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A Poly-dispersed EE Model

  • J. S. ShrimptonEmail author
  • S. Haeri
  • Stephen J. Scott
Chapter
Part of the Green Energy and Technology book series (GREEN)

Abstract

In this chapter, first a brief introduction to kinetic theory is provided to demonstrate the terminology which the authors believe helps in grasping the ideas and then, the basic definitions for the fluid–particle system are provided.

References

  1. 1.
    Minier JP, Peirano E (2001) The pdf approach to turbulent polydispersed two-phase ows. Phys Rep 352:1–214CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Pope SB (1994) On the relationship between stochastic Lagrangian models of turbulence and second-moment closures. Phys Fluids 6:973–985CrossRefzbMATHGoogle Scholar
  3. 3.
    Wells MR, Stock DE (1983) The effects of crossing trajectories on the dispersion of particles in a turbulent flow. J Fluid Mech 136:31–62CrossRefGoogle Scholar
  4. 4.
    Csanady GT (1963) Turbulent diffusion of heavy particles in the atmosphere. J Atmos Sci 20:201–208CrossRefGoogle Scholar
  5. 5.
    Boivin M, Simonin O, Squires KD (1998) Direct numerical simulation of turbulence modulation by particles in isotropic turbulence. J Fluid Mech 375:235–263CrossRefzbMATHGoogle Scholar
  6. 6.
    Stokes GG (1851) On the effect of the inertial friction of fluids on the motion of pendulums. Trans Camb Phil Soc 1Google Scholar
  7. 7.
    Gouesbet G, Berlemont A, Picart A (1984) Dispersion of discrete particles by continuous turbulent motion. extensive discussion of tchen’s theory, using a two - parameter family of lagrangian correlation functions. Phys Fluids 27:827–837CrossRefzbMATHGoogle Scholar
  8. 8.
    Ranade VV (2002) Computational flow modeling for chemical reactor engineering. Academic Press, San DiegoGoogle Scholar
  9. 9.
    Crowe C, Sommerfeld M, Tsuji Y (1998) Multiphase flows with droplets and particles. CRC Press, Boca RatonGoogle Scholar
  10. 10.
    Maxey MR, Riley JJ (1983) Equation of motion for small rigid sphere in non—uniform flow. Phys Fluids 4:883–889CrossRefGoogle Scholar
  11. 11.
    Picart A, Berlemont A, Gouesbet G (1982) De linfulence du terme de basset sur la diepersion de particules discretes dans le cadre de la theorie de tchen. CR Acad Sci Paris Ser II:295–305Google Scholar
  12. 12.
    Rudinger G (1980) Handbook of powder technology. Elsevier Scientific Publishing Co, AmesterdamGoogle Scholar
  13. 13.
    Voir D, Michaelides E (1994) The effect of history term on on the motion of rigid sphere in a viscous flow. Int J Multiph Flow 20:547CrossRefGoogle Scholar
  14. 14.
    Auton TR (1983) The dynamics of bubbles, drops and particles in motion in liquids. Ph.D. thesis, University of Cambridge, CambridgeGoogle Scholar
  15. 15.
    Auton TR, Hunts JCR, Prud’homme M (1988) The force exerted on a body in inviscid unsteady non-uniform rotational flow. J Fluid Mech 197:241–257CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Shrimpton JS, Yule AJ (1999) Characterisation of charged hydrocarbon sprays for application in combustion systems. Exp Fluids 26:460–469CrossRefGoogle Scholar
  17. 17.
    Watts RG, Ferrer R (1987) The lateral force on a spinning sphere: aerodynamics of a curveball. Am J Phys 55:1–40CrossRefGoogle Scholar
  18. 18.
    Scott SJ (2006) A pdf based method formodelling polysized particle laden turbulent flows without size class discretisation. PhD thesis, Imperial College LondonGoogle Scholar
  19. 19.
    Balachandar S (2009) A scaling analysis for pointparticle approaches to turbulent multiphase flows. Int J Multiph Flow 35:801–810CrossRefGoogle Scholar
  20. 20.
    Ferrante A, Elghobashi S (2004) On the physical mechanism of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J Fluid Mech 503:345–355CrossRefzbMATHGoogle Scholar
  21. 21.
    Wang L, Maxey M (1993) Settling velocity and concentration distribution of heavy particles in homogeneous isotropic turbulence. J Fluid Mech 256:27–68CrossRefGoogle Scholar
  22. 22.
