. .. Modèle-numérique, 2 Interaction directrices-roue à travers un calcul 2D, .3 Influence du point de fonctionnement sur les structures dans l'entrefer 160 7.2.4 Influence du modèle : comparaison SGE/SAS avec la configuration bidimensionnelle

. .. , Résumé : analyse des structures dans l'entrefer, p.161

. .. De-roue, 162 7.3.1 Points de fonctionnement étudiés, Réponse des VIAs à une excitation périodique en entrée

. .. Résumé,

, Conclusions et perspectives, p.169

. .. Conclusions, 170 8.1.2 Phénomènes instationnaires à l'origine de fluctuations de pression à basses fréquences dans la roue

A. De-la-dynamique-des-vias-À-travers-la and S. .. , 171 8.1.4 Instabilités en entrée de la roue

.. .. Modèle-numérique,

. .. Domaine, 121 6.1.3 Influence de la réduction du domaine de calcul

, Analyse de 5 points de fonctionnement et comparaison avec le modèle SAS pour la turbine 1

, Analyse des grandeurs statistiques

. .. De-vias, Analyse des topologies, p.129

, Influence du point de fonctionnement sur les fluctuations de pression dans la turbine 1

, Influence du type de VIAs sur les fluctuations de pression, p.132

, Influence de Q11 sur les fluctuations de pression, p.135

, Influence de n11 sur les fluctuations de pression, p.138

, Analyse comparative du comportement des fluctuations de pression de la turbine 2

.. .. Modèle-numérique,

, Influence de n11 sur les fluctuations de pression, p.143

. .. Conclusions-du-chapitre, , p.147

.. .. Calcul-de-l'interaction,

. .. Interaction, 159 7.2.3 Influence du point de fonctionnement sur les structures dans l'entrefer

, Influence du modèle : comparaison SGE/SAS avec la configuration bidimensionnelle

. .. , Résumé : analyse des structures dans l'entrefer, p.161

, Réponse des VIAs à une excitation périodique en entrée de roue

. .. Points-de-fonctionnement-Étudiés, , p.162

. .. Modèle-d'excitation-en-entrée, , p.163

, Réponse à l'excitation d'entrée

. .. Résumé,

. .. Conclusions, 170 8.1.2 Phénomènes instationnaires à l'origine de fluctuations de pression à basses fréquences dans la roue

, Analyse de la dynamique des VIAs à travers la SGE, p.171

. .. Instabilités-en-entrée-de-la-roue, , p.172

. .. Perspectives,

W. , A. Eckerle, and L. Langston, Horseshoe vortex formation around a cylinder, Journal of Turbomachinery, vol.109, 1986.

A. Hydro and F. , Analyse fréquentielle des mesures au laboratoire : Rappels et définitions. Document interne

H. Amblard, P. Henry, G. Borciani, G. Martin, P. Guiton et al., Comportement des turbines francis et des pompes-turbines à débit partielfonctionnement des turbines francis aux charges partielles. SOCIÉTÉ HYDROTECHNIQUE DE FRANCE Comité technique -Session n ? 127, 1985.

, Ansys cfx-solver modeling guide, ANSYS, 2015.

, Ansys fluent user's guide, ANSYS, 2015.

C. Argyropoulos and N. Markatos, Recent advances on the numerical modelling of turbulent flows, Applied Mathematical Modelling, vol.39, issue.2, pp.693-732, 2015.

T. Barth and D. Jepersen, The design and application of upwind schemes on unstructured meshes, 27th Aerospace Sciences Meeting, 1989.

C. Beaubien, Simulations numériques de l'écoulement turbulent dans un aspirateur de turbine hydraulique, 2013.

P. Benard, G. Balarac, V. Moureau, C. Dobrzynski, G. Lartigue et al., Mesh adaptation for large-eddy simulations in complex geometries, International Journal for Numerical Methods in Fluids, vol.81, issue.12, pp.719-740, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02130426

J. S. Bendat and A. G. Piersol, Random Data : Analysis and Measurement Procedures, 2000.

S. Bouajila, Analyse expérimentale et numérique des écoulements à charge partielle dans les turbines Francis -Étude des vortex inter-aubes, 2018.

