. La-troisième-série-de-plans-est-localisée-dans-les-pertuis, La répartition des plans de validation est illustrée à la figure 7.8. Ainsi, pour le point de fonctionnement PF4, chaque pertuis est décomposé en deux plans verticaux, les plans 1 et 2 pour le pertuis droit, figure 7.17 et 3 et 4 pour le pertuis gauche, figure 7.18. Ces plans permettent de visualiser la répartition à la fois verticale et transverse de l'écoulement dans les pertuis. Les figures de gauche représentent les champs moyens numériques et expérimentaux de la vitesse débitante ( ) La zone de mesures expérimentales est toujours représentée en trait plein noir sur les figures de gauche

H. Abe, H. Kawamura, and Y. Matsuo, Surface heat-flux fluctuations in a turbulent channel flow up to Re??=1020 with Pr=0.025 and 0.71, International Journal of Heat and Fluid Flow, vol.25, issue.3, pp.404-419, 2004.
DOI : 10.1016/j.ijheatfluidflow.2004.02.010

L. France-face-aux-enjeux-de-l-'hydroélectricité.-centre-pierre-mendès-france, Ministère de l'Économie des Finances et de l'Industrie, Janvier, 2007.

M. Agouzoul, M. Reggio, C. , and R. , A three-dimensional turbulent flow analysis in a draft tube, Hydraulic Machinery and Cavitation, vol.2, pp.567-575, 1988.

J. Aider and A. Daner, Large-eddy simulation study of upstream boundary conditions influence upon a backward-facing step flow, Comptes Rendus M??canique, vol.334, issue.7, pp.447-453, 2006.
DOI : 10.1016/j.crme.2006.05.004

K. Akselvoll and P. Moin, Large-eddy simulation of turbulent confined coannular jets, Journal of Fluid Mechanics, vol.106, issue.-1, pp.387-411, 1996.
DOI : 10.1063/1.857955

S. Armfield, N. Cho, F. , and C. , Prediction of turbulence quantities for swirling flow in conical diffusers, AIAA Journal, vol.28, issue.3, pp.3-453, 1990.
DOI : 10.2514/3.10414

J. Arpe, Analyse du champ de pression pariétale d'un diffuseur coudé de turbine Francis, 2003.

F. Avellan, Flow investigation in a francis draft tube : The FLINDT project, Proceedings of the Hydraulic Machinery and Systems 20th IAHR Symposium, 2000.

R. Bader, J. Fritz, Y. Mochkaai, W. Knapp, and R. Schilling, Experimental and theoretical loss analysis in a kaplan turbine, Turbine-99 Workshop on Draft Tube Flow, 1999.

G. Balarac, Etude numérique de la dynamique tourbillonnaire et du mélange dans les jets coaxiaux turbulents, 2006.

G. Balarac and O. Métais, The near field of coaxial jets: A numerical study, Physics of Fluids, vol.17, issue.6, pp.65102-65103, 2005.
DOI : 10.1063/1.1900786
URL : https://hal.archives-ouvertes.fr/hal-00265278

E. Balaras, C. Benocci, and U. Piomelli, Two-layer approximate boundary conditions for large-eddy simulation, AIAA Journal, vol.34, p.1111, 1996.

E. Berca, Instrumentation development for wall shear-stress applications in 3D complex flows, 2007.

J. Bergstöm and B. Gebart, Estimation of numerical accuracy for the flow field in a draft tube, International Journal of Numerical Methods for Heat & Fluid Flow, vol.9, issue.4, pp.472-486, 1999.
DOI : 10.1108/09615539910266620

L. Bernal and A. Roshko, Streamwise vortex structure in plane mixing layers, Journal of Fluid Mechanics, vol.14, issue.-1, pp.499-525, 1986.
DOI : 10.1017/S0022112084000781__S0022112084000781

G. Blommaert, Etude du comportement dynamique des turbines Francis : Contrôle actif de leur stabilité de fonctionnement, 2000.

