Application of Continuation Methods to Plane Premixed Laminar Flames

Abstract

The composition flammability limits of freely propagating premixed hydrogen-air and methane-air flames are investigated. A modified formulation of the plane premixed laminar flame problem is first derived. The resulting parameterized nonlinear two-point boundary value problem is then solved by phase-space, pseudo arclength, continuation methods that employ Euler predictors, Newton-like iterations and adaptive gridding techniques. The efficiency of the method is illustrated by studying the dependence of the peak temperature and the adiabatic flame speed on the equivalence ratio of hydrogen-air and methane-air mixtures. In particular, we discuss the calculation of lean and rich extinction limits in the absence of heat losses. These composition limits for plane adiabatic flames are shown to be physically irrelevant turning points due to flame thickening in finite length computational domains. These artificial turning points are also shown to be dependent on the length of the computational domain.