THESE de DOCTORAT - cerfacs

7.5 Conclusions 127
tion coefficient |R| does not imply a significative change in the Eigen-Frequency of the combustor.
Given the very large variations of |R| and Arg(R) considered in Fig. 7.8, the results
also demonstrate that the large disagreement between the computed (500 Hz) and observed
(250 Hz) mode for this combustion chamber cannot be only due to a wrong representation of
the inlet impedance. The results obtained from SNozzle and reported in table 7.1 suggest that
improving the inlet condition has in fact no effect on the result.
520
For |R| = 1
510
For Argument(R) = 0
Eigen Frequency (Hz)
500
480
460
440
420
Eigen Frequency (Hz)
509
508
507
506
400
−4 −2 0 2 4
Argument(R)
(a)
505
10 0 10 2
|R|
(b)
Figure 7.8: Eigen Frequency vs. Reflection Coefficient (Helmholtz solver results)
7.5 Conclusions
The approach used to model the compressor as an element that perturbs the acoustics of the
airline might be still too approximative. The inclusion of π ′ c ̸= 0 into the compressor acoustic
model might contribute to a stronger variation on both |R| and Arg(R) at the inlet of the
combustor. Nevertheless, it has been seen that the lowest possible eigen-frequency in the Aeroengine
combustor corresponds to a value around 410 Hz, which is still too far from what is
found in experiments: 250 Hz.
It is highly probable then that the resonant frequency found experimentally does not correspond
to an acoustic mode of the combustor. This frequency might be linked instead to a
combustion instability known as ‘rumble’, which is due to a coupling between entropy waves
convected at the mean flow and the acoustic waves generated at the high pressure distributor.
In order to verify if this instability mechanism is present, it is necessary to use an acoustic code
that accounts for the presence of a mean flow. i.e., to consider the complete set of Linearized
Euler Equations instead of the Helmholtz equation.