Numerical Simulation of the Dynamics of Turbulent Swirling Flames

A.8 FTF at Different Velocity Reference Position with 30 kW and 9.5% of Excitation
Amplitude
A.7.6
Swirler
The transfer matrix of the swirler was identified using LES/SI using only the
swirler and connecting tube without the combustion chamber as shown in
Fig. 5.30. The identification was carried out with 30 kW of power rating. Perturbations
on the characteristic ingoing waves were imposed at the inlet and
outlet using broadband excitation with a frequency limit to 6000 Hz and an
amplitude of 5% of the mean velocity. The transfer matrix was identified as a
MIMO system. Further details on MIMO identification for transfer matrices
are shown in [57, 160].
The transfer matrix of the swirler is shown in Fig. A.7 using the Scattering Matrix
representation. The scattering matrix is defined by:
( ) ( )
fd fu
= S(ω) . (A.74)
g u g d
where f and g are the Riemann invariants defined in Eq. (6.14). The elements
S 11 and S 22 of the scattering matrix represent the transmission of the acoustic
waves from upstream and downstream direction through the swirler, respectively;
while the elements S 12 and S 21 represent the reflection of the acoustic
waves by the presence of the swirler. A length correction between the reference
planes and the center of the swirler is included [83]. The element is introduced
in the network model using the identified UIRs together with the UIR
method specified in section 6.3 for evaluation of complex eigenfrequencies.
The transformation of the scattering matrix in terms of Riemann Invariants f
and g can be found in [50, 83].
A.8 FTF at Different Velocity Reference Position with 30 kW
and 9.5% of Excitation Amplitude
In Fig. A.8, the identified flame transfer function of the BRS burner with 30 kW
with acoustic velocity (u r ′ ) fluctuations measured at different reference position
is shown. The excitation amplitude is 9.5% of the mean inlet velocity.
The simulations were run for 2800000 iterations (0.35 s), considering the first
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