V. Chapitre, Traitement numérique : Mise en forme et tests de sensibilité -127- CHAPITRE VII Traitement numérique : Mise en forme et tests de sensibilité 1

B. Launder, An introduction to single-point closure methodology Simulation and Modeling of Turbulent Flows, 1996.

Y. Nagano, N. Kasagi, H. Kawamura, M. Maeda, H. Maekawa et al., Data-base on turbulent heat transfer. Data No. FW_PI001: transport processes of heat and momentum in the wall region of turbulent pipe flow, 1990.

P. Boulet and S. Moissette, Influence of the particle???turbulence modulation modelling in the simulation of a non-isothermal gas???solid flow, International Journal of Heat and Mass Transfer, vol.45, issue.20, pp.4201-4216, 2002.
DOI : 10.1016/S0017-9310(02)00126-6

M. Khalij, A. Tanière, and B. Oesterlé, Combined effects of particle?wall interactions and turbulent dispersion in gas?solid flows using accurate Lagrangian stochastic modeling, Proc. WCCM V, 5th World Congress on Computational Mechanics, 2002.

S. Moissette, Étude dynamique et thermique par modélisation eulérienne?lagrangienne des effets liés aux interactions turbulenceparticules dans un écoulement gaz?solide en conduite verticale nonisotherme , Thèse, 2001.

M. Sommerfeld, Modelling of particle-wall collisions in confined gas-particle flows, International Journal of Multiphase Flow, vol.18, issue.6, pp.905-926, 1992.
DOI : 10.1016/0301-9322(92)90067-Q

S. Lain, M. Sommerfeld, and J. Kussin, Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow, International Journal of Heat and Fluid Flow, vol.23, issue.5, pp.647-656, 2002.
DOI : 10.1016/S0142-727X(02)00160-1

B. Oesterlé and A. Petitjean, Simulation of particle-to-particle interactions in gas solid flows, International Journal of Multiphase Flow, vol.19, issue.1, pp.199-211, 1993.
DOI : 10.1016/0301-9322(93)90033-Q

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

M. Sommerfeld, Inter-particle collisions in turbulent flows: a stochastic Lagrangian model, Proc. 1st Int. Symp. on Turbulence and Shear Flow Phenomena, pp.265-270, 1999.

J. Sun and M. M. Chen, A theoretical analysis of heat transfer due to particle impact, International Journal of Heat and Mass Transfer, vol.31, issue.5, pp.969-975, 1988.
DOI : 10.1016/0017-9310(88)90085-3

M. Sommerfeld, S. Lain, and J. Kussin, Analysis of transport effects of turbulent gas?particle flow in a horizontal channel, Proc. ICMF 2001, Int. Conf. on Multiphase Flow, p.520, 2001.

G. Jepson, A. Poll, and W. Smith, Heat transfer from gas to wall in a gas/solids transport line, Trans. Inst. Chem. Eng, pp.41-207, 1963.

K. Abe and K. Et-suga, Towards the development of a Reynolds-averaged algebraic turbulent scalar-flux model, International Journal of Heat and Fluid Flow, vol.22, issue.1, pp.19-29, 2001.
DOI : 10.1016/S0142-727X(00)00062-X

J. Abrahamson, Collision rates of small particles in a vigorously turbulent fluid, Chemical Engineering Science, vol.30, issue.11, pp.1371-1379, 1975.
DOI : 10.1016/0009-2509(75)85067-6

F. H. Azad and M. F. Et-modest, Combined radiation and convection in absorbing, emitting and anisotropically scattering gas-particulate tube flow, International Journal of Heat and Mass Transfer, vol.24, issue.10, pp.1681-1698, 1981.
DOI : 10.1016/0017-9310(81)90077-6

T. Aihara, K. Yamamoto, K. Narusawa, T. Haraguchi, M. Ukaku et al., Experimental study on heat transfer of thermally developing and developed, turbulent, horizontal pipe flow of dilute air-solids suspensions, Heat and Mass Transfer, pp.109-120, 1997.

R. Avila and J. Et-cervantes, Analysis of the heat transfer coefficient in a turbulent particle pipe flow, International Journal of Heat and Mass Transfer, vol.38, issue.11, pp.1923-1932, 1995.
DOI : 10.1016/0017-9310(94)00321-L

P. Bagchi and S. Balachandar, Effect of turbulence on the drag and lift of a particle, Physics of Fluids, vol.15, issue.11, pp.11-3496, 2003.
DOI : 10.1063/1.1616031

G. Balzer and O. Et-simonin, turbulent eddy-viscosity derivation in dilute gas-solid turbulent flows, 8 th Workshop on Two-Phase Flow Predictions, 1996.

