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to the center of channel 1 (0 < y < 12 d). Numerical profiles are taken at z = 0 and at x = 190.72 d (46.72 d from the beginning of the perforated zone): this corresponds to the distance between the holes of row 1 and row 9. 12 10 a 12 10 b 8 8 y/d 6 y/d 6 4 4 2 2 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0 -20 -10 0 10 20 30x10 -3 U/U 1 V/U 1 Figure 14. Evaluation of models UM1 ( ) and UM2 ( ). Numerical timeaveraged velocity profiles at x = 190.72 d and z = 0 are compared to time- and spatial-averaged experimental data ( • ) at row 9. (a): streamwise velocity, (b): normal velocity. Streamwise velocity profiles are displayed in Fig. 14a. The experimental profile can be separated into two distinct regions: above y = 5 d, the velocity is not affected by effusion. On the contrary, near the plate, the profile is highly modified by effusion and shows a strong acceleration. From Fig. 14a, the model UM2 is more appropriate than UM1. The wall velocity for the UM1 profile is very small and does not correspond at all with the experimental value. Moreover, this low-velocity condition has a blocking effect on the main flow: the passage area is reduced and the main flow accelerates above this region. On the contrary, the use of UM2 allows to obtain reasonable results: differences between experimental and numerical values using UM2 are of order of 10%. Two types of discrepancies are observed: near the wall, the injected streamwise momentum flux seems too low to reach the experimental results. This is coherent with the observations of section III: the assumptions of model UM2 lead to an under-estimation of the injected non-viscous streamwise momentum flux. Further from the wall, the flow slightly accelerates. Fig. 14b displays the vertical velocity profiles. It is much more difficult to conclude on this figure. Eight profiles are insufficient to obtain a satisfying of the spatially-averaged vertical velocity: numerical simulations inject the good mass flow rate through the plate (the discharge coefficient is known from the small-scale LES) so at least the values near the perforated wall should be close to the ones obtained in the simulations. These calculations have shown the ability of model UM2 to reproduce a structure of the flow that presents satisfying results by comparison with the LARA experimental database. As could be guessed after the flux analysis in section III, the model UM1 injects a very small 21 of 26
streamwise momentum flux. As a consequence, the resulting flow is completely different from the one observed experimentally. Differences between experimental and numerical results are observed near the perforated plate, due to an under-estimation of the streamwise momentum flux. Computations also confirm that the objective of a uniform model for effusion cooling is to be representative of the fluxes at the perforated wall. Note also that for a better validation of the model, detailed experimental data are needed, ideally providing spatiallyaveraged velocity profiles. V. Conclusion In this paper, an adiabatic model to account for multi-perforated liners in combustion chamber flow simulations is described. It is separated into a suction model and an injection model to account for the effect of effusion at both sides of the plate. The modeling respects two important constraints: it is local and homogeneous. By local we mean that the effect of effusion through the perforated plate is assessed only from local quantities, without any reference to global parameters such as the distance to the beginning of the perforated zone for example. It is homogeneous because it does not impose any constraint in terms of grid size at the wall: the perforated plate is replaced by a homogeneous boundary condition on which the model is applied. Mendez et al. 30 have performed wall-resolved Large-Eddy Simulations of the flow around a multi-perforated plate in an isothermal case. The analysis of these results show that if the mass flow rate through the plate is known, the difficult task is to assess the streamwise momentum flux. It is also shown that the main contribution to the streamwise momentum flux is due to the inviscid injection of fluid through the hole: wall friction over the solid wall is approximately ten times smaller. This paper presents a way to reproduce the inviscid part of the streamwise momentum flux at the perforated wall. The model is built in two steps. First, the velocity fields at the hole inlet/outlet are approximated by constant values. Then, two homogeneous models are constructed from these approximated fields, conserving either the spatially-averaged velocities (UM1) or fluxes at the wall (UM2). Both models are implemented in an LES code. They are tested by reproducing the experimental configuration of two channel flows separated by a plate including a perforated region. The experimental perforated zone is replaced by the numerical homogeneous model. Both sides of the plate are coupled: the mass flow rate is not imposed but calculated locally from local conditions at both sides of the plate and from the perforated plate geometry. Results from simulations are compared with spatially-averaged experimental data. We show that the model built to reproduce the wall fluxes (UM2) is the best one. UM1 imposes a very low streamwise velocity at the wall, which is not observed in experiments. On 22 of 26
