Flow, Turbulence and Combustion

, Volume 82, Issue 1, pp 47–71 | Cite as

Two- and Four-Way Coupled Euler–Lagrangian Large-Eddy Simulation of Turbulent Particle-Laden Channel Flow

  • Bert Vreman
  • Bernard J. GeurtsEmail author
  • N. G. Deen
  • J. A. M. Kuipers
  • J. G. M. Kuerten
Open Access


Large-eddy simulations (LES) of a vertical turbulent channel flow laden with a very large number of solid particles are performed. The motivation for this research is to get insight into fundamental aspects of co-current turbulent gas-particle flows, as encountered in riser reactors. The particle volume fraction equals about 1.3%, which is relatively high in the context of modern LES of two-phase flows. The channel flow simulations are based on large-eddy approximations of the compressible Navier–Stokes equations in a porous medium. The Euler–Lagrangian method is adopted, which means that for each individual particle an equation of motion is solved. The method incorporates four-way coupling, i.e., both the particle-fluid and particle–particle interactions are taken into account. The results are compared to single-phase channel flow in order to investigate the effect of the particles on turbulent statistics. The present results show that due to particle–fluid interactions the mean fluid profile is flattened and the boundary layer is thinner. Compared to single-phase turbulent flow, the streamwise turbulence intensity of the gas phase is increased, while the normal and spanwise turbulence intensities are reduced. This finding is generally consistent with existing experimental data. The four-way coupled simulations are also compared with two-way coupled simulations, in which the inelastic collisions between particles are neglected. The latter comparison clearly demonstrates that the collisions have a large influence on the main statistics of both phases. In addition, the four-way coupled simulations contain stronger coherent particle structures. It is thus essential to include the particle–particle interactions in numerical simulations of two-phase flow with volume fractions around one percent.


Turbulence Particle-laden flow Large-eddy simulation Channel flow Inelastic collisions Coherent structures Four-way coupling Turbulence modulation 


