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4.2 The 2D premixed laminar flame 69
Ẑ = ˆR + 1
ˆR − 1
(4.13)
while the reflection coefficient ˆR is obtained by the relation (4.11).
4.2.3 Results
The exercise of validation, which is illustrated in Fig. 4.14, consists in comparing the pressure
field given by AVSP-f to the one obtained directly by the CFD computation performed with the
AVBP solver. The discrete Fourier transform is applied to the temporal pressure signals given
by the CFD so that they can be compared to the sound pressure spectrum evaluated by the
acoustic code. Figure 4.15 shows the Sound Pressure Level SPL predicted by both AVBP and
AVSP-f at three different positions downstream the pulsated flame.
CFD Method
p ′
DFT
ˆp
Direct Method
˙q ′
DFT
ˆ˙q
¯c
Ac. Analogy
COMPARISON
ˆp
Hybrid Method
Figure 4.14: Exercise of comparison: CFD method vs. Acoustic solver
A good agreement can be observed in Fig. (4.15). A peak at 500 Hz is seen which represents
the frequency at which the flame is excited. Peaks at 1000 and 1500 Hz are also observed. They
represent the most significative harmonics of the modulation frequency. A second case is also
evaluated. The inlet velocity is now pulsated at ± 2 m/s (see Fig. 4.16) which corresponds to
50% of the mean velocity at the inlet. The pressure signal obtained by the acoustic code also
corresponds very well to the pressure signal given by the CFD computation. Figure 4.17 shows
the SPL results.
It is important to emphasize that the acoustic boundary conditions implemented in the acoustic
code must correspond to those imposed in the CFD simulation if a good match between these
two different methods is expected. Several computations (not shown) were made for different
values of the impedance Ẑ at the outlet. As an example, for Ẑ = 1 (totally non-reflecting
condition) the amplitudes of the acoustic pressure evaluated by AVSP-f are 10% bigger than
those computed by the CFD tool.