Similarity solutions for granular flows in hoppers

Journal of Engineering Mathematics, 2005

The incompressible plastic flow equations for a Drucker-Prager yield law and a J 2 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.