  1. 1.
    Armenio, V., Piomelli, U., Fiorotto, V.: Effect of the subgrid scales on particle motion. Phys. Fluids 11, 3030 (1999)zbMATHCrossRefADSGoogle Scholar
  2. 2.
    Armenio, V., Fiorotto, V.: The importance of the forces acting on particles in turbulent flows. Phys. Fluids 13, 2437 (2001)CrossRefADSGoogle Scholar
  3. 3.
    Bagchi, P., Balachandar, S.: Effect of turbulence on the drag and lift of a particle. Phys. Fluids 15, 3496–3513 (2003)CrossRefADSGoogle Scholar
  4. 4.
    Boivin, M., Simonin, O., Squires, K.D.: On the prediction of gas–solid flows with two-way coupling using large-eddy simulation. Phys. Fluids 12, 2080–2090 (2000)CrossRefADSGoogle Scholar
  5. 5.
    Chester, S., Charlette, F., Meneveau, C.: Dynamic model for LES without test filtering: quantifying the accuracy of Taylor series approximations. Theor. Comput. Fluid Dyn. 15, 165–181 (2001)zbMATHCrossRefGoogle Scholar
  6. 6.
    Clark, R.A., Ferziger, J.H., Reynolds, W.C.: Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1 (1979)zbMATHCrossRefADSGoogle Scholar
  7. 7.
    Delnoij, E., Kuipers, J.A.M., van Swaaij, W.P.M.: A three-dimensional CFD model for gas-liquid bubble columns. Chem. Eng. Sci. 54, 2217–2226 (1999)CrossRefGoogle Scholar
  8. 8.
    Elghobashi, S., Truesdell, G.C.: On the two-way interaction between homogeneous turbulence and dispersed solid particles. I: Turbulence modification. Phys. Fluids A 5, 1790–1801 (1993)zbMATHCrossRefADSGoogle Scholar
  9. 9.
    Fede, P., Simonin, O.: Numerical study of the subgrid fluid turbulence effects on the statistics of heavy colliding particles. Phys. Fluids 18, 045103 (2006)CrossRefADSGoogle Scholar
  10. 10.
    Feng, Z.-G., Michaelides, E.E.: Proteus: a direct forcing method in the simulations of particulate flows. J. Comp. Phys. 202(1), 20–51 (January 2005)zbMATHCrossRefADSGoogle Scholar
  11. 11.
    Ferrante, A., Elghobashi, S.: On the physical mechanisms of two-way coupling in particle-laden isotropic turbulence. Phys. Fluids 15, 315–329 (2003)CrossRefADSGoogle Scholar
  12. 12.
    Ferry, J., Balachandar, S.: A fast Eulerian method for disperse two-phase flow. Int. J. Multiph. Flow 27, 1199–1226 (2001)zbMATHCrossRefGoogle Scholar
  13. 13.
    Fevrier, P., Simonin, O., Squires K.: Partioning of particle velocities in gas–solid turbulent flows into a continuous field and a spatially uncorrelated random distribution: theoretical formalism and numerical study. J. Fluid Mech. 533, 1–46 (2005)zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale model. Phys. Fluids A 3, 1760–1765 (1991)zbMATHCrossRefADSGoogle Scholar
  15. 15.
    Geurts, B.J., Kuerten, J.G.M.: Numerical aspects of a block-structured flow solver. J. Eng. Math. 27, 293 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Geurts, B.J., Fröhlich, J.: A framework for predicting accuracy limitations in large-eddy simulation. Phys Fluids 14, L41–L44 (2002)CrossRefADSGoogle Scholar
  17. 17.
    Geurts, B.J.: Elements of Direct and Large-Eddy Simulation. Edwards Publishing Inc. ISBN: 1-930217-07-2 (2003)Google Scholar
  18. 18.
    Geurts, B.J., Vreman, A.W.: Dynamic self-organization in particle-laden turbulent channel flow. Int. J. Heat Fluid Flow 27, 945–954 (2006)CrossRefGoogle Scholar
  19. 19.
    Goldschmidt, M.J.V., Beetstra, R., Kuipers, J.A.M.: Comparison of the kinetic theory of granular flow with 3D hard-sphere discrete particle simulations. Chem. Eng. Sci. 57, 2059–2075 (2002)CrossRefGoogle Scholar
  20. 20.
