Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 184
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Bertuola, Davide Volpato, Silvia Canu, Paolo and Santomaso, Andrea C. 2016. Prediction of segregation in funnel and mass flow discharge. Chemical Engineering Science, Vol. 150, p. 16.


    Dufek, Josef 2016. The Fluid Mechanics of Pyroclastic Density Currents. Annual Review of Fluid Mechanics, Vol. 48, Issue. 1, p. 459.


    Krishnaraj, K. P. and Nott, Prabhu R. 2016. A dilation-driven vortex flow in sheared granular materials explains a rheometric anomaly. Nature Communications, Vol. 7, p. 10630.


    Li, Dan Liu, Guodong Lu, Huilin Zhang, Qinghong Wang, Qi and Yu, Hongbing 2016. Numerical simulation of different flow regimes in a horizontal rotating ellipsoidal drum. Powder Technology, Vol. 291, p. 86.


    Lyakhovsky, Vladimir Ben-Zion, Yehuda Ilchev, Assen and Mendecki, Aleksander 2016. Dynamic rupture in a damage-breakage rheology model. Geophysical Journal International, Vol. 206, Issue. 2, p. 1126.


    Mandich, Kevin and Cattolica, Robert J. 2016. Stability of an inclined, pneumatically-transported system of particles. AIChE Journal, Vol. 62, Issue. 7, p. 2248.


    Ni, Changjiang Guo, En-Yu Zhang, Qingdong Jing, Tao and Wu, Junjiao 2016. Frictional-kinetic modeling and numerical simulation of core shooting process. International Journal of Cast Metals Research, Vol. 29, Issue. 4, p. 214.


    Redaelli, I. di Prisco, C. and Vescovi, D. 2016. A visco-elasto-plastic model for granular materials under simple shear conditions. International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 40, Issue. 1, p. 80.


    Saitoh, Kuniyasu and Mizuno, Hideyuki 2016. Anomalous energy cascades in dense granular materials yielding under simple shear deformations. Soft Matter, Vol. 12, Issue. 5, p. 1360.


    XU, Hailiang LI, Wang ZHAO, Hongqiang and XU, Shaojun 2016. Cuttings carrying characteristics of back-reaming pneumatic impactor exhaust during drilling operation. Petroleum Exploration and Development, Vol. 43, Issue. 1, p. 131.


    Armanini, A. 2015. Closure relations for mobile bed debris flows in a wide range of slopes and concentrations. Advances in Water Resources, Vol. 81, p. 75.


    Lee, Cheng-Hsien Huang, Zhenhua and Chiew, Yee-Meng 2015. A three-dimensional continuum model incorporating static and kinetic effects for granular flows with applications to collapse of a two-dimensional granular column. Physics of Fluids, Vol. 27, Issue. 11, p. 113303.


    Niedziela, D. Schmidt, S. Steiner, K. Zausch, J. and Zemerli, C. 2015. Continuum numerical simulation of multiphase granular suspension flow in the context of applications for the mechanical processing industry. International Journal of Mineral Processing, Vol. 136, p. 50.


    Schneiderbauer, Simon Puttinger, Stefan Pirker, Stefan Aguayo, Pablo and Kanellopoulos, Vasileios 2015. CFD modeling and simulation of industrial scale olefin polymerization fluidized bed reactors. Chemical Engineering Journal, Vol. 264, p. 99.


    Sun, Liyan Wang, Shuyan Lu, Huang Liu, Goudong Lu, Huilin Liu, Yang and Zhao, Feixiang 2015. Prediction of configurational and granular temperatures of particles using DEM in reciprocating grates. Powder Technology, Vol. 269, p. 495.


    Sun, Liyan Xu, Weiguo Lu, Huilin Liu, Guodong Zhang, Qinghong Tang, Qing and Zhang, Tianyu 2015. Simulated configurational temperature of particles and a model of constitutive relations of rapid-intermediate-dense granular flow based on generalized granular temperature. International Journal of Multiphase Flow, Vol. 77, p. 1.


    Wang, Shuyan Shao, Baoli Liu, Rui Zhao, Jian Liu, Yang Liu, Yikun and Yang, Shuren 2015. Comparison of numerical simulations and experiments in conical gas–solid spouted bed. Chinese Journal of Chemical Engineering, Vol. 23, Issue. 10, p. 1579.


    Yu, Yang Jia, Shaoyi Zhu, Guorui Tan, Wei and Chen, Xiaonan 2015. Numerical study of frictional model for dense granular flow. Powder Technology, Vol. 272, p. 211.


    Armanini, A. Larcher, M. Nucci, E. and Dumbser, M. 2014. Submerged granular channel flows driven by gravity. Advances in Water Resources, Vol. 63, p. 1.


    Berdichevsky, Victor L. 2014. Overcoming paradoxes of Drucker–Prager theory for unconsolidated granular matter. International Journal of Engineering Science, Vol. 83, p. 174.


    ×
  • Journal of Fluid Mechanics, Volume 377
  • December 1998, pp. 1-26

Analyses of slow high-concentration flows of granular materials

  • S. B. SAVAGE (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112098002936
  • Published online: 25 December 1998
Abstract

A theory intended for slow, dense flows of cohesionless granular materials is developed for the case of planar deformations. By considering granular flows on very fine scales, one can conveniently split the individual particle velocities into fluctuating and mean transport components, and employ the notion of granular temperature that plays a central role in rapid granular flows. On somewhat larger scales, one can think of analogous fluctuations in strain rates. Both kinds of fluctuations are utilized in the present paper. Following the standard continuum approach, the conservation equations for mass, momentum and particle translational fluctuation energy are presented. The latter two equations involve constitutive coefficients, whose determination is one of the main concerns of the present paper. We begin with an associated flow rule for the case of a compressible, frictional, plastic continuum. The functional dependence of the flow rule is chosen so that the limiting behaviours of the resulting constitutive relations are consistent with the results of the kinetic theories developed for rapid flow regimes. Following Hibler (1977) and assuming that there are fluctuations in the strain rates that have, for example, a Gaussian distribution function, it is possible to obtain a relationship between the mean stress and the mean strain rate. It turns out, perhaps surprisingly, that this relationship has a viscous-like character. For low shear rates, the constitutive behaviour is similar to that of a liquid in the sense that the effective viscosity decreases with increasing granular temperature, whereas for rapid granular flows, the viscosity increases with increasing granular temperature as in a gas. The rate of energy dissipation can be determined in a manner similar to that used to derive the viscosity coefficients. After assuming that the magnitude of the strain-rate fluctuations can be related to the granular temperature, we obtain a closed system of equations that can be used to solve boundary value problems. The theory is used to consider the case of a simple shear flow. The resulting expressions for the stress components are similar to models previously proposed on a more ad hoc basis in which quasi-static stress contributions were directly patched to rate-dependent stresses. The problem of slow granular flow in rough-walled vertical chutes is then considered and the velocity, concentration and granular temperature profiles are determined. Thin boundary layers next to the vertical sidewalls arise with the concentration boundary layer being thicker than the velocity boundary layer. This kind of behaviour is observed in both laboratory experiments and in granular dynamics simulations of vertical chute flows.

Copyright
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