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Turbulence Models

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Mathematical Modeling of Disperse Two-Phase Flows

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 114))

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Abstract

Several turbulence models are described in the present chapter. These models are closure relations for the equations developed in Chaps. 6 and 7. We make the distinction between the models for a continuous phase, which are simple extensions of the models derived classically for a single phase flow, and the models for a disperse phase. We also make the distinction between bubbly flows, characterized by “particles” lighter than the continuous fluid, and droplet flows, or particles laden flows, where the particles are heavier than the continuous phase, when it is necessary. Zero-equation, one-equation, two-equation and seven-equation models are presented separately.

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References

  • Bel Fdhila R (1991) Analyse expérimentale et modélisation d’un écoulement vertical à bulles dans un élargissement brusque. Thèse de Doctorat. Institut National Polytechnique de Toulouse

    Google Scholar 

  • Gatignol R (1983) The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow. Journal de Mécanique théorique et appliqué 1(2):143–160

    Google Scholar 

  • Grossetête C (1995a) Caractérisation expérimentale et simulations de l’évolution d’un écoulement diphasique à bulles ascendant dans une conduite verticale. Thèse de Doctorat. Ecole Centrale Paris

    Google Scholar 

  • Grossetête C (1995b) Experimental investigation and preliminary numerical simulations of void profile development in a vertical cylindrical pipe. In: Serizawa A, Fukano T, Bataille J (eds) 2nd International conference on multiphase flow. Kyoto, April 3–7, pp IF1-1-10

    Google Scholar 

  • Hanjalic K, Launder BE (1972) A Reynolds stress model of turbulence and its application to thin shear flows. J Fluid Mech 52:609–638

    Article  MATH  Google Scholar 

  • Ishii M (1975) Thermo-fluid dynamic theory of two-phase flow. Eyrolles, Paris

    MATH  Google Scholar 

  • Kataoka I, Serizawa A (1989) Basic equations of turbulence in gas-liquid two-phase flow. Int J Multiph Flow 15(5):843–855

    Article  MATH  Google Scholar 

  • Kataoka I, Serizawa A (1995) Modeling and prediction of turbulence in bubbly two-phase flow. In: Serizawa A, Fukano T, Bataille J (eds) 2nd International conference on multiphase flow. Kyoto, April 3–7, pp MO2 11-16

    Google Scholar 

  • Lance M (1979) Contribution à l’étude de la turbulence dans la phase liquide des écoulements à bulles. Thèse de Doctorat, Université Claude Bernard, Lyon

    Google Scholar 

  • Lance M, Bataille J (1991a) Turbulence in the liquid phase of a uniform bubbly air/water flow. J Fluid Mech 222:95–118

    Google Scholar 

  • Lance M, Marié JL, Bataille J (1991b) Homogeneous turbulence in bubbly flows. J Fluids Eng 113:295–300

    Google Scholar 

  • Lance M, Marié JL, Bataille J (1983) Modélisation de la turbulence de la phase liquide dans un écoulement à bulles, Société Hydrotechnique de France, Modèles Numériques en thermohydraulique diphasique et leur qualification expérimentale; application à la sureté des réacteurs nucléaires, recueil des communications, 3e séance, 17 novembre

    Google Scholar 

  • Lance M, Marié JL, Bataille J (1984) Modélisation de la turbulence de la phase liquide dans un écoulement à bulles, La Houille Blanche, No. 3/4

    Google Scholar 

  • Lance M, Marie JL, Bataille J (1987) Turbulent bubbly flows in simple configurations. In: Transient phenomena in multiphase flow, Dubrovnik, Yougoslavie, 24–30 May 1987

    Google Scholar 

  • Launder BE, Reece GJ, Rodi W (1975) Progress in the development of a Reynolds stress turbulence closure. J Fluid Mech 68(3):537–566

    Article  MATH  Google Scholar 

  • Lopez de Bertodano M, Lahey RT Jr, Jones OC (1994) Development of a K-ε model for bubbly two-phase flow. Trans ASME J Fluids Eng 116:128–134

    Article  Google Scholar 

  • Maxey MR, Riley JJ (1983) Equation of motion for a small rigid sphere in a nonuniform flow. Phys Fluids 26(4):883–889