    Gore, R.A., Crowe, C.T.: Effect of particle size on modulating turbulence intensity. Int. J. Multiph. Flow 15, 279–285 (1989)CrossRefGoogle Scholar
  21. 21.
    Hinze, J.O.: Turbulence: an Introduction to its Mechanism and Theory. McGraw-Hill, New York (1975)Google Scholar
  22. 22.
    Van der Hoef, M.A., Beetstra, R., Kuipers, J.A.M.: Lattice Boltzmann simulations of low Reynolds number flow past mono- and bi-disperse arrays of spheres: results for the permeability and drag force. J. Fluid Mech. 528, 233–254 (2005)zbMATHCrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Van der Hoef, M.A., van Sint Annaland, M., Deen, N.G., Kuipers, J.A.M.: Numerical simulation of gas–solid fluidized beds: a multiscale modeling strategy. Ann. Rev. Fluid Mech. 40, 47–70 (2008)CrossRefADSGoogle Scholar
  24. 24.
    Hoomans, B.P.B., Kuipers, J.A.M., Briels, W.J., van Swaaij, W.P.M.: Discrete particle simulation of bubble and slug formation in a two-dimensional gas-fluidized bed: a hard-sphere approach. Chem. Eng. Sci. 51, 99–118 (1996)CrossRefGoogle Scholar
  25. 25.
    Hoomans, B.P.B.: Granular dynamics of gas–solid two-phase flows. PhD-Thesis, University of Twente (1999)Google Scholar
  26. 26.
    Howard, R.J.A., Sandham, N.D.: Simulation and modeling of a skewed turbulent channel flow. Flow Turbul. Combust. 65, 83–109 (2000)zbMATHCrossRefGoogle Scholar
  27. 27.
    Hughes, T.J.R., Mazzei, L., Jansen, K.E.: Large eddy simulation and the variational multi-scale method. Comput. Vis. Sci. 3, 47 (2000)zbMATHCrossRefGoogle Scholar
  28. 28.
    Kuerten, J.G.M.: Subgrid modeling in particle-laden channel flow. Phys. Fluids 18, 025108 (2006)CrossRefADSGoogle Scholar
  29. 29.
    Kuerten, J.G.M., Vreman, A.W.: Can turbophoresis be predicted by large-eddy simulation? Phys. Fluids 17, 011701 (2005)CrossRefADSGoogle Scholar
  30. 30.
    Kulick, J.D., Fessler, J.R., Eaton, J.K.: Particle response and turbulence modification in fully developed channel flow. J. Fluid Mech. 277, 109–134 (1994)CrossRefADSGoogle Scholar
  31. 31.
    Lakehal, D., Smith, B.L., Milelli, M.: Large-eddy simulation of bubbly turbulent shear flows. J. Turbul. 3, 25 (2002)CrossRefADSGoogle Scholar
  32. 32.
    Leonard, A.: Energy cascade in large-eddy simulation of turbulent fluid flows. Adv. Geophys. 18, 237 (1974)CrossRefADSGoogle Scholar
  33. 33.
    Lilly, D.K.: A proposed modification of the Germano subgrid-scale closure method. Phys. Fluids A 4, 633 (1992)CrossRefADSGoogle Scholar
  34. 34.
    Li, Y., McLaughlin, J.B., Kontomaris, K., Portela, L.: Numerical simulation of particle-laden turbulent channel flow. Phys. Fluids 13, 2957–2967 (2001)CrossRefADSGoogle Scholar
  35. 35.
    Liss, E.D., Conway, S.L., Glasser, B.J.: Density waves in gravity-driven granular flow through a channel. Phys. Fluids 14, 3309–3326 (2002)CrossRefADSMathSciNetGoogle Scholar
  36. 36.
    Lohse, D., Bergmann, R.P.H.M., Mikkelsen, R., Zeilstra, C., Meer, R.M., van der Versluis, M., Weele, J.P., van der Hoef, M.A., van der Kuipers, J.A.M.: Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93 198003-1-198003-4 (2004)CrossRefADSGoogle Scholar
  37. 37.
    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. Multiph. Flow 29, 1017–1038 (2003)zbMATHCrossRefGoogle Scholar
  38. 38.
    Mathiesen, V., Solberg, T., Hjertager, B.H.: An experimental and computational study of multi-phase flow behavior in a circulating fluidized bed. Int. J. Multiph. Flow 26, 387–419 (2000)zbMATHCrossRefGoogle Scholar
  39. 39.