P. N. Baptista, F. A. Oliveira, J. C. Oliveira, and S. K. Sastry, Dimensionless analysis of fluid-to-particle heat transfer coefficients, Journal of Food Engineering, vol.31, issue.2, pp.199-218, 1997.
DOI : 10.1016/S0260-8774(96)00076-3

H. M. Barkla and . Et-auchterlonie, The Magnus or Robins effect on rotating spheres, Journal of Fluid Mechanics, vol.20, issue.03, pp.437-448, 1971.
DOI : 10.1063/1.1698540

M. Benabdallah, Simulation lagrangienne du transfert de chaleur dans un écoulement gazsolide en conduite, Thèse, 1995.

A. Berlemont, P. Desjonqueres, and G. Et-gouesbet, Particle lagrangian simulation in turbulent flows, International Journal of Multiphase Flow, vol.16, issue.1, pp.19-34, 1990.
DOI : 10.1016/0301-9322(90)90034-G

URL : https://hal.archives-ouvertes.fr/hal-00649743

A. Berlemont, M. S. Grancher, and G. Gouesbet, Heat and mass transfer coupling between vaporizing droplets and turbulence using a Lagrangian approach, Int. J. Heat and Mass Transfer, issue.16, pp.38-3023, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00649737

P. Bernard and A. Et-rovelstad, On the physical accuracy of scalar transport modeling in inhomogeneous turbulence, Physics of Fluids, vol.6, issue.9, pp.3093-3108, 1994.
DOI : 10.1063/1.868134

S. L. Bertoli, Radiant and convective heat transfer on pneumatic transport of particles: an analytical study, International Journal of Heat and Mass Transfer, vol.43, issue.13, pp.2345-2363, 2000.
DOI : 10.1016/S0017-9310(99)00280-X

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

R. G. Boothroyd and H. Et-haque, Fully developed heat transfer to a gaseous suspension of particles flowing turbulently in ducts of different size, ARCHIVE: Journal of Mechanical Engineering Science 1959-1982 (vols 1-23), vol.12, issue.3, pp.191-200, 1970.
DOI : 10.1243/JMES_JOUR_1970_012_034_02

R. G. Boothroyd and H. Et-haque, Experimental investigation of heat transfer in the entrance region of a heated duct conveying fine particles, Trans. Instn. Chem. Engrs, vol.48, pp.109-120, 1970.

P. Boulet, Simulation d'écoulements diphasiques turbulents anisothermes Application aux milieux dits « à phase dispersée », du type gaz-solide et gaz-gouttelettes, Habilitation à diriger des recherches à l, 2001.

P. Boulet and S. Et-moissette, Influence of the particle???turbulence modulation modelling in the simulation of a non-isothermal gas???solid flow, International Journal of Heat and Mass Transfer, vol.45, issue.20, pp.4201-4216, 2002.
DOI : 10.1016/S0017-9310(02)00126-6

E. S. Bourloutski, A. M. Bubenchikov, and A. V. Et-starchenko, The comparison of two approaches to numerical modelling of gas-particles turbulent flow and heat transfer in a pipe, Mechanics Research Communications, vol.29, issue.5, pp.437-445, 2002.
DOI : 10.1016/S0093-6413(02)00305-1

H. Brenner, The slow motion of a sphere through a viscous fluid towards a plane surface, Chemical Engineering Science, vol.16, issue.3-4, pp.242-251, 1961.
DOI : 10.1016/0009-2509(61)80035-3

A. Brucato, F. Grisafi, and G. Et-montante, Particle drag coefficients in turbulent fluids, Chemical Engineering Science, vol.53, issue.18, pp.3295-3314, 1998.
DOI : 10.1016/S0009-2509(98)00114-6

B. Dinh and T. , Étude numérique des actions hydrodynamiques sur une sphère en translation et rotation dans la gamme des nombres de Reynolds inférieurs à 50, Thèse de l'Institut National Polytechnique de Lorraine, 1992.

D. Burry and G. Et-bergeles, Dispersion of particles in anisotropic turbulent flows, International Journal of Multiphase Flow, vol.19, issue.4, pp.651-664, 1993.
DOI : 10.1016/0301-9322(93)90093-A

N. Caraman, J. Borée, and O. Simonin, Effect of collisions on the dispersed phase fluctuation in a dilute tube flow: Experimental and theoretical analysis, Physics of Fluids, vol.15, issue.12, pp.3602-3612, 2003.
DOI : 10.1063/1.1619136

V. Chagras, B. Oesterlé, and P. Boulet, Influence des collisions dans un ??coulement gaz???solide anisotherme en conduite verticale et horizontaleOn the influence of collisions in a turbulent non-isothermal gas???solid flow in vertical and horizontal pipes, M??canique & Industries, vol.4, issue.4, pp.385-389, 2003.
DOI : 10.1016/S1296-2139(03)00082-4

Z. Z. Chang, Etude de collisions interparticulaires en écoulement turbulent isotrope ou anisotrope par une approche lagrangienne à plusieurs trajectoires simultanées. Thesis, 1998.

