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

6.1 Practical premixed combustor configuration
boundary conditions equals 4% <strong>of</strong> the mean flow velocity in the combustion
configuration with two <strong>fuel</strong> injection stages <strong>and</strong> 3% for the one with three <strong>fuel</strong>
injection stages. The velocity fluctuations <strong>and</strong> the volume integrated heat release
rate, which are the signals used for the identification <strong>of</strong> the flame dynamics,
are recorded at the ”measurement” planes at every time step <strong>of</strong> the
simulation. To suppress possible turbulent contributions <strong>and</strong> to account for
density fluctuations <strong>of</strong> the <strong>fuel</strong>-air mixture, mass flow rate fluctuations were
exported instead <strong>of</strong> the velocity fluctuations. The ”measurement” plane at the
burner mouth was placed 5 mm upstream <strong>of</strong> the burner exit to minimize errors
due to the fluctuating flame front, which is able to travel slightly inside
the burner. At the point <strong>of</strong> injection the ”measurement” planes in the <strong>fuel</strong> line
<strong>and</strong> in the mixing section were placed 2.5 mm upstream <strong>of</strong> the stream crossing
point. The ”measurement” planes are also shown in Fig. 6.5.
The size <strong>of</strong> the grid is a compromise between computational effort <strong>and</strong> a sufficient
resolution <strong>of</strong> the flow structures <strong>and</strong> acoustics. Especially in the vicinity
<strong>of</strong> the swirler a fine grid was necessary to realize the flow separation at the
swirler blade <strong>and</strong> the secondary flow. The secondary flow further enhances the
mixing quality due to the additional imposed turbulence. It develops from the
point <strong>of</strong> flow separation <strong>and</strong> is due to the pressure gradient, which drives the
fluid to the middle <strong>of</strong> the swirler passage. The chosen grid predicts a slightly
higher strength <strong>of</strong> the passage vortex compared to a simulation case where
the boundary layer is fully resolved as described in H<strong>of</strong>fmann [44]. Figure 6.6
shows the critical area <strong>of</strong> the swirler with the passage vortex, which is highlighted
by stream lines.
In the present work the propagation <strong>of</strong> acoustic waves up to 2000 Hz are
resolved in the unsteady RANS context, reflecting the amplitude <strong>and</strong> the
phase <strong>of</strong> an acoustic wave correctly. The quality <strong>of</strong> an acoustic wave traveling
through the CFD domain can be judged by mainly two parameters: the
grid size or length <strong>of</strong> a grid cell △x <strong>and</strong> the time step △t <strong>of</strong> the simulation.
Both parameters can be combined into one parameter, the acoustic Courant-
Friedrichs-Lewy (aCFL) number, which is defined as:
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