Strain rate effects on the nonlinear development of hydrodynamically unstable flames

In this study we numerically implement the hydrodynamic model for a premixed flame as a nonlinear free boundary problem where the flame is tracked via a level set equation and the flow is described by a solution of the variable density Navier-Stokes equations. Unlike an earlier similar study, the present model is enriched by fully accounting for hydrodynamic strain in the flame stretch relation which, in turn, affects the local flame speed. The objective is to comprehensively analyze the effect of strain on the onset of the hydrodynamic instability and on the nonlinear development that takes place beyond its inception. The initial evolution is corroborated with the results of a linear stability analysis for which strain rate effects are fully included. We show that while strain provides an additional stabilizing effect on the short wavelength disturbances, thereby delaying the onset of the hydrodynamic instability, it acts to sharpen the cusps near the troughs of the corrugated flame that develops beyond the stability threshold resulting in a larger flame surface area and a higher propagation speed.