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

Numerical simulation
can be calculated for a single jet injected into a circular duct. J represents the
impulse ratio <strong>of</strong> the <strong>fuel</strong> <strong>and</strong> main stream <strong>and</strong> is defined as:
J = ρ F u 2 F
ρ A u 2 . (6.3)
A
The subscripts F <strong>and</strong> A represent again the <strong>fuel</strong> <strong>and</strong> main stream, respectively.
In configuration A, for example, the main flow velocity is equal to u A = 18.6
m/s. The density has a value <strong>of</strong> ρ A = 1.167 kg/m 3 . With the properties for the
<strong>fuel</strong> stream (u F = 85.6 m/s, ρ F = 0.66 kg/m 3 ) an impulse ratio <strong>of</strong> J = 12.0 is
computed for the present case. The <strong>fuel</strong> injection including stream lines <strong>and</strong>
the <strong>fuel</strong> mass fraction at a downstream location are presented exemplarily
for the configuration A in Fig. 6.4. The legend refers to the plane presented
whereas the colors <strong>of</strong> the streamlines indicate the amplitude <strong>of</strong> the velocity.
The <strong>fuel</strong> is distributed well over the radial direction, with the main part <strong>of</strong> the
<strong>fuel</strong> located in the middle between the outer wall <strong>and</strong> the center body. The
maximum depth according to Eqn. (6.2) would be 0.005 m, which is slightly
too low. The optimum number <strong>of</strong> circumferential holes was estimated according
to Holdeman et al. [45] <strong>and</strong> lies in the range between 6.1 <strong>and</strong> 10.2 for the
configuration analyzed (see appendix A.2 for more details). CFD simulations
with different numbers <strong>of</strong> holes showed that the configuration with eight injection
holes exhibits adequate mixing characteristics.
6.1.2 Numerical setup <strong>of</strong> the combustion system
To determine the flame transfer functions, a three-dimensional unsteady
RANS computation <strong>of</strong> the compressible turbulent reacting flow in the combustor
has been performed using the s<strong>of</strong>tware package ANSYS-CFX. According
to the discussion in chapter 2.3.2, the computational domain can be reduced
to the mixing section, the <strong>fuel</strong> injection holes, the axial swirler <strong>and</strong> the
combustion chamber. A sketch <strong>of</strong> the computational domain including the
”measurement” planes for case A, at which the time series <strong>of</strong> the required velocity
fluctuations are recorded, is shown in Fig. 6.5. To save computational
time only a 90 ◦ segment is simulated using periodic boundary conditions.
A second order backward Euler scheme <strong>and</strong> the high-resolution scheme were
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