Two Phase Flows and Waves pp 88-97 | Cite as

# Computations of Granular Flow in a Hopper

## Abstract

The flow of granular material in a hopper is a common industrial problem, but it is a problem without a good solution. Classical theories treat the material as an incompressible continuum in steady plastic yield; such theories cannot explain experimentally observed dynamics and dilantcy. Investigation of dynamic theories which include density variation is just beginning. We review the classical theory of granular flow in bins and present some of the recent developments on compressible flows. We borrow ideas from computational fluid dynamics in order to develop a method for the numerical simulation of compressible hopper flow.

## Keywords

Granular Material Flow Rule Granular Flow Granular Temperature Critical State Theory## Preview

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## References

- [1]R. M. Beam and R. F. Warming,
*An Implicit Factored Scheme for the Compressible Navier-Stokes Equations*, AIAA Jour., 16 (1978), pp. 393–402.CrossRefzbMATHGoogle Scholar - [2]R. Behringer, these proceedings.Google Scholar
- [3]C. Brennan and J. C. Pearce,
*Granular Material Flow in Two Dimensional Hoppers*, J. Appl. Mech., 45 (1978), pp. 43–50.CrossRefGoogle Scholar - [4]A. Drescher,
*An Experimental Investigation of Flow Rules for Granular Materials using Optically Sensitive Glass Particles*, Geotech., 26 (1976), pp. 591–601.CrossRefGoogle Scholar - [5]R. Jackson,
*Some Mathematical and Physical Aspects of Continuum Models for the Motion of Granular Materials, in The Theory of Dispersed Multiphase Flow, R. Meyer*(ed.), Academic Press (1983).Google Scholar - [6]A. W. Jenike,
*Steady Gravity Flow of Frictional-Cohesive Solids in Converging Channels*, J. Appl. Mech., 31 (1964), pp. 5–11.CrossRefGoogle Scholar - [7]J. T. Jenkins and M. W. Richman,
*Grad’s 13 Moment System for a Dense Gas of Inelastic Spheres, Arch. Rat’l Mech. Anal*., 87 (1985), pp. 355–377.zbMATHMathSciNetGoogle Scholar - [8]J. T. Jenkins and S. B. Savage,
*A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic Spherical Particles*, J. F. M., 130 (1983), pp. 187–202.CrossRefzbMATHGoogle Scholar - [9]P. C. Johnson and R. Jackson,
*Frictional-Collisional Constitutive Relations for Granular Materials*, J. F. M., 176 (1987), pp. 67–93.CrossRefGoogle Scholar - [10]K. R. Kaza and R. Jackson,
*The Rate of Discharge of Coarse Granular Material from a Wedge Shaped Hopper*, Powder Tech., 33 (1982), pp. 223–242.CrossRefGoogle Scholar - [11]R. Mlchalowskl,
*Flow of a Granular Material through a Plane Hopper*, Powder Tech., 39 (1984), pp. 29–40.CrossRefGoogle Scholar - [12]Z. Mroz and C. Szymanski,
*Gravity Flow of a Granular Material in a Converging Channel*, Arch. Mech. Stos., 23 (1971), pp. 897–917.zbMATHGoogle Scholar - [13]E. B. Pitman,
*The Stability of Granular Flow in Converging Hoppers*, SIAM J. Appl. Math., 48 (1988), pp 1033–1053.zbMATHMathSciNetGoogle Scholar - [14]E. B. Pitman and D. G. Schaeffer,
*Stability of Time Dependent Compressible Granular Flow in Two Dimensions*, Comm. Pure Appl. Math., 40 (1987), pp. 421–447.CrossRefzbMATHMathSciNetGoogle Scholar - [15]E. B. Pitman, D. G. Schaeffer and M. Shearer,
*Stability in Three Dimensional Critical State Theories of Plasticity*, in preparation.Google Scholar - [16]J. R. Prakash and K. K. Rao,
*Steady Compressible Flow of Granular Material through a Wedge Shaped Hopper: The Smooth Wall Radial Gravity Problem*, Chem. Eng. Sci., 43 (1988), pp. 479–494.CrossRefGoogle Scholar - [17]K. H. Roscoe, A. N. Schofield and C. P. Wroth,
*On the Yielding of Soils*, Geotech., 8 (1958), pp. 22–53.CrossRefGoogle Scholar - [18]S. B. Savage,
*Mass Flow of Granular Material from Coupled Velocity-Stress Fields*, Brit. J. Appl. Phys., 16 (1965), pp. 1885–1888.CrossRefGoogle Scholar - [19]D. G. Schaeffer and E. B. Pitman,
*III Posedness in Three Dimensional Plastic Flow*, Comm. Pure Appl. Math., 41 (1988), pp. 879–890.CrossRefzbMATHMathSciNetGoogle Scholar - [20]D. G. Schaeffer, M. Shearer and E. B. Pitman,
*Instability in Critical State Theories of Granular Flow, to appear*, SIAM J. Appl. Math.Google Scholar - [21]M. Shearer and D. G. Schaeffer,
*Foundations of the Quasi-dynamic Approximation in Critical State Plasticity*, preprint.Google Scholar - [22]H. C. Yee,
*Linearized Form of Implicit TVD Schemes for the Multidimensional Euler and Navier-Stokes Equations*, Comp. Math. Appl., 12 (1986), pp. 413–432.CrossRefzbMATHMathSciNetGoogle Scholar - [23]H. C. Yee and A. Harten,
*Implicit TVD Schemes for Hyperbolic Conservation Laws in Curvilinear Coordinates*, AIAA Jour., 25 (1987), pp. 266–274CrossRefGoogle Scholar