Skip to main content
SpringerLink
Log in

Statistical model of collisions of bidisperse particles in an anisotropic turbulent flow

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

A statistical model for describing the motion and collisions of a bidisperse mixture of particles in anisotropic turbulent flows is presented. The model is based on a kinetic equation for the particle velocity probability density function (PDF). The results are compared with the data of a direct numerical simulation of the sedimentation of a bidisperse mixture of particles under the action of the gravity force.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V.M. Alipchenkov and L.I. Zaichik, “Particle Collisions in a Turbulent Flow,” Fluid Dynamics 42(3), 419–432 (2007).

    MathSciNet  MATH  Google Scholar 

  2. C. Gourdel, O. Simonin, and E. Brunier, “Two-Maxwellian Equilibrium Distribution Function for the Modelling of a Binary Mixture of Particles,” in Proc. 6th Int. Conf. on Circulating Fluidized Beds. Frankfurt, Germany, Frankfurt (1999), 205–210.

  3. P. Fede and O. Simonin, “Application of a Perturbed Two-Maxwellian Approach for the Modelling of Kinetic Stress Transfer by Collision in Non-Equilibrium Binary Mixture of Inelastic Particles,” in Proc. ASME Fluids Eng. Division Summer Meeting and Exhibition. Houston, USA, 2005, Houston (2005), FEDSM2005-77127

  4. V.M. Alipchenkov and L.I. Zaichik, “Statistical Model of Particle Motion and Dispersion in an Anisotropic Turbulent Flow,” Fluid Dynamics 39(5), 735–747 (2004).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. V.M. Alipchenkov and L.I. Zaichik, “Modeling of the Turbulent Particle Motion in a Vertical Channel,” Fluid Dynamics 41(4), 531–544 (2006).

    Article  ADS  MATH  Google Scholar 

  6. S. Chapman and T.G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge Univ. Press, London, 1970).

    Google Scholar 

  7. C.K.K. Lun, S.B. Savage, D.J. Jeffry, and N. Chepurniy, “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 (1984).

    Article  ADS  MATH  Google Scholar 

  8. J.T. Jenkins and M.W. Richman, “Grad's 13-Moment System for a Dense Gas of Inelastic Spheres,” Arch. Rat. Mech. Anal. 87(4), 355–377 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  9. V.M. Alipchenkov and L.I. Zaichik, “Modeling the Dynamics of Colliding Particles in a Turbulent Shear Flow,” Fluid Dynamics 33(4), 552–558 (1998).

    Article  ADS  MATH  Google Scholar 

  10. L.I. Zaichik, O. Simonin, V.M. Alipchenkov, “Collision Rates of Bidisperse Inertial Particles in Isotropic Turbulence,” Phys. Fluids 18(3), 0351101-1–035110-13 (2006).

    Article  MathSciNet  Google Scholar 

  11. J. Abrahamson, “Collision Rates of Small Particles in a Vigorously Turbulent Fluid,” Chem. Eng. Sci. 30(11), 1371–1379 (1975).

    Article  Google Scholar 

  12. V.M. Alipchenkov and L.I. Zaichik, “Particle Collision Rate in a Turbulent Flow,” Fluid Dynamics 36(4), 608–618 (2001).

    Article  MATH  Google Scholar 

  13. Z. Dodin and T. Elpirin, “On the Collision Rate in Turbulent Flow with Gravity,” Phys. Fluids 14(8), 2921–2924 (2002).

    Article  ADS  Google Scholar 

  14. G.T. Csanady, “Turbulent Diffusion of Heavy Particles in the Atmosphere,” J. Atmos. Sci. 20(3), 201–208 (1963).

    Article  ADS  Google Scholar 

  15. E. Deutsch and O. Simonin, “Large-Eddy Simulation Applied to the Modelling of Particulate Transport Coefficients in Turbulent Two-Phase Flows,” in Proc. 8th Symp. on Turbulent Shear Flows. Munich, Germany, 1991 (Munich, 1991), 10-1-1–10-1-6.

  16. C. Gourdel, O. Simonin, and E. Bruner, “Modeling and Simulation of Gas-Solid Turbulent Flows with a Binary Mixture of Particles,” in Proc. 3rd Int. Conf. on Multiphase Flow, Lyons, France, 1998 (Lyons, 1998). CD-ROM, paper No. 504.

Download references

Authors
  1. V. M. Alipchenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. I. Zaichik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © V.M. Alipchenkov, L.I. Zaichik, 2007, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2007, Vol. 42, No. 4, pp. 94–106.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alipchenkov, V.M., Zaichik, L.I. Statistical model of collisions of bidisperse particles in an anisotropic turbulent flow. Fluid Dyn 42, 591–602 (2007). https://doi.org/10.1134/S0015462807040096

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0015462807040096

Keywords

Search

Navigation