N. Chegroun and B. Et-oesterlé, Étude numérique de la traînée, de la portance et du couple sur une sphère en translation et en rotation Actes 11 ème Congrès Français de Mécanique, pp.81-84, 1993.

T. F. Craft and N. Ince, Recent developments in second-moment closure for buoyancy-affected flows, Dynamics of Atmospheres and Oceans, vol.23, issue.1-4, pp.99-114, 1996.
DOI : 10.1016/0377-0265(95)00424-6

C. T. Crowe and I. Et-gillandt, Turbulence modulation of fluid-particle flows ? A basic approach, ICMF'98, 3 rd Int Conf. Multiphase Flow, p.337, 1998.

C. T. Crowe, On the relative importance of particle-particle collisions in gas-particle flows, Proceeding of the Conference on gas borne particles, pp.135-137, 1981.

C. T. Crowe, On models for turbulence modulation in fluid???particle flows, International Journal of Multiphase Flow, vol.26, issue.5, pp.719-727, 2000.
DOI : 10.1016/S0301-9322(99)00050-6

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

D. S. Dandy and H. A. Et-dwyer, A sphere in shear flow at finite Reynolds number: effect of shear on particle lift, drag, and heat transfer, Journal of Fluid Mechanics, vol.81, issue.-1, pp.381-410, 1990.
DOI : 10.1002/aic.690180219

S. C. Dennis, S. N. Singh, and D. B. Et-ingham, The steady flow due to a rotating sphere at low and moderate Reynolds numbers, Journal of Fluid Mechanics, vol.35, issue.02, pp.257-279, 1980.
DOI : 10.1007/BF01600773

C. A. Depew and E. R. Et-cramer, Heat Transfer to Horizontal Gas-Solid Suspension Flows, Journal of Heat Transfer, vol.92, issue.1, pp.77-82, 1970.
DOI : 10.1115/1.3449649

C. A. Depew and L. Et-farbar, Heat Transfer to Pneumatically Conveyed Glass Particles of Fixed Size, Journal of Heat Transfer, vol.85, issue.2, pp.164-171, 1963.
DOI : 10.1115/1.3686042

P. Desjonqueres, Modélisation lagrangienne du comportement de particules discrètes en écoulement turbulent, 1987.

D. Felice and R. , The voidage function for fluid-particle interaction systems, International Journal of Multiphase Flow, vol.20, issue.1, pp.153-159, 1994.
DOI : 10.1016/0301-9322(94)90011-6

S. Elghobashi, On predicting particle-laden turbulent flows, Applied Scientific Research, vol.1, issue.4, pp.309-329, 1994.
DOI : 10.1007/BF00936835

L. Farbar and C. A. Et-depew, Heat Transfer Effects to Gas-Solids Mixtures Using Solid Spherical Particles of Uniform Size, Industrial & Engineering Chemistry Fundamentals, vol.2, issue.2, pp.130-135, 1963.
DOI : 10.1021/i160006a008

L. Farbar and M. J. Morley, Heat Transfer to Flowing Gas-Solids Mixtures in a Circular Tube, Industrial & Engineering Chemistry, vol.49, issue.7, pp.1143-1150, 1957.
DOI : 10.1021/ie50571a038

F. Th, K. Schade, and D. Et-petrak, Numerical simulation and experimental investigation of a gas-solid two-phase flow in a horizontal channel, Int. J. Multiphase Flow, vol.19, pp.187-198, 1993.

R. Gatignol, The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow, J. Mec. Théor. Appl, vol.1, pp.143-160, 1983.

V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. J. Chem. Eng, vol.16, pp.359-368, 1976.

A. J. Goldman, R. G. Cox, and H. Et-brenner, Slow viscous motion of a sphere parallel to a plane wall???I Motion through a quiescent fluid, Chemical Engineering Science, vol.22, issue.4, pp.637-651, 1967.
DOI : 10.1016/0009-2509(67)80047-2

R. A. Gore and C. T. Et-crowe, Effect of particle size on modulating turbulent intensity, International Journal of Multiphase Flow, vol.15, issue.2, pp.279-285, 1989.
DOI : 10.1016/0301-9322(89)90076-1

K. S. Han, H. J. Sung, and M. K. Chung, Analysis of heat transfer in pipe carrying two-phase gasparticle suspension, Int. J. Heat Mass Transfer, vol.34, pp.69-78, 1991.

K. Hanjalic, Second Moment Reynolds-Stress " ) turbulence closures, Lecture Series 2000-03 of the Von Karman Institute for Fluid Dynamics, 2000.

E. Y. Harper and I. D. Chang, Maximum dissipation resulting from lift in a slow viscous shear flow, Journal of Fluid Mechanics, vol.13, issue.02, pp.209-225, 1968.
DOI : 10.1063/1.1705892

S. Hasegawa, R. Echigo, K. Kanemaru, K. Ichimiya, and M. Et-sanui, Experimental study on forced convective heat transfer of flowing gaseous solid suspension at high temperature, International Journal of Multiphase Flow, vol.9, issue.2, pp.131-145, 1983.
DOI : 10.1016/0301-9322(83)90048-4

J. He and O. Et-simonin, Numerical modelling of dilute gas-solid turbulent flows in vertical channel, EDF Report HE-44, A, vol.94021, 1994.

