  We investigate flame-acoustic interactions in a turbulent combustor during
the state of intermittency before the onset of thermoacoustic instability using
complex networks. Experiments are performed in a turbulent bluff-body
stabilized dump combustor where the inlet airflow rate is varied (a)
quasi-statically and (b) continuously. We construct a natural visibility graph
from the local heat release rate fluctuations at each location. Comparing the
average degree during epochs of high- and low-amplitude acoustic pressure
oscillations (p') during the state of intermittency, we detect frequency
modulation in heat release rate fluctuations. Through this approach, we
discover unique spatial patterns of cross-variable coupling between the
frequency of heat release rate fluctuations and amplitude of p'. The frequency
of local heat release rate fluctuations increases in regions of flame anchoring
owing to high-frequency excitation of the flow and flame during epochs of
high-amplitude p' dynamics. On the other hand, the frequency of heat release
rate fluctuations decreases in regions associated with flame front distortions
by large coherent vortices. In experiments with continuously varying airflow
rates, the spatial pattern of frequency modulation varies with an increase in
the average amplitude of p' owing to an increase in the epochs of periodic p'
dynamics and the size of vortices forming in the flow. Moreover, we discover
that the frequency of heat release rate fluctuations decreases even in regions
of flame anchoring when very large coherent structures are shed in the flow,
causing dynamic shifts in the location of flame anchoring. Our analysis thus
reveals and explains rich spatial patterns of flame-acoustic interactions in
turbulent reacting flows.
