(221e) A Systematic Approach to Predicting Mass Flow and Segregation Prevention from Vibrating Bins and Process Equipment Using the Radial Stress Theory

The theory behind the design of handling systems for bulk solids is the radial stress theory. This theory was developed in the 1960’s by Andrew Jenike and Jerry Johanson as they worked at the University of Utah. The original intent of the work was to help understand the complex stresses that act in typical process vessels. However, when the radial stress theory was coupled with the concept of a radial velocity, the theory was able to predict stresses in equipment as well as the expected velocity profiles in these pieces of process equipment. But the computing power in 1960 was marginal at best. So, these two researchers opted for the next best thing. The concept of flow-no-flow. It became possible and easy to measure a wall friction angle and an effective angle of internal friction and thereby predict a flow or no-flow criteria. Mass-flow and funnel-flow were terms coined to describe the fact that, under some conditions, solids may flow in only a central flow channel surrounded by stagnant zones of material. Pseudo concepts like first-in and last-out were used to determine process behavior and make decisions about segregation in process vessels, residence time distributions, or mixing in process vessels.

There is a relationship between the velocity profiles in process equipment and the residence time distribution of material passing through the process. The residence time distribution in any process can be used to determine the mixing behavior of a material passing through that piece of equipment. In contrast, knowing the velocity profile in the process equipment can be used to determine how a material prone to segregation might exit the process, allowing prediction of the expected quality leaving the process during flow through that process – especially during a draw-down operation where first-in last-out can make a difference.

It therefore stands to reason that understanding how external forces such as vibration on the product might affect such parameters as the wall friction angle, the effective internal angle of friction, the bulk strength of the material, and the internal angle of friction, could give rise to a means of predicting flow of a bulk material subject to vibration or other external forces.

It turns out that vibration in the bulk material near the wall surface depends on the tangential elastic properties of the material. Propagation of vibration away from the wall into the bulk depends on the bulk elastic modulus of the material at solid contact pressures acting in the process geometry. Propagation of vibration in both tangential directions as well as normal direction also depends on the local stiffness of the confining structure. Finally, the effect of vibration on the key flow properties depends on the frequency and acceleration amplitude of the vibration (i.e. how many g-forces can be transferred to the bulk material). With this in mind, if it is possible to relate wall friction angles, effective internal friction angles, bulk unconfined yield strength, and the internal friction angle to the vibration acceleration amplitude, then it is possible to predict flow in vibratory equipment. If it is also possible to relate the elastic properties of the bulk material to these key flow properties, then it will be possible to predict the flow, mixing, and segregation behavior of any material in vibrating process equipment using a theoretical and systems design approach.

This work will present the results and methods of how this is done and will use the results to predict the segregation and mixing capabilities of using vibrating bin bottoms during discharge and in continuous flow operations. Thus, engineers should be able to design powders to work well in vibratory process equipment or, at the very least, determine potential flow and quality problems with a select material.