G. Hetsroni, Particles-turbulence interaction, International Journal of Multiphase Flow, vol.15, issue.5, pp.735-746, 1989.
DOI : 10.1016/0301-9322(89)90037-2

C. M. Hrenya, E. J. Bolio, D. Chakrabarti, and J. L. Sinclair, Comparison of low Reynolds number k????? turbulence models in predicting fully developed pipe flow, Chemical Engineering Science, vol.50, issue.12, pp.1923-1941, 1995.
DOI : 10.1016/0009-2509(95)00035-4

C. M. Hrenya, S. Miller, T. Mallo, and J. L. Sinclair, Comparison of low Reynolds number k-?? turbulence models in predicting heat transfer rates for pipe flow, International Journal of Heat and Mass Transfer, vol.41, issue.11, pp.41-1543, 1998.
DOI : 10.1016/S0017-9310(97)00208-1

N. Huber and M. Et-sommerfeld, Characterization of the cross-sectional particle concentration distribution in pneumatic conveying systems, Powder Technology, vol.79, issue.3, pp.191-210, 1994.
DOI : 10.1016/0032-5910(94)02823-0

C. B. Hwang and C. A. Et-lin, A low Reynolds number two-equation kq-eq model to predict thermal fields, Int. J. of Heat and Mass Transfer, issue.17, pp.42-3217, 1999.

F. A. Jaberi, Temperature fluctuations in particle-laden homogeneous turbulent flows, International Journal of Heat and Mass Transfer, vol.41, issue.24, pp.4081-4093, 1998.
DOI : 10.1016/S0017-9310(98)00162-8

F. A. Jaberi and F. Et-mashayek, Temperature decay in two-phase turbulent flows, International Journal of Heat and Mass Transfer, vol.43, issue.6, pp.993-1005, 2000.
DOI : 10.1016/S0017-9310(99)00185-4

G. Jepson, A. Poll, and W. Smith, Heat transfer from gas to wall in a gas/solids transport line, Trans. Instn. Chem. Engrs, vol.41, pp.207-211, 1963.

D. Katoshevski, B. Zhao, G. Ziskind, and E. Et-bar-ziv, Experimental study of the drag force acting on a heated particle, Experimental study of the drag force acting on a heated particle, pp.73-86, 2001.
DOI : 10.1016/S0021-8502(00)00057-4

W. M. Kays, Turbulent Prandtl Number???Where Are We?, Journal of Heat Transfer, vol.116, issue.2, pp.284-295, 1994.
DOI : 10.1115/1.2911398

J. Kim and P. Et-moin, Transport of Passive Scalars in a Turbulent Channel Flow, Turbulent Shear Flows, vol.6, pp.85-96, 1989.
DOI : 10.1007/978-3-642-73948-4_9

G. Kohnen, M. Rüger, and M. Et-sommerfeld, Convergence behaviour for numerical calculation by the Euler/Lagrange method for strongly coupled phases, Numer. Meth. Multiphase Flows FED, vol.185, pp.191-202, 1994.

K. Kontomaris, T. Hanratty, and J. Et-mclaughlin, An algorithm for tracking fluid particles in a spectral simulation of turbulent channel flow, Journal of Computational Physics, vol.103, issue.2, pp.231-242, 1992.
DOI : 10.1016/0021-9991(92)90398-I

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

R. Kurose and S. Et-komori, Drag and lift forces on a rotating sphere in a linear shear flow, Journal of Fluid Mechanics, vol.384, pp.183-206, 1999.
DOI : 10.1017/S0022112099004164

S. Lain, D. Bröder, M. Sommerfeld, and M. F. Et-göz, Modelling hydrodynamics and turbulence in a bubble column using the Euler???Lagrange procedure, International Journal of Multiphase Flow, vol.28, issue.8, pp.1381-1407, 2002.
DOI : 10.1016/S0301-9322(02)00028-9

S. Lain, M. Sommerfeld, and J. Et-kussin, Experimental studies and modelling of four-way coupling in particle-laden horizontal channel flow, International Journal of Heat and Fluid Flow, vol.23, issue.5, pp.647-656, 2002.
DOI : 10.1016/S0142-727X(02)00160-1

S. Lain and M. Et-sommerfeld, Turbulence modulation in dispersed two-phase flow laden with solids from a Lagrangian perspective, International Journal of Heat and Fluid Flow, vol.24, issue.4, pp.616-625, 2003.
DOI : 10.1016/S0142-727X(03)00055-9

J. Laufer, Investigation of turbulent flow in a two-dimensional channel, 1951.

J. Laufer, The structure of turbulence in fully developed pipe flow, 1954.

B. E. Launder, On the Computation of Convective Heat Transfer in Complex Turbulent Flows, Journal of Heat Transfer, vol.110, issue.4b, 1988.
DOI : 10.1115/1.3250614

J. Lavieville, Simulations numériques et modélisation des interactions entre l'entraînement par la turbulence et les collisions interparticulaires en écoulements gaz-solide. Thèse, 1997.

