BSM - Bulk Solids Modelling
 
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Theory

The modelling process used by BSM is based on dimensional analysis, using the Buckingham Pi Theorem.

Variables of relevance to the flow of granular materials through transfer chutes are:

From these 8 variables in three dimensions, five dimensionless pi-groups can be determined:

Using the fact that the volumetric flow, and re-arranging terms, we can re-express the final pi-group as

- which we can call the Capacity Number.

The Froude number, which is ubiquitous in granular flow systems, expresses the ratio of the inertial to the gravitational forces. Practical experience has shown that maintaining this term as a constant allows close approximation to dynamic similarity in transfer chute flow.

The Capacity Number is merely an expression of the fact that the volumetric capacity varies with the velocity and the cross sectional area.

A notable result from this analysis is that terms involving mass flows and densities can be eliminated. This is an important result, for the practical implication is that modelling can be performed using materials with bulk densities differing from the ore while retaining similarity. Many people find this concept to be counter-intuitive.

Experience has shown that shape factor and angle of repose do not have a large effect on most ore flow systems. If the ore does have unusual properties, the material used to perform the modelling can be selected to provide the appropriate similarity.