S. Bouajila, J. Brammer, E. Flores, C. Ségoufin, and T. Maître, Modelization and simulation of francis turbine inter-blade vortices in partial load conditions, Advances in Hydroinformatics, pp.931-945, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01906000

S. Bouajila, T. D. Colombel, P. Lowys, and T. Maitre, Hydraulic phenomena frequency signature of francis turbines operating in part load conditions, 28th IAHR Symposium on Hydraulic Machinery and Systems, 2016.
URL : https://hal.archives-ouvertes.fr/hal-02011191

C. Brennen, Hydrodynamics of pumps. Hydrodynamics of Pumps, 2011.

P. Bénard, A. Viré, V. Moureau, G. Lartigue, L. Beaudet et al., Large-eddy simulation of wind turbines wakes including geometrical effects, Computers and Fluids, 2018.

P. Guo, Z. Wang, X. Luo, Y. Wang, and J. Zuo, Flow characteristics on the blade channel vortex in the francis turbine, IOP Conference Series : Materials Science and Engineering, vol.129, p.12038, 2016.

D. C. Wilcox, Reassessment of the scale-determining equation for advanced turbulence models, AIAA Journal, vol.26, pp.1299-1310, 1988.

O. Cadot, Introduction à la turbulence, cours de l'ENSTA-ParisTech 2A, Lecture, 2013.
URL : https://hal.archives-ouvertes.fr/cel-01228137

D. ?eli? and H. Ondrá?ka, The influence of disc friction losses and labyrinth losses on efficiency of high head francis turbine, Journal of Physics : Conference Series, vol.579, p.12007, 2015.

J. Chamberland-lauzon, C. Monette, B. Nennemann, M. Melot, S. Birk et al., Ruchonnet. Francis design and prediction technology for flexible operation, 29th IAHR Symposium on Hydraulic Machinery and Systems, 2018.

, Norme Internationale CEI 60193 -Turbines hydrauliques, pompes d'accumulation et pompes-turbines -Essais de réception sur modèle, 1999.

R. Comolet, Mécanique expérimentale des fluides -Tome 2 : Dynamique des fluides réels, 1963.

G. Constantinescu and T. Stoesser, Large-eddy simulation in hydraulics, vol.01, 2013.

A. Coutu, C. Monette, B. Nennemann, J. Lauzon, N. Ruchonnet et al., Specific speed effect on francis runner reliability under various operating conditions, American Journal of Hydropower, Water and Environment Sytems, vol.2, pp.11-15, 2017.

M. Davis, Design of flat plate leading edges to avoid flow separation, Aiaa Journal -AIAA J, vol.18, pp.598-600, 1980.

D. Amorim, Unsteady simulations with a high-order cfd code, 2015.

J. Decaix, A. Müller, F. Avellan, and C. Münch, RANS Computations of a Cavitating Vortex Rope at Full Load, 6th IAHR International Meeting of the Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, 2015.

C. Dobrzynski, MMG3D : User Guide, INRIA, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00681813

J. Donea, A. Huerta, J. Ponthot, and A. Rodríguez-ferran, Arbitrary Lagrangian-Eulerian Methods, vol.1, pp.413-437, 2004.

F. Doussot, Animations des résultats de la SGE

Y. Dubief and F. Delcayre, On coherent-vortex identification in turbulence, Journal of Turbulence -J TURBUL, vol.1, 2000.

C. Duprat, Unsteady numerical simulation of turbulent flow in hydraulic draft tube, with the aim of improving the efficiency, 2010.
URL : https://hal.archives-ouvertes.fr/tel-00540181

L. R. Eremeef, Turbines hydrauliques essais -cavitation. Techniques de l'ingénieur Frottement et usure, 2009.

J. Feng, X. Luo, G. Zhu, and G. Wu, Investigation on disk friction loss and leakage effect on performance in a francis model turbine, Advances in Mechanical Engineering, vol.9, issue.8, p.1687814017723792, 2017.

H. Foroutan, Simulation, Analysis, and Mitigation of Vortex Rope Formation in the Draft Tube of Hydraulic Turbines, 2014.

M. Frigo and S. G. Johnson, The design and implementation of FFTW3, Proceedings of the IEEE, vol.93, issue.2, pp.216-231, 2005.

M. Germano, U. Piomelli, P. Moin, and W. H. Cabot, A dynamic subgrid scale eddy viscosity model, Physics of Fluids A : Fluid Dynamics, vol.3, issue.7, pp.1760-1765, 1991.

L. Guedot, G. Lartigue, and V. Moureau, Design of high-order implicit filters on unstructured grids for the identification of large-scale features in large-eddy simulations, Ercoftac series, vol.20, pp.81-87, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01612110

J. Hart, Comparison of turbulence modeling approaches to the simulation of a dimpled sphere, Procedia Engineering, vol.147, pp.68-73, 2016.

P. Henry, M. Wegner, J. E. Graeser, ;. La, and . Blanche, Analyse expérimentale de la stabilité hydraulique de la turbine francisà charge partielle, vol.2, pp.3-1982, 1982.

