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

Introduction
2) equivalence ratio fluctuations (φ ′ i
): they are created by fluctuations <strong>of</strong>
the air mass flow past the injector i or <strong>of</strong> the pressure at the injector
i . These inhomogeneities are transported convectively to the flame,
where they lead to a modification <strong>of</strong> the enthalpy <strong>of</strong> reaction per unit
volume <strong>of</strong> the mixture (△H), laminar (s L ) <strong>and</strong> turbulent burning velocity
(s t ), flame position <strong>and</strong> hot gas temperature (”entropy waves”)
[14, 31, 53, 71, 99, 101, 107, 112].
The acoustic pressure (p ′ f l ) <strong>and</strong> velocity (u′ ) at the flame front could also
f l
modify the heat release rate. Their influence is rather small in practical applications
like gas turbines or domestic heaters <strong>and</strong> can therefore be neglected.
Other effects, like a fluctuating swirl, which changes mainly the flame area,
can also play a role but are not considered explicitly in the present work.
All effects mentioned lead to fluctuations in the heat release rate <strong>and</strong> thus to
a fluctuating volume expansion, which result in acoustic fluctuations (p ′ , u ′ ).
As shown in Fig. 1.1, the acoustic waves caused by the flame travel through the
combustion system <strong>and</strong> are partly reflected at the gas turbine parts, which are
located upstream <strong>and</strong> downstream <strong>of</strong> the combustion chamber. The amplitude
<strong>and</strong> phase <strong>of</strong> the reflection are determined by the acoustic characteristics
in terms <strong>of</strong> the <strong>impedance</strong> at the outlet <strong>of</strong> the compressor or at the inlet <strong>of</strong>
the turbine. The reflected waves are causing acoustic fluctuations at the flame
front, at the burner outlet <strong>and</strong> at the location <strong>of</strong> <strong>fuel</strong> injection, which give rise
to a direct or time-delayed response <strong>of</strong> the flame. The acoustic pressure fluctuations
in the vicinity <strong>of</strong> the flame <strong>and</strong> the fluctuating heat release rate form
therefore a thermodynamic feedback cycle, which is closed by the acoustics <strong>of</strong>
the combustion system. Whether the cycle excites or damps possible combustion
oscillations depends on the phase shift between the two characteristics
<strong>and</strong> is known as the Rayleigh criterion. According to Lord Rayleigh [105], who
discovered this correlation in the 19th century, the conditions for the occurrence
<strong>of</strong> instabilities are met, when heat is released at the moment <strong>of</strong> greatest
compression. In other words a combustion oscillation can occur if pressure
<strong>and</strong> heat release rate fluctuations are in phase, i.e. the integral <strong>of</strong> the product
<strong>of</strong> pressure <strong>and</strong> heat release rate fluctuations over a oscillation period T per is
6