A. M. Ahmed and S. Elghobashi, On the mechanisms of modifying the structure of turbulent homogeneous shear flows by dispersed particles, Physics of Fluids, vol.12, issue.11, pp.2906-2930, 2000.
DOI : 10.1063/1.1308509

A. Albrecht, Etude numérique des transferts dynamiques et thermiques au sein d'un mélange turbulent gaz-goutte-particule : application à la zone d'injection de charge d'un réacteur à lit fluidisé de FCC, Thèse de l'Institut National Polytechnique de Toulouse, 2001.

J. Angilella, Etude asymptotique et numérique de la modification de la turbulence par des particules inertielles, Thèse de l'Institut National Polytechnique de Toulouse, 1995.

S. Balachandar and M. R. Maxey, Methods for evaluating fluid velocities in spectral simulations of turbulence, Journal of Computational Physics, vol.83, issue.1, p.96, 1989.
DOI : 10.1016/0021-9991(89)90224-6

G. Balzer and O. Simonin, Three dimensional simulation of two-phase flow in industrial CFB boiler, 14th Conf. On Fluidized Bed Combustion, pp.1017-1022, 1997.

G. K. Batchelor, Theory of homogeneous turbulence, 1960.

M. Baum, Etude de l'allumage et de la structure des flammes turbulentes, Thèse de l'Ecole Centrale de Paris, 1994.

A. Berlemont, M. Grancher, and G. Gouesbet, On the Lagrangian simulation of turbulence influence on droplet evaporation, International Journal of Heat and Mass Transfer, vol.34, issue.11, pp.2805-2812, 1991.
DOI : 10.1016/0017-9310(91)90240-F

URL : https://hal.archives-ouvertes.fr/hal-00649740

M. Boivin, Etude de l'influence des particules sur la turbulence à partir des simulations directes et de simulations des grandes échelles d'écoulements diphasiques gaz-solides homogènes isotropes stationnaires, Thèse EDF-DRD, 1996.

M. Boivin, O. Simonin, and K. D. Squires, Direct numerical simulation of turbulence modulation by particles in isotropic turbulence, Journal of Fluid Mechanics, vol.375, pp.235-263, 1998.
DOI : 10.1017/S0022112098002821

M. Boivin, O. Simonin, and K. D. Squires, On the prediction of gas???solid flows with two-way coupling using large eddy simulation, Physics of Fluids, vol.12, issue.8, pp.2080-2090, 2000.
DOI : 10.1063/1.870453

H. Boughanem and A. Trouvé, Validation du code de simulation directe ntmix3d pour le calcul des écoulements turbulents réactifs, 1996.

J. Boussinesq, Théorie de l'écoulement tourbillonnant. Mémoire présenté par la division savante, p.1877

J. Boussinesq, Sur la résistance qu'oppose un liquide indéfini en repos, Comptes Rendus, Acad. Sci, p.1885

P. Chassaing, Turbulence en mécanique des fluides : analyse du phénomène dans une perspective de modélisation à l'usage de l'ingénieur, 1994.

R. Clift, J. R. Grace, and M. E. Weber, Bubbles, drops and particles, 1978.

C. T. Crowe, M. P. Sharma, and D. E. Stock, The Particle-Source-In Cell (PSI-CELL) Model for Gas-Droplet Flows, Journal of Fluids Engineering, vol.99, issue.2, pp.325-332, 1977.
DOI : 10.1115/1.3448756

G. T. Csanady, Turbulent Diffusion of Heavy Particles in the Atmosphere, Journal of the Atmospheric Sciences, vol.20, issue.3, pp.201-208, 1963.
DOI : 10.1175/1520-0469(1963)020<0201:TDOHPI>2.0.CO;2

E. Deutsch, Dipersion de particules dans une turbulence homogène isotrope stationnaire calculée par simulation numérique directe des grandes échelles, 1992.

E. Deutsch and O. Simonin, Large eddy simulation applied to the motion of particles in stationary homogeneous fluid turbulence. Turbulence Modification in Multiphase Flow, ASME-FED, vol.110, pp.35-42, 1991.

S. Elghobashi and T. W. , A two-equation turbulence model for two-phase flows, Physics of Fluids, vol.26, issue.4, pp.931-937, 1983.
DOI : 10.1063/1.864243

S. Elghobashi and G. C. , On the two???way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification, Physics of Fluids A: Fluid Dynamics, vol.5, issue.7, pp.1790-1801, 1993.
DOI : 10.1063/1.858854

R. Fdhila and O. Simonin, Eulerian prediction of a turbulent bubbly flow downstream of a sudden pipe expansion. 6th Workshop on Two-Phase Flow Prediction, pp.85-115, 1992.

