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Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Chapter


Abstract


  • Under certain circumstances, an industrial hopper which operates under the funnel-flow regime can be converted to the mass-flow regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two-dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45°. © 2005 Springer.

Publication Date


  • 2005

Citation


  • Cox, G. M., McCue, S. W., Thamwattana, N., & Hill, J. M. (2005). Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers. In Mathematics and Mechanics of Granular Materials (pp. 63-91). doi:10.1007/1-4020-4183-7_5

International Standard Book Number (isbn) 13


  • 9781402037818

Scopus Eid


  • 2-s2.0-84891991333

Web Of Science Accession Number


Book Title


  • Mathematics and Mechanics of Granular Materials

Start Page


  • 63

End Page


  • 91

Abstract


  • Under certain circumstances, an industrial hopper which operates under the funnel-flow regime can be converted to the mass-flow regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two-dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45°. © 2005 Springer.

Publication Date


  • 2005

Citation


  • Cox, G. M., McCue, S. W., Thamwattana, N., & Hill, J. M. (2005). Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers. In Mathematics and Mechanics of Granular Materials (pp. 63-91). doi:10.1007/1-4020-4183-7_5

International Standard Book Number (isbn) 13


  • 9781402037818

Scopus Eid


  • 2-s2.0-84891991333

Web Of Science Accession Number


Book Title


  • Mathematics and Mechanics of Granular Materials

Start Page


  • 63

End Page


  • 91