Flame acceleration and transition to detonation in non-uniform hydrogen-air mixtures in an obstructed channel with different obstacle arrangements

Numerical simulations were performed to study flame acceleration (FA) and deflagration-to-detonation transition (DDT) in non-uniform hydrogen-air mixtures in an obstructed channel. The fully compressible reactive Navier-Stokes equations coupled to a calibrated chemical-diffusive model were solved using a high-order numerical method on a dynamically adapting mesh. The simulations are in satisfactory agreement with previous experiments. For the cases with average H2 concentration 30 vol%, the presence of composition gradient weakens FA and causes delayed DDT due to lower total heat release since the unburned material is either fuelrich or fuel-lean, although the composition gradient leads to more unburned pockets. The effects of obstacle arrangement and blockage ratio were explored in the mixtures with a linear gradient at 50 vol% average H2 concentration. The results show that FA and DDT can be promoted by increasing blockage ratio from 0.3 to 0.6 or placing obstacles along the sidewalls with lower H2 concentration because the formation and flame properties of unburned pockets are enhanced. An analytical model for predicting FA in fuel-rich non-uniform mixtures is suggested and validated against the numerical simulations. The model shows that flame acceleration rate mainly depends on blockage ratio and the thermal expansion ratio in unburned pockets.