THESE de DOCTORAT - cerfacs

118 Chapter 6: Boundary conditions for low Mach number acoustic codes
values of R computed by SNozzle match the values of R given analytically when the wave
length is extremely large compared to L (Ω ≈ 0). This is shown in Figs 6.15 and 6.16.
" c
= 2
" c
= 4
9
8
¯M 2 =0.025
¯M 2 =0.05
¯M 2 =0.1
9
8
¯M 2 =0.025
¯M 2 =0.05
¯M 2 =0.1
7
7
Module of R
6
5
4
Module of R
6
5
4
3
3
2
2
1
1
0 0.05 0.1
!
0 0.05 0.1
!
(a)
(b)
Figure 6.15: Modulus of the Reflection Coefficient. Lines represent SNozzle solutions. Symbols
(◦) stands for Analytical results
.
From Fig. 6.15 it is observed that, for a given ¯π c , lower values of ¯M 2 lead to smaller values
of |R|. For high values of ¯π c , the magnitude or the reflection coefficient increases significantly
mainly for low forcing frequencies. It should be clear then that the inclusion of an enthalpy
jump is crucial for the estimation of acoustic boundaries to impose at the edge of a combustion
chamber within an aeronautical engine.