O. Bounous, Studies of the ERCOFTAC conical diffuser with openFOAM Applied Mechanics, Research Report, p.5, 2008.

D. Brennan, The numerical simulation of two-phases flows in settling tanks, 2001.

M. Breuer, B. Jaffrézic, and K. Arora, Hybrid LES???RANS technique based on a one-equation near-wall model, Theoretical and Computational Fluid Dynamics, vol.54, issue.8, pp.157-187, 2008.
DOI : 10.1007/s00162-007-0067-9

M. Breuer, B. Kniazev, A. , and M. , Development of wall models for LES of separated flows using statistical evaluations, Computers & Fluids, vol.36, issue.5, pp.817-837, 2007.
DOI : 10.1016/j.compfluid.2006.09.001

W. Cabot and P. Moin, Approximate wall boundary conditions in the large-eddy simulation of high reynolds number flow. Flow, Turbul, Combust, vol.63, p.269, 2000.

T. Cebeci, Behavior of turbulent flow near a porous wall with pressure gradient, AIAA Journal, vol.8, issue.12, pp.2152-2156, 1970.
DOI : 10.2514/3.6079

I. Celik, M. Klein, and J. Janicka, Assessment Measures for Engineering LES Applications, Journal of Fluids Engineering, vol.131, issue.3, 2009.
DOI : 10.1115/1.3059703

M. Cervantes and H. Gustavsson, On the Use of the Squire-Long Equation to Estimate Radial Velocities in Swirling Flows, Journal of Fluids Engineering, vol.129, issue.2, pp.209-217, 2007.
DOI : 10.1115/1.2409331

P. Clausen, S. Koh, and D. Wood, Measurements of a swirling turbulent boundary layer developing in a conical diffuser, Experimental Thermal and Fluid Science, vol.6, issue.1, pp.39-48, 1993.
DOI : 10.1016/0894-1777(93)90039-L

C. Da-silva, G. Balarac, and O. Métais, Transition in high velocity ratio coaxial jets analysed from direct numerical simulations, Journal of Turbulence, vol.4, 2003.
DOI : 10.1088/1468-5248/4/1/024

C. Da-silva and J. Pereira, Analysis of the gradient-diffusion hypothesis in large-eddy simulations based on transport equations, Physics of Fluids, vol.19, issue.3, p.35106, 2007.
DOI : 10.1063/1.2710284

F. Dambrine, Rapport sur les perspectives de développement de la production hydroélectrique en france. http ://www.developpement-durable.gouv.fr/energie/electric/pdf/rap- hydraulique-2006.pdf, Mars, 2006.

D. Ciocan, G. Avellan, F. Kueny, and J. , Optical measurement techniques for experimental analysis of hydraulic turbines rotor-stator interaction, ASME Fluid Engineering Conference, pp.11-15, 2000.

D. Ciocan, G. Mauri, S. Arpe, J. Kueny, and J. , Etude du champ instationnaire de vitesse en sortie de roue de turbine, étude expérimentale et numérique. 164 ème session SHF, Machine Hauliques : instationnarités et effets associés, 2000.

L. Davidson, Using isotropic synthetic fluctuations as inlet boundary conditions for unsteady simulations, Advances and Applications in Fluid Mechanics, vol.1, issue.1, pp.1-35, 2007.

D. Villiers and E. , The Potential of Large Eddy Simulation for the Modeling of Wall Bounded Flows, Imperial College of Science, Technology and Medicine, 2006.

I. Delbende, J. M. Chomaz, and P. Huerre, Absolute/convective instabilities in the Batchelor vortex: a numerical study of the linear impulse response, Journal of Fluid Mechanics, vol.355, pp.229-254, 1998.
DOI : 10.1017/S0022112097007787

J. Délery, Robert Legendre and Henri Werl??: Toward the Elucidation of Three-Dimensional Separation, Annual Review of Fluid Mechanics, vol.33, issue.1, pp.129-54, 2001.
DOI : 10.1146/annurev.fluid.33.1.129

G. Diurno, E. Balaras, and U. Piomelli, Wall-layer models for les of separated flow. Modern simulation strategies for turbulent flows, 2001.

