Flame fingers and interactions of hydrodynamic and thermodiffusive instabilities in laminar lean hydrogen flames

Lean hydrogen/air flames are prone to hydrodynamic and thermodiffusive instabilities. In this work, the con- tribution of each instability mechanism is quantified separately by performing detailed simulations of laminar planar lean hydrogen/air flames with different diffusivity models and equations of state to selectively suppress the hydrodynamic or thermodiffusive instability mechanism. From the analysis of the initial phase of the simulations, the thermodiffusive instability is shown to domi- nate the flame dynamics. If differential diffusion and, hence, the thermodiffusive instability is suppressed, the flame features a strong reduction of the instability growth rates, whereas if present, a wide range of unstable wave numbers is observed due to the strong destabilizing nature of differential diffusion. When instabili- ties are fully developed, lean hydrogen/air flames feature the formation of small-scale cellular structures and large-scale flame fingers. While the size of the former is known to be close to the most unstable wave length of a linear stability analysis, this work shows that flame fingers also originate from the thermodiffusive in- stability and most noteworthy, are not linked to an interaction of the two instability mechanisms. They are stable with respect to external perturbations and feature an enhanced flame propagation as the formation of a central cusp at their tip enables the co-existence of two strongly curved leading edges with high reac- tivity. The thermodiffusive instability is shown to significantly affect the flames’ consumption speed, while the consumption speed enhancement caused by the hydrodynamic instability is significantly smaller. Further, the surface area increase due to wrinkling is strongly diminished if one of the two instability mechanisms is missing. This is linked to a synergistic interaction between the two mechanisms, as the propagation of flame fingers is enhanced by the presence of the hydrodynamic instability due to a widening of the streamlines ahead of the flame fingers.