Acta Mechanica Sinica

, Volume 20, Issue 4, pp 354–365 | Cite as

Improved subgrid scale model for dense turbulent solid-liquid two-phase flows

  • Tang Xuelin
  • Qian Zhongdong
  • Wu Yulin
Article
Received:
Revised:

Abstract

The dense solid-phase governing equations for two-phase flows are obtained by using the kinetic theory of gas molecules. Assuming that the solid-phase velocity distributions obey the Maxwell equations, the collision term for particles under dense two-phase flow conditions is also derived. In comparison with the governing equations of a dilute two-phase flow, the solid-particle's governing equations are developed for a dense turbulent solid-liquid flow by adopting some relevant terms from the dilute two-phase governing equations. Based on Cauchy-Helmholtz theorem and Smagorinsky model, a second-order dynamic sub-grid-scale (SGS) model, in which the sub-grid-scale stress is a function of both the strain-rate tensor and the rotation-rate tensor, is proposed to model the two-phase governing equations by applying dimension analyses. Applying the SIMPLEC algorithm and staggering grid system to the two-phase discretized governing equations and employing the slip boundary conditions on the walls, the velocity and pressure fields, and the volumetric concentration are calculated. The simulation results are in a fairly good agreement with experimental data in two operating cases in a conduit with a rectangular cross-section and these comparisons imply that these models are practical.

