"We must go forward, not backward, upward, not forward, and always
twirling, twirling, twirling towards freedom." - Clin-ton

The flow of granular materials in a symmetric, vertical hopper is succesfully described by the Jenike radial solutions, which model particle paths as lines converging upon the vertex of a hopper in two-dimensions. [1] Mathematicians at Duke and NC State have generalized these equations to three-dimensions by developing a finite-element solution for an elasto-plastic model using the Jenike radial solutions as a basis. These new solutions allow for the possibility of secondary-circulation -- azimuthal swirling of the grains as the hopper drains. This effect should be dependent on the degree of asymmetry of the hopper relative to an axis aligned with gravity, as well as material properties. The purpose of this experimental study is to test for secondary-circulation in a tilted hopper for different tilt angles and hopper wall frictions. Preliminary results indicate the existence of secondary-circulation but the magnitude of the flow is too large to fit with the mathematical model.

1. A. W. Jenike, Powder Tech. 50, 229-235 (1987)

2. P. Gremaud and J. V. Matthews, J. Comp. Phys. 166, 63-83 (2001)

The flow of granular materials in a symmetric, vertical hopper is succesfully described by the Jenike radial solutions, which model particle paths as lines converging upon the vertex of a hopper in two-dimensions. [1] Mathematicians at Duke and NC State have generalized these equations to three-dimensions by developing a finite-element solution for an elasto-plastic model using the Jenike radial solutions as a basis. These new solutions allow for the possibility of secondary-circulation -- azimuthal swirling of the grains as the hopper drains. This effect should be dependent on the degree of asymmetry of the hopper relative to an axis aligned with gravity, as well as material properties. The purpose of this experimental study is to test for secondary-circulation in a tilted hopper for different tilt angles and hopper wall frictions. Preliminary results indicate the existence of secondary-circulation but the magnitude of the flow is too large to fit with the mathematical model.

1. A. W. Jenike, Powder Tech. 50, 229-235 (1987)

2. P. Gremaud and J. V. Matthews, J. Comp. Phys. 166, 63-83 (2001)

Back to seminar homepage