. Cheneau, We start from the Tulip flame obtained by ignition at the full pilot injection (? ign 100, 2015.

, A first bifurcation occurs leading to a Vflame. The flame keeps a V-shape when stabilizing ? 35 and ? 20 . Then, going down to ? 00 , a second bifurcation occurs

, Increasing ? back, this M-shape is preserved up to full pilot injection : ? 20 , ? 35 , ? 60 and ? 100 ) show very similar flame shapes and structures

, An additional point has been simulated from the V-flame at ? 60 : increasing ? up to ? 100 bis , the flame keeps a V-shape

B. and W. Sirignano, Droplet vaporization model for spray combustion calculations, To sum-up, two bifurcations occur during the whole cycle, leading to a remarkable tri-stable point for full pilot injection : ? ign 100 , ? 100 and ? 100 bis . Moreover, Références Abramzon, vol.32, p.112, 1989.

T. Agarwal, Development of diagnostics for the experimental studies of ignition in sprays, p.22, 2013.
URL : https://hal.archives-ouvertes.fr/tel-00969174

P. Albrecht, S. Bade, A. Lacarelle, C. O. Paschereit, and E. Gutmark, Instability control by premixed pilot flames, Journal of Engineering for Gas Turbines and Power, vol.132, issue.4, p.132, 2010.

D. W. Bahr, Technology for the design of high temperature rise combustors, Journal of Propulsion and Power, vol.3, issue.2, pp.179-186, 1987.

S. Balachandar, A scaling analysis for point-particle approaches to turbulent multiphase flows, Special Issue : Point-Particle Model for Disperse Turbulent Flows. (p. xiv, vol.35, p.42, 2009.

D. Ballal and A. Lefebvre, Flame propagation in heterogeneous mixtures of fuel droplets, fuel vapor and air, Symposium (International) on Combustion, vol.18, issue.1, p.46, 1981.

P. Baranger, M. Orain, and F. Grisch, Fluorescence spectroscopy of kerosene vapour : application to gas turbines, 43rd AIAA Aerospace Sciences Meeting and Exhibit, p.9, 2005.

S. Barbosa, Etude expérimentale de la dynamique de combustion d'un injecteur pauvre pré-mélangé étage swirlé, vol.17, p.81, 2008.

S. Barbosa, P. Scouflaire, and S. Ducruix, Characterization of the reactive flow field dynamics in a gas turbine injector using high frequency PIV. ArXiv e-prints, p.17, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00294938

S. Barbosa, P. Scouflaire, and S. Ducruix, Time resolved flowfield, flame structure and acoustic characterization of a staged multi-injection burner, Proceedings of the Combustion Institute, vol.32, issue.2, p.17, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00497672

S. Barbosa, P. Scouflaire, and S. Ducruix, Time resolved flowfield, flame structure and acoustic characterization of a staged multiinjection burner, Proceedings of the Combustion Institute, vol.32, issue.2, p.134, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00497672

J. Bardina, J. H. Ferziger, and W. C. Reynolds, Improved subgrid scale models for Large Eddy Simulation, 13th Fluid and Plasma Dynamics Conference, p.36, 1980.

H. Baya-toda, LES modeling and experimental study LES modeling and experimental study of wall-bounded flows in complex geometries, p.36, 2011.

R. Bilger, S. Stårner, and R. Kee, On reduced mechanisms for methane-air combustion in nonpremixed flames, Combustion and Flame, vol.80, issue.2, p.125, 1990.

M. Boger, D. Veynante, H. Boughanem, and A. Trouvé, Direct numerical simulation analysis of flame surface density concept for large eddy simulation of turbulent premixed combustion, Symposium (International) on Combustion, vol.27, issue.1, p.39, 1998.

M. Boileau, SGE de l'allumage diphasique des foyers aeronautiques, p.50, 2007.

K. Bray, P. A. Libby, and J. Moss, Unified modeling approach for premixed turbulent combustion-part I : General formulation, Combustion and Flame, vol.61, issue.1, p.39, 1985.

K. Bray and J. Moss, A unified statistical model of the premixed turbulent flame, Acta Astronautica, vol.4, issue.3, p.39, 1977.