, International Energy Agency. Harnessing Variable Renewables, 2011.

, International Energy Agency. The Power of Transformation, 2014.

Y. Ito, A. M. Shih, and B. K. Soni, Reliable isotropic tetrahedral mesh generation based on an advancing front method, IMR, 2004.

W. Jones and B. Launder, The prediction of laminarization with a two-equation model of turbulence, International Journal of Heat and Mass Transfer, vol.15, issue.2, pp.301-314, 1972.

A. Kolmogoroff, On degeneration of isotropic turbulence in an incompressible viscous liquid. Comptes Rendus (Doklady) de l'Académie des Sciences de l'URSS, p.31, 1941.

T. V. Kármán, Ueber den mechanismus des widerstandes, den ein bewegter körper in einer flüssigkeit erfährt, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-Physikalische Klasse, pp.509-517, 1911.

P. Lagrée, Boundary layer separation and asymptotics from 1904 to 1969, Comptes Rendus Mécanique, vol.345, issue.9, pp.613-619, 2017.

D. K. Lilly, Lectures in sub-synoptic scales of motion and two-dimensional turbulence, National Center for Atmospheric Research BOULDER, 1970.

X. Liu, Y. Luo, A. Presas, Z. Wang, and L. Zhou, Cavitation effects on the structural resonance of hydraulic turbines : Failure analysis in a real francis turbine runner, Energies, vol.11, issue.9, 2018.

M. V. Magnoli, Comparison of model measured runner blade pressure fluctuations with unsteady flow analysis predictions, 28th IAHR Symposium on Hydraulic Machinery and Systems, 2016.

N. Maheu, V. Moureau, P. Domingo, F. Duchaine, and G. Balarac, Large-eddy simulations of flow and heat transfer around a low-mach turbine blade, vol.20, 2012.

M. Malandain, N. Maheu, and V. Moureau, Optimization of the deflated conjugate gradient algorithm for the solving of elliptic equations on massively parallel machines, Journal of Computational Physics, vol.238, pp.32-47, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01657525

O. Manole, P. Labbé, J. Dompierre, and J. Trépanier, Anisotropic hybrid mesh adaptation using a metric field, 16th AIAA Computational Fluid Dynamics Conference, 2003.

B. Meddins, 2 -discrete signals and systems, Introduction to Digital Signal Processing, pp.16-40, 2000.

F. Menter, Zonal two equation k-w turbulence models for aerodynamic flows, AIAA Paper, 1993.

F. Menter and Y. Egorov, The scale-adaptive simulation method for unsteady turbulent flow predictions. part 1 : Theory and model description. Flow, Turbulence and Combustion, vol.85, pp.113-138, 2010.

P. Moin and J. Kim, Tackling turbulence with supercomputers, Scientific American, vol.276, pp.62-68, 1997.

C. Monette, H. Marmont, J. Chamberland-lauzon, A. Skagerstrand, A. Coutu et al., Cost of enlarged operating zone for an existing francis runner, IOP Conference Series : Earth and Environmental Science, vol.49, p.72018, 2016.

V. Moureau, P. Domingo, and L. Vervisch, Design of a massively parallel cfd code for complex geometries, Comptes Rendus Mécanique, vol.339, issue.2, pp.141-148, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01672172

V. Moureau, P. Domingo, and L. Vervisch, From large-eddy simulation to direct numerical simulation of a lean premixed swirl flame : Filtered laminar flame-pdf modeling, Combustion and Flame -COMBUST FLAME, vol.158, pp.1340-1357, 2011.
URL : https://hal.archives-ouvertes.fr/hal-01672168

O. Métais, Large eddy simulation of turbulence : Fundamentals and applications, 2018.

A. Müller, A. Favrel, C. Landry, K. Yamamoto, and F. Avellan, On the physical mechanisms governing self-excited pressure surge in francis turbines, IOP Conference Series : Earth and Environmental Science, vol.22, issue.3, p.32034, 2014.

T. Neidhardt, A. Jung, S. Hyneck, and J. Gummer, An alternative approach to the von karman vortex problem in modern hydraulic turbines, 2017.

C. Nicolet, N. Ruchonnet, and F. Avellan, One-dimensional modeling of rotor stator interaction in francis pump-turbine, Proceedings of the 11th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2006.

C. Nicolet, A. Zobeiri, P. Maruzewski, and F. Avellan, On the upper part load vortex rope in francis turbine : Experimental investigation, IOP Conference Series : Earth and Environmental Science, vol.12, issue.1, p.12053, 2010.

