DESIGN OF STORAGE SILOS AND HOPPERS

In beneficiation plant, In the general field of bulk solids handling, ensuring that both the storage of materials and the movement from storage will be carried out in an effective and efficient manner is essential. However, the flow out of bins and hoppers is well known to be often unreliable; as a result, considerable costs are incurred because of consequential losses in production. Problems that commonly occur in storage bin operation include particle segregation, erratic feeding, flooding, arching, piping, and adhesion to the bin walls—all of which reduce the bin capacity below the values specified by the manufacturer. For example, a poorly flowing material may cause an arch or bridge over the hopper outlet or a stable rathole within the bin (see Figure 1). On the other hand, a very flowable material (dry, fine powder) may become aerated and subsequently fluidize, causing potential flooding problems.
Where flow blockages occur in practice, a common response is to resort to flow-promoting devices, which add to the expense of the installation and often result in only a marginal improvement in reliability. In most cases, the problems that occur in practice are caused by inadequate design analysis together with a lack of knowledge of the relevant flow properties of the materials.
There are basically three flow patterns in bins: mass flow, funnel flow, and expanded flow (see Figure 2). Each of these flow patterns has its advantages and disadvantages. Mass flow refers to a flow pattern where all the material in the bin is in a downward motion whenever the feeder is discharging. In essence, the material column slides along the hopper wall. To attain this type of flow pattern, the hopper walls must be steep and smooth. Funnel flow occurs when the material moves strictly within a confined channel above the hopper outlet. The material outside this flow channel is at rest until the bin level drops and the material slides into the channel. The diameter of this flow channel is established essentially by the hopper outlet dimensions. However, when the cohesive strength of the material is high enough, the flow channel may possibly be emptied out without the upper layers in the bin sloughing off into the channel. In this case, a continual open channel will be formed right within the bin. Such a channel is referred to as a stable rathole (see Figure 1). Expanded flow exhibits themass-flow pattern in the lower hopper section up to the point where the stable rathole diameter is reached; then the flow pattern continues as funnel flow. The stable rathole diameter can be calculated when the flow properties are known.
Accurate measurement of the flow properties is essential for proper design of the storage bin and hopper. Once the shear tests have been completed, the values for unconfined yield strength ( fc) can be plotted in graphical form, as shown in Figure 11.4. The strength curves are referred to as flow functions (FF). Figure 3 shows three flow functions: for low-, medium-, and high-strength coals. (The lines marked 1.1, 1.2, and 1.3 represent flow factors [ff], which represent stresses in different shapes of hoppers. The intersection of FF and ff provides the critical value of the strength that is used in computing the critical arching dimension.)
Once the material strength is measured, the stresses within the granular material inside the bin can be calculated. If any arching or doming situation can develop inside the bin, the design engineer must make sure to create a geometric configuration of the bin or hopper such that the stresses in the material (s) will be larger than the strength of the material ( f ). The basic flow criterion requires that f < s in order to maintain gravity flow.
Figure 4 shows a typical graphical illustration of the pressure (p), strength, and stress distributions inside a bin and hopper. The bulk solid is unconsolidated at the top of the bin because p is about zero. While the bulk solid is flowing downward, it becomes consolidated under pressure p. For each value of pressure, corresponding values exist for the material strength and stress. Close to the apex of the hopper, the f-curve and s-curve intersect. Above this point, the flow criterion f < s is satisfied and gravity flow will occur. Below this intersection, we have f > s and arching will occur. Therefore, this intersection identifies the critical level in the hopper and also fixes the critical opening dimension (B). A thorough engineering analysis, based on the flow functions shown in Figure 11.4, would show that the critical arching diameters for a stainless steel-lined, conical mass-flow hopper are 0.55 m (1.8 ft) for low-strength coal, 0.91 m (3.0 ft) for medium-strength coal, and 1.83 m (6.0 ft) for high-strength coal. These values represent a typical case and are intended to demonstrate the variability of coal in terms of its flowability.
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