F. Ducros, Simulation numérique directes et des grandes échelles de couches limites compressibles, 1995.

C. Duprat, Etude paramétrique d'aspirateurs de centrale hydraulique. Master's thesis, 2006.
DOI : 10.1051/meca/2009055

J. Ferziger and M. Peri?, Computaional methods for fluid dynamics, 1995.

R. Friedrich and M. Arnal, Analysing turbulent backward-facing step flow with the lowpass-filtered navier-stokes equations, Journal of Wind Engineering and Industrial Aerodynamics, vol.35, pp.101-128, 1990.
DOI : 10.1016/0167-6105(90)90212-U

J. Fröhlich, C. Mellen, W. Rodi, L. Temmerman, and M. Leschziner, Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions, Journal of Fluid Mechanics, vol.526, pp.19-66, 2005.
DOI : 10.1017/S0022112004002812

J. Fröhlich, V. Terzi, D. Hybrid, and L. , RANS methods for the simulation of turbulent flows, Progress in Aerospace Sciences, pp.349-377, 2008.

C. Fureby, G. Tabor, H. Weller, and A. Gosman, A comparative study of subgrid scale models in homogeneous isotropic turbulence, Physics of Fluids, vol.9, issue.5, pp.1416-1429, 1997.
DOI : 10.1063/1.869254

M. Garcia-villalba, J. Fröhlich, R. , and W. , Identification and analysis of coherent structures in the near field of a turbulent unconfined annular swirling jet using large eddy simulation, Physics of Fluids, vol.18, issue.5, 2006.
DOI : 10.1063/1.2202648

D. Glaze and H. Frankel, Stochastic Inlet Conditions for Large-Eddy Simulation of a Fully Turbulent Jet, AIAA Journal, vol.41, issue.6, pp.1064-1073, 2003.
DOI : 10.2514/2.2073

M. Gonze, Simulation numérique des sillages en transition à la turbulence, 1993.

P. Granville, A Modified Van Driest Formula for the Mixing Length of Turbulent Boundary Layers in Pressure Gradients, Journal of Fluids Engineering, vol.111, issue.1, pp.94-97, 1989.
DOI : 10.1115/1.3243606

A. Gungor and S. Menon, Direct simulation of subgrid turbulence in a high-wallbounded flow, AIAA Journal, vol.3538, 2006.

W. Gyllenram and H. Nilsson, Very large eddy simulation of draft tube flow [51] Hébrard, J. Transferts thermiques des écoulements turbulents compressibles en conduites : étude par simulation numérique des grandes échelles, 23th IAHR Symposium on Hydraulic Machinery and Systems, 2004.

D. Hill, The computer simulation of dispersed two-phase flows, 1998.

C. Hirsch, Numerical computation of internal and external flows, 1991.

P. Hopping, Draft-tube measurements of water velocity and air concentration in the 1 :11.71 scale model of the hydroturbines for norris dam, 1992.

J. Hunt, A. Wray, and P. Moin, Eddies, stream, and convergence zones in turbulent flows, Annual research briefs, 1988.

R. Issa, Solution of the implicitly discretized fluid flow equations by operator splitting

D. Jacobs, Preconditioned conjugate gradient methods for solving systems of algebraic equation, Tech. Rep. RD, vol.80, 1980.

N. Jarrin, S. Benhamadouche, Y. Addad, L. , and D. , Synthetic turbulent inflow conditions for large eddy simulation, Proceedings, 4 ? International Turbulence Heat and Mass Transfer Conference, 2003.

