  Premixed flames propagating within small channels show complex combustion
phenomena that differ from flame propagation at conventional scales. Available
experimental and numerical studies have documented stationary/non-stationary
and/or asymmetric modes that depend on properties of the incoming reactant flow
as well as channel geometry and wall temperatures. The present work seeks to
illuminate mechanisms leading to symmetry-breaking and limit cycle behavior
that are fundamental to these combustion modes. Specifically, four cases of
lean premixed methane/air combustion -- two equivalence ratios (0.53 and 0.7)
and two channel widths (2 and 5mm) -- are investigated in a 2D configuration
with constant channel length and bulk inlet velocity, where numerical
simulations are performed using detailed chemistry. External wall heating is
simulated by imposing a linear temperature gradient as a boundary condition on
both walls. In the 2mm-channel, both equivalence ratios produce flames that
stabilize with symmetric flame fronts after propagating upstream. In the
5mm-channel, flame fronts start symmetric, although symmetry is broken almost
immediately after ignition. Further, 5mm channels produce instationary
combustion modes with dramatically different limit cycles: : in the leaner case
({\phi} = 0.53), the asymmetric flame front flops periodically, whereas in the
richer case ({\phi} = 0.7), flames with repetitive extinctions and ignitions
(FREI) are observed. In order to provide insights into mechanisms responsible
for flame dynamics, reaction fronts and flame fronts are captured and
differentiated. Results show that the loss of flame front symmetry originates
in a region where negative stretch rates close to the flame cusp show large
gradients/curvatures; thus, symmetry-breaking is attributed to a hydrodynamic
instability. Limit cycle behavior is [...]