Key Words

kinetic theory turbulent two-phase flow dynamic sub-grid-scale model conduit 
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Zhou LX. Theory and Modeling of Turbulent Two-Phase Flow and Combustion. Beijing: Tsinghua University Press, 1991 (in Chinese)Google Scholar
  2. 2.
    Enwald H, Perirano E, et al. Eulerian two-phase flow theory applied to fluidization.Int J Multiphase Flow, 1996, 22(Suppl.): 21–66CrossRefMATHGoogle Scholar
  3. 3.
    Zhang Y, Wilson JD, Lozowski EP. A trajectory simulation model for heavy particle motion in turbulent flow.ASME J Fluid Eng, 1989. 492–494Google Scholar
  4. 4.
    Tang XL, Tang HF, Wu YL. Silt abrasion of hydraulic runner with silt-laden two-phase flow analysis. In: Mei ZY et al. eds. The Second International Symposium on Fluid Machinery and Fluid Engineering (2nd ISFMFE), Beijing: China Science & Technology Press, 2000, 344–348Google Scholar
  5. 5.
    Wu YL, Oba R, Ikohagi T. Computation on turbulent dilute liquid-particle flows through a centrifugal impeller.Japanese J Multiphase Flow, 1994, 8(2): 118–125Google Scholar
  6. 6.
    Zhou LX, Chen T. Simulation of swirling gas-particle flows using USM andk-ε-k p two-phase turbulence models.Power Technology, 2001, 114: 1–11CrossRefGoogle Scholar
  7. 7.
    Wang Q, Squires KD. Large eddy simulation of particle deposition in a vertical turbulent channel flow.Int J Multiphase Flow, 1996, 22(4): 667–683CrossRefMATHGoogle Scholar
  8. 8.
    Boivin M, Simonin O, Squire KD. On the prediction of gas-solid flows with two-way coupling using large eddy simulation.Physics of Fluids, 2000, 12(8): 2080–2090CrossRefGoogle Scholar
  9. 9.
    Ni JR, Wang GQ, Borthwick AJL. Kinetic theory for particles in dilute and dense solid-liquid flows.Journal of Hydraulic Engineering, ASCE, 2000, 126(12): 893–903CrossRefGoogle Scholar
  10. 10.
    Ishii M. Thermo-Fluid Dynamic Theory of Two-Phase Flow. Paris: Eyrolles, 1975MATHGoogle Scholar
  11. 11.
    Pai S-I. Two-phase Flow. New York: Vieweg, 1977Google Scholar
  12. 12.
    Liu DY. Fluid Dynamics of Two-phase System. Beijing: Higher Education Press, 1993 (in Chinese)Google Scholar
  13. 13.
    Samuelsberg A, Hjertager BH. An experimental and numerical study of flow patterns in a circulating fluidized bed reactor.International Journal of Multiphase Flow, 2000, 22(3): 575–591CrossRefGoogle Scholar
  14. 14.
    Mathiesen V, Solberg T, Hjertager TH. An experimental and computational study of multiphase flow behavior in a circulating fluidized bed.International Journal of Multiphase Flow, 2000, 26: 387–419CrossRefMATHGoogle Scholar
  15. 15.
    Mathiesen V, Solberg T, et al. Predictions of gas/particle flow with an Eulerian model including a realistic particle size distribution.Power Technology, 2000, 112: 34–45CrossRefGoogle Scholar
  16. 16.
    Benyahia S, Arastoopour H, et al. Simulation of particles and gas flow behavior in the riser section of a circulating fluidized bed using the kinetic theory approach for the particulate phase.Power Technology, 2000, 112: 24–33CrossRefGoogle Scholar
  17. 17.
    Filippova O, Hanel D. Lattice-Boltzmann simulation of gas-particle flow in filters.Computers & Fluid, 1997, 26(7): 697–712MATHCrossRefGoogle Scholar
  18. 18.
    Moser RD, Kim J, Mansour NN. Direct numerical simulation of turbulent channel flow up toRe τ=590.Phys Fluids, 1999, (11): 943CrossRefMATHGoogle Scholar
  19. 19.
    Smagrinsky J. General circulation experiments with the primitive equations I.Mon Weather Review, 1963, 91(3): 99–165Google Scholar
  20. 20.
    Deardorff JW. A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers.J Fluid Mechanics, 1970, 41: 453–480MATHCrossRefGoogle Scholar
  21. 21.
    Leith CE, Backscatter S. In a subgrid-scale model: plane shear mixing layer.Phys Fluids, 1990, 2: 297CrossRefGoogle Scholar
  22. 22.
    Germano M, Piomelli U, et al. A dynamic subgridscale eddy viscosity model.Phys Fluids, 1991, A3(7): 1760–1765Google Scholar
  23. 23.
    Lilly DK. A proposed modification of the Germano subgrid-scale closure method.Phys Fluids A, 1992, 4(3): 633–635MathSciNetCrossRefGoogle Scholar
  24. 24.
    Zang Y, Street RL, Koseff JR. A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows.Phys Fluids A, 1993, 5(12): 3186–3196CrossRefGoogle Scholar
  25. 25.
    Ghosal S, Lund TS, et al. A dynamic localization model for large-eddy simulation of turbulent flows.J Fluid Mech, 1995, 286: 229–255MATHMathSciNetCrossRefGoogle Scholar
  26. 26.
    Bardina J, Ferziger JH, Reynolds WC. Improved subgrid-scale models for large-eddy simulation.AIAA Paper, 1980, (80): 1357Google Scholar
  27. 27.
    Chapman S, Cowling TG. The Mathematical Theory of Non-Uniform Cases. Third Edition, London: Cambridge University Press, 1970Google Scholar
  28. 28.
    Vincenti WG, Kruger GH Jr. Introduction to Physical Gas Dynamics, New York: John Wiley, 1965Google Scholar
  29. 29.
    Ding JX, Gidaspow D. A bubbling fluidization model using kinetic theory of granular flow.AIChE J, 1990, 36(4): 523–538CrossRefGoogle Scholar
  30. 30.
    Soo SL. Particulated and Continuum: Multiphase Fluid Dynamics. New York: Hemisphere Publication Corp, 1989Google Scholar
  31. 31.
    Wang ZY, Ning C. Experimental study of two-phase turbulent flow with hyperconcentration of coarse particles.Science in China, Ser A, 1984, 27(12): 1317–1327Google Scholar
  32. 32.
    Wang ZY, Ning C. Experimental study of laminated load.Science in China, Ser A, 1985, 28(1): 102–112Google Scholar
  33. 33.
    Ferziger JH. Large eddy numerical simulation of turbulent flows.AIAA J, 1977, 15(9): 1261–1267MATHCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2004

Authors and Affiliations

  • Tang Xuelin
    • 1
  • Qian Zhongdong
    • 2
  • Wu Yulin
    • 2
  1. 1.Department of Hydraulic and Hydropower EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Thermal EngineeringTsinghua UniversityBeijingChina

Personalised recommendations