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68 Chapter 4: Validation of the acoustic code AVSP-f Figure 4.13: 2D premixed laminar flame. Four snapshorts for one cycle. u ′ /ū = 0.1 Numerical scheme Lax-Wendroff 2 nd artificial viscosity 0.2 4 th artificial viscosity 0.05 CFL 0.7 grid type squares nodes 31574 P inlet 101300 Pa 300 K T inlet Table 4.1: Main parameters of the CFD computation frequency. The source term is then determined by the expression Source = −iω(γ − 1) ˆ˙ω T (4.12) where the heat capacity ratio γ is also obtained from the CFD computation. In addition to the source term of noise, the mean flow information is given to the acoustic code through the mean sound velocity ¯c. Two different types of boundary conditions are used in order to mimic the acoustic behavior of the burner boundaries. Both inlet and walls acoustic response are modeled assuming an acoustic velocity normal to the respective boundary û · n equal to zero. This boundary condition is representative of totally reflecting walls. The outlet is on the contrary characterized by a specific acoustic impedance Ẑ. This acoustic impedance is related to the reflection coefficient ˆR by
4.2 The 2D premixed laminar flame 69 Ẑ = ˆR + 1 ˆR − 1 (4.13) while the reflection coefficient ˆR is obtained by the relation (4.11). 4.2.3 Results The exercise of validation, which is illustrated in Fig. 4.14, consists in comparing the pressure field given by AVSP-f to the one obtained directly by the CFD computation performed with the AVBP solver. The discrete Fourier transform is applied to the temporal pressure signals given by the CFD so that they can be compared to the sound pressure spectrum evaluated by the acoustic code. Figure 4.15 shows the Sound Pressure Level SPL predicted by both AVBP and AVSP-f at three different positions downstream the pulsated flame. CFD Method p ′ DFT ˆp Direct Method ˙q ′ DFT ˆ˙q ¯c Ac. Analogy COMPARISON ˆp Hybrid Method Figure 4.14: Exercise of comparison: CFD method vs. Acoustic solver A good agreement can be observed in Fig. (4.15). A peak at 500 Hz is seen which represents the frequency at which the flame is excited. Peaks at 1000 and 1500 Hz are also observed. They represent the most significative harmonics of the modulation frequency. A second case is also evaluated. The inlet velocity is now pulsated at ± 2 m/s (see Fig. 4.16) which corresponds to 50% of the mean velocity at the inlet. The pressure signal obtained by the acoustic code also corresponds very well to the pressure signal given by the CFD computation. Figure 4.17 shows the SPL results. It is important to emphasize that the acoustic boundary conditions implemented in the acoustic code must correspond to those imposed in the CFD simulation if a good match between these two different methods is expected. Several computations (not shown) were made for different values of the impedance Ẑ at the outlet. As an example, for Ẑ = 1 (totally non-reflecting condition) the amplitudes of the acoustic pressure evaluated by AVSP-f are 10% bigger than those computed by the CFD tool.
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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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16 Chapter 1: General Introduction
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7 Computation of the Reflection Coe
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Chapter 7: Computation of the Refle
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Bibliography [1] AGARWAL, A., MORRI
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130 BIBLIOGRAPHY [30] FRAYSSÉ, V.,
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132 BIBLIOGRAPHY [62] NICOUD, F., B
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134 BIBLIOGRAPHY [93] SENSIAU, C. S
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