    Article  MATH  Google Scholar 

  • Minier JP, Peirano E (2001) The PDF approach to turbulent polydispersed two-phase flows. Phys Rep 352:1–214

    Article  MathSciNet  MATH  Google Scholar 

  • Morel C (1995) An order of magnitude analysis of the two-phase K-ε model. Int J Fluid Mech Res 22(3&4):21–44

    Article  MathSciNet  Google Scholar 

  • Morel C (1997) Modélisation multidimensionnelle des écoulements diphasiques gaz-liquide. Application à la simulation des écoulements à bulles ascendants en conduite verticale. Thèse de Doctorat, Ecole Centrale Paris

    Google Scholar 

  • Neiss C (2013) Modélisation et simulation de la dispersion turbulente et du dépôt de gouttes dans un canal horizontal. Thèse de Doctorat, Université de Grenoble

    Google Scholar 

  • Oesterlé B (2006) Ecoulements multiphasiques. Hermès-Lavoisier, Paris

    Google Scholar 

  • Peirano E, Leckner B (1998) Fundamentals of turbulent gas-solid flows applied to circulating fluidized bed combustion. Prog Energy Combust Sci 24(4): 59–296

    Google Scholar 

  • Peirano E, Minier JP (2002) Probabilistic formalism and hierarchy of models for polydispersed turbulent two-phase flows. Phys Rev E 65: 046301

    Google Scholar 

  • Pope SB (2000) Turbulent flows. Cambridge university press, Cambridge

    Google Scholar 

  • Reichardt H (1951) Vollstandige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Leitungen. ZAMM 31:208–219

    Article  Google Scholar 

  • Saif AA, Lopez de Bertodano MA (1996) Modified K-ε model for two-phase turbulent jets. In: ANS proceedings of 31st national heat transfer conference, Houston, Texas, 3–6 Aug

    Google Scholar 

  • Sato Y, Sekoguchi K (1975) Liquid velocity distribution in two-phase bubble flow. Int J Multiph Flow 2:79–95

    Article  Google Scholar 

  • Sato Y, Sadatomi M, Sekoguchi K (1981) Momentum and heat transfer in two-phase bubble flow. Int J Multiph Flow 7:167–190

    Article  MATH  Google Scholar 

  • Simonin O (1991) Modélisation numérique des écoulements turbulents diphasiques à inclusions dispersés. Ecole de Printemps CNRS de Mécanique des Fluides Numérique, Aussois

    Google Scholar 

  • Simonin O (1996) Continuum modelling of dispersed turbulent two-phase flows. In: Combustion in two-phase flows, Von Karman Institute Lectures, 29

    Google Scholar 

  • Simonin O (1999) Continuum modeling of dispersed turbulent two-phase flow, Modélisation statistique des écoulements gaz-particules, modélisation physique et numérique des écoulements diphasiques, Cours de l’X (Collège de Polytechnique) du 2–3 juin

    Google Scholar 

  • Tanière A (2010) Modélisation stochastique et simulation des écoulements diphasiques dispersés et turbulents, Habilitation à Diriger des Recherches, Université Henri Poincaré, Nancy I, soutenue le 25 juin 2010 à l’ESSTIN

    Google Scholar 

  • Tchen CM (1947) Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid, PhD thesis, De Technische Hogeschool, Delft

    Google Scholar 

  • Van Driest ER (1956) J Aeronaut Sci 23:1005

    Google Scholar 

  • 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(5): 505–511

    Google Scholar 

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Authors and Affiliations

  1. DRT/LITEN/DTNM/SERE/LRVM, Commissariat à l’Energie Atomique, Grenoble, France

    Christophe Morel

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  1. Christophe Morel
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Correspondence to Christophe Morel .

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Morel, C. (2015). Turbulence Models. In: Mathematical Modeling of Disperse Two-Phase Flows. Fluid Mechanics and Its Applications, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-319-20104-7_11

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  • DOI: https://doi.org/10.1007/978-3-319-20104-7_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20103-0

  • Online ISBN: 978-3-319-20104-7

  • eBook Packages: EngineeringEngineering (R0)

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