Numerical study of the effect of stepped distribution of obstacle height on flame acceleration in a stoichiometric hydrogen-air mixture

Numerical simulations were conducted to investigate the flame acceleration in a stoichiometric hydrogen-air mixture in obstructed channels with uniform and stepped distributions of obstacle height. The twodimensional, fully-compressible reactive Navier-Stokes equations coupled to a calibrated chemical-diffusive model were solved using a fifth-order numerical algorithm. The numerical method was validated against the experiment. The results show that the effect of obstacle height on flame propagation speed varies with the arrival position of the flame front. In the channel with uniform height obstacles, flame-vortex interaction dominates flame acceleration in the early stage. Flame speed increases with the blockage ratio since higher obstacles facilitate the formation of large vortices. As the flame continues to propagate, flame-shock interaction becomes dominant in flame acceleration. At this stage, flame speed first increases and then decreases with the blockage ratio, since the obstruction to the flame-shock by obstacles increases with the blockage ratio. To further explore the influence of obstacle height distribution on flame acceleration, a stepped distribution of obstacle height was designed by using the obstacle heights that produce the highest speed in different parts of the channel in uniform cases. It was found that the flame in the channel with stepped distribution reaches the end faster than in the uniform cases since the stepped case is more conducive to the flame stretching and perturbation in the early stage and the flame-shock interaction in the later stage. Furthermore, an optimized analytical model was developed to predict the flame acceleration in the channel with a stepped distribution of obstacle height.