Skip to main content
SpringerLink
Log in
Book cover

Chemical Reactor Modeling pp 503–541Cite as

Flows of Granular Materials

  • Chapter

  • 4702 Accesses

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   219.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson TB, Jackson R (1967) A Fluid Mechanical Description of Fluidized Beds. I & EC Fundamentals 6 (4):527-539

    Article  Google Scholar 

  2. Bagnold RA (1954) Experiments on a Gravity-Free Dispesion of Large Solid Spheres in a Newtonian Fluid Under Shear. Proc Roy Soc A225:49-63

    Google Scholar 

  3. Balzer G, Simonin O (1993) Extensions of Eulerian gas-solid flow modelling to dense fluidized bed prediction. In: Proc 5th Int Symp on refined flow modelling and turbulence measurements, ed Viollet PL, Paris, pp 417-424

    Google Scholar 

  4. Balzer G, Boelle A, Simonin O (1995) Eulerian gas-solid flow modelling of dense fluidized bed. Fluidization VIII, Int Symp of the Engineering Foundation, Tours, 14-19 May, pp 1125-1134

    Google Scholar 

  5. Barthod D, Del Pozo M, Mirgain C (1999) CFD-aided design improves FCC performance. Oil & Gas Journal 14:66-69

    Google Scholar 

  6. Bel Fdhila R, Simonin O (1992) 6th Workshop on Two-Phase Flow Predictions, Erlangen, FRG, pp. 264-273

    Google Scholar 

  7. Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena. Second Edition, John Wiley & Sons, New York

    Google Scholar 

  8. Boelle A, Balzer G, Simonin O (1995) Second order prediction of the particle phase stress tensor of inelastic spheres in simple shear dense suspensions. Gas-Solid Flows, ASME FED 228:9-18

    Google Scholar 

  9. Boemer A, Qi H, Renz U, Vasquez S, Boysan F (1995) Eulerian computation of fluidized bed hydrodynamics - A comparison of physical models. Fluidized Bed Combustion - Volume 2 ASME 1995

    Google Scholar 

  10. Campbell CS (1990) Rapid Granular Flows. Annu Rev Fluid Mech 22:57-92

    Article  Google Scholar 

  11. Chapman S, Cowling TG (1970) The Mathematical Theory of Non-Uniform Gases. Third edition, Cambridge Mathematical Library, Cambridge

    Google Scholar 

  12. Crowe CT, Chung JN, Troutt TR (1988) Particle Mixing in Free Shear Flows. Prog Energy Combust Sci 14:171-194

    Article  Google Scholar 

  13. Crowe CT, Troutt TR, Chung JN (1996) Numerical Models for Two-Phase Turbulent Flows. Annu Rev Fluid Mech 28:11-43.

    Article  MathSciNet  Google Scholar 

  14. Csanady GT (1963) Turbulent Diffusion of Heavy Particles in the Atmosphere. J Atm Sci 20:201-208

    Article  Google Scholar 

  15. Deutsch E, Simonin O (1991) Turbulence modification in multiphase flow. ASME FED 1:34-42

    Google Scholar 

  16. Ding J, Gidaspow D (1990) A bubbling fluidization model using kinetic theory of granular flow. AIChE J 36 (4):523-538

    Article  Google Scholar 

  17. Edwards CH Jr, Penny DE (1982) Calculus and Analytic Geometry. Prentice-Hall Inc, Englewood Cliffs, New Jersey

    Google Scholar 

  18. Elghobashi SE (1994) On predicting particle laden turbulent flows. Appl Sci Res 52:309-329.

    Article  Google Scholar 

  19. Enwald H, Peirano E, Almstedt AE (1996) Eulerian Two-Phase Flow Theory Applied to Fluidization. Int J Multiphase Flow 22:21-66 Suppl

    Article  MATH  Google Scholar 

  20. Enskog D (1922) Kinetische Theorie der Wärmeleitung, Reibung und Selbstdiffusion in gewissen verdichteten Gasen und Flüssigkeiten. Kungl Svenska Vet-Ak Handl 63(4):1-44

    Google Scholar 

  21. Gelperin NI, Einstein VG (1971) Heat transfer in fluidized beds. In: Fluidization, ed, Davidson JF, Harrison D, Academic Press, London and New York, pp:471-568

    Google Scholar 

  22. Gidaspow D (1994) Multiphase Flow and Fluidization-Continuum and Kinetic Theory Descriptions. Academic Press, Harcourt Brace & Company, Publishers, Boston

    MATH  Google Scholar 

  23. Gidaspow D, Huilin L, Manger E (1996) Kinetic theory of multiphase flow and fluidization: Validation and extension to binary mixtures. In: Nineteenth Int Cong of Theoretical and Appl Mech, August, Kyoto, Japan, pp 25-31