B. J. Legg and M. R. Et-raupach, Markov-chain simulation of particle dispersion in inhomogeneous flows: The mean drift velocity induced by a gradient in Eulerian velocity variance, Boundary-Layer Meteorology, vol.21, issue.1, pp.3-13, 1982.
DOI : 10.1007/BF00121796

J. Li and D. J. Et-mason, A computational investigation of transient heat transfer in pneumatic transport of granular particles, Powder Technology, vol.112, issue.3, pp.273-282, 2000.
DOI : 10.1016/S0032-5910(00)00302-8

M. Louge, J. M. Yusof, and J. T. Jenkins, Heat transfer in the pneumatic transport of massive particles, International Journal of Heat and Mass Transfer, vol.36, issue.2, pp.265-275, 1993.
DOI : 10.1016/0017-9310(93)80002-C

C. Ljus, B. Johansson, and A. E. Et-almstedt, Turbulence modification by particles in a horizontal pipe flow, International Journal of Multiphase Flow, vol.28, issue.7, pp.1075-1090, 2002.
DOI : 10.1016/S0301-9322(02)00020-4

J. M. Macinnes and F. V. Et-bracco, Stochastic particle dispersion modeling and the tracer???particle limit, Physics of Fluids A: Fluid Dynamics, vol.4, issue.12, pp.2809-2824, 1992.
DOI : 10.1063/1.858337

M. Maeda, K. Hishida, and T. Et-furutani, Optical measurements of local gas and particle velocity in an upward flowing dilute gas-solids suspension, Proc. Polyphase Flow and Transport Technology (Century 2-ETC, pp.211-216, 1980.

J. Magnaudet, M. Rivero, and J. Et-fabre, Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow, Journal of Fluid Mechanics, vol.16, issue.-1, p.97, 1995.
DOI : 10.1016/0301-9322(79)90024-7

F. Mashayek and D. B. Et-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

S. Matsumoto and S. Saito, MONTE CARLO SIMULATION OF HORIZONTAL PNEUMATIC CONVEYING BASED ON THE ROUGH WALL MODEL, Journal of Chemical Engineering of Japan, vol.3, issue.2, pp.223-230, 1970.
DOI : 10.1252/jcej.3.223

M. R. Maxey and J. J. Riley, Equation of motion for a small rigid sphere in a nonuniform flow, Physics of Fluids, vol.26, issue.4, pp.883-889, 1983.
DOI : 10.1063/1.864230

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

R. Mei, An approximate expression for the shear lift force on a spherical particle at finite reynolds number, International Journal of Multiphase Flow, vol.18, issue.1, pp.145-147, 1992.
DOI : 10.1016/0301-9322(92)90012-6

E. E. Michaelides, Heat transfer in particulate flows, International Journal of Heat and Mass Transfer, vol.29, issue.2, pp.265-273, 1986.
DOI : 10.1016/0017-9310(86)90233-4

E. E. Michaelides, Review???The Transient Equation of Motion for Particles, Bubbles, and Droplets, Journal of Fluids Engineering, vol.119, issue.2, pp.223-247, 1997.
DOI : 10.1115/1.2819127

E. E. Michaelides, Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles, and Drops???The Freeman Scholar Lecture, Journal of Fluids Engineering, vol.125, issue.2, pp.209-238, 2003.
DOI : 10.1115/1.1537258

R. Mittal, A Fourier-Chebyshev spectral collocation method for simulating flow past spheres and spheroids, International Journal for Numerical Methods in Fluids, vol.44, issue.7, p.921, 1999.
DOI : 10.1002/(SICI)1097-0363(19990815)30:7<921::AID-FLD875>3.0.CO;2-3

R. Mittal, Response of the sphere wake to freestream fluctuations. Theoritical and Computational Fluid Dynamics, pp.397-419, 2000.

S. Moissette, Etude dynamique et thermique par modélisation eulérienne-lagrangienne des effets liés aux interactions turbulence-particules dans un écoulement gaz-solide en conduite verticale non-isotherme, Thèse de l'Université Henri Poincaré -Nancy 1, 2001.

S. A. Morsi and A. J. Et-alexander, An investigation of particle trajectories in two-phase flow systems, Journal of Fluid Mechanics, vol.none, issue.02, pp.193-208, 1972.
DOI : 10.1017/S0022112072001806

A. S. Mulgi, Experimental research of gas flow with homogeneous sphere particles in a pipe, Turbulent Two-Phase Flows, p.47, 1979.