T. Butler and P. O'rourke, A numerical method for two dimensional unsteady reacting flows, Symposium (International) on Combustion, vol.16, issue.1, p.40, 1977.

M. Cailler, Virtual chemical mechanisms optimized to capture pollutant formation in turbulent flames, p.158, 2018.
URL : https://hal.archives-ouvertes.fr/tel-02283226

M. Cailler, N. Darabiha, D. Veynante, and B. Fiorina, Buildingup virtual optimized mechanism for flame modeling, Proceedings of the Combustion Institute, vol.36, issue.1, p.158, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01541938

S. Candel, Mécanique des fluides : cours. Dunod, p.81, 2001.

F. Charlette, C. Meneveau, and D. Veynante, A power-law flame wrinkling model for LES of premixed turbulent combustion part I : nondynamic formulation and initial tests, Combustion and Flame, vol.131, issue.1-2, p.40, 2002.

F. Charlette, C. Meneveau, and D. Veynante, A power-law flame wrinkling model for LES of premixed turbulent combustion part II : dynamic formulation, Combustion and Flame, vol.131, issue.1-2, p.135, 2002.

R. Chen, D. J. , J. Kelly, M. Namazian, and R. W. Schefer, A comparison of bluff-body and swirl-stabilized flames, Combustion Science and Technology, vol.71, issue.4-6, p.5, 1990.

B. Cheneau, A. Vié, and S. Ducruix, Large eddy simulations of a liquid fuel swirl burner : Flame characterization for pilot and multipoint injection strategies, Combustion, Fuels and Emissions(56680), V04AT04A064-V04AT04A064. (p. xvii, 105, vol.4, p.137, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01863988

B. Cheneau, A. Vié, and S. Ducruix, Characterization of the hysteresis cycle in a two-stage liquid-fueled swirled burner through numerical simulation, Proceedings of the Combustion Institute, p.131, 2019.
URL : https://hal.archives-ouvertes.fr/hal-02415520

O. Colin, Simulations aux grandes échelles de la combustion turbulente prémélangée dans les statoréacteurs, vol.52, p.53, 2000.

O. Colin, F. Ducros, D. Veynante, and T. Poinsot, A thickened flame model for large eddy simulations of turbulent premixed combustion, Physics of Fluids, vol.12, p.135, 1994.

O. Colin and M. Rudgyard, Development of high-order Taylor-Galerkin schemes for LES, Journal of Computational Physics, vol.162, issue.2, p.113, 2000.

L. Cunha-caldeira-mesquita, A. Vié, and S. Ducruix, Twophase flow large eddy simulations of a staged multipoint swirling burner : comparisons between euler-euler and euler-lagrange descriptions. GT2017-64489, Proceedings of the ASME 2017 : Turbine Technical Conference and Exposition, p.158, 2017.

L. Cunha-caldeira-mesquita, A. Vié, and S. Ducruix, Large eddy simulation of a two-phase staged swirling burner using an euler-lagrange approach : Validation of the injection strategy, Proceedings of the ASME 2018 : Turbine Technical Conference and Exposition, p.158, 2018.

P. Dagaut, On the kinetics of hydrocarbons oxidation from natural gas to kerosene and diesel fuel, Physical Chemistry Chemical Physics, vol.4, issue.11, p.41, 2002.

P. Dagaut and M. Cathonnet, The ignition, oxidation, and combustion of kerosene : A review of experimental and kinetic modeling, Progress in Energy and Combustion Science, vol.32, issue.1, p.55, 2006.
URL : https://hal.archives-ouvertes.fr/hal-02021199

S. Dhanuka, J. Driscoll, and H. Mongia, /06/21). Instantaneous flow structures in a reacting gas turbine combustor, 44th References AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. American Institute of Aeronautics and Astronautics, p.9, 2008.

S. K. Dhanuka, An experimental study of the stable and unstable operation of an LPP gas turbine combustor, p.9, 2008.

J. Dombard, B. Leveugle, L. Selle, J. Reveillon, T. Poinsot et al., Modeling heat transfer in dilute two-phase flows using the mesoscopic eulerian formalism, International Journal of Heat and Mass Transfer, vol.55, issue.5, p.46, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00811401

F. Ducros, F. Nicoud, and T. Poinsot, Wall-adapting local eddyviscosity models for simulations in complex geometries, Proceedings of 6th ICFD Conference on Numerical Methods for Fluid Dynamics, p.36, 1998.