N. Jarrin, S. Benhamadouche, D. Laurence, and R. Prosser, A synthetic-eddy-method for generating inflow conditions for large-eddy simulations, International Journal of Heat and Fluid Flow, vol.27, issue.4, pp.585-593, 2006.
DOI : 10.1016/j.ijheatfluidflow.2006.02.006

H. Jasak, Error analysis and estimation in the finite volume method with applications to fluid flows, 1996.

F. Juretic, Error analysis in finite volume CFD, 2004.

Y. Kaneda, L. , and D. , Tests of subgrid models in the near-wall region using represented velocity fields, Journal of Fluid Mechanics, vol.41, issue.-1, pp.349-373, 1983.
DOI : 10.1016/0017-9310(73)90125-7

A. Kempf, LES Validation from Experiments, Flow, Turbulence and Combustion, vol.148, issue.35, pp.351-373, 2007.
DOI : 10.1007/s10494-007-9128-9

M. Klein, A. Sadiki, and J. Janicka, A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations, Journal of Computational Physics, vol.186, issue.2, pp.652-665, 2003.
DOI : 10.1016/S0021-9991(03)00090-1

R. Kraichnan, Diffusion by a Random Velocity Field, Physics of Fluids, vol.13, issue.1, pp.22-31, 1965.
DOI : 10.1063/1.1692799

M. Landman, On the generation of helical waves in circular pipe flow. Phys, pp.5-738, 1990.

M. Landman, Time-dependent helical waves in rotating pipe flow, Journal of Fluid Mechanics, vol.174, issue.-1, pp.289-310, 1990.
DOI : 10.1017/S0022112080000146

B. Launder and C. Priddin, A comparison of some proposals for the mixing length near a wall, International Journal of Heat and Mass Transfer, vol.16, issue.3, pp.700-702, 1973.
DOI : 10.1016/0017-9310(73)90239-1

H. Le, P. Moin, K. , and J. , Direct numerical simulation of turbulent flow over a backward-facing step, Journal of Fluid Mechanics, vol.330, pp.349-373, 1997.
DOI : 10.1017/S0022112096003941

C. Le-ribault, S. Sarkar, and A. Stanley, Large eddy simulation of a plane jet, Physics of Fluids, vol.11, issue.10, 1999.
DOI : 10.1063/1.870165

S. Lee, S. Lele, and P. Moin, Simulation of spatially evolving turbulence and the applicability of Taylor???s hypothesis in compressible flow, Physics of Fluids A: Fluid Dynamics, vol.4, issue.7, pp.1521-1530, 1992.
DOI : 10.1063/1.858425

M. Lesieur, Turbulence in fluids, 1997.
URL : https://hal.archives-ouvertes.fr/hal-00261553

M. Lesieur, O. Métais, C. , and P. , Large-eddy simulations of turbulence, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00261551

T. Lund, X. Wu, and D. Squires, Generation of Turbulent Inflow Data for Spatially-Developing Boundary Layer Simulations, Journal of Computational Physics, vol.140, issue.2, pp.233-258, 1998.
DOI : 10.1006/jcph.1998.5882

R. Manceau, Modélisation statistique de la turbulence. 10 ème école de Printemps mécanique des fluides numérique du CNRS, 2007.

L. Mangani, Development and validation of an object orented CFD solver for heat transfer and combustion modeling in turbomachinery applications, 2008.

M. Manhart, Analysing near-wall behaviour in a separating turbulent boundary layer by DNS. Direct and Large-Eddy Simulation IV, 2001.

