Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-20T04:12:55.717Z Has data issue: false hasContentIssue false
  • English
  • Français

Evidence of higher-order effects in thermally driven rapid granular flows

Published online by Cambridge University Press:  25 February 2008

C. M. HRENYA ,
J. E. GALVIN  and
R. D. WILDMAN
C. M. HRENYA*
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
J. E. GALVIN
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA United States Department of Energy National Energy Technology Laboratory (NETL), Morgantown, WV 26507-0880, USA
R. D. WILDMAN
Affiliation:
Wolfson School of Mechanical and Manufacturing Engineering, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK
*
†Author to whom correspondence should be addressed: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Molecular dynamic (MD) simulations are used to probe the ability of Navier–Stokes-order theories to predict each of the constitutive quantities – heat flux, stress tensor and dissipation rate – associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect)

Type
Papers
Information
Journal of Fluid Mechanics , Volume 598 , 10 March 2008 , pp. 429 - 450
Copyright
Copyright © Cambridge University Press 2008

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

REFERENCES

Alam, M. & Luding, S. 2003 Rheology of bidisperse granular mixtures via event-driven simulations. J. Fluid Mech. 476, 69.CrossRefGoogle Scholar
Brey, J. J. & Ruiz-Montero, M. J. 2004 Simulation study of the Green–Kubo relations for dilute granular gases. Phys. Rev. E 70, 051301.Google ScholarPubMed
Brey, J. J., Dufty, J. W., Kim, C. S. & Santos, A. 1998 Hydrodynamics for granular flow at low density. Phys. Rev. E 58, 4638.Google Scholar
Brey, J. J., Ruiz-Montero, M. J. & Moreno, F. 2001 Hydrodynamics of an open vibrated system. Phys. Rev. E 63, 061305.Google ScholarPubMed
Brey, J. J., Ruiz-Montero, M. J., Maynar, P. & Garciade Soria, M. I. de Soria, M. I. 2005 Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases. J. Phys. Cond. Matter 17, S2489.CrossRefGoogle Scholar
Brey, J. J., Dominguez, A., Garciade Soria, M. I. de Soria, M. I. & Maynar, P. 2006 Mesoscopic theory of critical fluctuations in isolated granular gases. Phys. Rev. Lett. 96, 158002.CrossRefGoogle ScholarPubMed
Brilliantov, N. V. & Pöschel, T. 2004 Kinetic Theory of Granular Gases. Oxford University Press.CrossRefGoogle Scholar
Campbell, C. S. 1990 Rapid granular flows. Annu. Rev. Fluid Mech. 22, 57.CrossRefGoogle Scholar
Campbell, C. S. & Gong, A. 1986 The stress tensor in a two-dimensional granular shear flow. J. Fluid Mech. 164, 107.CrossRefGoogle Scholar
Carnahan, N. F. & Starling, K. E. 1969 Equation of state of non-attracting rigid spheres. J. Chem. Phys. 51, 635.CrossRefGoogle Scholar
Cercignani, C. 1987 The Boltzmann Equation and its Applications. Springer.Google Scholar
Ciccotti, G. & Tenebaum, A. 1980 Canonical ensemble and nonequilibrium states by molecular dynamics. J. Stat. Phys. 23, 767.CrossRefGoogle Scholar
Clause, P. J. & Mareschal, M. 1988 Heat-transfer in a gas between parallel plates – moment method and molecular-dynamics. Phys. Rev. A 38, 4241.CrossRefGoogle Scholar
Cordero, P. & Risso, D. 1998 Nonlinear transport laws for low density fluids. Physica A 257, 36.CrossRefGoogle Scholar
Curtis, J. S. & vanWachem, B. Wachem, B. 2004 Modeling particle-laden flows: a research outlook. AIChE J. 50, 2638.CrossRefGoogle Scholar
Dahl, S. R. & Hrenya, C. M. 2004 Size segregation in rapid, granular flows with continuous size distributions. Phys. Fluids 16, 1.CrossRefGoogle Scholar
Ferziger, J. H. & Kaper, H. G. 1972 Mathematical Theory of Transport Processes in Gases. Elsevier.Google Scholar
Galvin, J. E., Dahl, S. R. & Hrenya, C. M. 2005 On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures. J. Fluid Mech. 528, 207.CrossRefGoogle Scholar
Galvin, J. E., Hrenya, C. M. & Wildman, R. D. 2007 On the role of the Knudsen layer in rapid granular flows. J. Fluid Mech. 585, 73.CrossRefGoogle Scholar
Garz'o, V. & Dufty, J. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895.Google Scholar
Garzo, V. & Montanero, J. M. 2002 Transport coefficients of a heated granular gas. Physica A 313, 336.CrossRefGoogle Scholar
Goldhirsch, I. 2003 Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267.CrossRefGoogle Scholar
Goldhirsch, I. & Sela, N. 1996 Origin of normal stress differences in rapid granular flows. Phys. Rev. E 54, 4458.Google ScholarPubMed
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619.CrossRefGoogle ScholarPubMed
Goldhirsch, I., Noskowicz, S. H. & Bar-Lev, O. 2004 Theory of granular gases: some recent results and some open problems. J. Phys. Cond. Matter 17, 2591.CrossRefGoogle Scholar
