Skip to main content
SpringerLink
Log in

DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Deflecting wedge obstacles are often built to divert hazardous flows away from residential areas that are in the way of harm. When a rapid avalanche flow is deflected by an obstacle, this usually causes abrupt changes in the flow thickness and velocity and exhibits characteristics like oblique shock waves in the aerodynamic system or oblique hydraulic jumps in the open channel flows. In this study, the Discrete Element Method (DEM) is employed to simulate the motion of granular materials impinging on a wedge obstacle in an adjustable inclination chute. We use chutes with four different inclined angles combined with wedge obstacles having different angles to investigate the overall flow behavior. Both the flow velocity and the flow depth are obtained by averaging the numerical simulation data, and then the granular temperature and the shock angle are calculated. The results of the DEM simulation are compared with that of the classical oblique shock theory. We find that there is good agreement between the classical oblique granular shock theoretical calculations and the DEM simulation results. Moreover, the microdynamic variables related to flow structure such as the packing density and the coordination number are also discussed in the present study.

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. Massol-Chaudeur S., Berthiaux H., Dodds J.A.: Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer. Chem. Eng. Sci. 57, 4053–4065 (2002)

    Article  Google Scholar 

  2. Sudah O.S., Coffin-Beach D., Muzzio F.J.: Quantitative characterization of mixing of free-flowing granular material in tote (bin)-blenders. Powder Technol. 126, 191–200 (2002)

    Article  Google Scholar 

  3. Molina-Boisseau S., Bolay N.L.: The mixing of polymeric powder and the grinding medium in a shaker beadmill. Powder Technol. 123, 212–220 (2002)

    Article  Google Scholar 

  4. Vallance J.W.: Lahars. In: Sigurdsson, H., Houghton, B., McNutt, S.R., Rymer, H., Stix, J. (eds.) Encyclopedia of Volcanoes, pp. 601–616. Academic Press, San Diego (2000)

    Google Scholar 

  5. Iverson R.M.: The physics of debris-flows. Rev. Geophys. 35, 245–296 (1997)

    Article  ADS  Google Scholar 

  6. Savage S.B., Hutter K.: The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199, 177–215 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Sparks, R.S.J., Barclay, J., Calder, E.S., Herd, R.A., Luckett, R., Norton, G.E., Ritchie, L., Voight, S.R., Woods, A.W.: Generation of a debris avalanche and violent pyroclastic density current on 26 December (Boxing Day) 1997 at Soufriere Hills Volcano, Monserrat. In: The eruption of Soufriere Hills Volcano, Monserrat, from 1995 to 1999 (eds. Druitt & Kokelaar). Geological Society, London, Memoirs, 21, 409–435, (2002)

  8. Rouse H.: Fluid Mechanics for Hydraulic Engineers 1st edn. McGraw-Hill, New York (1938)

    Google Scholar 

  9. Ippen A.T.: Mechanics of supercritical flow. ASCE 116, 268–296 (1949)

    Google Scholar 

  10. Stoker J.J.: Water Waves: The Mathematical Theory with Applications. Wiley-Interscience, New York (1957)

    MATH  Google Scholar 

  11. Gray J.M.N.T., Wieland M., Hutter K.: Free surface flow of cohesionless granular avalanches over complex basal topography. Proc. R. Soc. Lond. A 455, 1841–1874 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Wieland M., Gray J.M.N.T., Hutter K.: Channelized free surface flow of cohesionless granular avalanches in a chute with shallow lateral curvature. J. Fluid Mech. 392, 73–100 (1999)

    Article  ADS  MATH  Google Scholar 

  13. Gray J.M.N.T., Tai Y.C., Noelle S.: Shock waves, dead-zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491, 161–181 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Hákonardóttir K.M., Hogg A.J.: Oblique shocks in rapid granular flows. Phys. Fluids 17, 0077101 (2005)

    Article  Google Scholar 

  15. Cui X., Gray J.M.N.T., Jóhannesson T.: Deflecting dams and the formation of oblique shocks in snow avalanches at Flateyri, Iceland. J. Geophys. Res. 112, F04012 (2007)

    Article  ADS  Google Scholar 

  16. Gray J.M.N.T., Cui X.: Weak, strong and detached oblique shocks in gravity driven granular free-surface flows. J. Fluid Mech. 579, 113–136 (2007)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Denlinger, R.P., Iverson, R.M.: Flow of variably fluidized granular masses across three-dimensional terrain 2. Numerical predictions and experimental tests. J. Geophys. Res. 553–566 (2001)

  18. Pouliquen O.: Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11, 542–548 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. Hutter K., Wang Y., Pudasaini S.P.: The Savage-Hutter avalanch model: how far can it be pushed. Philos. Trans. R. Soc. A 363, 1507–1528 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. De Toni S., Scotton P.: Two-dimensional mathematical and numerical model for the dynamics of granular avalanches. Cold Region Sci. Technol. 43, 36–48 (2005)