S. Ducruix, T. Schuller, D. Durox, and S. Candel, Combustion dynamics and instabilities : Elementary coupling and driving mechanisms, Journal of Propulsion and Power, vol.19, issue.5, p.132, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00183382

J. K. Dukowicz, A particle-fluid numerical model for liquid sprays, Journal of Computational Physics, vol.35, issue.2, p.44, 1980.

D. Durox, J. P. Moeck, J. Bourgouin, P. Morenton, M. Viallon et al., Flame dynamics of a variable swirl number system and instability control, Combustion and Flame, vol.160, issue.9, p.104, 2013.

D. Durox, K. Prieur, T. Schuller, and S. Candel, Different flame patterns linked with swirling injector interactions in an annular combustor, Journal of Engineering for Gas Turbines and Power, vol.138, issue.10, p.133, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01345634

D. Durox, T. Schuller, N. Noiray, and S. Candel, Experimental analysis of nonlinear flame transfer functions for different flame geometries, Proceedings of the Combustion Institute, vol.32, issue.1, p.132, 2009.

T. Edwards, M. Colket, N. Cernansky, F. Dryer, F. Egolfopoulos et al., Development of an experimental database and kinetic models for surrogate jet fuels, 45th AIAA Aerospace Sciences Meeting and Exhibit, p.41, 2007.

F. Fichot, F. Lacas, D. Veynante, and S. Candel, One-dimensional propagation of a premixed turbulent flame with a balance equation for the flame surface density, Combustion Science and Technology, vol.90, issue.1-4, p.39, 1993.

F. L. Filho, G. Kuenne, M. Chrigui, A. Sadiki, and J. Janicka, A consistent artificially thickened flame approach for spray combustion using les and the fgm chemistry reduction method : Validation in lean partially pre-vaporized flames, Combustion and Flame, vol.184, p.50, 2017.

B. Fiorina, R. Baron, O. Gicquel, D. Thevenin, S. Carpentier et al., Modelling non-adiabatic partially premixed flames using flame-prolongation of ildm, Combustion Theory and Modelling, vol.7, issue.3, p.38, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00256666

B. Fiorina, R. Vicquelin, P. Auzillon, N. Darabiha, O. Gicquel et al., A filtered tabulated chemistry model for les of premixed combustion, Combustion and Flame, vol.157, issue.3, p.39, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00472611

M. Foust, D. Thomsen, R. Stickles, C. Cooper, and W. Dodds, /06/22). Development of the ge aviation low emissions taps combustor for next generation aircraft engines, 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, p.9, 2012.

B. Franzelli, B. Fiorina, and N. Darabiha, A tabulated chemistry method for spray combustion, Proceedings of the Combustion Institute, vol.34, p.38, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01272971

B. Franzelli, E. Riber, M. Sanjosé, and T. Poinsot, A two-step chemical scheme for kerosene-air premixed flames, Combustion and Flame, vol.157, issue.7, p.135, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01272968

B. Franzelli, A. Vié, M. Boileau, B. Fiorina, and N. Darabiha, Large eddy simulation of swirled spray flame using detailed and tabulated chemical descriptions. Flow, Turbulence and Combustion, vol.98, p.135, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01480274

B. Franzelli, A. Vié, B. Fiorina, and N. Darabiha, Large eddy simulation of swirling kerosene/air spray flame using tabulated chemistry, ASME Turbo Expo 2013 : Turbine Technical Conference and Exposition, vol.1, p.115, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01272959

S. Freitag and C. Hassa, Spray characteristics of a kerosene jet in cross flow of air at elevated pressure, 22nd European Conference on Liquid Atomization and Spray Systems, 2008.