    Google Scholar 

  24. Grad H (1949) On the kinetic theory of rarified gases. Comm Pure and Appl Math 2:331-407

    Article  MATH  MathSciNet  Google Scholar 

  25. Gunn DJ (1978) Transfer of heat or mass to particles in fixed and fluidized beds. Int J Heat Mass Transfer 21:467-476

    Article  Google Scholar 

  26. He J, Simonin O (1993) Non-equilibrium prediction of the particle-phase stress tensor in vertical pneumatic conveying. Gas-Solid Flows, ASME FED 166, pp 253-263

    Google Scholar 

  27. Hinze JO (1975) Turbulence. 2nd edition, McGraw-Hill, New York

    Google Scholar 

  28. Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular Theory of Gases and Liquids. John Wiley & Sons, Inc., New York

    MATH  Google Scholar 

  29. Hrenya CM, Sinclair JL (1997) Effects of Particle-Phase Turbulence in Gas-Solid Flows. AIChE J 43 (4):853-869

    Article  Google Scholar 

  30. Jackson R (1997) Locally averaged equations of motion for a mixture of identical spherical particles and a Newtonian fluid. Chem Eng Sci 52(15):2457-2469

    Article  Google Scholar 

  31. Jenkins JT, Savage SB (1983) A Theory for Rapid Flow of Identical, Smooth, Nearly Elastic Spherical Particles. J Fluid Mech 130:187-202

    Article  MATH  Google Scholar 

  32. Jenkins JT, Richman MW (1985) Grad’s 13-Moment System for Dense Gas of Inelastic Spheres. Arch Ratio Mech Anal 87:355-377

    MATH  MathSciNet  Google Scholar 

  33. Jenkins JT, Mancini F (1987) Balance Laws and Constitutive Relations for Plane Flows of a Dense, Binary Mixture of Smooth, Nearly Elastic, Circular Disks. Journal of Applied Mechanics 54:27-34

    MATH  Google Scholar 

  34. Jenkins JT (1992) Boundary Conditions for Rapid Granular Flow: Flat, Frictional Walls. J Appl Mech - Trans ASME 59:120-127

    Article  MATH  Google Scholar 

  35. Johnson PC, Jackson R (1987) Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J Fluid Mech 176:67-93

    Article  Google Scholar 

  36. Johnson PC, Nott P, Jackson R (1990) Frictional-collisional equations of motion for particulate flows and their application to chutes. J Fluid Mech 210:501-535

    Article  Google Scholar 

  37. Jung J, Gidaspow D, Gamwo IK (2006) Bubble Computation, Granular Temperatures, and Reynolds Stresses. Chem Eng Comm 193:946-975

    Article  Google Scholar 

  38. Koch DL (1990) Kinetic theory for a monodispersed gas-solid suspension. Phys Fluids A 2:1711-1723

    Article  MATH  Google Scholar 

  39. Koch DL, Sangani AS (1999) Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: Kinetic theory and numerical simulations. J Fluid Mech 400:229-263

    Article  MATH  Google Scholar 

  40. Kubie J, Broughton J (1975) A model of heat transfer in gas fluidized beds. Int J Heat Mass Transfer 18:289-299

    Article  Google Scholar 

  41. Kuipers JAM, Prins W, van Swaaij WPM (1992) Numerical calculation of wall-to-bed heat transfer coefficients in gas-fluidized beds. AIChE J 38(7):1079-1091

    Article  Google Scholar 

  42. Lafi AY, Reyes Jr JN (1994) General Particle Transport Equation. Report OSU-NE-9409, Department of Nuclear Engineering, Origon State University, Origon

    Google Scholar 

  43. Lathouwers D, Bellan J (2000) Modelling and simulation of bubbling fluidized beds containing particle mixtures. Proc of the Comb Inst 28:2297-2304

    Article  Google Scholar 

  44. Lathouwers D, Bellan J (2001) Modelling of biomass pyrolysis for hydrogen production: The fluidized bed reactor. Proc of the 2001 DOE Hydrogen Program Review. NREL/CP-570-30535

    Google Scholar 

  45. Lathouwers D, Bellan J (2001) Modelling of dense gas-solid reactive mixtures applied to biomass pyrolysis in a fluidized bed. Int Journal of Multiphase Flow 27:2155-2187

    Article  MATH  Google Scholar 

  46. Lathouwers D, Bellan J (2001) Yield optimization and scaling of fluidized beds for tar production from biomass. Energy & Fuels 15:1247-1262

