Advertisement

Granular Matter

, Volume 17, Issue 2, pp 231–252 | Cite as

Computational modeling of the dynamics and interference effects of an erosive granular jet impacting a porous, compliant surface

  • Debanjan Mukherjee
  • Tarek I. Zohdi
Original Paper

Abstract

The general problem of a loosely flowing erosive granular jet undergoing impact with a compliant surface is common in many manufacturing processes, and also in the operating environment of a variety of machine parts. This paper presents a three-dimensional, collision-driven discrete particle simulation framework for investigating the dynamics of a jet of erosive particles impacting a surface with a specified porosity and compliance. The framework is capable of handling repeated collisions between incoming particles and rebounding particles, and between particles and surfaces. It is also capable of performing a coupled simultaneous calculation of sub-surface stresses in the material, assuming a certain porosity. Well illustrated numerical examples are presented with detailed analysis for investigations on the mechanics and energetics of the interfering collisions in eroding jets close to the target surface, on the effect of such interference on the material erosion, and on the evolving stress levels and potential damage zones under the action of impact. Particularly, the assumption of considering first-order collisions between oncoming and rebounding jet particles is re-examined. The influence of repeated collisions on energy transferred to the surface was found to be significant under conditions which involves high particle numbers or fluxes, and also high degrees of inelasticity. The overall trends for parametric variations were found to be in accordance with reported trends in the literature.

Keywords

Granular jet Solid particle erosion  Collisions  Discrete element method Interference effect 

Notes

Acknowledgments

This work was partly supported by Siemens Energy, and the authors would like to thank them for their support. The work has not been published in any other journal prior to this. There were no study participants involved in this work, as the work was purely computational. The authors also declare that they have no conflict of interest.