D. Galley, Etude de la stabilisation de flammes turbulentes prévaporisées prémélangées pauvres, p.5, 2006.

D. Galley, S. Ducruix, F. Lacas, and D. Veynante, Mixing and stabilization study of a partially premixed swirling flame using laser induced fluorescence, Combustion and Flame, vol.158, issue.1, p.134, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00644940

N. García-rosa, Phenomenes d'allumage d'un foyer de turbomachine en conditions de haute altitude, p.9, 2008.

E. Garnier, P. Sagaut, and N. Adams, Large Eddy Simulation for Compressible Flows. Scientific Computation, p.36, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01313539

A. Ghani and M. Gonzalez-flesca, Simulation, experimentation and modeling contributions to the analysis of high frequency combustion instabilities in liquid propellant rocket-engines, vol.100, p.159, 2015.

F. Grinstein, L. Margolin, and W. Rider, Implicit Large Eddy Simulation : Computing Turbulent Fluid Dynamics, p.36, 2007.

T. F. Guiberti, D. Durox, L. Zimmer, and T. Schuller, Analysis of topology transitions of swirl flames interacting with the combustor side wall, Combustion and Flame, vol.162, issue.11, pp.4342-4357, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01226366

A. Gupta, D. Lilley, and N. Syred, Swirl flows. Energy and engineering science series, p.5, 1984.

L. Hakim, Dynamics of transcritical coaxial flames in high-frequency transverse acoustic fields : Application to liquid rocket engine instabilities, p.159, 2013.

G. Hannebique, Etude de la structure des flammes diphasiques dans les brleurs aéronautiques, p.54, 2013.

G. Hannebique, P. Sierra, E. Riber, and B. Cuenot, Large eddy simulation of reactive two-phase flow in an aeronautical multipoint burner. Flow, Turbulence and Combustion, vol.90, p.138, 2013.

S. Hermeth, G. Staffelbach, L. Y. Gicquel, V. Anisimov, C. Cirigliano et al., Bistable swirled flames and influence on flame transfer functions, Combustion and Flame, vol.161, issue.1, p.133, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00930081

S. Honnet, K. Seshadri, U. Niemann, and N. Peters, A surrogate fuel for kerosene, Proceedings of the Combustion Institute, vol.32, issue.1, p.41, 2009.

Y. Huang and V. Yang, Dynamics and stability of leanpremixed swirl-stabilized combustion, Progress in Energy and Combustion Science, vol.35, issue.4, p.5, 2009.

Y. Huang and V. Yang, Dynamics and stability of leanpremixed swirl-stabilized combustion, Progress in Energy and Combustion Science, vol.35, issue.4, p.133, 2009.

M. Ihme and H. Pitsch, Prediction of extinction and reignition in nonpremixed turbulent flames using a flamelet/progress variable model : 2. application in LES of sandia flames D and E, Combustion and Flame, vol.155, issue.1, p.39, 2008.

F. Jaegle, Large eddy simulation of evaporating sprays in complex geometries using Eulerian and Lagrangian methods, p.9, 2009.
URL : https://hal.archives-ouvertes.fr/tel-00452501

F. Jaegle, J. Senoner, M. Garcia, F. Bismes, R. Lecourt et al., Eulerian and lagrangian spray simulations of an aeronautical multipoint injector, Proceedings of the Combustion Institute, vol.33, p.105, 2011.

T. Jaravel, Prediction of pollutants in gas turbines using Large Eddy Simulation, p.158, 2017.

P. Jenny, D. Roekaerts, and N. Beishuizen, Modeling of turbulent dilute spray combustion, Progress in Energy and Combustion Science, vol.38, issue.6, p.50, 2012.

A. Kaufmann, M. Moreau, O. Simonin, and J. Helie, Comparison between Lagrangian and mesoscopic Eulerian modelling approaches for inertial particles suspended in decaying isotropic turbulence, J. Comput. Phys, vol.227, p.46, 2008.

J. C. Keck and D. Gillespie, Rate-controlled partial-equilibrium method for treating reacting gas mixtures, Combustion and Flame, vol.17, issue.2, p.38, 1971.

A. R. Kernstein and C. K. Law, Percolation in combustion sprays I : Transition from cluster combustion to percolate combustion in nonpremixed sprays, Symposium (International) on Combustion, p.151, 1982.

A. R. Kerstein, W. T. Ashurst, and F. A. Williams, Field equation for interface propagation in an unsteady homogeneous flow field, Physical Review A, vol.37, issue.7, p.39, 1988.

