Skip to main content
×
Home
    • Aa
    • Aa

Impact of collisional versus viscous dissipation on flow instabilities in gas–solid systems

  • Xiaolong Yin (a1), John R. Zenk (a2), Peter P. Mitrano (a2) and Christine M. Hrenya (a2)
Abstract
Abstract

Flow instabilities encountered in the homogeneous cooling of a gas–solid system are considered via lattice-Boltzmann simulations. Unlike previous efforts, the relative contribution of the two mechanisms leading to instabilities is explored: viscous dissipation (fluid-phase effects) and collisional dissipation (particle-phase effects). The results indicate that the instabilities encountered in the gas–solid system mimic those previously observed in their granular (no fluid) counterparts, namely a velocity vortex instability that precedes in time a clustering instability. We further observe that the onset of the instabilities is quicker in more dissipative systems, regardless of the source of the dissipation. Somewhat surprisingly however, a cross-over of the kinetic energy levels is observed during the evolution of the instability. Specifically, the kinetic energy of the gas–solid system is seen to become greater than that of its granular counterpart (i.e. same restitution coefficient) after the vortex instability sets in. This cross-over of kinetic energy levels between a more dissipative system (gas–solid) and a less dissipative system (granular) can be explained by the alignment of particle motion found in a vortex. Such alignment leads to a reduction in both collisional and viscous energy dissipation due to the more glancing nature of collisions.

Copyright
Corresponding author
Email address for correspondence: hrenya@colorado.edu
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

K. Agrawal , P. N. Loezos , M. Syamlal & S. Sundaresan 2001 The role of meso-scale structures in rapid gas–solid flows. J. Fluid Mech. 445, 151.

J. J. Brey 1999 Origin of density clustering in a freely evolving granular gas. Phys. Rev. E 60, 3150.

N. Brilliantov , C. Saluena , T. Schwager & T. Pöschel 2004 Transient structures in a granular gas. Phys. Rev. Lett. 93, 134301.

R. Brito & M. H. Ernst 1998 Extension of Haff’s cooling law in granular flows. Europhys. Lett. 43, 497.

Z.-G Feng & E. E. Michaelides 2005 Proteus: a direct forcing method in the simulations of particulate flows. J. Comput. Phys. 202, 51.

V. Garzó 2005 Instabilities in a free granular fluid described by the Enskog equation. Phys. Rev. E 72, 021106.

B. J. Glasser , S. Sundaresan & I. G. Kevrekidis 1998 From bubbles to clusters in fluidized beds. Phys. Rev. Lett. 81, 1849.

I. Goldhirsch 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267.

I. Goldhirsch , M.-L. Tan & G. Zanetti 1993 A molecular dynamical study of granular fluids I: the unforced granular gas in two dimensions. J. Sci. Comput. 8, 1.

I. Goldhirsch & G. Zanetti 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619.

M. Hopkins & M. Louge 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47.

C. M. Hrenya , J. E. Galvin & R. D. Wildman 2008 Evidence of higher-order effects in thermally-driven, rapid granular flows. J. Fluid Mech. 598, 429.

D. L. Koch 1990 Kinetic theory for a monodisperse gas–solid suspension. Phys. Fluids A 2, 1711.

D. L. Koch & A. S. Sangani 1999 Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229.

A. Kudrolli , M. Wolpert & J. P. Gollub 1997 Cluster formation due to collisions in a granular material. Phys. Rev. Lett. 78, 1383.

A. J. C. Ladd & R. Verberg 2001 Lattice-Boltzmann simulation of particle-fluid suspensions. J. Stat. Phys. 104, 1191.

P. P. Mitrano , S. R. Dahl , D. J. Cromer , M. S. Pacella & C. M. Hrenya 2011 Instabilities in the homogeneous cooling of a granular gas: a quantitative assessment of kinetic-theory prediction. Phys. Fluids 23, 093303.

P. P. Mitrano , V. Garzó , A. M. Hilger , C. J. Ewasko & C. M. Hrenya 2012 Assessing a hydrodynamic description for instabilities in highly dissipative, freely cooling granular gases. Phys. Rev. E 85, 141303.

N.-Q. Nguyen & A. J. C. Ladd 2002 Lubrication corrections for lattice-Boltzmann simulations of particle suspensions. Phys. Rev. E 66, 046708.

J. R. Royer , D. J. Evans , L. Oyarte , Q. Guo , E. Kapit , M. E. Mobius , S. R. Waitukaitis & H. M. Jaeger 2009 High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459, 1110.

A. S. Sangani , G. Mo , H.-K. Tsao & D. L. Koch 1996 Simple shear flows of dense gas–solid suspensions at finite stokes numbers. J. Fluid Mech. 313, 309.

S. Tenneti , R. Garg , C. M. hrenya , R. O. Fox & S. Subramaniam 2010 Direct numerical simulation of gas–solid suspensions at moderate Reynolds number: quantifying the coupling between hydrodynamic forces and particle velocity fluctuations. Powder Technol. 203, 57.

A. Wachs 2009 A DEM-DLM/FD method for direct numerical simulation of particulate flows: sedimentation of polygonal isometric particles in a Newtonian fluid with collisions. Comput. Fluids 38, 1608.

R. D. Wildman , T. W. Martin , J. M. Huntley , J. T. Jenkins , H. Viswanathan , X. Fen & D. J. Parker 2008 Experimental investigation and kinetic-theory-based model of a rapid granular shear flow. J. Fluid Mech. 602, 63.

J. J. Wylie & D. L. Koch 2000 Particle clustering due to hydrodynamic interactions. Phys. Fluids 12, 964.

J. J. Wylie , D. L. Koch & J. C. Ladd 2003 Rheology of suspensions with high particle inertia and moderate fluid inertia. J. Fluid Mech. 480, 95.

J. J. Wylie , Q. Zhang & Y. Li 2009 Driven inelastic-particle systems with drag. Phys. Rev. E 79, 031301.

H. Xu , M. Louge & A. Reeves 2003 Solutions of the kinetic theory for bounded collisional granular flows. Contin. Mech. Thermodyn. 15, 321.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords:

Type Description Title
VIDEO
Movie

Yin et al. supplementary movie
Evolution of the coarse-grained particle velocity field at three different times: ReT = 30, e = 0.8, φ = 0.2, ρp /ρg = 1000.

 Video (64.4 MB)
64.4 MB
VIDEO
Movie

Yin et al. supplementary movie
Evolution of the coarse-grained particle velocity field at three different times: ReT = 30, e = 0.8, φ = 0.2, ρp /ρg = 1000.

 Video (18.0 MB)
18.0 MB

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 62 *
Loading metrics...

Abstract views

Total abstract views: 215 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 26th September 2017. This data will be updated every 24 hours.