THESE de DOCTORAT - cerfacs
THESE de DOCTORAT - cerfacs THESE de DOCTORAT - cerfacs
86 Chapter 5: Assessment of combustion noise in a premixed swirled combustor Pressure Fluctuation (Pa) M5 M6 M7 40 Premixer Combustion chamber 20 0 −20 −40 −0.2 −0.1 0 0.1 0.2 x (m) 0.3 0.4 0.5 (a) Pressure Wave from Eq. (2.63) Hybrid Computation Pressure Fluctuation (Pa) M5 M6 M7 40 Premixer Combustion chamber 20 0 −20 −40 −0.2 −0.1 0 0.1 0.2 x (m) 0.3 0.4 0.5 (b) Pressure fluctuation from LES Direct Computation Figure 5.17: Longitudinal pressure Waves oscillating at 954 Hz Pressure Fluctuation (Pa) M5 M6 M7 40 Premixer Combustion chamber 20 0 −20 −40 −0.2 −0.1 0 0.1 0.2 x (m) 0.3 0.4 0.5 (a) Pressure Wave from Eq. (2.63) Hybrid Computation Pressure Fluctuation (Pa) M5 M6 M7 40 Premixer Combustion chamber 20 0 −20 −40 −0.2 −0.1 0 0.1 0.2 x (m) 0.3 0.4 0.5 (b) Pressure fluctuation from LES Direct Computation Figure 5.18: Longitudinal pressure Waves oscillating at 1658 Hz
5.4 Filtering a LES pressure field to find the corresponding acoustic field 87 the acoustic energy. For low Mach number flows, the acoustic energy is defined as [74] E ac = p′2 ¯ρ ¯c + ¯ρu′2 (5.5) From the definition of the acoustic energy (Eq. 5.5), it is observed that even though pressure nodes takes place at a given location, the energy contained is different from zero: it is given by the acoustic velocity which is expected to be maximum at pressure nodes. As a consequence, spectra without strong local minima are obtained. The acoustic energy spectrum for microphones 5, 6 and 7 is shown in Figs. 5.19 and 5.20 Ac. Energy (J) − micro 5 Hybrid Computation Direct Computation: LES 10 −5 0 500 1000 1500 2000 2500 10 0 Frequency (Hz) Ac. Energy (J) − micro 6 Hybrid Computation Direct Computation: LES 10 −5 0 500 1000 1500 2000 2500 10 0 Frequency (Hz) Figure 5.19: Acoustic energy. Direct and hybrid approaches Ac. Energy (J)− micro 7 Hybrid Computation Direct Computation: LES 10 −5 0 500 1000 1500 2000 2500 10 0 Frequency (Hz) Figure 5.20: Acoustic energy. Direct and hybrid approaches Although there is an overall good agreement for the three microphones, the energy content is bigger for the signals coming from the direct approach. This is easily noticed at microphone 7 in Fig. 5.20. In the following, a procedure is exposed so that pure acoustic signals can be retrieved from the LES performed. 5.4 Filtering a LES pressure field to find the corresponding acoustic field Velocity fluctuations obtained by LES are composed of both hydrodynamics and acoustics
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5.4 Filtering a LES pressure field to find the corresponding acoustic field 87<br />
the acoustic energy. For low Mach number flows, the acoustic energy is <strong>de</strong>fined as [74]<br />
E ac = p′2<br />
¯ρ ¯c + ¯ρu′2 (5.5)<br />
From the <strong>de</strong>finition of the acoustic energy (Eq. 5.5), it is observed that even though pressure<br />
no<strong>de</strong>s takes place at a given location, the energy contained is different from zero: it is given by<br />
the acoustic velocity which is expected to be maximum at pressure no<strong>de</strong>s. As a consequence,<br />
spectra without strong local minima are obtained. The acoustic energy spectrum for microphones<br />
5, 6 and 7 is shown in Figs. 5.19 and 5.20<br />
Ac. Energy (J) − micro 5<br />
Hybrid Computation<br />
Direct Computation: LES<br />
10 −5<br />
0 500 1000 1500 2000 2500<br />
10 0 Frequency (Hz)<br />
Ac. Energy (J) − micro 6<br />
Hybrid Computation<br />
Direct Computation: LES<br />
10 −5<br />
0 500 1000 1500 2000 2500<br />
10 0 Frequency (Hz)<br />
Figure 5.19: Acoustic energy. Direct and hybrid approaches<br />
Ac. Energy (J)− micro 7<br />
Hybrid Computation<br />
Direct Computation: LES<br />
10 −5<br />
0 500 1000 1500 2000 2500<br />
10 0 Frequency (Hz)<br />
Figure 5.20: Acoustic energy. Direct and hybrid approaches<br />
Although there is an overall good agreement for the three microphones, the energy content is<br />
bigger for the signals coming from the direct approach. This is easily noticed at microphone<br />
7 in Fig. 5.20. In the following, a procedure is exposed so that pure acoustic signals can be<br />
retrieved from the LES performed.<br />
5.4 Filtering a LES pressure field to find the corresponding acoustic field<br />
Velocity fluctuations obtained by LES are composed of both hydrodynamics and acoustics
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