K. Kuo, Principles of combustion, p.151, 2005.

N. Lamarque, Schemas numeriques et conditions limites pour la simulation aux grandes echelles de la combustion diphasique dans les foyers d'hélicoptere, vol.9, p.52, 2007.

T. Lancien, Étude numérique de l'allumage diphasique de foyers annulaires multi-brûleurs, p.99, 2018.

T. Lancien, N. Dumont, K. Prieur, D. Durox, S. Candel et al., Uncertainty quantification of injected droplet size in mono-dispersed eulerian simulations, 9th International Conference on Multiphase Flow, p.111, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01780997

J. Lavedrine, SGE de l'écoulement diphasique dans des modèles d'injecteur de moteurs aéronautiques, 2008.

A. Lefebvre, Atomization and Sprays. Combustion, vol.8, 1989.

A. Lefebvre, Gas Turbine Combustion, p.104, 1999.

A. Lefebvre and D. Ballal, Gas Turbine Combustion : Alternative Fuels and Emissions, 2010.

J. Légier, Simulations numériques des instabilités de combustion dans les foyers aéronautiques, p.55, 2001.

J. Legier, T. Poinsot, and D. Veynante, Dynamically thickened flame les model for premixed and non-premixed turbulent combustion, Proc. of the summer program, p.40, 2000.

G. Li and E. J. Gutmark, Boundary condition effects on nonreacting and reacting flows in a mul-tiswirlcombustor, AIAA journal, vol.44, issue.3, p.7, 2006.

T. Lieuwen and V. Yang, Combustion Instabilities in Gas Turbine Engines : Operational Experience, Fundamental Mechanisms, and Modeling, Progress in Astronautics and Aeronautics, vol.210, p.104, 2005.

I. V. Litvinov, S. I. Shtork, P. A. Kuibin, S. V. Alekseenko, and K. Hanjalic, Experimental study and analytical reconstruction of precessing vortex in a tangential swirler, International Journal of Heat and Fluid Flow, vol.42, issue.0, p.6, 2013.

T. Lu and C. K. Law, A directed relation graph method for mechanism reduction, Proceedings of the Combustion Institute, vol.30, issue.1, p.38, 2005.

O. Lucca-negro and T. O'doherty, Vortex breakdown : a review, Progress in Energy and Combustion Science, vol.27, issue.4, p.5, 2001.

J. Luche, M. Reuillon, J. Boettner, and M. Cathonnet, Reduction of large detailed kinetic mechanisms : application to kerosene/air combustion, Combustion Science and Technology, vol.176, issue.11, p.55, 2004.

P. Malbois, Experimental investigation by laser diagnostics of the kerosene/air mixing and high-pressure swirl-stabilized lean premixed combustion from a low-NOx injection system, p.9, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01768863

P. Malbois, E. Salaün, F. Frindt, G. Cabot, L. Bouheraoua et al., Simultaneous equivalence ratio and flame structure measurements in a lean-premixed aero-engine injection system under relevant operating conditions, European Combustion Meeting, p.9, 2017.

P. Malbois, E. Salaün, F. Frindt, G. Cabot, B. Renou et al., Experimental investigation with optical diagnostics of a lean-premixed aero-engine injection system under relevant operating conditions, ASME Turbo Expo 2017 : Turbine Technical Conference and Exposition, vol.4, p.9, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01668918

G. Marchione, S. Ahmed, and E. Mastorakos, Ignition of turbulent swirling n-heptane spray flames using single and multiple sparks, Combustion and Flame, vol.156, issue.1, p.94, 2009.

L. Martinez, SGE de l'injection de carburant liquide dans les moteurs à combustion interne, p.53, 2009.

L. Martinez, A. Benkenida, and B. Cuenot, A model for the injection boundary conditions in the context of 3d simulation of diesel spray : Methodology and validation, Fuel, vol.89, issue.1, p.50, 2010.

