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

Numerical analysis <strong>of</strong> thermo-acoustic instabilities
perturbations. Hettel et al. [42] studied the response <strong>of</strong> a premixed turbulent
axial methane jet flame using unsteady RANS simulation with a sinusoidal
modulation <strong>of</strong> the inlet mass flow. A LES simulation <strong>of</strong> a double swirler
premixed burner was performed by Giauque et al. [36] at three different
frequencies. The simulation was able to identify two main flow structures,
namely a toroidal structure <strong>and</strong> a precessing vortex core attached to the center
<strong>of</strong> the axial swirler, which modulates the global heat release rate. The obvious
drawback <strong>of</strong> these approaches is that numerous simulations are necessary
to obtain a transfer function over a wide range <strong>of</strong> frequencies. To reduce the
computational effort Bohn et al. [12] used a sudden increase <strong>of</strong> the inlet mass
flow as excitation signal, which contains by design multiple frequencies. A
Laplace transformation <strong>of</strong> the resulting unit function response represents the
flame dynamics in the frequency domain. Polifke et al. [102] proposed an
advanced system identification method (CFD/SI) based on digital signal theory
to post-process time series data generated by transient CFD simulation
with broadb<strong>and</strong> excitation. The method uses auto- <strong>and</strong> cross-correlations
<strong>of</strong> time series <strong>of</strong> ”signals” <strong>and</strong> ”responses” <strong>and</strong> the Wiener-Hopf-Inversion
to identify unit impulse responses (UIR). The acoustic transfer function or
transfer matrix is obtained by a z-transform <strong>of</strong> the unit impulse responses. In
their work they successfully obtained the acoustic transfer matrix <strong>of</strong> a gauze
in a Rjike tube. Gentemann et al. applied the approach to determine the
transfer matrix <strong>of</strong> a sudden jump in cross-section in compressible flow [34]
<strong>and</strong> a flame transfer function <strong>of</strong> a perfect premixed combustion system [35].
In the latter case [35] the ”signal” is the velocity fluctuation close to the burner
exit, whereas the heat release rate fluctuation caused downstream is regarded
as the "response". A similar method was developed by Zhu et al. [6, 135],
which describes the flame response as an infinite impulse response (IIR) filter
model. The model coefficients are determined by a least square estimation
<strong>of</strong> the signals. As in [35], the ”outputs” <strong>of</strong> the IIR model are fluctuations <strong>of</strong>
heat release rate, while the ”inputs” are fluctuations <strong>of</strong> the flow variable.
A different method, based on steady state simulations, is proposed by van
Kampen et al. [129]. The authors calculated the transfer function using a
linear coefficient method in combination with an efficient order reduction
algorithm.
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