Impact of fuel supply impedance and fuel staging on gas turbine ...

3.3 Acoustic network model
tine. To roughly locate all eigenfrequencies <strong>of</strong> the system it is helpful to generate
a plot <strong>of</strong> the absolute values <strong>of</strong> the determinant for a fixed range <strong>of</strong> complex
frequencies. Figure 3.8 shows for example the determinant <strong>of</strong> a <strong>fuel</strong> <strong>supply</strong>
system consisting <strong>of</strong> a closed end, a duct, an area change including pressure
losses <strong>and</strong> an open end. The black line at C I−1 = 0 indicates the stability
limit according Eqn. (3.65). Possible eigenfrequencies can be found at the local
minima indicated by the black colour.
0.2
0.001
0
0.0001
(CI − 1)
−0.2
−0.4
1e−05
1e−06
−0.6
1e−07
500 1000 1500
Frequency [Hz]
1e−08
Figure 3.8: Stability map <strong>of</strong> a <strong>fuel</strong> <strong>supply</strong> system
The eigenfrequency analysis can only be applied if all elements <strong>of</strong> the network
model are defined in the complex frequency domain. Transfer matrices or
flame transfer functions obtained by experiments can therefore not be used
in their original formulation. To avoid this problem a method proposed by
Sattelmayer <strong>and</strong> Polifke [113, 114], which is based on control theory could be
used instead. The CFD/SI method, however, determines the acoustic characteristics
<strong>of</strong> transfer matrices <strong>and</strong> transfer functions in the time <strong>and</strong> frequency
domain. The time domain information obtained can be easily transformed
into the real or complex frequency domain as shown in chapter 5.
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