E. Masi and O. Simonin, Algebraic-closure-based moment method for unsteady eulerian simulations of non-isothermal particle-laden turbulent flows at moderate stokes numbers in dilute regime, Flow, turbulence and combustion, vol.92, issue.1-2, p.46, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01335782

E. Masi, O. Simonin, E. Riber, P. Sierra, and L. Gicquel, Development of an algebraic-closure-based moment method for unsteady Eulerian simulations of particle-laden turbulent flows in very dilute regime, International Journal of Multiphase Flow, vol.58, p.46, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01010316

M. R. Maxey and J. J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow, The Physics of Fluids, vol.26, issue.4, p.45, 1983.

U. Meier, S. Freitag, J. Heinze, L. Lange, E. Magens et al., Characterization of lean burn module air blast pilot injector with laser techniques, Journal of Engineering for Gas Turbines and Power, vol.135, issue.12, p.10, 2013.

U. Meier, J. Heinze, L. Lange, C. Hassa, L. Rackwitz et al., Characterisation of the combustion performance of low emission fuel injectors with laser measurements, CEAS Aeronautical Journal, vol.3, issue.1, p.10, 2012.

U. Meier, L. Lange, J. Heinze, C. Hassa, S. Sadig et al., Optical methods for studies of self-excited oscillations and the effect of dampers in a high pressure single sector combustor, Journal of Engineering for Gas Turbines and Power, vol.137, issue.7, p.10, 2015.

Y. Mery, Mechanisms of instabilities of high-frequency combustion and application in engines-rockets -Non confidentiel, p.159, 2010.

P. Moin and S. V. Apte, Large-eddy simulation of realistic gas turbine combustors, AIAA journal, vol.44, issue.4, p.7, 2006.

M. Moreau, O. Simonin, and B. Bédat, Development of gas-particle References, 2010.

. Euler-euler, LES approach : a priori analysis of particle sub-grid models in homogeneous isotropic turbulence. Flow Turbulence and Combustion, vol.84, p.129

F. Nicoud, H. Baya-toda, O. Cabrit, S. Bose, and J. Lee, Using singular values to build a subgrid-scale model for Large Eddy Simulations, Physics of Fluids, vol.23, issue.085106, p.36, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00802472

F. Nicoud and F. Ducros, Subgrid-scale stress modelling based on the square of the velocity gradient tensor. Flow, Turbulence and Combustion, vol.62, p.135, 1999.
URL : https://hal.archives-ouvertes.fr/hal-00910373

K. Oberleithner, M. Stöhr, S. H. Im, C. M. Arndt, and A. M. Steinberg, Formation and flame-induced suppression of the precessing vortex core in a swirl combustor : Experiments and linear stability analysis, Combustion and Flame, vol.162, issue.8, p.133, 2015.

M. Orain, F. Grisch, E. Jourdanneau, B. Rossow, C. Guin et al., Simultaneous measurements of equivalence ratio and flame structure in multipoint injectors using PLIF, Comptes Rendus Mécanique, vol.337, issue.6-7, p.9, 2009.

D. Paulhiac, Modélisation de la combustion d'un spray dans un brûleur aéronautique, vol.150, p.151, 2015.

P. Pepiot-desjardins and H. Pitsch, An efficient error-propagationbased reduction method for large chemical kinetic mechanisms, Combustion and Flame, vol.154, issue.1, p.38, 2008.

N. Peters, Turbulent Combustion. Cambridge Monographs on Mechanics, p.39, 2000.

N. Peters and B. Rogg, Reduced kinetic mechanisms for applications in combustion systems, vol.15, p.38, 2008.

N. D. Peters, B. Akih-kumgeh, and J. M. Bergthorson, Comparative analysis of chemical kinetic models using the alternate species elimination approach, Journal of Engineering for Gas Turbines and Power, vol.137, issue.2, p.38, 2014.

C. D. Pierce and P. Moin, Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion, Journal of Fluid Mechanics, vol.504, p.39, 2004.

H. Pitsch, A consistent level set formulation for large-eddy simulation of premixed turbulent combustion, Combustion and Flame, vol.143, issue.4, p.39, 2005.

H. Pitsch, Large-eddy simulation of turbulent combustion, Annu. Rev. Fluid Mech, vol.38, p.39, 2006.

T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, vol.101, issue.1, p.113, 1992.

T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, vol.101, issue.1, p.135, 1992.

T. Poinsot and D. Veynante, Theoretical And Numerical Combustion, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00270731

S. Pope, Pdf methods for turbulent reactive flows, Progress in Energy and Combustion Science, vol.11, issue.2, p.39, 1985.