M. Manhart, N. Peller, and C. Brun, Near-wall scaling for turbulent boundary layers with adverse pressure gradient, Theoretical and Computational Fluid Dynamics, vol.5, issue.23, pp.243-260, 2008.
DOI : 10.1007/s00162-007-0055-0

S. Mauri, J. Kueny, and F. Avellan, Flow simulation in an elbow diffuser : verification and validation, 21th IAHR Symposium on Hydraulic Machinery and Systems, 2002.
URL : https://hal.archives-ouvertes.fr/hal-00262263

S. Mauri, Numerical simulation and flow analysis of an elbow diffuser, 2000.

S. Mauri, J. Kueny, and F. Avellan, Werle?????Legendre Separation in a Hydraulic Machine Draft Tube, Journal of Fluids Engineering, vol.126, issue.6, pp.976-980, 2004.
DOI : 10.1115/1.1839930
URL : https://hal.archives-ouvertes.fr/hal-00262135

M. Donald, A. Fox, R. , V. Dewoestine, and R. , Effects of swirling inlet flow on pressure recovery conical diffusers, AIAA J, vol.9, issue.10, pp.2014-2018, 1971.

C. Mellen, J. Fröhlich, R. , and W. , Large-Eddy Simulation of the flow over periodic hills, Proceedings of the 16 ? IMACS world congress, 2000.

R. Moser, J. Kim, and N. Mansour, Direct numerical simulation of turbulent channel flow up to Re??=590, Physics of Fluids, vol.11, issue.4, pp.943-945, 1999.
DOI : 10.1063/1.869966

C. Münch, Simulation des grandes échelles d'écoulements turbulents compressibles en conduit courbe chauffé, 2005.

S. Muzaferija, Adaptive Finite Volume method for flow prediction using unstructured meshes and multigrid approach, 1994.

H. Nilsson, M. Page, M. Beaudoin, B. Gschaider, and H. Jasak, The open- FOAM turbomachinery working group, and conclusions from the turbomachinery session of the third openFOAM workshop, 24th IAHR Symposium on Hydraulic Machinery and Systems, 2008.

M. Nituch, S. Sjolander, and M. Head, Summary, Aeronautical Quarterly, vol.XXI, issue.03, pp.207-225, 1978.
DOI : 10.1016/S0065-2156(08)70370-3

I. Orlanski, A simple boundary condition for unbounded hyperbolic flows, Journal of Computational Physics, vol.21, issue.3, pp.251-269, 1976.
DOI : 10.1016/0021-9991(76)90023-1

M. Page and A. Giroux, Turbulent computation in turbine-99 draft tube. 8th annual conference of CFD society of Canada, 2000.

M. Page, A. Giroux, and B. Massé, Turbulent swirling flow computation in a conical diffuser with two commercial codes. CFD'96, Fourth Annual Conference of the CFD Society of Canada, 1996.

M. Page, B. Massé, and A. Giroux, Turbulent swirling flow computations in a conical diffuser. FIDAP User's Meeting, 1997.

J. Paik, F. Sotiropoulos, and M. Sale, Numerical Simulation of Swirling Flow in Complex Hydroturbine Draft Tube Using Unsteady Statistical Turbulence Models, Journal of Hydraulic Engineering, vol.131, issue.6, pp.441-455, 2005.
DOI : 10.1061/(ASCE)0733-9429(2005)131:6(441)

M. Pamiès, P. Weiss, E. Garnier, S. Deck, and P. Sagaut, Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows, Physics of Fluids, vol.21, issue.4, 2009.
DOI : 10.1063/1.3103881

F. Payette, Simulation de l'écoulement turbulent dans les aspiratuers de tubines hydrauliques : Impact des paramètres de modélisation, 2008.

C. Pierce and P. Moin, Method for generating equilibrium swirling inflow conditions

U. Piomelli, Large-eddy simulation of turbulent flows part 1 : Introduction. Lecture series on LES and related techniques theory and applications, 2008.