F. Nicoud and F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion, vol.62, pp.183-200, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00910373

M. Nishi, A. Zobeiri, S. Matsunagai, T. Kubotaf, and Y. Senoo, Study on swirl flow and surge in an elbow type draft tube, AIRH 10th Symposium 10E, Hydraulic Machinery and Equipment Associated with Energy Systems, vol.1, 1980.

L. Ntnu, Francis-99 workshop, 2014.

N. Odier, G. Balarac, and C. E. Corre, Numerical analysis of the flapping mechanism for a two-phase coaxial jet, International Journal of Multiphase Flow, vol.106, pp.164-178, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01824012

O. Pacot, C. Kato, Y. Guo, Y. Yamade, and F. Avellan, Large eddy simulation of the rotating stall in a pump-turbine operated in pumping mode at a part-load condition, Journal of Fluids Engineering, vol.138, 2016.

Y. Paquette, Fluid-Structure Interaction in Cavitation Erosion. Theses, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01734896

S. Pasche, F. Avellan, and F. Gallaire, Part load vortex rope as a global unstable mode, Journal of Fluids Engineering, p.139, 2017.

U. Piomelli, W. H. Cabot, P. Moin, and S. Lee, Subgrid scale backscatter in turbulent and transitional flows, Physics of Fluids A : Fluid Dynamics, vol.3, issue.7, pp.1766-1771, 1991.

M. Pluviose and C. Périlhon, Turbomachines mécanisme de la conversion d'énergie. Techniques de l'ingénieur Machines hydrauliques et thermiques : fondamentaux et concepts innovants, 2002.

H. G. Poll, J. C. Zanutto, and W. Ponge-ferreira, Hydraulic power plant machine dynamic diagnosis, Shock and Vibration, vol.13, pp.409-427, 2006.

L. Richardson, Weather prediction by numerical process, 1922.

H. Ritchie and M. Roser, Co 2 and greenhouse gas emissions. Our World in Data, 2019.

N. Ruchonnet, S. Alligné, C. Nicolet, and F. Avellan, Cavitation influence on hydroacoustic resonance in pipe, Journal of Fluids and Structures, 2011.

N. Ruchonnet, C. Nicolet, S. Alligné, and F. Avellan, Experimental investigation of cavitation influence on hydroacoustic resonance in pipe, 3rd Meeting IAHR Workgroup on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, 2009.

S. , R. Martinez, and W. Hughes, Bringing variable renewable energy up to scale : options for grid integration using natural gas and energy storage, ESMAP Technical Report. World Bank Group, 2015.

O. Sahni, A. Ovcharenko, K. Chitale, K. Jansen, and M. Shephard, Parallel anisotropic mesh adaptation with boundary layers for automated viscous flow simulations, Engineering with Computers, p.33, 2016.

P. Sarkar, G. Ghigliotti, M. Fivel, and J. Franc, Numerical investigation of the dynamics of pressure loading on a solid boundary from a collapsing cavitation bubble, 10th International Symposium on Cavitation, 2018.
URL : https://hal.archives-ouvertes.fr/hal-02066205

U. Seidel, B. Hübner, J. Löfflad, and P. Faigle, Evaluation of rsi-induced stresses in francis runners, IOP Conference Series : Earth and Environmental Science, vol.15, issue.5, p.52010, 2012.

J. Smagorinsky, General circulation experiments with the primitive equations, Monthly Weather Review, vol.91, issue.3, pp.99-164, 1963.

W. Song, H. Wang, and J. Li, Simulated calculation of interblade vortex in francis turbine's whole flow passage, 2011 International Conference on Consumer Electronics, Communications and Networks (CECNet), 2011.

C. Trivedi, M. Cervantes, and O. Dahlhaug, Experimental and numerical studies of a high-head francis turbine : A review of the francis-99 test case, Energies, vol.9, p.74, 2016.

H. Tryggeson, Analytical vortex solutions to Navier-Stokes equation, 2007.

F. Van-der-bos and B. Geurts, Commutator errors in the filtering approach to largeeddy simulation, Physics of Fluids, vol.17, p.35108, 2005.

H. Versteeg and W. Malalasekera, An introduction to computational fluid dynamicsthe finite volume method, 1995.

J. Wack and S. Riedelbauch, Numerical simulations of the cavitation phenomena in a francis turbine at deep part load conditions, Journal of Physics : Conf. Series, vol.656, issue.1, p.12074, 2015.

D. C. Wilcox, Comparison of two-equation turbulence models for boundary layers with pressure gradient, AIAA Journal, vol.31, issue.8, pp.1414-1421, 1993.