S. Pope and T. Providakis, Compétition entre Structures Aérodynamiques et Modes Acoustiques dans une Flamme Swirlée : Influence de la Répartition de Carburant, Ecole Centrale Paris. (p. xiii, xiv, xvi, xvii, vol.36, p.34, 2000.

T. Providakis, L. Zimmer, P. Scouflaire, and S. Ducruix, Characterization of the acoustic interactions in a two-stage multi-injection combustor fed with liquid fuel, Journal of Engineering for Gas Turbines and Power, vol.134, issue.11, pp.111503-111511, 2012.

T. Providakis, L. Zimmer, P. Scouflaire, and S. Ducruix, Characterization of the coherent structures in swirling flames stabilized in a twostage multi-injection burner : influence of the staging factor, Comptes Rendus Mecanique, vol.341, issue.1-2, pp.4-14, 2013.

A. Renaud, High-speed diagnostics for the study of flame stabilization and transient behaviour in a swirled burner with variable liquid-fuel distribution, vol.12, p.159, 2015.
URL : https://hal.archives-ouvertes.fr/tel-01261655

A. Renaud, S. Ducruix, P. Scouflaire, and L. Zimmer, Flame shape transition in a swirl stabilised liquid fueled burner, Proceedings of the Combustion Institute, vol.35, issue.3, p.142, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01189097

A. Renaud, S. Ducruix, and L. Zimmer, Bistable behaviour and thermo-acoustic instability triggering in a gas turbine model combustor, Proceedings of the Combustion Institute, vol.36, issue.3, p.142, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01424851

E. Riber, Développement de la méthode de simulation aux grandes échelles pour les écoulements diphasiques turbulents, p.53, 2007.

S. Roux, G. Lartigue, T. Poinsot, U. Meier, and C. Bérat, Studies of References mean and unsteady flow in a swirled combustor using experiments, acoustic analysis, and large eddy simulations, Combustion and Flame, vol.141, issue.1, 2005.

E. Salaün, P. Malbois, A. Vandel, G. Godard, F. Grisch et al., Experimental investigation of a spray swirled flame in gas turbine model combustor, 18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics, p.9, 2016.

M. Sanjose, Evaluation de la méthode Euler-Euler pour la SGE des chambres à carburant liquide, p.45, 2009.

M. Sanjosé, J. Senoner, F. Jaegle, B. Cuenot, S. Moreau et al., Fuel injection model for Euler-Euler and Euler-Lagrange Large-Eddy Simulations of an evaporating spray inside an aeronautical combustor, International Journal of Multiphase Flow, vol.37, issue.5, pp.514-529, 2011.

L. Schiller and A. Naumann, A drag coefficient correlation. Vdi Zeitung, vol.77, p.112, 1935.

P. J. Schmid, Dynamic mode decomposition of numerical and experimental data, Journal of Fluid Mechanics, vol.656, p.158, 2010.
URL : https://hal.archives-ouvertes.fr/hal-01020654

P. Schmitt, SGE de la combustion étagée dans les turbines a gaz et son interaction stabilité -polluants -thermique, p.32, 2005.

P. Schmitt, T. Poinsot, B. Schuermans, and K. Geigle, Large-eddy simulation and experimental study of heat transfer, nitric oxide emissions and combustion instability in a swirled turbulent high pressure burner, Journal of Fluid Mechanics, vol.570, p.109, 2007.

D. Schneider, U. Meier, W. Quade, J. Koopman, T. Aumeier et al., A new test rig for laser optical investigations of lean jet engine burners, p.10, 2010.

J. Senoner, SGE de l'écoulement diphasique dans un brûleur aéronautique par une approche Euler-Lagrange, p.9, 2010.

J. Senoner, M. Sanjosé, T. Lederlin, F. Jaegle, M. García et al., Eulerian and lagrangian large-eddy simulations of an evaporating two-phase flow, Comptes Rendus de l'Académie des Sciences -Mécanique, vol.337, issue.6-7, p.109, 2009.

J. Shepherd, C. Nuyt, J. Lee, and J. Woodrow, Flash point and chemical composition of aviation kerosene (jet A), p.37, 2000.