    Article  Google Scholar 

  47. Lathouwers D, Bellan J (2001) Modelling of dense gas-solid reactive mixtures applied to biomass pyrolysis in a fluidized bed. Proc of the 2001 US DOE Hydrogen Program Review. NREL/CP-570-28890

    Google Scholar 

  48. Laux H (1998) Modeling of Dilute and Dense Dispersed Fluid-Particle Flow. Dr Ing Thesis, Norwegian University of Science and Technology, Trondheim, Norway

    Google Scholar 

  49. Lun CKK, Savage SB, Jeffery DJ, Chepurniy N (1984) Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field. J Fluid Mech 140:223-256

    Article  MATH  Google Scholar 

  50. Liboff RL, (1998) Kinetic Theory: Classical, Quantum, and Relativistic Descriptions. Second Edition, John Wiley & Sons, Inc., New York

    Google Scholar 

  51. Manger E (1996) Modelling and Simulation of Gas/Solid Flow in Curvilinear Coordinates. Dr ing Thesis, Norwegian University of Science and Technology, Porsgrunn

    Google Scholar 

  52. Mathiesen V, Solberg T, Hjertager BH (2000) Predictions of gas/particle flow with an Eulerian model including a realistic particle size distribution. Powder Technology 112:34-45

    Article  Google Scholar 

  53. Mathiesen V, Solberg T, Hjertager BH (2000) An experimental and computational study of multiphase flow behavior in a circulating fluidized bed. Int J Multiphase Flow 26:387-419

    Article  MATH  Google Scholar 

  54. Maxwell JC (1866) On the dynamical theory of gases. Phil Trans R Soc Lond 157:49-88

    Google Scholar 

  55. Natarajan VVR, Hunt ML (1998) Kinetic theory analysis of heat transfer in granular flows. Int J Heat Trnsfer 41(13):1929-1944

    Article  MATH  Google Scholar 

  56. Ogawa S (1978) Multitemperature Theory of Granular Materials. In: Cowin S, Satake M ed, Proc US-Japan Seminar Continuum-Mechanical and Statistical Approaches in the Mechanics of Granular Materials. Gakujutsu Bunken Fukyukai, Tokyo, Japan, p. 208

    Google Scholar 

  57. Ogawa S, Umemura A, Oshima N (1980) On the Equations of Fully Fluidized Granular Materials. Z angew Math Phys 31:483-493

    Article  MATH  Google Scholar 

  58. Ocone R, Sundaresan S, Jackson R (1993) Gas-Particle Flow in a Duct of Arbitrary Inclination with Particle-Particle Interactions. AIChE J 39(8):1261-1271

    Article  Google Scholar 

  59. Patil DJ, Smit J, van Sint Ãnnaland M, Kuipers JAM (2006) Wall-to bed heat transfer in gas-solid bubbling fluidized beds. AIChE J 52(1):58-74

    Article  Google Scholar 

  60. Peirano E, Leckner B (1998) Fundamentals of Turbulent Gas-Solid Flows Applied to Circulating Fluidized Bed Combustion. Proc Energy Combust Sci 24:259-296

    Article  Google Scholar 

  61. Ramkrishna D (2000) Population Balances. Academic Press, San Diego

    Google Scholar 

  62. Reeks MW (1992) On the continnum equations for dispersed particles in nonuniform flows. Phys Fluids A 4:1290-1303

    Article  MATH  Google Scholar 

  63. Reeks MW (1993) On the constitutive relations for dispersed particles in nonuniform flows. I. Dispersion in simple shear flow. Phys Fluids A 5:750-761

    MATH  Google Scholar 

  64. Reyes Jr JN (1989) Statistically Derived Conservation Equations for Fluid Particle Flows. Nuclear Thermal Hydraulics 5th Winter meeting, Proc ANS Winter Meeting.

    Google Scholar 

  65. Savage SB, Jeffrey (1981) The Stress Tensor in a Granular Flow at High Shear Rates. J Fluid Mech. 110:255-272

    Google Scholar 

  66. Savage SB (1984) The Mechanics of Rapid Granular Flows. Adv Appl Mech 24:289-366

    MATH  Google Scholar 

  67. Savage SB (1987) Interparticle percolation and segragation in granular materials: A review. In: Selvadurai APS ed, Developments in Engineering Mechanics. Elsevier Science Publishers BV, Amsterdam, pp 347-363

    Google Scholar 

  68. Savage SB (1989) Flow of Granular Materials. In: Germain P, Piau M, Caillerie D (eds), Theoretical and Applied Mechanics. Elsevier Science Publishers B. V. (North-Holland)

    Google Scholar 

  69. Shahinpoor M (1983) Advances in the Mechanics and the flow of Granular Materials. Trans Tech Publications, Volume II, First edition, Clausthal-Zellerfeld, Germany

