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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
5.3 Combustion noise Analysis 83 Figure 5.10: Typical iso-surface of the instantaneous unsteady heat release rate ˙ω T Figure 5.11: Mean sound velocity ¯c over a longitudinal plane of the EC2 combustor (a) (b) (c) (d) (e) Figure 5.12: The combustion source of noise oscillating at 377 Hz. 5 snapshots during one cycle. was solved 500 times within a band of frequencies from 25 Hz to 2500 Hz, with a frequency step of f = 25 Hz. Overall good agreement is found between the direct and hybrid approaches. Figures 5.13 and 5.14 show the sound pressure levels obtained for microphones 5, 6 and 7 (see the location of M5, M6, M7 in Fig. 5.2). It is interesting to notice that the hybrid computation manages to recover not only the magnitude of the acoustic pressure over almost all the spectrum, but also the shape of the acoustic
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UNIVERSITE MONTPELLIER II SCIENCES
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An expert is a man who has made all
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Y gracias familia mía!!, que así
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Abstract Today, much of the current
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4 CONTENTS 3.4.1 Preconditioning .
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List of Figures 1.1 Main sources of
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8 LIST OF FIGURES 5.19 Acoustic ene
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List of Tables 1.1 EU recommended r
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14 Chapter 1: General Introduction
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2 Computation of noise generated by
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22 Chapter 2: Computation of noise
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132 BIBLIOGRAPHY [62] NICOUD, F., B
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134 BIBLIOGRAPHY [93] SENSIAU, C. S
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