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Figure 2. Principle of the large-scale isothermal LARA experiment. 18 side, with a primary flow of ‘hot gases’; the second one, denoted by ‘2’, represents the casing, with a secondary flow of ‘cooling air’ (Fig. 2). The two channels (height h = 120mm and width l = 400mm) are separated by a plate perforated with holes of diameter d = 5mm (0.5mm is the common value for gas turbines). Twelve rows of staggered holes are drilled into the plate that separates the two channels. A grid is placed at the outlet section of channel 2 in order to generate a pressure drop across the plate. Because the pressure is higher in the ‘casing side’, a fraction of the air flowing in channel 2 is injected through the perforated plate. The spacing between the holes corresponds to classical industrial applications: the distance between two rows of holes is 5.84 diameters in the streamwise direction and 3.37 diameters in the spanwise direction. Due to the staggered disposition of the perforations, the hole-to-hole distances are 2 × 5.84 and 2 × 3.37 diameters in the streamwise and spanwise directions respectively. The thickness of the plate being e = 10mm and holes being angled at α = 30 ◦ with the plate, the hole length-to-diameter ratio is 4. Note that the perforations are only angled in the direction of the main flow, without any spanwise component. Measurements are performed at ambient temperature. The LARA database has been used twice: first, the LES presented in section III deals with the same geometry as the LARA test rig. Numerical and experimental results are compared in Mendez et al. 30 Then, in section IV, a model for discrete effusion through a plate is implemented in our CFD code. The validation case is also the LARA experiment. One operating point has been considered: the pressure drop across the plate is ∆P = 42 Pa. The Reynolds number for the primary ‘hot’ flow (based on the duct centerline velocity U 1 and the half height of the rectangular duct h/2) is Re 1 = 17750, while it is Re 2 = 8900 for the secondary ‘cold’ flow. The characteristics are given upstream of the perforated zone, where the flow is fully-developed. The Reynolds number in the hole, based on the momentum in the jet core et the hole exit and the hole diameter is Re h = 2600. The ninth row has been 7 of 26
chosen to compare with numerical results because it is the location where measurements are most numerous. Further details about this experiment can be found in studies by Miron. 18,39 III. Construction of a model for effusion cooling from LES results To perform fast-running simulations of their combustion chambers in presence of effusion cooling, manufacturers need a model that reproduces the main effects of effusion on the main flow. This model must meet several criteria: • It has to provide information for both sides of the plate. Indeed, the current tendency is to include the casing when computing the flow in a combustion chamber; thus both the casing side (suction of cooling air) and the combustion chamber side (injection of this cooling air) must be modeled, • As the objective is to use coarse grids to have fast-running simulations, the flow near the wall would not be resolved: effusion through small holes (d ≈ 0.5 mm) imposes characteristic length scales that cannot be solved over coarse meshes. As a consequence, an appropriate model must represent the multi-perforated plate as a homogeneous boundary, without distinction between perforations and solid parts of the wall any more, • The model has to be local. Global parameters, such as the number of upstream rows, are often used for models related to effusion cooling (see for example Mayle and Camarata 40 for a model of the adiabatic effectiveness of the cooling). However, in a combustion chamber, the row number cannot always be defined, and the notion of upstream direction is a loosy concept for 3-D flows multiple inlets/outlets . To overcome this problem, it has been decided to look for a local model, that only depends on the flow conditions in the neighborhood of each point where the model is needed. To satisfy these criteria, the objective is to build a uniform model that only has local information as input data, and that reproduces correctly the fluxes at both sides of the perforated wall: this is inspired by what is done for wall-function boundary conditions for impermeable walls, where the wall friction and the wall heat flux are assessed in order to reproduce the macroscopic effect that the wall has on the main flow. The following sub-section aims at describing the reference simulations and their post-treatment in order to construct such a model. 8 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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Page 97 and 98: Chapitre 5 Simulations numériques
Page 99 and 100: 2 S. Mendez and F. Nicoud COMBUSTIO
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Page 103 and 104: 6 S. Mendez and F. Nicoud CALCULATI
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Page 113 and 114: 16 S. Mendez and F. Nicoud ROWS 1 3
Page 115 and 116: 18 S. Mendez and F. Nicoud Figure 1
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Page 119 and 120: 22 S. Mendez and F. Nicoud & Mahesh
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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: Simulations. The small-scale LES 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 and 158: part of the plate. Downstream of th
Page 159 and 160: streamwise momentum flux. As a cons
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
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ARTIFICIAL VISCOSITY MODELS A.2.1 T
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ARTIFICIAL VISCOSITY MODELS - 4 th
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ARTIFICIAL VISCOSITY MODELS As a co
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ARTIFICIAL VISCOSITY MODELS 202
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