THESE de DOCTORAT - cerfacs

92 Chapter 5: Assessment of combustion noise in a premixed swirled combustor
after extracting hydrodynamics is placed relatively far from that one predicted by the hybrid
approach, as can be observed from Fig. 5.25.
Pressure Fluctuation (Pa)
M5 M6 M7
40
Premixer
Combustion chamber
20
0
−20
−40
−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)
M5 M6 M7
40
Premixer
Combustion chamber
20
0
−20
−40
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(b) Pressure fluctuation from LES after filtering
Direct Computation
Figure 5.25: Longitudinal pressure Waves oscillating at 954 Hz
Pressure Fluctuation (Pa)
M5 M6 M7
40
Premixer
Combustion chamber
20
0
−20
−40
−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)
M5 M6 M7
40
Premixer
Combustion chamber
20
0
−20
−40
−0.2 −0.1 0 0.1 0.2
x (m)
0.3 0.4 0.5
(b) Pressure fluctuation from LES after filtering
Direct Computation
Figure 5.26: Longitudinal pressure Waves oscillating at 1658 Hz
Considering now the acoustic energy, it is observed from Figs. 5.27 and 5.28 that the values
predicted by the hybrid approach are in a good agreement to those computed by LES after
extracting the acoustic content from the complete pressure fluctuations. It is noticeable then
that the energy coming from hydrodynamic fluctuations has been removed.
Note that some caution must be taken when computing the Fourier transform of the divergence
of the velocity (See T1 Eq. 5.20). If a rectangular window is applied to the temporal signal, a
really good correspondance is seen only for frequencies lower than 400 Hz (not shown). On
the other hand, if a Gaussian window is applied, a good agreement is seen over the entire frequency
band, except at a very low frequencies. This is the case for the spectra shown (Figs. 5.21,
5.22, 5.27 and 5.28) where the signal does not capture the good acoustic level before 200 Hz.