References

  1. 1.
    Anand, K., Hovis, S.K., Conrad, H., Scattergood, R.O.: Flux effects in solid particle erosion. Wear 118(2), 243–257 (1987)CrossRefGoogle Scholar
  2. 2.
    Andrews, D.R., Horsfield, N.: Particle collisions in the vicinity of an eroding surface. J. Phys. D Appl. Phys. 16(4), 525–538 (1983)CrossRefADSGoogle Scholar
  3. 3.
    Arbelaez, D., Zohdi, T.I., Dornfeld, D.A.: Modeling and simulation of material removal with particulate flows. Comput. Mech. 42(5), 749–759 (2008)CrossRefzbMATHGoogle Scholar
  4. 4.
    Arbelaez, D., Zohdi, T.I., Dornfeld, D.A.: On impinging near-field granular jets. Int. J. Numer. Methods Eng. 80(6–7), 815–845 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Bitter, J.G.A.: A study of erosion phenomena. Part I. Wear 6(1), 5–21 (1963)Google Scholar
  6. 6.
    Brilliantov, N.V., Spahn, F., Hertzsch, J.M., Thorsten, P.: Model for collisions in granular gases. Phys. Rev. E 53(5), 5382–5392 (1996)CrossRefADSGoogle Scholar
  7. 7.
    Burzynski, T., Papini, M.: Analytical models of the interference between incident and rebounding particles within an abrasive jet: comparison with computer simulation. Wear 263(7–12), 1593–1601 (2007)CrossRefGoogle Scholar
  8. 8.
    Burzynski, T., Papini, M.: Analytical model of particle interference effects in divergent erosive jets. Tribol. Int. 43(3), 554–567 (2010)CrossRefGoogle Scholar
  9. 9.
    Camacho, G.T., Ortiz, M.: Computational modelling of impact damage in brittle materials. Int. J. Solids Struct. 33(2), 2899–2938 (1996)CrossRefzbMATHGoogle Scholar
  10. 10.
    Chaboche, J.L.: Continuum damage mechanics. J. Appl. Mech. 55(1), 59–64 (1988)CrossRefADSGoogle Scholar
  11. 11.
    Chen, X., Wang, R., Yao, N., Evans, A.G., Hutchinson, J.W., Bruce, R.W.: Foreign object damage in a thermal barrier system: mechanisms and simulations. Mater. Sci. Eng. A 352(1–2), 221–231 (2003)Google Scholar
  12. 12.
    Cheng, X., Varas, G., Citron, D., Jaeger, H., Nagel, S.: Collective behavior in a granular jet: emergence of a liquid with zero surface tension. Phys. Rev. Lett. 99(18), 188001 (2007)CrossRefADSGoogle Scholar
  13. 13.
    Ciampini, D., Spelt, J.K., Papini, M.: Simulation of interference effects in particle streams following impact with a flat surface. Part I. Theory and analysis. Wear 254(3–4), 237–249 (2003)CrossRefGoogle Scholar
  14. 14.
    Ciampini, D., Spelt, J.K., Papini, M.: Simulation of interference effects in particle streams following impact with a flat surface part II. Parametric study and implications for erosion testing and blast cleaning. Wear 254, 250–264 (2003)CrossRefGoogle Scholar
  15. 15.
    Cundall, P.A., Strack, O.D.L.: A discrete numerical model for granular assemblies. Géotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  16. 16.
    Duran, J.: Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials. Springer, New York (2000)CrossRefGoogle Scholar
  17. 17.
    Finnie, I.: Erosion of surfaces by solid particles. Wear 3, 87–103 (1960)CrossRefGoogle Scholar
  18. 18.
    Frenkel, D., Smit, B.: Understanding Molecular Simulation: From Algorithms to Applications. Academic Press (2001)Google Scholar
  19. 19.
    Gomes-Ferreira, C., Ciampini, D., Papini, M.: The effect of inter-particle collisions in erosive streams on the distribution of energy flux incident to a flat surface. Tribol. Int. 37(10), 791–807 (2004)CrossRefGoogle Scholar
  20. 20.
    Haff, P.K., Werner, B.T.: Computer simulation of the mechanical sorting of grains. Powder Technol. 48(3), 239–245 (1986)CrossRefGoogle Scholar
  21. 21.
    Hamilton, G.M.: Explicit equations for the stresses beneath a sliding spherical contact. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci. 197, 53–59 (1983)CrossRefGoogle Scholar
  22. 22.
    Hashin, Z., Shtrikman, S.: A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33(10), 3125–3131 (1962)CrossRefADSzbMATHGoogle Scholar
  23. 23.
    Hashin, Z., Shtrikman, S.: A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids 11(2), 127–140 (1963)CrossRefADSzbMATHMathSciNetGoogle Scholar
  24. 24.
    Hertz, H.: Miscellaneous Papers. Macmillan, New York (1896)zbMATHGoogle Scholar
  25. 25.
    Huang, Y.J., Chan, C.K., Zamankhan, P.: Granular jet impingement on a fixed target. Phys. Rev. E 82(3), 031307 (2010)CrossRefADSGoogle Scholar
  26. 26.
    Hutchings, I.M., Winter, R.E., Field, J.E.: Solid particle erosion of metals: the removal of surface material by spherical projectiles. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 348(1654), 379–392 (1976)CrossRefADSGoogle Scholar
  27. 27.
    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1987)Google Scholar
  28. 28.
    Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin (2005)Google Scholar
  29. 29.
    Lubachevsky, B.D., Stillinger, F.H.: Geometric properties of random disk packings. J. Stat. Phys. 60(5), 561–583 (1990)CrossRefADSzbMATHMathSciNetGoogle Scholar
  30. 30.
    Mattson, W., Rice, B.M.: Near-neighbor calculations using a modified cell-linked list method. Comput. Phys. Commun. 119(2–3), 135–148 (1999)CrossRefADSGoogle Scholar
  31. 31.
    Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)zbMATHMathSciNetGoogle Scholar