H. K. Myong and N. Et-kasagi, A new approach to the improvement of ? ? k turbulence model for wall-bounded shear flows, JSME Int. Journal, Series II, vol.33, issue.1, pp.63-72, 1990.

Y. Nagano, N. Kasagi, H. Kawamura, M. Maeda, H. Maekawa et al., Data-Base on Turbulent Heat Transfer, FW_PI001: Transport processes of heat and momentum in the wall region of turbulent pipe flow, 1990.

F. Odar and W. S. Et-hamilton, Forces on a sphere accelerating in a viscous fluid, Journal of Fluid Mechanics, vol.100, issue.02, pp.302-314, 1964.
DOI : 10.1063/1.1699949

B. Oesterlé and T. Et-bui-dinh, Experiments on the lift of a spinning sphere in a range of intermediate Reynolds numbers, Experiments in Fluids, vol.25, issue.1, pp.16-22, 1998.
DOI : 10.1007/s003480050203

B. Oesterlé and A. Et-petitjean, Simulation of particle-to-particle interactions in gas solid flows, International Journal of Multiphase Flow, vol.19, issue.1, pp.199-211, 1993.
DOI : 10.1016/0301-9322(93)90033-Q

B. Oesterlé and L. Et-zaichik, On Lagrangian time scales and particle dispersion modeling in anisotropic turbulent flows, 2004.

A. Pétrissans, Sur les modèles stochastiques lagrangiens de suivi de particules dans un champ turbulent et leur application en écoulement gaz-solide confinés, Thèse, 2001.

A. Pétrissans, B. Oesterlé, and A. Et-tanière, Dispersion predictions based on the fluid time scale seen by discrete particles, using first and second-order stochastic processes, Proc. of ASME FEDSM'00, pp.2000-11142, 2000.

S. B. Pope, On the relationship between stochastic Lagrangian models of turbulence and second???moment closures, Physics of Fluids, vol.6, issue.2, pp.973-985, 1994.
DOI : 10.1063/1.868329

S. B. Pope, Stochastic Lagrangian models of velocity in homogeneous turbulent shear flow, Physics of Fluids, vol.14, issue.5, pp.1696-1702, 2002.
DOI : 10.1063/1.1465421

S. B. Pope, Turbulent Flows, 2000.
URL : https://hal.archives-ouvertes.fr/hal-00338511

L. M. Portela, V. Ferrand, M. J. Biljard, and R. V. Et-oliemans, Effect of the turbulence-dynamics modification on turbulence models for particle-laden wall-bounded flows, Proc. of the 10 th Workshop on Two-Phase Flow Predictions, pp.1-10, 2002.

J. Pozorski and J. P. Et-minier, On the Lagrangian turbulent dispersion models based on the Langevin equation, International Journal of Multiphase Flow, vol.24, issue.6, pp.913-945, 1998.
DOI : 10.1016/S0301-9322(98)00016-0

J. Pozorski, M. Waclawczyk, and J. P. Et-minier, Probability density function computation of heated turbulent channel flow with the bounded Langevin model, Journal of Turbulence, vol.4, pp.1-23, 2003.
DOI : 10.1088/1468-5248/4/1/011

P. Rambaud, B. Oesterlé, and A. Et-tanière, Assessment of integral time scales in a gas-solid channel flow with relevance to particle dispersion modeling, Proc. of the 10 th Workshop on Two- Phase Flow Predictions, pp.182-194, 2002.

W. E. Ranz and W. R. Marshall, Evaporation from Drops, Chem. Eng. Prog, vol.48, pp.173-180, 1952.

M. Rizk and S. Et-elghobashi, The motion of a spherical particle suspended in a turbulent flow near a plane wall, Physics of Fluids, vol.28, issue.3, pp.806-817, 1985.
DOI : 10.1063/1.865048

M. Rokni and B. Et-sunden, Improved Modeling of Turbulent Forced Convective Heat Transfer in Straight Ducts, Journal of Heat Transfer, vol.121, issue.3, pp.712-719, 1999.
DOI : 10.1115/1.2826038

M. Rokni and B. Et-sunden, Calculation of turbulent fluid flow and heat transfer in ducts by a full Reynolds stress model, International Journal for Numerical Methods in Fluids, vol.21, issue.11, pp.147-162, 2003.
DOI : 10.1002/fld.466

S. I. Rubinow and J. B. Et-keller, The transverse force on a spinning sphere moving in a viscous fluid, Journal of Fluid Mechanics, vol.6, issue.03, pp.447-459, 1961.
DOI : 10.1007/BF01432457

P. G. Saffman and J. S. Turner, On the collision of drops in turbulent clouds, Journal of Fluid Mechanics, vol.33, issue.01, pp.16-30, 1956.
DOI : 10.1016/0095-8522(52)90002-0

P. G. Saffman, The lift on a small sphere in a slow shear flow, Journal of Fluid Mechanics, vol.6, issue.02, pp.385-400, 1965.
DOI : 10.1007/BF01432457

Y. Sato, E. Deutsch, and O. Et-simonin, Direct numerical simulations of heat transfer by solid particles suspended in homogeneous isotropic turbulence, International Journal of Heat and Fluid Flow, vol.19, issue.2, pp.187-192, 1998.
DOI : 10.1016/S0142-727X(97)10023-6

K. Schade, . Et-hädrich, and . Th, Investigation of wall roughness on particle-wall collision. ICMF'98, 3 rd Int Conf, Multiphase Flow, 1998.

