Abstract
The incompressible plastic flow equations for a Drucker-Prager yield law and a J2 flow rule are shown not to allow a steady single radial velocity component, for flows from a wedge-shaped hopper. The corresponding equations for two components of velocity are considered, using a series expansion of Kaza and Jackson, which connects asymptotically to Jenike’s radial solution. This asymptotic solution gives a poor model of mass flows about the orifice, and an improvement is obtained by considering the pressure variation along the axis of the wedge, but using the angular variations determined by the power-series method. Numerical difficulties occurred for certain parameter values, when solving the two-point boundary-value problem resulting from the asymptotic series method. The region of this parametric sensitivity is associated with an internal maximum in the pressure field, whose appearance tends to offer a conservative estimate for the mass-funnel flow transition.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
D.G. Schaeffer, Instability in the evolution equations describing incompresible granular flow. J. Diff. Equ. 66 (1987) 19–50.
K.C. Valanis and J.F. Peters, Ill-posedness of the initial and boundary value problems in non-associative plasticity. Acta Mech. 114 (1996) 1–25.
G.W. Baxter, R.P. Behringer, T. Fagert and G.A. Johnson, Pattern formation and time-dependence in flowing sand. In: D.D. Joseph and D.G. Schaeffer (eds.), Two-Phase Flows and Waves. Berlin: Springer-Verlag (1990) pp.1–28.
H.B. Mulhaus and I. Vardoulaki, The thickness of shear bands in granular materials. Geotechnique 37 (1987) 271–283.
R.M. Nedderman, U. Tuzun, S.B. Savage and G.T. Houlsby, Review Article Number 10: The flow of granular materials: Discharge rates from hopper. Chem. Eng. Sci. 37 (1982) 1597–1609.
R.L. Brown and J.C. Richards, Profile of flow of granules through apertures. Trans. Inst. Chem. Engng. 38 (1960) 243–250.
W.A. Beverloo, H.A. Leniger and J. van de Velde, The flow of granular solids through orifices. Chem. Eng. Sci. 15 (1961) 260–269.
C. Brennen and J.C. Pearce, Granular material flow in two-dimensional hoppers. J. Appl. Mech. 45 (1978) 43–50.
T.V. Nguyen, C. Brennen and R.H. Sabersky, Gravity flow of granular materials in conical hoppers. J. Appl. Mech. 46 (1979) 529–535.
A.W. Jenike, Steady gravity flow of frictional-cohesive solids in converging channels. J. Appl. Mech. 31 (1964) 5–11.
K.R. Kaza and R. Jackson, The rate of discharge of coarse granular material from a wedge-shaped mass flow hopper. Powder Technol. 33 (1982) 223–237.
G.J. Weir, The intrinsic cohesion of granular materials. Powder Technol. 104 (1999) 29–36.
P.A. Gremaud, J.V. Matthews and M. Shearer, Similarity solutions for hopper flows. In: J. Bona, K. Saxton and R. Saxton (eds.), Nonlinear PDEs, Dynamics and Continuum Physics. Providence, Rhode Island: AMS Contempory Mathematics, Series 255 (2000) pp. 79–95.
K.R. Kaza and R. Jackson, Boundary conditions for a granular material flowing out of a hopper or bin. Chem. Eng. Sci. 39 (1984) 915–916.
J.J. Johanson and A.W. Jenike, Stress and Velocity Fields in Gravity Flow of Bulk Solids. Salt Lake City, Utah: Bulletin No. 116, Bulletin of the University of Utah 53(21) (1962) 138 pp.
B.W. Laird and P.M. Roberts, Chemical Engineering. Tripos, Part 2. Research Project Report, University of Cambridge (1979).
R.L. Brown and J.C. Richards, Kinematics of the flow of dry powders and bulk solids. Rheology Acta 4 (1965) 153–165.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
Weir, G.J. (2005). Incompressible granular flow from wedge-shaped hoppers. In: Hill, J.M., Selvadurai, A. (eds) Mathematics and Mechanics of Granular Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4183-7_16
Download citation
DOI: https://doi.org/10.1007/1-4020-4183-7_16
Received:
Accepted:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3781-8
Online ISBN: 978-1-4020-4183-9
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)