V. Ferrand, Analyse physique d'un jet d'air turbulent chargé en gouttelettes. Diagnostic lasers applicable à l'injection d'essence dans les moteurs, Thèse de l'Institut National Polytechnique de Toulouse, 2001.

J. R. Fessler, J. D. Kulick, and J. K. Eaton, Preferential concentration of heavy particles in a turbulent channel flow, Physics of Fluids, vol.6, issue.11, p.3742, 1994.
DOI : 10.1063/1.868445

P. Février, Etude numérique des effets de concentration préférentielle et de correlation spatiale entre vitesses de particules solides en turbulence homogene isotrope stationnaire

D. Fleckhauss, K. Hishida, and M. Maeda, Effect of laden solid particles on the turbulent flow structure of a round free jet, Experiments in Fluids, vol.21, issue.5, 1987.
DOI : 10.1007/BF00277711

R. Gatignol, The Faxen formulae for a rigid sphere in an unsteady non uniform stokes flow, J. Méc. Th. Appl, vol.9, pp.143-160, 1983.

R. A. Gore and C. T. Crowe, Effect of particle size on modulating turbulence intensity

D. C. Haworth and S. B. Pope, A generalized Langevin model for turbulent flows, Physics of Fluids, vol.29, issue.2, pp.387-404, 1986.
DOI : 10.1063/1.865723

J. O. Hinze, TURBULENT FLUID AND PARTICLE INTERACTION, Prog. Heat Mass Transfer, vol.6, pp.433-452, 1972.
DOI : 10.1016/B978-0-08-017035-0.50028-8

K. Hishida, K. Takemoto, and M. Maeda, Turbulence structure of gas-solids two-phase circular jet., Transactions of the Japan Society of Mechanical Engineers Series B, vol.51, issue.467, pp.2330-2337, 1985.
DOI : 10.1299/kikaib.51.2330

K. Hishida, K. Takemoto, and M. Maeda, Turbulence Charactristics of Gas-Solids Two-Phase Confined Jet (Effect of Particle Density), JAPANESE JOURNAL OF MULTIPHASE FLOW, vol.1, issue.1, pp.56-59, 1985.
DOI : 10.3811/jjmf.1.56

L. Howarth and T. Karman, On the statistical theory of isotropic turbulence, Proc. of the Roy. Soc. Gottingen Nachrichte, pp.192-215, 1938.

H. H. Hu, Direct simulation of flows of solid-liquid mixtures, International Journal of Multiphase Flow, vol.22, issue.2, pp.335-352, 1996.
DOI : 10.1016/0301-9322(95)00068-2

H. H. Hu, N. A. Patankar, and M. Y. Zhu, Direct Numerical Simulations of Fluid???Solid Systems Using the Arbitrary Lagrangian???Eulerian Technique, Journal of Computational Physics, vol.169, issue.2, pp.427-462, 2001.
DOI : 10.1006/jcph.2000.6592

I. Kataoka and A. Serizawa, Basic equations of turbulence in gas-liquid two-phase flow, International Journal of Multiphase Flow, vol.15, issue.5
DOI : 10.1016/0301-9322(89)90045-1

D. Koch, Kinetic theory for a monodisperse gas???solid suspension, Physics of Fluids A: Fluid Dynamics, vol.2, issue.10, pp.1711-1723, 1990.
DOI : 10.1063/1.857698

J. D. Kulick, J. R. Fessler, and J. K. Eaton, Particle response and turbulence modification in fully developed channel flow, Journal of Fluid Mechanics, vol.226, issue.-1, pp.109-134, 1994.
DOI : 10.1016/0009-2509(56)80019-5

M. Lance, J. L. Marié, and J. Bataille, Homogeneous Turbulence in Bubbly Flows, Journal of Fluids Engineering, vol.113, issue.2, pp.107-113, 1991.
DOI : 10.1115/1.2909495

B. E. Launder and W. P. Jones, The prediction of laminarisation with a two-equations model of turbulence, Int. J. Heat Mass Tansfer, vol.15, pp.301-314, 1972.

B. E. Launder, G. J. Reece, and W. Rodi, Progress in the development of a Reynolds-stress turbulence closure, Journal of Fluid Mechanics, vol.61, issue.03, 1975.
DOI : 10.1063/1.1694422

J. Laviéville, Simulations numériques et modélisation des interactions entre l'entraînement par la turbulence et les collisions interparticulaires en écoulement gaz-solides, 1997.

