THESE de DOCTORAT - cerfacs

5.5 LES vs. Hybrid Results 91
400 Hz) that has been removed as it can be noted if comparing Figs. 5.16(b) and 5.23(b). The
acoustic field predicted by the hybrid computation is now much closer to that one predicted by
the direct method when considering the combustion chamber, as observed from Fig. 5.23.
Pressure Fluctuation (Pa)
M5 M6 M7
600
Premixer
Combustion chamber
400
200
0
−200
−400
−600
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(a) Pressure Wave from Eq. (2.63)
Hybrid Computation
Pressure Fluctuation (Pa)
600
M5 M6 M7
Premixer
Combustion chamber
400
200
0
−200
−400
−600
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(b) Pressure Wave from LES after filtering
Direct Computation
Figure 5.23: Longitudinal pressure Waves oscillating at 251 Hz
Considering the pressure wave at 377 Hz (Fig. 5.24), it is observed that it does not change too
much after filtering, as can be appreciated by comparing Fig. 5.15(b) with Fig. 5.24(b). As it has
been already stated in section 5.3.2, this pressure wave is mainly composed by acoustics since it
corresponds to the quarter wave mode of the combustion chamber. The resemblance between
hybrid and direct approaches results increases after filtering and is now remarkable.
Pressure Fluctuation (Pa)
M5 M6 M7
1000
Premixer
Combustion chamber
500
0
−500
−1000
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(a) Quarter pressure Wave from Eq. (2.63)
Hybrid Computation
Pressure Fluctuation (Pa)
M5 M6 M7
1000
Premixer
Combustion chamber
500
0
−500
−1000
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(b) Quarter pressure Wave from LES after filtering
Direct Computation
Figure 5.24: Longitudinal pressure Waves oscillating at 377 Hz
The local minimum around 1650 Hz shown in the SPL spectrum for microphone 6 (Fig. 5.21b)
is well recovered after extracting acoustics from LES. This is due to the fact that once hydrodynamic
fluctuations have been extracted, a pressure node close to microphone 6 appears as
shown by Fig. 5.26(b). On the contrary, the acoustic signal corresponding to microphone 5
Fig. 5.21(a) presents important differences with respect to the one computed by the hybrid approach.
The local minima around 1000 Hz corresponding to the hybrid method is recovered at
a lower frequency (around 750 Hz) and the pressure node observed in the combustion chamber