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

Numerical analysis <strong>of</strong> thermo-acoustic instabilities
Z 1
u' A,i
.
m F,i
u' F,i
u'
φ' A,i i
u' b
.
Q'
X
u'
x b
a)
x F,i
Z 2
u'A,i
.
m F,i
u' F,i
A,i
u'
φ' i
u' b
.
Q'
X
u'
x b
b)
x F,i
Figure 2.6: <strong>Impact</strong> <strong>of</strong> the combustion system acoustics on the description <strong>of</strong>
the flame dynamics
this case reflect the flame dynamics correctly. If the assumption <strong>of</strong> the ”stiff”
<strong>fuel</strong> injector does not hold, the SISO model would again neglect the influence
<strong>of</strong> equivalence ratio fluctuations, which result from velocity fluctuations in
the <strong>fuel</strong> injector u ′ F,i
. If the flame is described, on the other h<strong>and</strong>, by a SISO
model based on equivalence ratio fluctuations, the same considerations can
be obtained.
A SISO model can finally not describe the practical premixed flame dynamics
properly as it clearly depends on the acoustics <strong>of</strong> the entire combustion
system. It can only be represented by such a model if the <strong>fuel</strong> injectors are
placed at the burner exit <strong>and</strong> if they are acoustically ”stiff”. This is not the case
for most practical premixed combustion systems. The only physically meaningful
description <strong>of</strong> the flame is therefore the MISO model based on velocity
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