Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-29T13:41:52.643Z Has data issue: false hasContentIssue false
  • English
  • Français

Granular jet impact: probing the ideal fluid description

Published online by Cambridge University Press:  24 June 2014

Patric Müller ,
Arno Formella  and
Thorsten Pöschel
Patric Müller*
Affiliation:
Institute for Multiscale Simulation, Universität Erlangen-Nürnberg, 91052 Erlangen, Germany
Arno Formella
Affiliation:
Universidad de Vigo, Department of Computer Science, Ourense, Spain
Thorsten Pöschel
Affiliation:
Institute for Multiscale Simulation, Universität Erlangen-Nürnberg, 91052 Erlangen, Germany
*
†Email address for correspondence: patric.mueller@cbi.uni-erlangen.de
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the impact of a granular jet on a finite target by means of particle simulations. The resulting hydrodynamic fields are compared with theoretical predictions for the corresponding flow of an incompressible and rotation-free fluid. The degree of coincidence between the field obtained from the discrete granular system and the idealized continuous fluid flow depends on the characteristics of the granular system, such as granularity, packing fraction, inelasticity of collisions, friction and target size. In certain limits we observe a granular–continuum transition under which the geometric and dynamic properties of the particle jet and the fluid jet become almost identical.

JFM classification

Complex Fluids: Complex Fluids Granular media: Granular media Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 601 - 626
Copyright
© 2014 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bannerman, M. N., Sargant, R. & Lue, L. 2011 DynamO: a free O(N) general event-driven simulator. J. Comput. Chem. 32, 3329–3338.CrossRefGoogle ScholarPubMed
Bernu, B. & Mazighi, R. 1990 One-dimensional bounce of inelastically colliding marbles on a wall. J. Phys. A 23, 5745–5754.CrossRefGoogle Scholar
Brito, R. & Ernst, M. 1998 Extension of Haff’s cooling law in granular flows. Europhys. Lett. 43, 497–502.CrossRefGoogle Scholar
Cheng, X., Varas, G., Citron, D., Jaeger, H. M. & Nagel, S. R. 2007 Collective behavior in a granular jet: emergence of a liquid with zero surface tension. Phys. Rev. Lett. 99, 188001.CrossRefGoogle Scholar
Clanet, C. 2001 Dynamics and stability of water bells. J. Fluid Mech. 430, 111–147.CrossRefGoogle Scholar
Ellowitz, J., Guttenberg, N. & Zhang, W. W.2012 Perfect fluid flow from granular jet impact. arXiv:1201.5562v1 [physics.flu-dyn].Google Scholar
Ellowitz, J., Turlier, H., Gutenberg, N., Zhang, W. W. & Nagel, S. R. 2013 Still water: dead zones and collimated ejecta from the impact of granular jets. Phys. Rev. Lett. 111, 168001.CrossRefGoogle ScholarPubMed
Goldenberg, C. & Goldhirsch, I. 2006 Continuum mechanics for small systems and fine resolutions. In Handbook of Theoretical and Computational Nanotechnology (ed. Rieth, M. & Schommers, W.), vol. 4, pp. 329–386. American Scientific.Google Scholar
Goldhirsch, I. 1999 Scales and kinetics of granular flows. Chaos 9, 659–672.CrossRefGoogle ScholarPubMed
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293.CrossRefGoogle Scholar
Goldhirsch, I. 2010 Stress, stress asymmetry and couple stress: from discrete particles to contiuous fields. Granul. Matt. 12, 239–252.CrossRefGoogle Scholar
Gommeren, H. J. C., Heitzmann, D. A., Moolenaar, J. A. C. & Scarlett, B. 2000 Modelling and control of a jet mill plant. Powder Technol. 108, 147–154.CrossRefGoogle Scholar
Gurevich, M. I. 1965 Theory of Jets in Ideal Fluids. Academic Press.Google Scholar
Guttenberg, N. 2012 Microscopic dissipation in a cohesionless granular jet impact. Phys. Rev. E 85, 051303.CrossRefGoogle Scholar
Huang, Y. J., Chan, C. K. & Zamankhan, P. 2010 Granular jet impingement on a fixed target. Phys. Rev. E 82, 031307.CrossRefGoogle ScholarPubMed
Kapfer, S. C., Mickel, W., Mecke, K. & Schröder-Turk, G. E. 2012 Jammed spheres: Minkowski tensors reveal onset of local crystallinity. Phys. Rev. E 85, 030301.CrossRefGoogle ScholarPubMed
Kuppinger, G. 1990 Strahlen von Oberflächen. Metall 44, 43–52.Google Scholar
Lubachevsky, B. D. 1991 How to simulate billiards and similar systems. J. Comput. Phys. 94, 255–283.CrossRefGoogle Scholar
Lubachevsky, B. D. & Stillinger, F. H. 1990 Geometric properties of random disk packings. J. Stat. Phys. 60, 561–583.CrossRefGoogle Scholar
Luding, S. & McNamara, S. 1998 How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model. Granul. Matt. 1, 113–128.CrossRefGoogle Scholar
McNamara, S. & Young, W. R. 1991 Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids 4, 496–504.CrossRefGoogle Scholar
Müller, P., Krengel, D. & Pöschel, T. 2012 Negative coefficient of normal restitution. Phys. Rev. E 85, 041306.CrossRefGoogle ScholarPubMed
Müller, P. & Pöschel, T. 2012 Oblique impact of frictionless spheres: on the limitations of hard sphere models for granular dynamics. Granul. Matt. 14, 115–120.CrossRefGoogle Scholar
Pöschel, T. & Schwager, T. 2005 Computational Granular Dynamics – Models and Algorithms. Springer.Google Scholar
Sano, T. G. & Hayakawa, H. 2012 Simulation of granular jets: is granular flow really a perfect fluid? Phys. Rev. Lett. 86, 041308.Google ScholarPubMed
Savart, F. 1833 Mémoire sur le choc d’une veine liquid lancée contre un plan circulaire. Ann. Chim. Phys. 54, 55–87.Google Scholar
Schwager, T., Becker, V. & Pöschel, T. 2008 Coefficient of tangential restitution for viscoelastic spheres. Eur. Phys. J. E 27, 107–114.CrossRefGoogle ScholarPubMed
Schwager, T. & Pöschel, T. 2008 Coefficient of restitution for viscoelastic spheres: the effect of delayed recovery. Phys. Rev. E 78, 051304.CrossRefGoogle ScholarPubMed
Serero, D., Goldenberg, C., Noskowicz, S. H. & Goldhirsch, I. 2008 The classical granular temperature and slightly beyond. Powder Technol. 182, 257–271.CrossRefGoogle Scholar
Tan, M. -L. & Goldhirsch, I. 1998 Rapid granular flows as mesoscopic systems. Phys. Rev. Lett. 81, 3022–3025.CrossRefGoogle Scholar
Uehara, J. S., Ambroso, M. A., Ojha, R. P. & Durian, D. J. 2003 Low-speed impact craters in loose granular media. Phys. Rev. Lett. 90, 194301.CrossRefGoogle ScholarPubMed