    Berrouk A, Laurence D, Riley J, Stock D (2007) Stochastic modeling of inertial particle dispersion by subgrid motion for les of high reynolds number pipe flow. J Turbul 8Google Scholar
  23. 23.
    Shotorban B, Balachandar S (2006) Particle concentration in homogeneous shear turbulence simulated via lagrangian and equilibrium eulerian approaches. Phys Fluids 18Google Scholar
  24. 24.
    Minier JP, Peirano E, Chibbaro S (2004) Pdf model based on langevin equation for polydispersed two-phase flows applied to a bluff-body gas-solid flow. Phys Fluids A 16:2419–2431CrossRefGoogle Scholar
  25. 25.
    Chapman S, Cowling TG (1990) The mathematical theory Of non-uniform gases. Cambridge University Press, CambridgeGoogle Scholar
  26. 26.
    Gambosi TI (1994) Gaskinetic theory. Cambridge University Press, CambridgeGoogle Scholar
  27. 27.
    Bellomo N, Lo Schiavo M (1997) From the boltzmann equation to generalized kinetic models in applied sciences. Mathl Comput Model 26:43–76CrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Cercignani C (1975) Theory and application Of the boltzmann equation. Scottish Academic Press Ltd, New YorkGoogle Scholar
  29. 29.
    Cercignani C (1972) On the boltzmann equation for rigid spheres. Transp Theory Stat Phys 2:211–225CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Gidaspow (1994) Multiphase flow and fluidization. Academic Press, San DiegoGoogle Scholar
  31. 31.
    Frisch U (1991) Relation between the lattice boltzmann equation and the navier-stokes equations. Phys D 47:231–232CrossRefMathSciNetGoogle Scholar
  32. 32.
    McKean HP (1969) A simple model of the derivation of fluid mechanics from the boltzmann equation. Bull Am Math Soc 75:1–10CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Grad H (1964) Asymptotic theory of the boltzmann equation. Phys Fluids 6:147–181CrossRefMathSciNetGoogle Scholar
  34. 34.
    Campbell CS (1990) Rapid granular flows. Ann Rev Fluid Meeh 22:57–92CrossRefGoogle Scholar
  35. 35.
    Forterre Y, Pouliquen O (2008) Flows of dense granular media. Ann Rev Fluid Mech 40:1–24CrossRefMathSciNetGoogle Scholar
  36. 36.
    Goldhirsch I (2003) Rapid granular flows. Ann Rev Fluid Mech 35:267–293CrossRefMathSciNetGoogle Scholar
  37. 37.
    Neri A, Gidaspow D (2000) Riser hydrodynamics: simulation using kinetic theory. AIChE J 46:52–67CrossRefGoogle Scholar
  38. 38.
    Subramaniam S (2000) Statistical representation of a spray as a point process. Phys Fluids 12:2413–2431CrossRefGoogle Scholar
  39. 39.
    Peirano E, Chibbaro S, Pozorski J, Minier JP (2006) Mean-field/pdf numerical approach for polydispersed turbulent two-phase flows. Prog EnergyCombust Sci 32:315–371CrossRefGoogle Scholar
  40. 40.
    Pope S (1994) On the relationship between stochastic lagrangian models of turbulence and second-moment closures. Phys Fluids 6:973–985CrossRefzbMATHGoogle Scholar
  41. 41.
    Csanady G (1963) Turbulent diffusion of heavy particles in the atmosphere. J Atmos Sci 20:201–208CrossRefGoogle Scholar
  42. 42.
    Williams FA (1958) Spray combustion and atomization. Phys Fluids 1:541–545CrossRefzbMATHGoogle Scholar
  43. 43.
    Archambault MR, Edwards CF (2000) Computation of spray dynamics by direct solution of moment transport equations-inclusion of nonlinear momentum exchange. In: Eighth international conference on liquid atomization and spray systemsGoogle Scholar
  44. 44.
    Archambault MR, Edwards CF, McCormack RW (2003) Computation of spray dynamics bymoment transport equations i: theory and development. Atomization Sprays 13:63–87CrossRefGoogle Scholar
  45. 45.
    Archambault MR, Edwards CF, McCormack RW (2003) Computation of spray dynamics by moment transport equations ii: application to quasi-one dimensional spray. Atomization Sprays 13:89–115CrossRefGoogle Scholar
  46. 46.
    Domelevo K (2001) The kinetic sectional approach for noncolliding evaporating sprays. Atomization Sprays 11:291–303Google Scholar
  47. 47.
    Tambour Y (1980) A sectional model for evaporation and combustion of sprays of liquid fuels. Israel J Tech 18:47–56zbMATHGoogle Scholar
  48. 48.
    Haken H (1989) Synergetics: an overview. Rep Prog Phys 52:515–533CrossRefMathSciNetGoogle Scholar
