THESE de DOCTORAT - cerfacs

6.5 When entropy does not remain constant through a duct 111
6.5.3 Results
The 1D Flame system is considered compact since the flame thickness δ f remains small for all
the acoustic wave lengths λ studied. For this reason, the present analysis focuses mainly on the
effects of both the inflow Mach number ¯M 1 and the temperature jump ( ¯T 2 / ¯T 1 ).
Figure 6.9 shows the values of the coefficients R AA , T AA and T AS (see table 6.1) obtained by
both the analytical and the LEE approaches for two different values of ¯T 2 / ¯T 1 .
2
T 2 /T 1 =2
2
T 2 /T 1 =4
R AA
R AA
T AA
T AA
0.1 T AS
0 0.05 0.1 0.15 0.2
1.5
1.5
0.1 T AS
1
1
0.5
0.5
0
0 0.05 0.1 0.15 0.2
(a)
¯M 1
0
(b)
¯M 1
Figure 6.9: 1D Flame - Entropy Jump Case. Lines correspond to analytical solutions. Symbols
(△,▽,◦) represent SNozzle solutions
.
Good agreement is found between analytical solutions and SNozzle results. It is observed that
the lower the inflow Mach number ¯M 1 , the bigger the amplitude of all the waves w − 1 ,w+ 2 and
w S 2 . The temperature jump T 2/T 1 has a strong but opposite effect on both transmitted acoustic
wave and generated entropy wave. A high value of T 2 /T 1 generates a high amplitude entropy
wave. On the other hand, this high value of T 2 /T 1 creates a reduction of the amplitude of the
transmitted acoustic wave so that the energy of the fluctuations is conserved through the flame
[64].