NUMERICAL-SOLUTION OF THE 2-DIMENSIONAL PREMIXED LAMINAR FLAME EQUATIONS

The present paper presents a numerical solution method for the two-dimensional elliptic partial differential equations modeling a premixed laminar flame freely propagating at constant pressure between parallel plates having a constant, cool wall temperature. The technique developed is an efficient, semidirect (semi-iterative) method termed “multistep damped Picard iteration.” Picard linearization of the nonlinear terms together with variable damping as the solution progressed and a sparse matrix elliptic solver allowed rapid solution to be obtained as a limit of a convergent sequence of solutions. The flame-quenching limit was determined by iterating the solution with respect to the distance separating the plates and approaching the limit state to within a specific criterion. Global kinetics and average transport properties were used for a simulated propane-air mixture; radiation loss was neglected throughout the analysis. The method was used to study the effect of the “ignition temperature” on the flame parameters as well as to reveal the two-dimensional structure of the flame at the quenching limit. © 1979 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.