Dynamics of premixed hydrogen/air flames in unsteady flow

Fully resolved numerical simulations with finite rate chemical reactions and detailed molecular diffusion have been conducted for a series of laminar premixed hydrogen–air flames under atmospheric condition. The objective of the work is to study the influence of unsteadiness of the flow on the local and global flame dynamics. Two equivalence ratios with $Φ=0.5$ and 4 are considered, leading to a negative and a positive Markstein number Ma⁰ at steady-state condition. The flames are excited with oscillating inflows at pre-defined frequencies f to assess the effect of unsteady flame stretch on flame dynamics. The Damköhler number, defined by the ratio of the inverse frequency of the oscillations and flame transit time, is used to characterize the interactions between the flow and the chemical reactions based on their time scales. For both lean and rich flame conditions, the local flame speed S_l is less sensitive to the flame stretch in an unsteady flow, which results in a reduced magnitude of the Markstein number $|Ma¯|$⁠. In addition, $|Ma¯|$ is smallest when the time scale of the flow approaches the intrinsic time scale of the flame (⁠$Da≈1$⁠). The global consumption speed S_t, computed from integration of the fuel burning rate over the whole computational domain, yields a phase delay and a damped oscillation with respect to the unsteady inflow. The phase delay increases with f or decreasing Da, whereas the reverse trend has been found for the oscillation amplitude of S_t. The flame is not able to follow the unsteady flow or adjust its flame surface at high excitation frequencies with Da <1, and vice versa in the low frequency range with $Da≫1$⁠. An efficiency factor E has been introduced to model the damped response of the flame due to flow unsteadiness, which reproduces the asymptotic behavior of $E→0$ at $Da≪1$ and $E→1$ at $Da≫1$⁠. The simulation results reveal that the fluctuation time scale plays a significant role in elucidating the effect of flame–flow interaction, which should be considered for turbulent combustion modeling.