  This paper presents simulations of stoichiometric methane/air premixed flames
into a microchannel at atmospheric pressure. These simulations result from
numerical resolutions of reduced-order models. Indeed, combustion control into
microchannels would be allowed by fast simulations that in turn enable
real-time adjustments of the device's parameters. Former experimental studies
reported the occurrence of a Flame Repetitive Extinction/Ignition (FREI)
phenomenon provided that a temperature gradient is sustained at the channel's
walls. Conducting unsteady one-dimensional simulations including complex
chemistry, a late numerical study tried to explain the occurrence of this
phenomenon. The present study therefore explores low-dimensional models that
potentially reproduce the FREI phenomenon. Provided a calibration of some
empirical constants, an unsteady two-dimensional model including one-step
chemical reaction is shown to decently reproduce the FREI regime all along the
range of mixture flow rates investigated by the experimental studies.
Complementing the aforementioned numerical study, furthermore, when the
channel's diameter is varied, the two-dimensional model unveils an unstable
regime that a one-dimensional model cannot capture. As two-dimensional
hydrodynamics appears to play a key role into the flame's dynamics, therefore
the heat rate released by the microcombustor, one-dimensional models are not
believed to deliver an adequate strategy of combustion control into such
microchannels.
