Improving flow in hoppers with Sigma2-relaxation
Plane flow is less troublesome as axisymmetric flow. Sigma2-relaxation will show even less flow problems. By: Lyn Bates
Stresses on bulk materials can be applied as compressive, tensile or in shear. Whatever combination is applied can be resolved into principle stresses by means of Mohr’s circles. i.e, stresses acting normal to surfaces at right angles to each other without shear stresses.
Stresses applied on a sample in one principle plane induce a deformation, creating a reduced stress at 90° according to the Poisson’s ratio of the material (See fig. 2a). That is the change in the width per unit width of a material relative to its change in its length as a result of strain. Bulk material flowing down a conical converging channel has to deform in two planes under the compressive stresses of reducing diameter.
Product in a plane flow channel only converges is one plane so, despite being confined, it will flow down walls about 10° less steep that in a cone. A plane flow channel that widens slightly at 90° to the converging plane will allow a larger degree of relaxation to the converging stress than the reduction in the confining stress (see fig. 2b). This effect extends progressively over a wide channel, so may be exploited by a progressive extraction feeder to secure reliable flow through a smaller width of outlet slot and as mass flow convergence angles are relatively steep, enables mass flow in less steep hopper walls by even a minor degree of relaxation (sketch in fig 3).
If the degree of relaxation equaled the Poisson’s ratio, the material would be essentially unconfined and fail when the applied stress exceeded the unconfined failure stress.