  32. 32.
    Müller, P., Formella, A., Pöschel, T.: Granular jet impact: probing the ideal fluid description. J. Fluid Mech. 751, 601–626 (2014)CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    Müller, P., Pöschel, T.: Collision of viscoelastic spheres: compact expressions for the coefficient of normal restitution. Phys. Rev. E 84(2), 021302 (2011)CrossRefADSGoogle Scholar
  34. 34.
    Müller, P., Pöschel, T.: Two-ball problem revisited: limitations of event-driven modeling. Phys. Rev. E 83(4), 041304 (2011)CrossRefADSGoogle Scholar
  35. 35.
    Müller, P., Pöschel, T.: Event-driven molecular dynamics of soft particles. Phys. Rev. E 87(3), 033301 (2013)CrossRefADSGoogle Scholar
  36. 36.
    Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Heldermann, Berlin (1988)zbMATHGoogle Scholar
  37. 37.
    Nicholls, J.R., Jaslier, Y., Rickerby, D.S.: Erosion and foreign object damage of thermal barrier coatings. Mater. Sci. Forum 251–254, 935–948 (1997)CrossRefGoogle Scholar
  38. 38.
    Oden, J.T., Pires, E.B.: Nonlocal and nonlinear friction laws and variational principles for contact problems in elasticity. J. Appl. Mech. 50, 67–76 (1983)CrossRefADSzbMATHMathSciNetGoogle Scholar
  39. 39.
    Oka, Y.I., Nishimura, M., Nagahashi, K., Matsumura, M.: Control and evaluation of particle impact conditions in a sand erosion test facility. Wear 250(1–12), 736–743 (2001)CrossRefGoogle Scholar
  40. 40.
    Oka, Y.I., Okamura, K., Yoshida, T.: Practical estimation of erosion damage caused by solid particle impact. Wear 259(1–6), 95–101 (2005)CrossRefGoogle Scholar
  41. 41.
    Plantard, G., Papini, M.: Mechanical and electrical behaviors of polymer particles. Experimental study of the contact area between two particles. Experimental validation of a numerical model. Granul. Matter 7(1), 1–12 (2005)CrossRefGoogle Scholar
  42. 42.
    Pöschel, T., Schwager, T.: Computational Granular Dynamics: Models and Algorithms. Springer, Berlin (2005)Google Scholar
  43. 43.
    Ramanujam, N., Nakamura, T.: Erosion mechanisms of thermally sprayed coatings with multiple phases. Surf. Coat. Technol. 204(1–2), 42–53 (2009)CrossRefGoogle Scholar
  44. 44.
    Shäfer, J., Dippel, S., Wolf, D.E.: Force schemes in simulations of granular materials. J. Phys. I 6(1), 5–20 (1996)Google Scholar
  45. 45.
    Shipway, P.H., Hutchings, I.M.: A method for optimizing the particle flux in erosion testing with a gas-blast apparatus. Wear 174(1–2), 169–175 (1994)CrossRefGoogle Scholar
  46. 46.
    Stewart, D.E.: Rigid-body dynamics with friction and impact. SIAM Rev. 42(1), 3–39 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  47. 47.
    Torquato, S., Uche, O., Stillinger, F.: Random sequential addition of hard spheres in high Euclidean dimensions. Phys. Rev. E 74(6), 1–16 (2006)CrossRefMathSciNetGoogle Scholar
  48. 48.
    Uuemois, H., Kleis, I.: A critical analysis of erosion problems which have been little studied. Wear 31, 359–371 (1975)CrossRefGoogle Scholar
  49. 49.
    Vu-Quoc, L., Lesburg, L., Zhang, X.: An accurate tangential forcedisplacement model for granular-flow simulations: contacting spheres with plastic deformation, force-driven formulation. J. Comput. Phys. 196(1), 298–326 (2004)CrossRefADSzbMATHGoogle Scholar
  50. 50.
    Vu-Quoc, L., Zhang, X.: An accurate and effcient tangential force-displacement model for elastic frictional contact in particle flow simulations. Mech. Mater. 31(4), 235–269 (1999)CrossRefGoogle Scholar
  51. 51.
    Waitukaitis, S.R., Grütjen, H.F., Royer, J.R., Jaeger, H.M.: Droplet and cluster formation in freely falling granular streams. Phys. Rev. E 83(5), 051302 (2011)CrossRefADSGoogle Scholar
  52. 52.
    Walton, O.R., Braun, R.L.: Viscosity, granular temperature, and stress calculations for shearing assemblies of inelastic frictional disks. J. Rheol. 30(5), 949–980 (1986)CrossRefADSGoogle Scholar
  53. 53.
    Widom, B.: Random sequential addition of hard spheres to a volume. J. Chem. Phys. 44(10), 3888 (1966)CrossRefADSGoogle Scholar
  54. 54.
    Wriggers, P., Zavarise, G.: Computational Contact Mechanics. Springer, Berlin (2002)Google Scholar
  55. 55.
    Zhang, X., Vu-Quoc, L.: An accurate elasto-plastic frictional tangential force displacement model for granular-flow simulations: displacement-driven formulation. J. Comput. Phys. 225(1), 730–752 (2007)CrossRefADSzbMATHGoogle Scholar
  56. 56.
    Zohdi, T.I.: Bounding envelopes in multiphase material design. J. Elast. 66(1), 47–62 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  57. 57.
    Zohdi, T.I.: On the tailoring of microstructures for prescribed effective properties. Int. J. Fract. 118(4), 89–94 (2002)Google Scholar
  58. 58.
    Zohdi, T.I.: An introduction to modeling and simulation of particulate flows. In: Computational Science and Engineering, vol 4. Siam, Philadelphia (2007)Google Scholar
  59. 59.
    Zohdi, T.I.: On the dynamics of charged electromagnetic particulate jets. Arch. Comput. Methods Eng. 17(2), 109–135 (2010)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of California, BerkeleyBerkeleyUSA

Personalised recommendations