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

Numerical analysis <strong>of</strong> thermo-acoustic instabilities
lated to an equivalent element in the acoustic network model.
The identification <strong>of</strong> flame transfer functions by CFD/SI requires an excitation
<strong>of</strong> the flow variables to cause a system response. As the flame responds to mass
flow <strong>and</strong> equivalence ratio fluctuations two independent excitation signals are
required to discern the individual effects in the post-processing identification
step. The excitation in such a simulation should be provided by the boundary
conditions or adequate sources inside the CFD domain. A meaningful coupling
between CFD/SI <strong>and</strong> acoustic network model has to take into account
that the network model describes the system characteristics in terms <strong>of</strong> acoustic
variables. Therefore equivalence ratio fluctuations have to be expressed in
a suitable way as, e.g. described in Eqn. (2.10).
The excitation, the signal <strong>and</strong> its location, which will be used as the input to
identify F φ,i , determine the size <strong>of</strong> the simulated domain <strong>and</strong> therefore the
computational effort. It also affects the interface between CFD/SI <strong>and</strong> network
model <strong>and</strong> the corresponding network flame element. The kinematic
flame response F u , on the other h<strong>and</strong>, can be included in a straightforward
manner extracting the acoustic velocity fluctuations at the burner exit. Its
identification only requires the simulation <strong>of</strong> the combustion chamber if a
proper inlet boundary condition is set, which takes the flow conditions upstream
into account (e.g. swirling flow).
In the following different possibilities are discussed, which are denoted as A,
B, C <strong>and</strong> D. The comparison between the possibilities is shown in Fig. 2.7. The
columns present the computational domain required, the excitation <strong>and</strong> signals
extracted <strong>and</strong> their locations <strong>and</strong> the corresponding network flame element.
In case A the combustor, including swirler vanes, mixing section <strong>and</strong> part <strong>of</strong>
the <strong>fuel</strong> injectors is resolved as shown in the first row <strong>and</strong> first column. The
length <strong>of</strong> the <strong>fuel</strong> injectors, which have to be modeled, should be long enough
to ensure a well developed velocity pr<strong>of</strong>ile at the entry to the mixing section.
For this option, the <strong>fuel</strong> mass flow <strong>and</strong> the air mass flow are excited at the inlet
boundary condition <strong>of</strong> the <strong>fuel</strong> line <strong>and</strong> <strong>of</strong> the mixing section, respectively.
Here, the mass flow averaged velocity fluctuations upstream the <strong>fuel</strong> injec-
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