S. Lele, Compact finite difference schemes with spectral-like resolution, Journal of Computational Physics, vol.103, issue.1, pp.16-42, 1992.
DOI : 10.1016/0021-9991(92)90324-R

F. Mashayek, Direct numerical simulations of evaporating droplet dispersion in forced low Mach number turbulence, International Journal of Heat and Mass Transfer, vol.41, issue.17, pp.2601-2617, 1998.
DOI : 10.1016/S0017-9310(97)00326-8

F. Mashayek, Droplet???turbulence interactions in low-Mach-number homogeneous shear two-phase flows, Journal of Fluid Mechanics, vol.367, pp.163-203, 1998.
DOI : 10.1017/S0022112098001414

F. Mashayek and D. B. Taulbee, TURBULENT GAS-SOLID FLOWS, PART I: DIRECT SIMULATIONS AND REYNOLDS STRESS CLOSURES, Numerical Heat Transfer, Part B: Fundamentals, vol.68, issue.1, pp.1-29, 2002.
DOI : 10.1017/S002211207200268X

F. Mashayek and D. B. Taulbee, TURBULENT GAS-SOLID FLOWS, PART II: EXPLICIT ALGEBRAIC MODELS, Numerical Heat Transfer, Part B: Fundamentals, vol.4, issue.1
DOI : 10.1080/104077902753384983

B. Maury, Direct Simulations of 2D Fluid-Particle Flows in Biperiodic Domains, Journal of Computational Physics, vol.156, issue.2, pp.325-351, 1999.
DOI : 10.1006/jcph.1999.6365

M. R. Maxey, The gravitational settling of aerosol particles in homogeneous turbulence and random flow fields, Journal of Fluid Mechanics, vol.6, issue.-1, pp.441-465, 1987.
DOI : 10.1175/1520-0469(1986)043 2.0.CO;2

M. R. Maxey and J. J. Riley, Equation of motion for a small rigid sphere in a non uniform flow, Phys. of Fluids, vol.26, issue.4, pp.2883-2889, 1983.

D. Migdal and V. D. Agosta, A Source Flow Model for Continuum Gas-Particle Flow, Journal of Applied Mechanics, vol.34, issue.4, p.860, 1967.
DOI : 10.1115/1.3607848

R. S. Miller and J. Bellan, Direct numerical simulation of a confined three-dimensional gas mixing layer with one evaporating hydrocarbon-droplet-laden stream, Journal of Fluid Mechanics, vol.384, pp.293-338, 1999.
DOI : 10.1017/S0022112098004042

R. R. Mills, A. L. Kistler, V. O-'brien, and S. Corrsin, Turbulence and temperature fluctuations behind a heated grid, 1958.

J. P. Minier, Construction de la trajectoire d'une particule dans un écoulement turbulent. Rapport EDF, HE-44/88, 1988.

A. A. Mostafa and H. C. Mongia, On the interaction of particles and turbulent fluid flow, International Journal of Heat and Mass Transfer, vol.31, issue.10
DOI : 10.1016/0017-9310(88)90117-2

T. Passot and A. Pouquet, Numerical simulation of compressible homogeneous flows in the turbulent regime, Journal of Fluid Mechanics, vol.211, issue.-1, p.441, 1987.
DOI : 10.1017/S0022112085002026

T. Poinsot and S. Lele, Boundary conditions for direct simulations of compressible viscous flows, Journal of Computational Physics, vol.101, issue.1, pp.104-129, 1992.
DOI : 10.1016/0021-9991(92)90046-2

S. B. Pope, Lagrangian PDF Methods for Turbulent Flows, Annual Review of Fluid Mechanics, vol.26, issue.1, pp.23-63, 1994.
DOI : 10.1146/annurev.fl.26.010194.000323

L. M. Portela, V. Ferrand, M. J. Bijlard, and R. V. Oliemans, Effect of the turbulencedynamics modification on turbulence models for particle-laden wall-bounded flows, 10th Workshop on Two-Phase Flow Predictions, pp.195-204, 2002.

M. W. Reeks, On a kinetic equation for the transport of particles in turbulent flows, Physics of Fluids A: Fluid Dynamics, vol.3, issue.3, pp.446-456, 1991.
DOI : 10.1063/1.858101

J. Rotta, Statistiche theorie nichthomogener turbulenz i. Zeitschrift für Physik, p.547, 1951.
DOI : 10.1007/bf01330059

P. G. Saffman, On the Settling Speed of Free and Fixed Suspensions, Studies in Applied Mathematics, vol.51, issue.2, pp.16-30, 1973.
DOI : 10.1002/sapm1973522115

P. Sagaut, Large Eddy Simulation for Incompressible Flows. An Introduction, Measurement Science and Technology, vol.12, issue.10, 2002.
DOI : 10.1088/0957-0233/12/10/707

M. Sakiz and O. Simonin, Continuum modelling and Lagrangian simulation of the turbulent transport of particle kinetic stresses in a vertical gas-solid channel flow, 3rd International Conference on Multiphase Flows, 1998.