U. Piomelli, Wall-layer models for large-eddy simulations, Progress in Aerospace Sciences, vol.44, issue.6, pp.437-446, 2008.
DOI : 10.1016/j.paerosci.2008.06.001

H. Pitsch, D. De-lageneste, and L. , Large-eddy simulation of premixed turbulent combustion using a level-set approach, Proceedings of the Combustion Institute, vol.29, issue.2, 2001.
DOI : 10.1016/S1540-7489(02)80244-9

H. Pitsch and H. Steiner, Large-eddy simulation of a turbulent piloted methane/air diffusion flame (Sandia flame D), Physics of Fluids, vol.12, issue.10, pp.2541-2554, 2000.
DOI : 10.1063/1.1288493

P. Roache, Verification of Codes and Calculations, AIAA Journal, vol.36, issue.5, pp.696-702, 1998.
DOI : 10.2514/2.457

P. Roache, Code Verification by the Method of Manufactured Solutions, Journal of Fluids Engineering, vol.124, issue.1, 2002.
DOI : 10.1115/1.1436090

W. Rodi, J. Bonnin, and T. Buchal, (organisateurs) ERCOFTAC Workshop on Data Bases and Testing of Calculation Methods for Turbulent Flows, 1995.

R. Rogallo and P. Moin, Numerical Simulation of Turbulent Flows, Annual Review of Fluid Mechanics, vol.16, issue.1, pp.99-137, 1984.
DOI : 10.1146/annurev.fl.16.010184.000531

A. Ruprecht, T. Helmrich, T. Aschenbrenner, and T. Scherer, Simulation of vortex rope in a turbine draft tube, Proceedings of the Hydraulic Machinery and Systems 21th IAHR Symposium, 2002.

H. Rusche, Computational fluid dynamics of dispersed two-phase flows at high phase fractions, 1996.

P. Sagaut, Introduction à la simulation des grandes échelles pour les écoulements de fluide incompressible, 1998.

P. Sagaut, Large Eddy Simulation for Incompressible Flows. An Introduction, Measurement Science and Technology, vol.12, issue.10, 2001.
DOI : 10.1088/0957-0233/12/10/707

W. Schoppa and F. Hussain, Coherent structure dynamics in near-wall turbulence, Fluid Dynamics Research, vol.26, issue.2, pp.119-139, 2000.
DOI : 10.1016/S0169-5983(99)00018-0

J. Schüler, H. Pitsch, and P. Moin, Large-eddy simulation inflow conditions for coupling with reynolds-averaged flow solvers, AIAA J, vol.42, issue.3, pp.478-484, 2004.

U. Schumann, Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli, Journal of Computational Physics, vol.18, issue.4, pp.376-404, 1975.
DOI : 10.1016/0021-9991(75)90093-5

T. Shih, L. Povinelli, N. Liu, M. Potapczuk, and J. Lumley, A generalized wall function, 1999.

R. Simpson, A model for the backflow mean velocity profile, AIAA Journal, vol.21, issue.1, p.142, 1983.
DOI : 10.2514/3.8040

J. Smagorinsky, GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS, Monthly Weather Review, vol.91, issue.3, pp.99-164, 1963.
DOI : 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2

A. Smirnov, S. Shi, C. , and I. , Random Flow Generation Technique for Large Eddy Simulations and Particle-Dynamics Modeling, Journal of Fluids Engineering, vol.123, issue.2, pp.359-371, 2001.
DOI : 10.1115/1.1369598

P. Spalart, Strategies for turbulent modelling and simulations, Proc. Fourth Intl Symp

. Eng and . Turb, Modelling and Measurements, 1999.

P. Spalart, Strategies for turbulence modelling and simulations, International Journal of Heat and Fluid Flow, vol.21, issue.3, pp.252-263, 2000.
DOI : 10.1016/S0142-727X(00)00007-2

D. Spalding, A Single Formula for the ???Law of the Wall???, Journal of Applied Mechanics, vol.28, issue.3, pp.455-458, 1961.
DOI : 10.1115/1.3641728

R. Susan-resiga, D. Ciocan, G. Anton, I. Avellan, and F. , Analysis of the Swirling Flow Downstream a Francis Turbine Runner, Journal of Fluids Engineering, vol.128, issue.1, pp.177-189, 2006.
DOI : 10.1115/1.2137341

R. Susan-resiga, C. Vu, S. Muntean, D. Ciocan, G. Nennemann et al., Jet control of the draft tube vortex rope in francis turbines at partial discharge, Proceedings of 23st IAHR Symposium, 2006.

