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

Acoustic analysis
= F u (ω) u′ b (ω) N∑
+ F φ,i (ω)
ū b
i=1
(
u
′
F,i (ω)
ū F,i
− u′ A,i (ω)
)
ū A,i
¯ṁ F,i
∑ N
i=1 ¯ṁ F,i
. (7.2)
This equation is used in the next sections to explain <strong>and</strong> emphasize the various
interdependencies between the acoustic variables <strong>and</strong> the heat release
rate. Figure 7.3 clarifies the acoustic variables <strong>and</strong> main parameters, which
are used in the analysis.
Fuel injection stage i
L R,i
u' F,i u' b
u' A,i
φ' i
F,i
.
Q'
Mixing section
L F,i
Combustion chamber
Figure 7.3: Acoustic variables <strong>and</strong> main parameters used in the acoustic analysis
The design proposals <strong>and</strong> results derived are based on the operating condition
(see chapter 6.1) at which the flame transfer functions were determined.
The results are therefore only valid at <strong>and</strong> close to these conditions. To analyze
operating conditions far <strong>of</strong>f the current one, additional flame transfer
functions are required. However, the basic design guidelines are independent
<strong>of</strong> the design.
7.2.1 <strong>Impact</strong> <strong>of</strong> the <strong>fuel</strong> injection stage <strong>impedance</strong>
The acoustic <strong>impedance</strong> <strong>and</strong> the eigenfrequencies <strong>of</strong> the <strong>fuel</strong> injection stage
are changed in adjusting the length <strong>of</strong> the resonator tube L R,i , which is
mounted on the <strong>fuel</strong> plenum as described in the previous section. The <strong>fuel</strong>
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