A flame-controlling continuation method for generating S-curve responses with detailed chemistry

A flame controlling continuation method is formulated for the generation of the ignition-extinction S-curve characteristic of quasi-one-dimensional flames as well as the investigation of the associated flame structure and response, especially for states near the turning points. Using the counterflow premixed and diffusion flames as examples, the method capitalizes on the distinct nature of the profile and location of the scalars of the flame properties, such as the temperature and species concentrations, in response to changes in the flow strain rate. Thus instead of using the strain rule as an imposed parameter and the scalars as the flame responses, the value of a flame scalar at a given location y* is used as all internal boundary condition while the strain rate becomes the flame response. Consequently, by fixing y* and incrementing the value of the flame scalar, continuous mapping of the relation between the flame response and strain rate is accomplished. Sample calculations were performed for the premixed twin flame and for diffusion flames with equal and unequal exit velocities from the opposing nozzles. Continuations using one-point temperature controlling, two-point temperature controlling, and one point hydrogen radical concentration controlling were demonstrated. The method appears to be fairly expedient in implementation.