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UNIVERSITE MONTPELLIER II SCIENCES
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Table des matières Remerciements 7
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Remerciements Cette thèse a été
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Liste des symboles Lettres romaines
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Introduction générale La volonté
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Chapitre 1 Contexte industriel et s
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1.1 Les turbines à gaz pour les tu
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1.1 Les turbines à gaz a) b) GAZ C
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1.2 La simulation numérique des é
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1.3 Objectifs et plan de la thèse
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Chapitre 2 L’écoulement autour d
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2.1 Présentation de la configurati
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2.2 Perte de charge au passage d’
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2.3 La multi-perforation : aspects
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2.4 Caractérisation aérodynamique
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2.5 Modélisation de la multi-perfo
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Chapitre 3 Simulations des grandes
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3.2 Simulations des Grandes Echelle
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3.3 Le code de calcul AVBP 3.3.1 As
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3.3 Le code de calcul AVBP dans le
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3.3 Le code de calcul AVBP de sa st
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Chapitre 4 Simulations numériques
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4.1 Quelles simulations pour la mod
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4.2 Choix de la méthode de simulat
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4.2 Choix de la méthode de simulat
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4.3 Sensibilité des simulations au
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Chapitre 5 Simulations numériques
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2 S. Mendez and F. Nicoud COMBUSTIO
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4 S. Mendez and F. Nicoud (c) The i
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6 S. Mendez and F. Nicoud CALCULATI
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8 S. Mendez and F. Nicoud Name Numb
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Page 113 and 114: 16 S. Mendez and F. Nicoud ROWS 1 3
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Page 117 and 118: 20 S. Mendez and F. Nicoud 30 ◦ 3
Page 119 and 120: 22 S. Mendez and F. Nicoud & Mahesh
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Page 127 and 128: 30 S. Mendez and F. Nicoud Region t
Page 129 and 130: 32 S. Mendez and F. Nicoud Expressi
Page 131 and 132: 34 S. Mendez and F. Nicoud geometri
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Page 135 and 136: 38 S. Mendez and F. Nicoud Mendez,
Page 137 and 138: Chapitre 6 Un modèle adiabatique p
Page 139 and 140: ρ Mass density, kg/m 3 P T V i τ
Page 141 and 142: cence of the jets. This is particul
Page 143 and 144: Simulations. The small-scale LES re
Page 145 and 146: chosen to compare with numerical re
Page 147 and 148: pressure drop of 41 Pa is effective
Page 149 and 150: Region total plate hole solid wall
Page 151 and 152: This equality is almost verified at
Page 153 and 154: V U σ V inj jet cotan(α′ ) V U
Page 155 and 156: PERIODIC Z INFLOW 1 WALL 24 OUTFLOW
Page 157: part of the plate. Downstream of th
Page 161 and 162: 8 Fric, T. and Roshko, A., “Vorti
Page 163 and 164: Discussion sur la modélisation de
Page 165 and 166: 20 15 10 y/d 5 0 -5 -10 0.0 0.2 0.4
Page 167 and 168: Chapitre 7 Simulations numériques
Page 169 and 170: Primary flow (burnt gases) Secondar
Page 171 and 172: Figure 7: Nusselt number over the s
Page 173 and 174: the perforated plate. A Large-Eddy
Page 175 and 176: Les tableaux de flux permettent de
Page 177 and 178: Conclusion générale Dans cette é
Page 179 and 180: Conclusion générale En ce qui con
Page 181 and 182: Bibliographie AKSELVOLL, K. & MOIN,
Page 183 and 184: BIBLIOGRAPHIE CORON, X. 2001 Étude
Page 185 and 186: BIBLIOGRAPHIE HALE, C. A., PLESNIAK
Page 187 and 188: BIBLIOGRAPHIE LIEUWEN, T. & YANG, V
Page 189 and 190: BIBLIOGRAPHIE MOST, A. & BRUEL, P.
Page 191 and 192: BIBLIOGRAPHIE SCHILDKNECHT, M., MIL
Page 193: Annexes
Page 196 and 197: ARTIFICIAL VISCOSITY MODELS A.2.1 T
Page 198 and 199: ARTIFICIAL VISCOSITY MODELS - 4 th
Page 200 and 201: ARTIFICIAL VISCOSITY MODELS As a co
Page 202: ARTIFICIAL VISCOSITY MODELS 202
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