Skip to main content

Numerical Investigation of the Combined Effects of Gravity and Turbulence on the Motion of Small and Heavy Particles

  • Chapter
  • First Online:
New Results in Numerical and Experimental Fluid Mechanics IX

Abstract

Numerical studies [1, 2] show that the influence of gravity and turbulence on the motion of small and heavy particles is not a simple superposition. However, in [3] it is shown that these studies may be artificially influenced by the turbulence forcing scheme. In the present study, a new numerical setup to investigate the combined effects of gravity and turbulence on the motion of small and heavy particles is presented, where the turbulence is only forced at the inflow and is advected through the domain by a mean flow velocity. Within a transition region the turbulence develops to a physical state which shares similarities with grid-generated turbulence in wind tunnels. In this flow, trajectories of about 43 million small and heavy particles are advanced in time. It is found that for a specific particle inertia the particles fall faster in a turbulent flow compared with their fall velocity in quiescent flow. Additionally, specific regions within the turbulent vortices cannot be reached by the particles as a result of the particle vortex interaction. Therewith, the particles tend to cluster outside the vortices. These results are in agreement with the theory of Dávilla and Hunt [4].

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Woittiez, E.J.P., Jonker, H.J.J., Portela, L.M.: On the combined effects of turbulence and gravity on droplet collisions in clouds: a numerical study. J. Atmos. Sci. 66, 1926–1943 (2009)

    Article  Google Scholar 

  2. Ayala, O., Rosa, B., Wang, L.P., Grabowski, W.W.: Effects of turbulence on the geometric collision rate of sedimenting droplets. Part 1. Results from direct numerical simulation. New J. Phys. 10, 075015 (2008)

    Article  Google Scholar 

  3. Rosa, B., Parishani, H., Ayala, O., Wang, L.P., Grabowski, W.W.: Kinematic and dynamic pair collision statistics of sedimenting inertial particles relevant to warm rain initiation. J. Phys. Conf. Ser. 318, 072016 (2011)

    Article  Google Scholar 

  4. Dávila, J., Hunt, J.C.R.: Settling of small particles near vortices and in turbulence. J. Fluid Mech. 440, 117–145 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Saffman, P.G., Turner, J.S.: On the collision of drops in turbulent clouds. J. Fluid Mech. 1, 16–30 (1956)

    Article  MATH  Google Scholar 

  6. Squires, K.D., Eaton, J.L.: Preferential concentration of particles by turbulence. Phys. Fluids 3A, 1169–1178 (1991)

    Article  Google Scholar 

  7. Bec, J., Biferale, L., Cencini, M., Lanotte, A.S., Toschi, F.: Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536 (2010)

    Article  MATH  Google Scholar 

  8. Grabowski, W.W., Vaillancourt, P.: Comments on preferential concentration of cloud droplets by turbulence: effects on the early evolution of cumulus cloud droplet spectra. J. Atmos. Sci. 56, 1433–1436 (1999)

    Article  Google Scholar 

  9. Kunnen, R.P.J., Siewert, C., Meinke, M., Schröder, W., Beheng, K.: Numerically determined geometric collision kernels in spatially evolving isotropic turbulence relevant for droplets in clouds. Atmos. Res. 127, 8–21 (2013)

    Article  Google Scholar 

  10. Hartmann, D., Meinke, M., Schröder, W.: An adaptive multilevel multigrid formulation for Cartesian hierarchical grid methods. Comput. Fluids 37, 1103–1125 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  11. Batten, P., Goldberg, U., Chakravarthy, S.: Interfacing statistical turbulence closures with large-eddy simulation. AIAA J. 42(3), 485–492 (2004)

    Article  Google Scholar 

  12. Pope, S.B.: Turbulent Flows. Cambrigde University Press, Cambrigde (2000)

    Book  MATH  Google Scholar 

  13. Maxey, M.R., Riley, J.J.: Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883–889 (1983)

    Article  MATH  Google Scholar 

  14. Sundaram, S., Collins, L.R.: Numerical considerations in simulating a turbulent suspension of finite-volume particles. J. Comput. Phys. 124, 337–350 (1996)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christoph Siewert .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Siewert, C., Kunnen, R., Meinke, M., Schröder, W. (2014). Numerical Investigation of the Combined Effects of Gravity and Turbulence on the Motion of Small and Heavy Particles. In: Dillmann, A., Heller, G., Krämer, E., Kreplin, HP., Nitsche, W., Rist, U. (eds) New Results in Numerical and Experimental Fluid Mechanics IX. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 124. Springer, Cham. https://doi.org/10.1007/978-3-319-03158-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03158-3_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03157-6

  • Online ISBN: 978-3-319-03158-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics