THESE de DOCTORAT - cerfacs

90 Chapter 5: Assessment of combustion noise in a premixed swirled combustor
(
∂
c 2 ∂ ˆp )
ac
∂x i ∂x i
= iωγ ¯p ∂û i,LES
∂x i
} {{ }
T1
− iω γ ¯p ˆ˙ω T
c p K 0
} {{ }
T2
(5.20)
It has been found by the author that the contribution of T2 for this case should be neglected
as it is still not well understood. Indeed, results appear to be much better when this term is
neglected. As a consequence, Eq. (5.20) simplifies to:
F( ˆp ac ) = ∂ (
c 2 ∂ ˆp )
ac
= iωγ ¯p ∂û i,LES
(5.21)
∂x i ∂x i ∂x i
5.5 LES vs. Hybrid Results
Figures 5.21 and 5.22 show the Sound Pressure Level (SPL) given by the solution of Eq. (5.21)
(LES ‘Filtered’), the hybrid computation and the direct approach for microphones 5, 6 and 7.
SPL (dB) − micro 5
180
160
140
120
100
80
Hybrid Computation
Direct Computation: LES
Direct Computation; LES (Filtered)
SPL (dB) − micro 6
180
160
140
120
100
80
Hybrid Computation
Direct Computation: LES
Direct Computation; LES (Filtered)
60
0 500 1000 1500 2000 2500
Frequency (Hz)
60
0 500 1000 1500 2000 2500
Frequency (Hz)
Figure 5.21: Sound Pressure Levels from the direct and hybrid approaches
SPL (dB) − micro 7
180
160
140
120
100
80
Hybrid Computation
Direct Computation: LES
Direct Computation; LES (Filtered)
60
0 500 1000 1500 2000 2500
Frequency (Hz)
Figure 5.22: Sound Pressure Levels from the direct and hybrid approaches
After extracting the acoustic field from the complete pressure fluctuation field, it is seen that
results match pretty well with the values predicted by the hybrid method, especially for microphones
6 and 7. There is a high content of hydrodynamic fluctuations at low frequencies (before