Time-dependent solution of a premixed laminar flame

The one-dimensional, time-dependent, multicomponent premixed laminar flame is solved via a highly accurate method of lines approach. The neglect of pressure variations and viscous dissipation and the use of a Lagrangian spatial coordinate reduce the problem to a system of parabolic partial differential equations for the species concentrations and the temperature. Introducing an appropriate B-spline (finite element) basis for the spatial variation and imposing collocation and boundary conditions on the time-dependent coefficients produce a stiff ordinary initial value problem which can be solved by standard techniques. Physical results of special interest include the transient and steady-state profiles of fluid velocity, temperature, and species concentrations through the reaction zone and the upstream velocity (flame speed) of the combustible mixture required to asymptotically stabilize the flame. The analysis is illustrated for the case of an ozone decomposition flame and a comparison with other theoretical predictions shows that the use of less accurate methods can result in significant errors in the predicted values of minor species profiles and the flame speed.