P. Sierra, Modelling the dispersion and evaporation of sprays in aeronautical combustion chambers, p.49, 2012.

J. Smagorinsky, General circulation experiments with the primitive equations, Monthly Weather Review, vol.91, issue.3, p.48, 1963.

S. Volpiani and P. , Dynamic wrinkling flame model for large eddy simulations of turbulent premixed combustion, p.40, 2017.
URL : https://hal.archives-ouvertes.fr/tel-01476158

M. Stöhr, K. Oberleithner, M. Sieber, Z. Yin, and W. Meier, Experimental study of transient mechanisms of bistable flame shape transitions in a swirl combustor, Journal of Engineering for Gas Turbines and Power, vol.140, issue.1, p.133, 2017.

N. Syred, A review of oscillation mechanisms and the role of the precessing vortex core (PVC) in swirl combustion systems, Progress in Energy and Combustion Science, vol.32, issue.2, pp.93-161, 2006.

Q. Tang, J. Xu, and S. B. Pope, Probability density function calculations of local extinction and no production in piloted-jet turbulent methane/air flames, Proceedings of the Combustion Institute, vol.28, issue.1, p.39, 2000.

Y. Tong, E. Van-kalmthout, and D. Veynante, Direct numerical simulations analysis of flame surface density models for nonpremixed turbulent combustion, Experimental and Numerical Investigations of Flames Stabilized by Swirl Flow and Bluff-body :Flame Structures and Flame Instabilities (Media-Tryck, vol.10, p.39, 1998.

L. Vervisch, E. Bidaux, K. Bray, and W. Kollmann, Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches, Physics of Fluids, vol.7, issue.10, p.39, 1995.
URL : https://hal.archives-ouvertes.fr/hal-01655415

A. Vié, F. Doisneau, and M. Massot, On the Anisotropic Gaussian closure for the prediction of inertial-particle laden flows, Comm. in Comp. Physics, vol.17, issue.1, p.46, 2015.

A. Vié, B. Franzelli, Y. Gao, T. Lu, H. Wang et al., Analysis of segregation and bifurcation in turbulent spray flames : A 3d counterflow configuration, Proceedings of the Combustion Institute, vol.35, issue.2, p.158, 2015.

A. Vié, S. Jay, B. Cuenot, and M. Massot, Accounting for polydispersion in the eulerian large eddy simulation of the two-phase flow in an aeronautical-type burner, Flow, Turbulence and Combustion, vol.90, issue.3, p.115, 2013.

G. Wang, M. Boileau, and D. Veynante, Implementation of a dynamic thickened flame model for large eddy simulations of turbulent pre-References mixed combustion, Combustion and Flame, vol.158, issue.11, p.40, 2011.

G. Wang, M. Boileau, D. Veynante, and K. Truffin, Large eddy simulation of a growing turbulent premixed flame kernel using a dynamic flame surface density model, Special Issue on Turbulent Combustion, vol.159, issue.8, p.40, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00750192

P. Weigand, W. Meier, X. Duan, W. Stricker, and M. Aigner, January). Investigations of swirl flames in a gas turbine model combustor i. flow field, structures, temperature, and species distributions, Combustion and Flame, vol.144, issue.1-2, p.7, 2006.

C. K. Westbrook and F. L. Dryer, Simplified reaction mechanisms for the oxidation of hydrocarbon fuels in flames, Combustion Science and Technology, vol.27, issue.1-2, p.38, 1981.

P. Wolf, R. Balakrishnan, G. Staffelbach, L. Gicquel, and T. Poinsot, Using les to study reacting flows and instabilities in annular combustion chambers, Flow, Turbulence and Combustion, vol.88, issue.1-2, p.134, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00812024

A. Wulff and J. Hourmouziadis, Technology review of aeroengine pollutant emissions, Aerospace Science and Technology, vol.1, issue.8, p.2, 1997.

J. Xu and S. B. Pope, Pdf calculations of turbulent nonpremixed flames with local extinction, Combustion and Flame, vol.123, issue.3, p.39, 2000.

A. Yoshizawa, Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling, The Physics of Fluids, vol.29, issue.7, p.48, 1986.