Skip to main content
SpringerLink
Log in

Stochastic Lagrangian Simulation of Particle Deposition in Turbulent Channel Flows

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

We develop a new method for the derivation of stochastic normalized Langevin models for particle dispersion in non-homogeneous turbulent flows. Using the near-equilibrium assumptions we utilize the Chapman-Enskog expansion for the solution of corresponding Fokker-Planck equation to obtain the diffusion matrix and drift vector. To derive the drift vector we use the Furutsu-Novikov approach to obtain the exact asymptotic expression for the drift velocity, which provides the consistency of the proposed model with passive scalar modelling. We show the validity of the near-equilibrium assumptions for so-called diffusional particles in the viscous sublayer, which velocities are comparable to the local fluid velocities, despite the strong inhomogeneity of particle statistics near the wall. This justifies the suitability of proposed approach for the modelling of particle transport in wall-bounded turbulent flows. The results of simulation of particle concentration, second moments of particle velocity and deposition rates in particle-laden channel and pipe flows obtained with the proposed model demonstrate the good agreement with both experimental and DNS/Lagrangian tracking data in a wide range of particle Stokes number.

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. Balachandar, S., Eaton, J.K.: Turbulent dispersed multiphase flows. Ann. Rev. Fluid Mech. 42, 111–133 (2010)

    Article  Google Scholar 

  2. Soldati, A., Marchioli, C.: Physics and modelling of turbulent particle deposition and entrainment: Review of a systematic study. Int. J. Multiphase Flow 35, 827–839 (2009)

    Article  Google Scholar 

  3. Simonin, O., Deutsch, E., Minier, J.-P.: Eulerian prediction of fluid-particle correlated motion in turbulent two-phase flow. Appl. Sci. Res. 51, 275–283 (1993)

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  5. Wilson, J.D., Sawford, B.L.: Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere. Bound.-Layer Meteorol. 78, 191–210 (1996)

    Article  Google Scholar 

  6. Thomson, D.J.: Criteria for the selection of stochastic models of particle trajectories in turbulent flows. J. Fluid Mech. 180, 529–556 (1987)

    Article  MATH  Google Scholar 

  7. Minier, J.-P., Chibbaro, S., Pope, S.B.: Guidelines for the formulation of Lagrangian stochastic models for particle simulations of single-phase and dispersed two-phase turbulent flows. Phys. Fluids 26, 113303 (2014)

    Article  Google Scholar 

  8. Haworth, D.C., Pope, S.B.: A generalized Langevin model for turbulent flows. Phys. Fluids 29, 387–405 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Reeks, M.W.: On probability density function equations for particle dispersion in a uniform shear flow. J. Fluid Mech. 522, 263–302 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  10. Bocksell, T.L., Loth, E.: Stochastic modeling of particle diffusion in a turbulent boundary layer. Int. J. Multiphase Flow 32, 1234–1253 (2006)

    Article  MATH  Google Scholar 

  11. Arcen, B., Tanière, A.: Simulation of a particle-laden turbulent channel flow using an improved stochastic Lagrangian model. Phys. Fluids 21, 043303 (2009)

    Article  Google Scholar 

  12. Chibbaro, S., Minier, J.-P.: Langevin PDF simulation of particle deposition in a turbulent pipe flow. J. Aerosol Sci. 39, 555–571 (2008)

    Article  Google Scholar 

  13. Liu, B., Agarwal, K.: Experimental observation of aerosol deposition in turbulent flow. J. Aerosol Sci. 5, 145–155 (1974)

    Article  Google Scholar 

  14. Wilson, J.D., Legg, B.G., Thomson, D.J.: Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance. Bound.-Layer Meteorol. 27, 163–169 (1983)

    Article  Google Scholar 

  15. Thomson, D.J.: Random walk modelling of diffusion in inhomogeneous turbulence. Quart. J. R. Met. Soc. 110, 1107–1120 (1984)

    Article  Google Scholar 

  16. Dehbi, A.: Turbulent particle dispersion in arbitrary wall-bounded geometries: A coupled CFD-Langevin-equation based approach. Int. J. Multiphase Flow 34, 819–96828 (2008)

    Article  Google Scholar 

  17. Dehbi, A.: Validation against DNS statistics of the normalized Langevin model for particle transport in turbulent channel flows. Powder Technol. 200, 60–9668 (2010)

    Article  Google Scholar 

  18. Tanière, A., Arcen, B.: Prediction of a particle-laden turbulent channel flow: Examination of two classes of stochastic dispersion models. Int. J. Multiphase Flow 60, 1–10 (2014)

    Article  Google Scholar 

  19. Sikovsky, D.P.h: Singularity of inertial particle concentration in the viscous sublayer of wall-bounded turbulent flows. Flow Turb. Comb. 92, 41–64 (2014)

    Article  Google Scholar 

  20. Sawford, B.L.: Generalized random forcing in random walk turbulent dispersion models. Phys. Fluids 29, 3582–3585 (1986)

    Article  Google Scholar 

  21. Bragg, A., Swailes, D.C., Skartlien, R.: Drift-free kinetic equations for turbulent dispersion. Phys. Rev. E 86, 056306 (2012)

    Article  Google Scholar 

  22. Tchen, C.-M.: Mean value and correlation problems connected with the motion of small particles suspended in a turbulent fluid. Ph.D. Thesis, Delft (1947)