    Maxey, M.R., Riley, J.: Equation of motion for a small rigid sphere in a turbulent fluid flow. Phys. Fluids 26, 883 (1983)zbMATHCrossRefADSGoogle Scholar
  40. 40.
    Meyers, J., Geurts, B.J., Baelmans, M.: Database-analysis of errors in large-eddy simulations. Phys. Fluids 15, 2740 (2003)CrossRefADSGoogle Scholar
  41. 41.
    Meyers, J., Geurts, B.J., Baelmans, M.: Optimality of the dynamic procedure for large-eddy simulation. Phys. Fluids 17, 045108 (2005)CrossRefADSGoogle Scholar
  42. 42.
    Moin, P., Kim, J.: Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341 (1982)zbMATHCrossRefADSGoogle Scholar
  43. 43.
    Moran, J.C., Glicksman, L.R.: Mean and fluctuating gas phase velocities inside a circulating fluidized bed. Chem. Eng. Sci. 58, 1867–1878 (2003)CrossRefGoogle Scholar
  44. 44.
    Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Ret = 590. Phys. Fluids 11, 943–945 (1999)zbMATHCrossRefADSGoogle Scholar
  45. 45.
    Nicoud, F., Ducros, F.: Subgrid-scale stress modeling based on the square of the velocity gradient tensor. Flow Turbul. Combust. 62, 183–200 (1999)zbMATHCrossRefGoogle Scholar
  46. 46.
    Nieuwland, J.J.: Hydrodynamic modeling of gas–solid two-phase flows. PhD-Thesis, University of Twente (1995)Google Scholar
  47. 47.
    Okong’o, N.A., Bellan, J.: Consistent large-eddy simulation of a temporal mixing layer laden with evaporating drops. Part 1. Direct numerical simulation, formulation and a priori analysis. J. Fluid Mech. 499, 1–47 (2004)zbMATHCrossRefADSMathSciNetGoogle Scholar
  48. 48.
    Piomelli, U., Balaras, E.: Wall-layer models for large-eddy simulations. Ann. Rev. Fluid Mech. 34, 349 (2002)CrossRefADSMathSciNetGoogle Scholar
  49. 49.
    Pope, S.B.: Turbulent Flows. Cambridge University Press (2000)zbMATHGoogle Scholar
  50. 50.
    Powers, J.M.: Two-phase viscous modeling of compaction of granular materials. Phys. Fluids 16, 2975–2990 (2004)CrossRefADSGoogle Scholar
  51. 51.
    Reynolds, O.: On the dynamical theory of incompressible viscous fluids and the determination of the criterion. Phil. Trans. 186, 123 (1895)CrossRefADSGoogle Scholar
  52. 52.
    Righetti, M., Romano, G.P.: Particle–fluid interactions in a plane near-wall turbulent flow. J. Fluid Mech. 505, 93–121 (2004)zbMATHCrossRefADSGoogle Scholar
  53. 53.
    Sagaut, P.: Large Eddy Simulation for Incompressible Flows. Springer Verlag (2001)Google Scholar
  54. 54.
    Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather Rev. 91, 99 (1963)CrossRefADSGoogle Scholar
  55. 55.
    Squires, K.D., Eaton, J.K.: Particle response and turbulence modification in isotropic turbulence. Phys. Fluids A 7, 1191–1203 (1990)CrossRefADSGoogle Scholar
  56. 56.
    Squires, K.D., Simonin, O.: Recent advances and perspective of DNS and LES for dispersed two-phase flow. In: Proceedings of the 10th Workshop on Two-Phase Flow Predictions, Merseburg, pp. 152–163 (2002)Google Scholar
  57. 57.
    Stolz, S., Schlatter, P., Meyer, D., Kleiser, L.: High-pass filtered eddy-viscosity models for LES. In: Friedrich, R., Geurts, B.J., Metais, O. (eds.) Direct and Large-Eddy Simulation V: Muenchen. pp. 81–88. Kluwer, Dordrecht (2004)Google Scholar
  58. 58.
    Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., Jan Y.-J.: A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708–759 (2001)zbMATHCrossRefADSGoogle Scholar
  59. 59.
    Tsuji, Y., Morikawa, Y., Shiomi, H.: LDV measurements of an air-solid two-phase flow in a vertical pipe. J. Fluid Mech. 139, 417–434 (1984)CrossRefGoogle Scholar
  60. 60.
