  In this experimental study on a laboratory-scale turbulent annular combustor
with sixteen swirl-stabilized burners, we study the flame-flame and
flame-acoustic interactions during different dynamical states associated with
the longitudinal mode of the combustor. We simultaneously measure the acoustic
pressure and CH* chemiluminescence emission of the flame using a high-speed
camera. Upon increasing the equivalence ratio, the combustor undergoes the
following sequence of transition: combustion noise (CN) to low amplitude
longitudinal thermoacoustic instability (TAI) through the state of
intermittency (INT), and from low amplitude to high amplitude longitudinal TAI
through a secondary bifurcation. We report the first evidence of secondary
bifurcation from low amplitude TAI to high amplitude TAI for a turbulent
thermoacoustic system which allows us to test the flame response at two
different amplitude of perturbation in a natural setting. We find a significant
difference in the dynamics of the flame interactions during the periodic part
of intermittency and low and high amplitude TAI. Specifically, during the
periodic part of intermittency, the phase difference between the local heat
release rate (HRR) measured from various burners show significant phase slips
in time. During low amplitude TAI, there are fewer phase slips among the HRR
response of the burners, which result in a state of weak synchronization among
the flames. During high amplitude TAI, we find that the flames are in perfect
synchrony amongst themselves and with the pressure fluctuations. We then
quantify the degree of temporal and spatial synchronization between different
flames, and flames and pressure fluctuations using the Kuramoto order parameter
and the phase-locking value. We show that synchronization theory can be
conveniently used to characterize and quantify flame-acoustic interactions in
an annular combustor.