    Google Scholar 

  70. Shames IH (1962) Mechanics of fluids. McGraw-Hill, New York

    Google Scholar 

  71. Simonin O (1990) Eulerian formulation for particle dispersion in turbulent two-phase flows. Proc 5th workshop on two-phase flow predictions, Erlangen, FRG, pp 156-166

    Google Scholar 

  72. Simonin O, Viollet N, Méchitous N (1990) The modelling of turbulent recirculating high temperature flows loaded with particles. In: Plasma jets in the development of new materials technology, eds Solonenko OP, Fedorchenko AI, VSP publ, the Netherlands, pp 3-16

    Google Scholar 

  73. Simonin O, Viollet PL (1990) Prediction of an oxygen droplets pulverization in a compressible subsonic coflowing hydrogen flow. Numer Methods for Multiphase Flows, ASME FED 91:73-82

    Google Scholar 

  74. Simonin O, Balzer G, Deutsch E, Dalsecco S, Flour I, He J (1993) Numerical modelling of turbulent reactive two-phase flows with a dispersed phase. CFD applied to process engineering, IFP, Solaize, March 1993

    Google Scholar 

  75. Simonin O, Deutsch E, Minier JP (1993) Eulerian prediction of the fluid particle correlated motion in turbulent two phase flows. App Sci Res 51(1-2):275-283

    Article  MATH  Google Scholar 

  76. Simonin O (1995) Summerschool on Numerical Modelling and Prediction of Dispersed Two-Phase Flows. IMVU, Meserburg, Germany

    Google Scholar 

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

    Google Scholar 

  78. Sinclair JL (1997) Hydrodynamic Modeling. In: Grace JR, Evidan AA, Knowlton TM, Blackie, London, pp. 149-180

    Google Scholar 

  79. Srivastava A, Sundaresan S (2003) Analysis of a frictional-kinetic model for gas-particle flow. Powder Technology 129:72-85

    Article  Google Scholar 

  80. Taylor GI (1935) Statistical theory of turbulence: Parts I-III. Proc R Soc London Ser A 151:421-464

    Article  Google Scholar 

  81. Tchen CM (1947) Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. PhD thesis, Delft University of Technology

    Google Scholar 

  82. Tham MK, Gubbins KE (1971) Kinetic theory of multicomponent dense fluid mixtures of rigid spheres. J Chem Phys 55:268-279

    Article  Google Scholar 

  83. van Thai D, Minier JP, Simonin O, Freydier P, Olive J (1994) Multidimensional two-fluid model computation of turbulent dispersed two-phase flows. Numerical methods in multiphase flow ASME, Fluids Eng Div, FED 185:277-291

    Google Scholar 

  84. van Wachem BGM, Schouten JC, Krishna R, van den Bleek CM (1998) Eulerian Simulations of Bubbling Behaviour in Gas-Solid Fluidized Beds. Computers Chem Engng 22 Suppl:>S299-S306

    Google Scholar 

  85. van Wachem BGM, Schouten JC, van den Bleek CM, Krishna R, Sinclair JL (2001) Comparative Analysis of CFD Models of Dense Gas-Solid Systems. AIChE J 47(5):1035-1051

    Article  Google Scholar 

  86. Vincenti WG, Kruger CH Jr. (1967) Introduction to Physical Gas Dynamics. Second Printing, John Wiley and Sons, Inc., New York

    Google Scholar 

  87. Viollet PL, Simonin O, Olive J, Minier JP (1992) Modelling Turbulent two-phase flows in industrial equipment. In: Computational methods in applied sciences, ed Hirsh C, Elevier Sciences, New York, pp 213-224

    Google Scholar 

  88. Viollet PL, Simonin O (1994) Modelling dispersed two-phase flows: Closure, validation ans software development. Appl Mech Rev 47(6):S80-S84, Part 2, June

    Article  Google Scholar 

  89. Wang Q, Squires KD, Simonin O (1998) Large eddy simulation of turbulent gas-solid flows in a vertical channel and evaluation of second-order models. Int J Heat and Fluid Flow 19:505-511

    Article  Google Scholar 

  90. Yudine MI (1959) Physical considerations on heavy-particle diffusion. Atmospheric diffusion and air pollution, Advantages in geophysics 6, New York, Academic Press, pp 185-191

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Chem. Engineering, Georgia TechNorwegian Univ. of Science & Technology, N-7491 Trondheim, Norway

    Hugo A. Jakobsen (Prof.Dr.)

Authors
  1. Hugo A. Jakobsen
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jakobsen, H.A. (2009). Flows of Granular Materials. In: Chemical Reactor Modeling. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68622-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-68622-4_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25197-2

  • Online ISBN: 978-3-540-68622-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation