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

摘要

Steady propagation of premixed flames in straight channels is studiednumerically using the on-shell approach. A first numerical algorithm forsolving the system of nonlinear integro-differential on-shell equations ispresented. It is based on fixed-point iterations and uses simple (Picard)iterations or the Anderson acceleration method that facilitates separation ofdifferent solutions. Using these techniques, we scan the parameter space of theproblem so as to study various effects governing formation of curved flames.These include the thermal gas expansion and the finite-front-thickness effects,namely, the flame stretch, curvature, and compression. In particular, the flamecompression is demonstrated to have a profound influence on the flame, stronglyaffecting the dependence of its propagation speed on the channel width b.Specifically, the solutions found exhibit a sharp increase of the flame speedwith the channel width. Under a weak flame compression, this increase commencesat b/lambda_c = 2 - 3, where lambda_c is the cutoff wavelength, but this ratiobecomes significantly larger as the flame compression grows. The resultsobtained are also used to identify limitations of the analytical approach basedon the weak-nonlinearity assumption, and to revise the role of noise in theflame evolution.