Numerical study of strongly-nonlinear regimes of steady premixed flame propagation. The effect of thermal gas expansion and finite-front-thickness effects

Abstract

Steady propagation of premixed flames in straight channels is studied numerically using the on-shell approach. A first numerical algorithm for solving the system of nonlinear integro-differential on-shell equations is presented. It is based on fixed-point iterations and uses simple (Picard) iterations or the Anderson acceleration method that facilitates separation of different solutions. Using these techniques, we scan the parameter space of the problem so as to study various effects governing formation of curved flames. These include the thermal gas expansion and the finite-front-thickness effects, namely flame stretch, curvature, and compression. In particular, flame compression is demonstrated to have a profound influence on the flame, strongly affecting the dependence of its propagation speed on the channel width b. Specifically, the solutions found exhibit a sharp increase of flame speed with channel width. Under weak flame compression, this increase commences at b/λc ≈ 2 ∼ 3, where λc is the cutoff wavelength, but this ratio becomes significantly larger as the flame compression grows. The results obtained are also used to identify limitations of the analytical approach based on the weak-nonlinearity assumption, and to revise the role of noise in flame evolution.