L. Temmerman, M. Leschziner, C. Mellen, and J. Fröhlich, Investigation of wall-function approximations and subgrid-scale models in large eddy simulation of separated flow in a channel with streamwise periodic constrictions, International Journal of Heat and Fluid Flow, vol.24, issue.2, pp.157-237, 2003.
DOI : 10.1016/S0142-727X(02)00222-9

F. Tessicini, N. Li, and M. Leschziner, Large-eddy simulation of three-dimensional flow around a hill-shaped obstruction with a zonal near-wall approximation, International Journal of Heat and Fluid Flow, vol.28, issue.5, pp.894-908, 2007.
DOI : 10.1016/j.ijheatfluidflow.2007.01.006

F. Tessicini, L. Temmerman, and M. Leschziner, Approximate near-wall treatments based on zonal and hybrid RANS???LES methods for LES at high Reynolds numbers, International Journal of Heat and Fluid Flow, vol.27, issue.5, pp.789-799, 2006.
DOI : 10.1016/j.ijheatfluidflow.2006.03.024

S. Tridon, D. Ciocan, G. Barre, S. , T. et al., 3D time-resolved PIV measurement in a francis turbine draft tube, Proceedings of 24st IAHR Symposium, 2008.

S. Tridon, D. Ciocan, G. Barre, S. , T. et al., Experimental analysis of the swirling flow in a francis turbine draft tube : Focus on radial velocity component determination [130] Van Der Vorst, H. Bi-CGSTAB : A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, European Journal of Mechanics B/Fluids SIAM J. Scientific Computing, vol.13, issue.2, pp.631-644, 1992.

I. Veloudis, Z. Yang, J. Mc-guirk, P. , and G. , Assessement of the digital filter approach for generating large eddy simulation inlet conditions. Engineering Turbulence Modelling and experiments 6, 2005.

M. Wang and P. Moin, Dynamic wall modeling for large-eddy simulation of complex turbulent flows, Physics of Fluids, vol.14, issue.7, pp.2043-2051, 2002.
DOI : 10.1063/1.1476668

P. Wang and X. Bai, Large eddy simulations of turbulent swirling flows in a dump combustor: a sensitivity study, International Journal for Numerical Methods in Fluids, vol.36, issue.2, pp.99-120, 2005.
DOI : 10.1002/fld.781

L. Wenjun, Y. Jianming, T. Xuelin, W. Yulin, L. et al., Periodical unsteady turbulent flow computation through a draft tube by using LES, ASME, 2000.

G. Winckelmans, H. Jeanmart, C. , and D. , On the comparison of turbulence intensities from large-eddy simulation with those from experiment or direct numerical simulation, Physics of Fluids, vol.14, issue.5, p.1809, 2002.
DOI : 10.1063/1.1466824

A. Yoshizawa and K. Horiuti, A Statistically-Derived Subgrid-Scale Kinetic Energy Model for the Large-Eddy Simulation of Turbulent Flows, Journal of the Physical Society of Japan, vol.54, issue.8, pp.2834-2839, 1985.
DOI : 10.1143/JPSJ.54.2834

R. Zhang, F. Mao, J. Wu, S. Chen, Y. Wu et al., Characteristics and Control of the Draft-Tube Flow in Part-Load Francis Turbine, Journal of Fluids Engineering, vol.131, issue.2, pp.1-13, 2009.
DOI : 10.1115/1.3002318

R. K. Zhang, Q. D. Cai, J. Z. Wu, Y. L. Wu, S. H. Liu et al., THE PHYSICAL ORIGIN OF SEVERE LOW-FREQUENCY PRESSURE FLUCTUATIONS IN GIANT FRANCIS TURBINES, Modern Physics Letters B, vol.19, issue.28n29, pp.1527-1530, 2005.
DOI : 10.1142/S0217984905009821