THESE de DOCTORAT - cerfacs

82 Chapter 5: Assessment of combustion noise in a premixed swirled combustor
LES (AVBP)
p ′ LES
ASSUMPTION
DFT
Direct Method
ˆp acoustic
˙q ′
DFT
ˆ˙q
¯c
Negligible
hydrodynamic
contribution
COMPARISON ?
Ac. Analogy
ˆp acoustic
Hybrid Method
Figure 5.9: Exercise of comparison: Direct Approach vs. Hybrid Approach
approaches are compared for the 10 million cells mesh independently of experimental data.
As sketched in Fig. (5.9), hydrodynamic pressure fluctuations are assumed to be small when
considering results from the direct approach. Therefore, the acoustic field resulting from the
hybrid approach is directly compared to the pressure fluctuation field coming from direct computations.
The hybrid computation is performed in two steps. First, the source of combustion noise is
computed by postprocessing the data obtained from the LES computation as seen in Fig. (5.9).
The instantaneous heat release is given to the acoustic code in addition to the mean flow information
which is contained in the mean sound velocity. The acoustic tool AVSP-f computes the
acoustic field throughout the computational domain due to the given noise sources, the mean
flow field and the acoustic boundary conditions of the configuration. Figure (5.10) shows one
snapshot of the unsteady heat release rate obtained from LES whereas Fig. (5.11) illustrates the
mean sound velocity ¯c over a longitudinal cut of the EC2 combustor. The source of noise is
given to AVSP-f as a function of frequency. The discrete Fourier transform is therefore applied
to the temporal sources yielding as a consequence the modulus |Ŝ| and the argument arg(Ŝ) for
each frequency of interest. Figure 5.12 shows the combustion source for a frequency equal to
377 Hz. As an exercise of visualization, both argument and modulus of the source at 377 Hz are
combined so that S(t)
⏐ = |Ŝ|e iarg(Ŝ) e −iωt where ω = 2π · 377 rad/s. It is interesting to
f =377Hz
observe the monopolar behaviour of the combustion source of noise for this frequency, which
is the one corresponding to the highest level of pressure fluctuation (see the peak at around 377
Hz in Fig 5.13).
The simplified Phillips equation written in the zero Mach number limit given by Eq. (2.63)
is solved in the frequency domain. It consists then in solving the linear system Ax = b (see
Eq. 3.61) as many times as the number of desired frequencies f . For this case, the system Ax = b