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LES of a bi-periodic turbulent flow with effusion 5 LES of single jets in crossflow have been performed by Tyagi & Acharya (2003), Iourokina & Lele (2006), Peet (2006) and Renze, Meinke & Schröder (2006), using periodic boundary conditions in the spanwise direction to mimic a row of cooling jets. Iourokina & Lele (2006), Peet (2006) and Renze et al. (2006) have included the complete geometry (cooled channel, hole and plenum) used respectively by Pietrzyk, Bogard & Crawford (1989) and Sinha, Bogard & Crawford (1991) in the reference experiments. Note that only one row of holes is considered in these studies, which focus more on turbine blade FC than on combustion chamber wall cooling. From the short literature overview presented above, the following comments can be made, regarding the understanding and modelling of FCFC: (a) no detailed data about non-isothermal FCFC can be found in the open literature (apart from RANS results); only measurements of cooling efficiency and wall heat transfer are available. This is mainly because large temperature gradients impose small scale facilities for which achieving spatially resolved measurements is extremely challenging. A good way to proceed would be to rely on Direct Numerical or wall-resolved Large- Eddy Simulations (Mendez & Nicoud 2007). However, lack of experimental data remains problematic for obvious validation reasons, (b) even in the isothermal case, only a few studies focus specifically on FCFC and for these particular studies, only injection side results have been reported. Moreover, only Miron (2005) used a supply channel on the suction side, with only part of the secondary flow passing through the holes. In Yavuzkurt et al. (1980a,b) and Gustafsson (2001), the fluid injected through the holes flows on the suction side in a plenum, with very small velocity. Detailed data relevant to the suction, aperture and injection regions is still lacking for FCFC, even in isothermal situation. Such data is needed to support the development of wall models able to represent the effects of effusion on both sides of the plate, (c) a common difficulty in analysing experimental or numerical results relevant to FCFC is the dependency of the results on the position of the row where the flow is investigated. Several studies confirm the necessity to account for several rows before the FCFC situation is reached: Miron (2005) shows that the velocity profiles are still evolving after 10 rows of holes, while measurements have shown that cooling effectiveness stabilises only after a large number of rows (approximately 15 for Mayle & Camarata 1975; Rouvreau 2001). Although 10-15 rows are often considered to be enough to study FCFC (Bazdidi-Tehrani & Andrews 1994; Crawford et al. 1980; Metzger et al. 1973; Miron 2005), the independence of the results on the row position within the whole array of holes was never observed in previous studies and to the author’s knowledge the existence of such ‘self-similarity’ is still an open question. This situation makes questionable the generality of the conclusions drawn from the investigation of spatially evolving boundary layers over multi-perforated plates. Moreover, it is in contradiction with the development of a wall model that is local in space and provides the fluxes through the effusion plate independently of the position on the perforated plate. Due to the overall lack of relevant data, this is the authors’ viewpoint that the isothermal case should be considered until more maturity about FCFC has been reached. Notably, gaining insight about the aspiration and aperture flow structure still remains to be achieved in the isothermal FCFC case. Moreover, obtaining data where the row number is not a parameter of the problem would introduce new perspectives in terms of FCFC modelling. It is the objective of this paper to address these issues. More precisely, a synthetic flow relevant to FCFC is computed by wall-resolved Large-Eddy Simulation. The configuration corresponds to a bi-periodic flow where both the aspiration and the injection sides of the plate are computed. Because periodicity is assumed in both direc-
6 S. Mendez and F. Nicoud CALCULATION DOMAIN a b PRIMARY FLOW 24 d INFINITE PERFORATED WALL 2 d 10 d 11.68 d 6.74 d SECONDARY FLOW y z x Figure 2. From the infinite plate to the ‘bi-periodic’ calculation domain. (a): Geometry of the infinite perforated wall. (b): Calculation domain centred on a perforation; the bold arrows correspond to the periodic directions. The dimensions of the computational domain are provided. tions tangential to the plate, this flow corresponds to a case where the number of rows tends to infinity and the row position along the plate is no more a relevant parameter. The configuration of interest is described in § 2 along with some numerical details about the LES code. Velocity profiles are presented in §3, where the similarities/differences between the classical situation with a finite number of rows and the present synthetic flow are highlighted. A detailed description of the flow features is provided in § 4 and an analysis of the results in terms of wall modelling is presented in §5. 