    Google Scholar 

  23. Zaichik, L.I., Alipchenkov, V.M., Sinaiski, E.G.: Particles in turbulent flows. Wiley-VCH Verlag (2008)

  24. Swailes, D.C., Sergeev, Y.A., Parker, A.: Chapman-Enskog closure approximation in the kinetic theory of dilute turbulent gas-particulate suspensions. Phys. A 254, 517–547 (1998)

    Article  Google Scholar 

  25. Klyatskin, V.I.: Dynamics of stochastic systems. Elsevier, Dordrecht (2005)

    Google Scholar 

  26. Piquet, J.: Turbulent Flows: Models and Physics, 2nd. Springer, Berlin (2001)

    Google Scholar 

  27. Narayanan, C., Lakehal, D., Botto, L., Soldati, A.: Mechanism of the particle deposition in a fully developed turbulent open channel flow. Phys. Fluids 15, 763–775 (2003)

    Article  Google Scholar 

  28. Friedlander, S.K., Johnstone, H.F.: Deposition of suspended particles from turbulent gas stream. Ind. Eng. Chem. 49, 1151–1156 (1957)

    Article  Google Scholar 

  29. Hoyas, S., Jimenez, J.: Scaling of the velocity fluctuations in turbulent channels up to R e t =2003. Phys. Fluids 18, 011705 (2006)

    Article  Google Scholar 

  30. Belan, S., Fouxon, I., Falkovich, G.: Localization-delocalization transitions in turbophoresis of inertial particles. Phys. Rev. Lett. 112, 234502 (2014)

    Article  Google Scholar 

  31. Mito, Y., Hanratty, T.J.: Use of a modified Langevin equation to describe turbulent dispersion of fluid particles in a channel flow. Flow. Turb. Comb. 68, 1–26 (2002)

    Article  MATH  Google Scholar 

  32. Oesterlé, B., Zaichik, L.I.: Time scales for predicting dispersion of arbitrary-density particles in isotropic turbulence. Int. J. Multiphase Flow 32, 838–849 (2006)

    Article  MATH  Google Scholar 

  33. Marchioli, C., Soldati, A., Kuerten, J.G.M., Arcen, B., Taniere, A., Goldensoph, G., Squires, K.D., Cargnelutti, M.F., Portela, L.M.: Statistics of particle dispersion in direct numerical simulations of wall-bounded turbulence: Results of an international collaborative benchmark test. Int. J. Multiphase Flow 34, 879–893 (2008). Datasets are downloaded from the web at http://cfd.cineca.it/cfd/repository/

    Article  Google Scholar 

  34. Wu, X., Moin, P.: A direct numerical simulation study on the mean velocity characteristics in turbulent pipe flow. J. Fluid Mech. 608, 81–112 (2008)

    Article  MATH  Google Scholar 

  35. Oesterlé, B., Zaichik, L.I.: On Lagrangian time scales and particle dispersion modeling in equilibrium turbulent shear flows. Phys. Fluids 16, 3374–3384 (2006)

    Article  Google Scholar 

  36. Zaichik, L.I., Alipchenkov, V.M., Avetissian, A.R.: Transport and deposition of colliding particles in turbulent channel flows. Int. J. Heat Fluid Flow 30, 443–451 (2009)

    Article  Google Scholar 

  37. Iliopoulos, I., Hanratty, T.J.: Turbulent dispersion in a non-homogeneous field. J. Fluid Mech. 392, 45–71 (1999)

    Article  MATH  Google Scholar 

  38. Lenaers, P., Li, Q., Brethouwer, G., Schlatter, P., Orlu, R.: Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence. Phys. Fluids 24, 035110 (2012)

    Article  Google Scholar 

  39. Marchioli, C., Giusti, A., Salvetti, M.V., Soldati, A.: Direct numerical simulation of particle wall transfer and deposition in upward turbulent pipe flow. Int. J. Multiphase Flow 29, 1017–1038 (2003)

    Article  MATH  Google Scholar 

  40. Chen, M., McLaughlin, J.B.: A new correlation for the aerosol deposition rate in vertical ducts. J. Colloid Interface Sci. 169, 437–455 (1995)

    Article  Google Scholar 

  41. Bragg, A., Swailes, D.C., Skartlien, R.: Particle transport in a turbulent boundary layer: Non-local closures for particle dispersion tensors accounting for particle-wall interactions. Phys. Fluids 24, 103304 (2012)

    Article  Google Scholar 

  42. Ferry, J., Rani, S.L., Balachandar, S.: A locally implicit improvement of the equilibrium Eulerian method. Int. J. Multiphase Flow 29, 869–891 (2003)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Thermophysics, Siberian Branch of Russian Academy of Sciences, Acad. Lavryentiev Ave. 1, Novosibirsk, 630090, Russian Federation

    Dmitrii Ph. Sikovsky

  2. Novosibirsk State University, Pirogova street 2, Novosibirsk, 630090, Russian Federation

    Dmitrii Ph. Sikovsky

Authors
  1. Dmitrii Ph. Sikovsky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dmitrii Ph. Sikovsky.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sikovsky, D.P. Stochastic Lagrangian Simulation of Particle Deposition in Turbulent Channel Flows. Flow Turbulence Combust 95, 561–582 (2015). https://doi.org/10.1007/s10494-015-9634-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-015-9634-0

Keywords

Search

Navigation