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

3.3 Acoustic network model
pressure drop across the inlet is high enough, the <strong>supply</strong> lines upstream <strong>of</strong> the
inlet are acoustically decoupled from the remaining system. This kind <strong>of</strong> inlet
condition can therefore be seen as a ”hard wall” or a ”closed end”, where the
acoustic velocity disappears 8 :
[
1+ Mi M i − 1 ][ f i
g i
]
= 0. (3.59)
The end or outflow boundary condition <strong>of</strong> gas turbine systems is usually described
by an ”open end”, an reflecting exit or by a choked exit. A choked flow
may occur in a convergent nozzle for a subsonic inflow where the flow reaches
M = 1 at the location <strong>of</strong> smallest cross-sectional area. On the other h<strong>and</strong> an
”open end” is an outlet where the fluid enters into the atmosphere, which
is <strong>of</strong>ten true for many simple combustion test rigs. In this case the acoustic
pressure must vanish at the combustion chamber outlet. Thus the ”open end”
condition can be applied:
[
1+ Mi 1− M i
] [ f i
g i
]
= 0. (3.60)
The ”open end” implies that the downstream traveling acoustic waves are fully
reflected at the combustion chamber end. In the analyzed configuration a part
<strong>of</strong> the waves are leaving the outlet without being reflected. To account for the
reflection Eqn. (3.61) can be rewritten in the following way:
[
1+ Mi 1− M i
] [ f i
g i
]
= −|R f |. (3.61)
In terms <strong>of</strong> the frequency response analysis, explained in the next section, the
acoustic system has to be excited at a boundary condition. This is done, similar
to experiments, in using a loudspeaker to produce certain amplitudes <strong>of</strong>
8 The equations for the boundaries are adjusted to include the mean flow effect <strong>and</strong> to conserve the acoustic
energy.
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