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5 Conclusion
The present work adopts an approach of simultaneous multiple time and length
scales of
flow and acoustics to demonstrate that the time scales actually hasten to
approach each other in a lock-on, leading to combustion instability, rather than
presume equal time scales of the two processes
fl
priori in an ad hoc manner. The
results match with the experimental observations of shift in the dominant frequency
of pressure oscillations that accompanies a rise in their amplitude, as Re is varied.
The formulation formally brings out the coupling terms between the
à
ow and the
acoustics. The dilatation due to heat release is the acoustic energy source, but more
importantly, the acoustic Reynolds stress (ARS) is the source of the momentum to
the base
fl
flow to produce large-scale coherent vortices at
the expense of the small-scale structures as observed in experiments, which pro-
motes fuel-air mixing and aids combustion, leading to intense heat release until the
reactants are quickly consumed. Effectively, it causes high amplitudes of heat
release rate
fl
ow. The ARS churns the
fl
fluctuations that drive the acoustics, in turn. The simulations are able to
show the evolution of the
fl
uctu-
ations, rather than necessitating such an assumption that most analysis adopt.
Besides being based on a rigorous framework, the present approach brings out
rich physics of the problem, and is a computationally affordable alternative to
predict combustion instability in turbulent reacting
fl
flame into a compact source of heat release rate
fl
fl
flows in ducted geometries.
Acknowledgments This work was partly supported by the Deutsche Forschungsgameinschaft.
The National Centre for Combustion Research and Development is supported by the Department
of Science and Technology, Government of India.
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