Flame acceleration and transition to detonation in an array of square obstacles

We study flame acceleration and DDT in a two-dimensional staggered array of square obstacles by solving the compressible multidimensional reactive Navier–Stokes equations. The energy release rate for a stoichiometric H₂-air mixture is modeled by a one-step Arrhenius kinetics. The space between obstacles is filled with a stoichiometric H₂-air mixture at 1 atm and 298 K. Initially, the flow is at rest, and a flame is ignited at the center of the array. Computations show effects of the obstacles as a series of events leading to DDT. During the initial flame acceleration, the speed of the flame depends on the direction of flame propagation since some directions are more obstructed than others. This affects the macroscopic shape of the expanding burned region, which forms concave boundaries in more obstructed directions. As the flame accelerates, shocks form ahead of the flame, reflect from obstacles, and interact with the flame. There are more shock–flame interactions in more obstructed directions, and this leads to a greater flame acceleration and stronger leading shocks. When the shocks become strong enough, their collisions with obstacles ignite the gas mixture, and detonations form. The simulation shows four independent DDT events within a 90-degree sector, all in more obstructed directions. Resulting detonations spread in all directions. Some parts of detonation fronts are quenched by diffractions around obstacles, but they are reignited by collisions of decoupled shocks, or overtaken by other detonations. Thus detonations continue to spread and quickly burn all the material between the obstacles.