    Article  Google Scholar 

  21. Luca I., Hutter K., Tai Y.C., Kuo C.Y.: A hierarchy of avalanche models on arbitrary topography. ACTA Mech. 205, 121–149 (2009)

    Article  MATH  Google Scholar 

  22. Lu L.S., Hsiau S.S.: DEM simulation of particle mixing in a sheared granular flow. Particulogy 6, 445–454 (2008)

    Article  Google Scholar 

  23. Yang R.Y., Zou R.P., Yu A.B.: Microdynamic analysis of particle flow in a horizontal rotating drum. Powder Technol. 130, 138–146 (2003)

    Article  Google Scholar 

  24. Sinnott M.D., Cleary P.W.: Vibration-induced arching in a deep granular bed. Granul. Matter 11, 345–364 (2009)

    Article  Google Scholar 

  25. Faug T., Beguin R., Chanut B.: Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows. Phys. Rev. E 80, 021305 (2009)

    Article  ADS  Google Scholar 

  26. Silbert L.E., Ertas D., Grest G.S., Halsey T.C., Levine D., Plimptop S.J.: Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 051302 (2001)

    Article  ADS  Google Scholar 

  27. Teufelsbauer H., Wang Y., Chiou M.C.: Flow-obstacle interaction in rapid granular avalanches: DEM simulation and comparison with experiment. Granul. Matter 11, 209–220 (2009)

    Article  Google Scholar 

  28. Itasca Consulting Group Inc.: PFC3D—Particle Flow Code in three Dimensions, Minneapolis, USA (2010)

  29. Hanes D.M., Walton R.: Simulations and physical measurements of glass spheres flowing down a bumpy incline. Powder Technol. 109, 133–144 (2000)

    Article  Google Scholar 

  30. Sheng L.T., Kuo C.Y., Tai Y.C., Hsiau S.S.: Indirect measurements of streamwise solid fraction variations of granular flows accelerating down a smooth rectangular chute. Exp. Fluids 51, 1329–1342 (2011)

    Article  Google Scholar 

  31. Cundall P.A., Strack O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979)

    Article  Google Scholar 

  32. Lu L.S., Hsiau S.S.: Mixing in a vibrated granular beds with the effect of electrostatic force. Powder Technol. 160, 170–179 (2005)

    Article  Google Scholar 

  33. Pudasaini S.P., Hsiau S.S., Wang Y., Hutter K.: Velocity measurements in dry granular avalanches using image velocimetry technique and comparison with theoretical prediction. Phys. Fluids 17, 93–301 (2005)

    Article  Google Scholar 

  34. Pudasaini S.P., Hutter K., Hsiau S.S., Tai S., Wang Y., Katzenbach R.: Rapid flow of dry granular materials down inclined chutes impinging on rigid wall. Phys. Fluids 19, 53–302 (2007)

    Article  Google Scholar 

  35. Bunin G., Shokef Y., Levine D.: Frequency-dependent fluctuation–dissipation relations in granular gases. Phys. Rev. E 77, 051301 (2008)

    Article  ADS  Google Scholar 

  36. Campbell C.S.: Rapid granular flows. Annu. Rev. Fluid Mech. 22, 57–92 (1990)

    Article  ADS  Google Scholar 

  37. Hsiau S.S., Yang W.L.: Stresses and transport phenomena in sheared granular flows with different wall conditions. Phys. Fluids 14, 612–621 (2002)

    Article  ADS  Google Scholar 

  38. Yang R.Y., Yu A.B., McElroy L., Bao J.: Numerical simulation of particle dynamics in different flow regimes in a rotating drum. Powder Technol. 188, 170–177 (2008)

    Article  Google Scholar 

  39. German R.M.: Particle Packing Characteristics. Metal Powder Industries Federation, Princeton (1989)

    Google Scholar 

  40. Liu L.F., Zhang Z.P., Yu A.B.: Dynamic simulation of the centripetal packing of mono-sized spheres. Phys. A 268, 433–453 (1999)

    Article  Google Scholar 

  41. Yang R.Y., Zou R.P., Yu A.B.: Computer simulation of packing of fine particles. Phys. Rev. E 62, 3900–3908 (2000)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, National Central University, Jhongli, 32001, Taiwan, ROC

    S. H. Chou & S. S. Hsiau

  2. Department of Mechanical Engineering, Taipei Chengshih University of Science and Technology, Taipei, 11202, Taiwan, ROC

    L. S. Lu

Authors
  1. S. H. Chou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. S. Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. S. Hsiau
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. S. Hsiau.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chou, S.H., Lu, L.S. & Hsiau, S.S. DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles. Granular Matter 14, 719–732 (2012). https://doi.org/10.1007/s10035-012-0371-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-012-0371-y

Keywords

Search

Navigation