Haff, P. K. 1983 Grain flow as a fluid-mechanical problem. J. Fluid Mech. 134, 401.CrossRefGoogle Scholar
Herbst, O., Müller, P., Otto, M. & Zippelius, A. 2004 Local equation of state and velocity distributions of a driven granular gas. Phys. Rev. E 70, 051313.Google ScholarPubMed
Herbst, O., Müller, P. & Zippelius, A. 2005 Local heat flux and energy loss in a two-dimensional vibrated granular gas. Phys. Rev. E 72, 141303.Google Scholar
Hopkins, M. & Louge, M. 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47.CrossRefGoogle Scholar
Jenkins, J. T. 1998 Kinetic theory for nearly elastic spheres. In Physics of Dry Granular Media (ed. Hermann, H. J., Hovi, J. P. & Luding, S.). Kluwer.Google Scholar
Jenkins, J. T. & Richman, M. W. 1988 Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in dilute and dense limits. J. Fluid Mech. 192, 313.CrossRefGoogle Scholar
Kumaran, V. 1997 Velocity distribution function for a dilute granular material in shear flow. J. Fluid Mech. 340, 319.CrossRefGoogle Scholar
Kumaran, V. 2005 Kinetic model for sheared granular flows in the high Knudsen number limit. Phys. Rev. Lett. 95, 108001.CrossRefGoogle ScholarPubMed
Lasinski, M. E., Curtis, J. S. & Pekny, J. F. 2004 Effect of system size on particle-phase stress and microstructure formation. Phys. Fluids 16, 265.CrossRefGoogle Scholar
Liss, E. D. & Glasser, B. J. 2001 The influence of clusters on the stress in a sheared granular material. Powder Technol. 116, 116.CrossRefGoogle Scholar
Mackowski, D., Papadopoulos, D. H. & Rosner, D. E. 1999 Comparison of Burnett and DSMC predictions of pressure distributions and normal stress in one-dimensional, strongly nonisothermal gases. Phys. Fluids 11, 2108.CrossRefGoogle Scholar
Mareschal, M., Kestemont, E., Baras, F., Clementi, E. & Nicolis, G. 1987 Nonequilibrium states by molecular-dynamics – transport-coefficients in constrained fluids. Phys. Rev. A 35, 3883.CrossRefGoogle ScholarPubMed
Martin, T. W., Huntley, J. M. & Wildman, R. D. 2006 Hydrodynamic model for a vibrofluidized granular bed. J. Fluid Mech. 535, 325.CrossRefGoogle Scholar
MiDi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341.Google Scholar
Montanero, J. M., Santos, A. & Garz'o, V. 2007 First-order Chapman–Enskog velocity distribution function in a granular gas. Physica A 376, 75.CrossRefGoogle Scholar
Noskowicz, S. H., Bar-Lev, O., Serero, D. & Goldhirsch, I. 2007 Computer-aided kinetic theory and granular gases. Europhys. Lett. 79, 60001.CrossRefGoogle Scholar
Pöschel, T. & Schwager, T. 2005 Computational Granular Dynamics. Springer.Google Scholar
Press, W. H., Flannery, B. P., Teukolsky, S. A. & Vetterling, W. T. 1992 Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press.Google Scholar
Risso, D. & Cordero, P. 2002 Dynamics of rarefied gases. Phys. Rev. E 65, 021304.Google Scholar
Santos, A. & Garz'o, V. 1995 In Rarefied Gas Dynamics 19 (ed. Harvey, J. & Lord, G.). Oxford University Press.Google Scholar
Santos, A., Garzo, V. & Dufty, J. 2004 Inherent rheology of a granular fluid in uniform shear flow. Phys. Rev. E 061303.CrossRefGoogle Scholar
Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41.CrossRefGoogle Scholar
Shattuck, M. D., Bizon, C., Swift, J. B. & Swinney, H. L. 1999 Computational test of kinetic theory of granular media. Physica A 274, 158.CrossRefGoogle Scholar
Silbert, L. E., Grest, G. S., Brewster, R. & Levine, A. J. 2007 Rheology and contact lifetimes in dense granular flows. Phys. Rev. Lett. 99, 068002.CrossRefGoogle ScholarPubMed
Soto, R., Mareschal, M. & Risso, D. 1999 Departure from Fourier's law for fluidized granular media. Phys. Rev. Lett. 83, 5003.CrossRefGoogle Scholar
Sundaresan, S. 2000 Perspective: Modeling the hydrodynamics of multiphase flow reactors: Current status and challenges. AIChE J. 46, 1102.CrossRefGoogle Scholar
Sunthar, P. & Kumaran, V. 2001 Characterization of the stationary states of a dilute vibrofluidized granular bed. Phys. Rev. E 64, 041303.Google ScholarPubMed
Tan, M.-L. & Goldhirsch, I. 1997 Intercluster interactions in rapid granular shear flows. Phys. Fluids 9, 856.CrossRefGoogle Scholar
Walton, O. R. & Braun, R. L. 1986 Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech. 63, 73.CrossRefGoogle Scholar
Wassgren, C. & Curtis, J. S. 2006 The application of computational modeling to pharmaceutical materials science. MRS Bull. 31, 900.CrossRefGoogle Scholar
Wildman, R. D., Huntley, J. M. & Parker, D. J. 2001 Granular temperature profiles in three-dimensional vibrofludized granular beds. Phys. Rev. E 63, 061311.Google ScholarPubMed