A. Shimizu, S. Hasegawa, and H. Et-tanaka, Flow and heat transfer characteristics of gaseous solid suspension medium within circular riser tubes, JSME International Journal Series II, issue.3, pp.31-451, 1988.

F. Shotorban, F. Mashayek, and R. V. Et-pandya, Temperature statistics in particle-laden turbulent homogeneous shear flow, International Journal of Multiphase Flow, vol.29, issue.8, pp.1333-1353, 2003.
DOI : 10.1016/S0301-9322(03)00107-1

O. Simonin, E. Deutsch, and M. Et-boivin, Large eddy simulation and secon moment closure model of particle fluctuating motion in two phase turbulent shear flows, 9 th Int. Symp. On Turbulent Shear Flows, pp.85-115, 1993.

O. Simonin and K. D. Et-squires, On turbulence modification in dense particulate two-phase flows. Euromech. Colloqium 421 on Stongly-Coupled Dispersed Two-Phase Flows, 2001.

C. A. Sleicher and M. W. Et-rouse, A convenient correlation for heat transfer to constant and variable property fluids in turbulent pipe flow, International Journal of Heat and Mass Transfer, vol.18, issue.5, pp.677-683, 1975.
DOI : 10.1016/0017-9310(75)90279-3

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.992-994, 1991.
DOI : 10.1063/1.857979

R. M. So and T. P. Sommer, An explicit algebraic heat-flux model for the temperature field, International Journal of Heat and Mass Transfer, vol.39, issue.3, pp.455-465, 1996.
DOI : 10.1016/0017-9310(95)00157-5

M. Sommerfeld, Numerical simulation of the particle dispersion in turbulent flow : the importance of lift forces and particle-wall collision models. Symp. on Numerical Methods for Multiphase Flows, ASME-FED, vol.91, pp.11-18, 1990.

M. Sommerfeld, Modelling of particle-wall collisions in confined gas-particle flows, International Journal of Multiphase Flow, vol.18, issue.6, pp.905-926, 1992.
DOI : 10.1016/0301-9322(92)90067-Q

M. Sommerfeld, The importance of inter-particle collisions in a horizontal gas-solid channel flows, Gas-Particle Flow, ASME-FED, vol.228, pp.335-345, 1995.

M. Sommerfeld, Inter-particle collisions in turbulent flows: a stochastic lagrangian model, First International Symposium, Turbulence and Shear Flow Phenomena, 1999.

M. Sommerfeld, Overview and fundamentals, Lecture Series 2000-06 of the Von Karman Institute for Fluid Dynamics. Theoretical and experimental modeling of particulate flow, 2000.

M. Sommerfeld, Validation of a stochastic Lagrangian modelling approach for inter-particle collisions in homogeneous isotropic turbulence, International Journal of Multiphase Flow, vol.27, issue.10, pp.1829-1858, 2001.
DOI : 10.1016/S0301-9322(01)00035-0

M. Sommerfeld, Analysis of collision effects for turbulent gas???particle flow in a horizontal channel: Part I. Particle transport, International Journal of Multiphase Flow, vol.29, issue.4, pp.675-699, 2003.
DOI : 10.1016/S0301-9322(03)00031-4

M. Sommerfeld and N. Et-huber, Experimental analysis and modelling of particle-wall collisions, International Journal of Multiphase Flow, vol.25, issue.6-7, pp.1457-1489, 1999.
DOI : 10.1016/S0301-9322(99)00047-6

M. Sommerfeld and J. Kussin, Analysis of collision effects for turbulent gas-particle flow in a horizontal channel. Part II. Integral properties and validation, International Journal of Multiphase Flow, vol.29, issue.4, pp.701-718, 2003.
DOI : 10.1016/S0301-9322(03)00033-8

M. Sommerfeld, S. Lain, and J. Kussin, Analysis of transport effects of turbulent gas-particle flow in a horizontal channel, Proc. ICMF 2001, Int. Conf. on Multiphase Flow, 2001.

M. Sommerfeld and G. Et-zivkovic, Recent advances in the numerical simulation of pneumatic conveying through pipe systems, Periaux J. et Onate E. Invited Lectures and Special Technological Sessions of the First European Computational Fluid Dynamics Conference ad the First European Conference on Numerical Methods in Engineering, pp.201-212, 1992.

