The effect of large step pressure drops on strained premixed flames

A model of the interaction of pressure changes with strained premixed flames is formulated by extending previous work on interactions with nonstrained flames. By making the assumption of no divergence in the velocity field (∇ · u = 0) and writing the full equations in terms of mass-weighted coordinates (with explicit strain terms) following the flame sheet, we study the time-varying response of the mass burning rate to an imposed pressure disturbance. Numerical solution of the full nonlinear equations shows that strain has a strong effect on the flame response. It is found that, for large amplitude step pressure drops, the flame does not recover for moderate and small strain rates. As expected, for larger positive strain rates the flame recovers, because it is known that positive strain stabilizes premixed flames. The reverse happens for flames experiencing pressure drops in a convergent flow (negative strain). In this case, extinction of the flame by pressure drops becomes more likely as the convergence of the flow increases. Of particular interest for the negative strain case is the onset of the pulsating instability for a finite range of small values of pressure drop, which then gives way to a region of recovery if the pressure drop is larger, before finally for larger drops the extinction pressure drop is reached.