Evolution of lean hydrogen-air premixed flames under high-frequency acoustic forcing: flame morphology and displacement speed

Fully compressible numerical simulations of two-dimensional laminar lean hydrogen-air premixed flames have been performed, with the flame front subjected to acoustic forcing through the specification of a monopole-type sound source at the inflow. Simulations have been performed for acoustic frequencies ranging from 35~kHz to 500~kHz at two equivalence ratios, $\phi = 0.4$ and $\phi = 0.7$. During the flame-acoustic interaction, the flame evolves from an initially weakly stretched state to exponential perturbation growth, wrinkle interaction, and the formation of non-linear cellular structures, with distinct linear and non-linear stages identified from Fourier mode analysis. The instability dynamics depend strongly on both forcing frequency and equivalence ratio. In the case of $\phi=0.4$, the flame behaviour is strongly influenced by thermodiffusive instability, with a characteristic sequence of uniform cells, cell splitting, and cell merging. For $\phi=0.7$, weaker thermodiffusive effects result in a response more strongly governed by hydrodynamic instability and large-scale wrinkle growth. At low forcing frequencies, flame corrugations remain relatively uniform, whereas at high frequencies the flame front becomes increasingly modulated and develops envelope-like structures, which can be interpreted as the interaction between an intrinsic standing cellular mode and the imposed acoustic disturbance. In the linear growth regime, the density-weighted displacement speed, $S_d^*$, shows a linear correlation with total stretch rate, $K$, for all forcing frequencies. While in the non-linear growth regime, two distinct branches appear, corresponding to weakly stretched flame segments and strongly negatively curved segments associated with flame pinch-off.