TY - JOUR

T1 - Steady compressible flow of granular materials through a wedge-shaped hopper

T2 - The smooth wall, radial gravity problem

AU - Ravi Prakash, J.

AU - Kesava Rao, K.

PY - 1988/1/1

Y1 - 1988/1/1

N2 - A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

AB - A continuum model based on the critical state theory of soil mechanics is used to generate stress and density profiles, and to compute discharge velocities for the plane flow of cohesionless materials. Two types of yield loci are employed, namely, a yield locus with a corner, and a smooth yield locus. The yield locus with a corner leads to computational difficulties. For the smooth yield locus, results are found to be relatively insensitive to the shape of the yield locus, the location of the upper traction-free surface and the density specified on this surface. This insensitivity arises from the existence of asymptotic stress and density fields, to which the solution tends to converge on moving down the hopper. Numerical and approximate analytical solutions are obtained for these fields and the latter is used to derive an expression for the discharge velocity. This relation predicts discharge velocities to within 13% of the exact (numerical) values. While the assumption of incompressibility has been frequently used in the literature, it is shown here that in some cases, this leads to discharge velocities which are significantly higher than those obtained by the incorporation of density variation.

UR - http://www.scopus.com/inward/record.url?scp=0023825504&partnerID=8YFLogxK

U2 - 10.1016/0009-2509(88)87009-X

DO - 10.1016/0009-2509(88)87009-X

M3 - Article

AN - SCOPUS:0023825504

VL - 43

SP - 479

EP - 494

JO - Chemical Engineering Science

JF - Chemical Engineering Science

SN - 0009-2509

IS - 3

ER -