Numerical Simulation of the Dynamics of Turbulent Swirling Flames

Identification of Flame Transfer Functions using LES/SI
Figure 5.7: Power spectrum of acoustic velocity (u r ′ ) fluctuations at 0 and
70 mm upstream of the burner exit and of heat release ( ˙Q ′ ) normalized
by their mean values without filtering for case with 30 kW.
Comparing both FTFs with experiment, the case with 9.5% shows a better
agreement with the experiments and also on the low frequency limit, where
the amplitude should approach unity. The case with 6.5% of excitation amplitude
shows in the limit to 0 Hz an amplitude lower than 1; while in the case
with 9.5%, it approaches 1. Furthermore, the discrepancies in the phase for
frequencies higher than 300 Hz mentioned in section 5.2.3 are not present
with the excitation of 9.5%. The increase in signal-to-noise ratio by increasing
the signal amplitude can improve the identification. To evaluate linearity
and possible inaccuracy in the identification, harmonic excitations at 100 Hz
are run for 1040000 iterations, which represents 13 cycles with a time step of
1.25x10 −7 s. The first 240000 iterations are not taken into account, as they are
considered as a transition period. To determine the amplitude and phase for
the harmonic excitation, a pure-tone Fourier transform defined by [177]:
y (ω PT ) = 2 N
N∑
y(n∆t)e −iωPTn∆t , (5.4)
n=1
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