S. Wilhelm, Étude des pertes de charge dans un aspirateur de turbine bulbe par simulations numériques instationnaires, 2016.

S. Wilhelm, G. Balarac, O. Métais, and C. Ségoufin, Analysis of Head Losses in a Turbine Draft Tube by Means of 3D Unsteady Simulations. Flow, Turbulence and Combustion, vol.97, pp.1255-1280, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01339961

, World Energy Council. World energy resources, 2016.

K. Yamamoto, Hydrodynamics of Francis turbine operation at deep part load condition, 2017.

K. Yamamoto, A. Müller, A. Favrel, C. Landry, and F. Avellan, Pressure measurements and high speed visualizations of the cavitation phenomena at deep part load condition in a francis turbine, IOP Conference Series : Earth and Environmental Science, vol.22, issue.2, p.22011, 2014.

K. Yamamoto, A. Müller, A. Favrel, C. Landry, and F. Avellan, Numerical and experimental evidence of the inter-blade cavitation vortex development at deep part load operation of a francis turbine, IOP Conference Series : Earth and Environmental Science, vol.49, p.82005, 2016.

K. Yamamoto, A. Müller, A. Favrel, C. Landry, and F. Avellan, Flow characteristics and influence associated with inter-blade cavitation vortices at deep part load operations of a francis turbine, Journal of Physics : Conference Series, vol.813, p.12029, 2017.

X. Yexiang, W. Zhengwei, and Y. Zongguo, Experimental and numerical analysis of blade channel vortices in a francis turbine runner. Engineering Computations, vol.28, pp.154-171, 2011.

Y. Zeng, L. Zhang, J. Guo, Y. Guo, Q. Pan et al., Efficiency limit factor analysis for the francis-99 hydraulic turbine, Journal of Physics : Conference Series, vol.782, p.12008, 2017.

Y. Zhang, K. Liu, H. Xian, and X. Du, A review of methods for vortex identification in hydroturbines, Renewable and Sustainable Energy Reviews, vol.81, pp.1269-85, 2018.

L. Zhou, M. Liu, Z. Wang, D. Liu, and Y. Zhao, Investigation of channel vortices in francis turbines, 28th IAHR Symposium on Hydraulic Machinery and Systems, vol.49, pp.1030-1069, 2016.

L. Zhou, M. Liu, Z. Wang, D. Liu, and Y. Zhao, Numerical simulation of the blade channel vortices in a francis turbine runner, Engineering Computations, vol.34, pp.364-376, 2017.

Z. Zuo, Numerical predictions of the incipient and developed interblade vortex lines of a model francis turbine by cavitation calculations, Advances in Mechanical Engineering, 2013.

P. Zwart, A. Gerber, and T. Belamr, A two-phase flow model for predicting cavitation dynamics, Proceedings of the fifth international conference on multiphase flow, 2004.

, International Journal of Fluid Machinery and Systems

F. Doussot, G. Balarac, J. Brammer, and M. O. Ségoufin, 29th IAHR Symp. on Hydraulic Machinery and Systems, 2018.

P. Grunewald and . Diakonova, Energy Research & Social Science, vol.38, pp.58-66, 2018.

J. Wack and S. Riedelbauch, Journal of Physics: Conf. Series, vol.656, p.12074, 2015.

L. Zhou, M. Liu, Z. Wang, D. Liu, and Y. Zhao, 28th IAHR Symposium on Hydraulic Machinery and Systems, vol.49, pp.1030-1069, 2016.

K. Yamamoto, Hydrodynamics of Francis turbine operation at deep part load condition Ph, 2017.

L. Zhou, M. Liu, Z. Wang, D. Liu, and Y. Zhao, Engineering Computations, vol.34, pp.364-376, 2016.

S. Bouajila, D. Colombel, T. , L. , P. Maitre et al., 28th IAHR Symp. on Hydraulic Machinery and Systems, vol.49, pp.1010-1029, 2016.

S. Bouajila, J. Brammer, E. Flores, C. Ségoufin, and T. Maître, Advances in Hydroinformatics, pp.931-945, 2017.

Y. Zhang, K. Liu, and X. H. Du, Renewable and Sustainable Energy Reviews, vol.81, pp.1269-85, 2018.

P. Sagaut and C. Meneveau, Large Eddy Simulation for Incompressible Flows: An Introduction Scientific Computation, p.9783540263449, 2006.

L. Guedot, G. Lartigue, and V. Moureau, Physics of Fluids, vol.27, p.45107, 2015.