleration and transition to detonation. A closer analysis shows that the sharp angles of the triangular obstacles, when compared to the circular obstacles, are more conducive to flame stretching and convolution and thus facilitate flame acceleration and DDT. The results also show that the effect of obstacle shape does not correlate with obstacle area.