Y. Sato, K. Hishida, and M. Maeda, Effect of Dispersed Phase on Modification of Turbulent Flow in a Wall Jet, Journal of Fluids Engineering, vol.118, issue.2, pp.307-315, 1996.
DOI : 10.1115/1.2817378

L. Schiller and A. Nauman, A drag coefficient correlation, V.D.I. Zeitung, vol.77, pp.318-320, 1935.

O. Simonin, Prediction of the dispersed phase turbulence in particulate laden jet, Proc. Fourth Int. Symp. Gas-Solid Flows, pp.197-206, 1991.

O. Simonin, Combustion and turbulence in two-phase flows. Lecture Series 1996-02. Von Karman Institute for Fluid Dynamics, 1996.

O. Simonin, E. Deutsch, and M. Boivin, Large eddy simulation and second-moment closure model of particle fluctuating motion in two-phase turbulent shear flows. 9th Symp. On Turbulent Shear Flows, ASME, pp.85-115, 1995.

O. Simonin, E. Deutsch, and J. P. Minier, Eulerian prediction of the fluid/particle correlated motion in turbulent two-phase flows, Applied Scientific Research, vol.226, issue.1-2, pp.275-283, 1993.
DOI : 10.1007/BF01082549

O. Simonin, P. Février, and J. Laviéville, On the spatial distribution of heavy-particle velocities in turbulent flow: from continuous field to particulate chaos, Journal of Turbulence, vol.1, issue.040, 2002.
DOI : 10.1007/BF00250919

O. Simonin and K. D. Squires, On turbulence modification in dense particulate two-phase flows. Euromech coloqium 421 on strongly-coupled dispersed flows, 2001.

L. M. Smith and W. C. Reynolds, The dissipation???range spectrum and the velocity???derivative skewness in turbulent flows, Physics of Fluids A: Fluid Dynamics, vol.3, issue.5, pp.396-404, 1991.
DOI : 10.1063/1.857979

C. G. Speziale, Analytical Methods for the Development of Reynolds-Stress Closures in Turbulence, Annual Review of Fluid Mechanics, vol.23, issue.1, pp.107-157, 1991.
DOI : 10.1146/annurev.fl.23.010191.000543

K. D. Squires and J. K. Eaton, Particle response and turbulence modification in isotropic turbulence, Physics of Fluids A: Fluid Dynamics, vol.2, issue.7, pp.1191-1203, 1990.
DOI : 10.1063/1.857620

K. D. Squires and J. K. Eaton, Measurements of particle dispersion obtained from direct numerical simulations of isotropic turbulence, Journal of Fluid Mechanics, vol.224, issue.-1, pp.1-35, 1991.
DOI : 10.1017/S0022112075000468

K. D. Squires and J. K. Eaton, Preferential concentration of particles by turbulence, Physics of Fluids A: Fluid Dynamics, vol.3, issue.5, pp.1169-1178, 1991.
DOI : 10.1063/1.858045

K. D. Squires and J. K. Eaton, Effect of Selective Modification of Turbulence on Two-Equation Models for Particle-Laden Turbulent Flows, Journal of Fluids Engineering, vol.116, issue.4, pp.778-784, 1994.
DOI : 10.1115/1.2911849

G. G. Stokes, On the effect of the inertial friction of fluids on the motion of pendulums. Trans, 1851.

S. Sundaram and L. R. Collins, A numerical study of the modulation of isotropic turbulence by suspended particles, Journal of Fluid Mechanics, vol.379, pp.105-143, 1999.
DOI : 10.1017/S0022112098003073

D. B. Taulbee, F. Mashayek, and C. Barré, Simulation and Reynolds stress modeling of particle-laden turbulent shear flows, International Journal of Heat and Fluid Flow, vol.20, issue.4, pp.368-373, 1999.
DOI : 10.1016/S0142-727X(99)00028-4

C. M. Tchen, Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid, Thèse de l, 1947.

Q. Wang, K. D. Squires, and O. Simonin, Large eddy simulation of turbulent gas-solid flows in a vertical channel and evaluation of second-order models, International Journal of Heat and Fluid Flow, vol.19, issue.5, pp.505-511, 1998.
DOI : 10.1016/S0142-727X(98)10030-9

P. K. Yeung and S. B. Pope, An algorithm for tracking fluid particles in numerical simulations of homogeneous turbulence, Journal of Computational Physics, vol.79, issue.2, pp.373-416, 1988.
DOI : 10.1016/0021-9991(88)90022-8

L. I. Zaichik and A. A. Vinberg, Modelling of particle dynamics and heat tranfer in turbulent flows using equations for first and second moments of velocity and temperature fluctuations, 8th Int. Symp. on Turbulent Shear Flows, pp.1021-1026, 1991.