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

TL;DR

This study uses numerical simulations to analyze how high-frequency acoustic forcing affects the morphology and displacement speed of lean hydrogen-air premixed flames, revealing complex linear and non-linear instability behaviors.

Contribution

It provides new insights into the nonlinear evolution of flame instabilities under high-frequency acoustic forcing across different equivalence ratios.

Findings

Flame evolves from weakly stretched to cellular structures with distinct linear and nonlinear stages.

Instability dynamics depend strongly on forcing frequency and equivalence ratio.

At high frequencies, flames develop envelope-like structures due to interaction between intrinsic modes and acoustic disturbance.

Abstract

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.