2. Numerical method Results in the open literature show that the effusion flow highly depends on the configuration of interest: the flow at the end of a ten-row plate would be different from the one of a twenty-row plate. This situation is hardly tractable from a modelling point of view and not convenient for practical applications; the flow structure in three dimensional combustion chambers is neither simple nor known a priori, making the notion of number of upstream rows a fuzzy concept. Thus it has been decided to consider the asymptotic case where the flow is independent of the hole considered. The simulation is then designed to reproduce this ‘fully-developed’ turbulent flow with effusion. This choice presents several advantages: (a) The computational domain may contain only a small number of perforations (for example one), with periodic boundary conditions to reproduce the whole geometry of an infinite plate, as it is suggested in figure 2. Due to the staggered arrangement of the perforations, the computational domain is diamond-shaped, (b) The difficult question of the inlet and outlet boundary conditions in turbulent simulations (see Moin & Mahesh 1998) is eluded, (c) The computing effort is drastically reduced compared to spatially evolving flow, because the computational domain is smaller. With such a periodic calculation domain, the objective is to have information about the structure of the flow far from the first rows, when the film is established. However, this periodic option raises a problem: natural mechanisms that drive the flow, such as pressure gradients in the periodic directions, are absent. The flow has to be generated artificially in a way that does not modify the details of the flow structure.
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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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2.4 Caractérisation aérodynamique
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Page 67 and 68: 2.5 Modélisation de la multi-perfo
Page 69 and 70: Chapitre 3 Simulations des grandes
Page 71 and 72: 3.2 Simulations des Grandes Echelle
Page 73 and 74: 3.3 Le code de calcul AVBP 3.3.1 As
Page 75 and 76: 3.3 Le code de calcul AVBP dans le
Page 77 and 78: 3.3 Le code de calcul AVBP de sa st
Page 79 and 80: Chapitre 4 Simulations numériques
Page 81 and 82: 4.1 Quelles simulations pour la mod
Page 83 and 84: 4.2 Choix de la méthode de simulat
Page 85 and 86: 4.2 Choix de la méthode de simulat
Page 87 and 88: 4.3 Sensibilité des simulations au
Page 97 and 98: Chapitre 5 Simulations numériques
Page 99 and 100: 2 S. Mendez and F. Nicoud COMBUSTIO
Page 101: 4 S. Mendez and F. Nicoud (c) The i
Page 105 and 106: 8 S. Mendez and F. Nicoud Name Numb
Page 107 and 108: 10 S. Mendez and F. Nicoud x/d z/d
Page 109 and 110: 12 S. Mendez and F. Nicoud main, it
Page 111 and 112: 14 S. Mendez and F. Nicoud 1.0 a 1.
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 129 and 130: 32 S. Mendez and F. Nicoud Expressi
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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
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Page 143 and 144: Simulations. The small-scale LES re
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Page 149 and 150: Region total plate hole solid wall
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V U σ V inj jet cotan(α′ ) V U
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PERIODIC Z INFLOW 1 WALL 24 OUTFLOW
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part of the plate. Downstream of th
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streamwise momentum flux. As a cons
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8 Fric, T. and Roshko, A., “Vorti
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Discussion sur la modélisation de
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20 15 10 y/d 5 0 -5 -10 0.0 0.2 0.4
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Chapitre 7 Simulations numériques
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Primary flow (burnt gases) Secondar
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Figure 7: Nusselt number over the s
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the perforated plate. A Large-Eddy
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Les tableaux de flux permettent de
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Conclusion générale Dans cette é
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Conclusion générale En ce qui con
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Bibliographie AKSELVOLL, K. & MOIN,
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BIBLIOGRAPHIE CORON, X. 2001 Étude
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BIBLIOGRAPHIE HALE, C. A., PLESNIAK
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BIBLIOGRAPHIE LIEUWEN, T. & YANG, V
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BIBLIOGRAPHIE MOST, A. & BRUEL, P.
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BIBLIOGRAPHIE SCHILDKNECHT, M., MIL
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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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