  49. 49.
    Pope SB (1994) Lagrangian pdf methods for turbulent flows. Ann Rev Fluid Mech 26:23–63CrossRefMathSciNetGoogle Scholar
  50. 50.
    Simonin O (2000) Statistical and continuum modelling of turbulent reactive particulate flows. part 1: theoretical derivation of dispersed phase Eulerian modelling from probability density function kinetic equation. In: Lecure series, Von-Karman Institute for Fluid DynamicsGoogle Scholar
  51. 51.
    Gosman AD, Ioannides E (1983) Aspects of computer simulation of liquid-fueled combustors. J Energy 7:482–490CrossRefGoogle Scholar
  52. 52.
    Berlemont A, Desjonqueres P, Guesbet G (1990) Particle lagrangian simulation in turbulent flows. Int J Multiph Flow 16:19–34CrossRefzbMATHGoogle Scholar
  53. 53.
    Ormancey A, Martinon A (1984) Prediction of particle dispersion in turbulent flows. Phys-Chem Hydrodyn 5:229–244Google Scholar
  54. 54.
    Simonin O (2000) Statistical and continuum modelling of turbulent reactive particulate flows. part 2: application of a two-phase second-moment transport model for prediction of turbulent gas-particle flows. In: Lecure series, Von-Karman Institute for Fluid DynamicsGoogle Scholar
  55. 55.
    Perkins R, Ghosh S, Phillips J (1991) Interaction of particles and coherent structures in a plane turbulent air jet. Adv Turbul 3:93–100Google Scholar
  56. 56.
    Simonin O, Deutsch E, Minier JP (1993) Eulerian prediction of the fluid/particle correlated motion in turbulent two-phase flows. App Sci Res 51:275–283CrossRefzbMATHGoogle Scholar
  57. 57.
    Simonin O, Deutsch E, Bovin M (1993) Large eddy simulation and second-moment closure model of particle fluctuatingmotion in two-phase turbulent shear flows. Turbulent Shear Flows 9Google Scholar
  58. 58.
    Pope SB (1985) Pdf methods for turbulent reactive flows. Prog EnergyCombust Sci 11:119–192CrossRefMathSciNetGoogle Scholar
  59. 59.
    Pope S (1991) Application of the velocity-dissipation probability density function model in inhomogeneous turbulent flows. Phys Fluids A 3(8):1947–1957CrossRefzbMATHGoogle Scholar
  60. 60.
    Pope SB, Chen YL (1990) The velocity-dissipation probability density function model for turbulent flows. Phys Fluids A 2(8):1437–1449Google Scholar
  61. 61.
    Pope S (2001) Turbulent flows. Cambridge University Press, CambridgeGoogle Scholar
  62. 62.
    Minier JP, Pozorski J (1997) Derivation of a pdf model for turbulent flows based on principles from statistical physics. Phys Fluids 9(6):1748–1753CrossRefzbMATHMathSciNetGoogle Scholar
  63. 63.
    Peirano E, Leckner B (1998) Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion. Prog Energy Combust Sci 24:259–296CrossRefGoogle Scholar
  64. 64.
    Hanjalic K, Launder BE (1972) A reynolds stress model of turbulence and its application to thin shear flows. J Fluid Mech 52:609–638CrossRefzbMATHGoogle Scholar
  65. 65.
    Wouters HA, Peeters TWJ, Roekaerts D (1996) On the existence of a generalized langevin model representation for second-moment closures. Phys Fluids 8:1702–1704CrossRefzbMATHGoogle Scholar
  66. 66.
    Beck JC, Watkins AP (1999) Spray modelling using the moments of the droplet size distribution. In: ILASS-EuropeGoogle Scholar
  67. 67.
    Beck JC, Watkins AP (2000) Modelling polydispersed sprays without discretisation into droplet size classes. In: ILASS PasadenaGoogle Scholar
  68. 68.
    Beck JC, Watkins AP (2003) The droplet number moments approach to spray modelling: the development of heat and mass transfer sub-models. Int J Heat Fluid Flow 24:242–259CrossRefGoogle Scholar
  69. 69.
    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 Fluid Flow 19:505–511CrossRefGoogle Scholar
  70. 70.
    Simonin O, Deutsch E, Boivin M (1995) Comparison of large-eddy simulation and second-moment closure of particle fluctuating motion in two-phase turbulent shear flows. In: Turbulence and shear flows, vol 9. Springer, Berlin, pp 85–115Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK
  2. 2.University of SouthamptonSouthamptonUK
  3. 3.YorkUK

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