C. G. Speziale, On nonlinear K-l and K -?? models of turbulence, Journal of Fluid Mechanics, vol.23, issue.-1, pp.459-475, 1987.
DOI : 10.1063/1.865127

K. D. Squires and J. K. Et-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. Et-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

A. S. Sukomel, F. F. Tsvetkov, and R. V. Et-kerimov, A study of local heat transfer from a tube to a turbulent flow of gas bearing suspended solid particles, Ther. Eng, vol.14, pp.116-121, 1967.

J. Sun and M. M. Et-chen, A theoretical analysis of heat transfer due to particle impact, International Journal of Heat and Mass Transfer, vol.31, issue.5, pp.31-969, 1988.
DOI : 10.1016/0017-9310(88)90085-3

T. Tanaka and Y. Et-tsuji, Numerical simulation of gas-solid two-phase flow in a vertical pipe : on the effect of inter-particle collision, FED, 1991.

Y. Tsuji and Y. Morikawa, LDV measurements of an air???-solid two-phase flow in a horizontal pipe, Journal of Fluid Mechanics, vol.6, issue.-1, pp.385-409, 1982.
DOI : 10.1017/S0022112069002242

Y. Tsuji, Y. Morikawa, and O. Et-mizuno, Experimental Measurement of the Magnus Force on a Rotating Sphere at Low Reynolds Numbers, Journal of Fluids Engineering, vol.107, issue.4, pp.484-488, 1985.
DOI : 10.1115/1.3242517

Y. Tsuji, Y. Morikawa, and H. Et-shiomi, LDV measurements of an air-solid two-phase flow in a vertical pipe, Journal of Fluid Mechanics, vol.93, issue.-1, pp.417-434, 1984.
DOI : 10.1007/BF00536208

Y. Tsuji, Y. Morikawa, T. Tanaka, N. Nakatsukasa, and M. Et-nakatani, Numerical simulation of gas-solid two-phase flow in a two-dimensional horizontal channel, International Journal of Multiphase Flow, vol.13, issue.5, pp.671-684, 1987.
DOI : 10.1016/0301-9322(87)90044-9

P. H. Uhlher and C. G. Sinclair, The effect of free stream turbulence on the drag coefficient of spheres, Proc. Chemca '70, 1970.

W. S. Uijttewaal and R. V. Et-olieman, Particle dispersion and deposition in direct numerical and large eddy simulations of vertical pipe flows, Physics of Fluids, vol.8, issue.10, pp.2590-2604, 1996.
DOI : 10.1063/1.869046

K. Ushijima and R. J. Et-perkins, Evaluation of C 0 and T L in turbulent pipe or channel flows, Proc. Of ASME-FEDSM, Paper FEDSM99-7759, 1999.

O. Vermorel, Etude numérique et modélisation de la modulation de la turbulence dans un écoulement de nappe chargée en particules, Thèse, 2003.

L. P. Wang and D. E. Stock, Dispersion of Heavy Particles by Turbulent Motion, Journal of the Atmospheric Sciences, vol.50, issue.13, pp.1897-1913, 1993.
DOI : 10.1175/1520-0469(1993)050<1897:DOHPBT>2.0.CO;2

Q. Wang, K. D. Squires, M. Chen, and J. B. Et-mclaughlin, On the role of the lift force in turbulence simulations of particle deposition, International Journal of Multiphase Flow, vol.23, issue.4, pp.749-763, 1997.
DOI : 10.1016/S0301-9322(97)00014-1

W. D. Warnica, M. Renksizbulut, and A. B. Et-strong, Drag coefficient of spherical liquid droplets, Exp. Fluids, vol.18, p.265, 1994.

G. T. Wilkinson and J. R. Et-norman, Heat transfer to a suspension of solids in a gas, Trans. Instn. Chem. Engrs, vol.45, pp.314-318, 1967.

. Y. Yamamoto, M. Potthoff, T. Tanaka, T. Kashijima, and Y. Et-tsuji, Large-eddy simulation of turbulent gas???particle flow in a vertical channel: effect of considering inter-particle collisions, Journal of Fluid Mechanics, vol.442, pp.303-334, 2001.
DOI : 10.1017/S0022112001005092

L. L. Zaichik, A statistical model of particle transport and heat transfer in turbulent shear flows, Physics of Fluids, vol.11, issue.6, pp.1521-1534, 1999.
DOI : 10.1063/1.870015

N. A. Zarin and J. A. Et-nicholls, Sphere Drag in Solid Rockets???Non-Continuum and Turbulence Effects, Combustion Science and Technology, vol.34, issue.6, p.273, 1971.
DOI : 10.1080/00102207108952295

Q. Zhou and M. A. Et-leschziner, Modelling particle dispersion in anisotropic turbulence, Pro. ECCOMAS Comp. Fluid Dynamics Conf, pp.577-583, 1996.

L. Zimmer, Etude numérique et expérimentale de la turbulence en écoulement gaz-goutelettes. Applications aux rideaux d'eau en présence de vent latéral, Thèse de l'Université Henri Poincaré - Nancy 1, 2001.