    Verstappen, R.W.C.P., Veldman, A.E.P.: Symmetry-preserving discretization of turbulent flow. J. Comput. Phys. 187, 343–368 (2003)zbMATHCrossRefADSMathSciNetGoogle Scholar
  61. 61.
    Verstappen, R.W.C.P.: A synthesis of similarity and eddy-viscosity models. In: Friedrich, R., Geurts, B.J. Metais, O. (eds.) Direct and Large-Eddy Simulation V: Muenchen. pp. 89–96. Kluwer, Dordrecht (2004)Google Scholar
  62. 62.
    Vreman, A.W.: The filtering analog of the variational multi-scale method in large-eddy simulation. Phys. Fluids 15, L61–64 (2003)CrossRefADSMathSciNetGoogle Scholar
  63. 63.
    Vreman, A.W.: An eddy-viscosity model for turbulent shear-flow: algebraic theory and applications. Phys. Fluids 16, 3670–3681 (2004a)CrossRefADSGoogle Scholar
  64. 64.
    Vreman, A.W.: Turbulence characteristics of particle-laden pipe flow. J. Fluid Mech. 584, 235–279 (2007)zbMATHCrossRefADSMathSciNetGoogle Scholar
  65. 65.
    Vreman, A.W., Geurts, B.J., Deen, N.G., Kuipers, J.A.M.: Large-eddy simulation of a particle-laden turbulent channel flow. In: Friedrich, R., Geurts, B.J., Metais, O. (eds.) Direct and Large-Eddy Simulation V, pp. 271–278. Kluwer, Dordrecht (2004)Google Scholar
  66. 66.
    Vreman, B.: Direct and large-eddy simulation of the turbulent compressible mixing layer. PhD-Thesis, University of Twente (1995)Google Scholar
  67. 67.
    Vreman, B., Geurts, B., Kuerten, H.: Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer. Int. J. Numer. Methods Fluids 22, 297 (1996)zbMATHCrossRefADSGoogle Scholar
  68. 68.
    Vreman, B., Geurts, B.J., Kuerten, J.G.M.: Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390 (1997)zbMATHCrossRefADSMathSciNetGoogle Scholar
  69. 69.
    Yamamoto, Y., Potthoff, M., Tanaka, T. Kajishima, T., Tsuji, Y.: Large-eddy simulation of turbulent gas-particle flow in a vertical channel: effect of considering inter-particle collisions. J. Fluid Mech. 442, 303–334 (2001)zbMATHCrossRefADSGoogle Scholar
  70. 70.
    Wang, Q., Squires, K.D.: Large eddy simulation of particle deposition in a vertical turbulent channel flow. Int. J. Multiph. Flow 22, 667 (1996)zbMATHCrossRefGoogle Scholar
  71. 71.
    Wen, Y.C., Yu, Y.H.: Mechanics of fluidization. Chem. Eng. Prog. Symp. Ser. 62, 100–111 (1966)Google Scholar
  72. 72.
    Whitaker, S.: The Forchheimer equation: a theoretical development. Transp. Porous Media 25, 27–61 (1996)CrossRefGoogle Scholar
  73. 73.
    Young, J., Leeming, A.: A theory of particle deposition in turbulent pipe flow. J. Fluid Mech. 340, 129–159 (1997)zbMATHCrossRefADSGoogle Scholar
  74. 74.
    Zhang, D.Z., Prosperetti, A.: Momentum and energy equations for disperse two-phase flows and their closure for dilute suspensions. Int. J. Multiph. Flow 23, 425–453 (1997)zbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2008

Authors and Affiliations

  • Bert Vreman
    • 1
  • Bernard J. Geurts
    • 2
    • 3
    Email author
  • N. G. Deen
    • 4
  • J. A. M. Kuipers
    • 4
  • J. G. M. Kuerten
    • 5
  1. 1.Vreman ResearchNTThe Netherlands
  2. 2.Multiscale Modeling and Simulation, Department of Applied MathematicsUniversity of TwenteAEThe Netherlands
  3. 3.Anisotropic Turbulence, Fluid Dynamics LaboratoryEindhoven University of TechnologyMBThe Netherlands
  4. 4.Department of Chemical Engineering, J.M. Burgers Center, Faculty TNWUniversity of TwenteEnschedeThe Netherlands
  5. 5.Department of Mechanical Engineering, J.M. Burgers CenterTechnische Universiteit EindhovenMBThe Netherlands

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